Hydrological Time Series Research Articles

Using ARIMA and ETS models for forecasting water level changes for sustainable environmental management

It is vital to provide useful hydrological forecasts for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among other things. This paper introduces a simple and flexible hydrological time series forecasting framework. Predicting water levels is crucial, given the need for sustainable environmental management. The prognosis should be reasonable to persuade individuals to take proper precautions. While many methods have been developed to predict water levels, here the effectiveness of two approaches to predicting river water levels was assessed. For this purpose, nine years of data were used, which were divided into input data (2014–2021) and validation data (2022), on water levels in the Morava e Binçës river for the Vitia station, in the form of monthly time series records, to identify the best model among those used and to identify the information necessary for water resource management and hazard control. Models Autoregressive Integrated Moving Average(ARIMA) and Error Trend and Seasonality, or Exponential Smoothing (ETS), were examined using the R package to determine the most accurate. The results indicate the applicability of both models, as evidenced by the Root Mean Square Error (RMSE) and the Mean Absolute Error (MAE). The predictive analysis based on historical water levels allowed the identification of distinct periods characterized by high and low water levels between 2022 and 2024, which is important for the area in question due to the numerous flood events occurring here.

Hydrological Data Projection Using Empirical Mode Decomposition: Applications in a Changing Climate

This paper demonstrates the effectiveness and superiority of Empirical Mode Decomposition (EMD) in projecting non-stationary hydrological data. The study focuses on daily Sea Surface Temperature (SST) sequences in the Niño 3.4 region and uses EMD to forecast the probability of El Niño events. Applying the Mann–Kendall test at the 5% significance level reveals a significant increasing trend in SST changes in this region, particularly noticeable after 1980. This trend is associated with the occurrence of El Niño and La Niña events, which have a recurrence interval of approximately 8.4 years and persist for over a year. The modified Oceanic Niño Index (ONI) proposed in this study demonstrates high forecast accuracy, with 97.56% accuracy for El Niño and 89.80% for La Niña events. Additionally, the EMD of SST data results in 13 Intrinsic Mode Functions (IMFs) and a residual component. The oscillation period increases with each IMF level, with IMF7 exhibiting the largest amplitude, fluctuating between ±1 °C. The residual component shows a significant upward trend, with an average annual increase of 0.0107 °C. These findings reveal that the EMD-based data generation method overcomes the limitations of traditional hydrological models in managing non-stationary sequences, representing a notable advancement in data-driven hydrological time series modeling. Practically, the EMD-based 5-year moving process can generate daily sea temperature sequences for the coming year in this region, offering valuable insights for assessing El Niño probabilities and facilitating annual updates.

Multimodal Fusion of Optimized GRU–LSTM with Self-Attention Layer for Hydrological Time Series Forecasting

Multimodal Fusion of Optimized GRU–LSTM with Self-Attention Layer for Hydrological Time Series Forecasting

Streamflow Prediction Using Complex Networks.

The reliable prediction of streamflow is crucial for various water resources, environmental, and ecosystem applications. The current study employs a complex networks-based approach for the prediction of streamflow. The approach consists of three major steps: (1) the formation of a network using streamflow time series; (2) the calculation of the clustering coefficient (CC) as a network measure; and (3) the use of a clustering coefficient-based nearest neighbor search procedure for streamflow prediction. For network construction, each timestep is considered as a node and the existence of link between any node pair is identified based on the difference (distance) between the streamflow values of the nodes. Different distance threshold values are used to identify the critical distance threshold to form the network. The complex networks-based approach is implemented for the prediction of daily streamflow at 142 stations in the contiguous United States. The prediction accuracy is quantified using three statistical measures: correlation coefficient (R), normalized root mean square error (NRMSE), and Nash-Sutcliffe efficiency (NSE). The influence of the number of neighbors on the prediction accuracy is also investigated. The results, obtained with the critical distance threshold, reveal that the clustering coefficients for the 142 stations range from 0.799 to 0.999. Overall, the prediction approach yields reasonably good results for all 142 stations, with R values ranging from 0.05 to 0.99, NRMSE values ranging from 0.1 to 12.3, and the NSE values ranging from -0.89 to 0.99. An attempt is also made to examine the relationship between prediction accuracy and the catchment characteristics/streamflow statistical properties (drainage area, mean flow, coefficient of variation of flow). The results suggest that the prediction accuracy does not have much of a relationship with the drainage area and the mean streamflow values, but with the coefficient of variation of flow. The outcomes from this study are certainly promising regarding the application of complex networks-based concepts for the prediction of streamflow (and other hydrologic) time series.

