The Naryn River (Fig. ) originates in the Tien Shan mountains in Kyrgyzstan and flows west through the Ferghana Valley into Uzbekistan, where it merges with the Kara Darya River to form the Syr Darya. The river is an important source of freshwater for agriculture downstream in the heavily irrigated Ferghana Valley . According to the Randolph Glacier Inventory Version 6 , there are currently 1784 glaciers in the catchment. Glaciers are found at elevations ranging between 2815 and 5125 m and are predominantly located in the east of the catchment and to a lesser extent in the north-west. Rock glaciers are also common above around 3000 m, especially downslope of contemporary glacier termini, and these represent considerable (if unquantified) ice and future water resources. The catchment has an area of 57 833 km2, of which 1060 km2 or 1.8 % is glaciated. The monthly temperature climatology (1951–1970) averaged over the catchment varies between -13 ∘C in January and +11 ∘C in August, and the majority of the annual precipitation falls in spring and early summer (April–July) (see Fig. d). There are six gauging stations with long-term monthly observations commencing in 1951 and terminating between 1980 and 1995 (see Sect. ). Discharge at the six stations peaks in summer (June–August) due to glacier melting, with the exception of Aflatun, which is unglaciated and peaks sooner in spring (May) due to snow melting (Fig. ).

For the purposes of this study, we assume that streamflow at the gauging stations has a natural signal. The exception is the Uch-Kurgan station, where streamflow after 1975 is impacted by the management of the Toktogul reservoir . A high-resolution irrigation map of the catchment derived from the normalized difference vegetation index (NDVI) shows that the irrigated area is low (3 % area is irrigated), in contrast to the Ferghana Valley downstream (Fig. S1 in the Supplement). Irrigation is predominately clustered in the south-eastern part of the Naryn catchment.

DECIPHeR is a flexible hydrological modelling framework which is based on the dynamic TOPMODEL . The model can be spatially configured in any form, providing a distributed mosaic of interacting and spatially connected HRUs that allow different representations of water fluxes due to local conditions (i.e. geology, soils, slopes, vegetation) via different inputs (i.e. precipitation/evaporation), model structures and parameterizations. HRUs group together similar parts of the landscape to minimize run times of the model. This enables the user to run large ensembles of event data and climate simulations and provide probabilistic flow simulations essential for risk analysis. The user can use DECIPHeR to test different spatial configurations, from a fully gridded model to a lumped model set-up. Each HRU can be assigned its own processes and parameters, which allows for a more complex representation of spatially variable processes across the catchment. The capability to include spatially varying processes is particularly useful for modelling glaciers because the equations used to describe water storage and release from glaciated locations in the catchment will be different to unglaciated regions.

DECIPHeR simulates water storage, hydrologic partitioning and surface/subsurface flow for steeper shallow soils and/or groundwater-dominated watersheds. The model structure (as implemented in ) consists of three stores defining the soil profile (root zone, unsaturated and saturated storage), which are implemented as lumped stores for each HRU. Moisture is added to the soil root zone by rainfall input and removed only by evapotranspiration. Any excess precipitation is added to the unsaturated zone, where it is either routed directly as overland flow or added to the saturated zone. Changes to storage deficits in the saturated zone are dependent on this recharge from the unsaturated zone, fluxes from upslope HRUs and downslope flow out of each HRU. Subsurface flows for each HRU are distributed according to a flux distribution matrix based on accumulated area and slope. Channel flow routing is modelled using a set of time delay histograms. For a more detailed discussion of the original DECIPHeR model structure, please see .

While DECIPHeR has been applied to catchments in the UK , it has not been used for glacier or snow-fed rivers because cryospheric processes have not yet been included in the model. TOPMODEL, the forerunner of the dynamic TOPMODEL, did have a snowmelt scheme; however, seasonal variations in the degree day melt factor and snow sublimation were not included . DECIPHeR is implemented in two steps: (1) a digital terrain analysis (DTA) to set up and define the spatial complexity of the model domain and (2) ensemble simulation of that domain. The DTA is critical for defining the model complexity and landscape features that will separate HRUs, their equations, function types and parameterization. The DTA procedures also calculate the river network, routing path, catchment areas for each gauge and connectivity between the HRUs and HRUs to the stream network. More details on the DTA can be found in .

