Space-time variability of soil moisture droughts in the Himalayan region

Soil water is a major requirement for biomass production and therefore one of the most important factors for agriculture productivity. As agricultural droughts are related to declining soil moisture, this paper examines soil moisture drought in the transboundary Koshi River basin in the Central Himalayan region. By applying the J2000 hydrological model, daily spatially distributed soil moisture is derived for the entire basin over a 28-year period, 1980‒2007. A multi-site and multi-variable 15 approach – streamflow data at one station and evapotranspiration data at three stations – was used for the calibration and validation of the J2000 model. In order to identify drought conditions based on the simulated soil moisture, the Soil Moisture Deficit Index (SMDI) was then calculated, considering the derivation of actual from long-term soil moisture on a weekly timescale. To spatially sub-divide the variations in soil moisture, the river basin is partitioned into three distinct geographical areas, trans-Himalaya, the high and middle mountains, and the plains. Further, the SMDI is aggregated temporally to four 20 seasons – winter, pre-monsoon, monsoon, and post-monsoon – based on wetness and dryness patterns observed in the study area. The results indicate that the J2000 model can simulate the hydrological cycle of the basin with good accuracy. Considerable variation in soil moisture was observed in the three physiographic regions and across the four seasons due to high variation in precipitation and temperature conditions. Droughts have been increasing in frequency in the later years of the period under study, most visibly in the pre-monsoon season. Comparing the SMDI with the standardized precipitation index 25 (SPI) suggests that SMDI can reflect a higher variation of drought conditions than SPI. The novel contribution of this study is that a spatial and temporal variation of SMDI is calculated for the first time in the Central Himalayan region and for the Koshi River basin. This calculation is based on a high-resolution spatial representation of soil moisture, which was simulated using a fully distributed hydrological model. Our results suggest that both the occurrence and severity of droughts have increased in the Koshi River basin over the last three decades, especially in the winter and pre-monsoon seasons. The insights provided 30 into the frequency, spatial coverage, and severity of drought conditions can provide valuable inputs towards an improved management of water resources and greater agricultural productivity in the region.


Introduction 35
Droughts are considered one of the world's major social and economic hazards, and which have been increasing in recent decades. Given the central role of agricultural productivity in the economic development of a nation, water resource planners and managers need a system that can assess and forecast different forms of agricultural drought. There are different forms of drought but they are all linked to a great extent to precipitation and temperature variability (Mishra and Singh, 2010). There https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. plains, including other areas. In China, trends suggest that soil moisture droughts became more severe, prolonged, and frequent between 1950 and 2006, especially in northeastern and central China, suggesting an increased susceptibility to agricultural drought (Wang et al., 2011a). According to Su et al. (2018), in China, the estimated losses due to drought under a global 85 average temperature rise of 1.5°C will be ten times higher as compared with the reference period 1986-2005 and nearly threefold relative to 2006-2015. In Nepal too, a few studies have indicated increasing trends in different forms of drought. In the transboundary Koshi River basin (KRB), Shrestha et al. (2017) presented spatial and temporal trends in historically known drought events using the SPI. Joshi and Dangol (2018) suggested that the severe drought over the last ten years in one of the middle hill districts in the KRB 90 has caused major spring sources and rivers to dry up and compelled the local community to migrate to other areas with better water security. Wu et al. (2019) suggested significant spatial heterogeneity of droughts in the KRB with higher crop water shortage index (CWSI) values in its downstream (the plains of Nepal and India) and upstream regions (parts of China) than midstream (the middle and high mountains). Few studies have indicated warmer and wetter climate in the KRB towards the end of the century (Kaini et al. 2019;Rajbhandari et al. 2015) which might have adverse impacts on soil moisture and related 95 droughts in the future.
There are few agricultural droughts reported in the literature on the mountains region of Nepal. Some prominent drought events are the winter drought of 2005-2006 and the summer droughts of 1992 and 2005, which caused a decrease in agricultural production (Bhandari and Panthi, 2014;Dahal et al., 2016;Regmi, 2007).
The transboundary Koshi River basin, which straddles parts of China, Nepal, and India, faces both floods and droughts due to 100 its unique climatic system. The lowland Indo-Gangetic Plain, whose highly fertile lands provides food for millions of people, has a tropical climate dominated by the summer monsoon. The mountainous part in the southern Himalaya is also influenced by the monsoon but the spatial variation is very high due to the orographic effect. It has a temperate to alpine climate. The Tibetan Plateau in the northern part of the KRB has an alpine climate with dry and cold conditions, and is less influenced by the monsoon due to high mountain barriers. As such, there is great variability in the spatial distribution of annual precipitation, 105 ranging from 500 millimetres (mm) in the northern KRB to over 4,500 mm in southern Nepal (Karki et al., 2016).
This paper aims at assessing soil moisture droughts in the KRB. To understand soil moisture droughts, this paper considered the Soil Moisture Deficit Index (SMDI) as suggested by Narasimhan and Srinivasan (2005), for 28 years . For this purpose, the basin's soil moisture was simulated with the use of the process-based J2000 hydrological model, which was validated against observed discharge and evapotranspiration. The J2000 model has been successfully used to investigate 110 hydrological droughts in Central Vietnam (Firoz et al., 2018;Nauditt et al., 2017). This paper specifically investigates the spatial and temporal variability of soil moisture for the trans-Himalaya (Tibet), the high and middle mountains (Nepal), and the southern plains of the river basin (in Nepal and India). We also compared the SMDI with the SPI to identify the variation of the drought indication in space and time. SPI is a widely used index to characterise meteorological droughts on a range of timescales. To the best of our knowledge, soil moisture drought is being studied for the first time in the transboundary Koshi 115 River basin and this paper provides insights into its spatio-temporal variability in the historic time period under consideration.

