Hydrological Time Series Forecasting Research Articles

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.

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.

Correction to: The Performance Analysis of Robust Local Mean Mode Decomposition Method for Forecasting of Hydrological Time Series

Correction to: The Performance Analysis of Robust Local Mean Mode Decomposition Method for Forecasting of Hydrological Time Series

The Performance Analysis of Robust Local Mean Mode Decomposition Method for Forecasting of Hydrological Time Series

The Performance Analysis of Robust Local Mean Mode Decomposition Method for Forecasting of Hydrological Time Series

Hydrological time series prediction by extreme learning machine and sparrow search algorithm

Abstract In general, accurate hydrological time series prediction information is of great significance for the rational planning and management of water resource systems. Extreme learning machine (ELM) is an effective tool proposed for the single-layer feedforward neural network in regression and classification problems. However, the standard ELM model falls into a local minimum with a high probability in hydrological prediction problems since the randomly assigned parameters (like input-hidden weights and hidden biases) often remain unchanged in the learning process. For effectively improving the prediction accuracy, this paper develops a hybrid hydrological forecasting model where the emerging sparrow search algorithm (SSA) is firstly used to determine the satisfying parameter combinations of the ELM model, and then the Moore–Penrose generalized inverse method is chosen to analytically obtain the weight matrix between the hidden layer and output layer. The proposed method is used to forecast the long-term daily runoff series collected from three real-world hydrological stations in China. Based on several performance evaluation indexes, the results show that the proposed method outperforms several ELM variants optimized by other evolutionary algorithms in both training and testing phases. Hence, an effective evolutionary machine-learning tool is developed for accurate hydrological time series forecasting.

Dew Point Time Series Forecasting at the North Dakota

Hydrological time series forecasting is one of the hot topics in the domain of statistical hydrology. Providing accurate forecasting can contribute to diverse applications for catchment sustainability and management. Dew point temperature (Tdew) is one of the complex hydrological processes that highly essential to be quantified accurately for several catchment activities such as crops, agriculture, and others. In this study, three types of models’ recursive strategy, direct strategy, and DirRec which is the combination of recursive and direct strategies were adopted to obtain h-steps ahead predictions of Tdew. Ten years monthly scale dataset of Tdew at two meteorological stations (Beach and Cavalier) located at the North Dakota, USA, were used for the modeling development. The performance of the considered models was compared with two benchmark models: autoregressive moving average (ARIMA) and exponential smoothing (ETS). Modeling results indicated that, compared with the benchmark models, the proposed methods gave good results for the multi-ahead forecasting. For instance, for Cavalier station, the root mean squared prediction errors obtained from the proposed and benchmark methods when the forecast horizon is 12 are as follows: recursive strategy (RMSPE = 3.731) direct strategy (RMSPE = 3.385), DirRec (RMSPE = 3.141), ARIMA (RMSPE = 12.957), and ETS (RMSPE = 27.479).

Artificial Neural Network Approach for Hydrologic River Flow Time Series Forecasting

Artificial Neural Network Approach for Hydrologic River Flow Time Series Forecasting

Study on the Improvement of the Application of Complete Ensemble Empirical Mode Decomposition with Adaptive Noise in Hydrology Based on RBFNN Data Extension Technology

The complex nonlinear and non-stationary features exhibited in hydrologic sequences make hydrological analysis and forecasting difficult. Currently, some hydrologists employ the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method, a new time-frequency analysis method based on the empirical mode decomposition (EMD) algorithm, to decompose non-stationary raw data in order to obtain relatively stationary components for further study. However, the endpoint effect in CEEMDAN is often neglected, which can lead to decomposition errors that reduce the accuracy of the research results. In this study, we processed an original runoff sequence using the radial basis function neural network (RBFNN) technique to obtain the extension sequence before utilizing CEEMDAN decomposition. Then, we compared the decomposition results of the original sequence, RBFNN extension sequence, and standard sequence to investigate the influence of the endpoint effect and RBFNN extension on the CEEMDAN method. The results indicated that the RBFNN extension technique effectively reduced the error of medium and low frequency components caused by the endpoint effect. At both ends of the components, the extension sequence more accurately reflected the true fluctuation characteristics and variation trends. These advances are of great significance to the subsequent study of hydrology. Therefore, the CEEMDAN method, combined with an appropriate extension of the original runoff series, can more precisely determine multi-time scale characteristics, and provide a credible basis for the analysis of hydrologic time series and hydrological forecasting.

