MULTIPLICATIVE,SEASONAL ARIMA MODELS FOR LAKE ERIE AND LAKE ONTARIO WATER LEVELS1

ABSTRACT: Federal agencies in the U.S. and Canada continuously examine methods to improve understanding and forecasting of Great Lakes water level dynamics in an effort to reduce the negative impacts of fluctuating levels incurred by interests using the lakes. The short term, seasonal and long term water level dynamics of lakes Erie and Ontario are discussed. Multiplicative, seasonal ARIMA models are developed for lakes Erie and Ontario using standardized, monthly mean level data for the period 1900 to 1986. The most appropriate model identified for each lake had the general form: (1 0 1)(0 1 1)₁₂. The data for each lake were subdivided by time periods (1900 to 1942;1 943 to 1986) and the model coefficients estimated for the subdivided data were similar, indicating general model stability for the entire period of record. The models estimated for the full data sets were used to forecast levels 1,2,3, and 6 months ahead for a period of high levels (1984 to 1986). The average absolute forecast error for Lake Erie was 0.049m, 0.076m, 0.091 m and 0.128m for the 1, 2,3, and 6 month forecasts, respectively. The average absolute forecast error for Lake Ontario was 0.058m, 0.095m, 0.120m and 0.136m for the 1,2,3, and 6 month forecasts, respectively. The ARIMA models provide additional information on water level time series structure and dynamics. The models also could be coordinated with current forecasting methods, possibly improving forecasting accuracy.     

MONTHLY RUNOFF PREDICTIONS BASED ON RAINFALL FORECASTS IN A SMALL OKLAHOMA WATERSHED1

ABSTRACT: Conditions under which monthly rainfall forecasts translate into monthly runoff predictions that could support water resources planning and management activities were investigated on a small watershed in central Oklahoma. Runoff response to rainfall forecasts was simulated using the hydrologic model SWAT. Eighteen scenarios were examined that represented combinations of wet, average, and dry antecedent rainfall conditions, with wet, normal, and dry forecasted rainfall. Results suggest that for the climatic and physiographic conditions under consideration, rainfall forecasts could offer potential application opportunities in surface water resources but only under certain conditions. Pronounced wet and dry antecedent rainfall conditions were shown to have greater impact on runoff than forecasts, particularly in the first month of a forecast period. Large forecast impacts on runoff occurred under wet antecedent conditions, when the fraction of forecasted rainfall contributing to runoff was greatest. Under dry antecedent conditions, most of the forecasted rainfall was absorbed in the soil profile, with little immediate runoff response. Persistent three‐month forecasts produced stronger impacts on runoff than one‐month forecasts due to cumulative effects in the hydrologic system. Runoff response to antecedent conditions and forecasts suggest a highly asymmetric utility function for rainfall forecasts, with greatest decision‐support potential for persistent wet forecasts under wet antecedent conditions when the forecast signal is least dampened by soil‐storage effects. Under average and dry antecedent conditions, rainfall forecasts showed little potential value for practical applications in surface water resources assessments.     

EVALUATION OF PRACTICES IN WATER SUPPLY FORECASTING1

ABSTRACT: Snowmelt runoff is a primary source of water supply in much of the Western United States. Multipurpose planning requires long-range forecasts and the accuracy of the forecasts has a significant effect on economic benefits. In an effort to increase the accuracy of snowrnelt runoff forecasts, selected practices in water supply forecasting were evaluated. These practices include 1) using multiple regression in developing forecasting models;2) using a model that was calibrated to make forecasts an April 1 for making forecasts at other times;3) using maximum snow water equivalent measurements in forecast equations; and 4) using weighted snow water equivalent measurements for making forecasts. The results of a case study indicate that forecasting accuracy is significantly affected by these practices. Goodness-of-fit statistics may not be indicative of the accuracy of forecasts when the prediction equations are used to make forecasts for dates other than that used in calibration. The use of maximum snow water equivalentmeasurements and weighted averages did not improve forecast accuracy.     

