1 Introduction

Climate change represents one of the most pressing challenges of the twenty-first century, with far-reaching impacts on various environmental and socio-economic systems. One critical aspect of this phenomenon is its influence on global water resources. Changes in temperature, precipitation patterns, and the frequency and intensity of extreme weather events alter the availability and distribution of freshwater resources worldwide (Held and Soden 2006; Arnell and Gosling 2013; Yang et al. 2021; Caretta et al. 2022). The shift in supply reliability poses significant risks to agriculture, drinking water supply, and ecosystem health, emphasizing the need for a comprehensive understanding of climate-water interactions (Kundzewicz et al. 2008).

Drylands, which cover approximately 41% of the Earth's land surface and are home to over 2 billion people, are particularly vulnerable to climate change (Reynolds et al. 2007). These regions, characterized by low and highly variable precipitation, include arid, semi-arid, and dry sub-humid areas that are particularly sensitive to changes in climate due to their marginal water balance (Feng and Fu 2013). Climate projections indicate that drylands will experience greater temperature increases than the global average, possibly exacerbating water scarcity and desertification processes (Huang et al. 2016). With increasing population pressure, the future multifaceted dryland aridity changes are expected to strain already limited water resources, affecting agriculture, biodiversity, and human livelihoods (Schlaepfer et al. 2017; Lian et al. 2021).

Drylands often depend on seasonal runoff from high-mountain regions, which are also vulnerable to climate change (Hock et al. 2019). The impact on water resources is of great concern in these geographic contexts, especially in the regions where large downstream population numbers crucially depend on access to water in these fragile environments (Zaitchik et al. 2023). Central Asia, encompassing Afghanistan, Kazakhstan, Kyrgyzstan, Uzbekistan, Tajikistan, and Turkmenistan, is one such region and is characterized by its arid climate, high dependence on snow and glacier melt for annual runoff, and transboundary river systems (Jelen et al. 2021).

Previous studies researching selected catchments in the region have shown that river discharge characteristics are highly sensitive to future climate forcing (e.g. Siegfried et al. 2012; Didovets et al. 2021). For example, the importance of glacier melt in buffering summer and late summer discharge will gradually reduce after peak water low-lying catchments with little glaciation (Pohl et al. 2017; Su et al. 2022; Yao et al. 2022). Typical intraseasonal shifts of the hydrograph characteristics in snowmelt-dominated basins are expected to occur (Zhumabaev et al. 2024). The resulting changes in water availability across seasons and at interannual scales will significantly impact economic sectors (Shaw et al. 2022), infrastructure (The World Bank 2009), human livelihoods (Reyer et al. 2017; Xenarios et al. 2019), and ecosystems (Chen et al. 2022) and possibly constitute a security risk (Bernauer and Siegfried 2012).

Despite growing recognition of the impacts of climate change on water resources in Central Asia, several critical research gaps remain. One of them is that the paucity of in-situ data for hydrological model calibration and validation in the region has traditionally forced regional studies to work only at the level of the large river basins. In other words, no comprehensive regional study exists so far that resolves the 21st-century climate impacts at subcatchment levels across the major mountain ranges and zones of runoff formation. By paying tribute to the hydroclimatological complexity of this region, such a study could inform water managers about future challenges for proper preparedness and adaptation in a detailed and comprehensive manner. This would ultimately benefit national and transboundary strategies.

This study fills this research gap by focusing on the hydrology of high-mountain catchments in Central Asia using a newly available dataset on gauge locations and corresponding catchments (Marti et al. 2023). Climate impacts on the hydrology of 221 high-mountain catchments are assessed (Fig. 1). By analyzing these changes, we aim to provide insights into the future availability and management of water resources in this vulnerable region. Our findings will contribute to the broader understanding of climate impacts on semi-arid regions and support the development of adaptive strategies to enhance water security in Central Asia.

Fig. 1
figure 1

Overview of the study region with 221 subcatchments shared among the five large river basins (Marti et al. 2023). The large basins are color-coded (see legend). The norm-specific discharge of the individual subcatchments is shown by proportionally sized and colored bubbles. For coloring, quantiles are used over ten classes. The hillshade layer is SRTM topography (NASA JPL 2013). Permanent water bodies were taken from the global HydroLakes Database (Messager et al. 2016). River shapes are from the WMOBB River Network data (GRDC, Koblenz, Germany: Federal Institute of Hydrology (BfG) 2020). Country names are given using 3-digit codes, and borders are taken from the GADM database (GADM) (2022)

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Our approach and data are presented in Chapter 2. Results and discussion are in Chapter 3, whereas Chapter 4 concludes. The article is accompanied by Electronic Supplementary Material (ESM).

2 Methods and materials

2.1 Hydrological modeling and quantification of climate impacts

Model goals and data availability inform the choice of a hydrological modeling approach. Different approaches have been followed to study climate impacts in Central Asia (Siegfried et al. 2012; Loodin 2020; Didovets et al. 2021; Hu et al. 2021; Huang et al. 2022; Shannon et al. 2022). These modeling studies feature various levels of complexity, and often, they focus on a few selected representative catchments from which time series data are available over a longer period for model setup, calibration, and validation of dynamic models.

