Showing papers in "Hydrology and Earth System Sciences in 2022"

Uncertainty estimation with deep learning for rainfall–runoff modeling

Abstract: Abstract. Deep learning is becoming an increasingly important way to produce accurate hydrological predictions across a wide range of spatial and temporal scales. Uncertainty estimations are critical for actionable hydrological prediction, and while standardized community benchmarks are becoming an increasingly important part of hydrological model development and research, similar tools for benchmarking uncertainty estimation are lacking. This contribution demonstrates that accurate uncertainty predictions can be obtained with deep learning. We establish an uncertainty estimation benchmarking procedure and present four deep learning baselines. Three baselines are based on mixture density networks, and one is based on Monte Carlo dropout. The results indicate that these approaches constitute strong baselines, especially the former ones. Additionally, we provide a post hoc model analysis to put forward some qualitative understanding of the resulting models. The analysis extends the notion of performance and shows that the model learns nuanced behaviors to account for different situations.

The Great Lakes Runoff Intercomparison Project Phase 4: the Great Lakes (GRIP-GL)

Abstract: Abstract. Model intercomparison studies are carried out to test and compare the simulated outputs of various model setups over the same study domain. The Great Lakes region is such a domain of high public interest as it not only resembles a challenging region to model with its transboundary location, strong lake effects, and regions of strong human impact but is also one of the most densely populated areas in the USA and Canada. This study brought together a wide range of researchers setting up their models of choice in a highly standardized experimental setup using the same geophysical datasets, forcings, common routing product, and locations of performance evaluation across the 1×106 km2 study domain. The study comprises 13 models covering a wide range of model types from machine-learning-based, basin-wise, subbasin-based, and gridded models that are either locally or globally calibrated or calibrated for one of each of the six predefined regions of the watershed. Unlike most hydrologically focused model intercomparisons, this study not only compares models regarding their capability to simulate streamflow (Q) but also evaluates the quality of simulated actual evapotranspiration (AET), surface soil moisture (SSM), and snow water equivalent (SWE). The latter three outputs are compared against gridded reference datasets. The comparisons are performed in two ways – either by aggregating model outputs and the reference to basin level or by regridding all model outputs to the reference grid and comparing the model simulations at each grid-cell. The main results of this study are as follows: The comparison of models regarding streamflow reveals the superior quality of the machine-learning-based model in the performance of all experiments; even for the most challenging spatiotemporal validation, the machine learning (ML) model outperforms any other physically based model. While the locally calibrated models lead to good performance in calibration and temporal validation (even outperforming several regionally calibrated models), they lose performance when they are transferred to locations that the model has not been calibrated on. This is likely to be improved with more advanced strategies to transfer these models in space. The regionally calibrated models – while losing less performance in spatial and spatiotemporal validation than locally calibrated models – exhibit low performances in highly regulated and urban areas and agricultural regions in the USA. Comparisons of additional model outputs (AET, SSM, and SWE) against gridded reference datasets show that aggregating model outputs and the reference dataset to the basin scale can lead to different conclusions than a comparison at the native grid scale. The latter is deemed preferable, especially for variables with large spatial variability such as SWE. A multi-objective-based analysis of the model performances across all variables (Q, AET, SSM, and SWE) reveals overall well-performing locally calibrated models (i.e., HYMOD2-lumped) and regionally calibrated models (i.e., MESH-SVS-Raven and GEM-Hydro-Watroute) due to varying reasons. The machine-learning-based model was not included here as it is not set up to simulate AET, SSM, and SWE. All basin-aggregated model outputs and observations for the model variables evaluated in this study are available on an interactive website that enables users to visualize results and download the data and model outputs.

Deep learning methods for flood mapping: a review of existing applications and future research directions

Abstract: Abstract. Deep learning techniques have been increasingly used in flood management to overcome the limitations of accurate, yet slow, numerical models and to improve the results of traditional methods for flood mapping. In this paper, we review 58 recent publications to outline the state of the art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate, as they leverage inductive biases to better process the spatial characteristics of the flooding events. Models based on fully connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist in real-time flood warning during an emergency and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies. Furthermore, all reviewed models and their outputs are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Physics-based deep learning can be used to preserve the underlying physical equations resulting in more reliable speed-up alternatives for numerical models. Similarly, probabilistic models can be built by resorting to deep Gaussian processes or Bayesian neural networks.

Ensemble streamflow forecasting over a cascade reservoir catchment with integrated hydrometeorological modeling and machine learning

Abstract: Abstract. A popular way to forecast streamflow is to use bias-corrected meteorological forecasts to drive a calibrated hydrological model, but these hydrometeorological approaches suffer from deficiencies over small catchments due to uncertainty in meteorological forecasts and errors from hydrological models, especially over catchments that are regulated by dams and reservoirs. For a cascade reservoir catchment, the discharge from the upstream reservoir contributes to an important part of the streamflow over the downstream areas, which makes it tremendously hard to explore the added value of meteorological forecasts. Here, we integrate meteorological forecasts, land surface hydrological model simulations and machine learning to forecast hourly streamflow over the Yantan catchment, where the streamflow is influenced by both the upstream reservoir water release and the rainfall–runoff processes within the catchment. Evaluation of the hourly streamflow hindcasts during the rainy seasons of 2013–2017 shows that the hydrometeorological ensemble forecast approach reduces probabilistic and deterministic forecast errors by 6 % compared with the traditional ensemble streamflow prediction (ESP) approach during the first 7 d. The deterministic forecast error can be further reduced by 6 % in the first 72 h when combining the hydrometeorological forecasts with the long short-term memory (LSTM) deep learning method. However, the forecast skill for LSTM using only historical observations drops sharply after the first 24 h. This study implies the potential of improving flood forecasts over a cascade reservoir catchment by integrating meteorological forecasts, hydrological modeling and machine learning.