Study Area
The Koshi is a major tributary of the Ganges River. The transboundary Koshi River basin (KRB) is located in the Central Himalaya. The world's highest peak, Mt Everest (8,848 masl), and the world's third highest mountain, Mt Kanchenjunga (8,586 masl), are located in the KRB (Figure 1). The river drains a region extending from the trans-Himalaya (the northern 120 slopes of the Himalaya in China) to the southern slopes of Nepal, and flows to the Indo-Gangetic Plain in India. Its total catchment area is 87,570 km 2 at its confluence with the Ganges River in Kursela, India (Figure 1). It covers much of eastern Nepal barring the Mai-Kankai River basin which originates from the Siwalik Hills of Nepal ( Figure 1, inset map). Chatara is https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. a gauging station where the model has been calibrated and validated, covering about two-thirds (about 58,000 km 2 ) of the basin's area. 125 Based on topography, the KRB is divided into five physiographic regions. The Terai region in the south is a low-lying plains area (60-300 masl). The Siwalik region is a narrow, foothill belt with an elevation of 300-1,000 masl, while the middle mountain region, with steep slopes and deep-cut valleys, is the widest strip, with elevations of 1,000-3,000 masl. The high mountain region, with elevations above 3,000 masl, is to the north and generally above the snow line (Dhital, 2015). The trans-Himalaya represents the Tibetan Plateau, located in China. This study investigates drought conditions in three regions, which 130 will be referred to as trans-Himalaya, mountains, and plains in the sections that follow (Figure 1

Methodological Approach 135
This section introduces the J2000 hydrological model, presents the model input data, describes the modelling strategy, and the calculation of the SMDI and SPI.

