Forecasting monthly inflow with extreme seasonal variation using the hybrid SARIMA-ANN model

The optimal operation of dam reservoirs can be programmed and managed by predicting the inflow to these structures more accurately. To this end, there are various linear and nonlinear models. However, some hydrological problems like inflow with extreme seasonal variation are not purely linear or nonlinear. To improve the forecasting accuracy of this phenomenon, a linear Seasonal Auto Regressive Integrated Moving Average (SARIMA) model is combined with a nonlinear Artificial Neural Network (ANN) model. This new model is used to predict the monthly inflow to the Jamishan dam reservoir in West Iran. A comparison of the SARIMA and ANN models with the proposed hybrid model’s results is provided accordingly. More specifically, the models’ performance in forecasting base and flood flows is evaluated. The effect of changing the forecasting period length on the models’ accuracy is studied. The results of increasing the number of SARIMA model parameters up to five are investigated to achieve more accurate forecasting. The hybrid model predicts peak flood flows much better than the individual models, but SARIMA outperforms the other models in predicting base flow. The obtained results indicate that the hybrid model reduces the overall forecast error more than the ANN and SARIMA models. The coefficient of determination of the hybrid, ANN and SARIMA models were 0.72, 0.64 and 0.58, and the root mean squared error values were 1.02, 1.16 and 1.27 respectively, during the forecast period. Changing the forecasting length also indicated that these models can be used in the long term without increasing the forecast error.     

Spectral band decomposition combined with nonlinear models: application to indoor formaldehyde concentration forecasting

This paper proposes a new approach for forecasting continuous indoor air quality time series and in particular the concentration of a common air pollutant in offices like formaldehyde. Forecasting is achieved through the combination of the spectral band decomposition using fast Fourier transform and nonlinear time series modeling. Two nonlinear models have been tested: a threshold autoregressive (TAR) model and a Chaos dynamics-based modeling. This study shows the benefit of the Fourier decomposition coupled with nonlinear modeling of each extracted component, compared to forecasting applied directly on the raw data. Both TAR and Chaos dynamics models are able to reproduce nonlinearities, with slightly better performance in the case of the second model. These hybrid models provide good performance on forecast time horizon up to 12 h ahead.     

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.     

An improved time series model for monthly stream flows

This study aims to develop an improved time series model to overcome difficulties in modeling monthly short term stream flows. The periodic, serial dependent and independent components of the classical time series models are improved separately by information transfer from a surrounding long term gauging station to the considered flow section having short term records. Eventually, an improved model preserving the mathematical model structure of the classical time series model, while improving general and monthly statistics of the monthly stream flows, is derived by using the improved components instead of the short term model components in the time series modeling. The correlative relationships between the current short term and surrounding long term stations are used to improve periodic and serial dependent behaviors of monthly flows. Independent components (residuals) are improved via the parameters defining their theoretical probability distribution. The improved model approach is tested by using 50 year records of Göksu-Himmetli (1801) and Göksu-Gökdere (1805) flow monitoring stations located on the Ceyhan river basin, in south of Turkey. After 50 year records of the station 1801 are separated into five 10 year sub series, their improved and classical time series models are computed and compared with the real long-term (50 year) time series model of this station to reveal efficiencies of the improved models for each subseries (sub terms with 10 year observation). The comparisons are realized based on the model components, model estimates and general/monthly statistics of model estimates. Finally, some evaluations are made on the results compared to the regression method classically applied in the literature.     

Forecasting monthly precipitation using sequential modelling

In the hydrological cycle, rainfall is a major component and plays a vital role in planning and managing water resources. In this study, new generation deep learning models, recurrent neural network (RNN) and long short-term memory (LSTM), were applied for forecasting monthly rainfall, using long sequential raw data for time series analysis. “All-India” monthly average precipitation data for the period 1871–2016 were taken to build the models and they were tested on different homogeneous regions of India to check their robustness. From the results, it is evident that both the trained models (RNN and LSTM) performed well for different homogeneous regions of India based on the raw data. The study shows that a deep learning network can be applied successfully for time series analysis in the field of hydrology and allied fields to mitigate the risks of climatic extremes.     