Using a long short-term memory (LSTM) neural network to boost river streamflow forecasts over the western United States

Abstract: Abstract. Accurate river streamflow forecasts are a vital tool in the fields of water security, flood preparation and agriculture, as well as in industry more generally. Over the last century, physics-based models traditionally used to produce streamflow forecasts have become increasingly sophisticated, with forecasts improving accordingly. However, the development of such models is often bound by two soft limits: empiricism – many physical relationships are represented by computationally efficient empirical formulae; and data sparsity – the calibration of these models often requires long time-series of high-resolution observational data at both surface and subsurface levels. Artificial neural networks have previously been shown to be highly effective at simulating nonlinear systems where knowledge of the underlying physical relationships is incomplete. However, they also suffer from issues related to data sparsity. Recently, hybrid forecasting systems, which combine the traditional physics-based approach with statistical forecasting techniques, have been investigated for use in hydrological applications. In this study, we test the efficacy of a type of neural network, the long-short term memory (LSTM), at predicting streamflow at ten river gauge stations across various climatic regions of the western United States. The LSTM is trained on the catchment-mean meteorological and hydrological variables from the ERA5 and GloFAS-ERA5 reanalysis as well as historical streamflow observations. The performance of these hybrid forecasts is evaluated and compared to the performance of both raw and bias-corrected output from the Copernicus Emergency Management Service (CEMS) physics-based Global Flood Awareness System (GloFAS). Two periods are considered, a testing phase (June 2019 to June 2020), during which the models were fed with ERA5 data to investigate how well they simulated streamflow at the ten stations; and an operational phase (September 2020 to October 2021), during which the models were fed forecast variables from ECMWF's Integrated Forecast System (IFS), to investigate how well they could predict streamflow at lead times of up to ten days. All three models performed well in the testing phase, with the LSTM performing the best (skilful at nine stations, of which six were highly skilful). Similarly, the LSTM forecasts beat the raw and bias-corrected GloFAS forecasts during the operational phase, with skilful 5-day forecasts at nine stations, of which five were highly skilful. Implications and potential improvements to this work are discussed. In summary, this is the first time an LSTM has been used in a hybrid system to create a medium-range streamflow forecast, and in beating established physics-based models, shows promise for the future of neural networks in hydrological forecasting.

Deep learning rainfall–runoff predictions of extreme events

Abstract: Abstract. The most accurate rainfall–runoff predictions are currently based on deep learning. There is a concern among hydrologists that the predictive accuracy of data-driven models based on deep learning may not be reliable in extrapolation or for predicting extreme events. This study tests that hypothesis using long short-term memory (LSTM) networks and an LSTM variant that is architecturally constrained to conserve mass. The LSTM network (and the mass-conserving LSTM variant) remained relatively accurate in predicting extreme (high-return-period) events compared with both a conceptual model (the Sacramento Model) and a process-based model (the US National Water Model), even when extreme events were not included in the training period. Adding mass balance constraints to the data-driven model (LSTM) reduced model skill during extreme events.

Towards hybrid modeling of the global hydrological cycle

Abstract: Abstract. State-of-the-art global hydrological models (GHMs) exhibit large uncertainties in hydrological simulations due to the complexity, diversity, and heterogeneity of the land surface and subsurface processes, as well as the scale dependency of these processes and associated parameters. Recent progress in machine learning, fueled by relevant Earth observation data streams, may help overcome these challenges. But machine learning methods are not bound by physical laws, and their interpretability is limited by design. In this study, we exemplify a hybrid approach to global hydrological modeling that exploits the data adaptivity of neural networks for representing uncertain processes within a model structure based on physical principles (e.g., mass conservation) that form the basis of GHMs. This combination of machine learning and physical knowledge can potentially lead to data-driven, yet physically consistent and partially interpretable hybrid models. The hybrid hydrological model (H2M), extended from Kraft et al. (2020), simulates the dynamics of snow, soil moisture, and groundwater storage globally at 1∘ spatial resolution and daily time step. Water fluxes are simulated by an embedded recurrent neural network. We trained the model simultaneously against observational products of terrestrial water storage variations (TWS), grid cell runoff (Q), evapotranspiration (ET), and snow water equivalent (SWE) with a multi-task learning approach. We find that the H2M is capable of reproducing key patterns of global water cycle components, with model performances being at least on par with four state-of-the-art GHMs which provide a necessary benchmark for H2M. The neural-network-learned hydrological responses of evapotranspiration and grid cell runoff to antecedent soil moisture states are qualitatively consistent with our understanding and theory. The simulated contributions of groundwater, soil moisture, and snowpack variability to TWS variations are plausible and within the ranges of traditional GHMs. H2M identifies a somewhat stronger role of soil moisture for TWS variations in transitional and tropical regions compared to GHMs. With the findings and analysis, we conclude that H2M provides a new data-driven perspective on modeling the global hydrological cycle and physical responses with machine-learned parameters that is consistent with and complementary to existing global modeling frameworks. The hybrid modeling approaches have a large potential to better leverage ever-increasing Earth observation data streams to advance our understandings of the Earth system and capabilities to monitor and model it.

Hydrological concept formation inside long short-term memory (LSTM) networks

Abstract: Abstract. Neural networks have been shown to be extremely effective rainfall-runoff models, where the river discharge is predicted from meteorological inputs. However, the question remains: what have these models learned? Is it possible to extract information about the learned relationships that map inputs to outputs, and do these mappings represent known hydrological concepts? Small-scale experiments have demonstrated that the internal states of long short-term memory networks (LSTMs), a particular neural network architecture predisposed to hydrological modelling, can be interpreted. By extracting the tensors which represent the learned translation from inputs (precipitation, temperature, and potential evapotranspiration) to outputs (discharge), this research seeks to understand what information the LSTM captures about the hydrological system. We assess the hypothesis that the LSTM replicates real-world processes and that we can extract information about these processes from the internal states of the LSTM. We examine the cell-state vector, which represents the memory of the LSTM, and explore the ways in which the LSTM learns to reproduce stores of water, such as soil moisture and snow cover. We use a simple regression approach to map the LSTM state vector to our target stores (soil moisture and snow). Good correlations (R2>0.8) between the probe outputs and the target variables of interest provide evidence that the LSTM contains information that reflects known hydrological processes comparable with the concept of variable-capacity soil moisture stores. The implications of this study are threefold: (1) LSTMs reproduce known hydrological processes. (2) While conceptual models have theoretical assumptions embedded in the model a priori, the LSTM derives these from the data. These learned representations are interpretable by scientists. (3) LSTMs can be used to gain an estimate of intermediate stores of water such as soil moisture. While machine learning interpretability is still a nascent field and our approach reflects a simple technique for exploring what the model has learned, the results are robust to different initial conditions and to a variety of benchmarking experiments. We therefore argue that deep learning approaches can be used to advance our scientific goals as well as our predictive goals.