The following sections describe the modifications made to the DECIPHeR model to include snow and glacier processes (for a full description of the hydrology included in DECIPHeR, see ). We have altered the model to include a simple degree day snowmelt and glacier melt scheme. The degree day approach is a well-established method to calculate glacier and snow melting and only requires air temperature as an input. The equations implemented in DECIPHeR for snowmelt and ice melt are similar to those in the SWAT model . SWAT is one of the most widely used community hydrological models which have been applied to many snow-fed catchments . The evolutions of the snow and glacier depths are calculated every time step using the snow accumulation, melt and sublimation components. Temperature and precipitation are calculated at the HRU level by adjusting the gridded surface climate for elevation using a temperature lapse rate and a precipitation gradient. Glacier melt and snowmelt are added to the precipitation fields every time step and are then routed through the catchment. Figure  shows a conceptual diagram of the snow and glacier scheme added to the DECIPHeR model. All model parameters are sampled using Latin hypercube sampling.

The code is modified to read in two additional inputs: (1) air temperature, which is used for the degree day melting of ice and snow and to estimate the fraction of precipitation falling as rain or snow, and (2) the elevation of the forcing data which is used to apply a lapse rate correction to the surface temperature and precipitation fields. To reduce the number of HRUs, we do not classify glaciated regions as a function of accumulated area or slope, unlike in other parts of the catchment. HRUs located inside glaciers are only classified as a function of elevation, spatially varying climate and a unique ID that identifies the glacier. The spatial distribution of HRUs in the upper part of the catchment is shown in Fig. S2.

DECIPHeR requires a digital elevation model and information on the locations of gauging stations. Catchment elevation data are provided by the Multi-Error-Removed Improved-Terrain (MERIT) digital elevation model . The DEM has a spatial resolution of 3 arcsec (∼90 m at the Equator) and is pre-processed to remove any sinks or flat areas. Therefore we assume that all of the catchment area flows to the gauging outlets.

The location of the gauging stations and monthly discharge observations come from the Global Runoff Data Centre (GRDC). There are six gauging stations located the Naryn River catchment: Djumgol, Kekirim, Naryn, Toktogul reservoir, Aflatun, and Uch-Kurgan (Table ). The Toktogul reservoir gauging station is located immediately upstream of the reservoir dam and so is not affected by water abstraction. Discharge at the Uch-Kurgan station after 1975 is impacted by the reservoir management. Table  contains a list of the input and evaluation datasets used in this study.

Glacier outlines are used in the model to identify glaciated/non-glaciated HRUs and initial glacier thicknesses for each HRU. These are calculated using glacier outlines derived from Landsat Multispectral Scanner imagery for the 1970s . According to the Landsat data, 1472 glaciers existed in the catchment during the 1970s. Determining glacier thicknesses at the start of the simulation is problematic due to the lack of long-term observations. Therefore, we infer glacier thickness using the Glacier bed Topography (GlabTop2) method , where the glacier outlines from the 1970s and the MERIT DEM are used as input. Freely available python code to implement the GlabTop2 method was obtained from https://pypi.org/project/GlabTop2-py (last access: 17 December 2020). Glacier thicknesses are converted to units of m w.e. using an ice density of 917 kg m-3.

GlabTop2 is a useful technique to infer glacier thicknesses in the absence of observations; however, the method has some limitations that should be acknowledged. Firstly, the method uses a simple parameterization for the basal shear stress based on the elevation difference within a glacier. This can introduce a source of uncertainty into the initial ice thicknesses. Secondly, the method can produce very high ice thicknesses for locations with low slopes. Low slopes can appear in the MERIT DEM if a glacier has retreated and a glacier lake is formed or an existing lake expands. Two glaciers in the upper part of the catchment have very low slopes (flat) at the terminus and large ice thicknesses. The larger of these is Petrov Glacier which drains into the Petrov glacial lake. Observations show that Petrov Glacier has experienced accelerated retreat since the 1970s , and the lake area has more than doubled since 1980 . To correct for this, we take the mean thickness of a 5×5 pixel buffer upstream of the terminus for each of the two glaciers and replace the large thickness values with the fill value. Ice thicknesses before and after the fill values have been applied can be seen in the Supplement (Figs. S3 and S4, respectively). A third limitation is that the thickness estimate uses 1970s outlines, but our model simulations commence in 1951. In situ mass balance observations show that glaciers in the Tien Shan were in a quasi-stable state between the 1950s and the 1970s but experienced accelerated mass loss in the years that followed . The glaciers in the aforementioned studies were located outside of the Naryn catchment; however, we assume that the mass balance trends are representative of our study region.

