Understanding the role of the spatial-temporal variability of catchment water storage capacity and its runoff response using deep learning networks

The land surface of a watershed acts as a large reservoir, with its catchment water storage capacity (CWSC) influencing rainfall-runoff relationship. Estimating CWSC at global grid scale is challenging due to calibration complexity, limited spatial continuity, and data scarcity. To address this, a deep learning-based approach incorporates spatial reconstruction and temporal transfer for capturing spatio-temporal variations in watershed characteristics. The study focuses on the Global Runoff Data Centre dataset and presents a grid-based hydrological model. Findings demonstrate accurate identification of CWSC distribution, with the model achieving an R 2 of 0.92 and the runoff Kling–Gupta efficiency of 0.71 during validation. According to the CMIP6 projections, the global CWSC is anticipated to undergo a significant increase at a rate of 1.7 mm per decade under the SSP5-8.5 emission scenario. Neglecting spatio-temporal CWSC variability globally overestimates climate change’s impact on runoff, potentially reducing the projected long-term increase by up to 41%.


Introduction
The catchment water storage capacity (CWSC) is defined as the maximum water holding capacity of the land surface within a watershed (Gao et al 2014).It encompasses various components such as soil water storage capacity, vegetation retention capacity, and snowpack capacity (Pan et al 2020).The CWSC plays a crucial role in enabling watersheds to adapt to climate change, extreme events.It also satisfies fundamental vegetation and societal needs, such as agricultural water consumption and potable water requirements, particularly during drought conditions (McColl et al 2017).It serves as an important indicator for quantifying and comparing the water storage capabilities between different watersheds (Wang-Erlandsson et al 2022).
The CWSC has a significant impact on the runoff generated from rainfall within a watershed.The distribution of land cover and land use is a primary determinant of CWSC and has a direct influence on other factors, such as soil moisture.The relationship between soil moisture and CWSC is delineated by the correlation between the average and maximum values.For instance, watersheds with a higher degree of urbanization, characterized by impervious surfaces, tend to have lower storage capacity compared to predominantly forested or grassland watersheds (Singh et al 2020).The soil moisture conditions prior to a rainfall event can significantly affect the resulting runoff (Li et al 2022).Limited adaptability to water storage capacity within a watershed can result in insufficient temporary water storage, trapping the watershed in prolonged low-flow conditions and making it difficult to recover to pre-drought levels (Peel et al 2001, Saatchi et al 2013).Additionally, studies have demonstrated that CWSC is a critical factor for ecosystems.During periods of limited or inadequate precipitation, vegetation relies on soil moisture for photosynthesis and transpiration.When available soil moisture drops below critical thresholds, particularly in vegetation types without alternative drought coping strategies like tropical trees, vegetation mortality rates increase (Anderson et al 2018).Declining vegetation, soil degradation, and ecosystem decomposition in drought-prone regions may be linked to the watershed surpassing drought index thresholds.
Currently, there have been some individual studies (table S1) estimating CWSC using field observation methods and physical modeling at the site scale, as well as at the watershed scale using lumped hydrological models (Schenk andJackson 2002, Wang-Erlandsson et al 2016).Methods based on field observations can be utilized for estimating CWSC (Zeng 2001), which benefits from calculations based on vertical distribution (Jackson et al 1996).Schenk and Jackson (2002) employed a point-scale method to calculate root zone depths of biological communities, while Schenk et al (2009) utilized empirical regression models to translate vertical depths from field observation methods to other scales.Physical model approaches involve iteratively simulating net primary productivity (NPP) or evapotranspiration using soil physics equations and parameters at different depths (Ichii et al 2007(Ichii et al , 2009)).The annual water storage is obtained by cumulatively subtracting runoff and evapotranspiration from precipitation at each time step, with CWSC calculated as the difference between the maximum and minimum annual water storage within the computation period (Zhao et al 2016).Gao et al (2014) employed the cumulative deficit method to estimate watershed-scale CWSC in the United States and Thailand.Euser et al (2016) applied the water balance method to watersheds in New Zealand, utilizing interception and watershed storage to monitor soil water deficits caused by changes in precipitation and evapotranspiration.NASA's GRACE product is a key water storage calculation effort, which provides gridded, temporally-varying water storage estimates across the globe.However, there is a lack of systematic methods to estimate CWSC at the grid scale, which hampers the ability to accurately understand its dynamic variation.Estimations at the watershed scale typically rely on remote sensing precipitation data and evapotranspiration fluxes to estimate soil and plant-available water storage capacity (Stocker et al 2021).However, the exclusion of runoff from the estimations at the watershed scale imposes limitations on hydrological applicability.With the advancement of computer technology, models based on hydrological theory and numerical simulation methods have been gradually utilized.These models enable more precise calculations of CWSC, including three-dimensional geological models and hydrogeological simulations.However, calibration methods for hydrological models face challenges due to parameter discontinuity in space, making it difficult to generalize them to larger regional and global scales (Xie et al 2021).Currently, while there are various methods for estimating CWSC within a watershed, global-scale applications are limited.Few studies have focused on globally estimating CWSC from the perspective of rainfall-runoff relationships in hydrological models (Nijssen et al 2001, Beck et al 2015).Estimating the CWSC using traditional methods may not be advantageous when it comes to distributed hydrological models.
Accurately estimating spatio-temporal CWSC relies on identifying the parameters of hydrological models, which has become a recent research focus and bottleneck.Existing studies have indicated that the value of CWSC can vary based on watershed characteristics and climate conditions.Not only does CWSC change over time, but it also exhibits spatial variability.Currently, there is insufficient research on spatio-temporal correlation.Blöschl et al (2019) has repeatedly mentioned in their summary of 23 unresolved issues in the field of hydrology that model parameters play a crucial role in simulating rainfall-runoff relationships.It has conventionally been assumed that model parameters calibrated using historical data are also suitable for simulating future runoff scenarios in analyzing the impact of climate change.However, this assumption no longer holds under changing environmental conditions, as the non-stationarity of climate conditions has not been considered in future climate predictions ( For instance, rising temperatures may result in the melting of glaciers and reduced snow accumulation, both of which impact the storage capacity of the watershed.Changes in the distribution of land cover and atmospheric conditions can also affect the storage capacity.Moreover, alterations in vegetation cover and land use can influence evapotranspiration and infiltration processes in the watershed.Some significantly changing model parameters displayed a clear correlation with climate indices.Therefore, studying the spatio-temporal characteristics of hydrological model parameters contributes to understanding runoff responses under changing environmental conditions and enhancing the performance of constant parameter models. The goal of this study is to propose a deep learning network-based approach for mapping watershed characteristics, reconstructing parameter spaces, and assessing the impact of future scenarios on runoff.Firstly, a deep residual network (ResNet), is used to identify spatial variations in parameters in datadeficient regions by mapping watershed characteristics and CWSC.Secondly, an ensemble Kalman filter (EnKF) and a deep ResNet with multi-task outputs are employed to predict future CWSC under SSP5-8.5.Finally, the study investigates the impact of spatio-temporal variations in CWSC on changes in runoff.This evaluation helps assess how spatiotemporal variations in CWSC will affect the runoff quantity.

