Hydrological Applications Research Articles

Dynamic mode decomposition of GRACE satellite data

Advancements in satellite technology yield environmental data with ever improving spatial coverage and temporal resolution. This necessitates the development of techniques to discern actionable information from large amounts of such data. We explore the potential of dynamic mode decomposition (DMD) to discover the dynamics of spatially correlated structures present in global-scale data, specifically in observations of total water storage anomalies provided by GRACE satellite missions. Our results demonstrate that DMD enables data compression and extrapolation from a reduced set of dominant spatiotemporal structures. The accuracy of its predictions of global system dynamics is preserved in its reconstruction of local time series. These findings suggest potential uses of DMD in analysis of remote-sensing data for hydrologic applications.

Generalized bivariate Kummer-beta distribution with marginals defined on the unit interval.

In this paper, a generalized bivariate Kummer-beta distribution is proposed. The name derives from the fact that its particular cases include univariate Kummer-beta distributions. This distribution generalizes a number of existing bivariate beta distributions, including Nadarajah's bivariate distributions, Libby and Novick's bivariate beta distribution and a central bivariate Kummer-beta distribution. Various properties associated with this newly introduced distribution are derived. The derived properties include product moments, marginal densities, marginal moments, conditional densities, conditional moments, Rényi entropy and Shannon entropy. Motivated by possible applications in economics, genetics, hydrology, meteorology, nuclear physics, and reliability, we also derive distributions of the product and the ratio of the components following the proposed distribution. Parameter estimation by maximum likelihood method is discussed by deriving expressions for score functions. Inference based on maximum likelihood estimation supposes that the maximum likelihood estimators have zero bias and zero mean squared errors. A simulation study is performed to check this for finite samples.

Dynamics of real-time forecasting failure and recovery due to data gaps: A study using EnKF-based assimilation with the Lorenz model

Data assimilation-based real-time forecasting is widely used in meteorological and hydrological applications, where continuous data streams are employed to update forecasts and maintain accuracy. However, the reliability of the data source can be compromised due to sensor and communication failures or physical or cyber-attacks, and the impact of data stream failures on the accuracy of the forecasting system is not well understood. This study aims to systematically investigate the process of data stream failure and recovery for the first time. To achieve this, data gaps with varying lengths and timings are introduced to EnKF-based data assimilation system on the Lorenz model operating in both chaotic and periodic modes. Results show that the forecasting error grows exponentially in the chaotic mode but was limited in the periodic mode from the start of the data gap. For chaotic mode, the recovery of the system depends on the length of the data gap if the model error is not saturated; after saturation, the timing of the data stream recovery is important. Moreover, even long after restarting the data assimilation in the chaotic mode, the forecasting system cannot fully restore the original accuracy, while the periodic mode is generally resilient to disruption. This research introduces new metrics for quantifying system resilience and provides crucial insights into the long-term implications of data gaps, advancing our understanding of forecasting system behavior and reliability.

Calibration of TEROS 10 and TEROS 12 electromagnetic soil moisture sensors

AbstractThe TEROS 10 and TEROS 12 are widely used capacitance‐based sensors for measuring volumetric water content (), but few systematic studies of the measurement volume and accuracy of these sensors have been published. The objectives of this study were to (1) calibrate and validate these sensors in mineral soils, (2) determine the sensing volume of each sensor, and (3) evaluate the temperature sensitivity of the sensors. Both sensors were calibrated in the laboratory using columns of packed soil at multiple moisture levels from air‐dry to near saturation. Sensors were validated using additional laboratory and field measurements. The sensing volume was determined by quantifying the response of raw sensor outputs while increasing the level of oven‐dry sand, moist sand (0.100 cm3 cm−3), or water around the sensor in the radial and axial directions. Temperature sensitivity was tested in controlled conditions over a range of temperatures from 2°C to 40°C using encapsulated sensors in packed soil columns at constant . Linear calibration models resulted in mean absolute error ≤0.030 cm3 cm−3 for both sensors during laboratory and field validations. In moist sand, the sensing volume contributing 95% of the maximum sensor response was 439 cm3 for the TEROS 10 and 423 cm3 for the TEROS 12. Both sensors exhibited changes in of ≤0.02 cm3 cm−3 when subjected to a temperature change from 2°C to 40°C. For the soils considered here, both sensors demonstrated accuracy that is likely sufficient for a variety of agricultural and hydrological applications.