The focus of the regional study presented here is on the entire zone of runoff formation in southern and south-eastern high-mountain Central Asia (HMCA, Fig. 1). For most of the studied catchments, only historic specific norm discharge is available (Marti et al. 2023), which in itself is also a restriction for modeling. We thus focus our study on using a water balance model that accounts for catchment and climate characteristics with only a few parameters, and we use the simplified stochastic soil moisture dynamics model presented by Porporato et al. (2004). This model describes the catchment scale water balance and its components in a parsimonious way at daily time scales as

$${w}_{0}\frac{dx(t)}{dt}={P}_{d}\left(t\right)-{E}_{d}\left({E}_{m},x\left(t\right)\right)-{Q}_{d}\left(x\left(t\right),t\right),$$
(1)

where \(x\left(t\right)\) is the state variable, i.e., the effective relative soil moisture where \(x\left(t\right)=(s\left(t\right)-{s}_{w})/({s}_{1}-{s}_{w})\) with \(s\left(t\right)\) (-) being the relative soil moisture and \({s}_{1}\) (-) is the threshold above which rainfall in excess of available storage capacity is directly converted into runoff \({Q}_{d}\) (mm) under well-watered conditions or lost via deep percolation and drainage, and \({s}_{w}\) (-) is the wilting point of the soil. \({w}_{0}=\left({s}_{1}-{s}_{w}\right) n{ Z}_{r}\) (mm) is the maximum soil water storage available for evaporation with \({Z}_{r}\) (mm) being the rooting zone depth and \(n\) (-) being the porosity of the soil column. We refer to this model as the PSM model (Porporato et al. 2004; Daly et al. 2019; Porporato and Yin 2022).

\({P}_{d}\) (mm/day) is the daily rainfall modeled as a stochastic rare-event Poison process with constant frequency \(\lambda\) (1/day), delivering a daily rainfall event depth drawn from an exponential distribution with a mean \(\alpha\) (mm). The long-term average annual rainfall over a catchment can be expressed as \(P=\alpha \lambda {n}_{d}\) with \({n}_{d}\) being the number of days per year (Daly et al. 2019).

The PSM model assumes that actual daily evaporation \({E}_{d}\) (mm/d) depends linearly on the potential evaporation \({E}_{m}\) (mm/d), i.e., \({E}_{d}={E}_{m}x\left(t\right)\), thus accounting for evaporation reduction under increasing water stress (Daly et al. 2019). Under the simplifying assumption that \({E}_{m}\) is not dependent on time, i.e., shows no seasonality, an average annual rate of potential evaporation \({E}_{p}\) can be computed as \({E}_{p}={E}_{m}{n}_{d}\) (mm/a). In the following, the actual annual evaporation is denoted as \(E\). The annual average discharge \(Q\) (mm) can be computed similarly from daily values, i.e., \(Q={Q}_{d}{n}_{d}\).

Under steady-state conditions and with constant \(\alpha\) and \(\lambda\) and a linear dependence of evaporation on soil moisture, Daly et al. (2019) showed that the normalized water balance equation can be analytically solved as

$$\varepsilon =1-\frac{\Phi {\gamma }^{{~}^{\gamma }\!\left/ \!{~}_{\Phi }\right.-1}{e}^{-\gamma }}{\Gamma \left(\frac{\gamma }{\Phi }\right)-\Gamma \left(\frac{\gamma }{\Phi },\gamma \right)},$$
(2)

with \(\varepsilon =E/P\) being the evaporative fraction, \(\phi ={E}_{p}/P\) (-) being the aridity index and \(\gamma ={w}_{0}/\alpha\) (-) being the storage index of a basin. \(\gamma\) describes soil water under well-watered conditions normalized by the rainfall depth and determines how much water a catchment retains relative to average precipitation event depth. \(\Gamma (.)\) is the gamma function, and \(\Gamma (.,.)\) is the incomplete gamma function (Abramowitz Milton 1964). The long-term norm discharge can be written as

$$Q=P \rho \left(\Phi ,\gamma \right),$$
(3)

with

$$\rho \left(\Phi ,\gamma \right)= \frac{\Phi {\gamma }^{{~}^{\gamma }\!\left/ \!{~}_{\Phi }\right.-1}{e}^{-\gamma }}{\Gamma \left(\frac{\gamma }{\Phi }\right)-\Gamma \left(\frac{\gamma }{\Phi },\gamma \right)}$$
(4)

being the runoff coefficient. In the models studied here, increases in \(\gamma\) and \(\Phi\) are associated with a declining runoff coefficient.

