Valuing Green Infrastructure Technical Appendices natural capital P R O J E C T © 2019 International Bank for Reconstruction and Development / The World Bank 1818 H Street NW Washington DC 20433 Telephone: 202-473-1000 Internet: www.worldbank.org This work is a product of the staff of The World Bank with external contributions. The findings, interpretations, and conclusions expressed in this work do not necessarily reflect the views of The World Bank, its Board of Executive Directors, or the governments they represent. The World Bank does not guarantee the accuracy of the data included in this work. The boundaries, colors, denominations, and other information shown on any map in this work do not imply any judgment on the part of The World Bank concerning the legal status of any territory or the endorsement or acceptance of such boundaries. Rights and Permissions The material in this work is subject to copyright. Because The World Bank encourages dissemination of its knowledge, this work may be reproduced, in whole or in part, for noncommercial purposes as long as full attribution to this work is given. Attribution: Please cite the work as follows: “World Bank. 2019. Valuing Green Infrastructure: Technical Appendices. ©World Bank.” Any queries on rights and licenses, including subsidiary rights, should be addressed to World Bank Publications, The World Bank Group, 1818 H Street NW, Washington, DC 20433, USA; fax: 202-522-2625; e-mail: pubrights@ worldbank.org. [Cover photo: Aleksei Kazachok/Shutterstock.com | Dave Primov/Shutterstock.com Valuing Green Infrastructure Technical Appendices CONTENTS Appendix 1: Developing a baseline sediment budget: Kali Gandaki, Nepal 4 1. Baseline sediment budget for Kali Gandaki 4 2. Sampling stations and data availability 4 3. Methods 7 3.1. Deriving sediment rating curves 7 3.2. Sediment sampling and load calculations 7 3.3. Handling missing data 7 3.4. Sediment budget for Kali Gandaki 8 4. Results 8 4.1. Sediment rating curves for Kali Gandaki 8 4.2. Sediment loads and sediment budgets for Kali Gandaki 9 4.2.1. 2018-2019 Sediment summary 9 4.2.2. Longer-term averages 10 Appendix 2: Modeling landslide risk and valuing benefits 13 1. Introduction: Stochastic modeling of connected hillslope stability 13 2. Methods 13 2.1. Current best practice: single cell deterministic slope stability 13 2.2. Probabilistic factor of safety calculations 16 2.3. Connected landslide assessments 18 2.4. Sediment mobilization from road induced landslides 21 2.5. Landslide hazards for infrastructure 23 2.6. Modelling management interventions 23 3. Results 24 3.1. Modelled and empirical rainfall thresholds 24 3.2. Road and building exposure 26 3.3. Calibrating landslide contributions to sediment budgets 27 4. References 32 Appendix 3: Modeling sediment generation from roads 33 1. Methods 33 1.1. Modeling erosion from road surfaces and cut slopes 33 1.2. Modeling sediment mobilization from road cuts 34 2. Road data 37 3. Results 39 3.1. Erosion from road surfaces 39 3.2. Erosion from roads 41 3.3. Sediment generation from possibly road related landslides 44 4. References 45 Valuing Green Infrastructure: Technical Appendices 2 Appendix 4: Methods for valuing impacts of sediment on Kali Gandaki A 46 1. Introduction 46 2. Desander flushing 48 3. Damage to equipment 50 4. Peaking capacity 54 5. References 61 Appendix 5: Summary of data sources and parameter values, Kali Gandaki 63 References71 Appendix 6: Summary of data sources and parameter values, Mangla 73 References84 3 Valuing Green Infrastructure: Technical Appendices APPENDIX 1: DEVELOPING A BASELINE SEDIMENT BUDGET: KALI GANDAKI, NEPAL BASELINE SEDIMENT BUDGET 1.  Topography of the Kali Gandaki basin, Figure - 1:  location of gauging stations and their FOR KALI GANDAKI respective drainage area. Note that no Understanding the sediment budget of the Kali sampling was taken at Kali Gandaki Gandaki, i.e., the provenance and the processes Reservoir but values were interpolated generating sediment in the catchment, is crucial to from upstream observations design effective sediment management strategies. This section describes data collection efforts in the Kali Gandaki Basin and the henceforth derived sediment budget of the basin. SAMPLING STATIONS AND DATA 2.  AVAILABILITY A sediment sampling campaign was performed under supervision of Kathmandu University for five gauging stations Jomsom, Tatopani, Manghalgat, Nayapul and Modibeni. There are three stations on the main stem of the Kali Gandaki River. Jomsom is located at the end of the Mustang Plateau. Tatopani roughly marks the end of Kali Gandaki Gorge and Modibeni is located upstream of the confluence of the Kali Gandaki and the Modi River. Two additional stations are located on the major eastern and western tributaries. Manghalgat is located on the Myagdi River and Nayapul is located on the Modi River. The location of gauging stations is shown in Figure 1. Figure 1 also shows the drainage area of a sixth gauging station at the location of the Kali Gandaki reservoir. However, it should be noted that this station was not part of the current sampling and all analysis are based on past values reported by NEA and others. The sub-catchments covered by the drainage area are very heterogeneous in terms of Figure 2 shows a simplified overview of the drainage their climatic and morphologic conditions. Possibly network in the catchment and the location of the important factors related to the possible sediment gauging stations. It should be noted that there are no generation from each catchment are, for example, the direct observations of discharge for Kali Gandaki (only overall elevation and relief, the precipitation and the sediment concentration) and no measurements at all in glaciation. Glaciation and precipitation, as well as relief the Aadhi Khola River which enters into the reservoir is highest in watersheds draining the main chain of the of Kali Gandaki. Otherwise, it should be noted that Himalayas (Modi Beni, Manghalghat and Nayapul). Modi Beni station receives sediment from the entire Valuing Green Infrastructure: Technical Appendices 4 Mustang, the Kali Gandaki Gorge, and the Upper Kali Gandaki and the Myagdi Khola. The combined load from the Modi Khola and the Upper Kali Gandaki then presents the inflow into the lower Kali Gandaki reach with Kali Gandaki A at the downstream end. Schematic of the river network and the gauging stations in Kali Gandaki. Points and italic names Figure - 2:  indicate gauging stations and bold names refer to sub-catchments. It should be noted that there are no joint measurements for sediment and discharge in Kali Gandaki and no data at all for the Aadhi Khola river Mustang Plateau Jomsom Kaligandaki Gorge Myagdi Khola Tatopani Manghal Ghat Modi Upper Khola Kaligandaki Modi Beni Nayapul Lower Kaligandaki Aadhi Khola Kaligandaki 5 Valuing Green Infrastructure: Technical Appendices Overview over sub-basin characteristics of gauging stations used in this study. Elevated symbols Table - 1:  indicate data sources +: derived from the DEM (30 m resolution), *: ICMOD glacier dataset, # interpolated from DHM rain gauges using Kriging Drainage Mean σ Mean annual Glaciation Name River Description area Elevation elevation precipitation [%]* [km2]+ [m]+ [m]+ [mm]# Kali Mustang Jomsom 3165 4786 845 7.9 426.0 Gandaki Plateau Upper Kali Kali Tatopani Gandaki 782 3946 1251 9.8 1191.1 Gandaki Gorge Myagdi Myagdi Khola and Manghalghat 1095 3357 1509 12.6 2260.3 Khola Dhaulagiri Range Kali Middle Kali Modi Beni 840 2405 1092 1.5 2076.1 Gandaki Gandaki Modi Modi Khola and Nayapul 648 3192 1645 11.8 2988.0 Khola Annapurna Range Not covered in current Kaligand- Kali Gandaki sampling aki 1034 1245 365 0.0 2394.7 Reservoir campaign, Reservoir lower Kali Gandaki Available data on discharge and sediment concentration. Sources are: * Kathmandu University Table - 2:  sampling campaign, +: DHM, #: NEA Name Q (2018 - 2019) CS (2018 - 2019) Q (Other) QS (Other) 'Jomsom' n/a 65 weekly samples + Daily n/a 2009 – 2014+ 'Tatopani' 65 weekly samples* 65 weekly samples+ Daily n/a 2010 – 2014+ 'Manghalghat' 65 weekly samples* 65 weekly samples+ Daily n/a 2011 – 2015+ 'Modi Beni' 65 weekly samples* 65 weekly samples+ Daily n/a 2009 – 2013+ 'Nayapul' 65 weekly samples* 65 weekly samples+ Daily n/a 2011 – 2015+ 'Kali Gandaki n/a n/a n/a Sand and mud Reservoir' concentration from 2003 – 2015 at different locations in the reservoir and plant. Separated by sand and finer fractions. Mostly daily but partially fragmentary# Valuing Green Infrastructure: Technical Appendices  6 3. METHODS QS(t)=Q(t)*CS(t) With QS[t/d] and Q[m3/d] being the discharge 3.1. Deriving sediment rating curves of sediment and water, CS being the sediment concentration [t/m3] and t denoting the day of the year The discharge record for all stations is much more when a sample was taken. To calculate the total annual comprehensive than the sampling of sediment load, we assumed that the load is constant between concentrations. For most stations, there are at least three measurement dates. In addition to sediment samples more years of relatively recent discharge observations and discharge observations, there were various other (Table 2). These data sets can be used to extrapolate data available from previous studies and DHMs long the sediment transport in past years without sediment term monitoring (Table 2). observations by using sediment rating curves. A common way to generalize the non-linear relationship 3.3. Handling missing data between discharge Q and sediment concentration CS is to fit a non-linear regression of the form It should be noted that there were no reliable measurements for the most upstream station (Jomsom, CS = a* Qb Table 2), which is a major limitation, given that the drainage area of Jomsom station covers nearly half of The such derived equation can be used to estimate the total drainage area and that that particular area sediment loads from past discharge records. To is subject to very specific hydro- climatic conditions derive the regression parameters a and b we used a (high desert) (Figure 1, Table 1). least average residual (LAR) method, rather than the common sum of square errors (SSE) approach, We analyzed past discharge observations for Jomsom to find an optimal fit between the observed Q and the next downstream station, Tatopani, to and CS at each station. This choice was to give less estimate QJomsom and hence to calculate QS for Jomsom weight to some outliers observed for some stations for the 2018 – 2019 sampling campaign. To do so, we (notably in Nayapul) and to derive rating curves with compared the discharge for each day with a discharge characteristics mirroring the basic understanding of record in Jomsom with the discharge in Tatopani. The sediment transport processes, e.g., that CS increases comparison shows that the ratio is variable overproportionately with Q (i.e., b>1). over the year but can be well described by an average It should be noted that the rating curve approach 0.44. Hence, we calculated the sediment load in creates an analytic link between Q and CS but also Jomsom for the 2018/2019 sampling campaign from introduces some uncertainty (Asselman 2000). the observed sediment concentration in Jomsom and Nonetheless it is still widely used in engineering and assuming that water management applications. It should also be noted that the most downstream 3.2. Sediment sampling and load calculations station (Modi Beni) is still significantly upstream from KGA. The available gauging stations cover only Sampling took place from February 2018 – January around 6500 of 7500 km2 of the total drainage area 2019. Samples were taken at 5 gauging stations of KGA. While there are many years of sediment throughout the basin with a roughly weekly frequency. concentration measurements available in KGA (Table Sediment concentrations were derived using standard 2), we did not have access to discharge data at KGA. To procedures and multiple repetitions per site and estimate discharge at the KGA, we assumed that the date. As the staff derived samples wading in the river, discharge between the confluence of the Kali Gandaki it should be noted that samples are not taken across and the Modi Khola and KGA scales linearly with the entire cross section as high flows make crossing drainage area so that for any given day the rivers and wading impossible during most of the monsoon season. Discharge was derived for all =( + ) sampling locations from the DHM gauging stations, + so that total sediment discharge for each station can be calculated as 7 Valuing Green Infrastructure: Technical Appendices 3.4. Sediment budget for Kali Gandaki some information about each station’s drainage area. Specifically, the a parameter can be interpreted as The average sediment budget for different parts of the indicator for the erodibility of a catchment. The b Kali Gandaki catchment can hence be calculated for factor can be interpreted as indicator for the erosive different periods of time from the different stations; forces (Asselman 2000). Some of the most outstanding specifically, we can calculate: • Sediment budget for 2018/2019 from the parameter values are the a values for Jomsom and measured concentration and observed discharge Tatopani, which indicate a much greater erodibility at the five gauging stations upstream of KGA there than in the other parts of the catchment. This • Sediment budget for the 2009 – 2015 period finding is largely in line with our understanding as calculated from discharge data for that period and these parts of the catchment are being rapidly uplifting 2018/2019 sediment rating curves. and eroding, respectively consisting of erodible rock types (Fort 2015; Lavé J. and Avouac J. P. 2001). 4. RESULTS  arameters of sediment rating curves Table - 3: P for gauging stations in the Kali Gandaki 4.1. Sediment rating curves for Kali Gandaki catchment Table 3 shows the parameters fitted to discharge and Jomsom Tatopani Manghalghat Nayapul Modibeni sediment observations from the years 2018/2019. a 17.09 3.13 0.62 0.82 2.39 It should be noted that the parameters vary greatly b 1.40 1.49 1.47 1.30 1.19 between stations. Possibly, these parameters carry  bserved daily load (top) and cumulative load in the Kali Gandaki basin. Figure - 3: O 60000 50000 40000 Load [t/d] 30000 20000 10000 0 03.02.2018 18.02.2018 05.03.2018 20.03.2018 04.04.2018 19.04.2018 04.05.2018 19.05.2018 03.06.2018 18.06.2018 03.07.2018 18.07.2018 02.08.2018 17.08.2018 01.09.2018 16.09.2018 01.10.2018 16.10.2018 31.10.2018 15.11.2018 30.11.2018 15.12.2018 30.12.2018 14.01.2019 Jomsom Load [t/d] Date Tatopani Load [t/d] Manghagat Load [t/d] Modibeni Load [t/d] Nayapul Load [t/d] Valuing Green Infrastructure: Technical Appendices 8 25000000 20000000 Cumulative Load 15000000 10000000 5000000 0 03.02.2018 18.02.2018 05.03.2018 20.03.2018 04.04.2018 19.04.2018 04.05.2018 19.05.2018 03.06.2018 18.06.2018 03.07.2018 18.07.2018 02.08.2018 17.08.2018 01.09.2018 16.09.2018 01.10.2018 16.10.2018 31.10.2018 15.11.2018 30.11.2018 15.12.2018 30.12.2018 14.01.2019 Jomsom Load [t/d] Date Tatopani Load [t/d] Manghagat Load [t/d] Modibeni Load [t/d] Nayapul Load [t/d] Sediment loads and sediment budgets for 4.2.  • Kali Gandaki A, Lower Kali Gandaki: = Kali Gandaki , , , , (keeping in mind that sediment load in Kali 4.2.1. 2018-2019 Sediment summary Gandaki A is calculated from a mixture of different sources of discharge and sediment Figure 3 shows the instantaneous daily load, as well concentration and cannot be calculated for the cumulative load over the length of the sampling year 2018/ 2019). campaign in the five considered gauging stations. What is notable is the small sediment load of tributaries In terms of relative contribution, most sediment compared to the main stem of the Kali Gandaki, as originated from the Mustang Plateau and the middle visible for both the instantaneous observations and Kali Gandaki (around 30 % from each catchment). In daily values for Manghalgat and Nayapul station. The terms of sediment yield, i.e., tons produced per area contribution of each catchment, can be calculated of catchments, the Kali Gandaki Gorge and the middle as follows Kali Gandaki provide most sediment. The sediment • Jomsom, Mustang Kali Gandaki: yield from the Mustang is comparably low (<2000 t/ , = , km2/yr). It is notable, that the tributary catchments of • Tatopani, Kali Gandaki Gorge: the Myagdi Khola and Modi Khola have similarly low , = , , rates of sediment load, even though they receive nearly an order of magnitude more of rainfall. This indicates • Manghalgat, Myagdi Khola: that the soils and hillslopes in these catchments are , = , relatively harder to erode (low erodibility) while the • Nayapul, Modi Khola: , = , opposite is true for the Mustang Plateau. • Seti Beni, middle Kali Gandaki: , = , , , 9 Valuing Green Infrastructure: Technical Appendices Sediment contribution from each sub-catchments in terms of total load (top) and sediment yield Figure - 4:  (bottom) for 2018/2019, please refer to Figure 1 for the definition of the different sub-catchments 7.00E+06 6.00E+06 30.00% Sediment contribution 5.00E+06 25.00% 4.00E+06 20.00% [t/y] 3.00E+06 15.00% 2.00E+06 10.00% 1.00E+06 5.00% 0.00E+06 0.00% Mustang Kaligandaki Mayagdi Middle Modi Kaligandaki Gorge River Kaligandaki River 9000.00 8000.00 7000.00 6000.00 Yield[t/km2/yr] 5000.00 4000.00 3000.00 2000.00 1000.00 0.00 Mustang Kaligandaki Mayagdi Middle Modi Kaligandaki Gorge River Kaligandaki River 4.2.2. Longer-term averages terms of sediment yield, these data emphasize the high variability in yield between sub-catchments and Figure 5). This analysis also includes the joint analysis confirm the very high yields for the Kali Gandaki of discharge and sediment concentration at KGA. The Gorge upstream of Tatopani and the middle Kali average annual load at Kali Gandaki A is 31± 4.9 Mt/ Gandaki. yr of fine sediment. This is in a similar range than values reported elsewhere. For example, Struck et al. Neither this study nor Struck et al. (2015) report (2015) report 30 ± 3.2 Mt/yr for the 2011/2012, likely values for bed load (i.e., gravels and coarser), which calculated from the same sediment concentration can likely make a major difference in a mountain river data but using observed rather than interpolated with high transport capacity. Assuming that bedload discharge data, as has been done in this study. In Valuing Green Infrastructure: Technical Appendices 10 Average sediment loads from different parts of the catchment and their variation over multiple years can be estimated using the rating curve approach 4.00E+07 3.50E+07 3.00E+07 2.50E+07 Load [t/yr] 2.00E+07 1.50E+07 1.00E+07 5.00E+06 0.00E+06 Mustang Kaligandaki Mayagdi Modi Middle Lower Kaligandaki Gorge River River Kaligandaki Kaligandaki Total Load [t/yr] Added Load [t/yr] Total load and contribution of sub-catchments as derived from past discharge data and rating Figure - 5:  curves for 2009 – 2015 (not all years covered for all stations, see Table 1) 4.00E+07 3.50E+07 3.00E+07 2.50E+07 Load [t/yr] 2.00E+07 1.50E+07 1.00E+07 5.00E+06 0.00E+06 Mustang Kaligandaki Mayagdi Modi Middle Lower Kaligandaki Gorge River River Kaligandaki Kaligandaki Total Load [t/yr] Added Load [t/yr] 11 Valuing Green Infrastructure: Technical Appendices Yield of sub-catchments as derived from past discharge data and rating curves for 2009 – 2015 (not Figure - 6:  all years covered for all stations, see Table 1) 1.20E+04 1.00E+04 Yield [t/km2/yr] 8.00E+03 6.00E+03 4.00E+03 2.00E+03 0.00E+03 Mustang Kaligandaki Mayagdi Modi Middle Lower Kaligandaki Gorge River River Kaligandaki Kaligandaki Yield [t/km2/yr] might constitute 10 to 20% of the total load, the total load can be estimated in the range of 33 – 36 Mt/yr. The longer-term interpolation indicates that there is a significant variability in load from the Mustang Plateau and the Kali Gandaki Gorge, as well as from the Middle and Lower Kali Gandaki sub-catchments. The Mustang area and the Kali Gandaki Gorge have a very similar sediment load, each contributing around 5 – 7Mt/yr. What is evident, too, is that the Myagdi and Modi rivers contributed relatively little to the overall sediment budget for all years on record. Valuing Green Infrastructure: Technical Appendices 12 APPENDIX 2: MODELING LANDSLIDE RISK AND VALUING BENEFITS INTRODUCTION: STOCHASTIC 1.  2. METHODS MODELING OF CONNECTED This section describes the method for the stochastic HILLSLOPE STABILITY slope stability analysis, identification of LSOs and empirical estimation of downslope runout length. Approaches for landslide hazard mapping on We describe first some basics of the factor of safety catchment scales are commonly based on evaluating calculation and a statistical approach to determine the factor of safety equations on the scale of individual threshold saturation conditions and failure cells in a gridded model domain. Slope stability on the probabilities of individual cells in the model domain. level of individual cells is potentially a causal factor We then describe how we aggregate the derived in the creation of landslides. However, slope stability information for groups of conditionally unstable cells analysis on the scale of single cells does not consider for that are connected in downslope direction, so called the spatial connectivity of hillslope processes. This is a landslide objects (LSOs). We propose how LSOs can major limitation both for estimating the spatial extent be used to aggregate certain properties (i.e., failure of potential landslides and their downslope runout probabilities and threshold rainfall conditions) for zone and hence identifying structures at risk on the all cells belonging to an LSO and enable analyzing slide. Understanding connectivity of landslide prone properties of slope failure such as mobilized sediment cells is also crucial to estimate landslide magnitude volume and length of downslope runout which cannot in terms of sediment mobilization which information be derived from commonly applied analyses of slope is important for analyzing landslide hazards and stability on the scale of single cells. The model resolution landslide contributions to catchment sediment is identical to the resolution of the underlying DEM budgets. (30m for this study). It should be noted that coarser resolution will likely lead to a drastic underestimation Herein, we propose Landslide Objects (LSOs) as the of landslide probability, because local steep hillslope unit of analysis for catchment-scale landslide hazard gradients would be increasingly smoothed out. screenings. LSOs are identified from an analysis of downslope connectivity amongst failure prone cells. Current best practice: 2.1.  