Hydropower Potential of Run of River Schemes in the Himalayas under Climate Change: A Case Study in the Dudh Koshi Basin of Nepal

: In spite of the very large hydropower potential given from the melting snow and ice of Himalayas, Nepal’s population has little hydropower production. The high use of fossil fuels and biomasses results in measurable air pollution, even in the mountain areas. Hydropower planning and implementation, in the face of the changing climate, is therefore paramount important. We focus here on Nepal, and particularly on the Dudh Koshi river basin, with a population of ca. 170,000 people, within an area with large potential for hydropower production. Our main objectives are to (i) preliminarily design a local hydropower grid based on a distributed run of river ROR scheme, and (ii) verify the resilience of the grid against modified hydrology under perspective climate change, until the end of the century. To do so, we set up and tune the Poli-Hydro semi-distributed glacio-hydrological model, mimicking the complex hydrology of the area. We then modify a state of the art algorithm to develop and exploit a heuristic, resource-demand based model, called Poli-ROR . We use Poli-ROR to assess the (optimal) distribution of a number of ROR hydropower stations along the river network, and the structure of the local mini-grids. We then use downscaled outputs from three general circulation models GCMs (RCPs 2.6, 4.5, 8.5) from the Intergovernmental Panel on Climate Change IPCC AR5, to assess the performance of the system under future modified hydrological conditions. We find that our proposed method is efficient in shaping ROR systems, with the target of the largest possible coverage (93%), and of the least price (0.068 € kWh − 1 on average). We demonstrate also that under the projected hydrological regimes until 2100, worse conditions than now may occur, especially for plants with small drainage areas. Days with energy shortage may reach up to n f = 38 per year on average (against n f = 24 now), while the maximum daily energy deficit may reach as high as e def% = 40% (against e def% = 20% now). We demonstrate that our originally proposed method for ROR grid design may represent a major contribution towards the proper development of distributed hydropower production in the area. Our results may contribute to improve energy supply, and living conditions within the Dudh Koshi river. It is likely that our approach may be applied in Nepal generally. Impending climate change may require adaptation in time, including the use of other sources which are as clean as possible, to limit pollution. Our Poli-ROR method for grid optimization may be of use for water managers, and scientists with an interest in the design of optimal hydropower schemes in topographically complex catchments.

. Case study area. Dudh Koshi basin location, and topography. Weather and hydro stations used in the study are reported. AWS = Automatic Weather Station. Topography was extracted from ASTER GDEM, resampled at 300 m × 300 m.

Topography, Land Use, and Hydrological Data
The hydrological model Poli-Hydro requires as input spatial data of the basin (altitude, ice-cover, and land use), and meteorological data (temperature, precipitation). Spatial inputs, such as the fraction of vegetated soil fv, maximum soil water content Smax, and digital elevation model of the area (DEM, here ASTER GDEM) are required. These data were derived from public thematic maps, and aggregated to obtain regular square cells of 300 m × 300 m side. The curve number CN map was estimated by cross-referencing the land cover map provided by the International Center for Integrated Mountain Development ICIMOD [55], and the Soil and Terrain database for Nepal developed by FAO [44,56]. Soil cover data were also used for creating the map of the vegetated soil fraction [33,43].
The Poli-Hydro model requires (daily) inputs of total precipitation P, snow depth HS whenever available, temperature T, and values of instream flows Q for calibration/validation purposes. In Table  1, we report the measuring stations, and hydro-climatic variables used here.

Topography, Land Use, and Hydrological Data
The hydrological model Poli-Hydro requires as input spatial data of the basin (altitude, ice-cover, and land use), and meteorological data (temperature, precipitation). Spatial inputs, such as the fraction of vegetated soil f v , maximum soil water content S max , and digital elevation model of the area (DEM, here ASTER GDEM) are required. These data were derived from public thematic maps, and aggregated to obtain regular square cells of 300 m × 300 m side. The curve number CN map was estimated by cross-referencing the land cover map provided by the International Center for Integrated Mountain Development ICIMOD [55], and the Soil and Terrain database for Nepal developed by FAO [44,56]. Soil cover data were also used for creating the map of the vegetated soil fraction [33,43].
The Poli-Hydro model requires (daily) inputs of total precipitation P, snow depth HS whenever available, temperature T, and values of instream flows Q for calibration/validation purposes. In Table 1, we report the measuring stations, and hydro-climatic variables used here.
Remote sensing information was gathered to depict complex precipitation distribution within the catchment [22,57,58]. Namely, we used precipitation estimates from the tropical rainfall measuring mission TRMM (e.g., [59]). We used data from the 2B31 product, combined Precipitation Radar (PR)/TRMM Microwave Imager (TMI) rain-rate product, with path-integrated attenuation at 4 km horizontal, and 250 m vertical resolutions, processed by Bookhagen [60], and averaged over 12 years (1998-2005). In spite of displaying large overestimation of precipitation in the high altitudes (Alt > 3000 m a.s.l. or so), especially during winter (shown in [14]), TRMM estimates depict spatial distribution patterns of precipitation, not visible when using the (few) ground stations as here (see e.g., [61] for a similar issue in the Andes of Chile).

Demographic Data
The Poli-ROR model requires data of population, and their distribution. The demographic distribution was estimated from census of the government of Nepal, which was then spatialized with the aid of datasets coming from international organizations. The last census dates back to 2011 [46]. Nepal-wide data were integrated by using the location of the largest settlements nested into the basin [62], and a grid map of estimated population distribution [63]. We used the Worldpop data, which provide disaggregate country census data [64]. Prior to the use in population estimation, the Worldpop map was rescaled to match the model's resolution.