Hydrological time series forecasting using simple combinations: Big data testing and investigations on one-year ahead river flow predictability

Delivering useful hydrological forecasts is critical for urban and agricultural water management, hydropower generation, flood protection and management, drought mitigation and alleviation, and river basin planning and management, among others. In this work, we present and appraise a new simple and flexible methodology for hydrological time series forecasting. This methodology relies on (a) at least two individual forecasting methods and (b) the median combiner of forecasts. The appraisal is made by using a big dataset consisted of 90-year-long mean annual river flow time series from approximately 600 stations. Covering large parts of North America and Europe, these stations represent various climate and catchment characteristics, and thus can collectively support benchmarking. Five individual forecasting methods and 26 variants of the introduced methodology are applied to each time series. The application is made in one-step ahead forecasting mode. The individual methods are the last-observation benchmark, simple exponential smoothing, complex exponential smoothing, automatic autoregressive fractionally integrated moving average (ARFIMA) and Facebook’s Prophet, while the 26 variants are defined by all the possible combinations (per two, three, four or five) of the five afore-mentioned methods. The new methodology is identified as well-performing in the long run, especially when more than two individual forecasting methods are combined within its framework. Moreover, the possibility of case-informed integrations of diverse hydrological forecasting methods within systematic frameworks is algorithmically investigated and discussed. The related investigations encompass linear regression analyses, which aim at finding interpretable relationships between the values of a representative forecasting performance metric and the values of selected river flow statistics. We find only loose (but not negligible) relationships between the formed variable sets. These relationships could be exploited for improving (to some extent) future forecasting applications. The results of our big data forecasting experiment are lastly exploited for characterizing –in relative terms– one-year ahead river flow predictability. We believe that our findings have both practical and theoretical implications.

Application of Artificial Intelligence Method Coupled with Discrete Wavelet Transform Method

In modern hydrology one of the most important applications is hydrological time series forecasting, particularly for effective information related to reservoir system. In this study, artificial neural network (ANN) such as radial basis function neural network (RBFNN), coupled with time series decomposing method (TSDM), named as discrete wavelet transform (DWT) to forecast monthly time series at upper Yangtze River and Xianjiababa is taken as the forecast hydrological station. Data has been analyzed by comparing the simulation outputs delivered by models with two performance indices named as (a) correlation coefficient and root mean square errors, which can be denoted by (R)and (RMSE) respectively. Results show that time series decomposition technique discrete wavelet transform method have shown more accuracy and can play important role to improve the corrected in discharge prediction, as compared to single ANN's.

Discussion on the Choice of Decomposition Level for Wavelet Based Hydrological Time Series Modeling

The combination of wavelet analysis methods with data-driven models is a prevalent approach to conducting hydrological time series forecasting, but the results are affected by the accuracy of the wavelet decomposition of the series. The choice of decomposition level is one of the key factors for the wavelet decomposition. In this paper, the data of daily precipitation and streamflow time series measured in the upper reach of the Heihe River Basin in Northwest China were used as an example, and the influence of the decomposition level on wavelet-based hydrological time series forecasting was investigated. The true components of the precipitation series were identified, and the modeling results using 10 decomposition levels and two decomposition types were compared. The results affirmed that the wavelet-based modeling performance is sensitive to the choice of decomposition level, which is determined by the time series analyzed, but has no relation with the decomposition type used. The essence of the choice of decomposition level is to reveal the complex variability of hydrological time series under multi-temporal scales, and first knowing the true components of series could guide the choice of decomposition level. Through this study, the relationship among original series’ characteristics, the choice of decomposition level, and the accuracy of wavelet-based hydrological time series forecasting can be more clearly understood, and it can be an improvement for wavelet-based data-driven modeling.