Rain-fall modeling: An Application of Bayesian forecasting

The rainfall-runoff modeling is very useful for forecasting purposes. A good methodology for forecasting the future stream flow is a key requirement for designers and operators of water resources systems. A compromise between conceptual and classical time series modeling is applied to model the relationship between rainfall and runoff. The dynamic nonlinear model is composed of a probability distribution describing the observation, a link function relating its mean to the so called state parameters and a system of equations defining the evolution of these parameters. Its Bayesian nature permits to take into account subjective information, making forward intervention, defining monitoring schemes and introducing smoothing facilities. An application using the data of Fartura river's basin is reported. The assessment of the prior distribution is discussed and the predictive performance of the linear and the non-linear models is reported.     

Comparative study of monthly inflow prediction methods for the Three Gorges Reservoir

Due to the complexity of influencing factors and the limitation of existing scientific knowledge, current monthly inflow prediction accuracy is unable to meet the requirements of various water users yet. A flow time series is usually considered as a combination of quasi-periodic signals contaminated by noise, so prediction accuracy can be improved by data preprocess. Singular spectrum analysis (SSA), as an efficient preprocessing method, is used to decompose the original inflow series into filtered series and noises. Current application of SSA only selects filtered series as model input without considering noises. This paper attempts to prove that noise may contain hydrological information and it cannot be ignored, a new method that considerers both filtered and noises series is proposed. Support vector machine (SVM), genetic programming (GP), and seasonal autoregressive (SAR) are chosen as the prediction models. Four criteria are selected to evaluate the prediction model performance: Nash–Sutcliffe efficiency, Water Balance efficiency, relative error of annual average maximum (RE_max) monthly flow and relative error of annual average minimum (RE_min) monthly flow. The monthly inflow data of Three Gorges Reservoir is analyzed as a case study. Main results are as following: (1) coupling with the SSA, the performance of the SVM and GP models experience a significant increase in predicting the inflow series. However, there is no significant positive change in the performance of SAR (1) models. (2) After considering noises, both modified SSA-SVM and modified SSA-GP models perform better than SSA-SVM and SSA-GP models. Results of this study indicated that the data preprocess method SSA can significantly improve prediction precision of SVM and GP models, and also proved that noises series still contains some information and has an important influence on model performance.     

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.     

A nonlinear time series analysis using two‐stage genetic algorithms for streamflow forecasting

Streamflow forecasting is very important for the management of water resources: high accuracy in flow prediction can lead to more effective use of water resources. Hydrological data can be classified as non‐steady and nonlinear, thus this study applied nonlinear time series models to model the changing characteristics of streamflows. Two‐stage genetic algorithms were used to construct nonlinear time series models of 10‐day streamflows of the Wu‐Shi River in Taiwan. Analysis verified that nonlinear time series are superior to traditional linear time series. It is hoped that these results will be useful for further applications. Copyright © 2008 John Wiley & Sons, Ltd.     

Projecting climate change impacts on stream flow regimes with tracer‐aided runoff models ‐ preliminary assessment of heterogeneity at the mesoscale

The northern mid‐high latitudes form a region that is sensitive to climate change, and many areas already have seen – or are projected to see – marked changes in hydroclimatic drivers on catchment hydrological function. In this paper, we use tracer‐aided conceptual runoff models to investigate such impacts in a mesoscale (749 km²) catchment in northern Scotland. The catchment encompasses both sub‐arctic montane sub‐catchments with high precipitation and significant snow influence and drier, warmer lowland sub‐catchments. We used downscaled HadCM3 General Circulation Model outputs through the UKCP09 stochastic weather generator to project the future climate. This was based on synthetic precipitation and temperature time series generated from three climate change scenarios under low, medium and high greenhouse gas emissions. Within an uncertainty framework, we examined the impact of climate change at the monthly, seasonal and annual scales and projected impacts on flow regimes in upland and lowland sub‐catchments using hydrological models with appropriate process conceptualization for each landscape unit. The results reveal landscape‐specific sensitivity to climate change. In the uplands, higher temperatures result in diminishing snow influence which increases winter flows, with a concomitant decline in spring flows as melt reduces. In the lowlands, increases in air temperatures and re‐distribution of precipitation towards autumn and winter lead to strongly reduced summer flows despite increasing annual precipitation. The integration at the catchment outlet moderates these seasonal extremes expected in the headwaters. This highlights the intimate connection between hydrological dynamics and catchment characteristics which reflect landscape evolution. It also indicates that spatial variability of changes in climatic forcing combined with differential landscape sensitivity in large heterogeneous catchments can lead to higher resilience of the integrated runoff response. Copyright © 2012 John Wiley & Sons, Ltd.     