The J2000 hydrological model
J2000 is a modular, spatially distributed, process-oriented hydrological model developed inside the JAMS modelling system (Kralisch and Krause, 2006;Krause, 2001). The JAMS framework allows building hydrological models by combining 140 individual modelling components in a very flexible way. Existing JAMS models such as J2000 can therefore easily be adapted to address specific problems. Moreover, JAMS provides several functions that are often required during the development of hydrological models and application workflows, for example, for analysing model results or for performing model calibration or sensitivity analyses (Krause et al., 2009). To support more complex data processing tasks that typically occur when processing large datasets or during model calibration, the framework provides parallel computing functions (Kralisch and 145 Fischer, 2012) and service-based simulations on remote computer servers. The J2000 model has been widely used in river catchments around the globe including in the Himalayan region (Eeckman et al., 2019;Nepal et al., 2017;Shrestha and Nepal, 2019).
The J2000 model comprises modules to represent all important hydrological processes. A short description of the main process simulation modules is provided below. All of them contain some calibration parameters that have to be adapted during the 150 application of the model. A detailed description of these parameters, and the modules to which they are related, are provided in Nepal (2012). To represent hydrological processes within the watershed in a spatially distributed way, the spatial discretization concept of hydrological response units (HRUs) (Flügel, 1995) is used to delineate modelling entities. It will be described in section 3.2. A second type of modelling entity in J2000 are river segments (reaches), which are used to represent water transport in the river bed. The model uses a fixed temporal resolution of daily time steps. Accordingly, the hydrological 155 process simulation is performed at each time step and for each HRU. It can be summarised in the following way.
In a first step, climate input parameters that are provided as point data (for example, measurements at climate stations) are interpolated such that a local value is generated for each HRU and time step. These climate parameters include min/mean/max temperature, precipitation, humidity, sunshine duration, and wind speed.
The distribution of precipitation between rain and snow is simulated depending on the air temperature. To determine the 160 amount of rain and snow, it is assumed that temperatures below a certain threshold result in precipitation entirely as snow and those exceeding a second threshold results entirely in rainfall. The interception module uses a simple storage approach and assumes a maximum interception storage capacity based on the leaf area index (LAI) of the respective land cover. The snow https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. module calculates the different phases of snow accumulation, metamorphosis, and snowmelt. Snowmelt depends on the energy input provided by the air temperature, and the soil heat flux, and is considered as the potential melt rate. The snowpack can 165 store liquid water in its pores up to a certain critical density. In the model, the snowmelt runoff from the snowpack is passed to the soil module through infiltration. The antecedent soil moisture conditions influence the rate of infiltration (Krause, 2001).
In the glacier area, the same snowmelt process is applied. The glaciated area is divided into clean and debris-covered glaciers, based on slope and elevation. In the case of the KRB, glaciers at an elevation above 4,500 masl and with slopes greater than 15 degrees are considered as clean. Once the seasonal snow cover melts, glacier ice melt starts. This is estimated based on an 170 enhanced degree-day factor approach which takes into account temperature, radiation, and whether the glacier is clean or debris-covered. Rainfall on the glacier's surface is also taken into account. The run-off from the glacier area is separated into the components snowmelt, glacier ice melt, and rain run-off. All of them are then routed to the next stream in the reach networks (Nepal et al., 2014). The potential evapotranspiration is calculated according to the Penman-Monteith approach (Allen et al., 1998). This approach considers the meteorological input regionalized for each HRU in the first step to calculate the potential 175 evapotranspiration.
The central and most complex component of the J2000 model is the soil water module, which controls the regulation and distribution of the consecutive water fluxes. The soil zone of each HRU is subdivided into two storages according to the specific pore volumes of the soil. Middle pore storage (MPS) represents the pores with a diameter of 0.2-50 µm, in which water is held against gravity but can be reduced by plant transpiration as part of the evapotranspiration process. Therefore, in 180 the J2000 model context, soil moisture is considered up to the depth at which plant root depth can affect the availability of soil moisture. It is therefore different for different land cover types. The MPS thus represents the usable field capacity in the model.
Large pore storage (LPS) represents the pores with a diameter of more than 50 µm. These cannot hold water against gravity and provide the water fluxes for the subsequent compartments and run-off components using calibrated delay functions. The direct rainfall and other water inputs (for example, from snowmelt) can provide inputs to the soil water through the infiltration 185 process. Water in the LPS is distributed into lateral components (outflow as interflow) and vertical components (outflow as percolation), depending on the slope. Water storage will be depleted by the actual evapotranspiration, which is limited by the potential evapotranspiration and the actual water saturation of the MPS (Krause, 2001).
For the SMDI calculations, this study considered soil moisture as the water which is stored in the MPS. The LPS was not considered because the water in large pores is not used in evapotranspiration directly (only by diffusion to the MPS) and 190 leaches out of the soil. The water inputs for the soil module are from snowmelt, rainfall, and lateral fluxes from HRUs located upstream. First, infiltration is calculated by an empirical approach, based on actual soil moisture and the maximum infiltration parameter differentiated in summer, winter, and snow cover situations. Any water not able to infiltrate is stored at the surface in a depression storage up to a certain amount, and any surplus is treated as surface runoff and routed to the adjacent downstream HRU or river reach. Infiltrated water is distributed between the MPS and LPS depending on the actual water 195 saturation of these storages. The percolation is conveyed to the groundwater module. The interflow is routed to the next HRU or river reach.
The groundwater module of the J2000 model follows a simple storage concept, which contains two groundwater storages for each HRU. The storage in the upper groundwater zone can be considered as the weathered layer on top of bedrock (Supplementary Figure 1). Similarly, the storage in the lower groundwater zone represents saturated groundwater aquifers. 200 The input from percolation is distributed between the two storages depending on the slope of the model unit and a distribution parameter. The calculation of water discharge from the two storages is done according to the current storage amounts in the form of a linear outflow function using storage retention coefficients for the two storages.
The J2000 model features two routing modules. The lateral routing between HRUs describes water transfers within a flow cascade from one HRU to another from the upper catchment areas until it reaches a stream. The second routing module 205 simulates flow processes in a stream channel by using the commonly applied kinematic wave approach and the calculation of https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. velocity according to Manning and Strickler (Krause, 2001). The only model parameter that has to be estimated by the user is a routing coefficient, which influences the travel time of the water within a reach. In addition to the water transport within a reach, the routing module also simulates the water transfer to the adjacent downstream river reach until it reaches the catchment outlet. 210

Model input data
The J2000 model uses a representation of the catchment and its distributed hydrological characteristics based on hydrological response units (HRUs) (Flügel 1995). The Digital Elevation Model (DEM), and the land use, soil, and geology maps were analysed and combined in an overlay analysis to derive the HRUs (Error! Reference source not found.). Altogether, 18,557 HRUs were delineated within the Koshi River basin with an average size of the HRUs as 4.7 km 2 . The HRUs were further 215 separated into three regions (trans-Himalaya, mountains, and plains) for a spatially separated analysis of modelling results and SMDI calculations.
The discharge data and potential evapotranspiration (PET) data used to validate the model were acquired from the Department of Hydrology and Meteorology, Nepal (DHM). In addition, precipitation datasets of the Asian Precipitation -Highly-Resolved Observational Data Integration Towards Evaluation of Water Resources (APHRODITE) project and temperature datasets of 220 the Climate Forecast System Reanalysis (CFSR) project were used for the data-scarce trans-Himalaya region of the KRB. For the lowland plains of the river basin, datasets of the Indian Meteorological Department (IMD) were used for both precipitation and temperature. For the portion of the basin in Nepal, meteorological input datasets (pertaining to precipitation, temperature, relative humidity, wind, and sunshine hours) acquired from the DHM were used in the model. The number of stations for different climate variables are provided in Supplementary Table 1.  225 Based on the datasets used, Supplementary Table 2 shows the average monthly and annual precipitation and temperature for the period 1980-2007 of three physiographic regions of the KRB. The high and middle mountains get the highest annual precipitation (~2,100 mm) while the trans-Himalaya gets the lowest (~575 mm) with the plains (~1,600 mm) in between. Much of the precipitation in all these three regions falls during the monsoon season (June-September). The average monthly temperature differs drastically between the three regions. Trans-Himalaya exhibits the highest temperature variation with a 230 high of 7ºC during July (summer season) and a low of -13ºC during January (winter). The plains have the highest temperature for each month as it has the lowest elevation (30-280 m). The average monthly temperature varies from 16ºC to 30ºC in the plains. The average monthly temperature for the high and middle mountains has a range of 7ºC-20ºC ( Figure 2).

