Optimal Postprocessing Strategies With LSTM for Global Streamflow Prediction in Ungauged Basins

Streamflow prediction is a vital public service that helps to establish flash-flood early warning systems or assess the impact of projected climate change on water management. However, the availability of streamflow observations limits the utilization of the state-of-the-art streamflow prediction techniques to the basins where hydrometric gauging stations exist. Since the most river basins in the world are ungauged, the development of the specialized techniques for the reliable streamflow prediction in ungauged basins (PUB) is of crucial importance. In recent years, the emerging field of deep learning provides a myriad of new models that can breathe new life into the stagnating PUB methods. In the presented study, we benchmark the streamflow prediction efficiency of Long Short-Term Memory (LSTM) networks against the standard technique of GR4J hydrological model parameters regionalization (HMREG) at 200 basins in Northwest Russia. Results show that the LSTM-based regional hydrological model significantly outperforms the HMREG scheme in terms of median Nash-Sutcliffe efficiency (NSE), which is 0.73 and 0.61 for LSTM and HMREG, respectively. Moreover, LSTM demonstrates the comparable median NSE with that for basin-scale calibration of GR4J (0.75). Therefore, this study underlines the high utilization potential of deep learning for the PUB by demonstrating the new state-of-the-art performance in this field.

As a result of no direct measurement data, accurate stream flow prediction in ungauged basins has remained a challenge in water resource management and flood forecasting. To meet this challenge, advanced hydrological models can be integrated with remote sensing and machine learning techniques. Hydrological models are used to understand the dynamics of streamflow patterns while remotely sensed information provides real-time information on land surface conditions as well as weather parameters thus enhancing the accuracy of these models. Using classical approaches, machine learning methods enable the analysis of complex datasets to detect interrelations or patterns that may not be obvious. Therefore, an integrated approach is crucial for improving flow predictions in ungauged basins that ultimately support effective water management and flood mitigation strategies. This can become even more complicated with climate change as shown by Morocco's high sensitivity to irregular rainfall patterns brought about by climate variations. One such place is the Ouzoud watershed, which stretches 315.6 km 2 across Central High Atlas Mountains and is characterized by frequent flooding leading to socio-economic impacts. This study aims at assessing streamflow prediction methods particularly the Quantile-Quantile Plot (QPPQ) method endorsed by USGS for its applicability in predicting streamflow at ungauged locations. The study area includes both gauged and ungauged watersheds such as the Bernat River, Lakhdar River, Ghassaf River, and Tassaouet River, with Ouzoud River being the only ungauged basin. The geological setting is characterized by carbonate rocks (limestone) throughout the catchment. Mediterranean climate mountainous conditions prevail in this region that experience significant rainfall variations. Other watersheds within the survey site are those of Tassaout and Bernat which have different geological and climatic influences on streamflow patterns. The QPPQ method entails estimating the Flow Duration Curve (FDC) for the catchment of interest, identifying matching donor sites in terms of hydrological characteristics, transferring non-excessive probabilities from these donor sites and mapping these probabilities to streamflow estimates. The performance of the QPPQ method is assessed based on several statistical criteria including Correlation Coefficient (CC), Coefficient of Determination (R 2 ), Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), Nash-Sutcliffe Efficiency (NSE), and Kling-Gupta Efficiency (KGE). For instance, the CC value of 0.55 at Bernat River Sgatt station means that there exists a moderate linear relationship between predicted and observed streamflows while R 2 value at 0.36 indicates that about 36 % of the explained variation in observed flow is covered by predicted ones. Meanwhile, MAE=22.50 mirrors an average absolute prediction error while RMSE equals 55.01 in this case refers to the square root of mean squared prediction errors. Furthermore, NSE gives information concerning how far off the model's results are from the actual data with NSE=0.36 denoting a moderate fit and KGE which equals 0.34 showing good agreement in overall terms. Together, these measures expose the strengths and weaknesses of QPPQ as a streamflow prediction technique. Although the method gives some useful indications, it should be improved further by integrating it with more data sources and processes to increase the accuracy of its predictions and make them more reliable for ungauged basins. Graphical Summary of the Study Using the QPPQ Method Applied to a Gauged Basin (Bernat Basin) and an Ungauged Basin (Ouzoud Basin) • Improved QPPQ method enhances streamflow prediction in ungauged basins. • Seasonal analysis shows best QPPQ performance in winter, weakest in autumn. • Hybrid QPPQ with LSTM and RF improves prediction of extreme streamflows. • QPPQ shows strong results in Ouzoud Basin; basin-specific calibration is crucial. • Integrating remote sensing and machine learning supports water management.