Enhancing the Forecasting of Monthly Streamflow in the Main Key Stations of the River Nile Basin

Predicting the streamflow of rivers can have a significant economic impact, as this can help in agricultural water management and in providing protection from water shortages and possible flood damage. In this study, two statistical models have been used; Deseasonalized Autoregressive moving average model (DARMA) and Artificial Neural Network (ANN) to predict monthly streamflow which important for reservoir operation policy using different time scale, monthly and 1/3 monthly (ten-days) flow data for River Nile basin at five key stations. The streamflow series is deseasonalized at different time scale and then an appropriate nonseasonal stochastic DARMA (p, q) models are built by using the plots of Partial Auto Correlation Function (PACF) to determine the order (p) of DARMA model. Then the deseasonalized data for key stations are used as input to ANN models with lags equals to the order (p) of DARMA model. The performance of ANN and DARMA models are compared using statistical methods. The results show that the developed model (using 1/3 monthly (ten-days) and ANN) has the best performance to predict monthly streamflow at all key stations. The results also show that the relative error in the developed model result did not exceed 9% while in the traditional models reach to 68% in the flood months in the testing period. The result also indicates that ANN has considerable potential for river flow forecasting.     

Wavelet-ANFIS models for forecasting monsoon flows: Case study for the Gandak River (India)

WANFIS, a conjunction model of discreet wavelet transform (DWT) and adaptive neuro-fuzzy inference system (ANFIS) was developed for forecasting the current-day flow in a river when only available data are historical flows. Discreet wavelet transform decomposed the observed flow time series (OFTS) into wavelet components which captured useful information on three resolution levels. A smoothened flow time series (SFTS) was formed by filtering out the noise wavelet components and recombining the effective wavelet components. WANFIS model is essentially an ANFIS model with SFTS hydrograph as the input, while ANFIS and autoregression (AR) models, developed for comparison purpose, use OFTS hydrograph as input. For performance evaluation, the developed models were utilized for predicting daily monsoon flows for the Gandak River in Bihar state of India. During monsoon (June–October), this river carries large flows making the entire North Bihar unsafe for habitation or cultivation. Based on various performance indices, it was concluded that WANFIS models simulate the monsoon flows in the Gandak more reliably than ANFIS and AR models. The best performing WANFIS model, with four previous days’ flows as input, predicted the current-day Gandak flows with 80.7% accuracy while ANFIS and AR models predicted it with only 71.8 and 51.2% accuracies.     

Simulating and predicting river discharge time series using a wavelet‐neural network hybrid modelling approach

Accurate simulation and prediction of the dynamic behaviour of a river discharge over any time interval is essential for good watershed management. It is difficult to capture the high‐frequency characteristics of a river discharge using traditional time series linear and nonlinear model approaches. Therefore, this study developed a wavelet‐neural network (WNN) hybrid modelling approach for the predication of river discharge using monthly time series data. A discrete wavelet multiresolution method was employed to decompose the time series data of river discharge into sub‐series with low (approximation) and high (details) frequency, and these sub‐series were then used as input data for the artificial neural network (ANN). WNN models with different wavelet decomposition levels were employed to predict river discharge 48 months ahead of time. Comparison of results from the WNN models with those of the ANN models alone indicated that WNN models performed a more accurate prediction. Copyright © 2011 John Wiley & Sons, Ltd.     

A combined rotated general regression neural network method for river flow forecasting

ABSTRACT

This study focused on the performance of the rotated general regression neural network (RGRNN), as an enhancement of the general regression neural network (GRNN), in monthly-mean river flow forecasting. The study of forecasting of monthly mean river flows in Heihe River, China, was divided into two steps: first, the performance of the RGRNN model was compared with the GRNN model, the feed-forward error back-propagation (FFBP) model and the soil moisture accounting and routing (SMAR) model in their initial model forms; then, by incorporating the corresponding outputs of the SMAR model as an extra input, the combined RGRNN model was compared with the combined FFBP and combined GRNN models. In terms of model efficiency index, R², and normalized root mean squared error, NRMSE, the performances of all three combined models were generally better than those of the four initial models, and the RGRNN model performed better than the GRNN model in both steps, while the FFBP and the SMAR were consistently the worst two models. The results indicate that the combined RGRNN model could be a useful river flow forecasting tool for the chosen arid and semi-arid region in China.