single cell LSOs provide the spatial template for evaluating deterministic slope stability landslide failure probability and downslope hazards. Finally, LSOs are integrated in a probabilistic hazard Catchment-scale landslide zonation are commonly assessment driven by spatially generalized extreme- based on evaluating slope stability using the Mohr value distributions for precipitation. The resulting Coulomb failure criterion for individual cells in a framework is demonstrated in the case study of the model domain, e.g., an individual cell in a digital Kali Gandaki catchment in Nepal, where we model elevation model (DEM), assuming an infinite slope landslide occurrence probability as well as structures and a relative shallow and surface-parallel failure at risk, the possible economic loss, and benefits from mode. For a single cell i in a DEM, the factor of safety landslide mitigation. Despite the great uncertainty in is defined as the balance between shear strength, τi, input parameters, we show how the framework can be and shear stress, τm,i as used to identify locations and magnitudes of potential slope failures, assets at risk, and possible focal areas for = 1 landslide management, which makes the method one of interest fin the study of both catchment sediment With the assumption that cell i is prone to slope failure dynamics as well as hazard mapping and mitigation. when FSi<1. In its full form, FSi is defined as 13 Valuing Green Infrastructure: Technical Appendices + +( ) cos tan zi: soil depth, assumed to be the depth of a potential = 2 failure plane [m] αi: slope angle [deg] The equation is based on the following input variables: ϕi: soil internal angle of friction ci: soil cohesion [kPa] δci: added cohesion because of plant roots [kPa] It should be noted that the above notation distinguishes γs: unit weight of soil [kN/m3] between global variables, e.g., physical constants, and γw: unit weight of water [kN/m3] variables that vary spatially within a watershed and are m: soil water saturation [ - ] hence specific for a given cell (denoted by subscript i). Data sources, typical values and references for key input variables for the landslide model. Table - 3:  Input Typical values Data Source - Nepal Data source – Pakistan ci Set to 10 kPa for all cells where soil is Data on soil types and location of cells with no cells are present (as an estimated average over derived from the ISRIC-SOTER database values listed here: https://daac.ornl.gov/ SOILS/guides/Global_Hydrologic_Soil_ Group.html) and to infinity for all cells with no soil. Different soil types could be assigned different cohesion values if there was location specific evidence δci Additional soil cohesion because of roots Nepal-specific land use Global data from remote was set to 12 kPa (Vanacker et al. 2003), landcover map sensing provided by the for all cells where land use landcover European Space Agency maps indicated presence of forest γs Set to 16 Kn/m3 for all cells (Vanacker et n/a al. 2003). Different soil types could have significantly different densities and weights but such information was not available γw Set to 10 Kn/m3 for all cells (physical n/a constant) m Calculated for each cell based on a spatial 35 rainfall gauges with Global daily precipitation from interpolation of observed rainfall data 20 years of daily data remote sensing (TRMM) for (see Figure 6 ) (1995 - 2005). See 2000 – 2015 Figure 6 for location zi Derived from gridded global data Derived from the ISRIC-SOTER database αi Derived from the digital elevation model ASTER Digital Elevation Model (DEM), 30 m resolution ϕi Set to 15° according to lower estimates n/a (Vanacker et al. 2003) for all cells. Different soil types could be assigned different cohesion values if there was location specific evidence Valuing Green Infrastructure: Technical Appendices 14 The soil saturation will undergo major temporal Most of the variables can be determined using standard variations as a function of local infiltration and sub- procedure, specifically surface water inflow from the area draining to , AD,i, and the spatio-temporal variability in precipitation = 0 7 this area receives. To evaluate the soil saturation over a longer time period, the use of steady state hydraulic ET0j is the reference evapotranspiration and cj is the considerations is common practice (Montgomery crop-coefficient in cell j. The surface runoff can be David R. and Dietrich William E. 2010; Vanacker et determined using a standard approach based on, e.g., al. 2003). According to O’Loughlin (1986), the local the curve number method, i.e., soil saturation can be derived from 0.2 +0 .8 , =, < ( ) , = 3 8 0 and In this model, qi is the average subsurface flow to i 1000 from upslope [m3/s]. AD,i is the upslope area [m], bi is = 109 the downstream boundary length of cell i [m] and Ti is the transmissivity, which is calculated as and = 4 , =0 .2 10 [m2/s], with K being the saturated hydraulic In which CNj is the local curve number depending on conductivity [m/s]. In simple terms, the numerator is land use type and soil characteristics, which is described the water supplied from the area draining to i and in detail in standard engineering literature. Finally, the denominator is the local soil transmissivity at the we don’t consider for deep percolation (i.e., Q D,j=0), downstream boundary of cell i of length bi, i.e., how which will strongly depend on local geology and much water can be conveyed by subsurface flow at lithology. Thus, information which is not commonly the downstream boundary of i. Hence, if mi>1, water available on catchment scales. inflow is larger than subsurface drainage and overland flow occurs. The factor of safety for an individual cell i for longer term average hydrologic conditions can be calculated qi is the residual of precipitations minus losses to from the above equations. However, this approach evapotranspiration ET0, direct runoff QR, and deep (which is the current state of the art for catchment percolation QD. Hence scale hazard assessments) has two significant shortcomings: = 0  5 1. Calculations are based on long-term averages of soil moisture (typically annual means), while it is where each variable is in [m] and denotes the average evident from basic science and observations that over the upslope area of i. Alternative to such a spatial most landslides occur for individual extreme averaging, qi can be calculated to consider explicitly rainfall events for spatial variability in upslope conditions. Let j∈ADi 2. Calculations are considering all cells in the model be a cell located in the area draining to i. Then, the domain individually. Not considering for possible upstream contribution to subsurface flow is: connections between these cells disables estimating landslide magnitude and spatial extent. Both , = = ( , , )  6 parameters are crucial parameters for landslide risk assessments but not commonly available on It should be noted that i might also receive some catchment scales using standard FS-mapping percolation from the surface flow created upslope and approaches. flowing over i. However, we do not consider for this effect in here. 15 Valuing Green Infrastructure: Technical Appendices 2.2. Probabilistic factor of safety calculations With being the average for precipitation, evapotranspiration and runoff over a period of Most parameters in the Factor of Safety equation interest, e.g., the rainy season or the entire year. The + +( ) cos tan average runoff, can be estimated using a curve = 11 , number approach. vary in space but are constant for a single cell over a The curve number approach and a water balance for management-relevant time horizon (years to decades). cell i can also be a practical approach to determine Soil moisture conditions, however, vary on seasonal which threshold rainfall would be required to add and daily timescales as a function of variability in enough water to the seasonal soil wetness to reach the precipitation. The factor of safety equation allows threshold soil moisture conditions during an event e. one to derive the saturation which relates in a specific Let the water balance for cell i during event e be value of FSi as , ( + ) 1 19 = , 12 cos tan Where is the threshold rainfall, ET(e) is the Assuming that slope failure occurs when FSi≤1 allows evapotranspiration, QR,i(e) is the surface runoff, and to define mi* is the threshold saturation for slope QD,i(e) (assumed to be 0) is the deep percolation (all in failure at a value of FSi=1 [m]). Then, the threshold rainfall to reach the sum of , ( + ) 1 infiltration and evapotranspiration is = , 13 cos tan 20 Reaching the threshold saturation mi* is a function of threshold subsurface flow Qi* which can be derived from However, only a part of that rainfall would infiltrate locally, while 14 ( initial abstraction less  15 than precipitation) , else In tropical settings, failure of a slope will often occur when a rainfall event of a specific magnitude will add 21 soil moisture to an already partially saturated slope during the rainy season (Dahal and Hasegawa 2008; will describe the runoff created by event e on cell i. Gabet et al 2004). Hence, we can define Qi* as The partial conversion of precipitation to runoff will increase the required rainfall to reach threshold  16 conditions to: Respectively 22 17 To conclude, is the threshold precipitation for which the failure threshold will be exceeded for cell i Where is a represents the average subsurface flow under consideration of the hydrologic partitioning of from the upstream area through cell i, e.g., during rainfall in different components as well as for average the rainy season, and Qi (e)* is the critical moisture an antecedent moisture conditions. For management event e will need to add to result in an exceedance purposes it is now crucial to understand how likely of threshold conditions. Similar to equation 6, the is exceeded, which is a function of the local average subsurface flow can be estimated from the precipitation regime. water balance of the upslope area, assuming that cell i is at a seasonal equilibrium with regard to subsurface Let us assume that the maximum annual precipitation flow when event e occurs values at cell i can be described by an extreme value distribution of the form 18 Valuing Green Infrastructure: Technical Appendices  16 Fi*=1 – F (p < pi*| μi,σi ) derive the required spatially distributed information, 23 μi, σi can be derived from observed annual maximum rainfall values at available gauges and interpolated Where is the probability for precipitation p for the entire study area using krigging or a similar to occur in cell i, and μi and σi are the empirical scale interpolation approach (see Figure 6 for an example and location parameters of observed annual rainfall from the Kali Gandaki catchment) . maxima in cell i. The cumulative distribution of pi is then To conclude, the above method considers for • Natural spatial variability in static factors 24 controlling slope stability, namely hillslope gradient, soil cohesion and friction angle So that is the cumulative probability of • Spatial variability in factors which could be linked not exceeding p_i and to management decisions. Namely, the model considers for local root cohesion as well as for Fi*=1 – F (p < pi*| μi,σi ) 25 catchment scale changes in hydrology because of changing vegetation is the failure probability of cell i. • Changing seasonal as well as single event soil moisture conditions based on a curve number With the above method, and specifically by combining approach equations 22 and 25, the probability of slope failure • Spatial variability in extreme rainfall and the can be estimated for a specific cell. resulting spatial variability in probabilistic slope stability, i.e., how likely conditions at cell i result Typically, rainfall is measured at specific locations in a factor of safety smaller than one and hence in a catchment, only, while the proposed approach possible slope failure. requires μi, σi for each cell in the model domain. To Spatially generalized parameters of an extreme value distribution (Equation 23) for annual Figure - 6:  maximum precipitation in the Kali Gandaki catchment. Shown are the scale parameter μ and location parameter σ derived from observed rainfall time series at precipitation gauges (white squares) and interpolated for the whole study area using krigging. The resulting information can be used to calculate the exceedance probability for any rainfall value for each cell in the model domain. 17 Valuing Green Infrastructure: Technical Appendices 2.3. Connected landslide assessments completely dry conditions. This identifies areas without stable soil mantle Normally, landslides will not occur on the scale of 2. FS(mi=1)>1, unconditionally stable areas identify single cell. Rather, the failure of a single part of a slope pixels that will not fail even for completely slope within a wider area at near-threshold conditions wet conditions. might trigger the failure of the entire connected 3. FS(mi* )≤ 1 conditionally unstable areas identify area of failure-prone slope. Quantifying this spatial slope areas which can fail as a function of changing relation is also key to understand landslide magnitude soil moisture conditions. (slide extent and volume and mass of mobilized sediment). Determining landslide volume is relevant We filter all cells for which FS(m=1)>1 and with for catchment sediment and hazard management FS(m=0)<1, with the remaining cells identifying parts for three reasons. Firstly, because of the highly non- of a hillslope which are possibly prone to failure (Figure linear relation between landslide area and volume, it 7 a, red cells). We identify connected conditionally is crucial to determine the connected area of sliding unstable areas following a downslope gradient (Figure pixels rather than considering single pixels. Secondly, 7 b). A set of connected conditionally unstable cells is landslide volume will affect run-out length, i.e., how from now on treated as a single object, referred to as far mobilized sediment will travel downslope of the Landslide Object or LSO. i∈LSOk is a cell belonging to landslide scar and which additional assets it might the Landslide Object with identifier k, which includes damage on that path and how well a zone of landslides nk cells. We then assume that the Landslide Object has is connected to the river network. Thirdly, calculating certain properties as a function of the cells it entails. the mobilized volume is crucial to determine the contribution of landslides to overall sediment budget The challenge is now to identify the joint probability of a catchment. Common landslide hazard zonation with which cells of LSOk will fail. The probability of approaches on the scale of single pixels fall short in single cell failures is not independent, because (1) cells providing that information in a consistent manner. are physically connected to each other and (2) subject In this section, approaches to group single pixels to same or similar rainfall conditions. Instead of using on a hillslope into larger, failure-prone connected joint probabilities, we hence assume that the failure areas based on concepts of downslope geomorphic probability of LSOk is can be described as connectivity are introduced. We then describe how landslide volume is derived and how downslope zones  26 at risk in the run-out area are delineated. i.e., the mean failure probability of cells belonging to Identifying connected landslide objects LSOk. It should be noted that this assumption can be To identify cells which might be possibly unstable and replaced with alternatives, e.g., form failure-prone areas, we can analyze lowest and highest risk conditions of a watershed. According 27 to the factor of safety calculations, the lowest risk of failure for a cell will occur if saturation is null, i.e., Which would be a “weakest link” assumption, i.e., hillslope failure is triggered by the weakest element in min(FSi)=FS(mi=0) that slope failing. while the highest risk of failure occurs if soil is fully Estimating LSO volume saturated There is strong empirical evidence that the volume of a landslide increases non-linearly with its size. Based max(FSi)=FS(mi=1) on a global analysis of landslide scars, Larsen et al. (2010) propose a power-law relationship between based on these considerations there are three possible the surface area of a landslide and the volume of the conditions of a slope mobilized sediment as 1. FS(mi=0)<1, unconditionally unstable area identifies slope pixels which are not stable even for 28 Valuing Green Infrastructure: Technical Appendices 18 Derivation of connected landslide objects (LSOs) and failure probabilities. a: identification Figure - 7:  of conditionally unstable cells. b: grouping of conditionally unstable cells along downslope gradients. Different colors identify the resulting downslope-connected landslide objects (LSOs). c: identification of failure probability for single cells (blue fill colors) and aggregation of failure probability for each LSO scale (green to red outline colors). (with VLS and ALS being the volume and the area 29 of a landslides). Based on a set of more than 4000 observations, they found a best fit between Equation Where b is the side length of a cell in the DEM so that 28 for logα=0.86 (i.e., α=100.86=7.24) and γ=1.322 the volume of an LSO [m3] finally reads as with an R2=0.95. 30 Based on the above definitions, we can determine the area of a landslide object by summing the area of cells VLSO,k can be converted to a mass through the relation belonging to it as 19 Valuing Green Infrastructure: Technical Appendices 31 Where LLSO is the runout length and HLSO is the vertical distance between the start point of runout (i.e., the With lowest point on a landslide) and the downslope distance along the runout path (both in m). LLSO and HLSO are Estimating runout length not independent as a longer runout length will also Lastly, we can calculate the runout length as a function lead to a larger vertical distance. For computations in of mobilized sediment volume. How far sediment a gridded model domain, it is practical to calculate the will run out from a landslide scar is depending on condition in equation 32 for all cells along the possible the volume of the landslide, which controls the runout pathway downslope of a runout pathway. For energy mobilized during a landslide, but also on the each cell, the travelled distance as well as the vertical downslope topography. Hence, a larger landslide on a distance will increase. We assume that the landslide steep slope will travel farther than a smaller landslide runout stops as soon as the runout length from on a gentler slope. This effect has been studied equation 32 is less than the total travel distance to the empirically by Rickenmann (1999), see discussion in next downslope cell. Rickenmann (2005), based on runout observations from the Alps. Despite the different geography, the For the calculation, we can first define all cells between wide range of considered landslide volumes, runout LSOk ,and the channel network. This downslope lengths and geomorphic conditions seem to make this runout path is denoted as γk. Let h∈γk be a cell along model one of the most well-founded. γk. Then, δHh is the elevation difference from LSOk to h δHh=zLSOk-zh. And δLh is the runout length from LSOk to Runout length of an LSO can thus be calculated as h. Along γ, we can the continuously calculate the ratio between L and H. 32  onceptualization of runout modeling in a gridded domain, where individual cells can be on Figure - 8: C the runout path γ of multiple landslides. The longitudinal hillslope section A-B in the small pane indicates how runout length is calculated following an empirical relation developed by Rickenmann (2005). Valuing Green Infrastructure: Technical Appendices 20 F(h) = max(k, l, m) F There is an important distinction between the canals”) and other infrastructure might increase calculation of hazard for cells on an LSO and the landslide risks. However, the impacts of infrastructure, calculation of hazard along a runout path. This is e.g., roads, on slope stability is not explicitly considered because each cell on an LSO is unequivocally assigned in this study. This is mainly due to the complexity of to a single LSO. In contrast, downslope cells can be on road impacts on hillslopes and the many different the runout paths of multiple landslides (see Figure 2). failure mechanisms through which roads can trigger For example, let us assume that h∈γk,l,m is a cell on the slope failure. Most of the processes that link roads runout path of the three LSO denoted k,l and m. The to slope failure also act on much smaller scales than risk of h h h hhhhh and any assets on h to be affected the model resolution. This section also gives some by upslope landslides is hence the joint probability of outlook on how the landslide model and the derived k,l and m failing. That joint failure hazard for h, i.e., information could be used to estimate links between could be defined in various ways. For example, the roads and slope stability in the future and in cases probability that either of the upslope slides fail is where more data is available. F(h)=F(k) ∪F(l) ∪ F(m)33 Road cuts on steep slopes destabilize slope toes, which can initiate slope failure. Infiltration from cut slope The probability of these independent but not mutually ditches can increase soil saturation under the road exclusive events can be calculated as prism. Similarly, material dumped on the downslope (fill slope) increases the loading on slopes and can F(h)=F(k)+F(l)+ F(m) – (F(k)F(l) F(m)).34 decrease slope stability leading to smaller landslides in the fill material as well as to deeper seated landslides. Alternatively, we can also adopt a “worst case” In the Himalayas, such road induced landslides can approach significantly impact sediment budgets (Leibundgut et al. 2016; Sidle and Ziegler 2012; Hearn 2011). The F(h) = max(k, l, m) 35 potential failure mechanisms and impacts of roads on F landslides and vice versa are shown in Figure 9 and in which the runout hazard of a cell is defined by the Figure 10. maximum hazard from upslope landslides and which we adopt in this paper. Similarly, we can also calculate It should also be noted that some landslide the volume of upslope slides as susceptibility mapping approaches consider the presence of roads as a predictor. In such susceptibility- V(h)= Vk+Vl+ Vm 36 based approaches, various factors (e.g., topography, antecedent rainfall, land use and, possibly, roads) and the mean distance between cell h and each upslope are correlated to observed landslide occurrence via LSO. statistical methods. We did not adopt a susceptibility mapping approach for two main reasons. First, such 37 approaches require landslide inventories to train the model. Such inventories are not commonly available. 