Watershed zonation through hillslope clustering for tractably quantifying above- and below-ground watershed heterogeneity and functions

Abstract: Abstract. In this study, we develop a watershed zonation approach for characterizing watershed organization and functions in a tractable manner by integrating multiple spatial data layers. We hypothesize that (1) a hillslope is an appropriate unit for capturing the watershed-scale heterogeneity of key bedrock-through-canopy properties and for quantifying the co-variability of these properties representing coupled ecohydrological and biogeochemical interactions, (2) remote sensing data layers and clustering methods can be used to identify watershed hillslope zones having the unique distributions of these properties relative to neighboring parcels, and (3) property suites associated with the identified zones can be used to understand zone-based functions, such as response to early snowmelt or drought and solute exports to the river. We demonstrate this concept using unsupervised clustering methods that synthesize airborne remote sensing data (lidar, hyperspectral, and electromagnetic surveys) along with satellite and streamflow data collected in the East River Watershed, Crested Butte, Colorado, USA. Results show that (1) we can define the scale of hillslopes at which the hillslope-averaged metrics can capture the majority of the overall variability in key properties (such as elevation, net potential annual radiation, and peak snow-water equivalent – SWE), (2) elevation and aspect are independent controls on plant and snow signatures, (3) near-surface bedrock electrical resistivity (top 20 m) and geological structures are significantly correlated with surface topography and plan species distribution, and (4) K-means, hierarchical clustering, and Gaussian mixture clustering methods generate similar zonation patterns across the watershed. Using independently collected data, we show that the identified zones provide information about zone-based watershed functions, including foresummer drought sensitivity and river nitrogen exports. The approach is expected to be applicable to other sites and generally useful for guiding the selection of hillslope-experiment locations and informing model parameterization.

Trends and variability in snowmelt in China under climate change

Abstract: Abstract. Snowmelt is a major fresh water resource, and quantifying snowmelt and its variability under climate change is necessary for the planning and management of water resources. Spatiotemporal changes in snow properties in China have drawn wide attention in recent decades; however, country-wide assessments of snowmelt are lacking. Using precipitation and temperature data with a high spatial resolution (0.5′; approximately 1 km), this study calculated the monthly snowmelt in China for the 1951–2017 period, using a simple temperature index model, and the model outputs were validated using snowfall, snow depth, snow cover extent and snow water equivalent. Precipitation and temperature scenarios developed from five CMIP5 models were used to predict future snowmelt in China under three different representative concentration pathway (RCP) scenarios (RCP2.6, RCP4.5 and RCP8.5). The results show that the mean annual snowmelt in China from 1951 to 2017 is 2.41×1011 m3 yr−1. The mean annual snowmelt values in Northern Xinjiang, Northeast China and the Tibetan Plateau – China's three main stable snow cover regions – are 0.18×1011, 0.42×1011 and 1.15×1011 m3 yr−1, respectively. From 1951 to 2017, the snowmelt increased significantly in the Tibetan Plateau and decreased significantly in northern, central and southeastern China. In the whole of China, there was a decreasing trend in snowmelt, but this was not statistically significant. The mean annual snowmelt runoff ratios are generally more than 10 % in almost all third-level basins in West China, more than 5 % in third-level basins in North and Northeast China and less than 2 % in third-level basins in South China. From 1951 to 2017, the annual snowmelt runoff ratios decreased in most third-level basins in China. Under RCP2.6, RCP4.5 and RCP8.5, the projected snowmelt in China in the near future (2011–2040; mid-future –2041–2070; far future – 2071–2099) may decrease by 10.4 % (15.8 %; 13.9 %), 12.0 % (17.9 %; 21.1 %) and 11.7 % (24.8 %; 36.5 %) compared to the reference period (1981–2010), respectively. Most of the projected mean annual snowmelt runoff ratios in third-level basins in different future periods are lower than those in the reference period. Low temperature regions can tolerate more warming, and the snowmelt change in these regions is mainly influenced by precipitation; however, the snowmelt change in warm regions is more sensitive to temperature increases. The spatial variability in snowmelt changes may lead to regional differences in the impact of snowmelt on water supply.

A retrospective on hydrological catchment modelling based on half a century with the HBV model

Abstract: Abstract. Hydrological catchment models are important tools that are commonly used as the basis for water resource management planning. In the 1960s and 1970s, the development of several relatively simple models to simulate catchment runoff started, and a number of so-called conceptual (or bucket-type) models were suggested. In these models, the complex and heterogeneous hydrological processes in a catchment are represented by a limited number of storage elements and the fluxes between them. While computer limitations were a major motivation for such relatively simple models in the early days, some of these models are still used frequently despite the vast increase in computational opportunities. The HBV (Hydrologiska Byråns Vattenbalansavdelning) model, which was first applied about 50 years ago in Sweden, is a typical example of a conceptual catchment model and has gained large popularity since its inception. During several model intercomparisons, the HBV model performed well despite (or because of) its relatively simple model structure. Here, the history of model development, from thoughtful considerations of different model structures to modelling studies using hundreds of catchments and cloud computing facilities, is described. Furthermore, the wide range of model applications is discussed. The aim is to provide an understanding of the background of model development and a basis for addressing the balance between model complexity and data availability that will also face hydrologists in the coming decades.

A hydrologist's guide to open science

Abstract: Abstract. Open, accessible, reusable, and reproducible hydrologic research can have a significant positive impact on the scientific community and broader society. While more individuals and organizations within the hydrology community are embracing open science practices, technical (e.g., limited coding experience), resource (e.g., open access fees), and social (e.g., fear of weaknesses being exposed or ideas being scooped) challenges remain. Furthermore, there are a growing number of constantly evolving open science tools, resources, and initiatives that can be overwhelming. These challenges and the ever-evolving nature of the open science landscape may seem insurmountable for hydrologists interested in pursuing open science. Therefore, we propose the general “Open Hydrology Principles” to guide individual and community progress toward open science for research and education and the “Open Hydrology Practical Guide” to improve the accessibility of currently available tools and approaches. We aim to inform and empower hydrologists as they transition to open, accessible, reusable, and reproducible research. We discuss the benefits as well as common open science challenges and how hydrologists can overcome them. The Open Hydrology Principles and Open Hydrology Practical Guide reflect our knowledge of the current state of open hydrology; we recognize that recommendations and suggestions will evolve and expand with emerging open science infrastructures, workflows, and research experiences. Therefore, we encourage hydrologists all over the globe to join in and help advance open science by contributing to the living version of this document and by sharing open hydrology resources in the community-supported repository (https://open-hydrology.github.io, last access: 1 February 2022).

