Comparison of local and global approximators in multivariate chaotic forecasting of daily streamflow

ABSTRACT

Although it is conceptually assumed that global models are relatively ineffective in modelling the highly unstable structure of chaotic hydrologic dynamics, there is not a detailed study of comparing the performances of local and global models in a hydrological context, especially with new emerging machine learning models. In this study, the performance of a local model (k-nearest neighbour, k-nn) and, as global models, several recent machine learning models – artificial neural network (ANN), least square-support vector regression (LS-SVR), random forest (RF), M5 model tree (M5), multivariate adaptive regression splines (MARS) – was analysed in multivariate chaotic forecasting of streamflow. The models were developed for Australia’s largest river, the River Murray. The results indicate that the k-nn model was more successful than the global models in capturing the streamflow dynamics. Furthermore, coupled with the multivariate phase-space, it was shown that the global models can be successfully used for obtaining reliable uncertainty estimates for streamflow.     

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.     

Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error

Abstract

The seasonal flood-limited water level (FLWL), which reflects the seasonal flood information, plays an important role in governing the trade-off between reservoir flood control and conservation. A risk analysis model for flood control operation of seasonal FLWL incorporating the inflow forecasting error was proposed and developed. The variable kernel estimation is implemented for deriving the inflow forecasting error density. The synthetic inflow incorporating forecasting error is simulated by Monte Carlo simulation (MCS) according to the inflow forecasting error density. The risk analysis for seasonal FLWL control was estimated by MCS based on a combination of the forecasting inflow lead-time, seasonal design flood hydrographs and seasonal operation rules. The Three Gorges reservoir is selected as a case study. The application results indicate that the seasonal FLWL control can effectively enhance flood water utilization rate without lowering the annual flood control standard.

Editor D. Koutsoyiannis; Associate editor A. Viglione

Citation Zhou, Y.-L. and Guo, S.-L., 2014. Risk analysis for flood control operation of seasonal flood-limited water level incorporating inflow forecasting error. Hydrological Sciences Journal, 59 (5), 1006–1019.     

Evaporation modelling by heuristic regression approaches using only temperature data

Accurate estimation of pan evaporation (E_pan) is very important in water resources management, irrigation scheduling and water budget of lakes. This study investigates the accuracy of two heuristic regression approaches, multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in estimating pan evaporation using only temperature data as input. Monthly minimum temperature, maximum temperature and E_pan data from three Turkish stations were used, with month number (periodicity information) added as input to see its effect on estimation accuracy. The models were compared with the calibrated Hargreaves-Samani (CHS), Stephens-Stewart (SS) and multiple linear regression methods. Three different train-test splitting strategies (50%–50%, 60%–40% and 75%–25%) were employed for better evaluation of the applied methods. The results show that the MARS method generally estimated monthly E_pan with higher accuracy compared to the M5Tree, CHS and SS methods. When extraterrestrial radiation, calculated from Julian date and latitude information, was used as input to the SS instead of solar radiation, satisfactory estimates were obtained. A positive effect on model accuracy was observed when involving periodicity information in inputs and increasing training data length.     

Design and evaluation of SVR,MARS and M5Tree models for 1, 2 and 3-day lead time forecasting of river flow data in a semiarid mountainous catchment

Accurate and reliable river flow forecasts attained with data-intelligent models can provide significant information about future water resources management. In this study we employed a 50-model ensemble of three data-driven predictive models, namely the support vector regression (SVR), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) to forecast river flow data in a semiarid and ecologically significant mountainous region of Pailugou catchment in northwestern China. To attain stable and accurate forecast results, 50 different models were trained by randomly sampling the entire river flow data into 80% for training and 20% for testing subsets. To attain a complete evaluation of the ensemble-model based results, the global mean of six quantitative statistical performance evaluation measures: the coefficient of correlation (R), mean absolute relative error (MAE), root mean squared error (RMSE), Nash–Sutcliffe efficiency coefficient (NS), relative RMSE, and the Willmott’s Index (WI), and Taylor diagrams, including skill scores relative to a persistence model, were selected to assess the performances of the developed predictive models. The results indicated that all of the averaged R value attained was higher than 0.900 and all of the averaged NS values were higher than 0.800, representing good performance of the SVR, MARS and M5Tree models applied in the 1-, 2- and 3-day ahead modeling horizon, and this also accorded with the deductions made through an assessment of the Willmott’s Index. However, the M5Tree model outperformed both the SVR and MARS models (with NS?=?0.917 vs. 0.904 and 0.901 for 1-day, 0.893 vs. 0.854 and 0.845 for 2-day, and 0.850 vs. 0.828 and 0.810 for 3-day forecasting horizons, respectively), which was in concurrence with the high value of WI. Therefore, based on the ensemble of 50 models, the performance of the M5Tree can be considered as superior to the SVR and MARS models when applied in a problem of river flow forecasting at multiple forecast horizon. A detailed comparison of the overall performance of all three models evaluated through Taylor diagrams and boxplots indicated that the 1-day ahead forecasting results were more accurate for all of the predictive models compared to the 2- and 3-day ahead forecasting horizons. Data-intelligent models designed in this study indicate that the M5Tree method could successfully be explored for short-term river flow forecasting in semiarid mountainous regions, which may have useful implications in water resources management, ecological sustainability and assessment of river systems.     

