On the criteria of model performance evaluation for real-time flood forecasting

Model performance evaluation for real-time flood forecasting has been conducted using various criteria. Although the coefficient of efficiency (CE) is most widely used, we demonstrate that a model achieving good model efficiency may actually be inferior to the naïve (or persistence) forecasting, if the flow series has a high lag-1 autocorrelation coefficient. We derived sample-dependent and AR model-dependent asymptotic relationships between the coefficient of efficiency and the coefficient of persistence (CP) which form the basis of a proposed CE–CP coupled model performance evaluation criterion. Considering the flow persistence and the model simplicity, the AR(2) model is suggested to be the benchmark model for performance evaluation of real-time flood forecasting models. We emphasize that performance evaluation of flood forecasting models using the proposed CE–CP coupled criterion should be carried out with respect to individual flood events. A single CE or CP value derived from a multi-event artifactual series by no means provides a multi-event overall evaluation and may actually disguise the real capability of the proposed model.     

Assessing the skill of the UK Hydrological Outlook

ABSTRACT

The UK Hydrological Outlook (UKHO) is a seasonal forecast of future river flows and groundwater levels. The UKHO contains both presentations of outputs from models simulating future conditions and a high-level summary. The summary is produced by an expert panel of forecasters that considers the model outputs together with other recent hydrological and meteorological information. Whilst the skill and uncertainty of the individual models have been explored and published, this study sets out to establish the performance of the high-level summary, and presents such an assessment of the river flow forecasts at the 1-month timescale. Both qualitative and quantitative assessments are presented and compared with two naïve forecasting methods. The UKHO summary is found to have a similar Gerrity skill score to a “same as last month” forecast, an outcome that generates suggestions for improvements in how the different model outputs should be considered and presented in the high-level summary.     

Comparison of daily streamflow forecasts using extreme learning machines and the random forest method

ABSTRACT

Daily streamflow forecasting is a challenging and essential task for water resource management. The main goal of this study was to compare the accuracy of five data-driven models: extreme learning machine (basic ELM), extreme learning machine with kernels (ELM-kernel), random forest (RF), back-propagation neural network (BPNN) and support vector machine (SVR). The results show that the ELM-kernel model provided a superior alternative to the other models, and the basic ELM model had the poorest performance. To further evaluate the predictive capacities of the five models, the estimations of low flow and high flow in the testing dataset were compared. The RF model was slightly superior to the other models in predicting the peak flows, and the ELM-kernel model showed the highest prediction precision of low flows. There was no single model that showed obvious advantages over the other models in this study. Therefore, further exploration is required for the hydrological forecasting problems.     

Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach

Abstract

Hydrological models are commonly used to perform real-time runoff forecasting for flood warning. Their application requires catchment characteristics and precipitation series that are not always available. An alternative approach is nonparametric modelling based only on runoff series. However, the following questions arise: Can nonparametric models show reliable forecasting? Can they perform as reliably as hydrological models? We performed probabilistic forecasting one, two and three hours ahead for a runoff series, with the aim of ascribing a probability density function to predicted discharge using time series analysis based on stochastic dynamics theory. The derived dynamic terms were compared to a hydrological model, LARSIM. Our procedure was able to forecast within 95% confidence interval 1-, 2- and 3-h ahead discharge probability functions with about 1.40 m³/s of range and relative errors (%) in the range [–30; 30]. The LARSIM model and the best nonparametric approaches gave similar results, but the range of relative errors was larger for the nonparametric approaches.

Editor D. Koutsoyiannis; Associate editor K. Hamed

Citation Costa, A.C., Bronstert, A. and Kneis, D., 2012. Probabilistic flood forecasting for a mountainous headwater catchment using a nonparametric stochastic dynamic approach. Hydrological Sciences Journal, 57 (1), 10–25.     

Improving long-range hydrological forecasts with extended Kalman filters

Abstract

There is a continuing effort to advance the skill of long-range hydrological forecasts to support water resources decision making. The present study investigates the potential of an extended Kalman filter approach to perform supervised training of a recurrent multilayer perceptron (RMLP) to forecast up to 12-month-ahead lake water levels and streamflows in Canada. The performance of the RMLP was compared with the conventional multilayer perceptron (MLP) using suites of diagnostic measures. The results of the forecasting experiment showed that the RMLP model was able to provide a robust modelling framework capable of describing complex dynamics of the hydrological processes, thereby yielding more accurate and realistic forecasts than the MLP model. The performance of the method in the present study is very promising; however, further investigation is required to ascertain the versatility of the approach in characterizing different water resources and environmental problems.