2.4. Sediment mobilization from road induced Second, a susceptibility mapping approach would not landslides allow the representation of the different impacts that land use interventions have on landslides. However, Mountain roads can destabilize slopes through synergies between the LSO model and susceptibility various interactions with hillslope hydrology and soil mapping approaches should be explored in the future. mechanics. Besides, seeping irrigation canals (“hill 21 Valuing Green Infrastructure: Technical Appendices Links between road construction and road failure (Sidle and Ochiai 2006, p. 184) Figure - 9:  Road induced slope failures and their link to infrastructure damage and connectivity to streams Figure - 10:  (Hearn 2011). Valuing Green Infrastructure: Technical Appendices 22 The variability of processes contributing to possible 2. Evaluate the costs to treat an LSO road induced slope failure would require detailed 3. Evaluate the resulting change in LSO failure assessments of slope stability on the scale of single probability. slopes and is hardly feasible on a landscape scale. We hence do not explicitly model road-related reductions For points 1 and 2, this study uses data reported in the slope stability/ landslide model. by Dahal and Dahal (2017). From the methods reported therein, we focus on two types, tree and 2.5. Landslide hazards for infrastructure bamboo plantation, and installation of subsoil drains. This selection is because changes in root cohesion Landslide hazards for buildings and soil moisture can be directly represented in Building footprints are derived from Open Street the model by changing the wetness parameter m Maps. Footprints can possibly overlap with multiple and the root cohesion parameter δc in the landslide cells. However, each footprint is assigned to the cell model. Modeling hard engineering solutions is more which is closest to its center. If that cell is part of a challenging on catchment scales and, hence, is not landslide, we assume that the entire structure is part of this assessment. destroyed. As each building is located on a single cell, there is a one-to-one relationship between the We also acknowledge that such low-cost engineering landslide and runout hazard at the location of that measures are not suitable to address very large cell each structure. Note that the error introduced landslides with deep-seated failure planes. Hence, we by assigning each footprint to a single cell is likely classify landslides identified by the model into four rather small, as the size of cells (30 X 30 m, 900 m2) is groups with increasing magnitude and develop a very large compared to the typical building footprint. “prototype portfolio” of measures that can be applied However, the spatial relation between buildings and for the mitigation of the first three types. cells would require more detailed analysis when using a DEM with a high resolution (e.g., 1 or 5 m), in which Specifically, we propose the following classification: each footprint would cover many cells. 1. Shallow landslide (<1.5m) in the topsoil (i.e., landslide depth < soil depth). The minimum Landslide hazards for roads depth of an LSO is given by the cell size and is Road segments are derived as lines from Open Street around 1.4 m;hence, the 1.5 m threshold. Failure Maps. First, we identify all cells a road segment plane in the range of deeper rooting plants and traverses. Because a road can traverse many cells, trees. there is a many-to-one relationship between roads and 2. Landslide depth > 1.5 m but still in the topsoil. landslide, i.e., a road can traverse multiple potential Failure plane in the range of deep rooting trees. landslides and runout paths. Hence, we need to 3. Landslide depth > depth of the topsoil, but less aggregate the values for all relevant LSO and runout than 3 m. Failure plane in the bedrock (i.e., cannot paths for each of the road segments. The resulting be reached quickly by roots) but still possibly in fields and methods of aggregation for each road the range for soft/ grey-green engineering segment is shown below. Note that the methods of 4. Landslide depth > 3 m. Deep seated landslides aggregation can be easily altered for specific analyses. which would require massive engineering for Similar to buildings, we assume that a road is impacted mitigation. Not considered for mitigation measures by a landslide on a specific cell even if it traverses just a but useful information for hazard mapping and small fraction of that cell. However, we calculated the disaster awareness. exact length of road that traverses the unstable cell(s). To model the impact of different mitigation strategies, 2.6. Modelling management interventions we design a prototype mitigation strategy for landslide The intention of this study is to evaluate the cost- classes 1 – 3. It is challenging to quantify the impact of effectiveness of certain management measures. Hence, specific strategies on the parameters of the model and we need to derive information on three domains: the herein presented values are a first, expert-based 1. What management measures are available for attempt on the parameter estimation. We change landslides in the Himalayas, e.g., regarding the model parameters for all considered landslides required skills, materials and costs according to Table 5 below (e.g., for all landslides of 23 Valuing Green Infrastructure: Technical Appendices type 1, we apply the appropriate mitigation measure), Drainage system for failure prone Figure 12:  which then results in a change in probability of slope roadside slopes (Dahal et al, 2006) failure. This probability is then used to evaluate the change in value of roads and structures at risk and to quantify the changed sediment mobilization. Details of landslide interventions and Table - 5:  impacted model parameters. Landslide Interventions Impacted class parameters C1: Shallow I1: Plantation of • Soil cohesion: top soil grass and coir Increase soil netting on the cohesion entire landslide by 15 KPa surface (Vanacker et Reforestation al. 2003) C2: Deep I2: Reforestation • Soil cohesion: top soil Excavation of sub- Increase by 10 soil drains KPa (Vanacker et al. 2003) • Saturation: decrease m by 20 % 1 C3: Shallow I3: Excavation of • Saturation: bed rock deep drains decrease m by 20 % We simulate the following intervention scenarios: Scenarios Interventions Target landslide class 3. RESULTS A I1 C1 B I1 and I2 C1 and C2 C I3 C3 only 3.1. Modelled and empirical rainfall thresholds D I1, I2, I3 C1, C2, C3 Landslide inventories for the study area are absent. For all interventions, we assume that they are only Hence, we need to resort to some broader evidence feasible on hillslopes not more than 1 km away to test if the results produced by the proposed from a road, as they might require transport of method are reasonable. Dahal and Hasegawa (2008) large equipment and material. We also consider all found a good empirical relationship between hourly agricultural land, assuming that there will always be rainfall over a certain period D and the occurrence of some sort of access there, even if it does not show up landslides (Figure 12). in the road dataset. The reduction in soil saturation will depend on many local factors, such as soil type, slope, quality of the drainage works, etc., hence, we 1. assume the 0.2 value. However, the effectiveness of drainage for landslide prevention and its modeling on catchment scales would merit more detailed study. Valuing Green Infrastructure: Technical Appendices 24 Based on their findings, landslides are unlikely to Threshold duration vs. intensity Figure 12:  occur for rainfall intensities below relationship for landslides in Nepal (modified from Dahal and I = 73.9D-0.7938 Hasegawa, 2008) I [mm/hr] is the rainfall intensity and D in [h] is the length of an event. I can be interpreted as lowr boundary for pi*. As we are bound to daily data, we find that the threshold intensity should be mm I = 73.9 * 24-0.79 = 6.0017 39 h To make results compatible with our daily timescale, I would become ID=73.9 * 24-0.79 * 24 These general findings can now be compared to =73.9 * 240.21 results for Kali Gandaki (Figure 13). The mean mm precipitation threshold for LSOs in the study area is =144 40 d 264 mm and hence in the range expected from Dahal which gives us at least some estimation on the rainfall and Hasegawa’s results. Only 9.5 % of modeled LSOs intensity that triggers landslides in Nepal. The range fall below the threshold defined by 40. Based on the of rainfall conditions under which landslides were observed rainfall, we can translate these values in failure observed in the data of Dahal and Hasegawa (2008) probabilities (middle panel). It should be noted that is between around and there are also a significant number of LSOs for which This range is, obviously, a result of the landslide and threshold conditions are not reached (i.e., F(k)=0). The rainfall data used therein, but can provide an initial distribution of failure probabilities for all LSOs with estimation of the threshold of rainfall magnitude we F(k)>0 is shown in the right panel, indicating that the should expect. mean failure probability is around 0.16. Distribution of LSO threshold rainfall compared to the threshold proposed by Dahal and Figure 13:  Hasegawa (2008) (right). Distribution of LSO failure probability (center) and failure probability for LSOs with a non-zero failure probability. 25 Valuing Green Infrastructure: Technical Appendices 3.2. Road and building exposure of the segments at risk (~25 % of all segments) are in the lowest (< 5% pa) category. However, Key findings: compared to houses, a much greater percentage • Roads and buildings show a greatly different falls into higher risk classes (10 – 50 % pa). Similar exposure to landslides (Figure 14 and Figure 15). to houses, there are much more segments at risk These figures report how many buildings and because of a runout path, rather than because of road segments fall in probability classes (x axis). direct crossing of an LSO. The y axis reports to how much percent of the • Some visualization of landslide and runout risk total buildings and roads respectively are located for the middle Kali Gandaki are shown in Figure on potential landslides or runout paths shown on 16 and Figure 17. This shows that most buildings the x axis. are located outside of the most prominent zone of • Less than 10% of all buildings are on landslides landslide mobilization, but many more buildings or on downstream runout pathways (Figure 14, and roads are located in downslope areas that could yellow line). Of all buildings at risk, most fall be subject to runout from upstream landslides. in a low risk category (<10 %) and even in this Figure 17 shows that the most prominent category, much more structure are at risk because zone of landslide probability in the upper right they are located on runout pathways, rather than corner corresponds to an active steep escarpment directly on an LSO. (no vegetation). • Across all risk classes, more than 40% of roads are at risk (Figure 15, yellow line). Again, most  uildings at risk, binned by the failure probability of the landslide/runout they are located on. Figure 14: B Lines show cumulative values 25 On LSOs On Runout Cummulative, on LSO 20 Cummulative, on Runout Cummulative, all Percent of structures [%] 15 10 5 0 0 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.05 0.15 0.25 0.35 0.45 0.55 0.65 0.75 0.85 0.95 Failure probability[-] Valuing Green Infrastructure: Technical Appendices  26 Road segments at risk, binned by the failure probability of the landslide/runout they are located on. Figure 15:  Lines show cumulative values 50 On LSOs 45 On Runout Cummulative, on LSO 40 Cummulative, on Runout Cummulative, all 35 Percent of Road segment [%] 30 25 20 15 10 5 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 Failure probability[-] 3.3. Calibrating landslide contributions to Because landslides make up the largest part of the sediment budgets sediment budget of each sub-catchment, which is in line with the understanding that landslides and other The sediment budget for 5 sub-catchments in of mass movements are most important factors in the the Kali Gandaki can be determined from sediment sediment budget of Kali Gandaki (Struck et al. 2015), measurements performed by Kathmandu University. we focus calibration on the landslide model. Specifically, These measurements allow us to determine the we modify the soil cohesion by a calibration factor in contributions of the Mustang Plateau, the Kali Gandaki each sub-catchment. This assumption means that each Gorge, the middle and lower Kali Gandaki, the Modi sub-catchment is a homogeneous unit with regard Khola and Myagdi Khola tributaries. A key finding is to the geomorphic processes impacting landslides. the great diversity in sediment load and yield, which is While this is a simplification, it should be noted that not aligned with the spatial distribution of rainfall, in the sub-catchments are indeed distinct with regard the sense that the tributary catchments receiving most to their topography, climate and geology (lithology, of the basin’s precipitation do not contribute most to uplift, fracturing) and, hence, with some key factors the basin’s sediment budget. influencing landslides. It is, therefore, likely that each sub-catchment has a specific susceptibility to landslides, A comparison of observed sediment load to our multi- though we cannot yet provide a mechanistic model model approach with separate models for hillslope to explicitly reproduce the differences between the erosion (SDR), landslides, roads, and glaciers shows sub-catchments. To modify soil cohesion, the original that the models over-predict sediment load from the uniform value of 10 KPa was changed according to the tributaries and under-predict load from the Mustang values tabulated in Table 6. and the Kali Gandaki Gorge and makes some calibration of the multiple models necessary. 27 Valuing Green Infrastructure: Technical Appendices  esults of the stochastic connectivity of landslides and runout tool for an area on the middle Figure 16: R Kali Gandaki River. Red colors indicate landslide probability and brown colors indicate runout probability Valuing Green Infrastructure: Technical Appendices 28  esults of the stochastic connectivity of landslides and runout tool for an area on the middle Kali Figure 17: R Gandaki River. Transparent landslide and runout data overlaid over satellite imagery, showing the origins of the major landslides from an escarpment in the top right area. 29 Valuing Green Infrastructure: Technical Appendices  otal sediment load at different gauging stations (orange) and the contribution of the respective Figure 18: T sub-catchments (blue) Error indicators show ± 1 standard deviation 4.0E+07 3.5E+07 3.0E+07 2.5E+07 Load [t/yr] 2.0E+07 1.5E+07 1.0E+07 5.0E+06 0.0E+00 Mustang Upper Myagdi Modi Middle Lower Kaligandaki Kaligandaki River River Kaligandaki Kaligandaki Total load [t/yr] Added load [t/yr] Comparison of modelled and observed load from the uncalibrated multi-model package. Observed Figure 19:  load is the same as in Figure 18, error bars indicate ± 1 standard deviation in observed loads ×106 Glaciers 12 SDR Landslides Roads 10 Observations Standard deviation Sediment load [t/yr] 8 6 4 2 0 som l i i t ki pu an en lga da top dib ya Jom ha an Na ng Mo Ta lig Ma Ka Valuing Green Infrastructure: Technical Appendices 30  omparison of modelled and observed load from the multi-model package with a calibrated mass- Figure 20: C movement/landslide model (yellow)) . Observed load is the same as in Figure 18, error bars indicate ± 1 standard deviation in observed load. ×106 12 Glaciers SDR 10 Landslides Roads Observations Sediment load [t/yr] 8 Standard deviation 6 4 2 0 som ul ni i t ki en lga yap da pa dib Jom ha an to Na ng Mo Ta lig Ma Ka Table 6 gives the change cohesion in the different catchments, assuming that they have different soil types and are under the influence of different tectonic conditions, fractures, etc. Sub-catchment modifiers for soil cohesion, which were used to calibrate the landslide mode. The Table - 6:  baseline cohesion factor was derived from Vanacker et al. (2003). Note that no calibration was performed for the Mangla catchment as sediment data were not available and the baseline value was thus used for the whole catchment Catchment Soil cohesion (baseline) [kPa] Soil cohesion calibration factor Mustang 10 kP 0.85 KG Gorge 0.7 Myagdi River 1.2 Middle KG 0.725 Modi River 0.9 Lower KG 1.15 31 Valuing Green Infrastructure: Technical Appendices 4. REFERENCES Dahal, B.K., Dahal, R.K., 2017. Landslide hazard map: tool for optimization of low-cost mitigation. Geoenvironmental Disasters 4, 8. https://doi.org/10.1186/s40677-017-0071-3 Dahal, R.K., Hasegawa, S., 2008. Representative rainfall thresholds for landslides in the Nepal Himalaya. Geomorphology 100, 429–443. https://doi.org/10.1016/j.geomorph.2008.01.014 Dahal, R.K., Hasegawa, S., Masuseda, T., Yamanaka, M., 2006. Roadside Slope Failures in Nepal during Torrential Rainfall and their Mitigation, in: Disaster Mitigation of Debris Flows, Slope Failures and Landslides. Universal Academy Press, Inc. Tokyo, Japan. Gabet, E.J., Burbank, D.W., Putkonen, J.K., Pratt-Sitaula, B.A., Ojha, T., 2004. Rainfall thresholds for landsliding in the Himalayas of Nepal. Geomorphology 63, 131–143. https://doi.org/10.1016/j.geomorph.2004.03.011 Larsen, I.J., Montgomery, D.R., Korup, O., 2010. Landslide erosion controlled by hillslope material. Nature Geosci 3, 247–251. https://doi.org/10.1038/ngeo776 Montgomery David R., Dietrich William E., 2010. A physically based model for the topographic control on shallow landsliding. Water Resources Research 30, 1153–1171. https://doi.org/10.1029/93WR02979 O’Loughlin, E.M., 1986. Prediction of Surface Saturation Zones in Natural Catchments by Topographic Analysis. Water Resources Research 22, 794–804. https://doi.org/10.1029/WR022i005p00794 Rickenmann, D., 2005. Runout prediction methods, in: Debris-Flow Hazards and Related Phenomena. Springer, pp. 305–324. Rickenmann, Dieter. 1999. “Empirical Relationships for Debris Flows.” Natural Hazards 19 (1): 47–77. https:// doi.org/10.1023/A:1008064220727. Struck, M., Andermann, C., Hovius, N., Korup, O., Turowski, J.M., Bista, R., Pandit, H.P., Dahal, R.K., 2015. Monsoonal hillslope processes determine grain size-specific suspended sediment fluxes in a trans-Himalayan river. Geophys. Res. Lett. 42, 2015GL063360. https://doi.org/10.1002/2015GL063360 Vanacker, V., Vanderschaeghe, M., Govers, G., Willems, E., Poesen, J., Deckers, J., De Bievre, B., 2003. Linking hydrological, infinite slope stability and land-use change models through GIS for assessing the impact of deforestation on slope stability in high Andean watersheds. Geomorphology 52, 299–315. https://doi.org/10.1016/ S0169-555X(02)00263-5 Valuing Green Infrastructure: Technical Appendices 32 APPENDIX 3: MODELING SEDIMENT GENER- ATION FROM ROADS There is an important feedback loop between roads, on the downslope side (fill slope). The remaining infrastructure and livelihoods. On the one hand, roads material is commonly dumped on hillslopes below enable access of rural population to markets, healthcare the roads. Both cut slopes and dumped sediment and education. On the other hand, poorly constructed is typically poorly compacted and, hence, prone and non- strategically planned roads can increase to erosion. the risk of natural hazards such as landslides, and 3. Sediment generation from road-induced mobilize sediment that impacts downslope agriculture, landslides. Road interfere with slope stability via aquatic ecosystems, and water infrastructures. Roads three common mechanisms (Hearn 2011; Sidle are possibly a major source of sediment in many and Ochiai 2006). Himalayan catchments, where topography is very • Reduction of support by undercutting unstable steep and precipitation is high. Here, we describe slopes the development of a model to estimate erosion from • Increasing the load on fill slopes roads to (1) quantify the contribution of roads to basin •  Changing flow-paths of sub-surface flow sediment budgets, and (2) identify hotspots of road- and concentrating flows on unstable areas of related erosion and sediment generation, so as to (3) hillslopes propose areas where better road management could have the greatest benefit for catchment management. Because of the complexity of interactions between Herein, we describe the different components of the roads and sub-surface hydrology which eventually road model and present some results. leads to an increased landslide risk, this process is not considered explicitly, but via a spatial analysis of roads and landslide objects. 1. METHODS We quantify two main mechanisms for road sediment 1.1. Modeling erosion from road surfaces and generation based on a review of pertinent literature cut slopes and consider a third mechanism quantitatively. Water running off an unpaved road surface creates Specifically, these mechanisms are shear stress on the particles of the road surface, causing 1. Erosion of road surfaces and cut-slopes through sediment mobilization of sediment. Often, flow is not runoff. Heavy precipitation on unpaved but diffuse over the road surface but concentrates in ruts, compacted road surfaces can create significant which increases the erosive forces. Flow on roads is surface runoff, which, in turn, erodes the road derived from two distinct processes, direct runoff surface. Similarly, precipitation falling on a road from the road surface and intercepted runoff from cut-slope which are typically steeper and less uphill slopes. First, surfaces of unpaved roads are vegetated than natural slopes will cause erosion. often compacted, which reduces infiltration capacity Roads also intersect natural flow lines and can and increases the runoff per area of road surface. capture surface run-off from upslope, increasing Second, roads typically run in parallel to hillslope the runoff and erosion on the road surface. There contours and hence interrupt downslope flow path, is often a good connection between roads and the which run perpendicular to hillslopes. As a result, channel network, because roads often run along surface runoff from upslope is intercepted by a road. the slopes and frequently intersect the channel Ideally, roads are equipped with ditches on their network (Sidle et al. 2006). upslope side. These ditches collect upslope runoff, 2. Mobilization of sediment during road construction. and route it downslope and discharge the runoff in a Roads in the Himalayas are commonly built by controlled way (e.g., via a culvert to the next stream). cutting slopes and using the cut material as fill Ditches should be protected against erosion and/ 33 Valuing Green Infrastructure: Technical Appendices or equipped with sediment traps. However, many erosion is the most relevant source of sediment from mountain roads in Asia are not equipped with such roads (Arnáez et al. 2004), pointing to a need for more ditches-;, the upslope runoff is routed over the road local studies. Parameters in equation 42 are the slope surface, where it increases erosive forces (Sidle et al., of a road segment (S) [ - ], the area (Lr) [m] and width 2006). Roads will also intercept sediment travelling (WR)[m] of a road segment and P is the annual rainfall from upslope areas and can introduce preferential in [cm/yr]. pathways of sediment connectivity. 