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.     

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.     

Deep echo state network: a novel machine learning approach to model dew point temperature using meteorological variables

ABSTRACT

The potential of different models – deep echo state network (DeepESN), extreme learning machine (ELM), extra tree (ET), and regression tree (RT) – in estimating dew point temperature by using meteorological variables is investigated. The variables consist of daily records of average air temperature, atmospheric pressure, relative humidity, wind speed, solar radiation, and dew point temperature (T_dew) from Seoul and Incheon stations, Republic of Korea. Evaluation of the model performance shows that the models with five and three-input variables yielded better accuracy than the other models in these two stations, respectively. In terms of root-mean-square error, there was significant increase in accuracy when using the DeepESN model compared to the ELM (18%), ET (58%), and RT (64%) models at Seoul station and the ELM (12%), ET (23%), and RT (49%) models at Incheon. The results show that the proposed DeepESN model performed better than the other models in forecasting T_dew values.     

A new measure for assessing the efficiency of hydrological data-driven forecasting models

Abstract

There is a lack of consistency and generality in assessing the performance of hydrological data-driven forecasting models, and this paper presents a new measure for evaluating that performance. Despite the fact that the objectives of hydrological data-driven forecasting models differ from those of the conventional hydrological simulation models, criteria designed to evaluate the latter models have been used until now to assess the performance of the former. Thus, the objectives of this paper are, firstly, to examine the limitations in applying conventional methods for evaluating the data-driven forecasting model performance, and, secondly, to present new performance evaluation methods that can be used to evaluate hydrological data-driven forecasting models with consistency and objectivity. The relative correlation coefficient (RCC) is used to estimate the forecasting efficiency relative to the naïve model (unchanged situation) in data-driven forecasting. A case study with 12 artificial data sets was performed to assess the evaluation measures of Persistence Index (PI), Nash-Sutcliffe coefficient of efficiency (NSC) and RCC. In particular, for six of the data sets with strong persistence and autocorrelation coefficients of 0.966–0.713 at correlation coefficients of 0.977–0.989, the PIs varied markedly from 0.368 to 0.930 and the NSCs were almost constant in the range 0.943–0.972, irrespective of the autocorrelation coefficients and correlation coefficients. However, the RCCs represented an increase of forecasting efficiency from 2.1% to 37.8% according to the persistence. The study results show that RCC is more useful than conventional evaluation methods as the latter do not provide a metric rating of model improvement relative to naïve models in data-driven forecasting.

Editor D. Koutsoyiannis, Associate editor D. Yang

Citation Hwang, S.H., Ham, D.H., and Kim, J.H., 2012. A new measure for assessing the efficiency of hydrological data-driven forecasting models. Hydrological Sciences Journal, 57 (7), 1257–1274.     

