APPROACHES TO MULTIVARIATE MODELING OF WATER RESOURCES TIME SERIES1

ABSTRACT: Alternative approaches suggested for modeling multiseries of water resources systems are reviewed and compared. Most approaches fall within the general framework of multivariate ARMA models. Formal modeling procedures suggest a three-stage iterative process, namely: model identification, parameter estimation and diagnostic checks. Although a number of statistical tools are already available to follow such modeling process, in general, it is not an easy task, especially if high order vector ARMA models are used. However, simpler ARMA models such as the contemporaneous and the transfer-function models may be sufficient for most applications in water resources. Two examples of modeling bivariate and trivariate streamflow series are included. Alternative modeling procedures are used and compared by using data generation techniques. The results obtained suggest that low order models, as well as contemporaneous ARMA models, reproduce quite well the main statistical characteristics of the time series analyzed. It is assumed that the same conclusions apply for most water resources time series.     

Assessment of Alternative Methods for Statistically Downscaling Daily GCM Precipitation Outputs to Simulate Regional Streamflow

This study applied three statistical downscaling methods: (1) bias correction and spatial disaggregation at daily time scale (BCSD_daily); (2) a modified version of BCSD which reverses the order of spatial disaggregation and bias correction (SDBC), and (3) the bias correction and stochastic analog method (BCSA) to downscale general circulation model daily precipitation outputs to the subbasin scale for west‐central Florida. Each downscaled climate input dataset was then used in an integrated hydrologic model to examine differences in ability to simulate retrospective streamflow characteristics. Results showed the BCSD_daily method consistently underestimated mean streamflow because the highly spatially correlated small precipitation events produced by this method resulted in overestimation of evapotranspiration. Highly spatially correlated large precipitation events produced by the SDBC method resulted in overestimation of the standard deviation of wet season daily streamflow and the magnitude/frequency of high streamflow events. BCSA showed better performance than the other methods in reproducing spatiotemporal statistics of daily precipitation and streamflow. This study demonstrated differences in statistical downscaling techniques propagate into significant differences in streamflow predictions, and underscores the need to carefully select a downscaling method that reproduces precipitation characteristics important for the hydrologic system under consideration.     

A COMPARISON OF SOME DYNAMIC,LINEAR AND POLICY ITERATION METHODS FOR RESERVOIR OPERATION1

Within the past few years, a number of papers have been published in which stochastic mathematical programming models, incorporating first order Markov chains, have been used to derive alternative sequential operating policies for a multiple purpose reservoir. This paper attempts to review and compare three such mathematical modeling and solution techniques, namely dynamic programming, policy iteration, and linear programming. It is assumed that the flows into the reservoir are serially correlated stochastic quantities. The design parameters are assumed fixed, i.e., the reservoir capacity and the storage and release targets, if any, are predetermined. The models are discrete since the continuous variables of time, volume, and flow are approximated by discrete units. The problem is to derive an optimal operating policy. Such a policy defines the reservoir release as a function of the current storage volume and inflow. The form of the solution and some of the advantages, limitations and computational efficiencies of each of the models and their algorithms are compared using a simplified numerical example.     

STOCHASTIC ANALYSIS OF TIME-AGGREGATED HYDROLOGIC DATA1

Stochastic models fitted to hydrologic data of different time scales are interrelated because the higher time scale data (aggregated data) are derived from those of lower time scale. Relationships between the statistical properties and parameters of models of aggregated data and of original data are examined in this paper. It is also shown that the aggregated data can be more accurately predicted by using a valid model of the original data than by using a valid model of the aggregated data. This property is particularly important in forecasting annual values because only a few annual values are usually available and the resulting forecasts are relatively inaccurate if models based only on annual data are used. The relationships and forecasting equations are developed for general aggregation time and can be used for hourly and daily, daily and monthly or monthly and yearly data. The method is illustrated by using monthly and yearly streamflow data. The results indicate that various statistical characteristics and parameters of the model of annual data can be accurately estimated by using the monthly data and forecasts of annual data by using monthly models have smaller one step ahead mean square error than those obtained by using annual data models.     

1960~2019年静海高温天气变化特征分析及日高温概率模型

利用静海国家气象站1960~2019年日最高气温资料对静海高温天气发生的开始和结束时间、次数进行了统计,分析了持续高温天气过程的年际变化规律、时间演变特征,利用Mann-Kendall法对高温日数、年最高气温进行趋势检验;构建了日高温发生概率的“钟形”曲线模型,利用傅里叶变换分析日高温发生概率序列的主要分量,构建了基于傅里叶级数的日高温发生概率简化模型。结果表明:1960年至1996年静海年高温日数呈下降趋势,1997年开始年高温日数呈上升趋势,而年最高气温无显著的上升趋势;静海高温天气过程主要为持续1~2天的过程,近20年高温热浪发生次数明显增加;近60年高温日开始时间提前,结束时间推迟的趋势明显;模型较好的模拟了日高温发生概率的变化特征。     