1.2. Modeling sediment mobilization from road Herein, we focus on the effect of erosion from unpaved cuts roads, assuming that the sediment volume mobilized The second important mechanism of sediment from a road segment r can be defined as mobilization from roads is the displacement of hillslope soil and bedrock to create the road cut. Often, the VR,r=(VRS,r+VCS,r)*SDRr 41 cut material is disposed of on the downslope side of the road, a practice which is common in Nepal. The (Fu et al. 2010), where VR is the total erosion, VRS is unconsolidated sediment disposed on steep slopes is the erosion from a road surface, and VCS is the erosion then likely to become easily eroded and eventually from the cut slopes. SDR is the sediment delivery ratio transported to the stream network. The amount of between the drainage point of a road and the stream material that will be disposed of will depend on the road network. design, and specifically how much of the cut material will be used to construct the embankment (Figure 21). There are no specific studies for road-induced erosion In here, we assume that roads are constructed in full in the study area and no physically-based models benching design, i.e., that all displaced cut material is which could be applied for the case study to calculate disposed of. It should be noted that those designs with VR and VCS. Hence, the road model mentioned herein reuse of cut material for embankment construction relies on empirical models formulated for different often suffer from a failure and sediment mobilization geographies (often the Pacific North West of the from these embankments. United States, e.g., Luce and Black [1999]), which significantly increases uncertainty. However, we aim The amount of cut material can be determined to select a model that explicitly considers as many knowing the gradient of a hillslope on which a road is location-specific parameters as possible, so as to make constructed (α), the angle of the cut slope β, and the calculations specific for the study area. With the width of the road (WR). The cut area of the road prism absence of location-specific data, we use the equation is then proposed by Ramos-Scharròn et al (2007; 2005) to a calculate Ac,r = ha 44 2 VR,r=(-0.432+fg (S1.5 P))*Lr*Wr 42 (see Figure 22) for a definition sketch of triangle geometry) with Where fg is a grading factor and is set to 4.73 for freshly graded roads and to 1.88 for ungraded roads. As we ha = b sin (g) 45 have no information about the grading of roads, we sin(b) b = Wr 46 use the mean of the two values in this study. sin(g) Cut slope erosion is calculated as: sin(a) a = WR * 47 sin(g) VCS,k=0.09*VR,r43 and g = 180 – a – b 48 Indicating that sediment yield from cut slopes is These functions can be solved assuming that α is equal around one order of magnitude lower than erosion to the local terrain slope derived from the DEM, and, from the road surfaces, which is in line with findings using the road width from OSM data, and assuming a by Luce and Black (Luce and Black, 1999). It should utslope angle, β*, which can be used to calculate β via be noted that some studies indicate that cut-slope Valuing Green Infrastructure: Technical Appendices 34 Road construction practices with various degrees of reuse of cut material (dark grey) (Sidle and Figure 21:  Ochiai 2006). b = 180 – b* 49 link to actual conditions, as steeper hillslopes might consist of more competent soil and rock material and Without details on the design of each road it is hence allow for steeper cut slope angles. The resulting challenging to determine cut slope angles for all relationship between hillslope angle and cut material roads. We use of β* = 45° as default value. This value from the road prism is shown in Figure 23. is chosen based on field observations made during a field trip to the Kali Gandaki catchment (Figure 24). Calculating cut area of a full benched Figure 22:  It should be noted that these observed cut slope angles road (small panel) and the geometric exceed proposed values for mountain roads (Hearn definitions (large panel) 2011, p. 150) without additional stabilization. Also, many roads are built on hillslopes with gradients C C larger than 45°. From Figure 22, it is obvious that in these cases β* must be larger than 45°, as otherwise AC,R sides a and b of the road prism would not intersect. For a road segment r where α is larger than 40°, we define AC,R A b* = a * 1.1 50 B This condition is met for approximately 2% of all a b roads, as roads are built on slopes with as much as 60% gradient. β We can now calculate the volume of sediment β* =180-β* WR α mobilized by a road cut, assuming that the local slope A B of the terrain is equal to α. The assumptions of steeper ha cut slope angles on steeper hillslopes might even 35 Valuing Green Infrastructure: Technical Appendices  elationship between hillslope angle and Figure 23: R The volume of sediment that needs to be disposed the cut material from the road prism of after the construction of a road (VC,r [m3]) can be when applying equations 44-50 calculated as VC,r=AC,r*Lr 51 140 120 and Cut volume[m3/m of road] 100 MC,r=VC,r* ρS 52 80 With Lr being the length of a road segment and ρS 60 being the sediment density. It should also be noted that MC,r[t] does not have a time dimension. Equation 40 52 yields the sediment that needs to be disposed of 20 once, during the construction of the road. To calculate the annual contribution of the displaced material 0 to the sediment budget of a basin, we would need 0 10 20 30 40 50 60 70 to make assumptions about how many new roads Hillslope angle α[˚] are constructed per year, and how fast the sediment displaced during previous road constructions is Observed road construction practices in the Kali Gandaki catchment (pictures by D. Cutler). Cut Figure 24:  slope toe angles, β, are measured in Adobe Illustrator. All pictures show that relatively steep cut slopes (45° to 60°) are realized in soil or fractured rock, contributing to visibly high erosion (e.g., top right and bottom left panel). The top left and bottom right panels indicate how road-cut material is often only partially stabilized on the fill slope (bottom right) or disposed of in downslope channels (top left) Valuing Green Infrastructure: Technical Appendices  36 being eroded on the hillslopes. Most likely, erosion of information on surface material (Table 7, Black top). dumped cut material will be fastest in the first years For roads with black top, erosion from the road surface after the road construction. However, here we select is set to 0 in Equation 41 and only erosion from the a somewhat arbitrary time span of δ_(t,E) = 25 years, cut slope is considered, but it should be noted that after which we assume that dumped cut material has only a few road segments have information on surface either been eroded or stabilized by vegetation, and material available. Our observations from satellite assume that erosion rates are similar each year, so that imagery is that very few roads in Kali Gandaki have blacktop or concrete cover (mostly roads classified as MC,r “primary”) and even roads classified as “highway” or MC,r = 53 δt,E “secondary” mostly do not have blacktop. with MC,r in [t/yr]. Similarly, information on road width is not available from the Open Street Maps data, and we assigned 2. ROAD DATA information on road width based on the presumed Spatial data on road locations are derived from Open number of lanes and assuming that lanes are 4 m wide. Street maps. This information is crucial, as it allows Footpaths and road types used mainly by humans and us not only to locate roads, but also contains some pack animals are assigned a smaller width. It should information on road types and building material. be noted that even such small paths can produce Table 7 shows the road type information available for significant amounts of sediment (Sidle et al. 2006). the Kali Gandaki catchment. Most road segments don’t Some of these footpath segments display very steep have any information on their surface material. We slopes of 100% plus, which is not realistic; this is likely assigned information regarding the surface material, because of inaccurate mapping of the exact course and specifically if a road is black-topped or not, as a of these paths on steep hillslopes. Hence, we set the function of the road type for all road segments without maximum slope of all roads to 1 [m / m]. Road type table defining road parameters such as blacktop cover (1: blacktop, 0: no blacktop) Table - 7:  and width Road Type ID Type Count Total length [m] Blacktop Width 1 Bridleway 6 2565 0 2 2 Construction 4 630 0 2 3 Footway 316 90959 0 1 4 Living_street 5 883 0 4 5 Path 5400 2288972 0 1 6 Primary 16 34878 1 16 7 Residential 470 146279 0 4 8 Road 248 90574 0 4 9 Secondary 107 149593 0 8 10 Service 52 10251 0 4 11 Steps 25 2487 0 0.5 12 Tertiary 177 431202 0 4 13 Track 1294 770209 0 1 14 Trunk 31 66596 0 8 15 Unclassified 1404 1871361 0 4 16 Highway 10 5952 0 12 37 Valuing Green Infrastructure: Technical Appendices A brief analysis of the 7000 km of road network in Kali (highways, primary and secondary roads, trunk Gandaki reveals that small tracks and paths dominate roads) make up only a small part of the road network the road network (around 3500 km), and that the road by length; however, they are more relevant in terms of type is not specified for a large part (around 2250 km) total road area because of their larger width (Figure (Figure 25, top panel). A brief visual analysis of satellite 25, bottom panel). Small tracks and paths make up imagery of roads falling into that category reveals that less of the road area because of their small width. “unclassified” roads entail small and hardly visible Similar to the length statistics, most of the road area footpaths, as well as major roads. falls in the “unclassified” category. It should be noted that the area of “unclassified” roads is dependent on Major road types with possible blacktop cover their assumed width (4 m).  ummary statistics in terms of length and surface area of different road types present in the OSM Figure 25: S data-base for Kali Gandaki 3000 2500 Cumulative lenght [km] 2000 1500 1000 500 0 l d ck sec ath foo y ay ser y e idl k ay y y ps ing ion t ad tia ee vic r r ar wa n fie da tia tra tw ew ste tru ro str en p im ct ssi gh ter on tru sid pr cla Hi br ns re un liv co ×106 10 8 Cumulative area [m2] 6 4 2 0 l d ck sec ath foo y ay ser y e idl k ay y y ps ing ion t sid d tia ee vic r r ar wa n fie a da tia tra tw ew ste tru ro str en p im ct ssi gh ter on tru pr cla Hi br ns re un liv co Valuing Green Infrastructure: Technical Appendices 38 contributions to the sediment budget. Unclassified roads contribute the largest part (around 0.6 Mt/yr). 3. RESULTS Paths and tracks contribute a significant amount of sediment (see increase in cumulative curve in Figure 3.1. Erosion from road surfaces 26, top panel), not only because they have a relatively large cumulative area (Figure 25, bottom), but also Total erosion from road surfaces is between 0.5 and 4 because of their steep slope. Highways have the Mt/yr, as a function of the road grading factor, when highest erosion rates per segment; however, because the mean value of the grading factor is used, the result of their relatively small number (Figure 25), highways is around 1.1 Mt/yr. Analyzing road surface erosion do not contribute much to the cumulative sediment by road class shows which road types dominate road budget. Summary statistics in terms of surface erosion from members of different road classes (boxplots, top Figure 26:  panel) and the cumulative erosion over all road classes (green line, top panel). The bottom panel shows the relative erosion per road length for different road classes 39 Valuing Green Infrastructure: Technical Appendices  odelled erosion from road surfaces in Kali Gandaki. The color code indicates the sediment load Figure 27: M from road surface erosion aggregated over smaller sub-watersheds. Red points indicate the 500 road segments with the highest surface erosion Valuing Green Infrastructure: Technical Appendices 40 all located in the lower Kali Gandaki valley. It should With the absence of measurements, modelled road be noted that these 500 road segments (out of more erosion should be judged carefully, especially as the than 60,000) make up for more than 10% of the total calculation of erosion rates is based on an empirical road surface erosion. model for a different geography. However, modelled erosion rates per length of road (Figure 26, bottom) 3.2. Erosion from roads are in the range of value reported by Leibundgut et al. According to our calculations, the total removed (2016) for the earthen roads in the Phewa watershed material to build all roads in the Kali Gandaki watershed in eastern Nepal, who report values of up to 8000 accounts to 90 Mt (around 0.5 t/m of road). Assuming m3/km/yr, or 12800 t/km/yr (though these data sets that this cut sediment contributes to the sediment budget possibly include landslides as well as erosion from the over a time span of 25 years, this translates to around road surfaces). 3.5 Mt/yr (Figure 28). Large roads have the highest mobilization of cut materials (primary, secondary, and The spatial distribution of road surface erosions shows highways), because of their assumed larger width. For a clear pattern following slope and precipitation surface erosion, highways display the highest rates of gradients in the catchment. Erosion from road erosion, but do not contribute a lot to the cumulative surfaces is several orders of magnitude higher in steep sediment budget. This is different for cut material catchments in the lower Kali Gandaki, where most of mobilization, for which primary and secondary roads the precipitation occurs, and where road density is and highways make up for a significant part of the highest (Figure 27). Figure 27 also shows the 500 road cumulative mass (see “steps” in the green cumulative segments with the highest surface erosion, which are mass curve in Figure 28). Summary statistics in terms of surface erosion from members of different road classes (boxplots, top Figure 28:  panel) and the cumulative erosion over all road classes (green line, top panel). The bottom panel shows the relative erosion per road length for different road classes 41 Valuing Green Infrastructure: Technical Appendices  odelled mobilization of cut material from roads in Kali Gandaki. The color code indicates the Figure 29: M sediment load from road surface erosion aggregated over smaller sub-watersheds. Red points indicate the 500 road segments with the most mobilized cut material Valuing Green Infrastructure: Technical Appendices 42 Modelled sediment mobilization from landslides intersected by roads. All points indicate where a Figure 30:  landslide object (LSO) is intersected by a road. Colors of markers indicate in which risk category this intersections falls [following the modified categorization from (McAdoo et al. 2018)] 43 Valuing Green Infrastructure: Technical Appendices mirrors the geomorphic and meteorological drivers Cut sediment is a function of road width and the of landslides. Roads most commonly intersect local slope angle. Hence, the spatial distribution of landslides in the lower part of the Kali Gandaki cut material mobilization does not follow the spatial catchment, and along the road corridor in the Kali gradient of precipitation (Figure 29). Roads with the Gandaki Gorge. In the Mustang area, landslides major mobilization of cut material are, instead, wide are less common and the road network has a much roads constructed in steep terrain. Notably, road smaller extension, resulting in fewer intersections erosion is most emphasized along the major east-west between landslides and roads. and north-south corridors, the Pokhara-Baglung and Enlarged view of the central Kali Gandaki Figure 31:  Mid-Hill Highway (east-west) and the Beni-Jomsom Gorge, roads intersecting LSOs, and the Highway (north-south). Similar to surface erosion, risk class of the intersecting rod segments a small fraction of road segments mobilizes a major part of sediment (500 road segments with highest cut material mobilization contribute 22 % of total cut material (Figure 29, red dots 3.3. Sediment generation from possibly road related landslides In total, 2700 road segments intersect with LSOs. The possible sediment generation from these LSOs is more than 4 Mt. The distribution of risk classes amongst these road segments is nearly equal between category 1 and category 3; category 2 does not occur. This implies that landslide road intersections are either such that the road cuts above the potential failure plane and is in the topsoil, so that roots might be used to stabilize the slope (class 1), or the road cut intersects with the potential failure plane and reaches into the bedrock, which would make it hard to stabilize failure plane and bed rock – road cut intersections with plants (class 3). With regard to sediment mobilization, however, more sediment is derived from category 1 rather than from category 3 (3.1 vs. 1.2 Mt). The spatial distribution of landslides Valuing Green Infrastructure: Technical Appendices 44 4. REFERENCES Arnáez, J., Larrea, V., Ortigosa, L., 2004. Surface runoff and soil erosion on unpaved forest roads from rainfall simulation tests in northeastern Spain. CATENA 57, 1–14. https://doi.org/10.1016/j.catena.2003.09.002 Fu, B., Newham, L.T.H., Ramos-Scharrón, C.E., 2010. A review of surface erosion and sediment delivery models for unsealed roads. Environmental Modelling & Software 25, 1–14. https://doi.org/10.1016/j.envsoft.2009.07.013 Hearn, G.J., 2011. Slope Engineering for Mountain Roads. Geological Society of London. Leibundgut, G., Sudmeier-Rieux, K., Devkota, S., Jaboyedoff, M., Derron, M.-H., Penna, I., Nguyen, L., 2016. Rural earthen roads impact assessment in Phewa watershed, Western region, Nepal. Geoenviron Disasters 3, 13. https://doi.org/10.1186/s40677-016-0047-8 Luce, C.H., Black, T.A., 1999. Sediment production from forest roads in western Oregon. Water Resources Research 35, 2561–2570. https://doi.org/10.1029/1999WR900135 McAdoo, B.G., Quak, M., Gnyawali, K.R., Adhikari, B.R., Devkota, S., Rajbhandari, P.L., Sudmeier-Rieux, K., 2018. Roads and landslides in Nepal: how development affects environmental risk. Natural Hazards and Earth System Sciences 18, 3203–3210. https://doi.org/10.5194/nhess-18-3203-2018 Pelletier, J.D., Broxton, P.D., Hazenberg, P., Zeng, X., Troch, P.A., Niu, G.-Y., Williams, Z., Brunke, M.A., Gochis, D., 2016. A gridded global data set of soil, intact regolith, and sedimentary deposit thicknesses for regional and global land surface modeling. Journal of Advances in Modeling Earth Systems 8, 41–65. https:// doi.org/10.1002/2015MS000526 Ramos-Scharrón, C.E., MacDonald, L.H., 2007. Development and application of a GIS-based sediment budget model. Journal of Environmental Management 84, 157–172. https://doi.org/10.1016/j.jenvman.2006.05.019 Ramos-Scharrón, C.E., MacDonald, L.H., 2005. Measurement and prediction of sediment production from unpaved roads, St John, US Virgin Islands. Earth Surface Processes and Landforms 30, 1283–1304. https://doi. org/10.1002/esp.1201 Sidle, R.C., Ochiai, H., 2006. Landslides: processes, prediction and land use. American Geophysical Union, Washington, D.C. Sidle, R.C., Ziegler, A.D., 2012. The dilemma of mountain roads. Nature Geosci 5, 437–438. https://doi. org/10.1038/ngeo1512 Sidle, R.C., Ziegler, A.D., Negishi, J.N., Nik, A.R., Siew, R., Turkelboom, F., 2006. Erosion processes in steep terrain—Truths, myths, and uncertainties related to forest management in Southeast Asia. Forest Ecology and Management, Catchment Processes in Southeast Asia 224, 199–225. https://doi.org/10.1016/j.foreco.2005.12.019 45 Valuing Green Infrastructure: Technical Appendices APPENDIX 4: METHODS FOR VALUING IM- PACTS OF SEDIMENT ON KALI GANDAKI A 1. INTRODUCTION complicated by another market imperfection. Power production in Nepal has frequently failed to meet Interest in catchment area treatment in the Kali market demand at the prices NEA is charging at the Gandaki basin was largely spurred by concerns for the time. Figure 32 illustrates a typical situation. For effects of sediment on operations at the Kali Gandaki much of the day, NEA’s own, largely hydroelectric “A” Hydroelectric Plant (KGA). In the section below, generation assets, in combination with its purchases we consider three benefits that would accrue from from independent power producers (IPPs), were reduced sediment loading in the watershed: reduced sufficient to meet demand. Nepal imports power at costs of flushing the desanding basins; reduced costs all times, but imports are particularly important in of equipment maintenance; and preservation of meeting daily peak demand from about 5:00 pm to pondage capacity, which enhances the Plant’s ability to 11:00 pm. At such times, however, the combination of supply power during periods of peak demand. NEA generation, IPPs, and imports are insufficient to meet demand, resulting in the phenomenon illustrated We presented summary results and the basic intuitions by the dark-shaded, sharp peak in Figure 32: System underlying them in the main text. In this Appendix load curve for annual peak load day. Source: NEA we present formal analyses and details. In the section (2018): load shedding. below, we will treat each category of benefits in turn: avoided damage to equipment; avoided costs of The prospect of load shedding affects our analysis in desanding; and preservation of peaking capacity. several ways: • Scarcity determines economic value, and so values Before turning to these categories, however, we will will vary by time of day and season of year as the quickly review some overarching issues in economic availability of water for generation and of power valuation and some common themes in valuing for purchase from other sources varies sediment reductions in hydropower generation in • Because the availability of power and water for Nepal. We follow generally accepted principles of generating it vary, maintenance will be planned to economic