Anomaly detection in hydrological network time series via multiresolution analysis

The territorial extension of Brazil imposes logistic challenges on hydrologic monitoring and increases the chances of systematic observational errors, gauge displacements, downsampling during observation, and low density of streamflow samples on high water stage. Consequently, time series would exhibit artifacts such as gaps, high-frequency anomalies, inhomogeneity, and trends. An innovative anomaly detection system based on multiresolution analysis (MADE) was developed and used to detect synthetic anomalies in raw water stage time series. MADE uses both time and frequency as contextual attributes to identify anomalies. The balance between temporal and frequency resolution allows for capturing low-frequency coarse information and high-frequency details. On MADE, Generalized Extreme Studentized Deviate (GESD) detected short time anomalies on water stage wavelet faster modes (2-, 4-, and 8-days periods). For periods greater than 16 days, Wavelet Coherence and Multiple Wavelet Coherence detected similar water stage time series anomalies. MADE outperformed a Long Short-Term Memory model, a time regression neural network k-Nearest Neighbor model and an Empirical Data Analytics model coupled with clustering techniques on detecting both fast and slow time-scales synthetic anomalies introduced in a São Francisco River water stage time series, using time and frequency domain to pursuit point, collective and contextual anomalies.

Scalable and Interpretable Forecasting of Hydrological Time Series Based on Variational Gaussian Processes

Accurate streamflow forecasting is crucial for effectively managing water resources, particularly in countries like Colombia, where hydroelectric power generation significantly contributes to the national energy grid. Although highly interpretable, traditional deterministic, physically-driven models often suffer from complexity and require extensive parameterization. Data-driven models like Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) networks offer simplicity and performance but cannot quantify uncertainty. This work introduces Sparse Variational Gaussian Processes (SVGPs) for forecasting streamflow contributions. The proposed SVGP model reduces computational complexity compared to traditional Gaussian Processes, making it highly scalable for large datasets. The methodology employs optimal hyperparameters and shared inducing points to capture short-term and long-term relationships among reservoirs. Training, validation, and analysis of the proposed approach consider the streamflow dataset from 23 geographically dispersed reservoirs recorded during twelve years in Colombia. Performance assessment reveals that the proposal outperforms baseline Linear Autoregressive (LAR) and Long Short-Term Memory (LSTM) models in three key aspects: adaptability to changing dynamics, provision of informative confidence intervals through Bayesian inference, and enhanced forecasting accuracy. Therefore, the SVGP-based forecasting methodology offers a scalable and interpretable solution for multi-output streamflow forecasting, thereby contributing to more effective water resource management and hydroelectric planning.

A novel method of nonuniform phase space reconstruction for multivariate prediction of daily runoff

Phase space reconstruction is crucial for predicting chaotic hydrological time series. However, traditional multivariate phase space reconstruction methods, such as high-dimensional and low-dimensional phase space reconstruction (HDPSR and LDPSR) neglect variable interdependence, resulting in redundant information in the reconstructed phase space and affecting the model prediction accuracy. To address this limitation, this study proposes a new nonuniform phase space reconstruction (NUPSR) method that combines the minimum redundancy maximum relevance criterion and conditional entropy. Then, using HDPSR, LDPSR, NUPSR, particle swarm optimization (PSO), support vector regression (SVR), and bidirectional long- and short-term memory neural networks (BiLSTM), the models HDPSR-PSO-SVR, LDPSR-PSO-SVR, NUPSR-PSO-SVR, HDPSR-PSO-BiLSTM, LDPSR-PSO-BiLSTM, and NUPSR-PSO-BiLSTM are built to evaluate the performance of the NUPSR method. To demonstrate the effectiveness of the NUPSR method in multistep daily runoff prediction, the models PSO-NUPSR-BiLSTM, LDPSR-PSO-BiLSTM, and HDPSR-PSO-BiLSTM are also built. The multifactor daily runoff data from five hydrological stations in the Weihe River Basin are used to evaluate the prediction performance of all models. The results show that the state variables obtained by NUPSR are more independent and less redundant than those obtained by HDPSR and LDPSR, as evidenced by the embedded state variables and lower embedding dimension of NUPSR and the performance of the model based on NUPSR outperforms based on HDPSR and LDPSR. Particularly, the PSO-NUPSR-BiLSTM model exhibits a slower decrease in prediction accuracy compared to the other two models as the number of prediction steps increases. In summary, the NUPSR method effectively selects and reconstructs predictors, significantly improves the prediction accuracy of the coupled models, and has broad application prospects in multivariate prediction in fields such as hydrology.