Hydrological Model
We used here the Poli-Hydro model. This is a physically based, semi-distributed glacio-hydrological model, validated previously [25,65] with acceptable performance, including within the Dudh Koshi catchment [66]. Poli-Hydro tracks water budget in soil between two consecutive days, taking as input liquid precipitation (rainfall) R, and ice/snow melt, M I /M S . Melt is calculated using a hybrid degree day model [67], considering temperature T, and (global, topographically corrected) solar radiation G.
Poli-Hydro can also track glaciers' flow, necessary for long term assessment of climate change impact [25,61]. Initial ice thickness h ice,in on glaciers is strongly influenced by the superficial slope (i.e., the greater the slope, the thinner the ice). We estimated h ice,in as described by Oerlemans [68], by back calculation from the basal shear stress τ b (Pa). We assessed basal shear as a function of glacier's altitude jump ∆H as in Haeberli and Hoelzle [69]. Hydrological response is modeled via Nash model [70], with lag time t l,s,g = n s,g l s,g , i.e., for n s,g reservoirs (here, n s,g = 3) each with lag time l s,g , for overland flow, and subsurface flow, respectively (s, and g subscript). Once calibrated against observed stream flows, Poli-Hydro provides stream flow estimates within any section along the river network, and such estimates can be used for assessment of hydropower potential, as if they were (virtual) hydrometric stations. In Table 2, we report Poli-Hydro model main parameters [71], including calibration method, whenever required.
The model is well described elsewhere, and we provide here a short description using the flow chart in Figure 2a [49,67]. The modeling procedure, and tools are therein given according to 7 categories. These are, namely domain of investigation (e.g., hydrology, cryosphere), tools (e.g., hydrological model, snow melt model, etc.), functions linking variables (e.g., snow melt M s as a function of temperature, and radiation M s (T, G), etc.), necessary field surveys (ice melt from stakes, etc.), network data (of weather, snow depth, SCA from remote sensing, etc.), model outputs (e.g., ice melt in time at different time and place M i (t,s)), and model accuracy (i.e., objective measure of matching against observed stream flows).
Moreover, in the flow chart the procedure to develop hydrological projections is reported. We also give the information necessary to model each component, and the interactions between components. Specific implementation of the proposed method clearly requires tailoring for each case study, and depends upon the characteristics of the area, and the available data and tools. melt in time at different time and place Mi(t,s)), and model accuracy (i.e., objective measure of matching against observed stream flows). Moreover, in the flow chart the procedure to develop hydrological projections is reported. We also give the information necessary to model each component, and the interactions between components. Specific implementation of the proposed method clearly requires tailoring for each case study, and depends upon the characteristics of the area, and the available data and tools.

Energy Demand
Evaluation of energy demand was carried out according to three main sectors, namely (i) agriculture, (ii) residential, and (iii) tourism. Agricultural consumption was evaluated using the national energy consumption data given by the International Energy Agency IEA [2,72], in all villages identified as agricultural according to land cover analysis [43]. Due to differences of the living standards between rural and urban population, in the residential and tourist area, energy demand estimates (in Table 3) were made based upon a former study pursued in the upper part of the catchment [73]. These values were then refined considering a conversion from biomass fired heating Figure 2. Flow chart (a) Poli-Hydro model. The modeling procedure, and tools are given according to 7 categories, i.e., domain (e.g., hydrology, cryosphere), tools (e.g., hydrological model, snow melt model), functions (e.g., snow melt M s as a function of temperature, and radiation M s (T, G), etc.), necessary data from field surveys or other sources (ice melt from stakes, ice volume loss from topographic methods, earth observation from space EOS, etc.), data (weather, snow depth, SCA from remote sensing, etc.), model outputs (e.g., ice melt in time and space M i (t,s)), and model accuracy (e.g., Bias, NSE). Division in present, and future (projections) reported. Dashed lines indicate methods/data that could be used generally as alternatives in high altitude catchments, but were not used here (e.g., snow depth data were not available, etc.). In bold, most important model outputs. T(t) is daily temperature, P(t) daily precipitation, Q(t) is daily observed discharge at the outlet section, Q m (t) is daily modeled discharge at the outlet section. M i (t,s) is daily ice melt in a given place (cell) s, M s (t,s) is daily snow melt, q(t,s) is daily runoff in cell s, h ice (t,s) is daily ice depth, and V ice (t,s) daily ice flow velocity. SCA is the snow covered area. SWE is the snow water equivalent. ICA is the ice covered area, IWE m is the water equivalent of ice melt. NSE is the Nash-Sutcliffe efficiency. DTM is the digital terrain model. T f '(t), P f '(t) are (future/projected) the temperature and precipitation from GCMs before downscaling (biased); T f (t), P f (t) future daily temperature and precipitation after downscaling (unbiased). Q f (t) future projected discharges. (b) Poli-ROR iterative algorithm. Poli-ROR takes as input DEM, energy demand, and Q max,I calculated at each site i using outputs from Poli-Hydro (Section 4.3). Poli-ROR is performed by (i) area subdivision, or clustering, with the number of clusters giving the number of plants, and (ii) mini-grid construction, repeated iteratively until convergence (Section 4.5). M1 is Min-LCOE approach, M2 is Max-Connection approach. GGS i is grid generation score at each cluster/plant (Equation (8)), DI i demand indicator (Equation (9)), and RI i resource indicator (Equation (11)) thereby. P n,i is power at each cluster/plant i (Equation (2)), and E D,i energy demand thereby (Equation (3)).

Energy Demand
Evaluation of energy demand was carried out according to three main sectors, namely (i) agriculture, (ii) residential, and (iii) tourism. Agricultural consumption was evaluated using the national energy consumption data given by the International Energy Agency IEA [2,72], in all villages identified as agricultural according to land cover analysis [43]. Due to differences of the living standards between rural and urban population, in the residential and tourist area, energy demand estimates (in Table 3) were made based upon a former study pursued in the upper part of the catchment [73]. These values were then refined considering a conversion from biomass fired heating systems, to electricity-powered ones. This assumption is acceptable, since the energy demand of the inhabitants of the Dudh Koshi basin is extremely low compared to the hydroelectric potential of the area. Corrections were carried out considering the typical energy usage distribution among different sectors in the upper basin [74]. For tourism, energy demand was evaluated according to the tourist record provided by the Sagarmatha National Park Office, giving the number of tourists in each season. It was assumed that tourists were homogeneously distributed within the available lodges in the area. The location of the main lodges was provided by ICIMOD [75], providing information of the local energy demand. The tourist volume is higher from September to December and from March to May. The monsoon season (viz. the season with highest rainfall, and flows), and winter record very few tourists instead due to adverse climatic conditions. Thus, the former group of months was categorized as "trekking season" while the latter one as "rest of the year".