Grid-based distributed hydrological model
In hydrological modeling, the consideration of spatial distribution of CWSC poses challenges for lumped models in identifying relevant spatial parameters.This limitation necessitates the use of distributed hydrological models.In this context, a grid-based distributed hydrological model is adopted to address these challenges.It is crucial to provide a clear conceptual description of the CWSC and ensure that the number of model parameters remains reasonable.Figure S1 illustrates the construction of a distributed hydrological model that incorporates a function to represent the CWSC (Wang 2018, Xie et al 2020).To enhance the applicability of the model in simulating hydrological processes in cold regions worldwide, a snowmelt module is incorporated, which employs a snowmelt degree-day factor model (Zhuo and Tan 2021).The evaporation module is based on the generalized evaporation complementary theory (Moore andClarke 1981, Miralles et al 2011).Additionally, the routing module utilizes the instantaneous unit hydrograph and linear reservoir method.Detailed derivation process about the grid-based distributed hydrological model is explained in text S1.
To obtain the spatial distribution of continuous parameters for CWSC, a distributed hydrological model was implemented at the global grid scale using a calibration strategy with spatially sparse grids.This strategy utilized a combination of the grid's actual evapotranspiration and runoff depth products as the objective function.The SCE-UA algorithm was employed in conjunction with the spatially sparse grid for calibrating the model parameters.Multiobjective optimization of hydrological models is used to find the parameters to minimize the selected values of different objective functions.The conventional objective of calibration is to adjust the parameters to simulate the streamflow at the outlet.Both runoff and evaporation simulation are realized among each grid when multiple observations are available.The objective function, mean square error is converted into a weighted mean value: where i denotes the streamflow gauging stations and j denotes spatial grids; N Q is the number of the first objective variable for the runoff; N E is the total number of spatial grids for the evaporation.The warm-up period consisted of the first year, while the remaining 2/3 of the time series were designated as the calibration period for each grid.The last 1/3 was reserved as the validation period.