valuation e. g., (Freeman, Herriges, and occur at times at which the opportunity costs of Kling 2014): forgone generation are lowest • During periods of load shedding, the economic • Economic values are defined in the context of value of power must be inferred in the absence incremental (in the limit, marginal) changes; when we of meaningful prices. A shortage is defined, discuss a value of sediment reduction, we tie it to a in economic terms, as a situation in which the particular quantum of sediment reduction. quantity demanded exceeds that available at the • Economic values always reflect willingness to pay; what price being charged. Under such circumstances, it might cost to do something is relevant only to the price being charged is less than consumers’ the extent that someone is actually willing to bear willingness to pay, and therefore does not reveal the cost. economic value. Researchers have estimated actual willingness to pay from prices paid to Economists rely on prices to determine willingness to purchase electricity from alternative sources – pay when they are available. However, environmental usually private diesel generation; see e. g, (R. S. economists must often work in contexts in which Shrestha 2011; J. P. Shrestha and Shrestha 2016; prices are not observed because of externalities Timilsina and Toman 2016), or from surveys of (Kolstad 2011). Part of our challenge, then, is to infer users’ willingness to pay for expanded supply (see, what the price of sediment should be. This challenge is e. g., Karki, Mishra, and Shrestha 2010). Valuing Green Infrastructure: Technical Appendices  46  ystem load curve for annual peak load day. Source: NEA (2018) Figure 32: S • Nepal is experiencing rapid growth in both (Shrestha, et al., 2018; NEA Annual Report 2018). domestic generation capacity and demand for Whether this continues to be the case will depend power, as well as in power imports from India on developments in supply and demand that (see Figure 33). Even more explosive growth cannot now be forecast with precision. will likely occur in coming decades. The growth in supply has enabled NEA to more effectively With these considerations by way of context, we turn deploy its generation resources; it has recently now to the value of sediment reduction in reducing been reported that, for the first time in recent desanding costs, avoiding damages, and preserving memory, load shedding is not occurring in Nepal reservoir capacity. Expansion in electricity provision 2009 – 2018. Source: NEA 2018 Figure 33:  Total Energy Available & Peak Demand 8,000 1,600 7,000 1,400 6,000 1,200 5,000 1,000 GWh 4,000 800 MW 3,000 600 2,000 400 1,000 200 - - 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018* FISCAL YEAR Available Energy (GWh) NEA Hydro Generation NEA Thermal Generation Power Purchase from IPPs Power Purchase from India Peak Demand (MW) 47 Valuing Green Infrastructure: Technical Appendices 2. DESANDER FLUSHING half of this power is lost while one and then the other desanding basin is flushed, the power loss would be The designers of the Kali Gandaki “A” Plant were well 648 MWh. aware that sediment control would be a challenge, and planned the facility accordingly (ADB, 2004). Several Assigning a price to power is difficult, even during subsequent modifications to the plant have also been the off-peak hours when NEA has generally been devoted to better handling of sediment. able to meet demand. NEA’s tariff schedule lists literally hundreds of different rates depending on Sand that passes through the generating equipment class of customer (domestic, industrial, municipal, causes damage by abrading turbines, valves, vanes, and etc.), amount of consumption, current, voltage of other parts (see, e. g., NEA 2018 for a comprehensive transmission, time of day, and season of year. Moreover, list of repairs performed during a major overhaul).2 customers are generally charged a two- or more part To reduce the volume of sand passing through the tariff: a service or demand charge for connection, plus generating equipment, the Kali Gandaki plant is an energy charge per kWh consumed. Finally, there equipped with twin desanding basins. Each basin is a block-rate structure under which prices increase measures 14 meters in depth, 40 in width, and 187 with level of consumption. in length (Bishwakarma 2012). With the twin-basin design, it is possible to run the plant at half-power If determining a price per marginal kWh of power while one basin is being flushed. It takes between four produced is difficult, an alternative might be to estimate and five hours to flush each basin; as the basins only the cost to NEA of acquiring marginal power. NEA collect sediment when water flow (and hence, sediment imports power from India, and purchases power from load) in the river is high, this means that even when independent power producers. A figure of about NPR one basin is flushed, there is still sufficient flow in the 6 per kWh (US$ 0.054) might be a reasonable estimate other to operate the plant at half- power. of cost of supply from such sources. This is the average (across voltage transmission categories) rate agreed for Sediment suspended and transported in the river purchases from India’s Central Electricity Authority. varies dramatically and non-linearly with the volume NEA recently agreed to purchase solar power at a rate of flow (see Figure 34). Sediment accumulation and of 6.60 NPR per kWh, it has set a long-run average damage is a negligible concern during the dry season. price of 5.30 NPR per kWh for power purchase from However, when flow is high, active steps for sediment the new Upper Tamakoshi Plant and has paid about management are required to be carried out. . NEA 5.50 NPR per kWh for power purchases from PTC estimates that, under current conditions, the basins India, Ltd. (NEA 2018). are flushed about 22 times per season. The two basins are emptied sequentially each time they are flushed. However, NEA has paid a higher average price, 7.12 The general rule of thumb is to flush a basin when NPR (US$ 0.063) per kWh of electricity purchased, on sediment has accumulated to a depth of three meters. an annual basis (NEA 2018). However, NEA reports The accumulation is not so rapid, however, that it do not break down payments for purchased power by cannot be deferred until an off-peak period. season or time of day. As Figure 32 shows, however, reliance on imports increases markedly during periods We suppose, then, that each flush takes nine hours, and of peak demand. Thus, it might be reasonable to infer that it occurs during off-peak hours at times when the that power purchases are more expensive during plant would otherwise operate at full capacity. While peak hours. there may be some other costs involved in flushing the desanding basins, they appear to be de minimis, and we Returning to the NEA’s tariff schedule, there is will ignore them. Plant capacity is 144 MW, and so 9 variation between peak and off-peak prices, at least hours ∙ 144 MW = 1,296 MWh of power would be for larger customers. Time-of-day pricing is only generated with the plant operating at full capacity. If instituted for industrial and other large consumers A variety of sediments are transported in the Kali Gandaki. Landslides and major floods can mobilize boulders which, while they may 2. reduce reservoir capacity, are too heavy to be borne through the generating equipment. At the other extreme, very fine particles are easily transported, but they lack the mass to do severe damage. It is the sand-sized particles that are small enough to be suspended but large enough to damage equipment that are most problematic. Valuing Green Infrastructure: Technical Appendices 48 served by high-voltage lines. For such consumers, during which desander flushing occurs, 4.15 and 5.25 however, there is typically a one to three Rupee NPR/kWh “off peak” and 7.50 and 8.40 NPR/kWh per kWh difference between prices charged during “normal” for industrial customers with the highest (66 “peak” (5:00 pm to 11:00 pm) and “normal” times kV) and second-highest (33 kV) voltage service. Taking during the dry months between roughly November averages of these figures, assuming that six of the nine and April. Between roughly May and October, when hours required for desander flushing occur off-peak water is more plentiful, an additional “off peak” and the remaining three in the normal period, gives a period between 11:00 pm and 5:00 am is added, when, figure of 5.8 NPR (US$ 0.052)/kWh. prices are roughly half their peak value, a difference of about four to six Rupees per kWh, depending on All of the above considerations, in combination with service class. an appreciation of the imprecisions inherent in the assignation of such a figure, lead us to adopt an Finally, while it is difficult to say what combination estimate of 6 NPR (US$ 0.054) per kWh of power of meeting societal objectives and cost recovery any generation forgone for desander flushing. particular power price is intended to achieve, it seems reasonable to suppose that the marginal price charged Priced at 6 Rupees per kWh of off-peak power lost, the to the largest industrial customers might be most total opportunity cost of a single flushing event would representative of the value attached to power on the be 3.89 million Rupees (US$ 34,730).3 margin. These rates are, during the high-flow months Suspended sand concentration in the Kali Gandaki. Source: Morris (2014) Figure 34:  While desander flushing is a discrete event, we are assuming that the accumulation of sediment is sufficient to generate the need for at 3. least slightly more frequent flushes. 49 Valuing Green Infrastructure: Technical Appendices Expressing these figures in NPR per cubic meter of 3. DAMAGE TO EQUIPMENT sediment deposited, the volume of the desanding basins is 3 m deep ∙ 2 ∙40 m wide ∙187 m long = 44,880 The purpose of the desanding basins is to prevent m3. Dividing NPR 3.89 million by 44,880 m3 we have sand from passing through the generating equipment, about NPR 86.7 (US$ 0.77) per cubic meter of material where it damages the turbines, vanes, valves, and deposited in the desanding basins. This would be cost other parts. The desanding basins do not remove all savings per season. At a discount rate of 10%, the net sediments, however; some 1.7 million tons, of which present value of a one cubic meter reduction in the some 700,000 tons are sand, pass through the turbines amount of sand that settles in the basins every year every year (Morris, 2014). Damage is seasonal. would come to about NPR 867 (US$ 7.74) m-3. Sediment transport varies greatly with flow. During the dry season, it is virtually nil. Sand transport then It would be important to bear in mind that this figure spikes with the Monsoon. Morris finds that sand is the value of a one cubic meter reduction in the concentration varies as the fourth power of river flow volume of sand deposited in, and subsequently flushed (Morris 2014; see also, Chhetry and Rana 2015a). from, the desanding basins. To apply this figure in the Virtually the entire year’s load is delivered over a few valuation of a cubic meter of erosion prevention at any months in the summer, as illustrated in Figure 35. point in the watershed, we would have to multiply the Note that the vertical scale is logarithmic; the intervals figure we have just derived, 867 (US$ 7.74) NPR m-3, between dashed horizontal lines denote multiples by the fraction of sediment originating at that location of ten. that is deposited in the desanding basins. Sand concentration by month. Source: Morris (2014) Figure 35:  Valuing Green Infrastructure: Technical Appendices  50 Sand causes damage which may result in reduced Rana 2015b). While it seems intuitively obvious that operating efficiency of the generating equipment damaged equipment will be less efficient, the data do while it is in use, the need to conduct more frequent not reveal an obvious pattern to this efficiency loss. We repairs, and, possibly, its failure in use, which would have evaluated the data depicted in Figure 36 to see if lead to a need for immediate repairs. Unexpected a unit produced less power than did the other two in breakdowns might prove to be particularly costly the months before its overhaul (when presumably, it if they necessitated repairs during periods of peak would have been in service longer, and so its efficiency demand; repairs are generally scheduled for the dry would be reduced relative to the other two), or if a unit season when water flow in the river is not sufficient to produced more power than did the other two in the support continuous generation at full capacity (NEA months after its overhaul (when presumably, the other 2015; Chhetry and Rana 2014). two would have been in service longer, and so their efficiency would be reduced relative to the one that Figure 36 gives an indication of maintenance had just been overhauled). However, we have not been practices at the Kali Gandaki “A” Plant. It shows daily able to find any consistent pattern documenting such generation for a six-and-a-half-year period from the phenomena. Moreover, it does not seem reasonable to summer of 2011 through the end of calendar year ascribe all damage to sediment. Normal wear and tear 2017. Generation totals are color-coded by the unit may account for some of the need for maintenance. producing the power. Generally speaking, when water flow is high, all three generating units are operated Given these many uncertainties, our efforts to estimate simultaneously. When flow is low, one of the units is the benefits that would result from a reduction in often taken out of service. sediment delivery are necessarily speculative and have relied on indirect approaches. We have developed two Unit 1 was taken out of service for extended periods in methods for conducting this estimation. In the first, 2012, 2014, and 2017; Unit 2 in 2013 and 2016; Unit we took as a datum the observation that maintenance 3 in 2015. Generally, each unit is overhauled every was scheduled every third year. We then asked “Given third year, on a staggered basis. While major overhauls such information as is available on the financial and are generally recorded in NEA’s Annual Reports, opportunity costs of performing this maintenance, Figure 36 shows that each unit was also occasionally how much effect must abrasion have on the efficiency withdrawn from service for shorter periods.4 In the and reliability of the generating units so as to motivate absence of more detailed maintenance records, it the observed every-third-year overhaul pattern?” is difficult to infer what motivated these temporary Several factors made this calculation very imprecise: suspensions – if they were to perform necessary • We had no data on the relationship between repairs, or simply because the unit was not needed at sediment delivery, equipment damage, and a particular time. It is worth noting, though, that save efficiency loss, for an anomalous episode in the summer of 2016, all • NEA data on Kali Gandaki maintenance three units were almost always used simultaneously expenditures were not broken down by particular during the summer and fall months when water flow, procedures, and did not record opportunity costs and hence, generation potential, was greatest. of units being withdrawn from service, • Calibration of the model required identifying a It is difficult to characterize the effects of rate of efficiency loss such that maintenance would sediment damage on operating efficiency. Physical be performed in every third, rather than every measurements reveal that parts are eroded while they second, or every fourth, year. This admitted a are in service, with consequences that must surely wide range of possible rates of damage that would compromise performance and reliability (Chhetry and be consistent with the data. There were also short intervals during 2013 and 2016 during which generation was completely suspended. 4. 51 Valuing Green Infrastructure: Technical Appendices  aily power generation at the Kali Gandaki “A” Plant, July 2011 - January 2018. Source: data Figure 36: D provided by NEA Given these concerns, we developed a second method We do not have a reliable direct way to measure the and, in the interest of space, we will focus on it here. damage that sediment causes to equipment, but we While the mathematical details underlying the do have a relatively good way to measure the costs of approach are somewhat tedious, the basic economic flushing, as we demonstrated in the previous section. idea is simple. It is that the plant operator faces a What we are about to show is that if the operator tradeoff in operating the desanding basins. We noted trades off flushing costs against equipment damage above that the basins are flushed about 22 times to minimize their sum, we can use the marginal cost every year. This rate of flushing is determined by a of flushing sediment to estimate the marginal damage sort of rule-of-thumb: the basins are flushed when sediment causes. By the “equimarginal principle” the sediment accumulated in them reaches a depth of economic optimization, the operator will equate of three meters. The basins themselves, however, the cost of disposing of the marginal cubic meter of are much deeper than this. More sediment could be sediment via the desanding basins to the marginal allowed to accumulate between flushes. Alternatively, damage expected to arise from not disposing of it, the basins could be flushed more frequently. There and instead letting it pass through the generating would be some cost savings from allowing more equipment. sediment to accumulate between flushes; the plant would have to reduce to half power less frequently. The formal analysis proceeds as follows. Suppose the But the more sediment accumulates in the basins, total volume of sand that is borne in water diverted the less effective they are in removing sediment; for generation during year t is St. A fraction f(V) of this balanced against these cost savings from reduced sand will be settled out in the desanding basins. This flushing would be increased damages from more fraction depends on V, which we define as the volume sediment going through the turbines. Conversely, of accumulation reached before the basins are flushed. more frequent flushing would spare the turbines V is a variable under the control of the operator; the from damage, but increase the time during which operator decides the rule-ofthumb to follow in basin generation of power is curtailed. Valuing Green Infrastructure: Technical Appendices  52 flushing. We will suppose that ∂f ⁄ ∂V<0; if the operator  (A4.4) allows more sand to accumulate before flushing, the residence time of water in the basins will be shortened, where ε is defined at the logarithmic derivative of and less sand will settle in them. trapping efficiency with respect to the flushing rule When the operator adopts a practice of flushing the basins when the volume of sediment accumulated has reached V, she will flush the basins Expression (A4.4) encapsulates the “equimarginal condition” we are exploiting to estimate equipment Nt=f(V) St ⁄V damage. We do not know the marginal damage caused by sediment passing through the turbines, ∂D ⁄ ( ∂StG ), times per year. If each flush cost c, the total cost of but if we can estimate ε, we can relate it to a quantity flushing per year would then be we do know, the cost per desander flush, c ⁄ V. C(V,St )=c∙( f(V) St ) ⁄ V So using (A4.4) in (A4.3) Sand that is not detained in the desanding basins  (A4.5) and flushed away causes damage to the generating equipment. A fraction 1-f(V) of the total volume of To evaluate ε, we will suppose that the fraction of sand in water diverted for generation passes through sand that settles in the desanding basins depends on the turbines. Let the monetary value of damage done the residence time of sand-laden water in the basins. by this sand be D(V,St )=D([1-f(V)] St ). The dam operator Suppose the fraction remaining suspended in the should, then, adopt a flushing rule to minimize water in the desanding basins after water has been in the basins for a time τ will be C(V,St )+D(V,St )=c∙(f(V) St ) ⁄ V+D([1-f(V)] St ) (A4.1) A couple of clarifications may be helpful here. First, by “adopting a flushing rule,” we mean setting a level Suppose water is entering the desanding basins at a of V such that, when the volume of sand deposited in flow rate of r cubic meters per second. We will treat the basins reaches V, they will be flushed. Second, c is the two desanding basins as if they were a rectangular assumed to be a constant that is multiplied by f(V) St ⁄ V, prism of width W, length L, and height H. We will while D is assumed to be a function of [1-f(V)] St.] suppose also that sediment settles uniformly along the length of the basins and designate by h the depth Differentiating the sum in (A4.1) with respect to V and of sediment in the basin. This depth increases with setting the result to zero to find the flushing rule that deposition, of course. Note that width and length are would minimize the sum of costs and damages, fixed by the dimensions of the basin, and so only the depth of the sediment deposited in the basins can V(∂f/∂V) – f ∂D ∂f cSt – S = 0, (A4.2) vary. If length is measured in the direction of water V2 ∂StG ∂V t flow, then the rate at which water traverses the basins Where the amount of sand that is will be dL=r/W(H-h), where units are now meters not trapped in the desanding basins and, hence, that per second. Thus, the residence time of water in the passes through the turbines. desanding basins will be Now to find the value of a reduction in sand in the – water diverted for generation, differentiate the sum t = L/dL = (V – V)/r of costs and damages, (A4.1) with respect to St, finding Where the maximum volume of water that ∂(C + D) c ∂D could be held in the desanding basins when they are = (1– f) f+ (A4.3) empty, and V=WLh, the volume occupied by sand at ∂St V ∂StG the time the basins are flushed. Thus, the fraction that Simplifying and rearranging the optimization goes through the turbines will be condition for the flushing criterion, (A4.2) 53 Valuing Green Infrastructure: Technical Appendices translate into a net present value for a one cubic meter reduction in sediment delivery per year in perpetuity of almost 2000 NPR, or US$ 17.84. and the fraction settling in the desanding basins will be Let us make two final comments on this analysis: • This figure of 2000 NPR or US$ 17.84 per cubic meter is the sum of the value of avoided desander operating cost and avoided equipment damage. Differentiating with respect to V, The figure of 867 NPR or US$ 7.41 per cubic meter for avoided desander cost is already included in this sum; it should not be added to it. • This figure is an