Monthly Streamflow Time Series Research Articles

Do non-linearity and non-Gaussianity truly matter in streamflow forecasting? A comparative study between PAR(p) and vine copula for Brazilian streamflow time series.

This study evaluates the joint impact of non-linearity and non-Gaussianity on predictive performance in 23 Brazilian monthly streamflow time series from 1931 to 2022. We consider point and interval forecasting, employing a PAR(p) model and comparing it with the periodic vine copula model. Results indicate that the Gaussian hypothesis assumed by PAR(p) is unsuitable; gamma and log-normal distributions prove more appropriate and crucial for constructing accurate confidence intervals. This is primarily due to the assumption of the Gaussian distribution, which can lead to the generation of confidence intervals with negative values. Analyzing the estimated copula models, we observed a prevalence of the bivariate Normal copula, indicating that linear dynamic dependence is frequent, and the Rotated Gumbel 180°, which exhibits lower tail dependence. Overall, the temporal dynamics are predominantly shaped by combining these two types of effects. In point forecasting, both models show similar behavior in the estimation set, with slight advantages for the copula model. The copula model performs better during the out-of-sample analysis, particularly for certain power plants. In interval forecasting, the copula model exhibits pronounced superiority, offering a better estimation of quantiles. Consistently demonstrating proficiency in constructing reliable and accurate intervals, the copula model reveals a notable advantage over the PAR(p) model in interval forecasting.

A Machine-Learning Framework for Modeling and Predicting Monthly Streamflow Time Series

Having a complete hydrological time series is crucial for water-resources management and modeling. However, this can pose a challenge in data-scarce environments where data gaps are widespread. In such situations, recurring data gaps can lead to unfavorable outcomes such as loss of critical information, ineffective model calibration, inaccurate timing of peak flows, and biased statistical analysis in various applications. Despite its importance, predicting monthly streamflow can be a complex task due to its connection to random dynamics and uncertain phenomena, posing significant challenges. This study introduces an ensemble machine-learning regression framework for modeling and predicting monthly streamflow time series with a high degree of accuracy. The framework utilizes historical data from multiple monthly streamflow datasets in the same region to predict missing monthly streamflow data. The framework selects the best features from all available gap-free monthly streamflow time-series combinations and identifies the optimal model from a pool of 12 machine-learning models, including random forest regression, gradient boosting regression, and extra trees regressor, among others. The model selection is based on cross-validation train-and-test set scores, as well as the coefficient of determination. We conducted modeling on 26 monthly streamflow time series and found that the gradient boosting regressor with bagging regressor produced the highest accuracy in 7 of the 26 instances. Across all instances, the models using this method exhibited an overall accuracy range of 0.9737 to 0.9968. Additionally, the use of either a bagging regressor or an AdaBoost regressor improved both the tree-based and gradient-based models, resulting in these methods accounting for nearly 80% of the best models. Between January 1960 and December 2021, an average of 40% of the monthly streamflow data was missing for each of the 26 stations. Notably, two crucial stations located in the economically significant lower Athabasca Basin River in Alberta province, Canada, had approximately 70% of their monthly streamflow data missing. To address this issue, we employed our framework to accurately extend the missing data for all 26 stations. These accurate extensions also allow for further analysis, including grouping stations with similar monthly streamflow behavior using Pearson correlation.

Risk of Climate Change for Hydroelectricity Production in China Is Small but Significant Reductions Cannot Be Precluded for More Than a Third of the Installed Capacity