Spatial-varying parameter estimation 2.2.1. Deep ResNets based on convolution neural networks (CNNs)
Driven by the increasing computational power of computers and the availability of big data, unsupervised deep learning methods exhibit superior ana-

Spatial reconstruction learning framework for ungauged areas
The spatial interpolation method employed in regions with limited data is regression analysis, which utilizes other variables to establish a mapping relationship for predicting missing values.This approach necessitates the consideration of the correlations between these variables and the missing variable (Xie and Shen 2023).
The limitations of hydrological models in ungauged areas pose challenges in obtaining accurate CWSC, as well as extracting pertinent information from a vast amount of global data (Clark et al 2016, Zhang et al 2021).The construction of parameters in hydrological models is based on the response of observed variables within the watershed.The complex interactions and influences among processes at different scales contribute to the intricacy of parameter calibration.Calibration at the watershed scale introduces discontinuity in spatial parameters.
The input data for the deep ResNet comprises meteorological time series and underlying surface attributes.Detailed data is explained in text S2.Global image sample data is cropped into several fixedsize window samples through a sampling window.It can be treated as a large batch of global image inputs, aligning with the structure of CNNs.The output of the model is the CWSC at the grid scale.In regions where the Kling-Gupta efficiency (KGE) of the distributed hydrological model's runoff simulation exceeds zero, the calibration of the hydrological model enables the acquisition of CWSC parameters.However, in regions where the hydrological model is not applicable, such as highly arid areas, the establishment of a hydrological model is not feasible.Regions with negative KGE values in runoff simulation accuracy will be masked, and grids with an KGE greater than 0.60 will be divided into calibration and validation sets in 7:3.
Figure 1 illustrates the utilization of CWSC parameters from global land surface grids as the target label for the model.The process of the deep ResNet encompasses the following three steps: (  2, after obtaining the time-varying CWSC parameters during the historical stage using the EnKF method, these parameters are utilized as a new labeled sample set to enhance the physically consistent deep ResNet.To extend this process to future time changes, the previously calibrated deep ResNet requires expansion.Whereas the previous deep learning network structure possessed multiple inputs and a single output, incorporating time-varying meteorological elements and underlying surface as inputs, and time-averaged CWSC parameters as the output, a sequence-to-sequence deep learning network structure is introduced.This structure aligns the input of time-varying scenarios in the historical context with the output of time-varying CWSC parameters during