A Novel Online Hydrological Data Quality Control Approach Based on Adaptive Differential Evolution

The quality of hydrological data has a significant impact on hydrological models, where stable and anomaly-free hydrological time series typically yield more valuable patterns. In this paper, we conduct data analysis and propose an online hydrological data quality control method based on an adaptive differential evolution algorithm according to the characteristics of hydrological data. Taking into account the characteristics of continuity, periodicity, and seasonality, we develop a Periodic Temporal Long Short-Term Memory (PT-LSTM) predictive control model. Building upon the real-time nature of the data, we apply the Adaptive Differential Evolution algorithm to optimize PT-LSTM, creating an Online Composite Predictive Control Model (OCPT-LSTM) that provides confidence intervals and recommended values for control and replacement. The experimental results demonstrate that the proposed data quality control method effectively manages data quality; detects data anomalies; provides suggested values; reduces reliance on manual intervention; provides a solid data foundation for hydrological data analysis work; and helps hydrological personnel in water resource scheduling, flood control, and other related tasks. Meanwhile, the proposed method can also be applied to the analysis of time series data in other industries.

Water Flow Prediction Based on Improved Spatiotemporal Attention Mechanism of Long Short-Term Memory Network

The prediction of water plant flow should establish relationships between upstream and downstream hydrological stations, which is crucial for the early detection of flow anomalies. Long Short-Term Memory Networks (LSTMs) have been widely applied in hydrological time series forecasting. However, due to the highly nonlinear and dynamic nature of hydrological time series, as well as the intertwined coupling of data between multiple hydrological stations, the original LSTM models fail to simultaneously consider the spatiotemporal correlations among input sequences for flow prediction. To address this issue, we propose a novel flow prediction method based on the Spatiotemporal Attention LSTM (STA-LSTM) model. This model, based on an encoder–decoder architecture, integrates spatial attention mechanisms in the encoder to adaptively capture hydrological variables relevant to prediction. The decoder combines temporal attention mechanisms to better propagate gradient information and dynamically discover key encoder hidden states from all time steps within a window. Additionally, we construct an extended dataset, which preprocesses meteorological data with forward filling and rainfall encoding, and combines hydrological data from multiple neighboring pumping stations with external meteorological data to enhance the modeling capability of spatiotemporal relationships. In this paper, the actual production data of pumping stations and water plants along the East-to-West Water Diversion Project are taken as examples to verify the effectiveness of the model. Experimental results demonstrate that our STA-LSTM model can better capture spatiotemporal relationships, yielding improved prediction performance with a mean absolute error (MAE) of 3.57, a root mean square error (RMSE) of 4.61, and a mean absolute percentage error (MAPE) of 0.001. Additionally, our model achieved a 3.96% increase in R2 compared to the baseline model.

A framework for multivariate analysis of compound extremes based on correlated hydrologic time series

While hydrologic design has primarily relied on use of annual maxima values, many events of hydrologic interest such as active and break spells in monsoonal rains, heat waves, flash flooding from snowmelt, etc. manifest at time scales of days to weeks, and require daily (or finer resolution) data for proper characterization. Often combinations of several hydrologic variables herald highly impactful events and are labelled as compound extremes. Using a time-varying interval-censored estimation method of copula models, a novel multivariate approach for dealing with compound extremes under temporal dependence amongst variables and when data contain significant ties is developed here to enable the determination of design magnitudes and associated risk. The efficacy of this method is demonstrated over the Godavari River Basin, India, using daily precipitation and temperature data from a recent period (1977 to 2020) during the monsoon season. A conservative approach is proposed for estimating the design magnitudes of hydrologic variables in multivariate settings. The significance of ties and temporal dependence amongst precipitation and temperature data in estimation of design magnitudes of cold-wet compound extremes at specified probabilities of exceedance is explored at various spatial scales. Ties and temporal dependence are both shown to have a profound influence on design estimates. Since ties and temporal variation in dependence amongst hydrologic variables are ubiquitous features of most hydrologic data, this framework would be applicable for characterization of other compound extremes in hydrology.