Daily precipitation data are provided by the Asian Precipitation Highly-Resolved Observational Data Integration Towards Evaluation of Water Resources (APHRODITE) Russia and Monsoon Asia V1101 daily precipitation . These data have been shown to outperform other gridded precipitation datasets for hydrological modelling applications in central Asia . The APHRODITE data are constructed from a network of rain gauges across Asia which are interpolated onto a 0.25∘ grid. Daily air temperature, potential evaporation and elevation of the climate data come from the ERA5 back extension (ERA5 BE) 1950–1978 and ERA5 1979–2007 . These data have a spatial resolution of 0.25∘×0.25∘.

HRUs are calculated by categorizing the catchment according to the following.

81 elevation ranges consisting of 0–2000 m in increments of 100 and 2000–5200 m in increments of 50 m. These elevation bands are selected to downscale the temperature and precipitation which is used for snow and glacier model. The finer 50 m bands are used between elevations 2000 and 5200 m because glaciers are located within these elevation ranges in the catchment.

The initial snowpack depth is set to 0 m w.e., and its temperature is set to 0 ∘C. The initial glacier temperature is set to -5 ∘C. The calculation of the initial glacier thicknesses using the GlabTop2 method is described in Sect. . The model is spun up by repeating the first simulation year 1951 for 10 years. The spin-up time period is found by performing an idealized experiment in which precipitation forcing is kept constant through time and the temperature forcing is set to less than 0 ∘C to ensure there is no snow or ice melting. Under these conditions, the discharge reaches an equilibrium in approximately 10 years.

The model is calibrated for the period 1951–1970 to determine behavioural parameter sets, and then these are validated for the period 1971 to a variable end date between 1980 and 1995 depending on the availability of discharge observations at each gauging station. The calibration period is prior to the commissioning of the Toktogul reservoir in 1976 which affected the discharge at Uch-Kurgan. The model is run on a daily time step and monthly simulated discharge is calculated from daily values. Twelve additional parameters are added to DECIPHeR for the snow and glacier scheme. The parameters and their minimum and maximum sampling ranges are listed in Table . In total, 150 100 simulations using parameter combinations selected using Latin hypercube sampling are run . This form of stratified sampling is a more efficient and structured approach to generating a “near-random” sample for large multi-dimensional problems such as this. Model performance is assessed using the six evaluation metrics described in Sect.  below. The best 0.5 % performing simulations (see the section below for the methods) in the calibration period are used in the validation.

GLUE is a technique used to identify parameter sets which provide a good representation of the system . The approach assumes that there is no single optimum parameter that can be considered correct, but instead there is a set of “behavioural models” that describe the system equally well. In this study, we want to select models that perform well in simulating seasonal changes in discharge. The onset of snow melting affects the discharge during the spring, whereas peak discharge during the summer is affected by glacier melting. It is equally important to ensure that the model performs well during the autumn and winter. Station observations show that the warming in the Naryn basin over the period 1960–2007 occurred primarily during autumn and winter . Warming winter temperatures cause a reduction in snowpack accumulation when more precipitation falls in the form of rain rather than snow. This has an impact on the autumn and winter hydrograph. Therefore we use the following metrics to assess the model performance.

The Nash–Sutcliffe efficiency (NSE) is used to evaluate high flows and the timing of peak discharge, particularly from glacier melting during the summer. NSE values range between −∞ and 1 where NSE=1 is the optimal value. 19NSE=1-∑i=1nQiobs-Qisim2∑i=1nQiobs-Qiobs^2 Qiobs and Qisim is observed and simulated monthly discharge, Qiobs^ is the mean observed monthly discharge and n is the number of observations.