Plants' Design
Concerning water availability, we analyzed the typical yearly flow pattern at Rabuwa Bazar. Therein, one has a monsoonal season, with high flow rates and high variability, and a dry season with low, almost constant flows. Due to such seasonal effects, the maximum nominal flow of turbines must be close to the minimum site value. For this reason, the maximum nominal flow at a given site i was taken as with N y years of simulation, and Q 335,i (m 3 s −1 ) flow rate exceeded for 335 days in a year at site i, and EF i environmental flow as site i. The value of the environmental flow was fixed at 10% of the minimum mean monthly discharge, according to the Nepalese regulation. We considered as initial potential sites for a hydropower plant, those that satisfied three criteria. These criteria were (i) minimum area, i.e., a drainage area at the inlet point greater than 20 km 2 , to ensure a sufficient flow availability; (ii) minimum head, i.e., value of gross (before hydraulic losses) head compatible with the operating range of the chosen turbines (only impulse turbines were taken into account, due to the high slopes that characterize the study area); and (iii) maximum distance between the inlet and outlet of 1 km, to avoid excessive penstocks' length. For each of site, a nominal discharge Q n is chosen, to satisfy the daily energy demand of the closest village, i.e., Therein, ∆H net (m) is the net head, ρ w (ca. 1000 kg m −3 ) is water density, g (m s −2 ) is gravity acceleration, and η hydr , η el and η mec , are the hydraulic, electric and mechanic efficiencies, respectively. Instant power P n (t) (kW) is integrated over time to give an energy production covering for energy demand E D (kWh) over a certain period T.
The network is then iteratively modified. At each time step, the grid is extended, by connecting the demand point to the closest node of the network built at the former step, and by increasing the value of Q n to account for the energy demand of the whole grid. The maximum workable flow Q max,i is selected as in Equation (1). Penstocks' diameters are computed, to reduce head losses below a certain percentage e % of the gross head, and then rounded up according to commercial values: The electrical network is designed considering a distribution connecting the demand points belonging to the same mini-grid, and a transmission network connecting the individual houses inside each demand point. We chose to use medium-voltage (33 kV), considering the minimum linear distance, and the altitudinal difference between starting and ending points. A constrain of maximum length for each route was introduced, to limit voltage drops and an excessive ramification of the mini-grids. To evaluate the length of the transmission network L N , assumed to be in low-voltage (0.2 kV), it was hypothesized an evenly space distribution of the households inside the village where A Vi is the area of each village, A HH the area of influence assigned to each household, and NH the number of households in the village.

Cost Estimation
Grid cost assessment is carried out considering two mini-grids' components, namely (i) the hydroelectric plant, and (ii) the electrical network. The plant cost is thus estimated considering the average distribution of investment on a generic small hydropower plant [76], as reported in Figure 3. The cost of the turbo-generator set is computed using an empirical equation, specific for impulse turbines [76] c turb = 17.7P −0.36 where c turb is the specific cost in EUR(kWh) −1 of the group, turbine + alternator. The cost of the penstocks is derived from the same commercial tables used for the evaluation of the diameters. Finally, the total cost of the plant is derived giving to the penstock half share of the civil works cost. The costs of the electrical network are calculated, using the indications by IEA [3]. Finally, the levelized cost of the electricity LCOE is derived, and used in the subsequent procedure where I t are the investment costs at year t; OM t the operational and maintenance costs; E t the energy consumed yearly; with r discount rate.
Water 2020, 12, x FOR PEER REVIEW 9 of 29 is selected as in Equation (1). Penstocks' diameters are computed, to reduce head losses below a certain percentage e% of the gross head, and then rounded up according to commercial values: The electrical network is designed considering a distribution connecting the demand points belonging to the same mini-grid, and a transmission network connecting the individual houses inside each demand point. We chose to use medium-voltage (33 kV), considering the minimum linear distance, and the altitudinal difference between starting and ending points. A constrain of maximum length for each route was introduced, to limit voltage drops and an excessive ramification of the minigrids. To evaluate the length of the transmission network LN, assumed to be in low-voltage (0.2 kV), it was hypothesized an evenly space distribution of the households inside the village where AVi is the area of each village, AHH the area of influence assigned to each household, and NH the number of households in the village.

Cost Estimation
Grid cost assessment is carried out considering two mini-grids' components, namely (i) the hydroelectric plant, and (ii) the electrical network. The plant cost is thus estimated considering the average distribution of investment on a generic small hydropower plant [76], as reported in Figure 3. The cost of the turbo-generator set is computed using an empirical equation, specific for impulse turbines [76] = 17.7 . ∆ .
where cturb is the specific cost in EUR(kWh) −1 of the group, turbine + alternator. The cost of the penstocks is derived from the same commercial tables used for the evaluation of the diameters. Finally, the total cost of the plant is derived giving to the penstock half share of the civil works cost. The costs of the electrical network are calculated, using the indications by IEA [3]. Finally, the levelized cost of the electricity LCOE is derived, and used in the subsequent procedure where It are the investment costs at year t; OMt the operational and maintenance costs; Et the energy consumed yearly; with r discount rate.