The PSM model in Eqs. (3) and (4) does not represent cryosphere processes. Hence, glacier contributions are accounted for via available existing data on recent observed and future modeled glacier melt data (Rounce et al. 2023) and added separately to the modeled discharge. Hence,

$$Q\left(0\right)=P \rho \left(\Phi ,\gamma \right)+{Q}_{G}.$$
(5)

where \(Q\left(0\right)\) is the modeled discharge and \({Q}_{G}\) is the glacier imbalance ablation contribution during the baseline period from 1979—2011. In subcatchments without current glaciation or in scenarios and future periods where glaciation disappears under future climate change scenarios, we set \({Q}_{G}=0\). Model validation is done by comparing \({Q}_{obs}\) with \(Q\left(0\right)\) where \({Q}_{obs}\) is the observed norm discharge during the baseline period. Finally, snowmelt and snow accumulation dynamics are assumed to be irrelevant at the annual time scale.

We use CMIP6 climate model forcing and an empirical model that relates mean basin temperatures to the maximum soil water storage available to compute future runoff ratios for period 1 from 2011 to 2040, period 2 from 2041 to 2070, and period 3 from 2071 to 2100. For each catchment, the delta changes in discharge relative to the baseline period are computed as

$$\Delta Q=\frac{Q\left(i,s,m\right)-Q(0)}{Q(0)}= \frac{P\left(i,s,m\right) \rho \left(\Phi \left(i,s,m\right),\gamma \left(i,s,m\right)\right)+{Q}_{G}\left(i,s,m\right)- Q(0)}{Q(0)},$$
(6)

where \(i\) indicates the future climate period and \(s\) the scenario under consideration as computed using the climate model \(m\). Hence, when modeling future discharge for the individual basins, we compute future runoff ratios using future values of the aridity and storage indices that result from the corresponding GCM model runs and modeled changes in soils and add the corresponding future glacier discharge.

For the computation of \(\rho (\phi ,\gamma\)), numerical issues can arise when computing these terms using a machine precision environment (see Appendix A.2 in Daly et al. 2019). We address this issue by computing the numerical values for each combination of the aridity index and basin storage index using Wolfram Mathematica and its adaptive precision feature (Wolfram Research Inc. 2023). The \(\rho (\phi ,\gamma\)) terms for the individual catchments were computed with a precision of 200 digits.

2.2 Discharge and climate data

Long-term annual norm discharge data from 295 mountainous gauging stations from Kyrgyzstan, Kazakhstan, Uzbekistan, and Tajikistan are taken from Marti et al. (2023), together with the corresponding subcatchment geometries. We limit our study to subcatchments larger than 200 km2, an arbitrarily chosen cutoff value to avoid spurious statistics when sampling finite resolution raster values from comparatively small polygons. This results in 221 catchments used for this study (Fig. 1). The studied subcatchments cover a total area of 423′099 km2 with a median area of 1′428 km2.

(91 catchments are smaller than 1′000 km2). The area includes parts of Afghanistan (AFG), Kazakhstan (KAZ), Kyrgyzstan (KGZ), Tajikistan (TJK), and Uzbekistan (UZB).

Being part of the Aral Sea basin, the Amu Darya (area of contributing subcatchments is 230′782 km2) and Syr Darya (107′744 km2) are the two most significant basins in the region (colors in Fig. 1 highlight the large basins). These are followed by the Murghab-Harirud basin (63′415 km2), the Chu-Talas basin (15′266 km2), and the Issyk-Kul basin (5′924 km2). The mean subcatchment elevation is 2′791 m above mean sea level (masl), with a minimum of 877 masl and a maximum of 4′641 masl.

For the 221 catchments studied, the regionally averaged runoff ratio is ρ = 42%, approx. (see Marti et al. 2023 for a detailed description of data sources and Sect. 2.2). This is the fraction of the total water supply from the zone of runoff formation that, on average, discharges to the arid plains. There, most of this water is either used consumptively in irrigation and evapotranspired or drained and returned to the atmosphere later (Shults 1965). The small runoff ratios in northern Afghanistan confirm the extremely limited water availability there (Fig. 1). On the contrary, the western end of the Tien Shan mountains, the Fergana Range at the eastern end of the Fergana Valley, and the south side of the Gissar-Allay Range and the Western Pamirs are where the moist subcatchments are located. Table 1 summarizes the mean hydro-climatological basin statistics of the 221 catchments.

Table 1 Mean catchment statistics are tabulated. Qobs is measured historic norm specific discharge, P is the norm historical precipitation, T is the norm historical temperature, ϕ is the aridity index, ε is the evaporative fraction, and ρ the runoff ratio. All values are long-term averages in time and averaged in space across all corresponding subcatchments (see Marti et al. 2023 for more information)
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CHELSA V21 global daily high-resolution precipitation and temperature climatologies were processed over the Central Asian domain, and norm 2 meter (m) surface temperatures and total norm annual precipitation values in millimeters (mm) were computed for the catchments for the baseline period 01–01-1979 until 31–12-2011 (Karger et al. 2017, 2021). For the computation of subcatchment-specific mean raster statistics, we use the exactextractr R Package (Daniel Baston 2022) throughout. Precipitation event depth \(\alpha\) (mm) and event frequencies \(\lambda\) (a−1) for the baseline period were computed using a precipitation threshold of 1 mm per day, above which a wet day is counted. It follows that \(P= \alpha \lambda\), where \(P\) is the mean annual precipitation in mm.