Utilization of the Long Short-Term Memory network for predicting streamflow in ungauged basins in Korea

Large-sample hydrology datasets have become increasingly popular in recent years, providing hydro-meteorological time series and catchment attributes for thousands of catchments worldwide. However, the role of such catchment attributes in informing model regionalization, and particularly the effect of their level of spatial detail on prediction in ungauged basins (PUB), remains poorly explored. This study addresses this gap by examining whether catchment attributes derived from geological maps of varying levels of detail improve model regionalization and, in turn, PUB, for both a bucket-type model and a data-driven Long Short-Term Memory (LSTM) model across 130 catchments in two independent basins: the Moselle (27 100 km²) and the Garonne (13 730 km²). We conducted five modeling experiments: a benchmark without geological information and four geology-informed configurations with increasing levels of detail (random, global, continental, and regional). A fold-based space–time cross-evaluation strategy was used to assess model performance on both time periods and catchments unseen during calibration. Performance was evaluated using a modified Nash–Sutcliffe Efficiency (NSE) and a set of streamflow signatures describing flow variability, storage, and regime behavior. Across both basins and model types, benchmark experiments yielded the lowest space–time performance, followed by the random experiment and the global geology experiment, while the experiments using continental and regional geology consistently resulted in higher NSE values. Improvements were strongest for the bucket-type model, with the most detailed geological attributes leading to consistent gains in median performance and robustness. Differences among experiments were more pronounced for streamflow signatures. For the bucket-type model, only the experiments adopting the continental or regional geology reproduced observed signatures with Spearman’s correlations exceeding 0.60, whereas the LSTM model already showed reasonable skill in the benchmark case but still benefited systematically from increasing geological detail. Together, these results demonstrate that incorporating detailed geological information can enhance streamflow representation and model transferability in PUB applications, and that the level of geological detail is a critical, yet often overlooked, factor in large-sample hydrology and regionalization studies.

Modelling ungauged catchments using the catchment runoff response similarity

A dynamic water quality model, HYPE, was applied to a large, data-sparse region to study whether reliable information on water quantity and water quality could be obtained for both gauged and ungauged waterbodies. The model (called S-HYPE) was set up for all of Sweden (∼450 000 km2), divided into sub-basins with an average area of 28 km2. Readily available national databases were used for physiographic data, emissions and agricultural practices, fixed values for representative years were used. Daily precipitation and temperature were used as the dynamic forcing of the model. Model evaluation was based on data from several hundred monitoring sites, of which approximately 90% had not been used in calibration on a daily scale. Results were evaluated using the Nash-Sutcliffe efficiency (NSE), correlation and relative errors: 92% of the spatial variation was explained for specific water discharge, and 88% and 59% for total nitrogen and total phosphorus concentrations, respectively. Day-to-day variations were modelled with satisfactory results for water discharge and the seasonal variation of nitrogen concentrations was also generally well captured. In 20 large, unregulated rivers the median NSE for water discharge was 0.84, and the corresponding number for 76 partly-regulated river basins was 0.52. In small basins, the NSE was typically above 0.6. These major achievements relative to previous similar experiments were ascribed to the step-wise calibration process using representative gauged basins and the use of a modelling concept, whereby coefficients are linked to physiographic variables rather than to specific sites. Editor D. Koutsoyiannis Citation Strömqvist, J., Arheimer, B., Dahné, J., Donnelly, C. and Lindström, G., 2012. Water and nutrient predictions in ungauged basins: set-up and evaluation of a model at the national scale. Hydrological Sciences Journal, 57 (2), 229–247.

Runoff predictions in new-gauged basins using two transformer-based models

Prediction in Ungauged Basins (PUB) is an important task for water resources planning and management and remains a fundamental challenge for the hydrological community. In recent years, geostatistical methods have proven valuable for estimating hydrological variables in ungauged catchments. However, four major problems restrict the development of geostatistical methods. We established a new information diffusion model based on genetic algorithm (GIDM) for spatial interpolating of runoff in the ungauged basins. Genetic algorithms (GA) are used to generate high-quality solutions to optimization and search problems. So, using GA, the parameter of optimal window width can be obtained. To test our new method, seven experiments for the annual runoff interpolation based on GIDM at 17 stations on the mainstream and tributaries of the Yellow River are carried out and compared with the inverse distance weighting (IDW) method, Cokriging (COK) method, and conventional IDMs using the same sparse observed data. The seven experiments all show that the GIDM method can solve four problems of the previous geostatistical methods to some extent and obtains best accuracy among four different models. The key problems of the PUB research are the lack of observation data and the difficulties in information extraction. So the GIDM is a new and useful tool to solve the Prediction in Ungauged Basins (PUB) problem and to improve the water management.