Calibration and validation 235
The J2000 hydrological model was applied daily between 1979 and 2007. Since the PET is not calibrated in J2000, the model was validated with PET data from three locations (Kathmandu, Okhaldhunga, and Jiri) in the mountains of Nepal first ( Figure   1). Measured PET data at these locations was compared with PET data from the model. After this, the model was manually calibrated and validated with the discharge data at Chatara. We have taken base parameter sets from the Dudh Koshi River basin from Nepal et al. (2014). Nepal et al. (2017) also showed the spatial transferability of parameters from Dudh Koshi to 240 Tamor catchment within the Koshi River basin. Similarly, Eeckman et al. (2019) also used Dudh Koshi parameters for micro catchments (~5 km 2 ) within the Dudh Koshi basin and suggested that the parameters related to groundwater, surface run-off coefficient, and percolation may change due to the scale of the watershed. In this study as well, a few parameters such as surface and groundwater recession, percolation, and flood routing were changed to match the discharge response for the Koshi basin (Supplementary Table 3). The time period 1985-1995 was used for calibration and 1996-2007 for validation. Due to the 245 unavailability of discharge data from the Indian part of the river basin, the model was first calibrated and validated with the https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. discharge data at Chatara, Nepal ( Figure 1). After calibration and validation at Chatara, the model parameters were applied to the whole river basin (including those parts in India, area 87,530 km 2 ) to simulate the required variables of the downstream part of the Koshi. The results are compared with four efficiency criteria, namely, the NSE: Nash Sutcliffe Efficiency (Nash and Sutcliffe, 1970); KGE: Kling Gupta Efficiency (Gupta et al., 2009); R 2 (coefficient of determination); and PBIAS 250 (percentage bias). Based on the calibration and validation, soil moisture analysis was conducted for the period  (with 1979 as a warm-up period).

Calculation of the Soil Moisture Deficit Index
The Soil Moisture Deficit Index (SMDI), developed by Narasimhan and Srinivasan (2005), accounts for variability in soil moisture over a long period. Soil moisture can be derived from hydrological models as an intermediate result along with other 255 components of the hydrological cycle (for instance, discharge). Soil moisture is one of the most important parameters in assessing agricultural drought, and the number of SMDI applications to assess it has grown in recent years.
The SMDI was developed with three major characteristics: the ability to assess short-term dry conditions, the ability to indicate drought in any season, and the ability to function in any climatic zone. These characteristics of the SMDI are ideal for agricultural drought monitoring (Narasimhan and Srinivasan, 2005). The calculation of the SMDI involves the calculation of 260 the soil-water deficit (SD) from soil water/moisture (SW). An average weekly soil moisture product can be used as an indicator of short-term drought, depending upon the availability of soil moisture data at different depths or in a lumped way. The J2000 hydrological model computes soil moisture in the root zone of the soil profile. This is a useful index for identifying and monitoring droughts affecting agriculture. The SMDI has a value between -4 (extremely dry) to +4 (extremely wet) and is derived as defined in Equation 1. 265 The SMDI is categorized as extremely wet (+4 to +3), severely wet (+3 to +2), moderately wet (+2 to +1), normal (+1 to -1 ), moderately dry (-1 to -2), severely dry (-2 to -3), and extremely dry (-3 to -4), which reflect the range of soil moisture conditions. The equation for the calculation of the weekly SMDI is presented below: Where, w indicates week and y indicates year; SD = soil water deficit; MSW, min (SW), and max (SW) = median, minimum, and maximum soil water, respectively.
The calculation of the SMDI has been implemented in the JAMS modelling system using two individual JAMS components, 275 namely SMDI_DataCollect and SMDI_Calc. The first component is used to collect soil moisture data for each HRU during the normal hydrological simulation with J2000. In addition, this component also calculates long-term soil water statistics for each HRU (for example, MSWw). Once this is finished, the second component (SMDI_Calc) will calculate the SMDI values for each HRU based on their weekly soil moisture values (SWy,w) and long-term statistics (MSWw, minSWw, maxSWw). While weekly intervals are used as the default, the component can calculate SMDI values based on any given aggregation period, for 280 example, to consider individual characteristics of specific vegetation types. As described above, the HRUs were segregated into three geographical regions, trans-Himalaya, mountains, and plains, as the climatic conditions are different in each of these zones. Similarly, the SMDI values were analysed separately for four seasons: monsoon (June-September), post-monsoon (October-November), winter (December-February), and pre-monsoon (March-May). Since these seasons are defined based on variations in precipitation and temperature, the SMDI is calculated for these seasons to track the variation caused by these 285 meteorological drivers. https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.