Cutting-edge approaches for judging surface water dynamics in semi-arid environments: Integrating landsat 8 OLI/TIRS and HYDROSAM model

This research addresses the critical need to assess surface water dynamics in semi-arid regions of Andhra Pradesh, India, by using advanced Spectral Indices for hydrological applications and methodologies. It aims to answer how remote sensing data from Landsat 8 OLI/TIRS can be effectively used to monitor and classify surface water bodies. The study applies indices such as Normalized Difference Water Index (NDWI), Modified Normalized Difference Water Index (MNDWI), Normalized Difference Thermal Index (NDTI), and Water Ratio Index (WRI). Additionally, the Weighted Composite Index (WCI) and Normalized Composite Index (NCI) are integrated with Principal Component Analysis (PCA) for multi-criteria decision making. The HYDROSAM model successfully classifies and maps various categories of surface water bodies, including non-water features (53.62%), urban water zones (37.89%), seasonal water bodies (4.32%), transitional zones (2.17%), permanent water bodies (1.05%), and river bodies (0.95%). The resultant map was validated using the AUC-ROC curve, achieving an AUC of 0.820, indicating a high level of accuracy. This methodology provides a nuanced understanding of water resource distribution and availability in the region. The findings demonstrate the robustness and reliability of the HYDROSAM model in accurately assessing surface water characteristics, thereby providing critical insights for informed water resource management, strategic land-use planning, and effective ecological conservation. This innovative methodology not only fosters sustainable water resource management in semi-arid regions but also sets a precedent for advancing research in similar ecosystems globally.

An explainable hybrid framework for estimating daily reference evapotranspiration: Combining extreme gradient boosting with Nelder-Mead method

Accurate estimation of reference evapotranspiration (ETo) is essential for effective water resources management, irrigation system design, and various hydrological and agricultural applications. This study employed extreme gradient boosting (XGBoost) model, signal decomposition techniques, and XGBoost coupled with Nelder–Mead (NM) method to enhance ETo prediction across two meteorological stations in Iran. This study proposed a novel framework which lies in its comprehensive integration of advanced techniques to create a model that is both interpretable and highly accurate for ETo estimation. For this aim, sixty meteorological variables were categorized into solar and cloud-based, temperature-based, wind and humidity-based, and pressure-based groups to analyze their effect on ETo estimation. Feature selection methods, including the Gradient Boosting Machine, Kendall’s Tau, and Relief Algorithm, were employed to identify the most influential predictors. Variables with normalized weights equal to or greater than 0.9 were selected for model input, resulting in the top 10% of variables being utilized. The XGBoost models were then developed using these selected inputs (level 1), a wavelet-based hybrid was developed according to the most effective features (level 2), and the XGBoost model was coupled by NM algorithm (level 3) for ETo estimation. Results of estimated ETo by levels 1 to 3 were compared with four common empirical approaches. The results indicated that Kendall’s Tau-based feature selection provided the most accurate predictions in Shiraz, achieving an RMSE of 0.721 (mm/day) for solar and cloud-based variables during the test phase. Additionally, the application of wavelet analysis further refined the model inputs, which enhanced ETo estimation in most variable groups. Integrating the NM algorithm with XGBoost demonstrated significant improvements in ETo estimation, where it could improve RMSE to 0.091 and 0.155 (mm/day) for testing section in Fasa and Shiraz, respectively.

The legacy of STAHY: milestones, achievements, challenges, and open problems in statistical hydrology

ABSTRACT Statistical tools are crucial for a variety of hydrological applications, whether to model processes and enhance understanding and knowledge or to design infrastructure systems. Given the rapid evolution of statistical methods and the need for a solid theoretical foundation for their correct application, a multidisciplinary community STAtistics in HYdrology Working Group (STAHY-WG) aggregated under the International Association of Hydrological Sciences (IAHS) umbrella to contribute to this research field. Now, more than 15 years since its inception, this paper summarizes the main achievements of this productive community collaboration in four (of many) branches of statistical hydrology: extreme value analysis, multivariate analysis, time series analysis, and regionalization. The aim is to provide an overview of recent developments, offer practical suggestions (e.g. software packages), and outline future challenges to support scientists and practitioners in their endeavours within the realm of statistical hydrology studies.