Wavelet-Based Hydrological Time Series Forecasting

AbstractThese days wavelet analysis is becoming popular for hydrological time series simulation and forecasting. There are, however, a set of key issues influencing the wavelet-aided data preprocessing and modeling practice that need further discussion. This article discusses four key issues related to wavelet analysis: discrepant use of continuous and discrete wavelet methods, choice of mother wavelet, choice of temporal scale, and uncertainty evaluation in wavelet-aided forecasting. The article concludes with a personal reflection on solving the four issues for improving and supplementing relevant wavelet studies, especially wavelet-based artificial intelligence modeling.

Improving Forecasting Accuracy of Annual Runoff Time Series Using ARIMA Based on EEMD Decomposition

Hydrological time series forecasting is one of the most important applications in modern hydrology, especially for effective reservoir management. In this research, the auto-regressive integrated moving average (ARIMA) model coupled with the ensemble empirical mode decomposition (EEMD) is presented for forecasting annual runoff time series. First, the original annual runoff time series is decomposed into a finite and often small number of intrinsic mode functions (IMFs) and one residual series using EEMD technique for a deep insight into the data characteristics. Then each IMF component and residue is forecasted, respectively, through an appropriate ARIMA model. Finally, the forecasted results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original annual runoff series. Three annual runoff series from Biuliuhe reservoir, Dahuofang reservoir and Mopanshan reservoir, in China, are investigated using developed model based on the four standard statistical performance evaluation measures (RMSE, MAPE, R and NSEC). The results obtained in this work indicate that EEMD can effectively enhance forecasting accuracy and that the proposed EEMD-ARIMA model can significantly improve ARIMA time series approaches for annual runoff time series forecasting.

Improving forecasting accuracy of medium and long-term runoff using artificial neural network based on EEMD decomposition

Hydrological time series forecasting is one of the most important applications in modern hydrology, especially for the effective reservoir management. In this research, an artificial neural network (ANN) model coupled with the ensemble empirical mode decomposition (EEMD) is presented for forecasting medium and long-term runoff time series. First, the original runoff time series is decomposed into a finite and often small number of intrinsic mode functions (IMFs) and a residual series using EEMD technique for attaining deeper insight into the data characteristics. Then all IMF components and residue are predicted, respectively, through appropriate ANN models. Finally, the forecasted results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original annual runoff series. Two annual reservoir runoff time series from Biuliuhe and Mopanshan in China, are investigated using the developed model based on four performance evaluation measures (RMSE, MAPE, R and NSEC). The results obtained in this work indicate that EEMD can effectively enhance forecasting accuracy and the proposed EEMD-ANN model can attain significant improvement over ANN approach in medium and long-term runoff time series forecasting.

Wavelet Neural Modeling for Hydrologic Time Series Forecasting with Uncertainty Evaluation

An approach, with the basic idea of resampling wavelet neural parameters, was proposed for probabilistic forecasting of hydrologic time series by the wavelet neural model. Parameters in wavelet neural model are assumed as following uniform distribution, and both proper convergence criterion and likelihood function are used to train the wavelet neural structure and judge the acceptance of parameter set. By training and learning wavelet neural structure as many times (i.e., resampling neural parameters) until becoming stable, all sets of wavelet neural parameters are composed as the resampling results, based on which probabilistic forecasting of hydrologic time series is attained. Optimal forecasting result can be gained by computing mathematical mean of the resampling results, and uncertainty can be described by proper confidence interval. Results of one runoff example indicated the identical performance of the proposed approach and wavelet regression model, but both perform better than conventional neural model. The proposed approach has similar efficiency as the Bayesian method for uncertainty evaluation, and both show higher efficiency than traditional Monte-Carlo method. Choice of proper convergence criterion is an important task when using the proposed approach, because it directly determines the convergence rate, accuracy and uncertainty level of probabilistic forecasting result. Overall, several key issues should be carefully considered for obtaining more reasonable probabilistic forecasting results by the proposed approach, including choice of proper likelihood function, accurate wavelet decomposition of series, and determination of proper wavelet neural structure.