AbstractTo support the implementation of China's carbon neutrality target, this study assesses the impact of future climate change on hydroelectricity production (HP) in China. We developed a hydropower database for mainland China, which covers 92% of the installed capacity indicated by national statistics (352 GW in 2018). An HP model was applied to simulate monthly HP by 3,521 conventional plants at different levels of global warming (1°, 1.5°, 2°, and 3°C above preindustrial) using an ensemble of monthly streamflow time series computed by five global hydrological models (GHMs), where each global hydrological model was driven by four global climate models (GCMs). With a probability of 80%, limiting global warming to 1.5°C will constrain changes of national HP to the range of −1.4%–2.5% as compared to near‐present climate (1°C). In case of a 3°C world, this range more than doubles. HP is projected to likely increase in the two provinces Sichuan and Yunnan that encompass more than half of China's installed capacity. However, with a probability of about 10%, HP may decrease in a 3°C world by more than 15% in five provinces, and 40% of the installed capacity may suffer from an HP decrease of more than 5%. The uncertainty of projected HP changes is mainly due to the GCMs. We found that relative changes in annual HP and streamflow often differ in magnitude and direction as HP depends on seasonal streamflow patterns and installed capacities that determine the maximum flow through the turbines.

Assessment of Hydroclimatological Changes in Eastern Himalayan River Catchment of Northeast India

This article focuses on the assessment of climate change impacts on the hydroclimatology of the Subansiri River basin, which is the largest tributary of the Brahmaputra River in the northeastern part of India. Three representative concentration pathway (RCP) emission scenarios, namely, RCP2.6, RCP6.0, and RCP8.5, of three general circulation models (GCM) archived by the Geophysical Fluid Dynamics Laboratory (GFDL), were utilized for the projection of climatic variables (such as precipitation and temperature). Long-term (2011–2100) projections of precipitation and temperature for different emission scenarios were made using the statistical downscaling technique. The soil and water assessment tool (SWAT) hydrological model was used for hydrological modeling of the river basin. The observed streamflow series for the period of 2002–2013 has been utilized for calibration and validation of the hydrological model. Parameterization, uncertainty analysis, and parameter sensitivity analysis of the model were performed using a sequential uncertainty fitting (SUFI2) program. The coefficient of determination (R2) for the calibration and validation of the hydrological model on the monthly streamflow time series was found to be 0.86 and 0.80, respectively. Future projections of the precipitation and temperature suggest an increase in the annual average maximum temperature (Tmax), annual average minimum temperature (Tmin), and annual precipitation of the river basin. These projected climatic variables were used as the primary input in the hydrological model for the projection of the streamflow for the period of 2016–2100. The flow duration curve analysis of streamflow projections reveals an increase in the discharge for a particular percent of the dependable flow in the case of all the RCP scenarios. Water yield analysis also suggests an increase in the annual average water yield in all cases of emission scenarios.

On the Investigation of Monthly River Flow Generation Complexity Using the Applicability of Machine Learning Models

Streamflow is associated with several sources on nonstationaries and hence developing machine learning (ML) models is always the motive to provide a reliable methodology to understand the actual mechanism of streamflow. The current research was devoted to generating monthly streamflows from annual streamflow. In this study, three different ML models were applied for this purpose, including Multiple Additive Regression Trees (MART), Group Methods of Data Handling (GMDH), and Gene Expression Programming (GEP). The models were developed based on annual streamflow and monthly time index of three rivers (i.e., Upper Zab, Lower Zab, and Diyala) located in the north region of Iraq. The modeling results indicated an optimistic simulation for generating the monthly streamflow time series from annual streamflow time series. The potential of the MART model was superior to the GMDH and GEP models for Upper Zab River (R2 0.84, 0.64, and 0.47), Lower Zab River (R2 0.75, 0.46, and 0.40), and Diyala River (R2 0.78, 0.42, and 0.5). The results of RMSE were 113, 169, and 208 for Upper Zab River, 95, 149, and 0.5 for Lower Zab River, and 73, 118, and 109 for Diyala River. The results have proved the possibility of changing the timescale in generating streamflow data.