Transforming Hydrology Python Packages into Web Application Programming Interfaces: A Comprehensive Workflow Using Modern Web Technologies

The accessibility and deployment of complex hydrological models remain significant challenges in water resource management and research. This study presents a comprehensive workflow for converting Python-based hydrological models into web APIs, addressing the need for more accessible and interoperable modeling tools. The workflow leverages modern web technologies and containerization to streamline the deployment process. The workflow was applied to three distinct models: a GRACE downscaling model, a synthetic time series generator, and a MODFLOW groundwater model. The implementation process for each model was completed in approximately 15 min with a reliable internet connection, demonstrating the efficiency of the approach. The resulting APIs provide standardized interfaces for model execution, progress tracking, and result retrieval, facilitating integration with various applications. This workflow significantly reduces barriers to model deployment and usage, potentially broadening the user base for sophisticated hydrological tools. The approach aligns hydrological modeling with contemporary software development practices, opening new avenues for collaboration and innovation. While challenges such as performance scaling and security considerations remain, this work provides a blueprint for making complex hydrological models more accessible and operational, paving the way for enhanced research and practical applications in hydrology.

The Implementation of Multimodal Large Language Models for Hydrological Applications: A Comparative Study of GPT-4 Vision, Gemini, LLaVa, and Multimodal-GPT

The Implementation of Multimodal Large Language Models for Hydrological Applications: A Comparative Study of GPT-4 Vision, Gemini, LLaVa, and Multimodal-GPT

Effect of Land Use/Land Cover Maps on CN Method: Case Study over Kahramanmaras

The impact of Land Use/Land Cover (LULC) data obtained from various spatial resolution satellites on the distribution of the Curve Number (CN) across Kahramanmaras using the Soil Conservation Service (SCS)-CN technique was investigated in this research. This study aimed to examine the effect of LULC on runoff due to increasing urbanization in the last century and the conversion of forest areas to agricultural lands. CORINE data with a spatial resolution of 100 m, and Sentinel-2A data with spatial resolutions of 10, 20, and 60 m were utilized in the analysis. The results reveal that only the average CNs of the products are in close proximity, while there are significant discrepancies in the CN variation over the maps as the spatial resolution increases. The Sentinel-2A satellite findings revealed higher CN values compared to the CORINE dataset over the study area where three geographical regions, namely the Mediterranean, Eastern Anatolia, and Southeastern Anatolia. Additionally, the results show that an increase in urbanization triggers surface runoff potential and reduces it in agricultural and forest areas in the city. Thus, the updated and higher spatial resolution of LULC promises accurate flood forecasting and/or more scientific potential drought estimation as well as other hydrological applications.

Estimation of design precipitation using weather radar in Germany: A comparison of statistical methods

Study region:Germany. Study focus:Estimation of precipitation return levels on various temporal scales and with high spatial resolution is crucial for risk management and hydrological applications. Weather radars may provide this information, but design precipitation estimates from these instruments suffer from estimation biases and from the limited length of the available records. Here, the performance of two statistical methods for deriving design precipitation from 20 years of radar data for Germany is investigated: (a) a method based on peaks-over-threshold and an exponential distribution, operationally used for decades to compute design precipitation in Germany (DWA); and (b) a non-asymptotic approach that was recently shown to reduce estimation uncertainties related to short records (SMEV). The most recent official design precipitation for Germany derived from station data (KOSTRA-DWD-2020) are used as a benchmark. New Hydrological Insights for the RegionDesign precipitation from radar data tends to be lower than those derived from stations, due to the scale mismatch (point scale versus ∼1km2 of radar) and to biases in radar estimates of extremes. SMEV tends to underestimate more than DWA, especially for short durations. Larger uncertainties are reported for the DWA method, while SMEV estimates tend to be more stable and less influenced by statistical outliers. Application of the KOSTRA-DWD-2020 method on radar data leads to results closer to SMEV.