Calculation of the Standardized Precipitation Index
The Standardized Precipitation Index (SPI) is the most commonly-used indicator for detecting and characterising meteorological drought on different timescales. We calculated the seasonal SPI which was implemented as a JAMS component. The SPI is calculated based on a long-time series of precipitation data. The SPI measures precipitation anomalies 290 based on a comparison of observed total precipitation amounts for an accumulation period (for example, 1, 3, 12, or 48 months) with the long-term historic record for that period. The probability distribution of the historic record was fitted to a gamma distribution, which was then transferred to a normal distribution to get a mean SPI value of zero (McKee et al., 1993;McKee et al., 1995). To compare the seasonal SMDI with the SPI, we calculated the SPI data for the same period of four seasons used to calculate the SMDI. In this manner, the occurrence of drought based on the SPI and SMDI in different time intervals can be 295 compared.

Validation with potential evapotranspiration data
The PET validation was performed at three observed evaporation stations, at Kathmandu, Okhaldhunga, and Jiri in Nepal,300 where the PET was estimated using a class-A pan. Due to the lack of consistency in the PET data, it was not possible to validate the model results for a common period at all stations. These three stations were chosen for the validation of PET as they have data for a longer period with little missing data. The stations also depict elevations between 1,300-2,000 masl. The J2000 model calculates daily potential evapotranspiration using the Penman-Monteith equation (Allen et al., 1998). Further, these daily values were aggregated to monthly sums and compared with the observed data. 305 The graphical plots (time series and scatter plots), as well as the coefficient of determination (R 2 ), show that the model has simulated monthly PET at Okhaldhunga and Jiri stations relatively better than at the Kathmandu station ( Figure 3, Table 1).
Although the monthly variability is captured well in Kathmandu, the over-prediction in springtime is evident. This might be related to the fact that about 25% of the data was missing, a higher proportion as compared to the other two stations (15% in Jiri and 3% in Okhaldhunga). The overall amount of PET is captured well by the model indicated by PBIAS derivations from 310 -0.05% to 9.4%.

Validation with discharge data
The calibration was carried out using daily discharge data from 1985 to 1995 and validation was carried out from 1996 to 2007 using measurements at the Chatara discharge station. The calibrated parameters of the J2000 model for the Koshi river and their range are listed in Supplementary Table 3. 315 Figure 4 shows the comparison between observed and simulated daily streamflows at Chatara for the calibration and validation periods. Table 2 shows the statistical evaluation based on four chosen objective functions. Figure 4 indicates that the model reproduced the overall trend of observed data in the calibration period, which has been reflected in the NSE (0.95), KGE (0.93), and R 2 (0.95). However, there is some underestimation, especially during the flood season, during most of the initial years. The PBIAS is -4.6% during the calibration period, indicating reasonable model simulation with slight 320 underestimation. During the validation period, the overall hydrograph pattern is represented well as indicated by the NSE

Temporal and spatial variability of the soil moisture conditions
The temporal and spatial variability of soil moisture are mainly influenced by two kinds of factors. Precipitation, on the supply side, increases soil moisture. On the demand side, land use and land cover, temperature, and other climatic variables decrease the moisture content of the soil. Higher temperatures could increase evaporation and transpiration from the soil. Here, we 330 discuss the temporal and spatial variability of precipitation and temperature of the river basin, soil moisture variability, and the soil moisture drought index, as simulated by the calibrated and validated model.

Temporal variability of precipitation and temperature
The SMDI is calculated for the three study regions in the KRB (Figure 1) -trans-Himalaya, mountains and plains. Most of the variation in the soil moisture is due to the dynamic relationship of precipitation and temperature and other variables within 335 the basin. Figure

Temporal variability of soil moisture
The modelling applications provided data on the daily variability of the soil moisture (MPS) in J2000. The daily soil moisture 350 value of each modelling entity (HRU) is used to derive weekly SMDI as defined in Equation 1. Supplementary Figure 2 shows the variation in weekly soil moisture for the KRB. Figure 7 and Supplementary Figure 2 show the variation in soil moisture in each week; the most stressful period is around the pre-monsoon season. This is mainly due to low rainfall and high temperatures at that time of year, which causes higher evapotranspiration and less soil moisture. When precipitation begins during the monsoon season, the soil water content increases and saturation is reached at the maximum level. After the post-355 monsoon season, the soil moisture starts decreasing until the pre-monsoon season of the following year. About 3% of the basin's area is glaciated, and not considered for the analysis of soil moisture as there is no interaction between the glacier module and the soil module in the model. To demonstrate spatial and temporal variability, the SMDI values are shown for three physiographic regions in the basin in Figure 8. The analysis has been carried out for four seasons in the region: winter, pre-monsoon, monsoon, and post-monsoon.

Spatial and temporal variability of SMDI in the trans-Himalaya 365
The interannual variability of the SMDI in the trans-Himalaya region for all the four seasons is shown in Figure 8 (left) . Dry conditions (SMDI value below -1) are highly prominent during the winter and pre-monsoon seasons, and to a lesser degree during the post-monsoon season. The trans-Himalaya region is in a dry condition for most of the year especially during 1983-1995, and 2001-2007 during the winter and pre-monsoon seasons. More than half the total area of the trans-Himalaya region is under dry conditions between 2001 and 2007 in winter and in the pre-monsoon season during 1989-1992, 1994-1995, and 370 2001-2007. During the monsoon season, dry conditions are prevalent throughout the study period except for 1980, 1981, 1996, and 1998-2000. The occurrence of dry conditions is erratic in the post-monsoon season but with high spatial coverage, more than 70% in 1982, 1991, and 1994, and  Three of the lowest precipitation years during the study period occurred after 1998 (1998, 2005, and 2007). The average surface 375 temperature has also steadily increased in the winter season. Only positive temperature anomalies are observed after 1998 in the winter season.
In the pre-monsoon season, the dry conditions probably derive from the temperature, which increased after 1998 up to 2004 (Figrue 6). The three lowest years of monsoon precipitation occurred during 1982, 1983, and 2006, which coincides with the dry conditions in that period. A positive temperature anomaly is seen during the monsoon after 1987 barring a few years such 380 as 1992, 1996, and 1999, which also translates into dry conditions during those periods. However, the interannual variation in precipitation is low for the monsoon season in the region.
The data shows a positive post-monsoon temperature anomaly after 1999, except for 2004, which translates into the dry conditions in that period. Post-monsoon precipitation is highly variable in the region leading to high interannual variability in dryness in the region 385