Learning results of spatial reconstruction in ungauged areas
The label values of the CWSC parameters are used for model learning (pre-reconstruction) and the globally reconstructed CWSC parameters (postreconstruction).The findings unveil a consistent pattern, where the CWSC tends to be higher in temperate regions and lower in arid regions.Furthermore, the parameters exhibit a gradual decrease as one moves from the equator towards the poles.
Based on the findings presented in table S5, the model displayed varying accuracy throughout the training process for different image windows within the calibration and validation datasets, attributable to the utilization of distinct sample labels.The study highlights that adopting the mass curve technique resulted in poor performance of the CNN recognition network.In contrast, superior outcomes were observed when applying the hydrological model method for sample labeling, as it incorporates a more comprehensive range of runoff information.Training the model using the hydrological model method resulted in an increase in the R 2 of the validation dataset from 0.75 to 0.83, indicating enhanced sample accuracy.Hence, incorporating the hydrological model method during model training leads to improved learning performance.
The study conducted an analysis of the characteristic distribution of CWSC parameters following global reconstruction.Out of the 61 345 land surface 0.5 • grids worldwide, 39 874 grids (65%) were classified as the labeled region, exhibiting an KGE greater than 0.60, while the remaining 21 471 grids (35%) were classified as missing regions.The applicability of the hydrological models extends only to the labeled region, excluding arid regions and certain high-latitude areas.Figure S6 portrays the globally reconstructed CWSC parameters' spatial distribution probability density function, revealing a bimodal distribution for the global CWSC.The first peak corresponds to arid regions, and the second peak corresponds to temperate regions.Additionally, figures S6(c) and (d) illustrate the variation in global CWSC with latitude and longitude, demonstrating that the maximum values occur near the equator and gradually decrease towards the poles.

Time transfer learning results in future stages
Figure S7 illustrates the changes in CWSC under future scenarios using parameter transfer learning.The construction of a deep learning network architecture featuring multiple inputs and multiple outputs is proposed.The input variables capture the temporal fluctuations in historical scenarios, aligning with the corresponding output variables reflecting changes in basin storage capacity parameters during historical periods.Subsequently, we employ a meticulously calibrated multi-task output deep ResNet model to process the time-varying sequences under future scenarios, enabling the estimation of transfer learning outcomes for basin storage capacity parameters under future conditions.The depicted results present the average values derived from 20 global climate models across various emission scenarios.The findings indicate a significant global increase in CWSC, with a change rate range of 1.7 mm/10 years under the SSP5-8.5 emission scenario.Nevertheless, Western Europe, Eastern North America, and Southeastern South America exhibit notable decreasing trends, with a change rate range of −1.0-0 mm/10 years under the SSP5-8.5 emission scenario.Furthermore, both SSP2-4.5 and SSP5-8.5 scenarios demonstrate a stronger trend in future CWSC with increasing emission intensity.
Variations in precipitation patterns and distribution can contribute to alterations in CWSC, potentially resulting in heightened drought and water scarcity in certain regions, as well as more frequent flooding in others.The impact of human activities on CWSC should not be overlooked.For instance, the construction of reservoirs and water diversion structures can augment storage capacity.Similarly, changes in land use also exert an influence on CWSC.For example, forests and wetlands can enhance soil water retention capabilities, while urbanization and agriculture may lead to water loss and diminished storage capacity.Due to data limitations, this study solely provided simplified forecasts of the temporal variability of global CWSC parameters based on future climate change scenarios, without considering forthcoming data on human activities and land use changes.
Figure 4 illustrates the temporal trends of CWSC parameters across Köppen climate.The findings of this study reveal a notable upward trend in the annual average CWSC for tropical and temperate regions.In contrast, the arid and polar zones exhibit a significant decline in annual average CWSC.These trends have been rigorously analyzed and exhibit a high level of statistical confidence.Additionally, inland areas demonstrate a discernible but insignificant decreasing trend in annual average CWSC.Results about the time-varying trend of CWSC by continent are illustrated in figure S8.
Despite relatively abundant precipitation, the distribution is uneven within the tropical zone, often accompanied by brief yet intense rainfall episodes.Such climatic conditions give rise to short-term fluctuations in CWSC, resulting in alternating periods of brief floods and droughts.Moreover, elevated temperatures and intensive evaporation rates markedly contribute to accelerated soil moisture depletion, consequently leading to pronounced changes in water storage capacity.
Additionally, Africa and Asia demonstrate a notably substantial rise in the annual average CWSC.In contrast, South America and Europe display a remarkable decline in the annual average CWSC, both supported by statistical significance tests for trend analysis.Conversely, the annual average variations in CWSC in North America and Oceania do not exhibit significant trends.

