Assessment of flood forecasting lead time based on generalized likelihood uncertainty estimation approach

Real time updating of rainfall-runoff (RR) models is traditionally performed by state-space formulation in the context of flood forecasting systems. In this paper, however, we examine applicability of generalized likelihood uncertainty estimation (GLUE) approach in real time modification of forecasts. Real time updating and parameter uncertainty analysis was conducted for Abmark catchment, a part of the great Karkheh basin in south west of Iran. A conceptual-distributed RR model, namely ModClark, was used for basin simulation, such that the basin’s hydrograph was determined by the superposition of runoff generated by individual cells in a raster-based discretization. In real time updating of RR model by GLUE method, prior and posterior likelihoods were computed using forecast errors that were obtained from the results of behavioral models and real time recorded discharges. Then, prior and posterior likelihoods were applied to modify forecast confidence limits in each time step. Calibration of parameters was performed using historical data while distribution of parameters was modified in real time based on new data records. Two scenarios of rainfall forecast including prefect-rainfall-forecast and no-rainfall-forecast were assumed in absence of a robust rainfall forecast model in the study catchment. The results demonstrated that GLUE application could offer an acceptable lead time for peak discharge forecast at the expense of high computational demand.     

Including spatial distribution in a data‐driven rainfall‐runoff model to improve reservoir inflow forecasting in Taiwan

Multi‐step ahead inflow forecasting has a critical role to play in reservoir operation and management in Taiwan during typhoons as statutory legislation requires a minimum of 3‐h warning to be issued before any reservoir releases are made. However, the complex spatial and temporal heterogeneity of typhoon rainfall, coupled with a remote and mountainous physiographic context, makes the development of real‐time rainfall‐runoff models that can accurately predict reservoir inflow several hours ahead of time challenging. Consequently, there is an urgent, operational requirement for models that can enhance reservoir inflow prediction at forecast horizons of more than 3 h. In this paper, we develop a novel semi‐distributed, data‐driven, rainfall‐runoff model for the Shihmen catchment, north Taiwan. A suite of Adaptive Network‐based Fuzzy Inference System solutions is created using various combinations of autoregressive, spatially lumped radar and point‐based rain gauge predictors. Different levels of spatially aggregated radar‐derived rainfall data are used to generate 4, 8 and 12 sub‐catchment input drivers. In general, the semi‐distributed radar rainfall models outperform their less complex counterparts in predictions of reservoir inflow at lead times greater than 3 h. Performance is found to be optimal when spatial aggregation is restricted to four sub‐catchments, with up to 30% improvements in the performance over lumped and point‐based models being evident at 5‐h lead times. The potential benefits of applying semi‐distributed, data‐driven models in reservoir inflow modelling specifically, and hydrological modelling more generally, are thus demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

An evaluation of numerical weather prediction based rainfall forecasts

ABSTRACT

Assessment of forecast precipitation is required before it can be used as input to hydrological models. Using radar observations in southeastern Australia, forecast rainfall from the Australian Community Climate Earth-System Simulator (ACCESS) was evaluated for 2010 and 2011. Radar rain intensities were first calibrated to gauge rainfall data from four research rainfall stations at hourly time steps. It is shown that the Australian ACCESS model (ACCESS-A) overestimated rainfall in low precipitation areas and underestimated elevated accumulations in high rainfall areas. The forecast errors were found to be dependent on the rainfall magnitude. Since the cumulative rainfall observations varied across the area and through the year, the relative error (RE) in the forecasts varied considerably with space and time, such that there was no consistent bias across the study area. Moreover, further analysis indicated that both location and magnitude errors were the main sources of forecast uncertainties on hourly accumulations, while magnitude was the dominant error on the daily time scale. Consequently, the precipitation output from ACCESS-A may not be useful for direct application in hydrological modelling, and pre-processing approaches such as bias correction or exceedance probability correction will likely be necessary for application of the numerical weather prediction (NWP) outputs.