A Monte Carlo Propagation of the Full Variance‐Covariance of GRACE‐Like Level‐2 Data With Applications in Hydrological Data Assimilation and Sea‐Level Budget Studies

AbstractUnderstanding mass (re‐)distribution within the Earth system, and addressing global challenges such as the impact of climate change on water resources requires global time‐variable terrestrial water storage (TWS) estimates along with reasonable uncertainty fields. The Gravity Recovery and Climate Experiment (GRACE) and GRACE‐FO satellite missions provide time‐variable gravity fields with full variance‐covariance information. A rigorous uncertainty propagation of these errors to TWS uncertainties is mathematically challenging and computationally inefficient. We propose a Monte Carlo Full Variance‐Covariance (MCFVC) error propagation approach to precisely compute TWS uncertainties. We also establish theoretical criteria to predict the actual convergence and accuracy of MCFVC, showing a convergence after 10,000 realizations with the relative error of 2.8% for variance and 4.7% for covariance at the confidence level of 95%. This can be achieved in few seconds using a single CPU to compute the uncertainties of each 1° resolution globally gridded TWS field. A validation against the rigorous error propagation method indicates relative differences of less than 0.8%. A global uncertainty assessment shows that neglecting the covariance of gravity coefficients can considerably bias the TWS uncertainties, that is, up to 60%, in some basins like Eyre. Flexibility of MCFVC allows the quantification of filtering impacts on the uncertainty of TWS fields, for example, up to 35% in the Tocantins River Basin. An empirical model is provided to reproduce GRACE‐like TWS uncertainty fields for hydrological studies. Finally, experiments of GRACE(‐FO) data assimilation for hydrological applications and sea‐level budget estimation are presented that indicate the importance of accounting for the full covariance information in these studies.

GloRESatE: A dataset for global rainfall erosivity derived from multi-source data

Numerous hydrological applications, such as soil erosion estimation, water resource management, and rain driven damage assessment, demand accurate and reliable rainfall erosivity data. However, the scarcity of gauge rainfall records and the inherent uncertainty in satellite and reanalysis-based rainfall datasets limit rainfall erosivity assessment globally. Here, we present a new global rainfall erosivity dataset (0.1° × 0.1° spatial resolution) integrating satellite (CMORPH and IMERG) and reanalysis (ERA5-Land) derived rainfall erosivity estimates with gauge rainfall erosivity observations collected from approximately 6,200 locations across the globe. We used a machine learning-based Gaussian Process Regression (GPR) model to assimilate multi-source rainfall erosivity estimates alongside geoclimatic covariates to prepare a unified high-resolution mean annual rainfall erosivity product. It has been shown that the proposed rainfall erosivity product performs well during cross-validation with gauge records and inter-comparison with the existing global rainfall erosivity datasets. Furthermore, this dataset offers a new global rainfall erosivity perspective, addressing the limitations of existing datasets and facilitating large-scale hydrological modelling and soil erosion assessments.

Runoff Prediction for Hydrological Applications Using an INFO-Optimized Deep Learning Model

Runoff Prediction for Hydrological Applications Using an INFO-Optimized Deep Learning Model

Bridging spatio-temporal discontinuities in global soil moisture mapping by coupling physics in deep learning

