Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande1

Abudu, S., J.P. King, Z. Sheng, 2011. Comparison of the Performance of Statistical Models in Forecasting Monthly Total Dissolved Solids in the Rio Grande. Journal of the American Water Resources Association (JAWRA) 48(1): 10‐23. DOI: 10.1111/j.1752‐1688.2011.00587.x Abstract: This paper presents the application of autoregressive integrated moving average (ARIMA), transfer function‐noise (TFN), and artificial neural networks (ANNs) modeling approaches in forecasting monthly total dissolved solids (TDS) of water in the Rio Grande at El Paso, Texas. Predictability analysis was performed between the precipitation, temperature, streamflow rates at the site, releases from upstream reservoirs, and monthly TDS using cross‐correlation statistical tests. The chi‐square test results indicated that the average monthly temperature and precipitation did not show significant predictability on monthly TDS series. The performances of one‐ to three‐month‐ahead model forecasts for the testing period of 1984‐1994 showed that the TFN model that incorporated the streamflow rates at the site and Caballo Reservoir release improved monthly TDS forecasts slightly better than the ARIMA models. Except for one‐month‐ahead forecasts, the ANN models using the streamflow rates at the site as inputs resulted in no significant improvements over the TFN models at two‐month‐ahead and three‐month‐ahead forecasts. For three‐month‐ahead forecasts, the simple ARIMA showed similar performance compared to all other models. The results of this study suggested that simple deseasonalized ARIMA models could be used in one‐ to three‐month‐ahead TDS forecasting at the study site with a simple, explicit model structure and similar model performance as the TFN and ANN models for better water management in the Basin.     

A NEW LOOK AT FLOOD RISK DETERMINATION1

ABSTRACT: The probability distributions of annual peak flows used in flood risk analysis quantify the risk that a design flood will be exceeded. But the parameters of these distributions are themselves to a degree uncertain and this uncertainty increases the risk that the flood protection provided will in fact prove to be inadequate. The increase in flood risk due to parameter uncertainty is small when a fairly long record of data is available and the annual flood peaks are serially independent, which is the standard assumption in flood frequency analysis. But standard tests for serial independence are insensitive to the type of grouping of high and low values in a time series, which is measured by the Hurst coefficient. This grouping increases the parameter uncertainty considerably. A study of 49 annual peak flow series for Canadian rivers shows that many have a high Hurst coefficient. The corresponding increase in flood risk due to parameter uncertainty is shown to be substantial even for rivers with a long record, and therefore should not be neglected. The paper presents a method of rationally combining parameter uncertainty due to serial correlation, and the stochastic variability of peak flows in a single risk assessment. In addition, a relatively simple time series model that is capable of reproducing the observed serial correlation of flood peaks is presented.     

ANALYSIS AND MODELING OF LONG-TERM STREAM TEMPERATURES ON THE STEAMBOAT CREEK BASIN,OREGON: IMPLICATIONS FOR LAND USE AND FISH HABITAT1

ABSTRACT: Steamboat Creek basin is an important source of timber and provides crucial spawning and rearing habitat for anadromous steelhead trout (Oncorhynchus mykiss). Because stream temperatures are near the upper limit of tolerance for the survival of juvenile steelhead, the possible long-term effect of clear-cut logging on stream temperatures was assessed. Twenty-year (1969–1989) records of summer stream temperature and flow from four tributaries and two reaches of Steamboat Creek and Boulder Creek (a nearby unlogged watershed) were analyzed. Logging records for the Steamboat Creek basin and air temperature records also were used in the analysis. A time-series model of the components of stream temperature (seasonal cycle of solar radiation, air temperature, streamflow, an autoregressive term of order 1, and a linear trend variable) was fitted to the water-temperature data. The linear trend variable was significant in all the fitted models except Bend Creek (a tributary fed by cool ground-water discharge) and Boulder Creek. Because no trends in either climate (i.e., air temperature) or streamflow were found in the data, the trend variable was associated with the pre-1969 loss and subsequent regrowth of riparian vegetation and shading canopies.     