The bias in runoff ratio PBIAS is a measures of the tendency of the simulated data to be larger or smaller than the observations . A negative PBIAS indicates the model underestimates the discharge and a positive bias indicates the model overestimates the discharge. PBIAS close to zero indicates better model performance. 20PBIAS=∑i=1nQisim-Qiobs∑i=1nQiobs⋅100 The ratio of the root mean square error to the standard deviation of the observations (RSR) is used to evaluate the model performance for the four seasons, and therefore this provides four separate evaluation metrics (bringing the total to six). 21RSRseason=RMSESDobs=∑i=1nQiobs-Qisim2∑i=1nQiobs-Qiobs^2, where i is discharge for the months of spring (March, April, May), summer (June, July, August), autumn (September, October, November) and winter (December, January, February). Qiobs^ is the mean of the observed discharge. Better parameter sets have lower values of RSR. The units of RSR are dimensionless which makes it useful for comparing the model performance between the sub-catchments and with other studies.

In this study two different calibration techniques are tested.

ISC: individual-site calibration to find parameter sets best suited to individual sub-catchments. This approach parameterizes areas upstream of a gauge in a lumped way. This is different to the step-wise approach where each upstream to downstream catchment is calibrated sequentially, resulting in spatial differences between upstream–downstream parameters. Nonetheless, the ISC method allows us to identify the spatial variability in parameters across the catchment.

Model performance is assessed by calculating conditional probabilities from the six metrics described above. The final conditional probability values are combined with an equal weighting to give overall model performance, where higher conditional probability values (after all the normalization steps) indicate better model performance. Prior to calculating the conditional probability values, NSE values less than zero are set to zero. By doing so, we reject these simulations because they will have a zero conditional probability. The NSE is adjusted such that 22NSErev=1-NSE. This ensures that NSE values closer to zero represent good model performance and values closer to 1 represents poorer model performance. The absolute value of PBIAS is also calculated PBIAS. No prior adjustments are required for RSRseason because values close to zero are already considered good.

The metrics NSErev, PBIAS and RSRseason are normalized so that values vary from 0 (good performance) to 1 (poor performance). This is to account for the difference in units between the metrics and the fact that the upper bounds values for the metrics are different. PBIAS has units of percent and RSRseason and NSErev have dimensionless units. The upper bound value for NSErev and RSRseason is 1, whilst PBIAS can have an upper bound value exceeding 1. The above metrics are then normalized so that they are all on a scale of 0 to 1: 23Oc,i,m=Mc,i,m-minMc,I,mmaxMc,I,m-minMc,I,m, where Mc,i,m is the metric m at catchment c for simulation i and I=(1, 2, …, n) are the vector of simulations from 1 to the number of simulations n. max(Mc,I,m) and min(Mc,I,m) are the maximum and minimum values of the metrics across all simulations for each catchment.

Once normalized, the values for each simulation, for each metric, and for each catchment are then calculated as 24Lc,i,m=1-Oc,i,m, so that a higher value (between 0 and 1) reflects a better simulation for that metric. Finally the conditional probability values are then calculated so that for each metric and for each catchment all the simulations sum to 1. 25Lc,i,m=Lc,i,m∑i=1nLc,i,m, where n is the number of simulations. For the ISC method, a combined conditional probability measure is calculated for each sub-catchment (Θc,i) by multiplying the conditional probability measures derived from the six metrics. We assume the metrics contribute equally to the overall model performance. 26Θc,i=∏m=16Lc,i,m For the MSC method, catchment-wide conditional probability measures are calculated by multiplying Θc,i for each sub-catchment. We assume that the sub-catchments contribute equally to model performance. 27Θi=∏c=16Θc,i Simulations are ranked in order of descending conditional probability measure, where maximum values indicate good model performance. The best performing 0.5 % calibration simulations (n=751) are extracted and used to validate the discharge and spatial snow extent.