Spatial variability of SMDI in the mountains
The interannual variability of the SMDI in the mountains for all four seasons is shown in Figrue 8 (middle). Dry conditions (below an SMDI value of -1) are prominent in the pre-monsoon and post-monsoon seasons. The winter season shows wet conditions (above an SMDI value of 1) for most years except during 1980, 1981, 1990, 2000, and 2005. However, about 50% of the total area of the region experienced dry conditions in those years as well. More than 50% of the area experienced dry 390 conditions during the pre-monsoon season in 1980, 1988, 1991, 1992, 1995, and 1999.
The monsoon season is largely wet except for the years 1992 and 2005, when about 50% of the area observed dry conditions.
The post-monsoon season shows high variability regarding dry and wet conditions in this region with dry conditions prevalent in 1981, 1984, 1988, 1991, 1994, and 2000. The area under dry conditions seems to go up to 75% in some of these years. The

Spatial variability of SMDI in the plains
The interannual variability of the SMDI in the plains for all four seasons is shown in Figure 8 (right). Dry conditions (below 405 an SMDI value of -1) dominate in the pre-monsoon and post-monsoon seasons. During the winter season, wet conditions (above an SMDI value of +1) prevail for most years except 1982, 1992, 1994, 2005, and 2007. Between 30%-50% of the total area of the region is under dry conditions in those years in the winter. In the pre-monsoon season, most of the area is in severe dry conditions (below an SMDI value of -2) from 1991 to 1996. The monsoon season is largely wet in this region except during 1992, 1994, and 2005, when about 80% of the area has dry conditions, with some of the area under extreme dry condition 410 (below an SMDI value of -3) in 1998.
The post-monsoon season shows high variability in soil moisture conditions in this region with dry conditions prevalent in 1981, 1984, 1988-1994, 1997, 2000, and 2004-2007 This correlates with dry conditions in those periods. Only positive temperature anomalies can be seen in the pre-monsoon season after 1998. The dry conditions in the post-monsoon season may be attributed to the highly variable precipitation in this 420 region ( Figure 5) with values ranging between 50-300 mm. The three years with the lowest post-monsoon precipitation were 1981, 1984, and 1997. The temperature anomalies are also positive in most years after 1992. Figure 9 shows the SPI values for the four seasons and three regions during 1980-2007. The positive SPI values indicate a prevalence of higher precipitation than the long-term average and negative values indicate lower precipitation than the long-425 term average. Comparing SPI figures with SMDI ( Figure 8) indicates that SMDI shows a higher variation of soil moisture conditions than SPI for the same period.

Comparison of SMDI and SPI
In the trans-Himalaya, the period after 2001 has positive SPI values (Figure 9, left) in the pre-monsoon season in most areas whereas the SMDI (Figure 8, left) shows moderate to extreme dry conditions. In the winter season, the SMDI shows a higher degree of dryness than the SPI. In 1999 (winter), although the SPI is very low (one of the three lowest precipitation years), the 430 SMDI shows wetness in much of the area. Although 2006 (winter) shows the lowest SPI, only 25% of the area is under the severe dry conditions as per the SMDI value. Only in some years or in seasons therein do both the SPI and SMDI indicate similar dry conditions, such as in the winter of 2006, the pre-monsoon season of 1984, 1994, and 1996, the monsoon season in 1982, 1983, 1994, 2005, and 2006, and the post-monsoon season in 1981, 1991, and 1994. Figure 5 also indicates one of the lowest levels of precipitation during these periods. 435 In the mountains, the SMDI (Figure 8, middle) shows a higher variation in soil moisture conditions as compared to the SPI ( Figure, middle). In 1999 (winter), the SPI shows extreme values (below -2) in 50% of the area but the SMDI shows moderate to severe values in the equivalent area. It is only in some years that both the SPI and the SMDI indicate matching dry conditions-2006 (winter); 1992, 1995, 1996, and 2005 (pre-monsoon); 1992 and 2005 (monsoon); and 1981, 1984, 1991, and 1994 (post-monsoon). These periods also have the lowest rainfall as indicated in Figure 5. 440 In the plains as well, the SMDI (Figure 8, right) shows a higher variation in soil moisture conditions compared to the SPI (Figure 9, right). In the pre-monsoon and post-monsoon seasons, after 2004, the SPI shows normal conditions in the majority of the areas, whereas SMDI shows moderate dry conditions. During 1996During -2004, the SPI shows normal conditions whereas the SMDI shows moderate wet conditions. Only in some years do both the SPI and SMDI indicate matching soil https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. moisture conditions: 2001 and2006 (winter);1994, 1995, and 19961992, 1994, and 2005and 445 1981, 1984, 1991, and 1994. These periods also have the lowest rainfall as indicated in Figure 5.
From the above observations, it is evident that the SMDI is able to reflect variations in soil moisture conditions much better than SPI which usually shows normal conditions. The years for which both SPI and SMDI show matching drought conditions can be mainly attributed to them being the lowest rainfall periods ( Figure 5).