Heuristic Network Design Procedure, Poli-ROR
When dealing with decentralized energy network design at a regional scale as we are here, exact design procedures are rarely suitable, since they require introduction of questionable simplifications, and/or large computational times [65,77]. Here we chose to adopt a heuristic approach, adapted from a method introduced recently [78][79][80] to design mini-grids, powered by solar and wind energy. The method is suitable, because (i) the design procedure here is quite complex, and highly non-linear, and thus not suitable for classical approaches (e.g., linear programming), and (ii) the procedure allows to include a detailed description of the physical system involved, i.e., the hydrological, and hydroelectric set up of the area.
We developed a heuristic procedure, which we call Poli-ROR, based on a set of former heuristic indicators, proposed to support off-grid electrification projects [78]. Namely, we used (i) a resource indicator (hereon RI), that evaluates the economic convenience of producing energy from a specific plant, as compared to those located nearby, and (ii) a demand indicator (hereon DI) that evaluates the energy demand concentration at a given production point.
These two indicators are calculated, and then normalized (0-1) for every potential plant. Their value is then weighted by a parameter α (0-1), quantifying their relative importance, to obtain the suitability of a given point (stream section) I, to act as a production point for the mini-grid The grid generation score GGS is computed for each plant. The purpose of the heuristic indicators is to identify the most promising pairs, or coupled points of inlet and outlet, for the implementation of a mini-grid. To be identified as an attractive generation point, a plant should (i) display a high energy demand concentration to serve a large number of users (high DI), and (ii) exploit water resources efficiently, i.e., to be more economically convenient against surrounding points (high RI). The initial demand indicator for a possible production point i, DI 0 i is calculated by considering the set of N i closest demand points, and by weighting the influence of each of them by their distance from the plant location with ED j being the energy demand of the village j. A least distance L min was set to avoid a null denominator in case of points belonging to the same cell. While the definition of DI is somewhat straightforward, finding a suitable Resource Indicator RI is more complex. In facts, the most appropriate way to compare two different couples in terms of economical convenience would be by LCOE. However, for a single plant LCOE is not fixed a priori, but it is a function of the number of villages thereby connected. Therefore, to compare different plants/couples it was decided to assign to each one a unique value, chosen as the average LCOE for a fixed number of connected villages to that plant n i .
with PI i Potential Indicator for the plant i. Then, the initial Resource Indicator RI 0 is defined in analogy to DI 0 as where PI j are the values of the Potential Indicator of the N p plants located closer to the plant j.
The Poli-ROR heuristic procedure is performed according to two steps, namely by (i) area subdivision, or clustering, and (ii) mini-grid construction. The procedure is iteratively repeated until convergence is reached, as shown in Figure 2b.
First, the study area is partitioned into a number n r of sub-regions. Then in any sub-region, a possible generation point is selected, and a tentative mini-grid is constructed. During the construction phase, only demand points belonging to each sub-region are considered. The initial subdivision in sub-regions is then updated iteratively. The first/initial subdivision is carried out by applying a k-means clustering algorithm on the villages' geographical location, defining n r centroids (one for each region), and their relative sub-area of influence, each sub-area being identified by assigning each point of the space to the closest centroid.
In the subsequent iterations, since for each cluster a tentative mini-grid will be defined in the second step, the centroid location is modified to match the tentative plant location, and the sub-areas are subsequently re-evaluated. It is implicitly assumed that each village will be connected to the closest plant. The clustering procedure has five steps, i.e., (i) randomly choose k initial cluster (centroids), (ii) compute the distance from each point to each centroid, (iii) assign each point to the cluster with the closest centroid, (iv) recalculate k new centroids as centers of mass of the clusters resulting from the mini grid construction step, and (v) repeat points 1-4 until the centroid position does not change any more.
In the grid construction step, inside each sub-area the plant with the highest value of GGS in Equation (8) is selected, and the mini-grid is designed as explained in Section 4.3. Two possibly contrasting objectives need to be taken into account, namely (i) maximizing the share of inhabitants served, and (ii) minimizing the average LCOE of the mini-grid. Based upon which objective is seen as more relevant, two different approaches can be pursued.
First, the Min-LCOE approach can be used, hereon method M1. This includes the selection of a grid set up with the lowest local value of LCOE for each mini-grid. In this approach, the DI and RI indicators are evaluated by selecting a number of demand points N i , leading close to the average minimum LCOE value for all the different plants/couples. Second, the Max-Connection approach can be used, hereon method M2. Here, the two indicators DI and RI are evaluated, selecting as a number of surrounding points N i the maximum value for each pair.
The outcome of the heuristic optimization depends upon the values of three main parameters, namely the number of clusters (sub-regions) n r , the maximum length of the transmission line between two villages L max , and the weighting factor in Equation (8). To investigate such dependence, a sensitivity analysis was carried out. In Table 4, we report a resume of the Poli-ROR parameters, including their values, and those parameters that underwent a sensitivity analysis. After a preliminary screening, the hypothesis of adopting an electrical storage system (i.e., batteries) was deemed unfeasible, given the potentially required storage (i.e., size of batteries), and infrequent (i.e., few days per year) use of the storage. We thus assume that during dry days some plants will not be able to fully meet the energy demand of the inhabitants served, which will have to rely upon other energy sources (e.g., kerosene fed generators).

Future Scenarios
After having selected the best ROR scheme, the performances therein were evaluated under potentially changed future climate/hydrological conditions. The streamflow projections for the Dudh Koshi river were assessed by giving them as an input to Poli-Hydro temperature and precipitation projections. These were obtained by properly downscaling [81] the outputs of three GCMs, provided under the umbrella of the fifth coupled model intercomparison project CMIP5 (see Figure 2a). We considered three GCMs, namely ECHAM6 (European Centre Hamburg Model, version 6, [82]), CCSM4 (Community Climate System Model, version 4, [83]), and EC-Earth (European Consortium Earth system model, version 2.3, [84]), under three Representative Concentration Pathways scenarios (RCP 2.6, 4.5 and 8.5). Specifically, for each mini-grid we analyzed two indicators, i.e., the average number of days per year with daily energy supply below the demand (system failure) n f , and the maximum daily energy deficit in one year (e def ), which we used to benchmark the future performances against the present ones. Table 4. Hydroelectric input parameters for Poli-ROR, and values assigned. SA means that a sensitivity analysis was carried out to assign a best value, see Section 4.5.