The simulated catchment-wide glaciated area is compared to the Landsat-derived glaciated area for the best 0.5 % calibration simulations. The Landsat glaciated area is available for three time periods: the 1970s (1972–1977), which were used to calculate initial glacier thicknesses using GlabTop2, the late 1990s (1998–2000) and the mid-2000s (2002–2007). The observations have an uncertainty bound associated with the delineation process which was calculated by placing a buffer of approximately 1 pixel wide (for example, 79 m for observations in the 1970s) around the glacier polygons. The uncertainty is the difference between the glaciated area and the area extended by the buffer. Figure  shows the simulated glaciated area for the top 0.5 % simulations in the calibration overlaid with the Landsat observations. The simulated glaciated area overlaps the Landsat observations in the late 1990s and mid-2000s. The model produces a large range of estimates for the glaciated area (680–1196 km2) (5th–95th percentile limits) at the end of the simulation period. This range is larger than the observed uncertainty range of 903–948 km2. The uncertainty range in the model is 516 km2 (in 2007), which is more than 10 times greater than the uncertainty in the observed glaciated area (46 km2).

Figure  shows the initial glacier thickness and the mean annual thickness at the end of the simulation period in 2007 for a region in the upper part of the catchment. A thinning of the glaciers and retreat of the terminus from the initial glacier outlines in 1970 is evident. The plots show the median ensemble member of the best 0.5 % calibration simulations.

We evaluate the simulated spatial distribution of snow extent against MODIS 500 m resolution 8 d snow cover extent MOD10A2 version 6 for the period 2001–2007. Snow extent is an internal hydrological variable that was not used in the calibration and is complementary to the discharge time series, which is spatially integrated. MODIS snow extent does not contain information on the snow water equivalent; however, it is spatially distributed, which makes it particularly useful for the evaluation of distributed models .

Daily simulated snow depth for each HRU is output for three simulations from the best 0.5 % calibration simulations: 50th (median), 5th and 95th ensemble members. It was not feasible to output daily HRU snow depth for all 751 simulations due to the size of the data. Snow depth is converted from metres of water equivalent to metres using a density of 300 kg m-3, which is the mean density of settled snow. A spatial map of snow depth is generated by converting the snow depths on HRUs to a spatial grid using a map of HRU locations which was generated by the digital terrain analysis.

The MODIS sensor detects snow in a pixel if there is any snow present within an 8 d period. To compare this to the model output, we assume snow is present in the model if the snow depth exceeds 1 cm on any day within the 8 d MODIS observational period. This threshold is used because MODIS can begin to detect snow with an accuracy 40 % at this depth. Modelled snow extent is interpolated onto a 500 m grid for direct comparison with the MODIS data. Pixels where the MODIS data detect cloud cover are excluded from the analysis. Seasonal MODIS and simulated snow extent is calculated from the weekly data by selecting all the weeks that occur during a season and finding the most frequent state (i.e. snow or no-snow) for each pixel.

For each season, a binary classification scheme is used to enable a comparison between the MODIS and modelled seasonal snow extent. The classification scheme has been used in flood hazard modelling to validate simulated and observed flood hazard area maps . Four metrics of fit are used, which categorize the relative number of pixels which conform to one of the states in the contingency table (Table ).

The first is the hit rate (H), which is the proportion of snow pixels in the MODIS data that were reproduced by the model. 28H=M1O1M1O1+M0O1 H can range from 0 (none of the snow pixels in the MODIS data are snow pixels in the model data) to 1 (all of the snow pixels in the MODIS data are snow pixels in the model data).

The second metric is false alarm ratio (F), which indicates the proportion of snow pixels in the modelled that are not snow in the MODIS data. 29F=M1O0M1O0+M1O1 F can have values ranging from 0 (no false alarms) to 1 (all false alarms). F evaluates the tendency of the model to overpredict the snow extent.

The third is the critical success index (C), which evaluates both overprediction and underprediction in the model and can range from 0 (no match between modelled and MODIS data) to 1 (perfect match between modelled and MODIS data). 30C=M1O1M1O1+M1O0+M0O1 The fourth is the error bias (E) which evaluates the tendency of the model to underpredict or overpredict snow extent. 31E=M1O0M0O1 E=1 indicates no bias, 0≤E<1 indicates a tendency toward underprediction, and 1<E≤∞ indicates a tendency toward overprediction.