Assessment of the impact of spatial-temporal variation in CWSC on runoff
As shown in figure 5, the changes in CWSC can significantly influence the runoff process of a watershed.The increase in CWSC can have ramifications for future runoff, offering the potential to alleviate the occurrence of floods and droughts through enhanced water storage and release.Increasing storage capacity contributes to a reduction in flood frequency and mitigation of drought impacts by augmenting water availability during dry periods.This bears particular significance for drought-prone regions as it enhances the sustainable utilization of water resources.
Conversely, a decrease in CWSC can yield diverse effects on future hydrological runoff contingent upon watershed characteristics and the degree of storage capacity reduction.Diminished storage capacity may result in reduced soil moisture levels, influencing precipitation infiltration and evaporation.The inherent rise in soil moisture (e.g.caused by melting glaciers) could signify an increase in CWSC values.A decrease The increase in CWSC can potentially impact future runoff.This is because a greater amount of rainfall can be stored and released.On the other hand, a decrease in CWSC can result in reduced soil moisture content, subsequently affecting the infiltration evaporation of precipitation.This can lead to changes in the distribution and intensity of rainfall.
in CWSC could imply higher ET or lower percolation, affecting runoff differently.Consequently, this may induce alterations in rainfall distribution and intensity, thereby potentially elevating the risk of droughts or floods under certain circumstances.Reduced CWSC prompts modifications in streamflow, particularly during the culmination of dry seasons or periods of drought when storage capacity is insufficient.These changes can impact river ecosystems and human activities such as irrigation, power generation, and water supply.
To address this, the present study integrates the spatio-temporal variability of CWSC into the gridbased distributed hydrological model.We consider spatio-temporal variability of CWSC into the gridbased distributed hydrological models and analyze the impacts of constant parameters versus timevarying parameters on future runoff simulations.The objective is to assess and compare the impact of static parameters and time-varying parameters on future runoff simulations.Figure 6  The spatio-temporal variability of CWSC serves as a buffer for runoff response under climate change.In the near-future, global runoff depth demonstrates an increasing trend.However, due to an expansion in CWSC, the rate of runoff increase may decrease by 32% (reducing the difference in runoff depth increase from 12 mm to 8 mm).In the far-future, the rise in global CWSC will further decelerate the rate of runoff increase, potentially decreasing it by up to 41% (reducing the difference in runoff depth increase from 44 mm to 26 mm).
In the equatorial and humid zones, an increased water storage capacity of the basin primarily serves to attenuate the rate of runoff increase.With the ability to store more precipitation within the basin, soil water content is likely to increase correspondingly.Alterations in the water storage capacity of a watershed also exert an influence on surface runoff.A higher storage capacity results in a greater amount of precipitation being retained in the basin, leading to a potential decrease in surface runoff.Conversely, in arid and polar zones, amplified runoff predominates.A diminished storage capacity in the basin may cause a decrease in soil water content, as more precipitation is lost to the river or groundwater.A reduction in watershed capacity directs more precipitation towards rivers or groundwater, thereby augmenting surface runoff.

Discussions
The calibrated CWSC estimated using the calibration method in this study is subject to certain uncertainties.Firstly, gridded meteorological products are primarily derived from scattered weather stations, which exhibit substantial spatiotemporal heterogeneity.Particularly for large watersheds, the observations within the watershed may not adequately capture the spatiotemporal variability, thereby potentially affecting the simulation results of the model.Secondly, there are uncertainties in each stage of hydrological modeling, with errors stemming from observational uncertainties in input data.The uncertainties in input predictions imply that the model is subject to the uncertainty of input data, such as precipitation, temperature, and other measured inputs (Singh and Dutta 2017).In addition to meteorological data, spatial data such as elevation, vegetation type, and soil type are included as input data, which ultimately affect the accuracy of the dataset.
We compared the global reconstruction of CWSC with other similar parameter datasets such as the spatial distribution of global root zone depth (Schenk et al 2009, Wang-Erlandsson et al 2016).As shown in figure S9, all datasets exhibit relatively similar spatial distributions, decreasing from the equator to the poles.However, in tropical rainforest regions, the values from other datasets are consistently smaller than those estimated in this study.Global root zone depth tends to overestimate storage capacity in the Sahara Desert, Arabian Desert, and Western Australia Desert.The global root zone depth may not be as deep, particularly in humid regions near the equator.The study results indicate that global root zone depth is merely an estimation in the vertical dimension and cannot represent the generation of lateral flow and runoff because soil water is not only absorbed by roots but also retains more capacity for surface and subsurface runoff.The estimation of global root zone depth only utilizes precipitation and evaporation data types, lacking model validation.Even though actual evaporation products provided by models were used in calculations, the CWSC calculated using this method may not accurately simulate evaporation due to the lack of a model foundation, leading to significant uncertainty.
The nonlinearity of the model structure and parameter correlations can result in multiple local optima in the model, leading to significant uncertainties in the runoff simulation process.The dataset only considers constraints based on current climate conditions, while ignoring future changes.This research estimated and verified the CWSC based on meteorological data, potential surface characteristics, and runoff data from 1902 to 2014.However, when using data from different time periods, the estimated results may vary.Recent studies have indicated that soil water storage in the root zone changes due to climate change and deforestation, and vegetation alters the capacity to exploit groundwater storage and tree cover to cope with drought climate (Singh et al 2020).Consequently, the CWSC may vary over time.Moreover, this dataset primarily provides CWSC data for daily-scale hydrological models, and further research is needed to investigate the transformation relationship between parameters at different time scales.