A Comprehensive Review of Methods for Hydrological Forecasting Based on Deep Learning

Artificial intelligence has undergone rapid development in the last thirty years and has been widely used in the fields of materials, new energy, medicine, and engineering. Similarly, a growing area of research is the use of deep learning (DL) methods in connection with hydrological time series to better comprehend and expose the changing rules in these time series. Consequently, we provide a review of the latest advancements in employing DL techniques for hydrological forecasting. First, we examine the application of convolutional neural networks (CNNs) and recurrent neural networks (RNNs) in hydrological forecasting, along with a comparison between them. Second, a comparison is made between the basic and enhanced long short-term memory (LSTM) methods for hydrological forecasting, analyzing their improvements, prediction accuracies, and computational costs. Third, the performance of GRUs, along with other models including generative adversarial networks (GANs), residual networks (ResNets), and graph neural networks (GNNs), is estimated for hydrological forecasting. Finally, this paper discusses the benefits and challenges associated with hydrological forecasting using DL techniques, including CNN, RNN, LSTM, GAN, ResNet, and GNN models. Additionally, it outlines the key issues that need to be addressed in the future.

Enhancing long short-term memory (LSTM)-based streamflow prediction with a spatially distributed approach

Abstract. Deep learning (DL) algorithms have previously demonstrated their effectiveness in streamflow prediction. However, in hydrological time series modelling, the performance of existing DL methods is often bound by limited spatial information, as these data-driven models are typically trained with lumped (spatially aggregated) input data. In this study, we propose a hybrid approach, namely the Spatially Recursive (SR) model, that integrates a lumped long short-term memory (LSTM) network seamlessly with a physics-based hydrological routing simulation for enhanced streamflow prediction. The lumped LSTM was trained on the basin-averaged meteorological and hydrological variables derived from 141 gauged basins located in the Great Lakes region of North America. The SR model involves applying the trained LSTM at the subbasin scale for local streamflow predictions which are then translated to the basin outlet by the hydrological routing model. We evaluated the efficacy of the SR model with respect to predicting streamflow at 224 gauged stations across the Great Lakes region and compared its performance to that of the standalone lumped LSTM model. The results indicate that the SR model achieved performance levels on par with the lumped LSTM in basins used for training the LSTM. Additionally, the SR model was able to predict streamflow more accurately on large basins (e.g., drainage area greater than 2000 km2), underscoring the substantial information loss associated with basin-wise feature aggregation. Furthermore, the SR model outperformed the lumped LSTM when applied to basins that were not part of the LSTM training (i.e., pseudo-ungauged basins). The implication of this study is that the lumped LSTM predictions, especially in large basins and ungauged basins, can be reliably improved by considering spatial heterogeneity at finer resolution via the SR model.

Dissolving the mystery of subsurface controls on snowmelt–discharge dynamics in karst mountain watersheds using hydrologic timeseries

AbstractStreamflow generation in mountain watersheds is strongly influenced by snow accumulation and melt as well as groundwater connectivity. In mountainous regions with limestone and dolomite geology, bedrock formations can host karst aquifers, which play a significant role in snowmelt–discharge dynamics. However, mapping complex karst features and the resulting surface‐groundwater exchanges at large scales remains infeasible. In this study, timeseries analysis of continuous discharge and specific conductance measurements were combined with gridded snowmelt predictions to characterize seasonal streamflow response and evaluate dominant watershed controls across 12 monitoring sites in a karstified 554 km2 watershed in northern Utah, USA. Immense surface water hydrologic variability across subcatchments, years and seasons was linked to geologic controls on groundwater dynamics. Unlike many mountain watersheds, the variability between subcatchments could not be well described by typical watershed properties, including elevation or surficial geology. To fill this gap, a conceptual framework was proposed to characterize subsurface controls on snowmelt–discharge dynamics in karst mountain watersheds in terms of conduit flow direction, aquifer storage capacity and connectivity. This framework requires only readily measured surface water and climatic data from nested monitoring sites and was applied to the study watershed to demonstrate its applicability for evaluating dominant controls and climate sensitivity.