EDITOR M.C. Acreman ASSOCIATE EDITOR A. Viglione     

Seasonal ensemble generator for radar rainfall using copula and autoregressive model

Uncertainty analysis of radar rainfall enables stakeholders and users have a clear knowledge of the possible uncertainty associated with the rainfall products. Long-term empirical modeling of the relationship between radar and gauge measurements is an efficient and practical method to describe the radar rainfall uncertainty. However, complicated variation of synoptic conditions makes the radar-rainfall uncertainty model based on historical data hard to extend in the future state. A promising solution is to integrate synoptic regimes with the empirical model and explore the impact of individual synoptic regimes on radar rainfall uncertainty. This study is an attempt to introduce season, one of the most important synoptic factor, into the radar rainfall uncertainty model and proposes a seasonal ensemble generator for radar rainfall using copula and autoregressive model. We firstly analyze the histograms of rainfall-weighted temperature, the radar-gauge relationships, and Box and Whisker plots in different seasons and conclude that the radar rainfall uncertainty has strong seasonal dependence. Then a seasonal ensemble generator is designed and implemented in a UK catchment under a temperate maritime climate, which can fully model marginal distribution, spatial dependence, temporal dependence and seasonal dependence of radar rainfall uncertainty. To test its performance, 12 typical rainfall events (4 for each season) are chosen to generate ensemble rainfall values. In each time step, 500 ensemble members are produced and the values of 5th to 95th percentiles are used to derive the uncertainty bands. Except several outliers, the uncertainty bands encompass the observed gauge rainfall quite well. The parameters of the ensemble generator vary considerably for each season, indicating the seasonal ensemble generator reflects the impact of seasons on radar rainfall uncertainty. This study is an attempt to simultaneously consider four key features of radar rainfall uncertainty and future study will investigate their impacts on the outputs of hydrological models with radar rainfall as input or initial conditions.     

Radar rainfall uncertainty modelling influenced by wind

Radar‐based estimates of rainfall are affected by many sources of uncertainties, which would propagate through the hydrological model when radar rainfall estimates are used as input or initial conditions. An elegant solution to quantify these uncertainties is to model the empirical relationship between radar measurements and rain gauge observations (as the ‘ground reference’). However, most current studies only use a fixed and uniform model to represent the uncertainty of radar rainfall, without consideration of its variation under different synoptic regimes. Wind is such a typical weather factor, as it not only induces error in rain gauge measurements but also causes the raindrops observed by weather radar to drift when they reach the ground. For this reason, as a first attempt, this study introduces the wind field into the uncertainty model and designs the radar rainfall uncertainty model under different wind conditions. We separate the original dataset into three subsamples according to wind speed, which are named as WDI (0–2 m/s), WDII (2–4 m/s) and WDIII (>4 m/s). The multivariate distributed ensemble generator is introduced and established for each subsample. Thirty typical events (10 at each wind range) are selected to explore the behaviours of uncertainty under different wind ranges. In each time step, 500 ensemble members are generated, and the values of 5th to 95th percentile values are used to produce the uncertainty bands. Two basic features of uncertainty bands, namely dispersion and ensemble bias, increase significantly with the growth of wind speed, demonstrating that wind speed plays a considerable role in influencing the behaviour of the uncertainty band. On the basis of these pieces of evidence, we conclude that the radar rainfall uncertainty model established under different wind conditions should be more realistic in representing the radar rainfall uncertainty. This study is only a start in incorporating synoptic regimes into rainfall uncertainty analysis, and a great deal of more effort is still needed to build a realistic and comprehensive uncertainty model for radar rainfall data. Copyright © 2014 John Wiley & Sons, Ltd.     