Editor D. Koutsoyiannis; Associate editor not assigned     

Generalized autoregressive conditional heteroscedasticity modelling of hydrologic time series

The existence of time‐dependent variance or conditional variance, commonly called heteroscedasticity, in hydrologic time series has not been thoroughly investigated. This paper deals with modelling the heteroscedasticity in the residuals of the seasonal autoregressive integrated moving average (SARIMA) model using a generalized autoregressive conditional heteroscedasticity (GARCH) model. The model is applied to two monthly rainfall time series from humid and arid regions. The effect of Box–Cox transformation and seasonal differencing on the remaining seasonal heteroscedasticity in the residuals of the SARIMA model is also investigated. It is shown that the seasonal heteroscedasticity in the residuals of the SARIMA model can be removed using Box–Cox transformation along with seasonal differencing for the humid region rainfall. On the other hand, transformation and seasonal differencing could not remove heteroscedasticity from the residuals of the SARIMA model fitted to rainfall data in the arid region. Therefore, the GARCH modelling approach is necessary to capture the heteroscedasticity remaining in the residuals of a SARIMA model. However, the evaluation criteria do not necessarily show that the GARCH model improves the performance of the SARIMA model. Copyright © 2012 John Wiley & Sons, Ltd.     

A stepwise algorithm to detect significant time lags in ecological time series in terms of autocorrelation functions and ARMA model optimisation of pest population seasonal outbreaks

A central issue in population ecology is to determine the structure of negative feedback-density depend process which regulates population dynamics and seasonal fluctuations. In this work the incidence of population density dependences and seasonality was examined in fruit orchards of three closely related pest species (Adoxophyes orana, Anarsia lineatella and (Grapholita) Grapholitha molesta). Analysis included 13 moth population time series during 2003–2011. Additionally, considering that time lags and seasonality are fundamental characteristics of ecological organisation and pest management, the work aimed to introduce a step wise algorithm to detect significant population feedbacks, moth seasonality and population synchronisation of nearby locations. In the proposed procedure, each population-time series was first analysed on the basis of autocorrelation and partial autocorrelation. Moreover, assuming that each of the ecological variable, observed at successive time points, consist of a stochastic process, autoregressive moving average ARMA(p,q) models and seasonal autoregressive moving average models SARMA(p,q)x(P,Q) _S were fitted on data. The Akaike information criteria was further used by the stepwise algorithm for parameter optimization and model improvement. Model construction is accompanied by a presentation of the fitting results and a discussion of the heuristic benchmarks used to assess the forecasting performance of the models. Life cycles of populations belonging to same species appeared to synchronise by terms of their autocorrelation functions. Delayed density dependence and order was in most cases of lag:1 and 2, while lag >3 was not found more frequently as expected by chance. In A. orana and A. lineatella moth species lag = 1 delayed density dependence was significantly more frequent and in particular in nearby locations. However, the structure of the fitted models varied with respect to species and observation region. In some cases, seasonal models were considered to be more accurate in simulating moth population dynamics. Finally, to provide means in forecasting moth emergence and abundance, utile in pest management, the models were trained using 2003–2009 data sets and their forecasting performance were validated for each case using data sets of 2010–2011. In most cases, the constructed stochastic linear autoregressive models simulated the population outbreaks very well. Describing and forecasting stochastic population fluctuations is a basic tenet of theoretical and applied ecology, while detecting the relative roles of exogenous and endogenous mechanisms can partly describe the phenomenological behavior of pest population time series data and improve pest management.     