Nonlinear hydrological time series modeling to forecast river level dynamics in the Rio Negro Uruguay basin.

Floods significantly impact the well-being and development of communities. Hence, understanding their causes and establishing methodologies for risk prevention is a critical challenge for effective warning systems. Complex systems such as hydrological basins are modeled through hydrological models that have been utilized to understand water recharge of aquifers, available volume of dams, and floods in diverse regions. Acquiring real-time hydrometeorological data from basins and rivers is vital for establishing data-driven-based models as tools for the prediction of river-level dynamics and for understanding its nonlinear behavior. This paper introduces a hydrological model based on a multilayer perceptron neural network as a useful tool for time series modeling and forecasting river levels in three stations of the Rio Negro basin in Uruguay. Daily time series of river levels and rainfall serve as the input data for the model. The assessment of the models is based on metrics such as the Nash-Sutcliffe coefficient, the root mean square error, percent bias, and volumetric efficiency. The outputs exhibit varying model performance and accuracy during the prediction period across different sub-basin scales, revealing the neural network's ability to learn river dynamics. Lagged time series analysis demonstrates the potential for chaos in river-level time series over extended time periods, mainly when predicting dam-related scenarios, which shows physical connections between the dynamical system and the data-based model such as the evolution of the system over time.

Stage and discharge prediction from documentary time-lapse imagery

Imagery from fixed, ground-based cameras is rich in qualitative and quantitative information that can improve stream discharge monitoring. For instance, time-lapse imagery may be valuable for filling data gaps when sensors fail and/or during lapses in funding for monitoring programs. In this study, we used a large image archive (>40,000 images from 2012 to 2019) from a fixed, ground-based camera that is part of a documentary watershed imaging project (https://plattebasintimelapse.com/). Scalar image features were extracted from daylight images taken at one-hour intervals. The image features were fused with United States Geological Survey stage and discharge data as response variables from the site. Predictions of stage and discharge for simulated year-long data gaps (2015, 2016, and 2017 water years) were generated from Multi-layer Perceptron, Random Forest Regression, and Support Vector Regression models. A Kalman filter was applied to the predictions to remove noise. Error metrics were calculated, including Nash-Sutcliffe Efficiency (NSE) and an alternative threshold-based performance metric that accounted for seasonal runoff. NSE for the year-long gap predictions ranged from 0.63 to 0.90 for discharge and 0.47 to 0.90 for stage, with greater errors in 2016 when stream discharge during the gap period greatly exceeded discharge during the training periods. Importantly, and in contrast to gap-filling methods that do not use imagery, the high discharge conditions in 2016 could be visually (qualitatively) verified from the image data. Half-year test sets were created for 2016 to include higher discharges in the training sets, thus improving model performance. While additional machine learning algorithms and tuning parameters for selected models should be tested further, this study demonstrates the potential value of ground-based time-lapse images for filling large gaps in hydrologic time series data. Cameras dedicated for hydrologic sensing, including nighttime imagery, could further improve results.

Hydrological time series prediction based on IWOA-ALSTM

The prediction of hydrological time series is of great significance for developing flood and drought prevention approaches and is an important component in research on smart water resources. The nonlinear characteristics of hydrological time series are important factors affecting the accuracy of predictions. To enhance the prediction of the nonlinear component in hydrological time series, we employed an improved whale optimisation algorithm (IWOA) to optimise an attention-based long short-term memory (ALSTM) network. The proposed model is termed IWOA-ALSTM. Specifically, we introduced an attention mechanism between two LSTM layers, enabling adaptive focus on distinct features within each time unit to gather information pertaining to a hydrological time series. Furthermore, given the critical impact of the model hyperparameter configuration on the prediction accuracy and operational efficiency, the proposed improved whale optimisation algorithm facilitates the discovery of optimal hyperparameters for the ALSTM model. In this work, we used nonlinear water level information obtained from Hankou station as experimental data. The results of this model were compared with those of genetic algorithms, particle swarm optimisation algorithms and whale optimisation algorithms. The experiments were conducted using five evaluation metrics, namely, the RMSE, MAE, NSE, SI and DR. The results show that the IWOA is effective at optimising the ALSTM and significantly improves the prediction accuracy of nonlinear hydrological time series.