TIME SERIES ANALYSIS IN PERSPECTIVE1

ABSTRACT: By employing a set of criteria for classifying the capabilities of time series models, recent developments in time series analysis are assessed and put into proper perspective. In particular, the inherent attributes of a wide variety of time series models and modeling procedures presented by the authors of the 18 papers contained in this volume are clearly pointed out. Additionally, it is explained how these models can address many of the time series problems encountered when modeling hydrologic, water quality and other kinds of time series. For instance, families of time series models are now available for modeling series which may contain nonlinearities or may follow nonGaussian distributions. Based upon a sound physical understanding of a problem and results from exploratory data analyses, the most appropriate model to fit to a data set can be found during confirmatory data analyses by following the identification, estimation and diagnostic check stages of model construction. Promising future research projects for developing flexible classes of time series models for use in water resources applications are suggested.     

MODELING RAINFALL-RUNOFF PROCESS INCLUDING LOSSES1

ABSTRACT: Existing discrete, linear rainfall-runoff models generally require the effective rainfall of a given storm as the input for computing the runoff hydrograph. This paper proposes a method for estimating, simultaneously, the optimal values of model parameters and the rainfall losses frem the measured rainfall hyetograph and the runoff hydrograph. The method involves an ARMA model for the rainfall-runoff process and a nonlinear iterative technique. The number of model parameters to be estimated for the ARMA model is much less than the unit hydrograph model. Applications of the model to three different watersheds show that the computed runoff hydrographs agree well with the measurements.     

Optimization of the Resources Management in Fighting Wildfires

Wildfires lead to important economic, social, and environmental losses, especially in areas of Mediterranean climate where they are of a high intensity and frequency. Over the past 30 years there has been a dramatic surge in the development and use of fire spread models. However, given the chaotic nature of environmental systems, it is very difficult to develop real-time fire-extinguishing models. This article proposes a method of optimizing the performance of wildfire fighting resources such that losses are kept to a minimum. The optimization procedure includes discrete simulation algorithms and Bayesian optimization methods for discrete and continuous problems (simulated annealing and Bayesian global optimization). Fast calculus algorithms are applied to provide optimization outcomes in short periods of time such that the predictions of the model and the real behavior of the fire, combat resources, and meteorological conditions are similar. In addition, adaptive algorithms take into account the chaotic behavior of wildfire so that the system can be updated with data corresponding to the real situation to obtain a new optimum solution. The application of this method to the Northwest Forest of Madrid (Spain) is also described. This application allowed us to check that it is a helpful tool in the decision-making process.     

GROUND WATER SIMULATION USING A ONE DIMENSIONAL FLOW MODEL1

ABSTRACT: In projects involving ground water problems, dependence on the mathematical modeling of the ground water flow phenomena is inescapable. At present, two dimensional flow models, which require tremendous amounts of computer time and storage, are generally used. When such bulky models are used for planning purposes, the two requirements (computer time and storage) can severely limit the number of alternatives that can be considered. A simple quantity and quality simulation model is developed here which requires considerably less computer time and storage and gives reasonably accurate results. The model was applied to simulate a ground water basin in San Luis Rey River in Southern California. The results were compared with those obtained by a USGS model. It was found that the simple model gave results which were consistentaly within five percent of the USGS model results, while the requirements on computer time and storage were drastically reduced.     

A PARAMETRIC MODEL CALIBRATED WITH A PHYSICALLY BASED MODEL FOR RUNOFF PREDICTION FROM UNGAGED STREAMS1

ABSTRACT: Recent developments in the numerical solution of the governing partial differential equations for overland and channel flow should make possible physically based models which predict runoff from ungaged streams. However, these models, which represent the watershed by sets of intersecting planes, are complex and require much computer time. Parametric models exist that have the advantage of being relatively simple, and once calibrated are inexpensive to use and require limited data input. In this study, a procedure was developed for calibrating a parametric model against a physically based model, utilizing base areas of one acre and one square mile, with the expectation that base areas can be combined to model real watersheds. Simulation experiments with the physically based model showed that, for the one-acre base area, the dominant parameter (cell storage ratio, K) related to the slope and friction of the planes, whereas for one square-mile areas, the dominant parameters (K plus a lag factor, L) relate to channel properties. These parameters decreased exponentially as rainfall intensity increased.     