Future global circulation model (GCM) daily precipitation and temperature time series from the CMIP6 Coupled Model Intercomparison Project Phase 6 were accessed via the Copernicus Climate Change Service (C3S) Climate Data Store for the future period 2011 – 2100 and the historical reference period 1979—2011. Data from four models were downloaded and processed: UKESM1.0-LL (Tang et al. 2019), IPSL CM6A-LR (Boucher et al. 2018), MRI-ESM2-0 (Yukimoto et al. 2020), and GFDL-ESM4 (Krasting et al. 2018). GCM selection followed the one from the Intersectoral Impact Model Intercomparison Project (ISIMIP, see

https://www.isimip.org/documents/413/ISIMIP3b_bias_adjustment_fact_sheet_Gnsz7CO.pdf).

The following four Shared Socio-Economic Pathway (SSP) and Representative Concentrations Pathway (RCP) scenarios are investigated: SSP1 RCP 2.6, SSP2 RCP 4.5, SSP3 RCP 7.0, and SSP5 RCP 8.5 (Vuuren et al. 2011; Riahi et al. 2017). For brevity, we refer to these as SSP1-26, SSP2-45, SSP3-70, and SSP5-85 scenarios throughout the text. We assume steady-state conditions for three future periods: period 1 from 2011 – 2040, period 2 from 2041 – 2070, and period 3 from 2071 – 2100.

The GCM daily climate model raster fields of surface temperature and precipitation were used to compute the mean daily time series over the subcatchments. Using the historical GCM simulations from 1979 – 2011 compared to the zonal mean subcatchment statistics of the CHELSA V21 daily data, the individual time series were bias-corrected in R for each GCM model separately using quantile mapping available via the qmap R Package (Gudmundsson et al. 2012; R Core Team 2022). This GCM-model-specific bias correction was finally applied to all future periods and scenarios for each GCM model. Figure 2 shows the scenario and pathway-dependent changes of the distributions of the mean temperature and precipitation values over the 221 subcatchments ensembled over the 4 GCMs.

Fig. 2
figure 2

The left plate shows the scenario-dependent GCM averaged distributions of surface temperatures averaged over the subcatchments for the individual periods. The left plate shows the corresponding statistics for annual norm precipitation values. The baseline period (1979 – 2011) is denoted with p0 and shows the statistics of the historical observations from the CHELSA V21 dataset. p1—p3 denote the corresponding future climate periods. The boxplots visualize median values and first and third quartiles via the hinges. Data beyond the end of the whiskers are outliers that are plotted individually

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For the computation of the potential evaporation over the baseline period and the future periods 1–3, daily GCM temperature time series were used to compute subcatchment and period averaged \({E}_{p}\) values using the Jensen-Haise and McGuiness model formula as detailed in Oudin et al. (2005). These values were then bias-corrected using quantile mapping with subcatchment-averaged CHELSA V21 Penman \({E}_{p}\) values (Karger et al. 2017; Beck et al. 2020) for the historical reference (baseline) period. Finally, the bias correction was applied to the future climate periods for each GCM model.

2.3 Soil data

Different datasets are used for the spatial distribution of soil parameters over the subcatchments. For the soil porosity \(n\), the WCsat layer is taken from the HiHydroSoil V2.0 data (Simons et al. 2020). Rooting zone depth values were retrieved from three global data sets (Yang et al. 2016; Fan et al. 2017; Stocker et al. 2021) and subsequently compared (see Appendix A, ESM). We assume that the data by Fan et al. (2017) represents a good intermediate compromise product for the study region and compute D66 values at pixel levels, i.e., the depth above which 66% of the root biomass is located. We used Copernicus landcover information from the 100 m 2019 land cover product (Buchhorn et al. 2019) and available landcover class-dependent scaling factors (Hauser et al. 2022) to rescale the Fan et al. (2017) data and compute subcatchment averaged values (see Appendix B, ESM). Finally, for the computation of \({w}_{0}\) and \(\gamma\), we use the D66 \({Z}_{r}\) values (median value of 367 mm over subcatchments). Data from Simons et al. (2020) are taken for \({s}_{1}\) (WCsat data) and \({s}_{w}\) (WCpF4.2 data) (Fig. S5 in ESM, Appendix A, shows the difference between \({s}_{1}-{s}_{w}\)) and used together with porosity values to compute \({w}_{0}\) from \({Z}_{r}\).