4.2.4
Spatio-temporal drought events 450 SMDI values lower than -3.0 are considered here as extreme soil moisture-deficit conditions and can be interpreted as a 'drought'. To understand the spatio-temporal extent of droughts in the KRB, weekly events as a percentage of total weeks in a given season when the three regions are under extreme drought are shown in Figure 10. This shows the temporal variation in periods when droughts are most severe. The total number of weeks for each season are: winter and pre-monsoon (13 weeks each), monsoon (18 weeks) and post-monsoon (8 weeks). 455 In the trans-Himalaya, droughts are prominent in the pre-monsoon and winter seasons. A continuous drought can be seen during 2001-2007. In particular, in 50% of the area, drought occurred in at least half the pre-monsoon period (and up to 90% of the area in some places). In 2002 and 2007, more than 70% of winter weeks are under drought. Pre-monsoon drought is also frequent in all the years except 1980-1982 and 1996-2000. In the monsoon season, about 25% of the weeks witness drought in most years, with a few exceptions. Frequent droughts are also observed in 1982, 1991, 1994, and 2006 in the post-monsoon 460 season. In 1982, more than 60% of the area has a drought in about 90% of the weeks. Figure 10 (left) also suggests that there is an increasing trend in the frequency of droughts in recent years during winter and in the pre-monsoon season.
In the mountains (Figure 10, middle), drought is most prominent in the pre-monsoon and winter seasons. Continuous drought can be seen for about one-third of the winter season over about 15% of the land area every year, and in some years up to 25%-40%. Severe droughts are seen more frequently in the pre-monsoon season and over a wider area. In some years, such as in 465 1989, 1992, 1995, and 2006, drought occurred over more than 50% of the area and up to 75% in 1992. In the monsoon season, a smaller area is under drought as this region receives the highest precipitation then (Figure 2; Supplementary Table 2).
Droughts are less severe in the post-monsoon season, as compared to the pre-monsoon season. However, there are cases of drought in 40% of the weeks in 1991and 1994. In 1991, this was in 25% of the region and up to 50% in 1994 In the southern plains ( Figure 10, right), drought is prominent in the pre-monsoon and winter seasons. The magnitude of 470 drought is higher in the pre-monsoon season than the winter season. There are continuous drought events from 1989 to 1997 where, in 40% of the pre-monsoon weeks, the drought extends to more than 50% of the area, and in some years, up to 75% of the area. In 1995 in particular, up to half the region's area has drought for about 90%-100% of the pre-monsoon period. The drought is only visible in about 10% of the monsoon period in about 25% of the area. In the post-monsoon season of 1988 and 1994, nearly 75% of this region experiences drought for more than 40% of the weeks. This higher incidence of drought in the 475 plains is mainly due to it having the highest temperatures among the three regions of the KRB (Figure 2; Supplementary Table   2).
Thus, at the KRB scale, the higher incidence of soil moisture deficit is in the plains which is mainly due to higher temperatures.
In the trans-Himalaya, droughts persist for a higher number of weeks in the seasons mainly due to low precipitation. A higher frequency of drought is observed in the winter and pre-monsoon seasons. The monsoon season is least affected by the drought 480 due to abundant precipitation at this time but even so, about one-quarter of the season is affected (Figure 10).
We also looked at the maximum and average drought coverage for different seasons Figure 11. Here, we calculated the maximum area covered by drought in any particular week of the season, and the average area over all weeks of the season. While the variability of maximum area coverage in the trans-Himalaya region and the plains is higher than in the mountain regions, the pre-monsoon season in the mountains also shows a higher degree of variability compared to other seasons.
Although the average area affected by drought is lower during the monsoon season in all the regions, the maximum area coverage is higher than other seasons and in some years have reached more than 50% of the area in the trans-Himalaya and the plains. This indicates that, although wetness prevails in the monsoon season, drought could reach more than 25% of the 490 region's area for at least one week. During the post-monsoon season and in winter, the average area and maximum areal coverage have smaller differences, which indicates that the spatial coverage of drought prevails in most of the region during these seasons.