Citation Muluye, G. Y. (2011) Improving long-range hydrological forecasts with extended Kalman filters. Hydrol. Sci. J. 56(7), 1118–1128.     

Improvement of mid- to long-term runoff forecasting based on physical causes: application in Nenjiang basin,China

Abstract

An artificial neural network, mid- to long-term runoff forecasting model of the Nenjiang basin was established by deciding predictors using the physical analysis method, combined with long-term hydrological and meteorological information. The forecasting model was gradually improved while considering physical factors, such as the main flood season and non-flood season by stage, runoff sources and hydrological processes. The average relative errors in the simulation tests of the prediction model were 0.33 in the main flood season and 0.26 in the non-flood season, indicating that the prediction accuracy during the non-flood season was greater than that in the main flood season. Based on these standards, forecasting accuracy evaluation was conducted by comparing forecasting results with actual conditions: for 2001 to 2003 data, the pass rate of forecasting in the main flood season was 50%, while it was 93% in the non-flood season; for 2001–2010, the respective values were 45% and 72%. The accuracy of prediction was found to decrease as the length of record increases.

Editor D. Koutsoyiannis, Associate editor A. Viglione

Citation Li, H.-Y. Tian, L., Wu, Y., and Xie, M., 2013. Improvement of mid- to long-term runoff forecasting based on physical causes: application in Nenjiang basin, China. Hydrological Sciences Journal, 58 (7), 1414–1422.     

Comparison of data-driven modelling techniques for river flow forecasting

Abstract

Accurate forecasting of streamflow is essential for the efficient operation of water resources systems. The streamflow process is complex and highly nonlinear. Therefore, researchers try to devise alterative techniques to forecast streamflow with relative ease and reasonable accuracy, although traditional deterministic and conceptual models are available. The present work uses three data-driven techniques, namely artificial neural networks (ANN), genetic programming (GP) and model trees (MT) to forecast river flow one day in advance at two stations in the Narmada catchment of India, and the results are compared. All the models performed reasonably well as far as accuracy of prediction is concerned. It was found that the ANN and MT techniques performed almost equally well, but GP performed better than both these techniques, although only marginally in terms of prediction accuracy in normal and extreme events.

Citation Londhe, S. & Charhate, S. (2010) Comparison of data-driven modelling techniques for river flow forecasting. Hydrol. Sci. J. 55(7), 1163–1174.     

Streamflow forecasting using least-squares support vector machines

Abstract

This paper investigates the ability of a least-squares support vector machine (LSSVM) model to improve the accuracy of streamflow forecasting. Cross-validation and grid-search methods are used to automatically determine the LSSVM parameters in the forecasting process. To assess the effectiveness of this model, monthly streamflow records from two stations, Tg Tulang and Tg Rambutan of the Kinta River in Perak, Peninsular Malaysia, were used as case studies. The performance of the LSSVM model is compared with the conventional statistical autoregressive integrated moving average (ARIMA), the artificial neural network (ANN) and support vector machine (SVM) models using various statistical measures. The results of the comparison indicate that the LSSVM model is a useful tool and a promising new method for streamflow forecasting.

Editor D. Koutsoyiannis; Associate editor L. See

Citation Shabri, A. and Suhartono, 2012. Streamflow forecasting using least-squares support vector machines. Hydrological Sciences Journal, 57 (7), 1275–1293.     

A Modified Neural Network for Improving River Flow Prediction/Un Réseau de Neurones Modifié pour Améliorer la Prévision de L'Écoulement Fluvial

Abstract

Artificial neural network (ANN) models provide huge potential for simulating nonlinear behaviour of hydrological systems. However, the potential of ANN is yet to be fully exploited due to the problems associated with improving the model generalization performance. Generalization refers to the ability of a neural network to correctly process input data that have not been used for calibrating the neural network model. In the hydrological context, better generalization performance implies higher precision of forecasting. The primary objectives of this study are to explore new measures for improving the generalization performance of an ANN-based rainfall–runoff model, and to evaluate the applicability of the new measures. A modified neural network model (entitled goal programming (GP) neural network) for modelling the rainfall–runoff process has been developed, in which three enhancements are made as compared to the widely-used backpropagation (BP) network. The three enhancements are (a) explicit integration of hydrological prior knowledge into the neural network learning; (b) incorporation of a modified training objective function; and (c) reduction of network sensitivity to input errors. Seven watersheds across a range of climatic conditions and watershed areas in China were selected for examining the alternative networks. The results demonstrate that the GP consistently outperformed the BP both in the calibration and verification periods and three proposed measures yielded improvement of performance.     