Increasing temperatures and atmospheric CO2 concentrations are linked to root extensions (Iversen 2010; Hu et al. 2018). With strongly increasing temperatures in the Central Asia mountainous region (left plate Fig. 2) and the increasing atmospheric moisture supply there (right plate Fig. 2), ecosystem ranges likely increase across altitudinal zones. In other words, more deeply rooted vegetation becomes more abundant in the future in places where growth would have been unlikely during the baseline period. We account for these dynamics by establishing subcatchment-specific rooting depths and temperature relationships (see Fig. S6 in Appendix A, ESM).

2.4 Data on glacier melt

The PSM model does not represent cryosphere processes related to glaciers, permafrost, and snow. To account for the impact of climate change on the glacier contribution to basin runoff, per-glacier monthly projections of 17′993 glaciers located within the territory of the 221 basins were retrieved from Rounce et al. (2022). Glacier geometries are taken from the Randolph Glacier Inventory 6.0 (RGI Consortium 2017).

Glacier runoff \({Q}_{G}\) from 2000 to the end of the century were aggregated over each subcatchment and averaged over the baseline period and the three corresponding climate periods (Rounce et al. 2023). The glacier runoff projections have been calculated by Rounce et al. (2023) using the glacier-specific PyGem-OGGM models forced with CMIP6 climate models with the four emission scenarios considered. Table S2 in Appendix C (ESM) shows basin-aggregated statistics.

3 Results and discussion

3.1 PSM Model validation

To validate the PSM model (Eq. 4), we compute the runoff coefficient \(\rho \left(\Phi ,\gamma \right)\) for the baseline period and all basins and derive the modeled discharge as per Eq. 5, and add \({Q}_{G}(0)\) (Table S2, ESM) to the modeled discharge for comparison with observed norm discharge values. The results are shown in Fig. 3. The left plate shows the map of relative model errors for the baseline period. The scatter plot on the right side shows modeled norm discharge Q compared with observed baseline norm Q. Model validation confirms a satisfactory model performance in HMCA.

Fig. 3
figure 3

Relative model errors in % are shown in the map on the left. The plate on the right side compares the model with the observed norm discharge Q (mm). The red line in the right plate shows the 1:1 correspondence, and the blue line is the best-fit line using linear regression. The regression equation, the R2 value, and the p-value are also shown. See text for highlighted southwestern and northern regions

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Large relative model errors are observed in the lower-lying catchments of Afghanistan (region South-West in Fig. 3) and Arys River basin as well as Talas River basin (region North in Fig. 3). The errors might be related to low measurement precision, wrong basin delineation, unaccounted anthropogenic influences above gauges, wrong climate forcing data or erroneous soil data, or a combination of any of these factors. Under any circumstances, the geographic clustering of errors shows correlations in space that must emerge from an underlying pattern. One can speculate that the remoteness of the basins in the southwestern region contributed to low measurement precision there. On the other hand, in the Arys and Talas River basins in the north, anthropogenic influence in the low-lying catchments might cause large deviations from the modeled discharge.

We also compare PSM model projections with GCM projections for actual evaporation and relative soil moisture. More details are available in Appendix F (ESM, Figs. S67 and S68). Model projections compare favorably, which strengthens confidence in the PSM model results.

3.2 Analysis of climatic changes

For a comprehensive analysis of climate impacts, we compute the socio-economic pathway and target period-dependent relative changes in the key model variables, i.e., \(d{E(.)}_{p}/{E}_{p}\left(0\right)\), \(d\alpha (.)/\alpha \left(0\right)\), \(d\lambda (.)/\lambda \left(0\right)\) and \(d{w}_{0}(.)/{w}_{0}\left(0\right)\) as shown in Fig. 4 (numbers in parentheses are period identifiers where, for example, \({E}_{0}(0)\) refers to the norm potential evaporation during the baseline period and \((.)\) is a placeholder for the corresponding future climate periods).

Fig. 4
figure 4

Plate a: relative changes (in %, relative to baseline) in potential evaporation \({\mathbf{E}}_{\mathbf{p}}\) for different scenarios and target periods. Plate b: relative changes (in %, relative to baseline) in precipitation depth \({\varvec{\upalpha}}\) for different scenarios and target periods. Plate c: relative changes (in %, relative to baseline) in precipitation frequency \({\varvec{\uplambda}}\) for different scenarios and target periods. Plate d: relative changes (in %, relative to baseline) in \({\mathbf{w}}_{0}\) for different scenarios and target periods. All values are ensembled over GCM models

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Significant expected temperature increases in the region are expected with median delta changes of period 1: (SSP1-26: + 1.3 °C, SSP2-45: + 1.3 °C, SSP3-70: + 1.3 °C, SSP5-85: + 1.4 °C), period 2: (SSP1-26: + 1.9 °C, SSP2-45: + 2.3 °C, SSP3-70: + 2.7 °C, SSP5-85: + 3.1 °C), and period 3: (SSP1-26: + 1.9 °C, SSP2-45: + 3.1 °C, SSP3-70: + 4.6 °C, SSP5-85: + 5.6 °C), relative to the baseline (values are first ensembled over GCM models and the median taken over subcatchment values). Figs. S28 – S31 in the ESM shows the mapped changes. The corresponding boxplot of relative temperature changes is shown in Fig. S27.