Conclusions
The study utilized a deep learning network that mapped watershed characteristics and CWSC to identify spatial variations in parameter data for ungauged areas.It validated the transferability of CWSC parameter across different climatic regions.Additionally, a combination of EnKF and deep ResNet with multi-task outputs was employed to further predict watershed storage capacity for future periods.This study assess the impact of climate change on global runoff response, with a specific focus on the neglect of spatio-temporal variability in CWSC.It investigates the effects of such variability on runoff changes and evaluates the response under various historical and future climate scenarios.
The utilization of a deep learning network, which establishes a correlation between watershed characteristics and storage capacity, proves to be an effective method for reconstructing spatial variability and transfer learning in CWSC.It emphasizes that the neglect of such variability leads to an overestimation of climate change's impact on runoff at a global scale.The assessment of spatio-temporal variability parameters plays a crucial role in future climate change research, allowing for quantitative predictions of trends in CWSC and serving as a key factor in the development of future climate change response and warning systems.

Open Research
Yang et al 2020).The temporal variability of hydrological parameters has become a key topic of extensive research interest in recent years (White et al 2022).The effects of different climate conditions and human activities prevent the parameters obtained during the calibration period from representing the parameter values over the entire time series.The temporal variation of hydrological parameters demonstrates non-stationarity (Gao et al 2013, Xiong et al 2019, Aguirre-Gutiérrez et al 2020).
lytical and learning capabilities compared to statistical models (Kratzert et al 2019, Sit et al 2020).Deep learning networks have achieved remarkable success in the field of Earth science, deriving extensive applications in addressing challenges such as spatial missing data (Wang et al 2021), spatial down-scaling, and improvement of the spatial precipitation prediction (Pan et al 2019).CNNs enable automatic feature learning from vast amounts of data and generalize them to unfamiliar domains of the same nature (Shin et al 2016).The convolution and pooling layers of CNNs operate exclusively within local neighborhoods, facilitating the capture of local geometric characteristics and spatial patterns, as well as the extraction of relationships at larger scales within deeper layers (Shen 2018, Jiang et al 2020).The deep ResNet addresses the degradation problem by establishing a smoother gradient flow through the external network.Conventional statistical methods are incapable of capturing complex interactions and suffer from slow computation speeds.By utilizing parallel computation, ResNet achieves significantly faster processing despite its increased network complexity.The proposed model operates on a GPU cluster, with each step taking only 758 microseconds.Thus, it can execute computations on all global 0.5 • grids within approximately one hour.

Figure 1 .
Figure 1.The spatial reconstruction learning framework for ungauged areas.The process of the deep ResNet encompasses parameter identification, model learning, and missing data reconstruction.

Figure 2 .
Figure 2. The sequence-to-sequence framework for temporal transfer learning in future stages.Sequence-to-sequence structure aligns the input of time-varying scenarios in the historical context with the output of time-varying CWSC parameters during the historical stage.