estimate of the value of a cubic Thus meter of sediment in water diverted for power generation. While it applies to sediment that either is retained by, and flushed from, the desanding basins, or passes through the generating We can write equipment, it applies only to the roughly 15% of the annual sediment load (as estimated by (IHA) in water diverted for generation. To use this figure for estimating the value of sediment reduced at the or source of the reduction, one would need to know what fraction of such sediment would eventually be found in water diverted for generation. Thus, we have 4. PEAKING CAPACITY One of the most obvious reasons for concern over sediment transport in rivers used for hydroelectric Substituting in (A4.5), generation is that sediment fills reservoirs. The more sediment accumulates in a reservoir, the lower is its  (A4.6) storage volume. For several months of the year, storage capacity does Above, we have estimated the cost per cubic meter not matter. Flow in the Kali Gandaki varies from of sediment flushed, c ⁄ V, as 86.7 NPR/m3. An more than 1,000 cubic meters per second during International Hydropower Association study reports the Monsoon to as little as 50 during the winter that of the 15% of sediment that is suspended in water (Figure 37). diverted for generation at the Kali Gandaki Plant, 11% is removed by the desanding basins (IHA, n.d.), The turbines in the plant are designed to operate at a and so 4% is passed through the turbines. Thus, we maximum flow rate of 47 m3 ∙ s-1 through each of the suppose trapping efficiency, f, is 11/15 = 73%, and so three units, or 141 m3 ∙ s-1. When flow in the river is -f ⁄ ln( 1-f ) =0.56. While the depth of the desanding greater than this rate, some water is released over the basins is 14 meters, the partition between them only rises spillway. When flow is lower, the plant may either be to 11 meters. The basins are flushed when sand reaches run at less-than-full capacity, or water may be stored, a depth of 3 meters. Since the width and length of the and, consequently, less electricity generated, during basins are invariant with respect to sand deposition, parts of the day when demand is lower so that more So may be provided during the peak demand period of the evening hours. We are interested in assigning an economic value to or $1.78/m3. At a discount rate of 10%, this would storage in the reservoir. The Kali Gandaki plant was Valuing Green Infrastructure: Technical Appendices  54 Power generation and river flow at the Kali Gandaki “A” Plant 2011 - 2013. Source: Chhetry and Figure 37:  Rana 2015 120000 1400 100000 1200 1000 80000 800 60000 600 40000 400 20000 200 0 0 Jan. 2011 July 2011 Jan. 2012 July 2012 Jan. 2013 July 2013 Power generation in MWh per month (left axis) Average river flow in cubic meters per second (right axis) Flow required to support full generation potential (141 cubic meters per second) designed with pondage capacity of a little more than 3 million cubic meters. This is sometimes characterized (A4.7) as a six-hour peaking capacity, as a flow rate of 141 m3 ∙ s-1 is equivalent to 507,600 m3 ∙ h-1. As there is This objective is to be maximized over repeating 24- generally some inflow, however, the actual period of hour daily cycles. If Sθ is the amount of water stored in peak operation could extend longer. Over the course the reservoir at time θ and we can assume the flow of of its operation, however, the capacity of the reservoir water in the river is approximately constant at rate f at has declined as sediment has accumulated in it. In the any time of day,5 then remainder of this appendix, we develop an estimate of the economic value of reservoir capacity.  (A4.8) We begin by supposing that the plant operator A dot over a variable indicates its total derivative allocates water so as to provide consumers with benefits with respect to time. Expression (A4.8) just says the we will denote as v(xθ,θ). These benefits are realized change in reservoir volume at any point in time is the at a particular instant in time indexed by θ. They difference between inflow and discharge at that time. depend on the amount of electricity generated, which is proportional to the volume of water the operator There is, of course, also a limit as to how much can discharges, xθ. The value of electricity also depends on be stored in the reservoir. It cannot be drained below the time of day, θ. We suppose the operator’s objective some zero point, nor filled in excess of its capacity, is to maximize the sum (in the limit, the integral) of which we will denote as K, benefits over the course of a 24-hour daily cycle: Precipitation during a day might affect flow, but such variations may not be large and, of course, the “dry season” is characterized by a 5. general dearth of rain. Evaporation may be accommodated as a reduction in inflows. 55 Valuing Green Infrastructure: Technical Appendices 0≤S≤K (A4.9) objective, V(K), increase with an incremental increase in K? Differentiating V(K) we find: The limits in (A4.9) then imply that xθ=f if Sθ=0 or Sθ=K; (A4.10) if the reservoir were completely full, or if it were completely empty over any interval of time, the The second equality comes from the maximization discharge rate would have to be the same as the inflow conditions that ∂v ⁄ ∂x=λ and λ is constant; the third rate over that interval. equality comes about because over a 24-hour repeating cycle, the total amount of water discharged must equal Finally, as the plant is operated on a 24-hour cycle, the total flow available; and the final equality results suppose that S0=S24: at the end of a 24- hour period because river flow is independent of reservoir capacity. there must be as much water in the reservoir as there was at the beginning, so the cycle can be repeated While expression (A4.13) is, in a sense, trivial, it is again. worth underscoring that the mathematical argument substantiates the fundamental economic proposition. Consider now the solution to the problem just The value of an asset depends on how scarce it is. If the described. It is instructive first to consider the case in reservoir were never fully filled and drained in a 24- which the constraints in (A4.10) do not bind, and hence hour cycle – that is, if, as assumed in deriving (A4.7), that the operator’s choice of discharge rate is never the constraints in (A4.3) and their implication in (A4.4) constrained to equal river flow. This would mean the never arose – then there would be no economic loss reservoir was never completely filled nor completely associated with lost capacity. emptied. To solve this problem, introduce a costate variable, λ, to append (A4.8) to the integrand of (A4.7) Expression (A4.13) does not say that discharges never (in the language of optimal control theory, forming vary over the daily cycle, nor does it say that there is the Hamiltonian). A solution must satisfy no value in having the ability to store water at some point so as to be able to discharge more at another. If  (A4.11) demand varies over the course of the day, discharges would certainly vary so as to better serve demand. and Expression (A4.13) says, rather, that if discharges do  (A4.12) not vary by enough to invoke capacity constraints, then capacity (again, as distinguished from the ability Heuristically, the economic interpretation of the to vary discharges) will have no marginal value. costate variable, λ, is as the implied price of the state variable, which is, in this case, the volume of water held This begs the question of the conditions under which in the reservoir, S. Equation (A4.6) says that the value the capacity constraint binds. At the Kali Gandaki “A” of another liter of water in the reservoir is just the Plant, the maximum flow of water each generating marginal value of the power that could be generated turbine is designed to handle is 47 cubic meters per by releasing that liter. Equation (A4.6) says that, second, so the overall limit for all three of its turbines because the liter of water could be released at any time operating simultaneously would be 141 meters m3 ∙ of day, the operator should allocate water in storage s-1. Designate the maximum rate of discharge at which so as to keep its marginal value the same during every power can be generated as . When the rate of flow in minute of the day. If it were not, the operator should the river, f, exceeds there is obviously no need for allocate more discharges when they are more valuable storage capacity. When flow is less than the need for and fewer when they are less valuable. storage capacity depends on the difference between actual flow, f, and the maximum that can be used, . Denote by V(K) the value of the objective function, (A4.7), when the optimal sequence of discharges, {xθ}, This can be illustrated by considering an extreme is chosen. We are interested in the marginal value example. Recall from expression (A4.13) above of capacity, K; by how much does the value of the that the marginal value of capacity would be zero if Valuing Green Infrastructure: Technical Appendices  56 the reservoir were never fully filled and emptied The maximum designed flow at the Kali Gandaki within the same 24-hour operating cycle. It may be Plant is 141 m3 ∙ s-1, or 507,600 m3 ∙ h-1. Minimum instructive to ask, then, under what conditions of environmental flow is 4 m3 ∙ s-1, or 14,400 m3 ∙ s-1. So actual and maximum flow it would be physically possible to fully fill and drain the reservoir in the same 24-hour K≤6∙(507,600-14,400)=2,959,200 m3. cycle. It cannot be economically optimal to do what is physically impossible.6 Reservoir capacity would have to be less than about 3 million cubic meters to be binding under any circumstances. Recall that K is the capacity of the reservoir. Let us The rate of flow that minimizes the refill cycle length introduce one additional quantity: define x0 as the is about 72.5 m3 ∙ s-1. The minimum average flow in minimum allowable flow. At the Kali Gandaki Plant, the Kali Gandaki River at the dam site is about 55 m3 a minimum flow of 4 m3 ∙ s-1 should be maintained to ∙ s-1. At this flow, capacity would have to be less than sustain aquatic life in the river. If we take it as given about 2.77 million cubic meters to be binding. that the plant operates on a 24-hour peaking cycle, a necessary condition for reservoir capacity to bind While the original live storage capacity of the would be that reservoir was more than 3 million cubic meters, that capacity declined over time as sediment accumulated.  (A4.14) Interviews with NEA personnel indicated that capacity might have fallen below 2 million cubic meters in some The quickest possible option for filling the reservoir recent years. It seems, then, that capacity may have is to let water accumulate at the rate of f-x0, releasing declined enough to be scarce. only the minimum amount required, x0, while the reservoir is filling. This would take K ⁄ (f-x0) hours to However, this is not to say that that capacity was always accomplish. Then, when it is full, the quickest way to used. The dry season in Nepal typically runs from the empty the reservoir would be to discharge water at rate winter through early spring. When generating power, . As more water is flowing in all the time, though, the the level of water in the reservoir can be drawn down net rate of discharge would be -f. It would, then, take as low at 518 meters. Yet, this level was never reached K ⁄ ( -f) hours to empty at this rate. Note that discharging during many periods of generation (Figure 38). In fact, at a gross rate faster than is ruled out on the argument during some entire seasons (as shown by the yellow that there would be no point in discharging water that arrows in Figure 38), the level of water in the reservoir could later be used for generation. was never drawn below 520 meters. There was excess capacity. In earlier years Nepal was highly dependent The shortest possible duration for an empty-to-full-to- on the Kali Gandaki “A” plant for baseload electrical empty cycle results when the denominator of the generation. While the demand for power during peak middle expression in (A4.14), (f-x0 )( -f) is maximized. periods was high, deferring generation in off-peak Differentiating this expression and setting the result periods to provide peak power was not an option. to zero to find a maximum, In more recent years, however, increased availability of baseload power from other sources (particularly power purchases from India) have increased operating flexibility at the Kali Gandaki Plant. As a result, NEA’s Substituting into (A4.14), if reservoir capacity 2016/17 Annual Report indicates that in that fiscal year, comprises a binding constraint, we would need to have the Kali Gandaki and Nepal’s other hydroelectric plants were “operated in their full capacity during K≤6( -x0 ) (A4.15) peak time in dry season using their pondage capacity [for the] first time in the plants’ history”. While reservoir We might note in passing that if the marginal willingness to pay for power is determined by factors exogenous to the operation of the 6. plant, such as the cost of supply from alternative sources, a so-called “bang-bang” operating rule could be optimal. The reservoir should first be filled as rapidly as possible, then emptied as rapidly as possible, as we describe here. 57 Valuing Green Infrastructure: Technical Appendices  ourly reservoir water level, 2003 – 13. Figure 38: H Source: Morris (2014). capacity may not have been fully employed in the past, • Between θ3 and 24 hours, the operator is again it is likely to be so going forward. constrained to discharge as much water as flows in, as she cannot maintain less than zero volume Let us return to the constrained optimization problem in the reservoir: xθ=f for θ3≤θ< 24. defined by (A4.7) – (A4.10), and suppose now that • At time 24 the cycle begins again, with discharges each constraint in (A4.10) binds at some point in the held to less than flow to begin to refill the reservoir.7 day. That is, at some point the reservoir is empty, and at some later point, it is full. Over any interval during These assumptions lead to a multipart elaboration of which the reservoir is either full or empty, the rate of the objective, (A4.7): discharge is necessarily constrained to be equal to the rate of flow in the river, f. Suppose for simplicity, but not unrealistically, that  (A4.16) daily demand is a single-peaked function. Assume, then, that the operator adopts the following pattern: Now note that the intervals [0,θ1) and [θ2, θ3) are “free” • Starting at time 0, when the reservoir is empty, until in the sense that the operator can choose x’s on these some later time θ1, when it is full, she discharges intervals without being constrained by the capacity of less water than flows in: xθf for θ2≤θ< θ3.  (A4.18) The amount of power that can be generated by a cubic meter of water varies linearly with hydraulic head: the vertical distance between 7. the surface of the reservoir and the turbines below. There is, then, the possibility that what we have described as the fourth part of cycle might be dispensed with, in order to more rapidly build up head so that more power can be generated more quickly. As variation in head tends to be relatively small – on the order of 5 meters in roughly 110 – we abstract from this consideration. Valuing Green Infrastructure: Technical Appendices  58 on the interval [0,θ1), while  (A4.19)  (A4.23) and  (A4.20) Differentiating (A4.23) with respect to K, and rearranging on the interval [θ2, θ3). Equations (A4.17) – (A4.20) describe a sort of  (A4.24) “complementary slackness” condition; when the operator is free to choose the flow rate, xθ, the corresponding marginal value of capacity, λθ remains Using (A4.24) in (A4.22), constant. Heuristically, the operator should allocate flow so that there are no “arbitrage opportunities” to increase overall value on the time interval over which  (A2.25) choice is unconstrained. Conversely, constraints on flow would arise when the marginal value of capacity is rising (or falling) and it is impossible to generate A similar set of machinations, invoking the implicit any more (or less) power, given the limits of reservoir definition of θ2 and θ3 by capacity. As in the case in which the reservoir capacity constraint did not bind, we find the marginal value of capacity by differentiating (A4.16) with respect to K. Doing so, gives  (A4.26)  (A4.21) Using (A4.26) and (A4.25) in (A4.21) Note that we are condensing notation, avoiding subscripting subscripts by writing xi for xθi . Consider the two integrals on the right-hand side of the equal sign in (A4.21) first. The choice of x is only free when the reservoir is neither full nor empty. From (A4.17) – (A4.20), optimization over intervals in which the choice of discharge is not constrained implies that the marginal value of discharges is constant over such intervals. So This expression can be greatly condensed, as each of the quantities in square brackets must be zero. The  (A4.22) reason for this conclusion can be found in texts on dynamic optimization (see, e.g., Kamien and Schwartz 1981), but the heuristic argument is straightforward. Time θ1 is defined implicitly as the duration required Each of the terms in square brackets compares the to fill the reservoir, starting from time zero. So, by instantaneous value of discharging a cubic meter definition, of water immediately before and immediately after 59 Valuing Green Infrastructure: Technical Appendices the capacity constraint starts to bind. Consider, be valued at 6 NPR (US$ 0.054) per kWh. This was for example, the quantity in the first set of square based on both prices charged to large industrial users brackets. Its first term, v(x1, θ1 ), is the instantaneous and the cost of power purchase from India and IPPs. contribution to the operator’s objective at time θ1. During the dry season, prices to large industrial users The second term, λ1∙( f-x1 ), is the implicit value of during the “normal” hours outside the 5:00 – 11:00 the additional water stored in the reservoir at the pm peak period climb to about 8 NPR (US$ 0.071) last moment before it reaches full capacity. Balanced per kWH (7.5 NPR per kWh to those supplied at the against the sum of these two terms is the third, v(f,θ1 ), highest voltages, 8.4 NPR per kWh to those at the the value realized at time θ1 when discharges are next-highest). The cost of purchases from India and constrained to the flow rate, f, by having reached full. IPPs appear to remain at approximately 6 NPR (US$ Since the operator has the ability to choose a strategy 0.054) per kWh during the dry season. yielding a different “switch time,” θ1, if she has chosen that switch time optimally, a small variation in it should Again, however, it is the difference between the peak not yield a higher overall value.8 price and that at the time of alternative generation is forgone that determines the value of capacity. While Thus, the entire expression reduces to simply tariff schedules indicate peak prices on the order of 10 NPR (US$ 0.089) per kWh for large industrial users,  (A4.27) it may be too optimistic to assume that demand will consistently be met at these prices. Hence, we will While the mathematics underlying the derivation suppose that the marginal willingness to pay for power of (A4.27) may have been tedious, the intuition may be expected to differ by 6 NPR (US$ 0.054) per underlying the result is straightforward. If reservoir kWh between peak demand and other times. capacity constrains the operator’s choices, it is not because it forces her to produce less power over the We need to do a few more calculations to assign a course of a day than she would have liked to. Her net present value to the marginal meter of additional ability to generate power is constrained, but the capacity. Let r denote the amount of power that can be source of the constraint is the flow of the river, not generated by discharging a cubic meter of water. The the capacity of the reservoir. What the capacity of rated capacity of the Kali Gandaki plant is 144 MW the reservoir constrains is the operator’s choice of at a flow rate of 141 m3 ∙ s-1 = 507,600 m3 ∙ h-1. The when she can produce the power the river’s flow rate plant would then produce 144,000/507,600 = 0.284 allows. A marginal cubic meter of storage means that kWh per cubic meter of water discharged. Thus, the the operator can produce the corresponding amount value of the marginal cubic meter of capacity is 6 NPR of additional power when its value is high (λ3 ), but per kWh ∙ 0.284 kwh per cubic meter = 1.70 NPR by choosing to produce more power when it is most (US$ 0.015) per cubic meter for each day during valuable, she necessarily forgoes the option of using which that cubic meter of capacity is needed to serve that cubic meter of water to produce the same amount peak demand. of power when its value is lower (λ1 ). Next, let D represent the number of days in the dry Putting values to expression (A4.27) is difficult, as it season, when reservoir capacity constrains operations. is hard to predict how long the current conditions Capacity is only valuable when water flow in the under which supply may generally meet demand river is below that which is required to maintain full at posted prices will continue. We adopted above a generation. We will suppose this is the case for six figure of 6 NPR per kWh for the off-peak price of months, or 180 days, of the year. power. During the dry season, however, NEA only distinguishes between “normal” and “peak” power, Finally, a cubic meter of sediment that is not deposited eliminating the deeply discounted “off-peak” category. in the reservoir this year should not constrain capacity In the discussion of opportunity costs of forgone in any subsequent year. Hence, although we are only generation, we supposed that off-peak power might now analyzing the benefit of a one-time reduction Note also that the terms in square brackets in (A2.25) also provide formulae that could be used in conjunction with (A2.14) – (A2.17), 8. (A2.18), and (A2.20) to calculate the optimal allocation of discharges. Valuing Green Infrastructure: Technical Appendices  60 in sediment deposition to the reservoir, we should This figure is the value of reducing one cubic meter calculate the net present value of the flexibility the of sediment deposition at present, as the storage space it extra storage capacity affords all future operations. occupies would also be lost in all subsequent years. If To do this, we divide the seasonal benefit of capacity that cubic meter of storage space were lost and another by the discount rate, δ, which we will take to be 10% cubic meter were deposited next year, however, per annum. another cubic meter of storage lost would also not be available in all subsequent years, beginning next year. The calculations may be summarized by writing that Thus, in order to calculate the net present value of a the marginal value of reservoir capacity is one-cubic meter reduction in storage loss in each and every subsequent year, we would need to take the net present value of each year’s storage loss’s net present value. This would mean dividing the figure above a second time Using our figures above of D = 180 days, δ = 10%, by the discount rate of 10%, resulting in a value of r = 0.284 kWh/m3, and λP - λ0 US$ 273.60 for a reduction in sediment deposition of = 6 NPR (US$ 0.054) per kWh, this marginal value one cubic meter every year in perpetuity. would be 3064 NPR, or US$ 27.36. 