Predictability of Monthly Streamflow Time Series and its Relationship with Basin Characteristics: an Empirical Study Based on the MOPEX Basins

Machine learning (ML) models have been applied to monthly streamflow forecasting in recent decades. In this study, forecasting skills of eight ML models are evaluated based on the Model Parameter Estimation Experiment (MOPEX) dataset. We consider two skill scores, i.e., the Nash–Sutcliffe efficiency (NSE) and the adjusted NSE (ANSE), and the latter is the skill score based on the interannual mean monthly value (MMV) as the reference (benchmark) model. Furthermore, NSE of the MMV model (NSEmmv) is used as a measure of the seasonality of monthly streamflow, as it is the ratio of variance explained by the MMV process. An important result is that forecasting skills of ML models for monthly streamflow are largely controlled by NSEmmv. Moreover, based on comparisons of different ML models, we have found that the selection of models is not a dominating factor impacting the final skill. Three key factors influencing NSE, i.e., NSEmmv, the base flow index (BFI) and the aridity index (AI), are explored in this paper. Specifically, NSEmmv impacts NSE directly and is the predominant factor; BFI influences the memory of the monthly streamflow and therefore influences NSE. The relationship between AI and NSE is much complex and indirect. Firstly, basins with higher AI tend to have lower NSEmmv, and this will lead to lower NSE; secondly, basins with higher AI tend to have lower BFI, which will also lead to lower NSE; thirdly, for a given BFI level, basins with higher AI tend to have higher memory and higher NSE. For ANSE, basins with AI between 1 and 2 show higher ANSE, which corresponds to higher autocorrelation coefficients.

Comparison of support vector regression and extreme gradient boosting for decomposition-based data-driven 10-day streamflow forecasting

We recently addressed data-driven monthly streamflow forecasting using a decomposition-based model that relies on Fourier transform (FT) to decompose the monthly streamflow time series into 4 components, with each component comprising of contiguous frequencies and being forecasted independently by support vector regression (SVR). The model, called FT-SVR, is capable of achieving near-perfect monthly inflow forecasting for China’s Three Gorges Dam (TGD). In this paper, we adapt FT-SVR to 10-day streamflow forecasting and the TGD is still taken as the case for study. The 10-day inflow time series is decomposed into 7 components, and each component contains an appropriate small number of contiguous frequencies. We also investigate forecasting each decomposed component by extreme gradient boosting (XGBoost) and the investigated model is accordingly named as FT-XGBoost. XGBoost uses an ensemble of trees as the input–output mapping. The maximum number of iterations for solving convex quadratic programming in SVR is considerably reduced and the parameter calibration process to develop each independent SVR or XGBoost model is enhanced. We compare FT-SVR and FT-XGBoost on three different decomposition strategies: the centered 10-day inflow time series, 4 decomposed components like our previous work, and 7 components. Experimental results on the TGD case study demonstrate that FT-SVR with the decomposition strategy of 7 components is able to derive again near-perfect 10-day streamflow forecasting results, significantly better than FT-SVR with the other decomposition strategies and FT-XGBoost with all the decomposition strategies, while with parameter calibration being performed as efficiently as FT-XGBoost on each decomposition strategy.

Comparative assessment of time series and artificial intelligence models to estimate monthly streamflow: A local and external data analysis approach

River flow rates are important for water resources projects. Given this, the current study explored the use of autoregressive (AR) and moving average (MA) techniques as individual time series models and compared them to the same models hybridized with an autoregressive conditional heteroscedasticity (ARCH) model to estimate monthly streamflow. In addition, two artificial intelligence (AI) approaches, namely, multivariate adaptive regression splines (MARS) and gene expression programming (GEP), were explored. The performance of each of these models in estimating monthly streamflow was compared based on local and external data analyses. Using the local data analysis approach, streamflow data at each target station was estimated using observed streamflow at the same station. The external data analysis approach used neighboring station streamflow data to estimate streamflow data for the target station. The Beinerahe Roodbar and Pole Astaneh stations on the Sefidrood River, Iran, as well as the Port Elgin and Walkerton stations on the Saugeen River, Canada, were used as study areas. Upstream and downstream monthly streamflow time series data were used. The performance of all models was compared using three error metrics, including the root mean square error, mean absolute error, and correlation coefficient. The results showed that the hybrid time series models (i.e., AR-ARCH and MA-ARCH) outperformed the conventional AR and MA models. A comparison of all applied models revealed that the hybrid AR-ARCH and MA-ARCH time series models performed better than the AI techniques, when using a local data analysis approach. The external data analysis approach was more accurate for monthly streamflow estimation than the local data analysis approach. To conclude, based on the outcomes of the AI models under the external data analysis approach, nearby data can be used to estimate streamflow of a target station when the target station streamflow data are not available.