The launch of Soil Moisture Active Passive (SMAP) satellite in 2015 has resulted in significant achievements in global soil moisture mapping. Nonetheless, spatiotemporal discontinuities in the soil moisture products have arisen due to the limitations of its orbit scanning gap and retrieval algorithms. To address these issues, this paper presents a physics-constrained gap-filling method, PhyFill for short. The PhyFill method employs a partial convolutional neural network technique to explore spatial domain features of the original SMAP soil moisture data. Then, it incorporates variations in soil moisture induced by precipitation events and dry-down events as penalty terms in the loss function, thereby accounting for monotonicity and boundary constraints in the physical processes governing the dynamic fluctuations of soil moisture. The PhyFill model was applied to SMAP soil moisture data, resulting in continuous spatially daily soil moisture data on a global scale. Three validation strategies are employed: visual inspection through global pattern, simulated missing-region validation, and soil moisture validation with in situ measurements. The results indicated that the reconstructed soil moisture achieved a higher spatial coverage with satisfactory spatial continuity with neighbouring pixels. The simulated validation of the missing regions revealed that the averaged unbiased root mean square difference (ubRMSD) and correlation coefficient (R) were 0.01 m3/m3 and 0.99, respectively versus the gap filled SMAP product. The core validation sites demonstrated that the reconstructed soil moisture data has a consistent ubRMSD compared with the original SMAP soil moisture data (0.04 m3/m3vs. 0.04 m3/m3). The PhyFill method can generate globally continuous, high accurate soil moisture estimates, providing remarkable support for advanced hydrological applications, e.g., global soil moisture dry-down events and patterns.

Bias correction of the hourly satellite precipitation product using machine learning methods enhanced with high-resolution WRF meteorological simulations

Accurate precipitation data are crucial in atmospheric and hydrological studies, especially for water resource management and disaster early warning. Satellite precipitation product (SPP) with high spatiotemporal resolution has been regarded as a valuable alternative precipitation source to ground observations. However, the hourly SPP generally performs poorly compared to daily SPP, thereby bias correction is urgently required. This study investigates the viability of utilizing machine learning methods to correct the bias of the hourly Integrated Multi-satellitE Retrievals for Global Precipitation Measurement-Early (IMERG-E) product. Meanwhile, the Weather Research and Forecasting (WRF) model is utilized to generate high-resolution fields of four hourly meteorological variables, namely, temperature at 2 m (TEMP2), specific humidity at 2 m (Q2), wind direction at 10 m (WDIR10), and wind speed at 10 m (WSPD10), which further serve as covariates in machine learning models to enhance the correction process. Four machine learning models were developed, i.e., Random Forest (RF) and Bidirectional Long Short-Term Memory Networks (Bi-LSTM) without WRF-simulated covariates, and RF-WRF and Bi-LSTM-WRF with meteorological covariates. The results demonstrated that incorporating WRF-simulated meteorological covariates improved model performance. Specifically, correlation coefficient (CC) values increased from 0.47 (RF) to 0.51 (RF-WRF) and rose from 0.55 (Bi-LSTM) to 0.60 (Bi-LSTM-WRF), along with reduced root mean square error (RMSE) and increased critical success index (CSI) values. Furthermore, two Bi-LSTM models consistently outperformed two RF models. Overall, the Bi-LSTM-WRF model emerged as the most effective correction method, which increased CC from 0.43 (IMERG-E) to 0.60, reduced RMSE from 1.91 mm to 1.08 mm, and enhanced CSI from 0.34 to 0.41. This study underscores the potential of integrating high-resolution WRF meteorological outputs into machine learning frameworks for correcting hourly SPPs, contributing significantly to the advancement of precipitation estimation in meteorological and hydrological applications.

Exploring patterns in precipitation intensity–duration–area–frequency relationships using weather radar data

Abstract. Accurate estimations of extreme precipitation return levels are critical for many hydrological applications. Extreme precipitation is highly variable in both space and time; therefore, to better understand and manage the related risks, knowledge of their probability at different spatial–temporal scales is crucial. We employ a novel non-asymptotic framework to estimate extreme return levels (up to 100 years) at multiple spatial–temporal scales from weather radar precipitation estimates. The approach reduces uncertainties and enables the use of relatively short archives typical of weather radar data (12 years in this case). We focus on the eastern Mediterranean, an area of high interest due to its sharp climatic gradient, containing Mediterranean, semi-arid, and arid areas across a few tens of kilometres, and its susceptibility to flash flood. At-site intensity–duration–area–frequency relations are derived from radar precipitation data at various scales (10 min–24 h, 0.25–500 km2) across the study area, using ellipses of varying axes and orientations to account for the spatial component of storms. We evaluate our analysis using daily rain gauge data over areas for which sufficiently dense gauge networks are available. We show that extreme return levels derived from radar precipitation data for 24 h and 100 km2 are generally comparable to those derived from averaging daily rain gauge data over a similar areal scale. We then analyse differences in multi-scale extreme precipitation over coastal, mountainous, and desert regions. Our study reveals that the power-law scaling relationship between precipitation and duration (simple scaling) weakens for increasing area sizes. This finding has implications for temporal downscaling. Additionally, precipitation intensity varies significantly for different area sizes at short durations but becomes more similar at long durations, suggesting that, in the region, areal reduction factors may not be necessary for computing return levels over long durations. Furthermore, the reverse orographic effect, which causes decreased precipitation for hourly and sub-hourly durations, diminishes for larger areas. Finally, we discuss the effects of orography and coastline proximity on extreme precipitation intensity over different spatial–temporal scales.