Identification of best predictors for forecasting seasonal rainfall and runoff in Australia

The first step towards developing a reliable seasonal runoff forecast is identifying the key predictors that drive rainfall and runoff. This paper investigates the lag relationships between rainfall across Australia and runoff across southeast Australia versus 12 atmospheric‐oceanic predictors, and how the relationships change over time. The analysis of rainfall data indicates that the relationship is greatest in spring and summer in northeast Australia and in spring in southeast Australia. The best predictors for spring rainfall in eastern Australia are NINO4 [sea surface temperature (SST) in western Pacific] and thermocline (20 °C isotherm of the Pacific) and those for summer rainfall in northeast Australia are NINO4 and Southern Oscillation Index (SOI) (pressure difference between Tahiti and Darwin). The relationship in northern Australia is greatest in spring and autumn with NINO4 being the best predictor. In western Australia, the relationship is significant in summer, where SST2 (SST over the Indian Ocean) and II (SST over the Indonesian region) is the best predictor in the southwest and northwest, respectively. The analysis of runoff across southeast Australia indicates that the runoff predictability in the southern parts is greatest in winter and spring, with antecedent runoff being the best predictor. The relationship between spring runoff and NINO4, thermocline and SOI is also relatively high and can be used together with antecedent runoff to forecast spring runoff. In the northern parts of southeast Australia, the atmospheric‐oceanic variables are better predictors of runoff than antecedent runoff, and have significant correlation with winter, spring and summer runoff. For longer lead times, the runoff serial correlation is reduced, especially over the northern parts, and the atmospheric‐oceanic variables are likely to be better predictors for forecasting runoff. The correlations between runoff versus the predictors vary with time, and this has implications for the development of forecast relationship that assumes stationarity in the historical data. Copyright © 2010 John Wiley & Sons, Ltd.     

Hydrological model sensitivity to parameter and radar rainfall estimation uncertainty

Radar estimates of rainfall are being increasingly applied to flood forecasting applications. Errors are inherent both in the process of estimating rainfall from radar and in the modelling of the rainfall–runoff transformation. The study aims at building a framework for the assessment of uncertainty that is consistent with the limitations of the model and data available and that allows a direct quantitative comparison between model predictions obtained by using radar and raingauge rainfall inputs. The study uses radar data from a mountainous region in northern Italy where complex topography amplifies radar errors due to radar beam occlusion and variability of precipitation with height. These errors, together with other error sources, are adjusted by applying a radar rainfall estimation algorithm. Radar rainfall estimates, adjusted and not, are used as an input to TOPMODEL for flood simulation over the Posina catchment (116 km²). Hydrological model parameter uncertainty is explicitly accounted for by use of the GLUE (Generalized Likelihood Uncertainty Estimation). Statistics are proposed to evaluate both the wideness of the uncertainty limits and the percentage of observations which fall within the uncertainty bounds. Results show the critical importance of proper adjustment of radar estimates and the use of radar estimates as close to ground as possible. Uncertainties affecting runoff predictions from adjusted radar data are close to those obtained by using a dense raingauge network, at least for the lowest radar observations available. Copyright © 2004 John Wiley & Sons, Ltd.     

降雨输入对实时洪水预报精度与预见期的影响

针对降雨输入不确定性对实时洪水预报影响的问题,本文采用不考虑未来预报降雨、考虑未来预报降雨、考虑预报降雨的降雨量误差和降雨时间误差4种方法,以陕西省两个半湿润流域（陈河流域和大河坝流域）为研究区域,分析不同预见期和不同降雨输入情况下洪水预报的精度.研究表明：相对于不考虑未来降雨情况,考虑未来降雨后在预报预见期较长时对预报结果精度提升较大,在预见期较短时对预报结果精度提升不显著;暴雨中心位置不同对预报精度影响也不同,当暴雨中心位于流域下游时降雨量误差对流量预报误差影响更大;降雨量误差主要影响洪量相对误差和洪峰相对误差,且这种影响是线性的,对确定性系数的影响是非线性的二次函数,降雨时间误差主要影响峰现时间误差.     