In line with temperature increases, the relative increases in median potential evaporation are for period 1: (SSP1-26: + 3.8%, SSP2-45: + 3.8%, SSP3-70: + 3.8%, SSP5-85: + 4.2%), period 2: (SSP1-26: + 5.5%, SSP2-45: + 7.0%, SSP3-70: + 8.2%, SSP5-85: + 9.8%), and period 3: (SSP1-26: + 5.7%, SSP2-45: + 9.8%, SSP3-70: + 14.6%, SSP5-85: + 19.0%). The Figs. S7 – S11 in the ESM show the corresponding boxplot and maps.

The GCM model runs suggest a significant modulation of precipitation depths \(\alpha\) and frequencies \(\lambda\) over the entire climate projection horizon. The median per period and scenario increases in precipitation depths \(\alpha\) are for period 1: (SSP1-26: + 4.3%, SSP2-45: + 4.4%, SSP3-70: + 4.6%, SSP5-85: + 5.2%), period 2: (SSP1-26: + 5.9%, SSP2-45: + 6.1%, SSP3-70: + 6.8%, SSP5-85: + 8.9%), and period 3: (SSP1-26: + 5.8%, SSP2-45: + 9.8%, SSP3-70: + 12.6%, SSP5-85: + 13.1%). The corresponding boxplot is shown in Fig. 4 (plate b), and the mapped changes are shown in Figs. S13 – S16, ESM. Median per period and scenario decreases for precipitation frequency 

\(\lambda\) are period 1: (SSP1-26: -0.3%, SSP2-45: -0.6%, SSP3-70: + 0.0%, SSP5-85: -0.8%), period 2: (SSP1-26: + 0.6%, SSP2-45: -1.7%, SSP3-70: -1.5%, SSP5-85: -1.3%), and period 3: (SSP1-26: -0.6%, SSP2-45: -0.8%, SSP3-70: -2.6%, SSP5-85: -3.1%) (boxplot in Fig. 4, plate c, and maps in S18 – S21).

The projected decline in precipitation frequency is offset by a stronger increase in precipitation event depth, thus indicating a slightly wetter precipitation future in Central Asia. More precisely, the relative increases in median per period and scenario precipitation values are period 1: (SSP1-26: + 4.2%, SSP2-45: + 4.1%, SSP3-70: + 4.9%, SSP5-85: + 4.3%), period 2: (SSP1-26: + 6.7%, SSP2-45: + 4.6%, SSP3-70: + 5.5%, SSP5-85: + 8.0%), and period 3: (SSP1-26: + 5.5%, SSP2-45: + 8.2%, SSP3-70: + 11.4%, SSP5-85: + 10.1%). Figs. S23 – S26 (ESM) show the geographic distribution of relative increases in precipitation values. Fig. S22 (ESM) shows the boxplot of the median delta changes.

The significant changes in the HMCA temperatures translate into changes in the maximum water available for evaporation over the root zone. For the relative median delta changes in \({w}_{0}\) averaged of GCM models and scenarios, we get for period 1: (SSP1-26: + 0.2%, SSP2-45: + 0.2%, SSP3-70: + 0.2%, SSP5-85: + 0.3%), period 2: (SSP1-26: + 0.3%, SSP2-45: + 0.4%, SSP3-70: + 0.5%, SSP5-85: + 0.6%), and period 3: (SSP1-26: + 0.3%, SSP2-45: + 0.6%, SSP3-70: + 0.8%, SSP5-85: + 1.0%). The corresponding boxplot is shown in Fig. 4, plate d, and the maps are in Figs. S33 – S36 (ESM).

The relative changes in discharge contributions from glacier ablation relative to the baseline are for period 1: (SSP1-26: + 24.3%, SSP2-45: + 24.0%, SSP3-70: + 26.1%, SSP5-85: + 29.3%), period 2: (SSP1-26: + 3.9%, SSP2-45: + 9.0%, SSP3-70: + 7.5%, SSP5-85: + 7.4%), and period 3: (SSP1-26: -13.7%, SSP2-45: -11.4%, SSP3-70: -11.1%, SSP5-85: -13.1%), respectively. The corresponding boxplot and maps are shown in Figs. S37 – S41 (ESM).

The median figures show that the regional impact on glacier ablation discharge in the future period p3 (2071 – 2100) is moderate. However, there are locations where the bulk of the warm-season discharge is generated from glacier ablation and glacier wastage has progressed significantly by then. Chu and Naryn River basins must be highlighted in this regard (see plate c, Fig. S41, ESM), where a strong reduction of glacier discharge is expected. This reduction of summer glacier discharge has important management implications for existing or yet-to-be-build manmade storage in the affected basins.