A new method for predicting precipitation δ18O distribution based on deep learning and spatio-temporal clustering

ABSTRACT Predicting precipitation δ18O accurately is crucial for understanding water cycles, paleoclimates, and hydrological applications. Yet forecasting its spatio-temporal distribution remains challenging due to complex climate interactions and extreme events. We developed a method combining spatio-temporal clustering and deep learning neural networks to improve multi-site, multi-year precipitation δ18O predictions. Using a comprehensive dataset from 33 German sites (1978–2012), our model considers precipitation δ18O and its controlling factors, including precipitation and temperature distribution. We applied the K-means ++ method for classification and divided data into training and prediction sets. The convolutional neural network (CNN) model extracted spatial features, while the bi-directional long short-term memory (Bi-LSTM) model focused on temporal features. Spatio-temporal clustering using K-means ++ improved forecast accuracy and reduced errors. This study highlights the potential of deep learning and clustering techniques for forecasting complex spatio-temporal data and offers insights for future research on isotope distributions.

Advances in remote sensing based soil moisture retrieval: applications, techniques, scales and challenges for combining machine learning and physical models

Soil Moisture (SM) monitoring is crucial for various applications in agriculture, hydrology, and climate science. Remote Sensing (RS) offers a powerful tool for large-scale SM retrieval. This paper explores the advancements in RS techniques for SM estimation. We discuss the applications of these techniques, along with the advantages and limitations of traditional physical models and data-driven Machine Learning (ML) based approaches. The paper emphasizes the potential of combining ML and physical models to leverage the strengths of both approaches. We explore the challenges associated with this integration and future research directions to improve the accuracy, scalability, and robustness of RS-based SM retrieval. Finally, the paper also discusses a few issues such as input data selection, data availability, ML complexity, the need for public datasets for benchmarking, and analysis.

Comparative Analysis of Snowmelt-Driven Streamflow Forecasting Using Machine Learning Techniques

The rapid advancement of machine learning techniques has led to their widespread application in various domains, including water resources. However, snowmelt modeling remains an area that has not been extensively explored. In this study, we propose a state-of-the-art (SOTA) deep learning sequential model, leveraging a Temporal Convolutional Network (TCN), for snowmelt forecasting of the Hindu Kush Himalayan (HKH) region. To evaluate the performance of our proposed model, we conducted a comparative analysis with other popular models, including Support Vector Regression (SVR), Long Short-Term Memory (LSTM), and Transformer models. Furthermore, nested cross-validation (CV) was used with five outer folds and three inner folds, and hyperparameter tuning was performed on the inner folds. To evaluate the performance of the model, the Mean Absolute Error (MAE), Root-Mean-Square Error (RMSE), R square (R2), Kling–Gupta Efficiency (KGE), and Nash–Sutcliffe Efficiency (NSE) were computed for each outer fold. The average metrics revealed that the TCN outperformed the other models, with an average MAE of 0.011, RMSE of 0.023, R2 of 0.991, KGE of 0.992, and NSE of 0.991 for one-day forecasts of streamflow. The findings of this study demonstrate the effectiveness of the proposed deep learning model as compared to traditional machine learning approaches for snowmelt-driven streamflow forecasting. Moreover, the superior performance of this TCN highlights its potential as a promising deep learning model for similar hydrological applications.