Ensemble rainfall forecasting with numerical weather prediction and radar‐based nowcasting models

The overall objective of this study is to improve the forecasting accuracy of the precipitation in the Singapore region by means of both rainfall forecasting and nowcasting. Numerical Weather Predication (NWP) and radar‐based rainfall nowcasting are two important sources for quantitative precipitation forecast. In this paper, an attempt to combine rainfall prediction from a high‐resolution mesoscale weather model and a radar‐based rainfall model was performed. Two rainfall forecasting methods were selected and examined: (i) the weather research and forecasting model (WRF); and (ii) a translation model (TM). The WRF model, at a high spatial resolution, was run over the domain of interest using the Global Forecast System data as initializing fields. Some heavy rainfall events were selected from data record and used to test the forecast capability of WRF and TM. Results obtained from TM and WRF were then combined together to form an ensemble rainfall forecasting model, by assigning weights of 0.7 and 0.3 weights to TM and WRF, respectively. This paper presented results from WRF and TM, and the resulting ensemble rainfall forecasting; comparisons with station data were conducted as well. It was shown that results from WRF are very useful as advisory of anticipated heavy rainfall events, whereas those from TM, which used information of rain cells already appearing on the radar screen, were more accurate for rainfall nowcasting as expected. The ensemble rainfall forecasting compares reasonably well with the station observation data. Copyright © 2012 John Wiley & Sons, Ltd.     

Modelling radar-rainfall estimation uncertainties using elliptical and Archimedean copulas with different marginal distributions

Abstract

Given that radar-based rainfall has been broadly applied in hydrological studies, quantitative modelling of its uncertainty is critically important, as the error of input rainfall is the main source of error in hydrological modelling. Using an ensemble of rainfall estimates is an elegant solution to characterize the uncertainty of radar-based rainfall and its spatial and temporal variability. This paper has fully formulated an ensemble generator for radar precipitation estimation based on the copula method. Each ensemble member is a probable realization that represents the unknown true rainfall field based on the distribution of radar rainfall (RR) error and its spatial error structure. An uncertainty model consisting of a deterministic component and a random error factor is presented based on the distribution of gauge rainfall conditioned on the radar rainfall (GR|RR). Two kinds of copulas (elliptical and Archimedean copulas) are introduced to generate random errors, which are imposed by the deterministic component. The elliptical copulas (e.g. Gaussian and t-copula) generate the random errors based on the multivariate distribution, typically of decomposition of the error correlation matrix using the LU decomposition algorithm. The Archimedean copulas (e.g. Clayton and Gumbel) utilize the conditional dependence between different radar pixels to obtain random errors. Based on those, a case application is carried out in the Brue catchment located in southwest England. The results show that the simulated uncertainty bands of rainfall encompass most of the reference raingauge measurements with good agreement between the simulated and observed spatial dependences. This indicates that the proposed scheme is a statistically reliable method in ensemble radar rainfall generation and is a useful tool for describing radar rainfall uncertainty.

Editor D. Koutsoyiannis; Associate editor S. Grimaldi     

Propagation of uncertainties in interpolated rainfields to runoff errors

Conditional daily rainfields were generated using collocated raingauge radar data by a kriging interpolation method, and disaggregated into hourly rainfields using variants of the method of fragments. A geographic information system (GIS)-based distributed rainfall–runoff model was used to convert the hourly rainfields into hydrographs. Using the complete radar rainfall as input, the rainfall–runoff model was calibrated based on storm events taken from nested catchments. Performance statistics were estimated by comparing the observed and the complete radar rainfall simulated hydrographs. Degradation in the hydrograph performance statistics by the simulated hourly rainfields was used to identify runoff error propagation. Uncertainty in daily rainfall amounts alone caused higher errors in runoff (depth, peak, and time to peak) than those caused by uncertainties in the hourly proportions alone. However, the degradation, which reduced with runoff depth, caused by the combined uncertainties was not significantly different from that caused by the uncertainty of amounts alone.     