Improving streamflow estimation in ungauged basins using a multi-modelling approach

ABSTRACT

In this study, a multi-modelling approach is proposed for improved continuous daily streamflow estimation in ungauged basins using regionalization—the process of transferring hydrological data from gauged to ungauged watersheds. Four regionalization models, two data-driven and two hydrological, were used for continuous daily streamflow estimation. Comparison of the individual models reveals that each of the four models performed well on a limited number of ungauged basins while none of them performed well for the entire 90 selected watersheds. The results obtained from the four models are evaluated and reported in a deterministic way by a model combination approach along with its uncertainty range consisting of 16 ensemble members. It is shown that a combined model of the four individual models performed well on all 90 watersheds and the ensemble range can account for the uncertainty of models. The combined model was more efficient and appeared more robust compared to the individual models. Furthermore, continuous ranked probability scores (CRPS) calculated for the ensemble model outputs indicate better performance compared to individual models and competitive with the combined model.

EDITOR A. Castellarin ASSOCIATE EDITOR G. Di Baldassarre     

BIBLIOGRAPHIE

Abstract

Time series modelling approaches are useful tools for simulating and forecasting hydrological variables and their change through time. Although linear time series models are common in hydrology, the nonlinear time series model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model, has rarely been used in hydrology and water resources engineering. The GARCH model considers the conditional variance remaining in the residuals of the linear time series models, such as an ARMA or an ARIMA model. In the present study, the advantages of a GARCH model against a linear ARIMA model are investigated using three classes of the GARCH approach, namely Power GARCH, Threshold GARCH and Exponential GARCH models. A daily streamflow time series of the Matapedia River, Quebec, Canada, is selected for this study. It is shown that the ARIMA (13,1,4) model is adequate for modelling streamflow time series of Matapedia River, but the Engle test shows the existence of heteroscedasticity in the residuals of the ARIMA model. Therefore, an ARIMA (13,1,4)-GARCH (3,1) error model is fitted to the data. The residuals of this model are examined for the existence of heteroscedasticity. The Engle test indicates that the GARCH model has considerably reduced the heteroscedasticity of the residuals. However, the Exponential GARCH model seems to completely remove the heteroscedasticity from the residuals. The multi-criteria evaluation for model performance also proves that the Exponential GARCH model is the best model among ARIMA and GARCH models. Therefore, the application of a GARCH model is strongly suggested for hydrological time series modelling as the conditional variance of the residuals of the linear models can be removed and the efficiency of the model will be improved.

Editor D. Koutsoyiannis; Associate editor C. Onof

Citation Modarres, R. and Ouarda, T.B.M.J., 2013. Modelling heteroscedasticty of streamflow times series. Hydrological Sciences Journal, 58 (1), 1–11.     

Forecasting streamflow by combination of a genetic input selection algorithm and wavelet transforms using ANFIS models

ABSTRACT

In this study, a data-driven streamflow forecasting model is developed, in which appropriate model inputs are selected using a binary genetic algorithm (GA). The process involves using a combination of a GA input selection method and two adaptive neuro-fuzzy inference systems (ANFIS): subtractive (Sub)-ANFIS and fuzzy C-means (FCM)-ANFIS. Moreover, the application of wavelet transforms coupled with these models is tested. Long-term data for the Lighvan and Ajichai basins in Iran are used to develop the models. The results indicate considerable improvements when GA selection and wavelet methods are used in both models. For example, the Nash-Sutcliffe efficiency (NSE) coefficient for Lighvan using FCM-ANFIS is 0.74. However, when GA selection is applied, the NSE is improved to 0.85. Moreover, when the wavelet method is added, the performance of new hybrid models shows noticeable enhancements. The NSE value of wavelet-FCM-ANFIS is improved to 0.97 for Lighvan basin.

Editor D. Koutsoyiannis Associate editor E. Toth     

Author Index 1991

Abstract

Evapotranspiration (ET) is an important process in the hydrological cycle and needs to be accurately quantified for proper irrigation scheduling and optimal water resources systems operation. The time variant characteristics of ET necessitate the need for forecasting ET. In this paper, two techniques, namely a seasonal ARIMA model and Winter's exponential smoothing model, have been investigated for their applicability for forecasting weekly reference crop ET. A seasonal ARIMA model with one autoregressive and one moving average process and with a seasonality of 52 weeks was found to be an appropriate stochastic model. The ARIMA and Winter's models were compared with a simple ET model to assess their performance in forecasting. The forecast errors produced by these models were very small and the models would be promisingly of great use in real-time irrigation management.     