3.3 Quantification of climate impacts

Using the D66 \({Z}_{r}\) as representative rooting depth values, the median GCM-ensembled period and scenario-dependent specific norm discharge values and relative changes to the baseline period are illustrated in Fig. 5, plates a and b, respectively. Expected relative increases in specific discharge are as follows for period 1 (SSP1-26: + 3.5%, SSP2-45: + 4.2%, SSP3-70: + 5.5%, SSP5-85: + 3.8%), period 2 (SSP1-26: + 5.6%, SSP2-45: + 0.8%, SSP3-70: + 0.4%, SSP5-85: + 5.0%), and period 3 (SSP1-26: + 1.1%, SSP2-45: + 3.8%, SSP3-70: + 4.1%, SSP5-85: -2.7%). Detailed spatial changes are provided in Figs. S42 – S46 (ESM).

Fig. 5
figure 5

The statistics of period and scenario-dependent norm discharge values are shown in Plate a. Plate b shows corresponding delta changes relative to the baseline values. The modeled discharge during the baseline period is taken as a reference (p0 in plate a) and not observed discharge. This is done to not pollute delta changes with model errors

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The effect of the glacier imbalance ablation on augmenting future discharge is noticeable. Relative median delta changes in specific discharge, net glacier contributions, are smaller with values as follows: period 1 (SSP1-26: + 1.9%, SSP2-45: + 0.6%, SSP3-70: + 3.2%, SSP5-85: + 1.5%), period 2 (SSP1-26: + 3.7%, SSP2-45: -1.2%, SSP3-70: -2.1%, SSP5-85: + 2.2%), and period 3 (SSP1-26: + 1.4%, SSP2-45: + 3.7%, SSP3-70: + 3.3%, SSP5-85: -4.7%).

Table 2 summarizes period- and scenario-specific median changes relative to the baseline. The table reveals that increases in temperatures and precipitation result in greater aridity, higher actual evaporation, and lower runoff coefficients. dT is the delta change in temperatures, dP(.)/P(0) denotes the relative change in precipitation, dΦ(.)/Φ(0) is the relative change in the aridity index (Figs. S47 – S51, ESM), d(.)/(0) is the relative change in the basin storage index (Figs. S52 – S56, ESM), dρ(.)/ρ(0) is the relative change in runoff coefficient (Figs. S57 – S61, ESM), dE(.)/E(0) is the relative change in actual evaporation (Figs. S62 – S66, ESM), and dQ(.)/Q(0) is the relative change in discharge that includes glacier contributions.

Table 2 GCM-ensembled period- and scenario-dependent changes of median discharge values. Changes are measured relative to the baseline period
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The regional median values reported in Table 2 obscure a more nuanced picture regarding the geographic distribution of the relative changes. Figure 6 exemplifies the relative changes of specific norm discharge under scenario SSP5-85. The overall statistics remain relatively stable throughout the twenty-first century, as is shown in plate d, Fig. 6. However, model results reveal intriguing geographic patterns in climate impacts (plates a–c, Fig. 6) that complicate simplistic explanations. Different mechanisms in subbasins and across altitude zones result in geographically distinct climate impacts over the twenty-first century.

Fig. 6
figure 6

Plates a – c show the geographic distributions of the delta changes in GCM-ensembled norm discharge for periods 1 – 3 under SSP5-85, relative to the baseline period. Data are in percentages. Notice the nonlinear bins for coloring. Plate d shows the histograms of the period-specific delta changes. The modeled discharge during the baseline period is taken as a reference. This is done to not pollute delta changes with model errors. Figs. S43 – S45 (ESM) show the maps and histograms for the other scenarios

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On the one hand, a drying in the zone of runoff formation in the Tien Shan mountains becomes apparent as the glacier wastage accelerates there and depletes the land ice over the course of the twenty-first century (see northern and north-eastern basins in maps in Fig. 6). This affects the Syr Darya and especially its main tributary, i.e., the Naryn River, and Chu and Talas River basins. On the other hand, much of the higher-lying Gissar-Alay and Pamir mountains will experience increases in discharge over the entire twenty-first century. These are mostly related to increased glacier imbalance ablation (compare with Fig. S41, ESM) and the fact that peak water occurs later there (see Table S2, ESM). In all areas of significant glaciation, increased glacier ablation (Figs. S38 – S41, ESM) stabilizes discharge over all three future climate periods until after peak meltwater from glacier ablation.

The stabilizing effect on discharge from glacier melt depends on the climate scenario and basin and glacier elevation. Peak water occurs later in all basins under less extreme climate scenarios than the high-emission one (compare, e.g., plate c in Fig. S41 with plate c in Fig. 6). In the Naryn, for example, the end-of-century discharge decay in period p3 is less pronounced than in scenario SSP5-85.

Table 3 summarizes values per basin. Over the course of the twenty-first century, Amu Darya is expected to experience increases in norm-specific discharge relative to baseline values. The exact value depends on the timing of the arrival of peak meltwater and, thus, the speed with which temperatures increase in high-mountain Central Asia. Based on these change statistics, the water availability in the Syr Darya basin is not expected to change significantly. Both in the Chu-Talas and Isyk-Kul basins, a reduction in norm-specific discharge is expected relative to baseline values.