Predicting streamflow in ungauged basins remains a significant challenge in hydrological studies. In recent years, data-driven models have been shown to outperform traditional physics-based models in streamflow prediction for ungauged catchments. However, few studies have examined the potential of such models for predicting streamflow in ungauged basins within India. This study aims to evaluate the performance of two machine learning models, namely Support Vector Regression (SVR) and Random Forest (RF), alongside two deep learning models, Long Short-Term Memory (LSTM) and Bi-LSTM, in the context of streamflow regionalization within the Krishna River Basin in India. Each prediction model is trained using meteorological variables as input features, with streamflow as the output variable. K-means clustering is employed to group selected catchments (based on data availability) into an optimum number of clusters based on spatial proximity and physical similarity. It is assumed that catchments within a cluster share homogeneous characteristics. Regionalization is achieved by sharing model parameters across catchments within the same cluster. For each cluster, one gauged catchment is designated as the donor catchment, while the others are treated as pseudo-ungauged. Each proposed model is trained and tested using the meteorological inputs and streamflow data available at the gauged donor catchment. The trained model for each cluster is then transferred to the remaining receptor catchments within the cluster, where the meteorological variables corresponding to each ungauged catchment are used as inputs. The performance of the models in ungauged catchments is rigorously evaluated by comparing the simulated streamflow against observed streamflow using metrics such as Nash-Sutcliffe Efficiency (NSE), Root Mean Squared Error (RMSE), Coefficient of Determination (R²), and Percentage Bias (PBIAS). This study highlights the advantages of utilizing data-driven methods for streamflow prediction in both gauged and ungauged basins, particularly due to their ability to capture complex, non-linear relationships between meteorological inputs and streamflow generation. The findings of this study are expected to be instrumental in water resources planning and management, flood assessment, and the design of hydraulic structures in the Krishna River Basin.

Geomorphology-based rainfall–runoff models are particularly helpful for predicting hydrology in ungauged basins. The robustness, generality and flexibility of the modelling approach make it able to deal with a wide variety of processes, events and scales. It allows a rainfall–runoff transfer function to be estimated for any basin without needing to measure discharge. The aim of this study is to transpose hydrological observations from gauged to ungauged basins to predict streamflow hydrographs. It considers pairs of nested and neighbouring basins, the first one providing information for the second ungauged one. A time-series of the donor basin's discharge is deconvoluted by inverting its geomorphology-based transfer function to assess the time-series of net rainfall. The latter is then transposed to the receiver basin, where it is convoluted with the reciever basin's transfer function to predict the hydrograph therein. The methodology was implemented with virtual and real rainfall–runoff events on a set of basins in temperate Brittany, France. Different time scales and spatial configurations were tested. Goodness-of-fit of model predictions varied by basin pair. High prediction accuracy was observed when transposing hydrographs between nested basins differing greatly in size. Several ways to improve the approach are identified by relaxing simplifying assumptions.

Making useful Predictions in Ungauged Basins is an incredibly difficult task given the limitations of hydrologic models to represent physical processes appropriately across the heterogeneity within and among different catchments. Here, we introduce a new method for this challenge, Bayes empirical Bayes, that allows for the statistical pooling of information from multiple donor catchments and provides the ability to transfer parametric distributions rather than single parameter sets to the ungauged catchment. Further, the methodology provides an efficient framework with which to formally assess predictive uncertainty at the ungauged catchment. We investigated the utility of the methodology under both synthetic and real data conditions, and with respect to its sensitivity to the number and quality of the donor catchments used. This study highlighted the ability of the hierarchical Bayes empirical Bayes approach to produce expected outcomes in both the synthetic and real data applications. The method was found to be sensitive to the quality (hydrologic similarity) of the donor catchments used. Results were less sensitive to the number of donor catchments, but indicated that predictive uncertainty was best constrained with larger numbers of donor catchments (but still adequate with fewer donors).