Hybrid modelling approach to prairie hydrology: fusing data-driven and process-based hydrological models

Abstract

Much of the prairie region in North America is characterized by relatively flat terrain with many depressions on the landscape. The hydrological response (runoff) is a combination of the conventional runoff from the contributing areas and the occasional overflow from the non-contributing areas (depressions). In this study, we promote the use of a hybrid modelling structure to predict runoff generation from prairie landscapes. More specifically, the Soil and Water Assessment Tool (SWAT) is fused with artificial neural networks (ANNs), so that SWAT and the ANN module deal with the contributing and non-contributing areas, respectively. A detailed experimental study is performed to select the best set of inputs, training algorithms and hidden neurons. The results obtained in this study suggest that the fusion of process-based and data-driven models can provide improved modelling capabilities for representing the highly nonlinear nature of the hydrological processes in prairie landscapes.

Editor D. Koutsoyiannis; Associate editor L. See     

Uncertainty,entropy, scaling and hydrological stochastics. 2. Time dependence of hydrological processes and time scaling / Incertitude,entropie, effet d'échelle et propriétés stochastiques hydrologiques. 2. Dépendance temporelle des processus hydrologiques et échelle temporelle

Abstract

The well-established physical and mathematical principle of maximum entropy (ME), is used to explain the distributional and autocorrelation properties of hydrological processes, including the scaling behaviour both in state and in time. In this context, maximum entropy is interpreted as maximum uncertainty. The conditions used for the maximization of entropy are as simple as possible, i.e. that hydrological processes are non-negative with specified coefficients of variation and lag-one autocorrelation. In the first part of the study, the marginal distributional properties of hydrological processes and the state scaling behaviour were investigated. This second part of the study is devoted to joint distributional properties of hydrological processes. Specifically, it investigates the time dependence structure that may result from the ME principle and shows that the time scaling behaviour (or the Hurst phenomenon) may be obtained by this principle under the additional general condition that all time scales are of equal importance for the application of the ME principle. The omnipresence of the time scaling behaviour in numerous long hydrological time series examined in the literature (one of which is used here as an example), validates the applicability of the ME principle, thus emphasizing the dominance of uncertainty in hydrological processes.     

Improving the performance of data-driven techniques through data pre-processing for modelling daily reservoir inflow

Abstract

The effect of data pre-processing while developing artificial intelligence (AI) -based data-driven techniques, such as artificial neural networks (ANN), model trees (MT) and linear genetic programming (LGP), is studied for Pawana Reservoir in Maharashtra, India. The daily one-step-ahead inflow forecasts are compared with flows generated from a univariate autoregressive integrated moving average (ARIMA) model. For the full-year data series, a large error is found mainly due to the occurrence of zero values, since the reservoir is located in an intermittent river. Hence, all the techniques are evaluated using two data series: 18 years of daily full-year inflow data (from 1 January to 31 December); and 18 years of daily monsoon season inflow data (from 1 June to 31 October) to take into account the intermittent nature of the data. The relevant range of inputs for each category is selected based on autocorrelation and partial autocorrelation analyses of the inflow series. Conventional pre-processing methods, such as transformation and/or normalization of data, do not perform well because of the large variation in magnitudes, as well as the many zero values (65% of the full-year data series). Therefore, the input data are pre-processed into un-weighted moving average (MA) series of 3 days, 5 days and 7 days. The 3-day MA series performs better, maintaining the peak inflow pattern as in the actual data series, while the coarser-scale (5-day and 7-day) MA series reduce the peak inflow pattern, leading to more errors in peak inflow prediction. The results indicate that AI methods are powerful tools for modelling the daily flow time series with appropriate data pre-processing, in spite of the presence of many zero values. The time-lagged recurrent network (TLRN) ANN modelling technique applied in this study maps the inflow forecasting in a better way than the standard multilayer perceptron (MLP) neural networks, especially in the case of the seasonal data series. The MT technique performs equally well for low and medium inflows, but fails to predict the peak inflows. However, LGP outperforms the other AI models, and also the ARIMA model, for all inflow magnitudes. In the LGP model, the daily full-year data series with more zero inflow values performs better than the daily seasonal models.

Citation Jothiprakash, V. & Kote, A. S. (2011) Improving the performance of data-driven techniques through data pre-processing for modelling daily reservoir inflow. Hydrol. Sci. J. 56(1), 168–186.     