Figure 3 .
Figure 3. Spatial distribution of continuous global grid parameters.Figure (a) illustrates the CWSC (catchment water storage capacity) parameters prior to reconstruction, serving as the labels for the deep learning model.Figure (b) shows the CWSC parameters after reconstruction, exhibiting a globally continuous distribution.
Figure S5 demonstrates the performance of the distributed hydrological model during both the calibration and validation periods on global grids, achieving an average KGE of 0.58 and a median of 0.72.The simulated data is derived from the hydrological model and the observation data refers to runoff depth.From a global viewpoint, the model exhibited higher simulation accuracy (the KGE range: 0.60-0.90) in wet regions, whereas its accuracy was relatively lower (the KGE range: 0.20-0.60) in semi-arid regions like the central United States and high-latitude cold regions.The spatial distribution of CWSC parameters in the global grid-based distributed model was represented based on figure 3.Each grid in this depiction had a uniform area, with color indicating the magnitude of the respective CWSC parameter.The study identified higher values of the parameter in low-latitude regions near the equator, while progressively decreasing values were observed when moving from wet to arid regions.Similarly, high-latitude areas generally exhibited lower parameter values, corroborating the patterns obtained from the lumped model simulations.Nevertheless, data-deficient areas, including deserts in the western parts of mid-latitude continents and Greenland, still impose limitations where the hydrological model cannot be applied.Consequently, these data gaps hinder a comprehensive understanding of the complete global distribution of CWSC.

Figure 4 .
Figure 4.The time-varying trend of CWSC (Catchment Water Storage Capacity) by Köppen climate classification.It reveals a notable upward trend in the annual average CWSC for tropical and temperate regions.In contrast, the arid and polar zones exhibit a significant decline in annual average CWSC.AWI means the Alfred Wegener Institute climate model, MPI means Max Planck Institute climate model, and ssp means shared socio-economic pathways.

Figure 5 .
Figure 5. Schematic diagram of the impact of changes in CWSC (catchment water storage capacity) on watershed runoff process.The increase in CWSC can potentially impact future runoff.This is because a greater amount of rainfall can be stored and released.On the other hand, a decrease in CWSC can result in reduced soil moisture content, subsequently affecting the infiltration evaporation of precipitation.This can lead to changes in the distribution and intensity of rainfall.
illustrates the utilization of data from multiple climate models in this study to input future meteorological data into a distributed hydrological model for predicting runoff.The figure displays the average runoff depth across grid cells for the historical period (1970-2014), near-future (2015-2059), and far-future (2060-2100), based on data from 20 climate models.At a global scale, neglecting the temporal and spatial variability of CWSC leads to an overestimation of climate change's impact on runoff.The impact of spatio-temporal variability of CWSC on global runoff by Köppen climate classification in future scenarios is illustrated in figure 7.

Figure 6 .
Figure 6.The impact of spatio-temporal variability of CWSC on global runoff in future scenarios.The figure presents the grid-average runoff depth for historical period (1970-2014), near-term future (2015-2059), and long-term future (2060-2100).The values represent the mean runoff depth across the grid based on the data from 20 different climate models.