A four-stage hybrid model for hydrological time series forecasting.

Hydrological time series forecasting remains a difficult task due to its complicated nonlinear, non-stationary and multi-scale characteristics. To solve this difficulty and improve the prediction accuracy, a novel four-stage hybrid model is proposed for hydrological time series forecasting based on the principle of ‘denoising, decomposition and ensemble’. The proposed model has four stages, i.e., denoising, decomposition, components prediction and ensemble. In the denoising stage, the empirical mode decomposition (EMD) method is utilized to reduce the noises in the hydrological time series. Then, an improved method of EMD, the ensemble empirical mode decomposition (EEMD), is applied to decompose the denoised series into a number of intrinsic mode function (IMF) components and one residual component. Next, the radial basis function neural network (RBFNN) is adopted to predict the trend of all of the components obtained in the decomposition stage. In the final ensemble prediction stage, the forecasting results of all of the IMF and residual components obtained in the third stage are combined to generate the final prediction results, using a linear neural network (LNN) model. For illustration and verification, six hydrological cases with different characteristics are used to test the effectiveness of the proposed model. The proposed hybrid model performs better than conventional single models, the hybrid models without denoising or decomposition and the hybrid models based on other methods, such as the wavelet analysis (WA)-based hybrid models. In addition, the denoising and decomposition strategies decrease the complexity of the series and reduce the difficulties of the forecasting. With its effective denoising and accurate decomposition ability, high prediction precision and wide applicability, the new model is very promising for complex time series forecasting. This new forecast model is an extension of nonlinear prediction models.

Investigation of Empirical Mode Decomposition in Forecasting of Hydrological Time Series

In this study, a nonparametric technique to set up a river stage forecasting model based on empirical mode decomposition (EMD) is presented. The approach is based on the use of the EMD and artificial neural networks (ANN) to forecast next month’s monthly streamflows. The proposed approach is applied to a real case study. The data from station on the Kizilirmak River in Turkey was used. The mean square errors (MSE), mean absolute errors (MAE) and correlation coefficient (R) statistics were used for evaluating the accuracy of the EMD-ANN model. The accuracy of the EMD-ANN model was then compared to the artificial neural networks (ANN) model. The results showed that EMD-ANN approach performed better than the ANN in predicting stream flows. The most accurate EMD-ANN model had MSE = 0.0132, MAE = 0.0883 and R = 0.8012 statistics, respectively.

Random Modeling of Daily Rainfall and Runoff Using a Seasonal Model and Wavelet Denoising

Instead of Fourier smoothing, this study applied wavelet denoising to acquire the smooth seasonal mean and corresponding perturbation term from daily rainfall and runoff data in traditional seasonal models, which use seasonal means for hydrological time series forecasting. The denoised rainfall and runoff time series data were regarded as the smooth seasonal mean. The probability distribution of the percentage coefficients can be obtained from calibrated daily rainfall and runoff data. For validated daily rainfall and runoff data, percentage coefficients were randomly generated according to the probability distribution and the law of linear proportion. Multiplying the generated percentage coefficient by the smooth seasonal mean resulted in the corresponding perturbation term. Random modeling of daily rainfall and runoff can be obtained by adding the perturbation term to the smooth seasonal mean. To verify the accuracy of the proposed method, daily rainfall and runoff data for the Wu-Tu watershed were analyzed. The analytical results demonstrate that wavelet denoising enhances the precision of daily rainfall and runoff modeling of the seasonal model. In addition, the wavelet denoising technique proposed in this study can obtain the smooth seasonal mean of rainfall and runoff processes and is suitable for modeling actual daily rainfall and runoff processes.