Feed forward Artificial Neural Network model to predict the average summer-monsoon rainfall in India

In the present research, possibility of predicting average summer-monsoon rainfall over India has been analyzed through Artificial Neural Network model. In formulating the ANN — based predictive model, three-layer network has been constructed with sigmoid non-linearity. The monthly summer monsoon rainfall totals, tropical rainfall indices and sea surface temperature anomalies have been considered as predictors while generating the input matrix for the ANN. The data pertaining to the years 1950–1995 have been explored to develop the predictive model. Finally, the prediction performance of neural net has been compared with persistence forecast and Multiple Linear Regression forecast and the supremacy of the ANN has been established over the other processes.     

Probabilistic radar rainfall nowcasts using empirical and theoretical uncertainty models

Weather radar has a potential to provide accurate short‐term (0–3 h) forecasts of rainfall (i.e. radar nowcasts), which are of great importance in warnings and risk management for hydro‐meteorological events. However, radar nowcasts are affected by large uncertainties, which are not only linked to limitations in the forecast method but also because of errors in the radar rainfall measurement. The probabilistic quantitative precipitation nowcasting approach attempts to quantify these uncertainties by delivering the forecasts in a probabilistic form. This study implements two forms of probabilistic quantitative precipitation nowcasting for a hilly area in the south of Manchester, namely, the theoretically based scheme [ensemble rainfall forecasts (ERF)‐TN] and the empirically based scheme (ERF‐EM), and explores which one exhibits higher predictive skill. The ERF‐TN scheme generates ensemble forecasts of rainfall in which each ensemble member is determined by the stochastic realisation of a theoretical noise component. The so‐called ERF‐EM scheme proposed and applied for the first time in this study, aims to use an empirically based error model to measure and quantify the combined effect of all the error sources in the radar rainfall forecasts. The essence of the error model is formulated into an empirical relation between the radar rainfall forecasts and the corresponding ‘ground truth’ represented by the rainfall field from rain gauges measurements. The ensemble members generated by the two schemes have been compared with the rain gauge rainfall. The hit rate and the false alarm rate statistics have been computed and combined into relative operating characteristic curves. The comparison of the performance scores for the two schemes shows that the ERF‐EM achieves better performance than the ERF‐TN at 1‐h lead time. The predictive skills of both schemes are almost identical when the lead time increases to 2 h. In addition, the relation between uncertainty in the radar rainfall forecasts and lead time is also investigated by computing the dispersion of the generated ensemble members. Copyright © 2013 John Wiley & Sons, Ltd.     

Uncertainty based modeling of rainfall-runoff: Combined differential evolution adaptive Metropolis (DREAM) and K-means clustering

Simulation of rainfall-runoff process in urban areas is of great importance considering the consequences and damages of extreme runoff events and floods. The first issue in flood hazard analysis is rainfall simulation. Large scale climate signals have been proved to be effective in rainfall simulation and prediction. In this study, an integrated scheme is developed for rainfall-runoff modeling considering different sources of uncertainty. This scheme includes three main steps of rainfall forecasting, rainfall-runoff simulation and future runoff prediction. In the first step, data driven models are developed and used to forecast rainfall using large scale climate signals as rainfall predictors. Due to high effect of different sources of uncertainty on the output of hydrologic models, in the second step uncertainty associated with input data, model parameters and model structure is incorporated in rainfall-runoff modeling and simulation. Three rainfall-runoff simulation models are developed for consideration of model conceptual (structural) uncertainty in real time runoff forecasting. To analyze the uncertainty of the model structure, streamflows generated by alternative rainfall-runoff models are combined, through developing a weighting method based on K-means clustering. Model parameters and input uncertainty are investigated using an adaptive Markov Chain Monte Carlo method. Finally, calibrated rainfall-runoff models are driven using the forecasted rainfall to predict future runoff for the watershed. The proposed scheme is employed in the case study of the Bronx River watershed, New York City. Results of uncertainty analysis of rainfall-runoff modeling reveal that simultaneous estimation of model parameters and input uncertainty significantly changes the probability distribution of the model parameters. It is also observed that by combining the outputs of the hydrological models using the proposed clustering scheme, the accuracy of runoff simulation in the watershed is remarkably improved up to 50% in comparison to the simulations by the individual models. Results indicate that the developed methodology not only provides reliable tools for rainfall and runoff modeling, but also adequate time for incorporating required mitigation measures in dealing with potentially extreme runoff events and flood hazard. Results of this study can be used in identification of the main factors affecting flood hazard analysis.     