EFFECTIVENESS OF DROUGHT POLICIES FOR MUNICIPAL WATER MANAGEMENT1

During the 1976–77 drought, three principal mechanisms were used to reduce water use in Utah communities: price increases, maximum monthly use restrictions, and restrictions on outdoor watering times. A regression model was developed to explain observed changes in water use, with price, type of restriction, household size, and summer rainfall as independent variables. For an average system, a 1 percent increase in price would reduce water use by 0.07 to 0.09 percent. A 1 percent increase in outdoor watering time restriction reduces use by 0.064 to 0.075 percent. A 1 percent increase in quantity restrictions leads to a reduction in water use of 0.014 to 0.054 percent. The effectiveness of rationing policies is influenced by system characteristics. For example, outdoor watering time restrictions were less effective in systems with above average household size and below average monthly use.     

THE ACCURACY OF WATER USE FORECASTS: EVALUATION AND IMPLICATIONS1

ABSTRACT: Forecasts of 1980 river basin water use presented in the reports of the 1960 Senate Select Committee on National Water Resources and in the Water Resources Council's First National Water Assessment of 1968 were compared to estimates of actual use in 1980 to assess the accuracy of efforts to forecast future water use. Results show that the majority of the forecasts were substantially in error. In general, the First National Assessment forecasts erred by a smaller margin, but tended to repeat the regional patterns of overestimation (underestimation) exhibited in the Senate Select Committee forecasts. Moreover, forecasts of the two groups that came within 20 percent of the 1980 withdrawals, in general were accurate, not because of superior prediction, but because of offsetting errors in forecast components. This performance leads us to conclude that water use forecasts, regardless of the time-frame or the forecast method employed, are likely to always be highly inaccurate. Accordingly, if such forecasting efforts are to be of value in contemporary water resources planning, forecasters should direct their attention toward methods which will illuminate the determinants of the demand for water.     

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.     

REAL-TIME MANAGEMENT OF WATER QUALITY IN THE SAN JOAQUIN RWER BASIN,CALIFORNIA1

ABSTRACT: In the San Joaquin River Basin, California, a realtime water quality forecasting model was developed to help improve the management of saline agricultural and wetland drainage to meet water quality objectives. Predicted salt loads from the water quality forecasting model, SJRIODAY, were consistently within ± 11 percent of actual, within ± 14 percent for seven-day forecasts, and within ± 26 percent for 14-day forecasts for the 16- month trial period. When the 48 days dominated by rainfall/runoff events were eliminated from the data set, the error bar decreased to ± 9 percent for the model and ± 11 percent and ± 17 percent for the seven-day and 14-day forecasts, respectively. Constraints on the use of the model for salinity management on the San Joaquin River include the number of entities that control or influence water quality and the lack of a centralized authority to direct their activities. The lack of real-time monitoring sensors for other primary constituents of concern, such as selenium and boron, limits the application of the model to salinity at the present time. A case study describes wetland drainage releases scheduled to coincide with high river flows and significant river assimilative capacity for salt loads.     

FORECAST UNCERTAINTY IN WATER SUPPLY RESERVOIR OPERATION1

ABSTRACT: This research investigates the benefits of forecasting in water supply systems. Questions relating operational losses to forecast period and accuracy are addressed. Some simple available forecasting techniques are assessed for their accuracy and applicability. These issues are addressed through the use of a simulation model of the Cedar and South Fork Tolt Rivers, where the system is modeled as a single purpose reservoir supplying municipal and industrial water to the Seattle metropolitan area. The following conclusions were made for this system: (1) reservoir operation deteriorates markedly with the loss of forecast accuracy; (2) the optimal length of forecasting period is five months; (3) reservoir operation may be improved by as much as 88 percent if perfect predictive abilities are available; (4) the mean of the historic data is not recommended to predict future flows because Markov methods are always superior; and (5) lag-one autoregressive Markov schemes exhibit about a 9 percent improvement in operation over no forecasting.     

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.     