Multiscale modelling of monthly streamflows using MEMD-GP coupled approach

ABSTRACTThis study presented multiscale characterization of monthly streamflow time series using Multivariate Empirical Mode Decomposition (MEMD) and developed an innovative approach for streamflow prediction by coupling MEMD with Genetic Programming (GP). Firstly, the possible hydro-climatic teleconnection of monthly streamflows of Mahanadi river basin in India with two large-scale climate oscillations of ElNiño Southern Oscillation (ENSO) and Equatorial Indian Ocean Oscillation (EQUINOO) is investigated by applying MEMD based Time-Dependent Intrinsic Correlation (TDIC) analysis. The TDIC analysis showed that the association between large-scale climate oscillations and streamflows is not unique always, but both the nature and strength of the association varies with time scales and over the time domain. Based on this finding, the study proposed MEMD-GP coupled approach for streamflow prediction, in which different modes corresponding to different process scales obtained by the MEMD are predicted separately using GP; and summation of these predicted modes provides the monthly streamflow at the station. A statistical performance evaluation based on multiple criteria showed that the proposed approach performs better than the multiple linear regression, M5 model tree and GP models for monthly streamflow prediction including extreme low and high flows, due to its unique capability to include the significant predictors at different time scales.

Application of Entropy Spectral Method for Streamflow Forecasting in Northwest China.

Streamflow forecasting is vital for reservoir operation, flood control, power generation, river ecological restoration, irrigation and navigation. Although monthly streamflow time series are statistic, they also exhibit seasonal and periodic patterns. Using maximum Burg entropy, maximum configurational entropy and minimum relative entropy, the forecasting models for monthly streamflow series were constructed for five hydrological stations in northwest China. The evaluation criteria of average relative error (RE), root mean square error (RMSE), correlation coefficient (R) and determination coefficient (DC) were selected as performance metrics. Results indicated that the RESA model had the highest forecasting accuracy, followed by the CESA model. However, the BESA model had the highest forecasting accuracy in a low-flow period, and the prediction accuracies of RESA and CESA models in the flood season were relatively higher. In future research, these entropy spectral analysis methods can further be applied to other rivers to verify the applicability in the forecasting of monthly streamflow in China.

Long Term Streamflow Forecasting Using a Hybrid Entropy Model

In this paper, the development and evaluation of an entropy based hybrid data driven model coupled with input selection approach and wavelet transformation is investigated for long-term streamflow forecasting with 10 years lead time. To develop and test the models, data including 45 years of monthly streamflow time series from Taleghan basin, located in northwest of Tehran, are employed. For this purpose, first the performance of a maximum entropy forecasting model is evaluated. To boost the accuracy, an auto-correlation method with %95 confidence levels was carried out to determine the optimum order of the entropy model. Nevertheless, the basic entropy model, as expected, was only able to reach Nash-Sutcliffe efficiency (NSE) index of 0.35 during the test period. On the other hand, data driven models such as artificial neural networks (ANN) have shown to yield good accuracy in modeling complicated and nonlinear systems. Thus, to improve the performance of the maximum entropy model, an entropy-based hybrid model using evolutionary ANN (ENN) was proposed for further investigation. The proposed model with seasonality index substantially improved the test NSE to 0.51 and provided more accurate results than the basic entropy model. Moreover, when wavelet transform was applied to preprocess the input data, the model shows a slight improvement (NSE = 0.54).