Development and validation of a new MODIS snow-cover-extent product over China

Abstract: Abstract. Based on MOD09GA/MYD09GA surface reflectance data, a new MODIS snow-cover-extent (SCE) product from 2000 to 2020 over China has been produced by the Northwest Institute of Eco-Environment and Resources (NIEER), Chinese Academy of Sciences. The NIEER MODIS SCE product contains two preliminary clear-sky SCE datasets – Terra-MODIS and Aqua-MODIS SCE datasets and a final daily cloud-gap-filled (CGF) SCE dataset. The first two datasets are generated mainly through optimizing snow-cover discriminating rules over land-cover types, and the latter dataset is produced after a series of gap-filling processes such as aggregating the two preliminary datasets, reducing cloud gaps with adjacent information in space and time, and eliminating all gaps with auxiliary data. The validation against 362 China Meteorological Administration (CMA) stations shows that during snow seasons the overall accuracy (OA) values of the three datasets are larger than 93 %, all of the omission error (OE) values are constrained within 9 %, and all of the commission error (CE) values are constrained within 10 %. Bias values of 0.98, 1.02, and 1.03 demonstrate on a whole that there is no significant overestimation nor a significant underestimation. Based on the same ground reference data, we found that the new product accuracies are obviously higher than standard MODIS snow products, especially for Aqua-MODIS and CGF SCE. For example, compared with the CE of 23.78 % that the MYD10A1 product shows, the CE of the new Aqua-MODIS SCE dataset is 6.78 %; the OA of the new CGF SCE dataset is up to 93.15 % versus 89.54 % of MOD10A1F product and 84.36 % of MYD10A1F product. Besides, as expected, snow discrimination in forest areas is also improved significantly. An isolated validation at four forest CMA stations demonstrates that the OA has increased by 3–10 percentage points, the OE has dropped by 1–8 percentage points, and the CE has dropped by 4–21 percentage points. Therefore, our product has virtually provided more reliable snow knowledge over China; thereby, it can better serve for hydrological, climatic, environmental, and other related studies there.

Flood forecasting with machine learning models in an operational framework

Abstract: Abstract. Google's operational flood forecasting system was developed to provide accurate real-time flood warnings to agencies and the public with a focus on riverine floods in large, gauged rivers. It became operational in 2018 and has since expanded geographically. This forecasting system consists of four subsystems: data validation, stage forecasting, inundation modeling, and alert distribution. Machine learning is used for two of the subsystems. Stage forecasting is modeled with the long short-term memory (LSTM) networks and the linear models. Flood inundation is computed with the thresholding and the manifold models, where the former computes inundation extent and the latter computes both inundation extent and depth. The manifold model, presented here for the first time, provides a machine-learning alternative to hydraulic modeling of flood inundation. When evaluated on historical data, all models achieve sufficiently high-performance metrics for operational use. The LSTM showed higher skills than the linear model, while the thresholding and manifold models achieved similar performance metrics for modeling inundation extent. During the 2021 monsoon season, the flood warning system was operational in India and Bangladesh, covering flood-prone regions around rivers with a total area close to 470 000 km2, home to more than 350 000 000 people. More than 100 000 000 flood alerts were sent to affected populations, to relevant authorities, and to emergency organizations. Current and future work on the system includes extending coverage to additional flood-prone locations and improving modeling capabilities and accuracy.

Exploring the possible role of satellite-based rainfall data in estimating inter- and intra-annual global rainfall erosivity

Abstract: Abstract. Despite recent developments in modeling global soil erosion by water, to date, no substantial progress has been made towards more dynamic inter- and intra-annual assessments. In this regard, the main challenge is still represented by the limited availability of high temporal resolution rainfall data needed to estimate rainfall erosivity. As the availability of high temporal resolution rainfall data will most likely not increase in future decades since the monitoring networks have been declining since the 1980s, the suitability of alternative approaches to estimate global rainfall erosivity using satellite-based rainfall data was explored in this study. For this purpose, we used the high spatial and temporal resolution global precipitation estimates obtained with the National Oceanic and Atmospheric Administration (NOAA) Climate Data Record (CDR) Climate Prediction Center MORPHing (CMORPH) technique. Such high spatial and temporal (30 min) resolution data have not yet been used for the estimation of rainfall erosivity on a global scale. Alternatively, the erosivity density (ED) concept was also used to estimate global rainfall erosivity. The obtained global estimates of rainfall erosivity were validated against the pluviograph data included in the Global Rainfall Erosivity Database (GloREDa). Overall, results indicated that the CMORPH estimates have a marked tendency to underestimate rainfall erosivity when compared to the GloREDa estimates. The most substantial underestimations were observed in areas with the highest rainfall erosivity values. At the continental level, the best agreement between annual CMORPH and interpolated GloREDa rainfall erosivity maps was observed in Europe, while the worst agreement was detected in Africa and South America. Further analyses conducted at the monthly scale for Europe revealed seasonal misalignments, with the occurrence of underestimation of the CMORPH estimates in the summer period and overestimation in the winter period compared to GloREDa. The best agreement between the two approaches to estimate rainfall erosivity was found for fall, especially in central and eastern Europe. Conducted analysis suggested that satellite-based approaches for estimation of rainfall erosivity appear to be more suitable for low-erosivity regions, while in high-erosivity regions (> 1000–2000 MJ mm ha−1 h−1 yr−1) and seasons (> 150–250 MJ mm ha−1 h−1 month−1), the agreement with estimates obtained from pluviographs (GloREDa) is lower. Concerning the ED estimates, this second approach to estimate rainfall erosivity yielded better agreement with GloREDa estimates compared to CMORPH, which could be regarded as an expected result since this approach indirectly uses the GloREDa data. The application of a simple-linear function correction of the CMORPH data was applied to provide a better fit to GloREDa and correct systematic underestimation. This correction improved the performance of CMORPH, but in areas with the highest rainfall erosivity rates, the underestimation was still observed. A preliminary trend analysis of the CMORPH rainfall erosivity estimates was also performed for the 1998–2019 period to investigate possible changes in the rainfall erosivity at a global scale, which has not yet been conducted using high-frequency data such as CMORPH. According to this trend analysis, an increasing and statistically significant trend was more frequently observed than a decreasing trend.

How well are we able to close the water budget at the global scale?