Rainfall stochastic modeling for runoff forecasting

Rainfall fields estimation over a catchment area is an important stage in many hydrological applications. In this context, weather radars have several advantages because a single-site can scan a vast area with very high temporal and spatial resolution. The construction of weather radar systems with dual polarization capability allowed progress on radar rainfall estimation and its hydro-meteorological applications. For these applications of radar data it is necessary to remove the ground clutter contamination with an algorithm based on the backscattering signal variance of the differential reflectivity. The calibration of the GDSTM model (Gaussian Displacements Spatial-Temporal Model), a cluster stochastic generation model in continuous space and time, is herewith presented. In this model, storms arrive in a Poisson process in time with cells occurring in each storm that cluster in space and time. The model is calibrated, using data collected by the weather radar Polar 55C located in Rome, inside a square area of 132 × 132 km², with the radar at the centre. The GDSTM is fitted to sequences of radar images with a time interval between the PPIs scans of 5 min. A generalized method of moment procedure is used for parameter estimation. For the validation of the ability of the model to reproduce internal structure of rain event, a geo-morphological rainfall-runoff model, based on width function (WFIUH), was calibrated using simulated and observed data. Several rainfall fields are generated with the stochastic model and later they are used as input of the WFIUH model so that the forecast discharges can be compared to the observed ones.     

Assimilation of Doppler Weather Radar Radial Velocity and Reflectivity Observations in WRF-3DVAR System for Short-Range Forecasting of Convective Storms

In this paper the impact of Doppler weather radar (DWR) reflectivity and radial velocity observations for the short range forecasting of a tropical storm and associated rainfall event have been examined. Doppler radar observations of a tropical storm case that occurred during 29–30 October 2006 from SHARDWR (13.6° N, 80.2° E) are assimilated in the WRF 3DVAR system. The observation operator for radar reflectivity and radial velocity is included within latest version of WRF 3DVAR system. Keeping all model physics the same, three experiments were conducted at a horizontal resolution of 30?km. In the control experiment (CTRL), NCEP Final Analysis (FNL) interpolated to the model grid was used as the initial condition for 48-h free forecast. In the second experiment (NODWR), 6-h assimilation cycles have been carried out using all conventional (radiosonde and surface data) and non-conventional (satellite) observations from the Global Telecommunication System (GTS). The third experiment (DWR) is the same as the second, except Doppler radar radial velocity and reflectivity observations are also used in the assimilation cycle. Continuous 6-h assimilation cycle employed in the WRF-3DVAR system shows positive impact on the rainfall forecast. Assimilation of DWR data creates several small scale features near the storm centre. Additional sensitivity experiments were conducted to study the individual impact of reflectivity and radial velocity in the assimilation cycle. Radar data assimilation with reflectivity alone produced large analysis response on both thermodynamical and dynamical fields. However, radial velocity assimilation impacted only on dynamical fields. Analysis increments with radar reflectivity and radial velocity produce adjustments in both dynamical and thermodynamical fields. Verification of QPF skill shows that radar data assimilation has a considerable impact on the short range precipitation forecast. Improvement of the QPF skill with radar data assimilation is more clearly seen in the heavy rainfall (for thresholds >7?mm) event than light rainfall (for thresholds of 1 and 3?mm). The spatial pattern of rainfall is well simulated by the DWR experiment and is comparable to TRMM observations.     