Parameter
Description  Table 5 and Figure 4 report the performance of the Poli-Hydro model. The parameters governing ice and snow melt (degree day, and the radiation factors, see Table 2) were calibrated against snow data (Table 1, see also [71]). Tuning of the hydrological parameters was pursued against the observed discharge at Rabuwa Bazar (see the calibration method in Table 2). We used monthly flow averages for K, and k g regulating flow volumes, and daily flows for lag times, t l,s , t l,g . The entire period of simulation was subdivided into calibration CAL (2003-2007), and validation VAL (2008-2013) subsets, and the year 2009 was not used due to lack of observed data. We used three indicators, namely Bias (average percentage error), NSE (Nash-Sutcliffe Efficiency, or explained variance) ln NSE (NSE of logarithmic values), given in Table 5. In calibration, Poli-Hydro overestimates the monthly cumulative discharge by Bias = +7%, and in validation it underestimates by Bias = −12%. On an annual basis, calibration would lead to Bias = +16%, while in the validation one has Bias = 0%, and NSE = 0.71, 0.66, respectively. Analysis of the flow contributions (not shown, see e.g., [85]) demonstrated that stream flows at Rabuwa bazar are mainly given by rainfall (ca. 69% of the yearly flows), and groundwater flow (ca. 23%), and overland flow from ice and snow melt is marginal (conversely to flow in the highest altitudes, see [71]). Clearly, a largest contribution is given during monsoonal season, displaying heavy precipitation, and highest temperature (i.e., larger snow and ice melt). In Figure 4, we report model adaptation. Therein, the model visibly reproduces poorly peak discharge. Notice that Poli-Hydro model is not designed to reproduce high flows, say for flood assessment, also given its daily resolution, and such exercise clearly requires other methods. However, given the complex hydrology of the catchment, and the large difficulties in proper flow estimation thereby, as widely reported in the literature (e.g., [74]), the model provides an acceptable flow depiction for the purpose here, i.e., for hydropower assessment.

Poli-ROR
Since heuristic optimization is sensitive to three main parameters nr, Lmax, and α, we carried out a sensitivity analysis, SA. We used both optimization approaches, Min-LCOE, M1 and Max-Connection, M2. In Figure 5 we report the results of the SA, focusing upon the number of connected villages. Particularly, it is shown therein the SA of nr and Lmax (with α = 0.5). To assess the performances of the model with different input parameters, we varied the number of initial clusters nr within 10-100, with steps of 10 units, while for Lmax values of 1500, 2000 and 2500 m were selected. On the x axis, it is reported the final number of clusters nr (which may differ slightly from the initial value, because the algorithm automatically removes mini-grids able to connect few villages). Figure  5a,b display on the y axis the share of connected villages globally (M1, M2), against nr. Lmax is relevant, because the larger Lmax, the larger the share. Increasing nr above a certain value (ca. nr = 20) does not largely change the share of villages connected. However, given the complex hydrology of the catchment, and the large difficulties in proper flow estimation thereby, as widely reported in the literature (e.g., [74]), the model provides an acceptable flow depiction for the purpose here, i.e., for hydropower assessment.

Poli-ROR
Since heuristic optimization is sensitive to three main parameters n r , L max , and α, we carried out a sensitivity analysis, SA. We used both optimization approaches, Min-LCOE, M1 and Max-Connection, M2. In Figure 5 we report the results of the SA, focusing upon the number of connected villages. Particularly, it is shown therein the SA of n r and L max (with α = 0.5). To assess the performances of the model with different input parameters, we varied the number of initial clusters n r within 10-100, with steps of 10 units, while for L max values of 1500, 2000 and 2500 m were selected. On the x axis, it is reported the final number of clusters n r (which may differ slightly from the initial value, because the algorithm automatically removes mini-grids able to connect few villages). Figure 5a,b display on the y axis the share of connected villages globally (M1, M2), against n r . L max is relevant, because the larger L max , the larger the share. Increasing n r above a certain value (ca. n r = 20) does not largely change the share of villages connected. A similar analysis (not shown for shortness) of LCOE, demonstrated that an increase in nr tends to increase the average cost of electricity, with values from 0.064 to 0.084 € kWh −1 . This may be because more mini-grids, and thus smaller plants in terms of nominal power, do not profit from scale effects. Apparently, no large influence of Lmax is seen.
We then pursued an SA against the parameter α (0-1), quantifying the relative importance of RI, A similar analysis (not shown for shortness) of LCOE, demonstrated that an increase in n r tends to increase the average cost of electricity, with values from 0.064 to 0.084 € kWh −1 . This may be because more mini-grids, and thus smaller plants in terms of nominal power, do not profit from scale effects. Apparently, no large influence of L max is seen.
We then pursued an SA against the parameter α (0-1), quantifying the relative importance of RI, and DI for assessment of the grid generation score GGS in Equation (8), using different values of L max , and of number of initial clusters n r . Similar results were however obtained for different values of L max , and n r . The results are not shown here for shortness (see [86]), but shortly commented. Both with M1, and M2, an increase in α decreases the average LCOE, and larger changes are observed within α = 0-0.5. This seems in accordance with the meaning of the resource indicator RI, which evaluates the economical convenience of producing energy from a given hydro-power plant. Accordingly, a higher weight applied to such indicator results into a minor cost of the final configuration. Concerning the share of served villages, giving more importance to the demand concentration upon a plant DI (i.e., decreasing α in Equation (8) should result into a greater number of villages served. However, no large variation is observed when using M1 (Min-LCOE) method (with the exception of α = 0), and even an opposite trend is seen using M2 (Max-Connection), with saturation to ca. 90% of villages served for α = 0.5 or so. As a possible explanation one may state that giving more importance to DI results into less, or even no importance of the hydro-power plant capacity. Therefore, it may happen that, even though a plant is surrounded by high demand, it would not have the sufficient capacity to satisfy such demand fully. This is especially true for the M2 method, which tends to create more extended mini-grids. According to the results of the SA, one can conclude that Poli-ROR algorithm is stable, and leads to better grid design for 0.5 < α < 1. For eolic, and photovoltaic based mini-grids, Ranaboldo et al. [79] obtained a somewhat different set of values (0 < α < 0.5). However, this may be because hydro-power is more site-dependent, with respect to the other two sources. We thus decided to select a value of α = 0.5, fit in both ranges.
Since the primary objective of the study is to serve the highest possible share of the population, and further doing so at the least cost, the best solution here seems the one obtained using method M2 (L max = 2500, n r = 19, α = 0.5), leading to 93% of connected villages, with a relatively low LCOE of 0.068 € kWh −1 , comparable to the cost of purchasing electricity from the Nepalese electrical grid, which varies from 0.042-0.07 € kWh −1 , depending on the hour of the day. Moreover, even though some failure occurs (i.e., at times, energy demand cannot be met fully), even in the worst-case scenario, ca. 87% of the daily energy demand is satisfied. A summary of the characteristics of the so designed mini-grid is reported in Table 6. In Figure 6, the mini-grid (designed plants) is sketched, with indication of the failure days per year n f . Table 6. Poli-ROR. Optimal solution. Characteristics of the best mini-grid (see Figure 6) designed (Methods M2, L max = 2500, n r = 19, α = 0.5). ID is identification code for the plant. ∆H gross is vertical jump (before hydraulic losses), Q max is maximum nominal flow, P nom is nominal power, E supplied is daily mean energy produced, S d is drainage area of the basin, n f is number of days with failure, e def% , maximum percentage daily deficit.