5. REFERENCES (NatCap) The Natural Capital Project. 2013. “Sediment and Nutrient Model Parameter Database.” Stanford, CA. http://www.naturalcapitalproject.org/invest/. Bank, Asian Development. 2004. “PROJECT COMPLETION REPORT ON THE KALI GANDAKI ‘A’ HYDROELECTRIC PROJECT.” Bishwakarma, Meg B. 2012. “Performance Improvement of Headworks: A Case of Kalignadaki A Hydropweor Project through Physical Hydraulic Modelling.” Cardinael, Rémi, Viviane Umulisa, Anass Toudert, Alain Olivier, Louis Bockel, and Martial Bernoux. 2018. “Revisiting IPCC Tier 1 Coefficients for Soil Organic and Biomass Carbon Storage in Agroforestry Systems.” Environmental Research Letters 13 (12): 124020. https://doi.org/10.1088/1748-9326/aaeb5f. Chhetry, Balendra, and Kumar Rana. 2015a. “Effect of Sand Erosion on Turbine Components: A Case Study of Kali Gandaki ‘A’ Hydroelectric Project (144 MW), Nepal.” Hydro Nepal: Journal of Water, Energy and Environment 17: 24–33. https://doi.org/10.3126/hn.v17i0.13270. ———. 2015b. “Effect of Sand Erosion on Turbine Components: A Case Study of Kali Gandaki ‘A’ Hydroelectric Project (144 MW), Nepal.” Hydro Nepal: Journal of Water, Energy and Environment. https://doi.org/10.3126/hn.v17i0.13270. Dahal, Nagmindra, and Roshan M Bajracharya. 2013. “Effects of Sustainable Soil Management Practices on Distribution of Soil Organic Carbon in Upland Agricultural Soils of Mid-Hills of Nepal.” Nepal Journal of Science and Technology 13 (1): 133–41. https://doi.org/10.3126/njst.v13i1.7452. Freeman, Myrick A, Joseph A Herriges, and Catherine L Kling. 2014. The Measurement of Environmental Resource Values: Theory and Methods. The Measurement of Environmental Resource Values. IHA. n.d. “Nepal - Kali Gandaki Case Study.” 61 Valuing Green Infrastructure: Technical Appendices Kamien, Morton S, and Nancy L. Schwartz. 1981. Dynamic Optimization: The Calculus of Variations and Optimal Control in Economics and Management. New York: Elsevier. Karki, Nava Raj, Arbind Kumar Mishra, and Jayandra Shrestha. 2010. “Industrial Customer Outage Cost Analysis: A Case Study of Nepal.” International Journal of Systems Assurance Engineering and Management. https://doi. org/10.1007/s13198-010-0011-z. Kawashima, Shigekazu. 2007. “Conserving Reservoir Water Storage: An Economic Appraisal.” Water Resources Research. https://doi.org/10.1029/2006WR005090. Kolstad, Charles. 2011. Intermediate Environmental Economics: International Edition. Oxford University Press. Morgan, R.P.C., D.D.V. Morgan, and H.J. Finney. 1982. “Stability of Agricultural Ecosystems: Documentation of a Simple Model for Soil Erosion Assessment.” Collaborative Paper CP-82–59. Morris, Gregory. 2014. “Sustainable Sediment Management: Kali Gandaki 144 MW Hydropower Dam, Nepal.” Rickenmann, Dieter. 1999. “Empirical Relationships for Debris Flows.” Natural Hazards 19 (1): 47–77. https://doi. org/10.1023/A:1008064220727. Ruesch, Aaron, and Holly K. Gibbs. 2008. “New IPCC Tier-1 Global Biomass Carbon Map For the Year 2000.” Oak Ridge, Tennessee. Shrestha, Jayandra Prasad, and Namrata Tusuju Shrestha. 2016. “Expansion Planning of Electricity Generating System Using the VALORAGUA and WASP-IV Models in Nepal.” Hydro Nepal: Journal of Water, Energy and Environment. https://doi.org/10.3126/hn.v19i0.15352. Shrestha, Ratna Sansar. 2011. “Electricity Crisis (Load Shedding) in Nepal, Its Manifestations and Ramifications.” Hydro Nepal: Journal of Water, Energy and Environment. https://doi.org/10.3126/hn.v6i0.4187. Timilsina, Govinda R., and Mike Toman. 2016. “Potential Gains from Expanding Regional Electricity Trade in South Asia.” Energy Economics. https://doi.org/10.1016/j.eneco.2016.08.023. Wischmeier, W H, and D Smith. 1978. “Predicting Rainfall Erosion Losses: A Guide to Conservation Planning.” Washington DC: U.S. Department of Agriculture, Agriculture Handbook No. 537. Valuing Green Infrastructure: Technical Appendices  62 APPENDIX 5: SUMMARY OF DATA SOURCES AND PARAMETER VALUES, KALI GANDAKI HILLSLOPE EROSION (INVEST SDR MODEL) Table A5.1. Baseline USLE C (crop) factors used in hillslope erosion modeling Land use/land cover Baseline USLE C USLE C value source class value Global average value for built up areas, from InVEST coefficient Airport 0.2853 literature database (NatCap 2013) Wischmeier and Smith 1978, Table 10, "no appreciable canopy" Barren land 0.45 with 0% ground cover Global average value for built up areas, from InVEST coefficient Built up 0.2853 literature database (NatCap 2013) Wischmeier and Smith 1978, Table 10, "appreciable brush or Bush 0.08 bushes" with 50-75% cover, 40% ground cover Wischmeier and Smith 1978, Table 10, "no appreciable canopy" Cliff 0.45 with 0% ground cover Global average value for forest, from InVEST coefficient Forest 0.004 literature database (NatCap 2013) Forest value (0.004) divided by 0.26, to match literature findings Forest - degraded 0.0154 of forest rehabilitation impacts Glacier 0.0001 Assumed extremely little erosion from glaciers Wischmeier and Smith 1978, Table 10, Herbaceous (based on Grass 0.091 studies of species composition in Mustang) "no appreciable canopy" with 60% ground cover Nursery 0.246 Average value for bare ground and grass Orchard 0.2 Average value from global studies of orchards and tree plantations Pond or Lake 0.04 Global average values for different water body types Wischmeier and Smith 1978, Table 10, "no appreciable canopy" Sand 0.45 with 0% ground cover Wischmeier and Smith 1978, Table 10, "no appreciable canopy" Scattered tree 0.45 with 0% ground cover Snow 0.0001 Assuming extremely little erosion from permanent snow Waterbody 0.04 Global average values for different water body types Average of C values by crop type, weighted by the area grown in Cultivation - Kaski 0.2799 that crop in Kaski district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Average of C values by crop type, weighted by the area grown in Cultivation - Syangja 0.2909 that crop in Syangja district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). 63 Valuing Green Infrastructure: Technical Appendices Land use/land cover Baseline USLE C USLE C value source class value Average of C values by crop type, weighted by the area grown in Cultivation - Gulmi 0.2085 that crop in Gulmi district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Average of C values by crop type, weighted by the area grown in Cultivation - 0.1988 that crop in Mustang district, according to the Nepal Department Mustang of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Average of C values by crop type, weighted by the area grown in Cultivation - Myagdi 0.2413 that crop in Myagdi district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Average of C values by crop type, weighted by the area grown in Cultivation - Parbat 0.2954 that crop in Parbat district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Average of C values by crop type, weighted by the area grown in Cultivation - Baglung 0.3427 that crop in Baglung district, according to the Nepal Department of Irrigation. C values from (Morgan, Morgan, and Finney 1982). Table A5.2: Baseline USLE P (practice) factors used in hillslope erosion modeling Land use/land cover Baseline USLE P USLE P value source class value Airport 1 Assumes that no erosion control practices are done Barren land 1 Assumes that no erosion control practices are done Built up 1 Assumes that no erosion control practices are done Bush 1 Assumes that no erosion control practices are done Cliff 1 Assumes that no erosion control practices are done Forest 1 Assumes that no erosion control practices are done Forest - degraded 1 Assumes that no erosion control practices are done Glacier 1 Assumes that no erosion control practices are done Grass 0.8 Assumes little to no management Nursery 1 Assumes that no erosion control practices are done Orchard 1 Assumes that no erosion control practices are done Pond or Lake 1 Assumes that no erosion control practices are done Sand 1 Assumes that no erosion control practices are done Scattered tree 1 Assumes that no erosion control practices are done Snow 1 Assumes that no erosion control practices are done Waterbody 1 Assumes that no erosion control practices are done Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Kaski 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Valuing Green Infrastructure: Technical Appendices  64 Land use/land cover Baseline USLE P USLE P value source class value Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Kaski 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al 2009 Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Syangja 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Syangja 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Gulmi 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Gulmi 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Cultivation - Value is equal to average of p-factors reported in Shrestha 2016, Mustang <=5% 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari Mustang >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Myagdi 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Myagdi 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. 65 Valuing Green Infrastructure: Technical Appendices Land use/land cover Baseline USLE P USLE P value source class value Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Parbat 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Parbat 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Baglung 0.48 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari <=5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Assumes some soil management practices and terracing in place. Value is equal to average of p-factors reported in Shrestha 2016, Cultivation - Baglung 0.46 Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Valuing Green Infrastructure: Technical Appendices  66 Table A5.3: USLE C (crop) factors for management activities Activity USLE C Land use/land cover class USLE C value source value Cultivation - Kaski <=5% slope with soil and water Same as baseline 0.2799 conservation practices Cultivation - Kaski >5% slope with terrace Same as baseline 0.2799 improvement Cultivation - Syangja <=5% slope with soil and Same as baseline 0.2909 water conservation practices Cultivation - Syangja >5% slope with terrace Same as baseline 0.2909 improvement Cultivation - Gulmi <=5% slope with soil and Same as baseline 0.2085 water conservation practices Cultivation - Gulmi >5% slope with terrace Same as baseline 0.2085 improvement Cultivation - Mustang <=5% slope with soil and Same as baseline 0.1988 water conservation practices Cultivation - Mustang >5% slope with terrace Same as baseline 0.1988 improvement Cultivation - Myagdi <=5% slope with soil and Same as baseline 0.2413 water conservation practices Cultivation - Myagdi >5% slope with terrace Same as baseline 0.2413 improvement Cultivation - Parbat <=5% slope with soil and Same as baseline 0.2954 water conservation practices Cultivation - Parbat >5% slope with terrace Same as baseline 0.2954 improvement Cultivation - Baglung <=5% slope with soil and Same as baseline 0.3427 water conservation practices Cultivation - Baglung >5% slope with terrace Same as baseline 0.3427 improvement Global average value for forest, Forest - degraded with rehabilitation 0.004 from InVEST coefficient literature database (NatCap 2013) Wischmeier & Smith (1978), value Grass with rangeland management 0.043 for 80% ground cover Barren land with landslide rehabilitation 0.45 Same as baseline 67 Valuing Green Infrastructure: Technical Appendices Table A5.4. USLE P (practice) factors for management activities Land use/land cover Activity USLE P USLE P value source class value Cultivation - Kaski Value is equal to minimum of p-factors reported in Shrestha 2016, <=5% slope with Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari soil and water 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Kaski Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Cultivation - Value is equal to minimum of p-factors reported in Shrestha 2016, Syangja <=5% Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari slope with soil and 0.11 et al 2009., Das and Bauer 2012, Narain et al. 1998, Munish 2002, water conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Syangja Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Cultivation - Gulmi Value is equal to minimum of p-factors reported in Shrestha 2016, <=5% slope with Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari soil and water 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Gulmi Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Cultivation - Value is equal to minimum of p-factors reported in Shrestha 2016, Mustang <=5% Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari slope with soil and 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, water conservation Ban et al. 2016, based on application in equivalent slope class. practices Cultivation - Value is equal to minimum of p-factors reported in Shrestha 2016, Mustang >5% Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari 0.11 slope with terrace et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, improvement Ban et al. 2016, based on application in equivalent slope class. Cultivation - Value is equal to minimum of p-factors reported in Shrestha 2016, Myagdi <=5% Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari slope with soil and 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, water conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Myagdi Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 terrace improvement et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Valuing Green Infrastructure: Technical Appendices  68 Land use/land cover Activity USLE P USLE P value source class value Cultivation - Parbat Value is equal to minimum of p-factors reported in Shrestha 2016, <=5% slope with Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari soil and water 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Parbat Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Cultivation - Value is equal to minimum of p-factors reported in Shrestha 2016, Baglung <=5% Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari slope with soil and 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, water conservation Ban et al. 2016, based on application in equivalent slope class. practices Value is equal to minimum of p-factors reported in Shrestha 2016, Cultivation - Baglung Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari >5% slope with 0.11 et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Forest - degraded Same as baseline 1 with rehabilitation Grass with rangeland Assumes some management practices in place. 0.8 management Barren land Value is equal to p-factors reported for similar activities in with landslide 0.125 Shrestha 2016. rehabilitation For assessing the degraded scenario, all USLE P values were set to 1, indicating that no management activities are done. 69 Valuing Green Infrastructure: Technical Appendices Carbon storage L and cover and land use-based baseline carbon stock values used in this study. Table A5.5:  Carbon LULC class stored Source(s) (Mg/ha) Cliff 1 Ruesch and Gibbs 2008 Ruesch and Gibbs 2008 Cultivation 34.25 Dahal and Bajracharya 2013 Ruesch and Gibbs, 2008 Grass 35.25 Dahal and Bajracharya 2013 Barren Land 1 Ruesch and Gibbs, 2008 Bush 37 Ruesch and Gibbs, 2008 Pond or Lake 0 Ruesch and Gibbs, 2008 Sand 1 Ruesch and Gibbs, 2008 Waterbody 0 Ruesch and Gibbs, 2008 Built Up 1 Ruesch and Gibbs, 2008 Nursery 5 Ruesch and Gibbs, 2008 Airport 0 Ruesch and Gibbs, 2008 MoFSC 2016 Scattered Tree 27.48 Ruesch and Gibbs, 2008 Dahal and Bajracharya, 2013 Snow 0 Ruesch and Gibbs, 2008 Glacier 0 Ruesch and Gibbs, 2008 Ruesch and Gibbs 2008 Orchard 92.25 Dahal and Bajracharya, 2013 Forest - Middle MoFSC, 2016 102.92 Mountains Dahal and Bajracharya, 2013 MoFSC, 2016 Forest - High Mountains 178.23 Dahal and Bajracharya, 2013 MoFSC, 2016 Forest - High Himal 178.23 Dahal and Bajracharya, 2013 To calculate the carbon sequestration from watershed (e.g. hedgerows, tree species intercropped with annual management interventions, we assume changes in crops). above- and below-ground and soil organic carbon pools based on the type of land use land cover at the We apply the mean response ratio of 1.4 from intervention site and the type of intervention. For soil Cardinael et al. (2018) to soil and water conservation and water conservation, hill terrace improvement, and terrace improvement activities, based on studies degraded forest rehabilitation, and degraded grazing of conversion from cropland to silvoarable practices land rehabilitation, we use data from (Cardinael et in warm temperate Asia (n=7). This value is similar to al. 2018), which give a mean response ratio reflecting one reported by (Dahal and Bajracharya 2013), who the ratio of soil organic carbon (SOC) before and after found a mean response ratio of 1.5 from adoption implementation of a variety of agroforestry practices of sustainable soil management practices across four Valuing Green Infrastructure: Technical Appendices 70 districts of Nepal. For grassland rehabilitation, we use Dahal and Bajracharya (2013) study in Nepal, because the mean response ratio of 1.05 reported by Cardinael there are a larger number of study sites included in the et al. (2018) for conversion of grassland to silvopasture Cardinael study, and because the reported coefficients in temperate regions (n=9). For rehabilitation of have recently been included in the improved 2006 degraded forest, mean response ratio values were IPCC National GHG Inventory Guidelines. We not available, so we assume a response ratio of 1.4 for convert tons of C stored to CO2 equivalents (CO2e) forests rehabilitated in the middle mountain region. using the standard conversion factor of 3.667. We opted to use Cardinael et al. (2018) values over the REFERENCES (MoFSC) Ministry of Forests and Soil Conservation. 2016. “National Forest Reference Level of Nepal (2000 – 2010).” Kathmandu, Nepal. https://redd.unfccc.int/files/nepal_frl_jan_8__2017.pdf. (NatCap) The Natural Capital Project. 2013. “Sediment and Nutrient Model Parameter Database.” Stanford, CA. http://www.naturalcapitalproject.org/invest/. Atreya, Kishor, Subodh Sharma, Roshan M. Bajracharya, and Neeranjan P. Rajbhandari. 2008. “Developing a Sustainable Agro-System for Central Nepal Using Reduced Tillage and Straw Mulching.” Journal of Environmental Management. https://doi.org/10.1016/j.jenvman.2007.03.017. Ban, Jeevan, Insang Yu, and Sangman Jeong. 2016. “Estimation of Soil Erosion Using RUSLE Model and GIS Techniques for Conservation Planning from Kulekhani Reservoir Catchment, Nepal.” Journal of Korean Society of Hazard Mitigation 16: 323–30. https://doi.org/10.9798/KOSHAM.2016.16.3.323. Cardinael, Rémi, Viviane Umulisa, Anass Toudert, Alain Olivier, Louis Bockel, and Martial Bernoux. 2018. “Revisiting IPCC Tier 1 Coefficients for Soil Organic and Biomass Carbon Storage in Agroforestry Systems.” Environmental Research Letters 13 (12): 124020. https://doi.org/10.1088/1748-9326/aaeb5f. Chalise, Devraj, Lalit Kumar, and Paul Kristiansen. 2019. “Land Degradation by Soil Erosion in Nepal: A Review.” Soil Systems . https://doi.org/10.3390/soilsystems3010012. Dahal, Nagmindra, and Roshan M Bajracharya. 2013. “Effects of Sustainable Soil Management Practices on Distribution of Soil Organic Carbon in Upland Agricultural Soils of Mid-Hills of Nepal.” Nepal Journal of Science and Technology 13 (1): 133–41. https://doi.org/10.3126/njst.v13i1.7452. Das, Romy, and Siegfried Bauer. 2012. “Bio-Economic Analysis of Soil Conservation Technologies in the Mid- Hill Region of Nepal.” Soil and Tillage Research. https://doi.org/10.1016/j.still.2012.01.016. K, Munish. 2002. “Impact of Soil & Water Conservation on Erosion Loss and Yield of Kharif Crops under Ravenous Watershed.” Proceedings of Indian Association of Soil & Water Conservationists Dehradun c: 301–3. Maskey, R.B., D. Joshi, and P.L. Maharjan. 1992. “Management of Slopping Lands for Sustainable Agriculture in Nepal.” In: IBSRAM (International Board for Soil Research, Management) (Ed.), Technical Report on the Management of Slopping Lands for Sustainable Agriculture in Asia. Phase I, 1988-1991, Network Document No. 2. Thailand. 71 Valuing Green Infrastructure: Technical Appendices Morgan, R.P.C., D.D.V. Morgan, and H.J. Finney. 1982. “Stability of Agricultural Ecosystems: Documentation of a Simple Model for Soil Erosion Assessment.” Collaborative Paper CP-82–59. Narain, Pratap, R.K. Singh, N.S. Sindhwal, and P. Joshie. 1998. “Agroforestry for Soil and Water Conservation in the Western Himalayan Valley Region of India 1. Runoff, Soil and Nutrient Losses.” Agroforestry Systems 39: 175–189. https://link-springer-com.stanford.idm.oclc.org/content/pdf/10.1007%2F978-94-007-7723-1.pdf. Ruesch, Aaron, and Holly K. Gibbs. 2008. “New IPCC Tier-1 Global Biomass Carbon Map For the Year 2000.” Oak Ridge, Tennessee. Shrestha, Ser Bahadur. 2016. “Soil erosion and payment for sediment retention in kulekhani watershed.” Agricultural and Forestry University (Nepal). Tiwari, Krishna R, Bishal K Sitaula, Roshan M Bajracharya, and Trond B∅rresen. 2009. “Runoff and Soil Loss Responses to Rainfall, Land Use, Terracing and Management Practices in the Middle Mountains of Nepal.” Acta Agriculturae Scandinavica, Section B — Soil & Plant Science 59 (3): 197–207. https://doi. org/10.1080/09064710802006021. Wischmeier, W H, and D Smith. 