A new parameter parsimonious rainfall–run‐off model, the Distance Distribution Dynamics (DDD) model, is used to simulate hydrological time series at ungauged sites in the Lygne basin in Norway. The model parameters were estimated as functions of catchment characteristics determined by geographical information system. The multiple regression equations relating catchment characteristics and model parameters were trained from 84 calibrated catchments located all over Norway, and all model parameters showed significant correlations with catchment characteristics. The significant correlation coefficients (with p‐value < 0.05) ranged from 0.22 to 0.55. The suitability of DDD for predictions in ungauged basins was tested for 17 catchments not used to estimate the multiple regression equations. For ten of the 17 catchments, deviations in Nash–Sutcliffe efficiency (NSE) criteria between the calibrated and regionalised model were less than 0.1, and for two calibrated catchments within the Lygne basin, the deviations were less than 0.08. The median NSE for the regionalized DDD for the 17 catchments for two time series was 0.66 and 0.72. Deviations in NSE between calibrated and regionalised models are well explained by the deviations between calibrated and regressed parameters describing spatial snow distribution and snowmelt respectively. The quality of the simulated run‐off series for the ungauged sites in the Lygne basin was assessed by comparing flow indices describing high, medium and low flow estimated from observed run‐off at the 17 catchments and for the simulated run‐off series. The indices estimated for the simulated series were generally well within the ranges defined by the 17 observed series. Copyright © 2014 John Wiley & Sons, Ltd.

Abstract. Prediction of streamflow at ungauged catchments requires transfer of hydrologic information (e.g., model parameters, hydrologic indices, streamflow values) from gauged (donor) to ungauged (receiver) catchments. A common metric used for the selection of ideal donor catchments is the spatial proximity between donor and receiver catchments. However, it is not clear whether information transfer among nearby catchments is suitable across a wide range of climatic and geographic regions. We examine this issue using the data from 756 catchments within the continental United States. Each catchment is considered ungauged in turn and daily streamflow is simulated through distance-based interpolation of streamflows from neighboring catchments. Results show that distinct geographic regions exist in US where transfer of streamflow values from nearby catchments is useful for retrospective prediction of daily streamflow at ungauged catchments. Specifically, the high predictability catchments (Nash-Sutcliffe efficiency NS > 0.7) are confined to the Appalachian Mountains in eastern US, the Rocky Mountains, and the Cascade Mountains in the Pacific Northwest. Low predictability catchments (NS < 0.3) are located mostly in the drier regions west of Mississippi river, which demonstrates the limited utility of gauged catchments in those regions for predicting at ungauged basins. The results suggest that high streamflow similarity among nearby catchments (and therefore, good predictability at ungauged catchments) is more likely in humid runoff-dominated regions than in dry evapotranspiration-dominated regions. We further find that higher density and/or closer distance of gauged catchments near an ungauged catchment does not necessarily guarantee good predictability at an ungauged catchment.

Classification of drainage basins into groups with similar response to meteorological forcing can be very helpful in cases of transfer of hydrological information in space such as in streamflow prediction in ungauged basins. It is also critical for the implementation of the Water Framework Directive and related legislative tools of the EU such as the Flood Directive. The focus is testing the ability to classify drainage basins using climate-based variables and geomorphometric characteristics as predictors. Precipitation is selected as the climate-based variable, since this is commonly measured in the majority of basins. Geomorphometric characteristics include, among others, the average ground slope and drainage density; these are derived from a Digital Terrain Model. The employed methodology involves two steps. In the first step we perform unsupervised classification through using the fuzzy c-means method to identify basin classes that serve as the reference classes in the second step of analysis. A set of hydrological signatures is used in the first step, which includes the runoff ratio, the baseflow index, the slope of the flow duration curve, and the snow day ratio. In the second step we perform supervised classification through using the k-Nearest Neighbour method which maps predictors to basin classes. Last, the success rate of the obtained classification is assessed through using jack-knife re-sampling. Twenty-four gauged basins in mainland Greece are used, which are classified into four classes. The employed methodology proved to be successful in more than 95 % of cases of recognition of the class for an ungauged basin.

This study suggests a radical approach to hydrologic predictions in ungauged basins, addressing the long standing challenge of issuing predictions when in-situ river discharge does not exist. A simple but powerful rationale for measuring and modeling river discharge is proposed, using coupled advances in hydrologic modeling and satellite remote sensing. Our approach presents a Surrogate River discharge driven Model (SRM) that infers Surrogate River discharge (SR) from remotely sensed microwave signals with the ability to mimic river discharge in varying topographies and vegetation cover, which is then used to calibrate a hydrological model enabling physical realism in the resulting river discharge profile by adding an estimated mean of river discharge via the Budyko framework. The strength of SRM comes from the fact that it only uses remotely sensed data in prediction. The approach is demonstrated for 130 catchments in the Murray Darling Basin (MDB) in Australia, a region of high economic and environmental importance. The newly proposed SR (SRL, representing L-band microwave) boosts the Nash-Sutcliffe Efficiency (NSE) of modeled flow, showing a mean NSE of 0.54, with 70% of catchments exceeding NSE 0.4. We conclude that SRM effectively predicts high-flow and low-flow events related to flood and drought. Overall, this new approach will significantly improve catchment simulation capacity, enhancing water security and flood forecasting capability not only in the MDB but also worldwide.