The spatial distribution of the hit rates, misses and false alarms are shown in Fig.  for the median (50th percentile simulation) of the best 0.5 % calibration runs. (See Figs. S17 and S18 for the 5th and 95th percentile limit simulations.) Seasonal hit rates, misses and false alarms averaged over the years of MODIS observations 2001–2007 are summarized in Table . Seasonal snow extent is predicted reasonably well with mean hit rates exceeding 0.86 (median ensemble member). The model captures the complete snow cover observed in winter and the snow that persists at high elevations in the upper part of the catchment in the summer. Most noticeable is the poorer model performance in autumn, where there is a large positive bias (33.53 % median ensemble member) and a high number of false alarms (0.42 median ensemble member). This indicates that the model is overpredicting the snow extent in autumn. The best 0.5 % calibration simulations produce good estimates for discharge but at the same time predict a range of snow extent values. This can be seen in the fraction of the catchment covered in snow (Fig. ) where NSE values range from 0.78 to 0.89 (95th–5th percentile limits simulations), with most of the model uncertainty occurring in the winter.

Adding the snow and glacier model to DECIPHeR makes it possible to disentangle the relative contributions of snow melting, glacier melting and rainfall to the total runoff and to determine the timing of when each component influences river flow. It is important to establish these present-day baseline conditions because these will change under future climate change scenarios. Figure  shows the percentage contribution of snow melting, glacier melting and rainfall to the total annual runoff averaged over the years 1951–2007. The discharge components are calculated using the 0.5 % best calibration parameters for the Uch-Kurgan station located at the outlet of the catchment. Snow melting is the largest contributor, consisting of 41 %–91 %, followed by the rain component (8 %–43 %) and the glacier component (0 %–15 %), where the ranges represent the 5th–95th percentile simulations across all the gauging stations. The glacier melt contribution is largest for the Naryn sub-catchment, comprising 4 %–15 % of the annual discharge. This is the headwater sub-catchment located in the Tien Shan mountains and has the largest glaciated area. In contrast, the glacier melting contribution at Aflatun is zero because this sub-catchment contains no glaciers. Figure  shows that the rainfall component is larger at the 95th percentile simulations than at the 5th and 50th percentile simulations. This is because the lapse rate at the 95th percentile simulations is higher (22 % 100 m-1) than at the 5th (1 % 100 m-1) and 50th (6 % 100 m-1) percentile simulations.

To determine whether there have been any statistically significant changes in the simulated discharge components since 1951, we do a trend detection analysis using a Mann–Kendall test and Sen's slope estimator with a significance level of 5 % on the 50th percentile discharge predictions (black line in Fig. ). A trend detection is also run on the annual mean air temperature, potential evapotranspiration, precipitation and observed annual mean discharge. The trends are listed in Table . Despite a warming of 0.12–0.2∘ per decade, we only see a statistically significant trend in the observed discharge at Uch-Kurgan which is affected by the management of the Toktogul reservoir and at Ust Kekirim. There are no statistically significant trends in the glacier melt fraction and only small positive trends in the snowmelt and negative trends in the rainfall fractions of less than 1 % per decade at some of the gauging stations. The glacier melt and snowmelt fractions exhibit an anti-correlation which happens because the glacier melting occurs when the snowpack is depleted and the ice is exposed (Fig. ).

Monthly hydrographs averaged over the period 1951–2007 show that discharge from snow melting peaks in the spring (April and May) (Fig. ). Peak discharge from glacier melting happens later during the summer (June, July, August and September) after the snowpack has melted and glacier surfaces are exposed. This seasonal signal is seen at all the gauging stations except for Aflatun, where there are no glaciers. The glacier melt contribution is very high in August, where the upper range is 66 % for the Naryn sub-catchment and 41 % for Ust Kekirim. The percentage contributions of snowmelt, glacier melt and precipitation to the monthly runoff are listed in Table S4.