1978. “Predicting Rainfall Erosion Losses: A Guide to Conservation Planning.” Washington DC: U.S. Department of Agriculture, Agriculture Handbook No. 537. Valuing Green Infrastructure: Technical Appendices 72 APPENDIX 6: SUMMARY OF DATA SOURCES AND PARAMETER VALUES, MANGLA HILLSLOPE EROSION (INVEST SDR MODEL) Table A6.1. Baseline USLE C (crop) factors used in hillslope erosion modeling Land use/land cover Baseline USLE USLE C value source class C value Cropland: rainfed 0.2654 Average of C values from (Morgan, Morgan, and Finney 1982) Herbaceous cover 0.091 Wischmeier and Smith 1978, Table 10, Herbaceous "no appreciable canopy" with 60% ground cover Tree or shrub cover 0.0765 Average of Shrubland and Tree cover: mixed leaf type Cropland: irrigated 0.2654 Wischmeier and Smith 1978, Table 10, "appreciable brush or or post-flooding bushes" with 50-75% cover, 40% ground cover Mosaic cropland 0.2087 Weighted average of Cropland: rainfed (70%) and Tree or shrub (>50%) / natural cover, Shrubland and Tree cover: mixed leaf type (30%) vegetation (tree: shrub: herbaceous cover) (<50%) Mosaic natural 0.1332 Weighted average of Tree or shrub cover, Shrubland and Tree vegetation (tree: cover: mixed leaf type (70%) and Cropland: rainfed (30%) shrub: herbaceous cover) (>50%) / cropland (<50%) Tree cover: 0.0192 Low value from InVEST coefficient literature database (NatCap broadleaved: 2013), modified to assume degraded condition by dividing by evergreen: closed to 0.26, to match literature findings of forest rehabilitation impacts open (>15%) (Shrestha 2016) Tree cover: 0.0308 High value from InVEST coefficient literature database (NatCap broadleaved: 2013), modified to assume degraded condition by dividing by deciduous: closed to 0.26, to match literature findings of forest rehabilitation impacts open (>15%) (Shrestha 2016) Tree cover: 0.0269 Mid-high value from InVEST coefficient literature database broadleaved: (NatCap 2013), modified to assume degraded condition deciduous: closed by dividing by 0.26, to match literature findings of forest (>40%) rehabilitation impacts (Shrestha 2016) Tree cover: 0.0192 Low value from InVEST coefficient literature database (NatCap needleleaved: 2013), modified to assume degraded condition by dividing by evergreen: closed to 0.26, to match literature findings of forest rehabilitation impacts open (>15%) (Shrestha 2016) Tree cover: 0.0154 Mid-low value from InVEST coefficient literature database needleleaved: (NatCap 2013), modified to assume degraded condition evergreen: closed by dividing by 0.26, to match literature findings of forest (>40%) rehabilitation impacts (Shrestha 2016) 73 Valuing Green Infrastructure: Technical Appendices Land use/land cover Baseline USLE USLE C value source class C value Tree cover: 0.0308 High value from InVEST coefficient literature database (NatCap needleleaved: 2013), modified to assume degraded condition by dividing by deciduous: closed to 0.26, to match literature findings of forest rehabilitation impacts open (>15%) (Shrestha 2016) Tree cover: 0.0269 Mid-high value from InVEST coefficient literature database needleleaved: (NatCap 2013), modified to assume degraded condition deciduous: closed by dividing by 0.26, to match literature findings of forest (>40%) rehabilitation impacts (Shrestha 2016) Tree cover: 0.0231 Middle value from InVEST coefficient literature database mixed leaf type (NatCap 2013), modified to assume degraded condition (broadleaved and by dividing by 0.26, to match literature findings of forest needleleaved) rehabilitation impacts (Shrestha 2016) Mosaic tree and 0.0809 Weighted average of Shrubland and Tree cover: mixed leaf type shrub (>50%) / (70%) and Herbaceous (30%) herbaceous cover (<50%) Mosaic herbaceous 0.0867 Weighted average of Herbaceous (70%) and Shrubland and Tree cover (>50%) / tree cover: mixed leaf type (30%) and shrub (<50%) Shrubland 0.13 Wischmeier and Smith 1978, Table 10, average of "appreciable brush or bushes" with 75% & 25% cover, 40% ground cover Grassland 0.091 Wischmeier and Smith 1978, Table 10, Herbaceous "no appreciable canopy" with 60% ground cover Sparse vegetation 0.4131 Weighted average of Bare areas (90%) and Shrubland, Tree cover: (tree: shrub: mixed leaf type, and Herbaceous (10%) herbaceous cover) (<15%) Tree cover: flooded: 0.001 Assumed that very minimal erosion is possible. saline water Shrub or herbaceous 0.001 Assumed that very minimal erosion is possible. cover: flooded: fresh/ saline/brackish water Urban areas 0.2853 Global average value for built up areas, from InVEST coefficient literature database (NatCap 2013) Bare areas 0.45 Wischmeier and Smith 1978, Table 10, "no appreciable canopy" with 0% ground cover Water b odies 0 Assumed that no erosion is possible. Permanent snow and 0.0001 Assumed that very minimal erosion is possible. ice Valuing Green Infrastructure: Technical Appendices 74 Table A6.2: Baseline USLE P (practice) factors used in hillslope erosion modeling Land use/land cover Baseline USLE USLE P value source class P value Cropland: rainfed 0.88 Assumes little to no management practices currently in place. Value is equal to max of p-factors reported in Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016. Herbaceous cover 1 Assumes that no erosion control practices are done Tree or shrub cover 1 Assumes that no erosion control practices are done Cropland: irrigated 0.88 Assumes little to no management practices currently in place. or post-flooding Value is equal to max of p-factors reported in Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016. Mosaic cropland 0.916 Weighted average of 75% of cropland value and 25% of average of (>50%) / natural Mixed trees and Shrubland. vegetation (tree: shrub: herbaceous cover) (<50%) Mosaic natural 0.964 Weighted average of 25% of cropland value and 75% of average of vegetation (tree: Mixed trees and Shrubland. shrub: herbaceous cover) (>50%) / cropland (<50%) Tree cover: 1 Assumes that no erosion control practices are done broadleaved: evergreen: closed to open (>15%) Tree cover: 1 Assumes that no erosion control practices are done broadleaved: deciduous: closed to open (>15%) Tree cover: 1 Assumes that no erosion control practices are done broadleaved: deciduous: closed (>40%) Tree cover: 1 Assumes that no erosion control practices are done needleleaved: evergreen: closed to open (>15%) Tree cover: 1 Assumes that no erosion control practices are done needleleaved: evergreen: closed (>40%) Tree cover: 1 Assumes that no erosion control practices are done needleleaved: deciduous: closed to open (>15%) 75 Valuing Green Infrastructure: Technical Appendices Land use/land cover Baseline USLE USLE P value source class P value Tree cover: 1 Assumes that no erosion control practices are done needleleaved: deciduous: closed (>40%) Tree cover: 1 Assumes that no erosion control practices are done mixed leaf type (broadleaved and needleleaved) Mosaic tree and 1 Assumes that no erosion control practices are done shrub (>50%) / herbaceous cover (<50%) Mosaic herbaceous 1 Assumes that no erosion control practices are done cover (>50%) / tree and shrub (<50%) Shrubland 1 Assumes that no erosion control practices are done Grassland 1 Assumes that no erosion control practices are done Sparse vegetation 1 Assumes that no erosion control practices are done (tree: shrub: herbaceous cover) (<15%) Tree cover: flooded: 1 Assumes that no erosion control practices are done saline water Shrub or herbaceous 1 Assumes that no erosion control practices are done cover: flooded: fresh/ saline/brackish water Urban areas 1 Assumes that no erosion control practices are done Bare areas 1 Assumes that no erosion control practices are done Water bodies 1 Assumes that no erosion control practices are done Permanent snow and 1 Assumes that no erosion control practices are done ice Valuing Green Infrastructure: Technical Appendices  76 Table A6.3: USLE C (crop) factors for management activities Land use/land cover class Activity USLE C value USLE C value source Cropland: rainfed <=5% slope 0.2654 Same as baseline with soil and water cons Cropland: rainfed >5% slope with 0.2654 Same as baseline terrace improvement Cropland: irrigated or post- 0.2654 Same as baseline flooding <=5% slope with soil and water cons Cropland: irrigated or post- 0.2654 Same as baseline flooding >5% slope with terrace improvement Mosaic cropland (>50%) / natural 0.2087 Same as baseline vegetation (tree: shrub: herbaceous cover) (<50%) <=5% slope with soil and water cons Mosaic cropland (>50%) / natural 0.2087 Same as baseline vegetation (tree: shrub: herbaceous cover) (<50%) >5% slope with terrace improvement Mosaic natural vegetation (tree: 0.1332 Same as baseline shrub: herbaceous cover) (>50%) / cropland (<50%) <=5% slope with soil and water cons Mosaic natural vegetation (tree: 0.1332 Same as baseline shrub: herbaceous cover) (>50%) / cropland (<50%) >5% slope with terrace improvement Mosaic cropland (>50%) / natural 0.1876 Changed C factor for 30% of area that is vegetation (tree: shrub: herbaceous natural vegetation to 0.006, value of "mixed cover) (<50%) <=5% slope with forest" in good condition. forest rehabilitation Mosaic cropland (>50%) / natural 0.1876 Changed C factor for 30% of area that is vegetation (tree: shrub: herbaceous natural vegetation to 0.006, value of "mixed cover) (<50%) >5% slope with forest" in good condition. forest rehabilitation Mosaic natural vegetation (tree: 0.0838 Changed C factor for 70% of area that is shrub: herbaceous cover) (>50%) natural vegetation to 0.006, value of "mixed / cropland (<50%) <=5% slope forest" in good condition. with forest rehabilitation Mosaic natural vegetation (tree: 0.0838 Changed C factor for 70% of area that is shrub: herbaceous cover) (>50%) / natural vegetation to 0.006, value of "mixed cropland (<50%) >5% slope with forest" in good condition. forest rehabilitation Mosaic cropland (>50%) / natural 0.1876 Changed C factor for 30% of area that is vegetation (tree: shrub: herbaceous natural vegetation to 0.006, value of "mixed cover) (<50%) <=5% slope with forest" in good condition. C factor for 70% soil and water cons AND forest of area that is cropland remains same as rehabilitation baseline. 77 Valuing Green Infrastructure: Technical Appendices Land use/land cover class Activity USLE C value USLE C value source Mosaic cropland (>50%) / natural 0.1876 Changed C factor for 30% of area that is vegetation (tree: shrub: herbaceous natural vegetation to 0.006, value of "mixed cover) (<50%) >5% slope with forest" in good condition. C factor for 70% terrace AND forest rehabilitation of area that is cropland remains same as baseline. Mosaic natural vegetation (tree: 0.0838 Changed C factor for 70% of area that is shrub: herbaceous cover) (>50%) / natural vegetation to 0.006, value of "mixed cropland (<50%) <=5% slope with forest" in good condition. C factor for 30% soil and water cons AND forest of area that is cropland remains same as rehabilitation baseline. Mosaic natural vegetation (tree: 0.0838 Changed C factor for 70% of area that is shrub: herbaceous cover) (>50%) / natural vegetation to 0.006, value of "mixed cropland (<50%) >5% slope with forest" in good condition. C factor for 30% terracing AND forest rehabilitation of area that is cropland remains same as baseline. Tree cover: broadleaved: 0.005 InVEST coefficient literature database evergreen: closed to open (>15%) (NatCap 2013), assuming forest in good with forest rehabilitation condition Tree cover: broadleaved: 0.008 InVEST coefficient literature database deciduous: closed to open (>15%) (NatCap 2013), assuming forest in good with forest rehabilitation condition Tree cover: broadleaved: 0.007 InVEST coefficient literature database deciduous: closed (>40%) with (NatCap 2013), assuming forest in good forest rehabilitation condition Tree cover: needleleaved: 0.005 InVEST coefficient literature database evergreen: closed to open (>15%) (NatCap 2013), assuming forest in good with forest rehabilitation condition Tree cover: needleleaved: 0.004 InVEST coefficient literature database evergreen: closed (>40%) with (NatCap 2013), assuming forest in good forest rehabilitation condition Tree cover: needleleaved: 0.008 InVEST coefficient literature database deciduous: closed to open (>15%) (NatCap 2013), assuming forest in good with forest rehabilitation condition Tree cover: needleleaved: 0.007 InVEST coefficient literature database deciduous: closed (>40%) with (NatCap 2013), assuming forest in good forest rehabilitation condition Tree cover: mixed leaf type 0.006 InVEST coefficient literature database (broadleaved and needleleaved) (NatCap 2013), assuming forest in good with forest rehabilitation condition Grassland with rangeland mgmt. 0.043 Change C factor to Wischmeier and Smith 1978, grassland with 80% vegetation cover Cropland: rainfed <=5% slope 0.2654 Same as baseline with soil and water cons Cropland: rainfed >5% slope with 0.2654 Same as baseline terrace improvement Valuing Green Infrastructure: Technical Appendices 78 Table A6.4. USLE P (practice) factors for management activities Land use/land cover Activity USLE P USLE P value source class value Cropland: rainfed 0.48 Average of p-factors reported in Ahmad and Khan 2001, <=5% slope with soil Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise and water cons et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Cropland: rainfed 0.46 Average of p-factors reported in Ahmad and Khan 2001, >5% slope with terrace Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise improvement et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Cropland: irrigated or 0.48 Average of p-factors reported in Ahmad and Khan 2001, post-flooding <=5% Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise slope with soil and water et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et cons al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Cropland: irrigated 0.46 Average of p-factors reported in Ahmad and Khan 2001, or post-flooding >5% Shrestha 2016, Maskey et al. 1992, Atreya et al. 2008, Chalise slope with terrace et al. 2019, Tiwari et al. 2009, Das and Bauer 2012, Narain et improvement al. 1998, Munish 2002, Ban et al. 2016, based on application in equivalent slope class. Mosaic cropland (>50%) 0.636 Weighted average of p-factor for cropland and natural / natural vegetation vegetation. P-factor for cropland is average of p-factors (tree: shrub: herbaceous reported in Ahmad and Khan 2001, Shrestha 2016, Maskey cover) (<50%) <=5% et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. slope with soil and water 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, cons Ban et al. 2016, based on application in equivalent slope class. Mosaic cropland (>50%) 0.622 Weighted average of p-factor for cropland and natural / natural vegetation vegetation. P-factor for cropland is average of p-factors (tree: shrub: herbaceous reported in Ahmad and Khan 2001, Shrestha 2016, Maskey cover) (<50%) >5% et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. slope with terrace 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, improvement Ban et al. 2016, based on application in equivalent slope class. Mosaic natural 0.844 Weighted average of p-factor for cropland and natural vegetation (tree: shrub: vegetation. P-factor for cropland is average of p-factors herbaceous cover) reported in Ahmad and Khan 2001, Shrestha 2016, Maskey (>50%) / cropland et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. (<50%) <=5% slope 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, with soil and water cons Ban et al. 2016, based on application in equivalent slope class. Mosaic natural 0.838 Weighted average of p-factor for cropland and natural vegetation (tree: shrub: vegetation. P-factor for cropland is average of p-factors herbaceous cover) reported in Ahmad and Khan 2001, Shrestha 2016, Maskey (>50%) / cropland et al. 1992, Atreya et al. 2008, Chalise et al. 2019, Tiwari et al. (<50%) >5% slope with 2009, Das and Bauer 2012, Narain et al. 1998, Munish 2002, terrace improvement Ban et al. 2016, based on application in equivalent slope class. Mosaic cropland (>50%) 0.916 Weighted average of p-factor for cropland (70%) and natural / natural vegetation vegetation (30%). P-factor for forest rehabilitation = 1. (tree: shrub: herbaceous cover) (<50%) <=5% slope with forest rehabilitation 79 Valuing Green Infrastructure: Technical Appendices Land use/land cover Activity USLE P USLE P value source class value Mosaic cropland (>50%) 0.916 Weighted average of p-factor for cropland (70%) and natural / natural vegetation vegetation (30%). P-factor for forest rehabilitation = 1. (tree: shrub: herbaceous cover) (<50%) >5% slope with forest rehabilitation Mosaic natural 0.964 Weighted average of p-factor for cropland (30%) and natural vegetation (tree: shrub: vegetation (70%). P-factor for forest rehabilitation = 1. herbaceous cover) (>50%) / cropland (<50%) <=5% slope with forest rehabilitation Mosaic natural 0.964 Weighted average of p-factor for cropland (30%) and natural vegetation (tree: shrub: vegetation (70%). P-factor for forest rehabilitation = 1. herbaceous cover) (>50%) / cropland (<50%) >5% slope with forest rehabilitation Mosaic cropland (>50%) 0.636 Weighted average of p-factor for cropland with soil and water / natural vegetation conservation (70%) and natural vegetation (30%). P-factor for (tree: shrub: herbaceous forest rehabilitation = 1. cover) (<50%) <=5% slope with soil and water cons AND forest rehabilitation Mosaic cropland (>50%) 0.622 Weighted average of p-factor for cropland with soil and water / natural vegetation conservation (70%) and natural vegetation (30%). P-factor for (tree: shrub: herbaceous forest rehabilitation = 1. cover) (<50%) >5% slope with terrace AND forest rehabilitation Mosaic natural 0.844 Weighted average of p-factor for cropland with soil and water vegetation (tree: shrub: conservation (30%) and natural vegetation (70%). P-factor for herbaceous cover) forest rehabilitation = 1. (>50%) / cropland (<50%) <=5% slope with soil and water cons AND forest rehabilitation Mosaic natural 0.838 Weighted average of p-factor for cropland with soil and water vegetation (tree: shrub: conservation (30%) and natural vegetation (70%). P-factor for herbaceous cover) forest rehabilitation = 1. (>50%) / cropland (<50%) >5% slope with terracing AND forest rehabilitation Tree cover: broadleaved: 1 Default value, assumes no active sediment management evergreen: closed to practices. open (>15%) with forest rehabilitation Valuing Green Infrastructure: Technical Appendices 80 Land use/land cover Activity USLE P USLE P value source class value Tree cover: broadleaved: 1 Default value, assumes no active sediment management deciduous: closed to practices. open (>15%) with forest rehabilitation Tree cover: 1 Default value, assumes no active sediment management broadleaved: deciduous: practices. closed (>40%) with forest rehabilitation Tree cover: 1 Default value, assumes no active sediment management needleleaved: practices. evergreen: closed to open (>15%) with forest rehabilitation Tree cover: 1 Default value, assumes no active sediment management needleleaved: practices. evergreen: closed (>40%) with forest rehabilitation Tree cover: 1 Default value, assumes no active sediment management needleleaved: practices. deciduous: closed to open (>15%) with forest rehabilitation Tree cover: 1 Default value, assumes no active sediment management needleleaved: practices. deciduous: closed (>40%) with forest rehabilitation Tree cover: mixed leaf 1 Default value, assumes no active sediment management type (broadleaved and practices. needleleaved) with forest rehabilitation Grassland with 0.8 Assumes some sediment management practices in place. rangeland mgmt. 81 Valuing Green Infrastructure: Technical Appendices Carbon storage  AND COVER AND LAND USE-BASED BASELINE CARBON STOCK VALUES USED IN TABLE A6.5: L THIS STUDY, FROM RUESCH AND GIBBS (2008). Carbon stored (Mg/ha) by Eco floristic Zone Subtropical Subtropical Steppe Mountain LULC class Cropland: rainfed 5 5 Herbaceous cover 5 4 Tree or shrub cover 47.43 46.36 Cropland: irrigated or post-flooding 5 5 Mosaic cropland (>50%) / natural vegetation (tree: shrub: 13.49 13.17 herbaceous cover) (<50%) Mosaic natural vegetation (tree: shrub: herbaceous cover) 24.8 24.07 (>50%) / cropland (<50%) Tree cover: broadleaved: evergreen: closed to open (>15%) 57.86 55.71 Tree cover: broadleaved: deciduous: closed to open (>15%) 57.86 55.71 Tree cover: broadleaved: deciduous: closed (>40%) 57.86 55.71 Tree cover: needleleaved: evergreen: closed to open (>15%) 57.86 55.71 Tree cover: needleleaved: evergreen: closed (>40%) 57.86 N/A Tree cover: needleleaved: deciduous: closed to open (>15%) 57.86 N/A Tree cover: needleleaved: deciduous: closed (>40%) 57.86 N/A Tree cover: mixed leaf type (broadleaved and needleleaved) 57.86 N/A Mosaic tree and shrub (>50%) / herbaceous cover (<50%) 34.7 33.65 Mosaic herbaceous cover (>50%) / tree and shrub (<50%) 17.73 16.71 Shrubland 37 N/A Grassland 4.5 4 Sparse vegetation (tree: shrub: herbaceous cover) (<15%) 4.23 N/A Tree cover: flooded: saline water 57.86 55.71 Shrub or herbaceous cover: flooded: fresh/saline/brackish 21 20.5 water Urban areas 1 1 Bare areas 1 N/A Water bodies 0 0 Permanent snow and ice 0 N/A Valuing Green Infrastructure: Technical Appendices 82 To calculate the carbon sequestration from watershed We apply the mean response ratio of 1.4 from management interventions, we assume changes in Cardinael et al. (2018) to soil and water conservation above- and below-ground and soil organic carbon and terrace improvement activities, based on pools based on the type of land use land cover at studies of conversion from cropland to silvoarable the intervention site and the type of intervention. practices in warm temperate Asia (n=7). For For soil and water conservation, hill terrace grassland rehabilitation, we use the mean response improvement, degraded forest rehabilitation, and ratio of 1.05 reported by Cardinael et al. (2018) for degraded grazing land rehabilitation, we use data conversion of grassland to silvopasture in temperate from Cardinael et al. (2018), which give a mean regions (n=9). For rehabilitation of degraded forest, response ratio reflecting the ratio of soil organic mean response ratio values were not available, so carbon (SOC) before and after implementation of we assume a response ratio of 1.4 for forests. We a variety of agroforestry practices (e.g. hedgerows, convert tons of C stored to CO2 equivalents (CO2e) tree species intercropped with annual crops). using the standard conversion factor of 3.667. 83 Valuing Green Infrastructure: Technical Appendices REFERENCES (NatCap) The Natural Capital Project. 2013. “Sediment and Nutrient Model Parameter Database.” Stanford, CA. http://www.naturalcapitalproject.org/invest/. Atreya, Kishor, Subodh Sharma, Roshan M. Bajracharya, and Neeranjan P. Rajbhandari. 2008. “Developing a Sustainable Agro-System for Central Nepal Using Reduced Tillage and Straw Mulching.” Journal of Environmental Management. https://doi.org/10.1016/j.jenvman.2007.03.017. Ban, Jeevan, Insang Yu, and Sangman Jeong. 2016. “Estimation of Soil Erosion Using RUSLE Model and GIS Techniques for Conservation Planning from Kulekhani Reservoir Catchment, Nepal.” Journal of Korean Society of Hazard Mitigation 16: 323–30. https://doi.org/10.9798/KOSHAM.2016.16.3.323. 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