MFAM模型在河流水质污染模拟及预测中的应用

文中以时间序列分析为基础，介绍了均值生成函数这一崭新概念，并且经成份因子提取分析推导建立了模拟序列的数字模型（简记为MFAM），经对黄河下游花园口断面的1988-1989年实测水质污染指标溶解氧（DO），氨氧，化学耗氧量（COD），五日生化需氧量（BOD5）等序列模拟，结果表明MFAM模型能较好地模拟河流水质污染指标的变化趋势，拟合平均误差只有5.2-6.4%，MFAM模型应用于预测1990-1991年水质污染指标变化，结果表明预测精度达85%以上，文中最后得出结论：MFAM模型应用于河流污染模拟和预测，是完全可行且十分方便。     

BAYESIAN MODELS OF FORECASTED TIME SERIES1

Bayesian Processor of Forecasts (BPF) combines a prior distribution, which describes the natural uncertainty about the realization of a hydrologic process, with a likelihood function, which describes the uncertainty in categorical forecasts of that process, and outputs a posterior distribution of the process, conditional upon the forecasts. The posterior distribution provides a means of incorporating uncertain forecasts into optimal decision models. We present fundamentals of building BPF for time series. They include a general formulation, stochastic independence assumptions and their interpretation, computationally tractable models for forecasts of an independent process and a first-order Markov process, and parametric representations for normal-linear processes. An example is shown of an application to the annual time series of seasonal snowmelt runoff volume forecasts.     

FRACTIONAL DIFFERENCING MODELING IN HYDROLOGY1

ABSTRACT: Fractional differencing is a tool for modeling time series which have long-term dependence; i.e., series in which the correlation between distant observations, though small, is not negligible. Fractionally differenced ARIMA models are formed by permitting the differencing parameter d in the familiar Box-Jenkins ARIMA(p, d, q) models to take nonintegral values; they permit the simultaneous modeling of the long-term and short-term behavior of an observed time series. This paper discusses the usefulness of fractional differencing to time-series modeling, with emphasis on hydrologic applications. A methodology for fitting fractionally differenced ARIMA models is described, and examples are presented.     

AN EVALUATION OF WEEKLY AND MONTHLY TIME SERIES FORECASTS OF MUNICIPAL WATER USE1

ABSTRACT: A cascade model for forecasting municipal water use one week or one month ahead, conditioned on rainfall estimates, is presented and evaluated. The model comprises four components: long term trend, seasonal cycle, autocorrelation and correlation with rainfall. The increased forecast accuracy obtained by the addition of each component is evaluated. The City of Deerfield Beach, Florida, is used as the application example with the calibration period from 1976–1980 and the forecast period the drought year of 1981. Forecast accuracy is measured by the average absolute relative error (AARE, the average absolute value of the difference between actual and forecasted use, divided by the actual use). A benchmark forecast is calculated by assuming that water use for a given week or month in 1981 is the same as the average for the corresponding period from 1976 to 1980. This method produces an AARE of 14.6 percent for one step ahead forecasts of monthly data and 15.8 percent for weekly data. A cascade model using trend, seasonality and autocorrelation produces forecasts with AARE of about 12 percent for both monthly and weekly data while adding a linear relationship of water use and rainfall reduces the AARE to 8 percent in both cases if it is assumed that rainfall is known during the forecast period. Simple rainfall predictions do not increase the forecast accuracy for water use so the major utility of relating water use and rainfall lies in forecasting various possible water use sequences conditioned on sequences of historical rainfall data.     

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.     

紫外光谱结合正交试验设计同时测定水中苯系物

利用正交试验设计,以光谱预处理、特征筛选及多元校正方法为考察因素,每个因素的4种不同方法为水平,确定了水中3种苯系物（苯酚、苯胺及苯甲酸）紫外光谱数据的最佳分析方法,从而建立了其定量校正模型。对于苯酚、苯胺及苯甲酸,其光谱预处理、特征筛选及多元校正分别采用一阶导数+无信息变量消除法（UVE）+偏最小二乘回归（PLSR）,Savitzky-Golay平滑+变量结合种群分析法（VCPA）+PLSR,Savitzky-Golay平滑+移动窗口偏最小二乘法（MWPLS）+PLSR。在独立测试集上3组分的预测误差均方根（RMSEP）分别为0.809 4、0.796 3和0.945 4。水样加标回收实验的回收率为97.79%~103.84%,相对标准偏差（RSD）小于3%。该方法可作为一种同时测定水中苯系物的简便有效方法。