Abstract: Abstract. The water budget equation describes the exchange of water between the land, ocean, and atmosphere. Being able to adequately close the water budget gives confidence in our ability to model and/or observe the spatio-temporal variations in the water cycle and its components. Due to advances in observation techniques, satellite sensors, and modelling, a number of data products are available that represent the components of water budget in both space and time. Despite these advances, closure of the water budget at the global scale has been elusive. In this study, we attempt to close the global water budget using precipitation, evapotranspiration, and runoff data at the catchment scale. The large number of recent state-of-the-art datasets provides a new evaluation of well-used datasets. These estimates are compared to terrestrial water storage (TWS) changes as measured by the Gravity Recovery And Climate Experiment (GRACE) satellite mission. We investigated 189 river basins covering more than 90 % of the continental land area. TWS changes derived from the water balance equation were compared against GRACE data using two metrics: the Nash–Sutcliffe efficiency (NSE) and the cyclostationary NSE. These metrics were used to assess the performance of more than 1600 combinations of the various datasets considered. We found a positive NSE and cyclostationary NSE in 99 % and 62 % of the basins examined respectively. This means that TWS changes reconstructed from the water balance equation were more accurate than the long-term (NSE) and monthly (cyclostationary NSE) mean of GRACE time series in the corresponding basins. By analysing different combinations of the datasets that make up the water balance, we identified data products that performed well in certain regions based on, for example, climatic zone. We identified that some of the good results were obtained due to the cancellation of errors in poor estimates of water budget components. Therefore, we used coefficients of variation to determine the relative quality of a data product, which helped us to identify bad combinations giving us good results. In general, water budget components from ERA5-Land and the Catchment Land Surface Model (CLSM) performed better than other products for most climatic zones. Conversely, the latest version of CLSM, v2.2, performed poorly for evapotranspiration in snow-dominated catchments compared, for example, with its predecessor and other datasets available. Thus, the nature of the catchment dynamics and balance between components affects the optimum combination of datasets. For regional studies, the combination of datasets that provides the most realistic TWS for a basin will depend on its climatic conditions and factors that cannot be determined a priori. We believe that the results of this study provide a road map for studying the water budget at catchment scale.

Unraveling the contribution of potential evaporation formulation to uncertainty under climate change

Abstract: Abstract. The increasing air temperature in a changing climate will impact actual evaporation and have consequences for water resource management in energy-limited regions. In many hydrological models, evaporation is assessed using a preliminary computation of potential evaporation (PE), which represents the evaporative demand of the atmosphere. Therefore, in impact studies, the quantification of uncertainties related to PE estimation, which can arise from different sources, is crucial. Indeed, a myriad of PE formulations exist, and the uncertainties related to climate variables cascade into PE computation. To date, no consensus has emerged on the main source of uncertainty in the PE modeling chain for hydrological studies. In this study, we address this issue by setting up a multi-model and multi-scenario approach. We used seven different PE formulations and a set of 30 climate projections to calculate changes in PE. To estimate the uncertainties related to each step of the PE calculation process, namely Representative Concentration Pathway (RCP) scenarios, general circulation models (GCMs), regional climate models (RCMs) and PE formulations, an analysis of variance (ANOVA) decomposition was used. Results show that mean annual PE will increase across France by the end of the century (from +40 to +130 mm y−1). In ascending order, uncertainty contributions by the end of the century are explained by PE formulations (below 10 %), RCPs (above 20 %), RCMs (30 %–40 %) and GCMs (30 %–40 %). However, under a single scenario, the contribution of the PE formulation is much higher and can reach up to 50 % of the total variance. All PE formulations show similar future trends, as climatic variables are co-dependent with respect to temperature. While no PE formulation stands out from the others, the Penman–Monteith formulation may be preferred in hydrological impact studies, as it is representative of the PE formulations' ensemble mean and allows one to account for the coevolution of climate and environmental drivers.

Preprocessing approaches in machine-learning-based groundwater potential mapping: an application to the Koulikoro and Bamako regions, Mali

Abstract: Abstract. Groundwater is crucial for domestic supplies in the Sahel, where the strategic importance of aquifers will increase in the coming years due to climate change. Groundwater potential mapping is a valuable tool to underpin water management in the region and, hence, to improve drinking water access. This paper presents a machine learning method to map groundwater potential. This is illustrated through its application in two administrative regions of Mali. A set of explanatory variables for the presence of groundwater is developed first. Scaling methods (standardization, normalization, maximum absolute value and max–min scaling) are used to avoid the pitfalls associated with reclassification. Noisy, collinear and counterproductive variables are identified and excluded from the input dataset. A total of 20 machine learning classifiers are then trained and tested on a large borehole database (n=3345) in order to find meaningful correlations between the presence or absence of groundwater and the explanatory variables. Maximum absolute value and standardization proved the most efficient scaling techniques, while tree-based algorithms (accuracy >0.85) consistently outperformed other classifiers. The borehole flow rate data were then used to calibrate the results beyond standard machine learning metrics, thereby adding robustness to the predictions. The southern part of the study area presents the better groundwater prospect, which is consistent with the geological and climatic setting. Outcomes lead to three major conclusions: (1) picking the best performers out of a large number of machine learning classifiers is recommended as a good methodological practice, (2) standard machine learning metrics should be complemented with additional hydrogeological indicators whenever possible and (3) variable scaling contributes to minimize expert bias.

Improved understanding of regional groundwater drought development through time series modelling: the 2018–2019 drought in the Netherlands

Abstract: Abstract. The 2018–2019 drought in north-western and central Europe caused severe damage to a wide range of sectors. It also emphasised the fact that, even in countries with temperate climates, adaptations are needed to cope with increasing future drought frequencies. A crucial component of drought management strategies is to monitor the status of groundwater resources. However, providing up-to-date assessments of regional groundwater drought development remains challenging due to the limited availability of high-quality data. This limits many studies to small selections of groundwater monitoring sites, giving an incomplete image of drought dynamics. In this study, a time series modelling-based method for data preparation was developed and applied to map the spatio-temporal development of the 2018–2019 groundwater drought in the south-eastern Netherlands, based on a large set of monitoring data. The data preparation method was evaluated for its usefulness and reliability for data validation, simulation, and regional groundwater drought assessment. The analysis showed that the 2018–2019 meteorological drought caused extreme groundwater drought throughout the south-eastern Netherlands, breaking 30-year records almost everywhere. Drought onset and duration were strongly variable in space, and higher-elevation areas suffered from severe drought well into 2020. Groundwater drought development appeared to be governed dominantly by the spatial distribution of rainfall and the landscape type. The time series modelling-based data preparation method was found to be a useful tool to enable a spatially detailed record of regional groundwater drought development. The automated time series modelling-based data validation improved the quality and quantity of useable data, although optimal validation parameters are probably context dependent. The time series simulations were generally found to be reliable; however, the use of time series simulations rather than direct measurement series can bias drought estimations, especially at a local scale, and underestimate spatial variability. Further development of time-series-based validation and simulation methods, combined with accessible and consistent monitoring data, will be valuable to enable better groundwater drought monitoring in the future.