Statistical and Hybrid Methods Implemented in a Web Application for Predicting Reservoir Inflows during Flood Events

Reservoir management is a critical component of flood management, and information on reservoir inflows is particularly essential for reservoir managers to make real‐time decisions given that flood conditions change rapidly. This study's objective is to build real‐time data‐driven services that enable managers to rapidly estimate reservoir inflows from available data and models. We have tested the services using a case study of the Texas flooding events in the Lower Colorado River Basin in November 2014 and May 2015, which involved a sudden switch from drought to flooding. We have constructed two prediction models: a statistical model for flow prediction and a hybrid statistical and physics‐based model that estimates errors in the flow predictions from a physics‐based model. The study demonstrates that the statistical flow prediction model can be automated and provides acceptably accurate short‐term forecasts. However, for longer term prediction (2 h or more), the hybrid model fits the observations more closely than the purely statistical or physics‐based prediction models alone. Both the flow and hybrid prediction models have been published as Web services through Microsoft's Azure Machine Learning (AzureML) service and are accessible through a browser‐based Web application, enabling ease of use by both technical and nontechnical personnel.     

面向管理决策的标准化流域水环境模型评估验证技术框架研究

不规范的流域水环境模型应用增加了决策风险。从过程管理的角度来看,我国尚未针对流域水环境模型的评估与验证建立标准化的技术流程,模型标准化应用水平较低。在总结已有研究成果以及先进管理经验的基础上,本文构建了标准化的流域水环境模型评估验证技术框架,提出了对应用于流域水环境管理决策的模型开展评估验证的基本原则、工作流程和技术要求,并通过案例研究验证了技术框架的可行性。技术框架引入了结构合理性评估、参数识别与灵敏度分析、模拟效果评估、不确定性分析等模型评估验证的关键技术,结合不同的模型类型、决策功能等特征给出了原则性的技术要求和应用建议。研究成果充分考虑了我国的环境管理需求,与现阶段环境模拟技术要求、环境监测能力和数据条件相适应,在理论探讨和技术实现层面具备明确的可行性,将促进我国流域水环境模型的规范化、标准化和本地化应用。     

FORECASTING QUARTER-MONTHLY RIVERFLOW1

Recent developments with respect to transfer function-noise models are reviewed and used to model and forecast quarter-monthly (i.e., near-weekly) natural inflows to the Lac St-Jean reservoir in the Province of Quebec, Canada. The covariate series are rainfall and snowmelt, the latter being a novel derivation from daily rainfall, snowfall and temperature series. It is clearly demonstrated using the residual variance and the Akaike information criterion that modeling is improved as one starts with a deseasonalized ARMA model of the inflow series and successively adds transfer functions for the rainfall and snowmelt series. It is further demonstrated that the transfer function-noise model is better than a periodic autoregressive model of the inflow series. A split-sample experiment is used to compare one-step-ahead forecasts from this transfer function-noise model with forecasts from other stochastic models as well as with forecasts from a so-called conceptual hydrological model (i.e., a model which attempts to mathematically simulate the physical processes involved in the hydrological cycle). It is concluded that the transfer function-noise model is the preferred model for forecasting the quarter-monthly Lac St-Jean inflow series.     

Accuracy improvement of various short-term load forecasting models by a novel and unified statistical data-filtering method

ABSTRACT

Time-series and machine-learning methods are being strongly exploited to improve the accuracy of short-term load forecasting (STLF) results. In developing countries, power consumption behaviors could be suddenly changed by different customers, e.g. industrial customers, residential customers, so the load-demand dataset is often unstable. Therefore, reliability assessment of the load-demand dataset is obviously necessary for STLF models. Hence, this paper proposes a novel and unified statistical data-filtering method with the best confidence interval to eliminate unexpected noises/outliers of the input dataset before performing various short-term load forecasting models. This proposed novel data-filtering method, so-called the data pre-processing method, is also compared to other existing data-filtering methods (e.g. Kalman filter, Density-Based Spatial Clustering of Applications with Noise, Wavelet transform, and Singular Spectrum Analysis). By using an SCADA system?-based database of a typical 22kV distribution network in Vietnam, NYISO database, and PJM-RTO database, case studies of short-term load forecasting have been conducted with a conventional ARIMA model, an ANN forecasting model, an LSTM-RNN model, an LSTM-CNN combined model, a deep auto-encoder (DAE) network, a Wavenet-based model, a Wavenet and LSTM hybrid model, and a Wavelet Neural Network (WNN) model, which are to validate the novel and unified statistical data-filtering method proposed. The achieved numerical results demonstrate which the accuracy of the aforementioned STLF models can be significantly improved due to the proposed statistical data-filtering method with the best confidence interval of the input load dataset. The proposed statistical data-filtering method can considerably outperform the existing data-filtering methods.     