다층 퍼셉트론 인공신경망 모형을 이용한 가뭄예측

장기간의 가뭄에 의한 피해를 최소화하기 위해서는 유역에 적합한 가뭄관리 대책의 수립과 함께 미래에 발생하게 될 가뭄을 미리 예측할 수 있는 기술이 구축되어야 한다. 또한 미래의 가뭄에 대한 합리적 대응 방안을 수립하기 위해서는 가뭄의 지속기간(duration)과 심도(severity)의 정량적인 예측이 선행되어야 한다. 본 연구에서는 수문 시계열의 예측에 가장 많이 이용되고 있는 대표적인 통계학적 기법인 인공신경망 모형(Artificial Neural Network Model)과 가뭄지수를 이용하여 남한지역의 서울, 대전, 대구, 광주 등의 4개 기상관측소를 선정하여 가뭄예측을시도하였다. 가뭄 예측을 위하여 남한지역 내 선정한 기상관측소의 관측된 과거 강수량 자료를 이용하여 산정된 SPI (Standardized Precipitation Index)를 입력변수로 하여 다층 퍼셉트론(Multi Layer Perceptron) 인공신경망 모델에 적용하였으며, 매개변수 보정을 위한 학습기간으로 1976~2000년과 2001~2010년을 예측을 위한 검증기간으로 선정하여, 학습 및 예측을 시도하였다. 학습된 최적의 예측모형을 이용하여 서로 다른 선행예보시간(1~6개월)을 갖고 SPI (3), SPI (6), SPI (12)별로 가뭄을 예측하였으며, 가뭄예측 결과, SPI (3)의 경우에는 1개월 선행예보에서만 좋은 결과를 나타내었으며, SPI (6)의 경우 1~3개월 후의 가뭄을 예측하는 경우에 비교적 관측자료와 잘 일치하는 결과를 나타내었다. SPI (12)의 경우에는 약5개월 후까지의 가뭄예측에 양호한 결과를 나타내었다. In order to minimize the damages caused by long-term drought, appropriate drought management plans of the basin should be established with the drought forecasting technology. Further, in order to build reasonable adaptive measurement for future drought, the duration and severity of drought must be predicted quantitatively in advance. Thus, this study, attempts to forecast drought in Korea by using an Artificial Neural Network Model, and drought index, which are the representative statistical approach most frequently used for hydrological time series forecasting. SPI (Standardized Precipitation Index) for major weather stations in Korea, estimated using observed historical precipitation, was used as input variables to the MLP (Multi Layer Perceptron) Neural Network model. Data set from 1976 to 2000 was selected as the training period for the parameter calibration and data from 2001 to 2010 was set as the validation period for the drought forecast. The optimal model for drought forecast determined by training process was applied to drought forecast using SPI (3), SPI (6) and SPI (12) over different forecasting lead time (1 to 6 months). Drought forecast with SPI (3) shows good result only in case of 1 month forecast lead time, SPI (6) shows good accordance with observed data for 1-3 months forecast lead time and SPI (12) shows relatively good results in case of up to 1~5 months forecast lead time. The analysis of this study shows that SPI (3) can be used for only 1-month short-term drought forecast. SPI (6) and SPI (12) have advantage over long-term drought forecast for 3~5 months lead time.

Bayesian-combined wavelet regressive modeling for hydrologic time series forecasting

Wavelet regression (WR) models are used commonly for hydrologic time series forecasting, but they could not consider uncertainty evaluation. In this paper the AM-MCMC (adaptive Metropolis-Markov chain Monte Carlo) algorithm was employed to wavelet regressive modeling processes, and a model called AM-MCMC-WR was proposed for hydrologic time series forecasting. The AM-MCMC algorithm is used to estimate parameters' uncertainty in WR model, based on which probabilistic forecasting of hydrologic time series can be done. Results of two runoff data at the Huaihe River watershed indicate the identical performances of AM-MCMC-WR and WR models in gaining optimal forecasting result, but they perform better than linear regression models. Differing from the WR model, probabilistic forecasting results can be gained by the proposed model, and uncertainty can be described using proper credible interval. In summary, parameters in WR models generally follow normal probability distribution; series' correlation characters determine the optimal parameters values, and further determine the uncertain degrees and sensitivities of parameters; more uncertain parameters would lead to more uncertain forecasting results and hard predictability of hydrologic time series.