Future Flows, and Hydropower Potential
We focus here upon two specific time-windows, or periods. Period 1 P1 is at mid-century (2041-2050), while period 2 P2 is at the end of century (2091-2100). In Figure 7 below we report mean annual variations (percentage) of precipitation ΔP%, and stream flows ΔQ%, for P1, and P2, against the control run period CR (2004-2013), for different RCPs, and GCMs, plus the mean value for each RCP. Precipitation variations would be mostly positive during P1, P2. On average precipitation would increase by +7.5% in P1, and +8.5 during P2, with large variability; however, with visible projected decrease (−5.98%) only under RCP8.5 of ECHAM6 at half a century [11,66,71].

Future Flows, and Hydropower Potential
We focus here upon two specific time-windows, or periods. Period 1 P1 is at mid-century (2041-2050), while period 2 P2 is at the end of century (2091-2100). In Figure 7 below we report mean annual variations (percentage) of precipitation ∆P % , and stream flows ∆Q % , for P1, and P2, against the control run period CR (2004-2013), for different RCPs, and GCMs, plus the mean value for each RCP. Precipitation variations would be mostly positive during P1, P2. On average precipitation would increase by +7.5% in P1, and +8.5 during P2, with large variability; however, with visible projected decrease (−5.98%) only under RCP8.5 of ECHAM6 at half a century [11,66,71].
From Figure 8 above, at half century P1, flow duration would not change largely from now. From Figure 8 above, at half century P1, flow duration would not change largely from now. Conversely, at the end of century P2, low flows (i.e., for duration 180+ days) would increase, at least at the basin outlet in Rabuwa, which would suggest increase of hydropower potential (i.e., for the highest discharges, or longer periods of flow above turbine capacity). However, the potential for change of production depends upon complex interaction of stream flow, and turbine capacity for each hydropower station. During P1 under RCP, 8.5 nf is the smallest, while during P2 it increases with the RCP. This is possibly due to a large ice melt contribution during P1 under the warmest RCP8.5, which initially provides additional flows at thaw. However, during P2 ice would be largely depleted under RCP8.5, and nf increases accordingly. Compared to CR, a great number of the designed plants showed a decline of performances. In the worst case, the inhabitants will not be covered for ca. 40 days (plants 15,19) per year (vs. 24 under historical conditions, plant 2), and will further have a least energy production of ca. 60% (plant 1) of their demand (87% under historical conditions, plant 2). To test the performances of the designed grid under our potential future hydrological scenarios, we used the projected flow duration curves during P1, and P2 as inputs to Poli-ROR, to calculate the corresponding hydropower potential. As reported, we assessed the average number of failure days per year n f , and the maximum daily energy deficit per year e def% . Figure 9 below reports graphically the average (between the three GCMs) projected number of n f , and e def% for P1, and P2 under our three RCPs for the different plants, in numerical order (see location of the plants in Figure 6, Section 5.2). 6. Discussion

Improvement in Grid Design Using Poli-ROR
The heuristic construction procedure we used here as a base was developed for wind, and solar From Table 6, Figure 6 (Section 5.2), and Figure 9 above, one finds that ROR plants that drain the largest catchments, and in general plants along the main stem of the river, are less (little) affected, given that their nominal discharge (Q max ) is small (marginal) with respect to normal flows. In the smallest (highest) catchments, during P1, and P2 e def% increases from RCP 2.6 to RCP 8.5, reaching 20% or more (in the S-E area in Figure 6).
During P1 under RCP, 8.5 n f is the smallest, while during P2 it increases with the RCP. This is possibly due to a large ice melt contribution during P1 under the warmest RCP8.5, which initially provides additional flows at thaw. However, during P2 ice would be largely depleted under RCP8.5, and n f increases accordingly. Compared to CR, a great number of the designed plants showed a decline of performances. In the worst case, the inhabitants will not be covered for ca. 40 days (plants 15,19) per year (vs. 24 under historical conditions, plant 2), and will further have a least energy production of ca. 60% (plant 1) of their demand (87% under historical conditions, plant 2).

