Applying non-parametric Bayesian networks to estimate maximum daily river discharge: potential and challenges

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.

Streamflow prediction in ungauged basins (PUB) is challenging, and Long Short‐Term Memory (LSTM) is widely used to for such predictions, owing to its excellent migration performance. Traditional LSTM forced by meteorological data and catchment attribute data barely highlight the optimum data integration strategy for LSTM and its migration from data‐rich basins to ungauged ones. In this study, we experimented with 1,897 global catchments and found that LSTM‐corrected Global Hydrological Models (GHMs) outperformed uncorrected GHMs, improving the median Nash‐Sutcliff efficiency (NSE) from 0.03 to 0.66. Notably, there was a large gap between traditional LSTM modeling in ungauged basins and autoregressive modeling in data‐rich basins, and GHM‐forced LSTM were an effective way to close this gap in ungauged basins. The spatial heterogeneity of the performance of GHM‐forced LSTM was mainly influenced by three metrics (dryness, the leaf area index and latitude), which described the hydrological similarity among catchments. Weaker hydrological similarity among continental catchments results in larger variability in GHM‐forced LSTM, with the best performance in Siberia (NSE, 0.54) and the worst in North America (NSE, 0.10). However, the migration performance of GHM‐forced LSTM was significantly improved (NSE, 0.63) in ungauged basins when hydrological similarity was considered. This study stressed the advantages of GHM‐forced LSTM and due significance should be attached to hydrological similarities among catchments to improve hydrological prediction in ungauged catchments.

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

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.

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.

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.

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.

The parameters of hydrological models should be determined before applying those models to estimate or predict hydrological processes. The Xin’anjiang (XAJ) hydrological model is widely used throughout China. Since the prediction in ungauged basins (PUB) era, the regionalization of the XAJ model parameters has been a subject of intense focus; nevertheless, while many efforts have targeted parameters related to runoff yield using in-site data sets, classic regression has predominantly been applied. In this paper, we employed remotely sensed underlying surface data and a machine learning approach to establish models for estimating the runoff routing parameter, namely, CS, of the XAJ model. The study was conducted on 114 catchments from the Catchment Attributes and MEteorology for Large-sample Studies (CAMELS) data set, and the relationships between CS and various underlying surface characteristics were explored by a gradient-boosted regression tree (GBRT). The results showed that the drainage density, stream source density and area of the catchment were the three major factors with the most significant impact on CS. The best correlation coefficient (r), root mean square error (RMSE) and mean absolute error (MAE) between the GBRT-estimated and calibrated CS were 0.96, 0.06 and 0.04, respectively, verifying the good performance of GBRT in estimating CS. Although bias was noted between the GBRT-estimated and calibrated CS, runoff simulations using the GBRT-estimated CS could still achieve results comparable to those using the calibrated CS. Further validations based on two catchments in China confirmed the overall robustness and accuracy of simulating runoff processes using the GBRT-estimated CS. Our results confirm the following hypotheses: (1) with the help of large sample of catchments and associated remote sensing data, the ML-based approach can capture the nonstationary and nonlinear relationships between CS and the underlying surface characteristics and (2) CS estimated by ML from large samples has a robustness that can guarantee the overall performance of the XAJ mode. This study advances the methodology for quantitatively estimating the XAJ model parameters and can be extended to other parameters or other 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.

On the development of regionalization relationships for lumped watershed models: The impact of ignoring sub-basin scale variability

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.

Modelling ungauged catchments using the catchment runoff response similarity

The focus in the search for more reliable predictions in ungauged basins (PUB) has generally been on reducing uncertainty in watershed models (mainly their parameters). More recently, however, we seem to remember that the ultimate objective is not to define the parameters of a specific model but to understand the watershed: What behavior do we expect the ungauged watershed to exhibit? And what behavior should not occur in a particular ungauged watershed? The answers to these questions actually provide additional information that can be assimilated in watershed models for uncertainty reduction in PUB. This extension to hydrologic modeling approaches provides a quantitative link between watershed modeling and statistical hydrology as well as process hydrology that has to be explored. We witness a convergence of approaches—Bayesian, set theoretic, and optimization based—toward utilizing this link. The result is an opportunity for the (quantitative) dialog between modelers, statistical hydrologists, and experimentalists. We close our discussion of this development by presenting new and exciting research questions that we now have to address.

Reduction of uncertainty in hydrologic predictions is important for water resources development and management, especially in ungauged basins. The objective of this study was to predict rainfall and runoff in an ungauged basin located in a mountainous region of northern Thailand by using a weather radar to estimate rainfall and a modeling approach to simulate rainfall-runoff processes. The calibrated Ze-R relationship (Ze=18R1.45) was used to estimate rainfall over a gauged basin and an assumed ungauged basin. The runoff simulations in the gauged and ungauged basins were conducted using the quasi-distributed hydrological model HEC-HMS. The simulation results in the gauged basin, for both calibration and verification, were in agreement with the observed data. Model parameters in the assumed ungauged basin were estimated using transposition and regionalization techniques. The predicted direct runoff hydrograph in the assumed ungauged basin using radar measured rainfall and the regionalization technique matches well with the measurements at the basin outlet. Based on the study results, the radar rainfall estimates and regionalization of the hydrologic model parameters are promising alternatives for improved hydrologic predictions in ungauged basins.

The meltwater percolation process through the snowpack greatly influences its physical and mechanical properties. The percolation process is important for understanding the spring avalanche phenomenon as well as the meltwater runoff for basin hydrology studies. The permeability of individual snow layers depends on parameters such as porosity, pore connectivity and the geometrical shape of the pores. Snowpack equivalent permeability plays an important role in governing the transmission of meltwater through the different layers of the snowpack. In this paper, we present the design, fabrication and installation of a snowmelt lysimeter at Patsio field research station, Himachal Pradesh, India, and determine the snowpack equivalent permeability using lysimeter discharge data. The snowmelt lysimeter, having a collector area of 6.25 m2 and a high-capacity snowmelt measuring tipping bucket, was installed on flat ground near the observatory with a data acquisition system. Snowmelt discharge measurements were made for two melt seasons, 2006/07 and 2007/08. Snow and meteorological data were collected at 15 min intervals using a semi-automatic weather station. The hourly surface snowmelt was estimated using an energy-balance approach. The maximum daily discharge was >2 mm w.e.h−1 for most of the observation period. The daily mean wave speed of the meltwater front varied from 109 to 285 mm h−1 for a daily mean discharge range of 0.6–1.8 mm w.e.h−1, while wave speeds for a particular melt flux of 2 mm w.e.h−1 varied between 113 and 486 mm h−1. The pore-size distribution index was estimated using the power-fit relation between wave speed and discharge. The equivalent permeability of the snowpack was found to vary between 3.4 × 10−8 and 9.9 × 10−12 m2.