PAR(p)-vine copula based model for stochastic streamflow scenario generation

Synthetic streamflow data is vital for the energy sector, as it feeds stochastic optimisation models that determine operational policies. Considered scenarios should differ from each other, but be the same from a statistical point of view, i.e., the scenarios must preserve features of the original time series such as the mean, variance, and temporal dependence structures. Traditionally, linear models are applied for this task. Recently, the advent of copulas has led to the emergence of an alternative that overcomes the drawbacks of linear models. In this context, we propose a methodology based on vine copulas for the stochastic simulation of periodic streamflow scenarios. Copula-based models that focus on single-site inflow simulation only consider lag-one time dependence. Therefore, we suggest an approach that incorporates lags that are greater than one. Furthermore, the proposed model deals with the strong periodicity that is commonly present in monthly streamflow time series. The resulting model is a non-linear periodic autoregressive model. Our results indicate that this model successfully simulates scenarios, preserving features that are observed in historical data.

Entropy Theory for Streamflow Forecasting

Streamflow forecasting is used in river training and management, river restoration, reservoir operation, power generation, irrigation, and navigation. In hydrology, streamflow forecasting is often done using time series analysis. Although monthly streamflow time series are stochastic, they exhibit seasonal and periodic patterns. Therefore, streamflow forecasting entails modeling two main aspects: seasonality and correlation structure. Spectral analysis can be employed to characterize patterns of streamflow variation and identify the periodicity of streamflow. That is, it permits to extract significant information for understanding the streamflow process and prediction thereof. For forecasting streamflow, spectral analysis has, however, not yet been widely applied. Streamflow spectra can be determined using entropy theory. There are three ways to employ entropy theory: (1) Burg entropy, (2) configurational entropy, and (3) relative entropy. In either way, the methodology involves determination of spectral density, determination of parameters, and extension of autocorrelation function. This paper reviews the methods of spectral analysis using the entropy theory and tests them using streamflow data.

Copula-based modeling and stochastic simulation of seasonal intermittent streamflows for arid regions

Streamflow is often intermittent in arid and semi-arid regions. Stochastically simulated data play a key role in managing water resources with intermittent streamflows. The stochastic modeling of intermittent streamflow that incorporates the seasonality of key statistics is a difficult task. In the current study, the product model was tested to simulate the intermittent monthly streamflow by employing the periodic Markov chain (PMC) model for occurrence and the periodic gamma autoregressive (PGAR) and copula models for amount. The copula models were tested in a previous study for the simulation of yearly streamflow, resulting in successful replication of the key and operational statistics of historical data; however, the copula models have never been tested on a monthly time scale. The intermittent models were applied to the Colorado River system in the present study. A few drawbacks of the PGAR model were identified, such as significant underestimation of minimum values on an aggregated yearly time scale and restrictions of the parameter boundaries. Conversely, the copula models do not present such drawbacks but show feasible reproduction of key and operational statistics. We concluded that the copula models combined with the PMC model is a feasible method for the simulation of intermittent monthly streamflow time series.

A Conjunction Method of Wavelet Transform-Particle Swarm Optimization-Support Vector Machine for Streamflow Forecasting

Streamflow forecasting has an important role in water resource management and reservoir operation. Support vector machine (SVM) is an appropriate and suitable method for streamflow prediction due to its best versatility, robustness, and effectiveness. In this study, a wavelet transform particle swarm optimization support vector machine (WT-PSO-SVM) model is proposed and applied for streamflow time series prediction. Firstly, the streamflow time series were decomposed into various details (Ds) and an approximation (A3) at three resolution levels (21-22-23) using Daubechies (db3) discrete wavelet. Correlation coefficients between eachDsubtime series and original monthly streamflow time series are calculated.Dscomponents with high correlation coefficients (D3) are added to the approximation (A3) as the input values of the SVM model. Secondly, the PSO is employed to select the optimal parameters,C,ε, andσ, of the SVM model. Finally, the WT-PSO-SVM models are trained and tested by the monthly streamflow time series of Tangnaihai Station located in Yellow River upper stream from January 1956 to December 2008. The test results indicate that the WT-PSO-SVM approach provide a superior alternative to the single SVM model for forecasting monthly streamflow in situations without formulating models for internal structure of the watershed.