Figure 7 .
Figure 7.The impact of spatio-temporal variability of CWSC on global runoff by Köppen climate classification in future scenarios.
The Python codes of the deep residual network developed for the global reconstruction results are available at https://zenodo.org/record/8371859.The global construction map of CWSC in this study can be gathered from an open-access data server https:// zenodo.org/record/5598405.The data on global runoff data is based are available in(Hong et al 2007).For more information, please visit www.bafg.de/GRDC/.The data on meteorological data is based are available in CRU TS Gridded Data.For more information, please visit https://data.ceda.ac.uk/badc/cru/ data/cru_ts/cru_ts_4.03.The data on future data is based are available in General Circulation Model (GCM) Products.For more information, please visit https://esgf-node.llnl.gov/projects/cmip6/. Roo A D and Dijk A I J M V 2015 Global maps of streamflow characteristics based on observations from several thousand catchments J. Hydrometeorol.16 1478-501 Blöschl G et al 2019 Twenty-three unsolved problems in hydrology (UPH)-a community perspective Hydrol.Sci.J. 64 1141-58 Clark M P et al 2016 Improving the theoretical underpinnings of process-based hydrologic models Water Resour.Res.52 2350-65 Euser T D B, McMillan H K, Hrachowitz M, Winsemius H C and Savenije H H 2016 Influence of soil and climate on root zone storage capacity Water Resour.Res.52 2009-24 Evensen G 1994 Sequential data assimilation with a nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics J. Geophys.Res.99 10143-62 Gao H, Hrachowitz M, Schymanski S J, Fenicia F, Sriwongsitanon N and Savenije H H G 2014 Climate controls how ecosystems size the root zone storage capacity at catchment scale Geophys.Res.Lett.41 7916-23 Gao P, Geissen V, Ritsema C J, Mu X M and Wang F 2013 Impact of climate change and anthropogenic activities on stream flow and sediment discharge in the wei river basin, China Hydrol.Earth Syst.Sci. 17 961-72 Hong Y, Adler R F, Hossain F, Curtis S and Huffman G J 2007 A first approach to global runoff simulation using satellite rainfall estimation Water Resour.Res.43 Huang Z et al 2018 Reconstruction of global gridded monthly sectoral water withdrawals for 1971-2010 and analysis of their spatiotemporal patterns Hydrol.Earth Syst.Sci.22 2117-33 Ichii K, Hashimoto H, White M A, Potter C, Hutyra L R, Huete A R, Myneni R B and Nemani R R 2007 Constraining rooting depths in tropical rainforests using satellite data and ecosystem modeling for accurate simulation of gross primary production seasonality Glob.Change Biol.13 67-77 Ichii K, Wang W, Hashimoto H, Yang F, Votava P, Michaelis A R and Nemani R R 2009 Refinement of rooting depths using satellite-based evapotranspiration seasonality for ecosystem modeling in california Agric.For.Meteorol.149 1907-18 Jackson R B, Canadell J, Ehleringer J R, Mooney H A, Sala O E and Schulze E-D 1996 A global analysis of root distributions for terrestrial biomes Oecologia 108 389-411 Jiang S, Zheng Y and Solomatine D 2020 Improving AI system awareness of geoscience knowledge: symbiotic integration of physical approaches and deep learning Geophys.Res.Lett.47 e2020GL088229 Kratzert F, Klotz D, Herrnegger M, Sampson A K, Hochreiter S and Nearing G S 2019 Toward improved predictions in ungauged basins: exploiting the power of machine learning Water Resour.Res.55 11344-54 Li W, Migliavacca M, Forkel M, Denissen J M C, Reichstein M, Yang H, Duveiller G, Weber U and Orth R 2022 Widespread increasing vegetation sensitivity to soil moisture Nat.Commun.13 3959 Li Z, Liu P, Deng C, Guo S, He P and Wang C 2016 Evaluation of estimation of distribution algorithm to calibrate computationally intensive hydrologic model J. Hydrol.Eng.21 04016012 Luo X R, Liu P, Dong Q J, Zhang Y J, Xie K and Han D Y 2023 Exploring the role of the long short-term memory model in improving multi-step ahead reservoir inflow forecasting J. Flood Risk Manage.16 e12854 McColl K A, Wang W, Peng B, Akbar R, Gianotti D J S, Lu H, Pan M and Entekhabi D 2017 Global characterization of surface soil moisture drydowns Geophys.Res.Lett.44 3682-90 Miralles D G, Holmes T R H, Jeu R A M D, Gash J H, Meesters A G C A and Dolman A J 2011 Global land-surface evaporation estimated from satellite-based observations Hydrol.Earth Syst.Sci. 15 453-69 Moore R J and Clarke R T 1981 A distribution function approach to rainfall runoff modeling Water Resour.Res. 17 1367-82 ReferencesAguirre-Gutiérrez J et al 2020 Long-term droughts may drive drier tropical forests towards increased functional, taxonomic and phylogenetic homogeneity Nat.Commun.111-10 Anderson L O, Neto G R, Cunha A P, Fonseca M G, Moura Y M D, Dalagnol R, Wagner F H and Aragão L E O E C D 2018 Vulnerability of amazonian forests to repeated droughts Phil.Trans.R. Soc.B 373 20170411Beck H E,