大别山库区降水预报性能评估及应用对策

对降水预报进行性能评估及应用对策研究可以更好地发挥降水预报在水库调度中的决策支持作用.基于大别山库区近10 a汛期(2007—2016年5月1日—9月30日)24~168 h共7个预见期降水预报和地面降水观测资料,采用正确率、TS评分、概率统计、ROC曲线以及CTS等方法评估大别山库区降水预报性能,并以响洪甸水库为重点研究区域分析降水预报在水库调度中的应用对策.结果表明:1)大别山库区各量级的降水预报都有正预报技巧;24~72 h预见期降水预报的TS评分较高且空报率、漏报率也较低,具有较高的预报性能;但96 h及以上预见期降水预报性能明显下降,中雨以上量级空报率、漏报率较大,特别是对大暴雨及其以上量级的降水预报性能显著下降.2)大别山库区预报降水量级与实况降水量级基本符合,预报降水量级大于等于实况降水量级的概率超过75%;虽然降水预报量级上呈现出过度预报的现象,但降水过程预报对水库调度仍有较好的应用价值,应用时要考虑到降水预报量级可能存在偏差.3)转折性天气预报96 h及以上预见期CTS评分较低,但72 h以内预见期的性能明显改进,尤其是24 h预见期CTS评分也提高到了38.2%;水库调度可从长预见期的降水预报获取降水过程及其可能发生转折的信息,根据短预见期的降水预报进行调度方案调整.     

Effect of streamflow forecast uncertainty on real-time reservoir operation

Various hydrological forecast products have been applied to real-time reservoir operation, including deterministic streamflow forecast (DSF), DSF-based probabilistic streamflow forecast (pseudo-PSF, pPSF), and ensemble or probabilistic streamflow forecast (denoted as real-PSF, rPSF). DSF represents forecast uncertainty in the form of deterministic forecast errors, pPSF a conditional distribution of forecast uncertainty for a given DSF, and rPSF a probabilistic uncertainty distribution. Compared to previous studies that treat the forecast products as ad hoc inputs for reservoir operation models, this paper attempts to model the dynamic evolution of uncertainties involved in the various forecast products and explores their effect on real-time reservoir operation decisions. Through a hypothetical example of a single-objective real-time reservoir operation model, the results illustrate that forecast uncertainty exerts significant effects. Reservoir operation efficiency, as measured by a utility function, decreases as the forecast uncertainty increases but the magnitude depends on the forecast products used. In general, the utility of the reservoir operation with rPSF is nearly as high as the utility obtained with a perfect forecast. Meanwhile, the utilities of DSF and pPSF are similar to each other but not as high as rPSF. Moreover, streamflow variability and reservoir capacity can change the magnitude of the effects of forecast uncertainty, but not the relative merit of DSF, pPSF, and rPSF.     

Long‐lead seasonal rainfall forecasting using time‐delay recurrent neural networks: a case study

A temporal artificial neural network‐based model is developed and applied for long‐lead rainfall forecasting. Tapped delay lines and recurrent connections are two different components that are used along with a static multilayer perceptron network to design a time‐delay recurrent neural network. The proposed model is, in fact, a combination of time‐delay and recurrent neural networks. The model is applied in three case studies of the Northwest, West, and Southwest basins of Iran. In addition, an autoregressive moving average with exogenous inputs (ARMAX) model is used as a baseline in order to be compared with the time‐delay recurrent neural networks developed in this study. Large‐scale climate signals, such as sea‐level pressure, that affect the rainfall of the study area are used as the predictors in the models, as well as the persistence between rainfall data. The results of winter‐spring rainfall forecasts are discussed thoroughly. It is demonstrated that in all cases the proposed neural network results in better forecasts in comparison with the statistical ARMAX model. Moreover, it is found that in two of three case studies the time‐delay recurrent neural networks perform better than either recurrent or time‐delay neural networks. The results demonstrate that the proposed method can significantly improve the long‐lead forecast by utilizing a non‐linear relationship between climatic predictors and rainfall in a region. Copyright © 2007 John Wiley & Sons, Ltd.