Improvement in Grid Design Using Poli-ROR
The heuristic construction procedure we used here as a base was developed for wind, and solar systems [79], and did not include the clustering step, which we introduced originally. This step was necessary because of the inherently different characteristics of hydropower networks. The original methodology, when applied to the hydropower problem, provided physically unfeasible networks. For instance, the designed grids may overlap on one another, with crossing of cables, and pipes. Water resources in a catchment is distributed along a (river) network, and not homogeneously spread like wind or radiation, and accordingly there is only one set of possible generation (source) points, belonging to the river. Moreover, hydropower plants generally require a larger nominal power, to produce energy with competitive price. Therefore, they are usually not convenient either for stand-alone systems, or for very small grids, and due to their branching nature, extended distribution networks are more prone to overlapping. To overcome this issue, we sought to partition the catchment in clusters as reported. Each cluster has a set of villages, inlet and outlet points, starting from which one mini-grid is designed, avoiding overlapping, and other unacceptable features.
Here we provide a comparison between the two methods, to give an insight of the gain from the clustering step. In Figure 10, we report the designed network obtained using the original method by Ranaboldo et al. [79], and the Poli-ROR algorithm (method M2). We used here L max = 2500, and α = 0.5, and a layout with an equal number of mini-grids, n r = 24, for fair comparison. Visually, the Ranaboldo et al. [79] model constructs more branched grids with respect to Poli-ROR. This leads to a major drawback, that transmissions lines belonging to one grid tend to intersect with those from other grids, as reported. In facts, at each step the original method looks out for the local optimum of each plant, and shapes the best mini-grid configuration (in terms of LCOE), considering only the demand points that have not been connected yet. As a result, the last mini-grids designed will try to connect very sparse demand points, with a high chance of intersecting already existing connections.
An example is seen in Figure 10a, where the original algorithm provides in the Central-Western part of the catchment two grids, namely grid 1 (dark red dots), and grid 17 (light green dots), very sparse, and displaying long connection patterns. Conversely, in Figure 10b, our algorithm provides three different grids (1, dark red 5, light red, 10, yellow) in the same area, that are much smaller and better clustered, thereby decreasing the mean connection length, related cost, and chance of intersection.
Similarly, in the South-Eastern part of the basin in Figure 10a, one has less organized, overlapping grids (especially 9, orange, and 22, light blue), whereas in Figure 10b, much better clustered grids are provided [24,33,59,87].  Another drawback of the method is that there is no control over the desired number of production points. Contrarily, in Poli-ROR the areas of influence for each plants are predefined, so that each demand point is tentatively connected to the closest plant. In addition, a better control on the desired number of hydro-power plants can be exerted, specifying the initial number of cluster n r . Differences also occur in terms of energy cost. The original algorithm finds a configuration with an average LCOE = 0.091 € kWh −1 , +34% than the one determined by Poli-ROR, LCOE = 0.068 € kWh −1 . Since the expansion process of the original algorithm aims at reaching the minimum local cost of each mini-grid, at each step some villages are obviously excluded. Most of the time, such villages are the ones located the furthest away from water. As a consequence, trying to connect them independently or with small mini-grids will result in a high per capita cost. Based on some sensitivity analysis upon L max , the only variable parameter in the original method (not shown, see Manara [86]), we found that the original model is always among the subsets with the worst economical performances, with an average LCOE considerably higher, and a share of connected villages nearby 90% or so, slightly lower than the best solution from Poli-ROR (93%). As such, Poli-ROR provides an improved approach to network design, namely one with a (much) lower cost as from LCOE, and a more feasible spatial pattern.

Potentially Modified Hydropower Potential under Climate Change
Climate change modifies the hydrological cycle, which clearly affects water resources availability. Among others, Soncini et al. [71] studied future flows in the upper part (closed at Periche) of the Dudh Koshi basin. In that study, the authors found that for such high altitude catchment, stream flows would increase in monsoon season, but would decrease yearly (−4% vs. CR on average) during 2045-2054. At the end of the century, a large reduction would occur in all seasons, i.e., −26% on average during 2090-2099.
Here, we found mostly increased streamflow overall, which suggests that future precipitation (and rainfall during monsoon) will be the most defining factor of hydropower potential.
Among others, Gautam et al. [26] suggested that hydropower plants in the Himalayas will suffer increasingly from climate change henceforth, especially those relying heavily upon the buffering of high altitude snow/ice reservoirs. Pathak [88] put forward that the increasing trend of glacial retreat, the variability of temperature, and precipitation may impact water resources and hydropower development in Nepal. Decreased runoff may affect hydropower development, but there is large uncertainty about future spatial variability of climate drivers. Here we found that the highest plants taking water from the smallest catchments would be more sensitive. However, the definition of the vulnerability depends upon complex topography, and climate, and requires accurate local hydrological modeling. Shrestha et al. [71] studied modified discharges in the Kulekhani watershed due to climate change, and power generation from the regulated Kulekhani reservoir. They considered future climate conditions from the A2 and B2 scenarios of the HadCM3 GCM for three periods (2010-2039, 2040-2069 and 2070-2099). They projected decreased yearly precipitation in all periods, with a decrease in precipitation/stream flows during the wet months (May-September), and increase during the dry months (October to April). Assuming hydropower plant operations for 7 h per day during CR period (1982-2009), average power production was projected to decrease by −30% for A2 and B2 scenarios.
Here, under potentially constant, or even increased stream flows in response to increased precipitation, the hydropower network may perform worse in some nodes. Clearly, in our case, given the lack of storage in ROR schemes, potentially buffering for water shortage period [89], the grid may suffer from periods of low flows, especially during the dry season. Notice that one may design the mini grid by feeding Poli-ROR with projected future stream flow series, maybe under a worst case scenario approach. This exercise was not pursued, as it is beyond the scope of the present work, but it may be of interest for future developments.
Among others, Hussain et al. [27] provided further ground for investigating the impact of climate change upon hydropower development in the Himalayas. They suggested that climate change induced extreme events are also major challenges to hydropower infrastructures (e.g., for rapidly enlarging glacial lakes GLs, [87]). Such facets require further investigation, and coupling hydropower risk analysis with glacio-hydrological models may help in this effort.