Historical incidence of drought
We examined historical drought events and their impacts on agriculture based on the published literature. The soil moisture 495 drought derived by our study also matches the historical drought events in Nepal mainly of 2005Nepal mainly of -2006Nepal mainly of (winter) and 1992Nepal mainly of and 2005. Dahal et al. (2016) and Shrestha et al. (2017) reported dry spells in central Nepal during the winter of 2005-2006 and their implications for agriculture. Our results for the same year also showed that more than 75% of the area in the mountains had an SMDI below -1. Drought (SMDI < -3) occurred in more than half the Koshi River basin's area for more than 40% of the 500 winter. This winter drought of 2005-2006 had the highest spatial coverage in the mountains region over the 28-year period under study (Figures 8 and 10). Dahal et al. (2016) reported less than 30% winter rainfall in 2005-2006, with some areas receiving no precipitation at all. As a consequence, paddy production decreased by 13% compared to the previous year; in some districts in the eastern and central region of Nepal (where the Koshi River basin is located), the reduction in yields was 20%-50%. About 7% of the land under paddy was also reportedly left fallow. Wheat production was adversly affected as well. 505 As the winter drought of 2005-2006 affected the whole of Nepal, a decrease in paddy and wheat production was also reported from the western region. Subsistence hill and mountain farmers were affected in particular as they tend to be more dependent on rainfed agriculture than farmers in the plains, where irrigation infrastructure is prevalent. Regmi (2007) reported that agricultural production declined by 27%-39% that year in a few districts in the Eastern Development Region compared to the previous year. On average, yields in the Eastern Development Region were about 10% lower than the previous year and almost 510 15% of the land under paddy was left fallow. Dahal et al. (2016) and Shrestha et al. (2017) also discussed the summer drought of 2005 in central Nepal. Our analysis also showed the 2005 monsoon drought as the largest in terms of area; more than 50% of the mountains area experienced drought (SMDI < -3.0) in 25% of the weeks (Figure 10). Bhandari and Panthi (2014) reported the 1992 drought in the monsoon season in western Nepal. The insufficient and untimely 515 rainfall contributed to reduced soil moisture, resulting in an agricultural drought and consequent crop failures. From our own analysis, 1992 is reported to have the highest soil moisture deficit for the pre-monsoon and monsoon seasons, during which nearly 90% of the area in the mountains have SMDI values lesser than -1.0, with a higher degree of dryness in the pre-monsoon season (Figure 8). The drought that year (SMDI < -3.0) was the highest for the pre-monsoon season and second-highest for the monsoon season when about 75% and 45% respectively of the basin's area in the mountains experienced droughts for more 520 than 25% of the weeks. Even during the winter of 1992, 40% of the basin's area suffered drought for 25% of the weeks (and over half the winter season in 25% of the area) ( Figure 10). Shrestha et al. (2017) also reported the severe summer drought of 1992, based on SPI indices using both observed and satellite data. Shrestha et al. (2000) showed a good agreement between the deficit rainfall in 1992 in Nepal and the El Nino of 1992 and 1993.
Although Bhandari and Panthi (2014)'s analysis was mostly focused on western Nepal, the monsoon's influence extends 525 throughout Nepal, as it passes from eastern through to western Nepal. In the KRB, 1992 was among the three lowest rainfall https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. years in the pre-monsoon and monsoon season. Our assumption is that a similar drought condition must have occurred in the eastern mountain districts of the Koshi as well. We didn't find information about reported droughts in trans-Himalaya and Bihar for the period under study. While the trans-Himalaya part of the KRB has little agriculture land, the presence of irrigation infrastructure in Bihar makes the context quite 535 different from the mountains, where agriculture is mainly rainfed.

Conclusions
This study looks at the Soil Moisture Deficit Index (SMDI) in the transboundary Koshi River basin straddling China, Nepal, and India by applying the process-based J2000 hydrological model. The model has been calibrated and validated using multisite evapotranspiration and discharge data. This study presents the first comprehensive results of the spatial and temporal 540 variability of soil moisture for the Koshi River basin.
The application of the model has resulted in the following conclusions: 1) The J2000 model can simulate the different parts of the hydrograph for the entire simulation period. However, flood peaks and overall flooding periods have been simulated with a slightly lower accuracy for some years.
2) The temporal variability of soil moisture indicates that the highest stress is during the pre-monsoon season. The results also suggest that the SMDI represents soil moisture conditions better than the SPI, as the latter depends only on precipitation. On the other hand, in the SMDI, both precipitation (as a supply) and evapotranspiration (as a demand) have been duly reflected. Our results suggest that the SMDI can provide a better understanding of soil moisture variation and related 560 droughts, and hence might be useful in the agricultural sector, on which millions depend in this entire region. The insights into the frequency, spatial coverage, and severity of drought conditions throughout the basin can further provide valuable inputs towards an improved management of water resources and the planning of agricultural production. In addition, the understanding of soil moisture processes from this study and response to climatic variables can be expanded to understand the future climate change impact on soil moisture conditions. 565 https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.
Code availability: The source code for the JAMS-J2000 hydrological model and SMDI and SPI calculation are available at http://jams.uni-jena.de/downloads/.
Data availability: The model outcome of both hydrological and soil moisture dataset can be made available upon request. The details of model input data are provided in Supplementary Table 1 and can be accessed freely, except a few stations data which 570 was provided by the Department of Hydrology and Meteorology. These observed data is not allowed to distribute publicly by the department.
Author contribution: All authors contributed to analysis, writing, review and editing. SN, SP, NS and SK contributed to the conceptualization of the study. SK implemented the SMDI and SPI modules in JAMS modelling system. SN, SP and NS collected model input data, performed simulations and contributed and wrote the original draft and visualization. 575      https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License. https://doi.org/10.5194/hess-2020-337 Preprint. Discussion started: 26 August 2020 c Author(s) 2020. CC BY 4.0 License.