Future water temperature of rivers in Switzerland under climate change investigated with physics-based models

Abstract: Abstract. River ecosystems are highly sensitive to climate change and projected future increase in air temperature is expected to increase the stress for these ecosystems. Rivers are also an important socio-economic factor impacting, amongst others, agriculture, tourism, electricity production, and drinking water supply and quality. In addition to changes in water availability, climate change will impact river temperature. This study presents a detailed analysis of river temperature and discharge evolution over the 21st century in Switzerland. In total, 12 catchments are studied, situated both on the lowland Swiss Plateau and in the Alpine regions. The impact of climate change is assessed using a chain of physics-based models forced with the most recent climate change scenarios for Switzerland including low-, mid-, and high-emission pathways. The suitability of such models is discussed in detail and recommendations for future improvements are provided. The model chain is shown to provide robust results, while remaining limitations are identified. These are mechanisms missing in the model to correctly simulate water temperature in Alpine catchments during the summer season. A clear warming of river water is modelled during the 21st century. At the end of the century (2080–2090), the median annual river temperature increase ranges between +0.9 ∘C for low-emission and +3.5 ∘C for high-emission scenarios for both lowland and Alpine catchments. At the seasonal scale, the warming on the lowland and in the Alpine regions exhibits different patterns. For the lowland the summer warming is stronger than the one in winter but is still moderate. In Alpine catchments, only a very limited warming is expected in winter. The period of maximum discharge in Alpine catchments, currently occurring during mid-summer, will shift to earlier in the year by a few weeks (low emission) or almost 2 months (high emission) by the end of the century. In addition, a noticeable soil warming is expected in Alpine regions due to glacier and snow cover decrease. All results of this study are provided with the corresponding source code used for this paper.

Regional, multi-decadal analysis on the Loire River basin reveals that stream temperature increases faster than air temperature

Abstract: Abstract. Stream temperature appears to be increasing globally, but its rate remains poorly constrained due to a paucity of long-term data and difficulty in parsing effects of hydroclimate and landscape variability. Here, we address these issues using the physically based thermal model T-NET (Temperature-NETwork) coupled with the EROS semi-distributed hydrological model to reconstruct past daily stream temperature and streamflow at the scale of the entire Loire River basin in France (105 km2 with 52 278 reaches). Stream temperature increased for almost all reaches in all seasons (mean =+0.38 ∘C decade−1) over the 1963–2019 period. Increases were greatest in spring and summer, with a median increase of + 0.38 ∘C (range =+0.11 to +0.76 ∘C) and +0.44 ∘C (+0.08 to +1.02 ∘C) per decade, respectively. Rates of stream temperature increases were greater than for air temperature across seasons for the majority of reaches. Spring and summer increases were typically greatest in the southern part of the Loire basin (up to +1 ∘C decade−1) and in the largest rivers (Strahler order ≥5). Importantly, air temperature and streamflow could exert a joint influence on stream temperature trends, where the greatest stream temperature increases were accompanied by similar trends in air temperature (up to +0.71 ∘C decade−1) and the greatest decreases in streamflow (up to −16 % decade−1). Indeed, for the majority of reaches, positive stream temperature anomalies exhibited synchrony with positive anomalies in air temperature and negative anomalies in streamflow, highlighting the dual control exerted by these hydroclimatic drivers. Moreover, spring and summer stream temperature, air temperature, and streamflow time series exhibited common change points occurring in the late 1980s, suggesting a temporal coherence between changes in the hydroclimatic drivers and a rapid stream temperature response. Critically, riparian vegetation shading mitigated stream temperature increases by up to 0.16 ∘C decade−1 in smaller streams (i.e. < 30 km from the source). Our results provide strong support for basin-wide increases in stream temperature due to joint effects of rising air temperature and reduced streamflow. We suggest that some of these climate change-induced effects can be mitigated through the restoration and maintenance of riparian forests.

The role of morphology in the spatial distribution of short-duration rainfall extremes in Italy

Abstract: Abstract. The dependence of rainfall on elevation has frequently been documented in the scientific literature and may be relevant in Italy, due to the high degree of geographical and morphological heterogeneity of the country. However, a detailed analysis of the spatial variability of short-duration annual maximum rainfall depths and their connection to the landforms does not exist. Using a new, comprehensive and position-corrected rainfall extreme dataset (I2-RED, the Improved Italian-Rainfall Extreme Dataset), we present a systematic study of the relationship between geomorphological forms and the average annual maxima (index rainfall) across the whole of Italy. We first investigated the dependence of sub-daily rainfall depths on elevation and other landscape indices through univariate and multivariate linear regressions. The results of the national-scale regression analysis did not confirm the assumption of elevation being the sole driver of the variability of the index rainfall. The inclusion of longitude, latitude, distance from the coastline, morphological obstructions and mean annual rainfall contributes to the explanation of a larger percentage of the variance, even though this was in different ways for different durations (1 to 24 h). After analyzing the spatial variability of the regression residuals, we repeated the analysis on geomorphological subdivisions of Italy. Comparing the results of the best multivariate regression models with univariate regressions applied to small areas, deriving from morphological subdivisions, we found that “local” rainfall–topography relationships outperformed the country-wide multiple regressions, offered a uniform error spatial distribution and allowed the effect of morphology on rainfall extremes to be better reproduced.

Using a long short-term memory (LSTM) neural network to boost river streamflow forecasts over the western United States

Abstract: Abstract. Accurate river streamflow forecasts are a vital tool in the fields of water security, flood preparation and agriculture, as well as in industry more generally. Traditional physics-based models used to produce streamflow forecasts have become increasingly sophisticated, with forecasts improving accordingly. However, the development of such models is often bound by two soft limits: empiricism – many physical relationships are represented empirical formulae; and data sparsity – long time series of observational data are often required for the calibration of these models. Artificial neural networks have previously been shown to be highly effective at simulating non-linear systems where knowledge of the underlying physical relationships is incomplete. However, they also suffer from issues related to data sparsity. Recently, hybrid forecasting systems, which combine the traditional physics-based approach with statistical forecasting techniques, have been investigated for use in hydrological applications. In this study, we test the efficacy of a type of neural network, the long short-term memory (LSTM), at predicting streamflow at 10 river gauge stations across various climatic regions of the western United States. The LSTM is trained on the catchment-mean meteorological and hydrological variables from the ERA5 and Global Flood Awareness System (GloFAS)–ERA5 reanalyses as well as historical streamflow observations. The performance of these hybrid forecasts is evaluated and compared with the performance of both raw and bias-corrected output from the Copernicus Emergency Management Service (CEMS) physics-based GloFAS. Two periods are considered, a testing phase (June 2019 to June 2020), during which the models were fed with ERA5 data to investigate how well they simulated streamflow at the 10 stations, and an operational phase (September 2020 to October 2021), during which the models were fed forecast variables from the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecasting System (IFS), to investigate how well they could predict streamflow at lead times of up to 10 d. Implications and potential improvements to this work are discussed. In summary, this is the first time an LSTM has been used in a hybrid system to create a medium-range streamflow forecast, and in beating established physics-based models, shows promise for the future of neural networks in hydrological forecasting.