Limitations, and Outlooks
Some limitations may have hampered the current study, and development of Poli-Hydro, and Poli-ROR models. The low spatial density of meteorological stations and the relatively high percentage of missing data in the series made the hydrological modelling particularly challenging, especially for precipitation, which is knowingly characterized by an extremely high spatial variability in the complex Himalayan topography [58]. Data requirements for hydrological modeling, and portability of Poli-Hydro model are discussed elsewhere (e.g., [49]), and hydro-meteorological information is necessary. It should be noted that one could indeed use observed stream flows-although these are seldom measured over a dense network of stations-as required for spatially distributed assessment. However, if one was interested in hydrological projections pending future climate scenarios, hydrological modeling would be warranted. In cryospheric driven catchments such as those explored here, modeling of the snow/ice component seems necessary, at least in the high altitudes, and field data may be necessary. Here, we could exploit the findings of former studies.
Some limitations to application of the Poli-ROR algorithm were given by sparse information of population distribution, and their present and forecast energy demand. The grids were further designed under the simplistic hypothesis of being completely powered by hydropower energy, which made it necessary to limit the maximum nominal flow at each plant, to provide dependable energy production as far as possible. Despite such assumptions, and thanks to the abundance of water in the region, it was possible to largely fulfil energy demand. Whenever applying the method to other contexts, integration with other energy sources must be explored.
Some future developments may therefore be sketched. First, one would need to survey the actual spatial distribution of the population and their energy consumption patterns, including their variation in space and time, also to evaluate need of batteries to balance daily fluctuations. Moreover, since the use of electrical storage systems is not a viable option even for few days, one needs to explore the feasibility of (small) water storage, and/or backup generators. One could modify Poli-ROR to support planning of hybrid mini-grids, based on a mix of renewable energy sources (i.e., solar, wind). Moreover, it would be of interest to test the Poli-ROR algorithm to other study areas, to evaluate its performance and robustness.
Mini-hydro is a cost-competitive solution for rural electrification when adequately planned. Funding support programs in this direction could dramatically improve the living quality of the inhabitants, and as well decrease the pressure on the surrounding environment, still fostering tourism in this largely visited region. Even at a national level, exploiting the richness of the water resource could be an optimal strategy to mitigate pollution, and move to renewable energy sources. Models explicitly coupling catchment scale/regional hydrological modeling and hydropower potential analysis, including the potential effects of future climate change as we did here, may be of help in this effort.
Our study presents a tool to preliminarily assess hydropower potential, under a basin scale assessment. Clearly, details of the construction of specific ROR plants would need to be discussed based upon specific local focus. The design and construction of ROR plants indeed pose some critical points.
The presence of ROR schemes, and generally of hydropower plants, may impact river flow. Here, no reservoir is designed, so no regulation will occur. Moreover, we explicitly included a consideration of environmental flow release downstream of each plant in our analysis, to maintain the acceptable hydro-morphic quality of the river. However, in the design and construction phase of ROR plants, specific attention would be devoted to environmental conditions in the stream.
Furthermore, the design of each ROR power plant will have to include proper sediment load management (trapping structures, trapping efficiency, periodic removal via flushing, scouring, or trucking), which will require site-specific assessment. Recent studies provide large scale estimates of sediment load within the mountain catchments of Nepal, and within Koshi river, including Dudh Koshi here. Among others, Sangroula [15] reported sediment sampling at Chatara station of Koshi river, showing an average amount of annual sediment yield in the order of 2800 ton km −2 year −1 . Accordingly, sediment management in the area is critical.
The construction and operation of hydropower plants in topographically and societally complex areas of the Himalayas is a complex topic, with large socio-economic and political implications (e.g., [90,91]).
Overall, locally produced hydropower may give benefits to local people, possibly helping touristic activity, and reducing the pollution produced through the burning of kerosene, and other fuels for heating/cooking, as done nowadays.
A main risk associated with hydropower development in Nepal, and generally in the Himalayas, clearly relates to collapse of (large) dams and subsequent flood propagation in the wake of a geological (e.g., landslide), hydro-meteorological (e.g., flood), glacial (e.g., glacial lake outburst floods, GLOFs), or seismic (earthquake) event [90].
Given that ROR plants do not require large, potentially dangerous water storage, the risk for the downstream population may be decreased in this sense.
Potential topographic, and geomorphological changes in the catchment were not addressed here. The Koshi catchment overall is quite large. So, unless for very small headwater catchments, one can expect that local changes, possibly related to rapid mass movements such as landslides or debris flows, or transitions from glacial to not glacial landscapes, would not change largely hydrology.
Nor have we accounted here for seismic activity-however knowingly intense. Seismic activity, in our understanding, may affect ROR schemes in two possible ways; namely, (i) by damaging the network, and (ii) by modifying topography (i.e., causing changes in the landscape by faulting, and triggering landslides, etc.), with fallout upon hydrology, and energy production.
Accordingly, once the ROR network is designed, it should be then built according to anti-seismic rules and regulations, independently of the climate.
Notice also that a distributed ROR network may be more resilient in the face of natural disasters, because it is unlikely that all plants would break down at the same time.
However, the topic of network reliability against natural hazards does not fall strictly within the purview of hydrological sciences, and it clearly needs be tackled in further studies.

Conclusions
Nepal has large potential for hydropower production, to offset large use of fossil fuels, and air pollution thereby. Hydropower planning and implementation, both as (i) micro-hydro with ROR systems, and (ii) large hydropower regulation, is very necessary, especially in the face of the changing climate and increasing energy demand henceforth. In this study, we coupled a state of the art hydrological model Poli-Hydro, suitable for mimicking the complex hydrology of high altitude catchments, with a heuristic algorithm Poli-ROR¸to pursue the exercise of designing a mini hydro-power grid for the topographically complex Dudh Koshi catchment at the toe of mount Everest. Poli-ROR is based upon some demand-production indicators proposed in the present literature, and on the spatial distribution of the settlements to be served. Poli-ROR was compared against another recent design algorithm for energy grid design, providing evidence of some improvement. The resilience of the electrification scheme to potential future changes of climate/hydrology was also verified. We showed that mini-hydro here may be a suitable technology, able to satisfy local energy demand for 90% + of the population, with a cost comparable to that on the national grid. However, due to lack of storage, some plants may not be able to fully supply energy requirements for few days a year. This mismatch may be exacerbated, especially for those scenarios with the highest values of radiative forcing, and bring large cryospheric depletion at the highest altitudes. The method developed here profits from a knowledge of the hydrological processes within the case study catchment, and therefore requires basic hydrological information and modelling. However, at the cost of reasonable hydrological data gathering and subsequent modelling, the Poli-ROR algorithm is a powerful tool-usable for supporting the long-term design of ROR schemes, and generally for planning at a regional level. Poli-ROR surely provides a link between general, basin scale hydropower potential assessment, and subsequent site-specific analysis, that can be scaled and applied to other areas and topographically complex catchments. The presence of ROR schemes in the area may provide tremendous benefit to the population locally, by decreasing pollution, increasing the available energy, and fostering sustainable tourism; therefore, our preliminary findings may be of great use in this sense for scientists, water managers, policy makers.
Hydropower development in this area clearly does not only encompass technical issues, but it entails a large array of socio-economic and political implications. Within this complex framework, our approach may provide a technical help to hydropower planning.