IDENTIFICATION OF AQUIFER DISPERSIVITIES: METHODS OF ANALYSIS AND PARAMETER UNCERTAINTY1

ABSTRACT: This paper presents a method for estimating aquifer dispersivities in solute transport models. Sensitivity equations are derived for the calculation of sensitivity coefficients. A modified Gauss-Newton algorithm is used to perform the least-squares minimization. A statistical procedure is outlined to assess reliability of the estimated parameters. The solute transport model is solved by the upstream weighted, multiple cell balance method which combines the concepts of local mass balance and finite element approximations. A one-dimensional solute transport problem in a vertical column system is first used to illustrate the inverse technique. A second example considers the parameter identification problem for three-dimensional solute transport with a unidirectional steady and uniform flow field. The third example solves the parameter identification problem in a three-dimensional, stream-aquifer, solute transport system with steady state flow. Numerical experiments are conducted to study data requirements for parameter identification.     

SHORT-TERM FORECASTING OF SNOWMELT RUNOFF USING ARMAX MODELS1

ABSTRACT: Time series models of the ARMAX class were investigated for use in forecasting daily riverflow resulting from combined snowmelt/rainfall. The Snowmelt Runoff Model (Martinec-Rango Model) is shown to have a form similar to the ARMAX model. The advantage of the ARMAX approach is that analytical model identification and parameter estimation techniques are available. In addition, previous forecast errors can be included to improve forecasts and confidence limits can be estimated for the forecasts. Diagnostic checks are available to determine if the model is performing properly. Finally, Kalman filtering can be used to allow the model parameters to vary continuously to reflect changing basin runoff conditions. The above advantages result in improved flow forecasts with fewer model parameters.     

MERITS OF STATISTICAL CRITERIA FOR THE PERFORMANCE OF HYDROLOGICAL MODELS1

ABSTRACT: The performance of a hydrological model is usually assessed first by visual inspection of the measured and computed hydrographs. Numerous statistical criteria are available for numerical evaluations of model accuracy in each single year, in a particular season of the year, or in a sequence of years or seasons. In the last case, the problem of computing the overall result has to be considered. If too many criteria are used and the criteria are switched frequently, an assessment of a model's performance becomes difficult for a potential user. Therefore, this paper concentrates on just three criteria and their combined evaluation: The Nash-Sutcliffe coefficient, which compares the model computed discharge with the average measured discharge; the “coefficient of gain from daily means” in which a uniform average discharge is replaced by daily average discharges; and the volumetric difference between the total measured and computed runoff. The three criteria are combined in a three dimensional representation that allows intercomparisons of model performance in a single diagram.     

Analysis and prediction of flow from local source in a river basin using a Neuro-fuzzy modeling tool

Traditionally, the multiple linear regression technique has been one of the most widely used models in simulating hydrological time series. However, when the nonlinear phenomenon is significant, the multiple linear will fail to develop an appropriate predictive model. Recently, neuro-fuzzy systems have gained much popularity for calibrating the nonlinear relationships. This study evaluated the potential of a neuro-fuzzy system as an alternative to the traditional statistical regression technique for the purpose of predicting flow from a local source in a river basin. The effectiveness of the proposed identification technique was demonstrated through a simulation study of the river flow time series of the Citarum River in Indonesia. Furthermore, in order to provide the uncertainty associated with the estimation of river flow, a Monte Carlo simulation was performed. As a comparison, a multiple linear regression analysis that was being used by the Citarum River Authority was also examined using various statistical indices. The simulation results using 95% confidence intervals indicated that the neuro-fuzzy model consistently underestimated the magnitude of high flow while the low and medium flow magnitudes were estimated closer to the observed data. The comparison of the prediction accuracy of the neuro-fuzzy and linear regression methods indicated that the neuro-fuzzy approach was more accurate in predicting river flow dynamics. The neuro-fuzzy model was able to improve the root mean square error (RMSE) and mean absolute percentage error (MAPE) values of the multiple linear regression forecasts by about 13.52% and 10.73%, respectively. Considering its simplicity and efficiency, the neuro-fuzzy model is recommended as an alternative tool for modeling of flow dynamics in the study area.     

A Simple Process‐Based Snowmelt Routine to Model Spatially Distributed Snow Depth and Snowmelt in the SWAT Model1

Abstract: We present a method to integrate a process‐based (PB) snowmelt model that requires only daily temperature and elevation information into the Soil and Water Assessment Tool (SWAT) model. The model predicts the spatiotemporal snowpack distribution without adding additional complexity, and in fact reduces the number of calibrated parameters. To demonstrate the utility of the PB model, we calibrate the PB and temperature‐index (TI) SWAT models to optimize agreement with stream discharge on a 46‐km² watershed in northwestern Idaho, United States, for 10 individual years and use the calibrated parameters for the year with the best agreement to run the model for 15 remaining years. Stream discharge predictions by the PB and TI model were similar, although the PB model simulated snowmelt more accurately than the TI model for the remaining 15‐year period. Spatial snow distributions predicted by the PB model better matched observations from LandSat imagery and a SNOTEL station. Results for this watershed show that including PB snowmelt in watershed models is feasible, and calibration of TI‐based watershed models against discharge can incorrectly predict snow cover.