Development of a national 7-day ensemble streamflow forecasting service for Australia

Abstract: Abstract. Reliable streamflow forecasts with associated uncertainty estimates are essential to manage and make better use of Australia's scarce surface water resources. Here we present the development of an operational 7 d ensemble streamflow forecasting service for Australia to meet the growing needs of users, primarily water and river managers, for probabilistic forecasts to support their decision making. We test the modelling methodology for 100 catchments to learn the characteristics of different rainfall forecasts from Numerical Weather Prediction (NWP) models, the effect of statistical processing on streamflow forecasts, the optimal ensemble size, and parameters of a bootstrapping technique for calculating forecast skill. A conceptual rainfall–runoff model, GR4H (hourly), and lag and route channel routing model that are in-built in the Short-term Water Information Forecasting Tools (SWIFT) hydrologic modelling package are used to simulate streamflow from input rainfall and potential evaporation. The statistical catchment hydrologic pre-processor (CHyPP) is used for calibrating rainfall forecasts, and the error reduction and representation in stages (ERRIS) model is used to reduce hydrological errors and quantify hydrological uncertainty. Calibrating raw forecast rainfall with CHyPP is an efficient method to significantly reduce bias and improve reliability for up to 7 lead days. We demonstrate that ERRIS significantly improves forecast skill up to 7 lead days. Forecast skills are highest in temperate perennially flowing rivers, while it is lowest in intermittently flowing rivers. A sensitivity analysis for optimising the number of streamflow ensemble members for the operational service shows that more than 200 members are needed to represent the forecast uncertainty. We show that the bootstrapping block size is sensitive to the forecast skill calculation. A bootstrapping block size of 1 month is recommended to capture maximum possible uncertainty. We present benchmark criteria for accepting forecast locations for the public service. Based on the criteria, 209 forecast locations out of a possible 283 are selected in different hydro-climatic regions across Australia for the public service. The service, which has been operational since 2019, provides daily updates of graphical and tabular products of ensemble streamflow forecasts along with performance information, for up to 7 lead days.

Improving hydrologic models for predictions and process understanding using neural ODEs

Abstract: Abstract. Deep learning methods have frequently outperformed conceptual hydrologic models in rainfall-runoff modelling. Attempts of investigating such deep learning models internally are being made, but the traceability of model states and processes and their interrelations to model input and output is not yet fully understood. Direct interpretability of mechanistic processes has always been considered an asset of conceptual models that helps to gain system understanding aside of predictability. We introduce hydrologic neural ordinary differential equation (ODE) models that perform as well as state-of-the-art deep learning methods in stream flow prediction while maintaining the ease of interpretability of conceptual hydrologic models. In neural ODEs, internal processes that are represented in differential equations, are substituted by neural networks. Therefore, neural ODE models enable the fusion of deep learning with mechanistic modelling. We demonstrate the basin-specific predictive performance for 569 catchments of the continental United States. For exemplary basins, we analyse the dynamics of states and processes learned by the model-internal neural networks. Finally, we discuss the potential of neural ODE models in hydrology.

Theoretical and empirical evidence against the Budyko catchment trajectory conjecture

Abstract: Abstract. The Budyko framework posits that a catchment's long-term mean evapotranspiration (ET) is primarily governed by the availabilities of water and energy, represented by long-term mean precipitation (P) and potential evapotranspiration (PET), respectively. This assertion is supported by the distinctive clustering pattern that catchments take in Budyko space. Several semi-empirical, nonparametric curves have been shown to generally represent this clustering pattern but cannot explain deviations from the central tendency. Parametric Budyko equations attempt to generalize the nonparametric framework, through the introduction of a catchment-specific parameter (n or w). Prevailing interpretations of Budyko curves suggest that the explicit functional forms represent trajectories through Budyko space for individual catchments undergoing changes in the aridity index, PETP, while the n and w values represent catchment biophysical features; however, neither of these interpretations arise from the derivation of the Budyko equations. In this study, we reexamine, reinterpret, and test these two key assumptions of the current Budyko framework both theoretically and empirically. In our theoretical test, we use a biophysical model for ET to demonstrate that n and w values can change without invoking changes in landscape biophysical features and that catchments are not required to follow Budyko curve trajectories. Our empirical test uses data from 728 reference catchments in the United Kingdom (UK) and United States (US) to illustrate that catchments rarely follow Budyko curve trajectories and that n and w are not transferable between catchments or across time for individual catchments. This nontransferability implies that n and w are proxy variables for ETP, rendering the parametric Budyko equations underdetermined and lacking predictive ability. Finally, we show that the parametric Budyko equations are nonunique, suggesting their physical interpretations are unfounded. Overall, we conclude that, while the shape of Budyko curves generally captures the global behavior of multiple catchments, their specific functional forms are arbitrary and not reflective of the dynamic behavior of individual catchments.

Isotopic offsets between bulk plant water and its sources are larger in cool and wet environments

Abstract: Abstract. Isotope-based approaches to study plant water sources rely on the assumption that root water uptake and within-plant water transport are non-fractionating processes. However, a growing number of studies have reported offsets between plant and source water stable isotope composition for a wide range of ecosystems. These isotopic offsets can result in the erroneous attribution of source water used by plants and potential overestimations of groundwater uptake by the vegetation. We conducted a global meta-analysis to quantify the magnitude of these plant source water isotopic offsets and explored whether their variability could be explained by either biotic or abiotic factors. Our database compiled 112 studies spanning arctic to tropical biomes that reported the dual water isotope composition (δ2H and δ18O) of plant (stem) and source water, including soil water (sampled following various methodologies and along a variable range of depths). We calculated plant source 2H offsets in two ways: a line conditioned excess (LC-excess) that describes the 2H deviation from the local meteoric water line and a soil water line conditioned excess (SW-excess) that describes the deviation from the soil water line, for each sampling campaign within each study. We tested for the effects of climate (air temperature and soil water content), soil class, and plant traits (growth form, leaf habit, wood density, and parenchyma fraction and mycorrhizal habit) on LC-excess and SW-excess. Globally, stem water was more depleted in 2H than in soil water (SW-excess < 0) by 3.02±0.65 ‰ (P < 0.05 according to estimates of our linear mixed model and weighted by sample size within studies). In 95 % of the cases where SW-excess was negative, LC-excess was negative, indicating that the uptake of water that had not undergone evaporative enrichment (such as groundwater) was unlikely to explain the observed soil–plant water isotopic offsets. Soil class and plant traits did not have any significant effect on SW-excess. SW-excess was more negative in cold and wet sites, whereas it was more positive in warm sites. The climatic effects on SW-excess suggest that methodological artefacts are unlikely to be the sole cause of observed isotopic offsets. Our results would imply that plant source water isotopic offsets may lead to inaccuracies when using the isotopic composition of bulk stem water as a proxy to infer plant water sources.