Nonlinear analysis of seasonality and stochasticity of the Indus River

Abstract

One of the world's largest irrigation networks, based on the Indus River system in Pakistan, faces serious scarcity of water in one season and disastrous floods in another. The system is dominated both by monsoon and by snow and glacier dynamics, which confer strong seasonal and inter-annual variability. In this paper two different forecasting methods are utilized to analyse the long-term seasonal behaviour of the Indus River. The study also assesses whether the strong seasonal behaviour is dominated by the presence of low-dimensional nonlinear dynamics, or whether the periodic behaviour is simply immersed in random fluctuations. Forecasts obtained by nonlinear prediction (NLP) and the seasonal autoregressive integrated moving average (SARIMA) methods show that the performance of NLP is relatively better than the SARIMA method. This, along with the low values of the correlation dimension, is indicative of low-dimensional nonlinear behaviour of the hydrological dynamics. A relatively better performance of NLP, using an inverse technique, may also be indicative of the low-dimensional behaviour. Moreover, the embedding dimension of the best NLP forecasts is in good agreement with the estimated correlation dimension. This provides evidence that the nonlinearity inherent in the monthly river flow due to the snowmelt and the monsoon variations dominate over the high-dimensional components and might be exploited for prediction and modelling of the complex hydrological system.

Citation Hassan, S. A. & Ansari, M. R. K. (2010) Nonlinear analysis of seasonality and stochasticity of the Indus River. Hydrol. Sci. J. 55(2), 250–265.     

Simulation of river flow in Britain under climate change: Baseline performance and future seasonal changes

Climate change is likely to manifest in river flow changes across the globe, which could have wide-ranging consequences for society and the natural environment. A number of previous studies used the UK Climate Projections 2009 (UKCP09) to investigate the potential impacts on river flows in Britain, but these projections were recently updated by the release of UKCP18, thus there is a need to update flow studies. Here, the UKCP18 Regional (12 km) projections are applied using a national-scale grid-based hydrological model, to investigate potential future changes in seasonal mean river flows across Great Britain. Analysis of hydrological model performance using baseline climate model data (1980–2010) shows relatively good agreement with use of observation-based data, particularly after application of a monthly precipitation bias-correction. Analysis of seasonal mean flow changes for two future time-slices (2020–2050 and 2050–2080) suggests large decreases in summer flows across the country (median −45% by 2050–2080), but possible increases in winter flows (median 9% by 2050–2080), especially in the north and west. Information on the potential range of flow changes using the latest projections is necessary to develop appropriate adaptation strategies, and comparisons with previous projections can help update existing plans, although such comparisons are often not straightforward.     

Hydrological Outlook UK: an operational streamflow and groundwater level forecasting system at monthly to seasonal time scales

This paper describes the development of the first operational seasonal hydrological forecasting service for the UK, the Hydrological Outlook UK (HOUK). Since June 2013, this service has delivered monthly forecasts of streamflow and groundwater levels, with an emphasis on forecasting hydrological conditions over the next three months, accompanied by outlooks over longer time horizons. This system is based on three complementary approaches combined to produce the outlooks: (i) national-scale modelling of streamflow and groundwater levels based on dynamic seasonal rainfall forecasts, (ii) catchment-scale modelling where streamflow and groundwater level models are driven by historical meteorological forcings (i.e. the Ensemble Streamflow Prediction, ESP, approach), and (iii) a catchment-scale statistical method based on persistence and historical analogues. This paper provides the background to the Hydrological Outlook, describes the various component methods in detail and then considers the impact and usefulness of the product. As an example of a multi-method, operational seasonal hydrological forecasting system, it is hoped that this overview provides useful information and context for other forecasting initiatives around the world.     

Impact of time-scale of the calibration objective function on the performance of watershed models

Many of the continuous watershed models perform all their computations on a daily time step, yet they are often calibrated at an annual or monthly time-scale that may not guarantee good simulation performance on a daily time step. The major objective of this paper is to evaluate the impact of the calibration time-scale on model predictive ability. This study considered the Soil and Water Assessment Tool for the analyses, and it has been calibrated at two time-scales, viz. monthly and daily for the War Eagle Creek watershed in the USA. The results demonstrate that the model's performance at the smaller time-scale (such as daily) cannot be ensured by calibrating them at a larger time-scale (such as monthly). It is observed that, even though the calibrated model possesses satisfactory ‘goodness of fit’ statistics, the simulation residuals failed to confirm the assumption of their homoscedasticity and independence. The results imply that evaluation of models should be conducted considering their behavior in various aspects of simulation, such as predictive uncertainty, hydrograph characteristics, ability to preserve statistical properties of the historic flow series, etc. The study enlightens the scope for improving/developing effective autocalibration procedures at the daily time step for watershed models. Copyright © 2007 John Wiley & Sons, Ltd.