What can we learn from long hydrological time-series? The case of rainfall data at Collegio Romano, Rome, Italy

In this work, we explore the statistical behavior of one of the longest rainfall time-series in Italy and in the world, covering the period 1782–2017. Some standard and innovative statistical tools are applied to test the variability and change of the process across all values (in average, but also in terms of extremes) and scales (from days to years). An oscillation pattern occurs across all the time scales, from years to decades, limited by the sample length. It implies that there are no particular periods of variability, apart from seasonality, and no statistically significant trends, such that the process can be fully characterized in terms of the Hurst coefficient. Despite its exceptional length, the dataset is still insufficient to adequately capture the complex behavior of rainfall over the time scales, especially with regards to extremes, and to separate anthropogenically induced change from natural variability based on the data alone. Our findings suggest that samples of limited length do not allow robust statistical predictions, raising concerns about statistical analyses based on a limited dataset, even a relatively large one.

Learning from Polar Representation: An Extreme-Adaptive Model for Long-Term Time Series Forecasting

In the hydrology field, time series forecasting is crucial for efficient water resource management, improving flood and drought control and increasing the safety and quality of life for the general population. However, predicting long-term streamflow is a complex task due to the presence of extreme events. It requires the capture of long-range dependencies and the modeling of rare but important extreme values. Existing approaches often struggle to tackle these dual challenges simultaneously. In this paper, we specifically delve into these issues and propose Distance-weighted Auto-regularized Neural network (DAN), a novel extreme-adaptive model for long-range forecasting of stremflow enhanced by polar representation learning. DAN utilizes a distance-weighted multi-loss mechanism and stackable blocks to dynamically refine indicator sequences from exogenous data, while also being able to handle uni-variate time-series by employing Gaussian Mixture probability modeling to improve robustness to severe events. We also introduce Kruskal-Wallis sampling and gate control vectors to handle imbalanced extreme data. On four real-life hydrologic streamflow datasets, we demonstrate that DAN significantly outperforms both state-of-the-art hydrologic time series prediction methods and general methods designed for long-term time series prediction.

A comparative study of satellite altimetry-based and DEM-based methods for estimating lake water volume changes.

This study compared two different methods, the satellite altimetry-based and DEM (digital elevation model)-based, for estimating lake water volume changes. We focused on 34 lakes in China as the testing sites to compare the two methods for lake water volume changes from 2005 to 2020. The satellite altimetry-based method used water levels provided by the DAHITI (Database for Hydrological Time Series of Inland Waters) data and surface areas derived from Landsat imagery. The DEM-based method used the SRTM DEM data in combination with Landsat-derived lake extents. Our results showed a high degree of consistency in lake water volume changes estimated between the two methods (R2 > 0.90), but each method has its limitations. In terms of temporal coverage, the satellite altimetry-based method with the DAHITI data is limited by missing water level data in certain periods. The performance of the DEM-based method in extracting lake shore boundaries in regions with flat terrains (slope <1.5°) is not satisfactory. The DEM-based method has complete regional applicability (100%) in the Tibetan Plateau (TP) Lake Region, yet its effectiveness drops significantly in the Xinjiang and Eastern China Plain Lake Regions, with applicability rates of 50 and 40%, respectively.

Review of Machine Learning Methods for River Flood Routing

River flood routing computes changes in the shape of a flood wave over time as it travels downstream along a river. Conventional flood routing models, especially hydrodynamic models, require a high quality and quantity of input data, such as measured hydrologic time series, geometric data, hydraulic structures, and hydrological parameters. Unlike physically based models, machine learning algorithms, which are data-driven models, do not require much knowledge about underlying physical processes and can identify complex nonlinearity between inputs and outputs. Due to their higher performance, lower complexity, and low computation cost, researchers introduced novel machine learning methods as a single application or hybrid application to achieve more accurate and efficient flood routing. This paper reviews the recent application of machine learning methods in river flood routing.