Ecosystem adaptation to climate change: the sensitivity of hydrological predictions to time-dynamic model parameters

Abstract: Abstract. Future hydrological behavior in a changing world is typically predicted based on models that are calibrated on past observations, disregarding that hydrological systems and, therefore, model parameters may change as well. In reality, hydrological systems experience almost continuous change over a wide spectrum of temporal and spatial scales. In particular, there is growing evidence that vegetation adapts to changing climatic conditions by adjusting its root zone storage capacity, which is the key parameter of any terrestrial hydrological system. In addition, other species may become dominant, both under natural and anthropogenic influence. In this study, we test the sensitivity of hydrological model predictions to changes in vegetation parameters that reflect ecosystem adaptation to climate and potential land use changes. We propose a top-down approach, which directly uses projected climate data to estimate how vegetation adapts its root zone storage capacity at the catchment scale in response to changes in the magnitude and seasonality of hydro-climatic variables. Additionally, long-term water balance characteristics of different dominant ecosystems are used to predict the hydrological behavior of potential future land use change in a space-for-time exchange. We hypothesize that changes in the predicted hydrological response as a result of 2 K global warming are more pronounced when explicitly considering changes in the subsurface system properties induced by vegetation adaptation to changing environmental conditions. We test our hypothesis in the Meuse basin in four scenarios designed to predict the hydrological response to 2 K global warming in comparison to current-day conditions, using a process-based hydrological model with (a) a stationary system, i.e., no assumed changes in the root zone storage capacity of vegetation and historical land use, (b) an adapted root zone storage capacity in response to a changing climate but with historical land use and (c, d) an adapted root zone storage capacity considering two hypothetical changes in land use. We found that the larger root zone storage capacities (+34 %) in response to a more pronounced climatic seasonality with warmer summers under 2 K global warming result in strong seasonal changes in the hydrological response. More specifically, streamflow and groundwater storage are up to −15 % and −10 % lower in autumn, respectively, due to an up to +14 % higher summer evaporation in the non-stationary scenarios compared to the stationary benchmark scenario. By integrating a time-dynamic representation of changing vegetation properties in hydrological models, we make a potential step towards more reliable hydrological predictions under change.

A two-step merging strategy for incorporating multi-source precipitation products and gauge observations using machine learning classification and regression over China

Abstract: Abstract. Although many multi-source precipitation products (MSPs) with high spatio-temporal resolution have been extensively used in water cycle research, they are still subject to considerable uncertainties due to the spatial variability of terrain. Effective detection of precipitation occurrence is the key to enhancing precipitation accuracy. This study presents a two-step merging strategy to incorporate MSPs (GSMaP, IMERG, TMPA, PERSIANN-CDR, CMORPH, CHIRPS, and ERA-Interim) and rain gauges to improve the precipitation capture capacity and precipitation intensity simultaneously during 2000–2017 over China. Multiple environment variables and the spatial autocorrelation between precipitation observations are selected as auxiliary variables in the merging process. Three machine learning (ML) classification and regression models, including gradient boosting decision tree (GBDT), extreme gradient boosting (XGBoost), and random forest (RF), are adopted and compared. The strategy first employs classification models to identify wet and dry days in warm and cold seasons, then combines regression models to predict precipitation amounts based on wet days. The results are also compared with those of traditional methods, including multiple linear regression (MLR), ML regression models, and gauge-based Kriging interpolation. A total of 1680 (70 %) rain gauges are randomly chosen for model training and 692 (30 %) for performance evaluation. The results show that: (1) The multi-sources merged precipitation products (MSMPs) perform better than original MSPs in detecting precipitation occurrence under different intensities, followed by Kriging. The average Heidke Skill Score (HSS) of MSPs, Kriging, and MSMPs is 0.30–0.69, 0.71, 0.79–0.8, respectively. (2) The proposed method significantly alleviates the bias and deviation of original MSPs in temporal and spatial. The MSMPs strongly correlate with gauge observations with the CC of 0.85. Moreover, the modified Kling-Gupta efficiency (KGE) improves by 17 %–62 % (MSMPs: 0.74–0.76) compared with MSPs (0.34–0.65). (3) The spatial autocorrelation factor (KP) is the most important variable in models, which contributes considerably to improving the model accuracy. (4) The proposed method outperforms MLR and ML regression models, and XGBoost algorithm is more recommended for large-scale data merging owing to its high computational efficiency. This study provides a robust and reliable method to improve the performance of precipitation data with full consideration of multi-source information. This method could be applied globally and produce large-scale precipitation products if rain gauges are available.

Globally widespread and increasing violations of environmental flow envelopes

Abstract: Abstract. Human actions and climate change have drastically altered river flows across the world, resulting in adverse effects on riverine ecosystems. Environmental flows (EFs) have emerged as a prominent tool for safeguarding the riverine ecosystems, but at the global scale, the assessment of EFs is associated with high uncertainty related to the hydrological data and EF methods employed. Here, we present a novel, in-depth global EF assessment using environmental flow envelopes (EFEs). Sub-basin-specific EFEs are determined for approximately 4400 sub-basins at a monthly time resolution, and their derivation considers the methodological uncertainties related to global-scale EF studies. In addition to a lower bound of discharge based on existing EF methods, we introduce an upper bound of discharge in the EFE. This upper bound enables areas to be identified where streamflow has substantially increased above natural levels. Further, instead of only showing whether EFs are violated over a time period, we quantify, for the first time, the frequency, severity, and trends of EFE violations during the recent historical period. Discharge was derived from global hydrological model outputs from the ISIMIP 2b ensemble. We use pre-industrial (1801–1860) quasi-natural discharge together with a suite of hydrological EF methods to estimate the EFEs. We then compare the EFEs with recent historical (1976–2005) discharge to assess the violations of the EFE. These violations most commonly manifest as insufficient streamflow during the low-flow season, with fewer violations during the intermediate-flow season, and only a few violations during the high-flow season. The EFE violations are widespread and occur in half of the sub-basins of the world during more than 5 % of the months between 1976 and 2005, which is double compared with the pre-industrial period. The trends in EFE violations have mainly been increasing, which will likely continue in the future with the projected hydroclimatic changes and increases in anthropogenic water use. Indications of increased upper extreme streamflow through EFE upper bound violations are relatively scarce and dispersed. Although local fine-tuning is necessary for practical applications, and further research on the coupling between quantitative discharge and riverine ecosystem responses at the global scale is required, the EFEs provide a quick and globally robust way of determining environmental flow allocations at the sub-basin scale to inform global research and policies on water resources management.