Pre-processing of data-driven river flow forecasting models by singular value decomposition (SVD) technique

ABSTRACT

An appropriate streamflow forecasting method is a prerequisite for implementation of efficient water resources management in the water-limited, arid regions that occupy much of Iran. In the current research, monthly streamflow forecasting was combined with three data-driven methods based on large input datasets involving 11 precipitation stations, a natural streamflow, and four climate indices through a long period. The major challenges of rainfall–runoff modelling are generally attributed to complex interacting processes, the large number of variables, and strong nonlinearity. The sensitivity of data-driven methods to the dimension of input/output datasets would be another challenge, so large datasets should be compressed into independently standardized principal components. In this study, three pre-processing techniques were applied: singular value decomposition (SVD) provided more efficient forecasts in comparison to principal component analysis (PCA) and average values of inputs in all networks. Among the data-driven methods, the multi-layer perceptron (MLP) with 1-month lag-time outperformed radial basis and fuzzy-based networks. In general, an increase in monthly lag-time of streamflow forecasting resulted in a decline in forecasting accuracy. The results reveal that SVD was highly effective in pre-processing of data-driven evaluations.     

Probabilistic calibration of a distributed hydrological model for flood forecasting

Abstract

The complexity of distributed hydrological models has led to improvements in calibration methodologies in recent years. There are various manual, automatic and hybrid methods of calibration. Most use a single objective function to calculate estimation errors. The use of multi-objective calibration improves results, since different aspects of the hydrograph may be considered simultaneously. However, the uncertainty of estimates from a hydrological model can only be taken into account by using a probabilistic approach. This paper presents a calibration method of probabilistic nature, based on the determination of probability functions that best characterize different parameters of the model. The method was applied to the Real-time Interactive Basin Simulator (RIBS) distributed hydrological model using the Manzanares River basin in Spain as a case study. The proposed method allows us to consider the uncertainty in the model estimates by obtaining the probability distributions of flows in the flood hydrograph.

Citation Mediero, L., Garrote, L. & Martín-Carrasco, F. J. (2011) Probabilistic calibration of a distributed hydrological model for flood forecasting. Hydrol. Sci. J. 56(7), 1129–1149.     

Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics

Abstract

Seasonality is an important hydrological signature for catchment comparison. Here, the relevance of monthly precipitation–runoff polygons (defined as scatter points of 12 monthly average precipitation–runoff value pairs connected in the chronological monthly sequence) for characterizing seasonality patterns was investigated to describe the hydrological behaviour of 10 catchments spanning a climatic gradient across the northern temperate region. Specifically, the research objectives were to: (a) discuss the extent to which monthly precipitation–runoff polygons can be used to infer active hydrological processes in contrasting catchments; (b) test the ability of quantitative metrics describing the shape, orientation and surface area of monthly precipitation–runoff polygons to discriminate between different seasonality patterns; and (c) examine the value of precipitation–runoff polygons as a basis for catchment grouping and comparison. This study showed that some polygon metrics were as effective as monthly average runoff coefficients for illustrating differences between the 10 catchments. The use of precipitation–runoff polygons was especially helpful to look at the dynamics prevailing in specific months and better assess the coupling between precipitation and runoff and their relative degree of seasonality. This polygon methodology, linked with a range of quantitative metrics, could therefore provide a new simple tool for understanding and comparing seasonality among catchments.

Editor Z.W. Kundzewicz; Associate editor K. Heal

Citation Ali, G., Tetzlaff, D., Kruitbos, L., Soulsby, C., Carey, S., McDonnell, J., Buttle, J., Laudon, H., Seibert, J., McGuire, K., and Shanley, J., 2013. Analysis of hydrological seasonality across northern catchments using monthly precipitation–runoff polygon metrics. Hydrological Sciences Journal, 59 (1), 56–72.     

Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records

Abstract

New mathematical programming models are proposed, developed and evaluated in this study for estimating missing precipitation data. These models use nonlinear and mixed integer nonlinear mathematical programming (MINLP) formulations with binary variables. They overcome the limitations associated with spatial interpolation methods relevant to the arbitrary selection of weighting parameters, the number of control points within a neighbourhood, and the size of the neighbourhood itself. The formulations are solved using genetic algorithms. Daily precipitation data obtained from 15 rain gauging stations in a temperate climatic region are used to test and derive conclusions about the efficacy of these methods. The developed methods are compared with some naïve approaches, multiple linear regression, nonlinear least-square optimization, kriging, and global and local trend surface and thin-plate spline models. The results suggest that the proposed new mathematical programming formulations are superior to those obtained from all the other spatial interpolation methods tested in this study.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi

Citation Teegavarapu, R.S.V., 2012. Spatial interpolation using nonlinear mathematical programming models for estimation of missing precipitation records. Hydrological Sciences Journal, 57 (3), 383–406.