Effective typhoon characteristics and their effects on hourly reservoir inflow forecasting

This paper describes the identification of effective typhoon characteristics and the development of a new type of hourly reservoir inflow forecasting model with the effective typhoon characteristics. Firstly, a comparison of support vector machines (SVMs), which is a novel kind of neural networks (NNs), and back-propagation networks (BPNs) is made to select an appropriate NN-based model. The results show that SVM-based models are more appropriate than BPN-based models because of their higher accuracy and much higher efficiency. In addition, effective typhoon characteristics for improving forecasting performance are identified from all the collected typhoon information. Then the effective typhoon characteristics (the position of the typhoon and the distance between the typhoon center and the reservoir) are added to the proposed SVM-based models. Next, a performance comparison of models with and without effective typhoon characteristics is conducted to clearly highlight the effects of effective typhoon characteristics on hourly reservoir inflow forecasting. To reach a just conclusion, the performance is evaluated by cross validation, and the improvement in performance due to the addition of effective typhoon characteristics is tested by paired comparison t-tests at the 5% significance level. The results confirm that effective typhoon characteristics do improve the forecasting performance and the improvement increases with increasing lead-time, especially when the rainfall data are not available. For four- to six-hour ahead forecasts, the improvement due to the addition of effective typhoon characteristics increases from 3% to 18% and from 10% to 113% for Categories I (rainfall data are available) and II (rainfall data are not available), respectively. In conclusion, effective typhoon characteristics are recommended as key inputs for reservoir inflow forecasting during typhoons. The proposed SVM-based models with effective typhoon characteristics are expected to provide more accurate forecasts than BPN-based models. The proposed modeling technique is also expected to be useful to support reservoir operation systems and other disaster warning systems.     

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.     

Applying wavelet transformation and artificial neural networks to develop forecasting-based reservoir operating rule curves

ABSTRACT

In order to provide more accurate reservoir-operating policies, this study attempts to implement effective monthly forecasting models. Seven inflow forecasting schemes, applying discrete wavelet transformation and artificial neural networks are proposed and provided to forecast the monthly inflow of Dez Reservoir. Based on some different performance indicators the best scheme is achieved comparing to the observed data. The best forecasting model is coupled with a simulation-optimization framework, in which the performance of five different reservoir rule curves can be compared. Three applied rules are based on conventional Standard operation policy, Regression rules, and Hedging rule, and two others are forecasting-based regression and hedging rules. The results indicate that forecasting-based operating rule curves are superior to the conventional rules if the forecasting scheme provides results accurately. Moreover, it can be concluded that the time series decomposition of the observed data enhances the accuracy of the forecasting results efficiently.     

Univariate streamflow forecasting using commonly used data-driven models: literature review and case study

Eight data-driven models and five data pre-processing methods were summarized; the multiple linear regression (MLR), artificial neural network (ANN) and wavelet decomposition (WD) models were then used in short-term streamflow forecasting at four stations in the East River basin, China. The wavelet–artificial neural network (W-ANN) method was used to predict 1-month-ahead monthly streamflow at Longchuan station (LS). The results indicate better performance of MLR and wavelet–multiple linear regression (W-MLR) in analysing the stationary trained dataset. Four models showed similar performance in 1-day-ahead streamflow forecasting, while W-MLR and W-ANN performed better in 5-day-ahead forecasting. Three reservoirs were shown to have more influence on downstream than upstream streamflow and models had the worst performance at Boluo station. Furthermore, the W-ANN model performed well for 1-month-ahead streamflow forecasting at LS with consideration of a deterministic component.     

A real-time stage Muskingum forecasting model for a site without rating curve

Abstract

An adaptive model for on-line stage forecasting is proposed for river reaches where significant lateral inflow contributions occur. The model is based on the Muskingum method and requires the estimation of four parameters if the downstream rating curve is unknown; otherwise only two parameters have to be determined. As the choice of the forecast lead time is linked to wave travel time along the reach, to increase the lead time, a schematization of two connected river reaches is also investigated. The variability of lateral inflow is accounted for through an on-line adaptive procedure. Calibration and validation of the model were carried out by applying it to different flood events observed in two equipped river reaches of the upper-middle Tiber basin in central Italy, characterized by a significant contributing drainage area. Even if the rating curve is unknown at the downstream section, the forecast stage hydrographs were found in good agreement with those observed. Errors in peak stage and time to peak along with the persistence coefficient values show that the model has potential as a practical tool for on-line flood risk management.     

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.     

Daily reservoir inflow forecasting using artificial neural networks with stopped training approach

In this paper, an early stopped training approach (STA) is introduced to train multi-layer feed-forward neural networks (FNN) for real-time reservoir inflow forecasting. The proposed method takes advantage of both Levenberg–Marquardt Backpropagation (LMBP) and cross-validation technique to avoid underfitting or overfitting on FNN training and enhances generalization performance. The methodology is assessed using multivariate hydrological time series from Chute-du-Diable hydrosystem in northern Quebec (Canada). The performance of the model is compared to benchmarks from a statistical model and an operational conceptual model. Since the ultimate goal concerns the real-time forecast accuracy, overall the results show that the proposed method is effective for improving prediction accuracy. Moreover it offers an alternative when dynamic adaptive forecasting is desired.     