Table 3 Median per period and scenario relative changes in specific discharge values in percentages are shown for each large basin. The numbers in the parenthesis are the values corresponding to specific scenarios, i.e., (SSP1-26, SSP2-45, SSP3-70, SSP5-85)
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The projected precipitation increase translates into increased discharge in the Murghab-Harirud basin relative to the baseline period. However, it should be remembered that relative model errors are high in this region (left plate in Fig. 3) and that the specific discharge is very low to start with (Fig. 1). Under these circumstances, even a + 50% median increase of the corresponding specific runoff relative to the baseline will not dramatically increase water availability there in the future.

4 Conclusions

To study climate impacts in the HMCA region, we have applied a simple, parsimonious conceptual model of soil moisture dynamics to account for the essential components of the soil water balance at the catchment level. The model includes soil water storage, threshold-triggered runoff, deep infiltration, and water storage-dependent evaporation. State variables and fluxes are driven by intermittent stochastic rainfall, whose location-dependent variability is characterized by precipitation frequency and depth. The model delivers plausible results regarding hydrological climate projections, and a detailed picture of impacts emerges for the first time at a highly granular and nuanced level for high-mountain Central Asia. Model results confirm that simple “wet gets wetter and dry gets drier” paradigmatic thinking is inadequate in complex hydro-climatological domains. The results confirm that the basins studied will experience localized impacts depending on location-specific basin characteristics, climate forcing, and glaciation levels.

Numerous model limitations exist. For example, the daily rainfall distribution is assumed to be a Poison process, which could not be validated because of the lack of available in-situ data in the remote region (Verma et al. 2011). In relation to the cryosphere, the contributions from melting land ice can easily be added to modeling results under corresponding climate scenarios. Hence, considering the dynamics of destorage due to glacier melt can yield a good understanding of the corresponding implications on hydrology over the course of the twenty-first century. However, neither seasonal nor permanent snow storage is accounted for in the model (see, e.g., Feng et al. 2015). Research has shown that the scatter of real-world data around Budyko’s curve is also influenced by catchment snow ratios (Zhang et al. 2015), apart from the other controls such as vegetation, the seasonality characteristics of precipitation, soil properties (as implemented in the PSM model), and topographic factors (Greve et al. 2016). For example, Berghuijs et al. (2014) have used data from the contiguous United States to show decreasing snow fraction in precipitation is associated with lower streamflow at the annual and multi-annual time scales. This effect cannot be captured with the PSM model, as demonstrated here. Finally, in our model formulation, we only indirectly account for future permafrost dynamics via the \(T\) and \({w}_{0}\) empirical relationship and the implied dynamics under a warming scenario. Permafrost thawing and additional contributions to discharge are not considered here explicitly.

While being computationally extremely efficient, the analytical solution of the PSM model is limited to steady-state conditions. The model helps us to understand total water availability and inter-period changes therein. However, it assumes instantaneous shifts between climate periods and uniform annual norm discharge regimes, preventing the study of discharge seasonality. For instance, with increasing warming and the shift of discharge regimes from nival-glacial to pluvial-nival, cold season discharge between October and March will increase and, with that, the potential for hydropower production when electricity demand for heating is high. As Siegfried et al. (2012) have shown focusing on the Syr Darya river basin, the mismatch between water availability during the warm season and crop water demand will increase. With a rebalancing of cold to warm season discharge ratios to higher values and strongly increasing evaporative water demands downstream in irrigated agriculture (for irrigation and crop cooling alike), there will be an increasing water gap emerging that can only be managed in selected basins with the help of sufficient-volume man-made storage.

Under the assumption that agricultural production in the downstream countries of the region remains viable from a plant physiological perspective and that it continues to be important for food self-sufficiency and the production of cash crops as well as for livelihoods, a boom in the construction of reservoirs will likely occur. These reservoirs cannot only offset the loss of glacier water storage but, when equipped with hydropower, can contribute to a green energy transition in the region at the same time. However, under such an increasing infrastructure investment scenario, care must be taken that habitat fragmentation in the mountain rivers does not translate into adverse ecological outcomes.

The climate projections suggest that Central Asia will experience a wetter precipitation future. Rainfall intensity and frequency are expected to increase in parts of the fragile mountain region. This has the potential to change the risk landscape in a critical manner and requires more in-depth studies with a focus on the future developments of hydrometeorological extremes. Future research in this direction should focus on floods and investigate the potential for prolonged dry spells, which can translate into widespread hardship in the region. Finally, local stakeholders need to be sensitized that a wetter precipitation future in the region does not necessarily translate into an increased availability of water for economic purposes. Instead, management challenges will increase with the ongoing aging of infrastructure, the loss of storage (loss of land ice and reservoir volume due to siltation), increasing population numbers, and a more erratic hydro-climate.