Performance of an artificial neural network on forecasting the daily occurrence and annual depth of rainfall at a tropical site

Performance of a feed‐forward back‐propagation artificial neural network on forecasting the daily occurrence and annual depth of rainfall at a single meteorological station is presented. Both short‐term and long‐term forecasting was attempted, with ground level data collected by the meteorological station in Colombo, Sri Lanka (79° 52′E, 6° 54′N) during two time periods, 1994–2003 and 1869–2003. Two neural network models were developed; a one‐day‐ahead model for predicting the rainfall occurrence of the next day, which was able to make predictions with a 74·3% accuracy, and one‐year‐ahead model for yearly rainfall depth predictions with an 80·0% accuracy within a ± 5% error bound. Each of these models was extended to make predictions several time steps into the future, where accuracies were found to decrease rapidly with the number of time steps. The success rates and rainfall variability within the north‐east and south‐west monsoon seasons are also discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

Flood forecasting and infiltration modeling/Prévision de crue et modélisation de l’infiltration

Abstract

Abstract The role of accuracy in the representation of infiltration on the effectiveness of real-time flood forecasting models was investigated. A simple semi-distributed model of conceptual type with adaptive estimate of hydraulic characteristics included in the infiltration component was selected. Infiltration was described by a very accurate approach recently formulated for complex rainfall patterns, or alternatively through a simpler formulation known as an extension of the classical time compression approximation. The results indicated that, for situations involving a significant rainfall variability in space, the inaccuracy in the representation of infiltration cannot be corrected by the adaptive component of the rainfall–runoff model. A preliminary analysis of the role of an approximation of saturated hydraulic conductivity to be used in each homogeneous area of the semi-distributed model used both in non-adaptive version and in real-time is also presented.     

Hydroclimate variability and long-lead forecasting of rainfall over Thailand by large-scale atmospheric variables

Abstract

The development of statistical relationships between local hydroclimates and large-scale atmospheric variables enhances the understanding of hydroclimate variability. The rainfall in the study basin (the Upper Chao Phraya River Basin, Thailand) is influenced by the Indian Ocean and tropical Pacific Ocean atmospheric circulation. Using correlation analysis and cross-validated multiple regression, the large-scale atmospheric variables, such as temperature, pressure and wind, over given regions are identified. The forecasting models using atmospheric predictors show the capability of long-lead forecasting. The modified k-nearest neighbour (k-nn) model, which is developed using the identified predictors to forecast rainfall, and evaluated by likelihood function, shows a long-lead forecast of monsoon rainfall at 7–9 months. The decreasing performance in forecasting dry-season rainfall is found for both short and long lead times. The developed model also presents better performance in forecasting pre-monsoon season rainfall in dry years compared to wet years, and vice versa for monsoon season rainfall.

Editor Z.W. Kundzewicz

Citation Singhrattna, N., Babel, M.S. and Perret, S.R., 2012. Hydroclimate variability and long-lead forecasting of rainfall over Thailand by large-scale atmospheric variables. Hydrological Sciences Journal, 57 (1), 26–41.     

Wavelet analysis-based projection pursuit autoregression model and its application in the runoff forecasting of Li Xiangjiang basin

ABSTRACT

The wavelet analysis technique was combined in this study with the projection pursuit autoregression (PPAR) model, and a new mid- and long-term runoff forecasting model, the wavelet analysis-based PPAR (PPAR-WA) is proposed, which realizes runoff forecasting from the perspective of the internal mechanism of a sequence. The runoff forecasting of the leading hydropower station in the Li Xianjiang cascade reservoirs in China was carried out to test the performance of the proposed model, and the accuracy and stability of the forecasting results were evaluated and analysed. The results show that the average relative error of the forecasting period can reach 9.6%, and the best relative error is less than 5% in some years. In addition, compared with PPAR, a back-propagation neural network and autoregression moving average model through three evaluation indexes, the results of PPAR-WA have higher accuracy and stronger stability. So, it has a certain value of popularization and application.