DEVELOPMENT AND TESTING OF A SNOWMELT-RUNOFF FORECASTING TECHNIQUE1

ABSTRACT: The snowmelt-runoff model (SRM) was used to produce accurate simulations of streamfiow during the snowmelt period (April-September) for ten years on the Rio Grande Basin (3419 km²) near Del Norte, Colorado, U.S.A. In order to use SRM in the forecast situation, it was necessary to develop a family of snow cover depletion curves for each elevation zone based on accumulated snow water equivalent on April 1. Selection of an appropriate curve for a particular year from snow course measurements allows input of the daily snow cover extent to SRM for forecast purposes. Data from three years (1980, 1981, and 1985) were used as a quasi-forecast test of the procedure. In these years forecasted snow cover extent data were input to SRM, but observed temperature and precipitation data were used. The resulting six-month hydrographs were very similar to the hydrographs in the ten simulation years previously tested based on comparisons of performance evaluation criteria. Based on this result, the Soil Conservation Service (SCS) requested SRM forecasts for 1987 on the Rio Grande. Using the same procedure but with SCS estimated temperature and precipi-tation data, SRM produced a forecast hydrograph that had a r²= 0.82 and difference in seasonal volume of 4.4 percent. To approximate actual operational conditions, SRM computed daily flows were updated every seven days with measured flows. The resulting forecast hydrograph had a R²= 0.90 and a difference in volume of 3.5 percent. The method developed needs to be refined and tested on additional years and basins, but the approach appears to be applicable to operational runoff forecasting using remote sensing data.     

Daily Updating of Operational Statistical Seasonal Water Supply Forecasts for the western U.S.1

Abstract: Official seasonal water supply outlooks for the western United States are typically produced once per month from January through June. The Natural Resources Conservation Service has developed a new outlook product that allows the automated production and delivery of this type of forecast year‐round and with a daily update frequency. Daily snow water equivalent and water year‐to‐date precipitation data from multiple SNOTEL stations are combined using a statistical forecasting technique (“Z‐Score Regression”) to predict seasonal streamflow volume. The skill of these forecasts vs. lead‐time is comparable to the official published outlooks. The new product matches the intra‐monthly trends in the official forecasts until the target period is partly in the past, when the official forecasts begin to use information about observed streamflows to date. Geographically, the patterns of skill also match the official outlooks, with highest skill in Idaho and southern Colorado and lowest skill in the Colorado Front Range, eastern New Mexico, and eastern Montana. The direct and frequent delivery of objective guidance to users is a significant new development in the operational hydrologic seasonal forecasting community.     

Developing Subseasonal to Seasonal Climate Forecast Products for Hydrology and Water Management

We describe a new effort to enhance climate forecast relevance and usability through the development of a system for evaluating and displaying real‐time subseasonal to seasonal (S2S) climate forecasts on a watershed scale. Water managers may not use climate forecasts to their full potential due to perceived low skill, mismatched spatial and temporal resolutions, or lack of knowledge or tools to ingest data. Most forecasts are disseminated as large‐domain maps or gridded datasets and may be systematically biased relative to watershed climatologies. Forecasts presented on a watershed scale allow water managers to view forecasts for their specific basins, thereby increasing the usability and relevance of climate forecasts. This paper describes the formulation of S2S climate forecast products based on the Climate Forecast System version 2 (CFSv2) and the North American Multi‐Model Ensemble (NMME). Forecast products include bi‐weekly CFSv2 forecasts, and monthly and seasonal NMME forecasts. Precipitation and temperature forecasts are aggregated spatially to a United States Geological Survey (USGS) hydrologic unit code 4 (HUC‐4) watershed scale. Forecast verification reveals appreciable skill in the first two bi‐weekly periods (Weeks 1–2 and 2–3) from CFSv2, and usable skill in NMME Month 1 forecast with varying skills at longer lead times dependent on the season. Application of a bias‐correction technique (quantile mapping) eliminates forecast bias in the CFSv2 reforecasts, without adding significantly to correlation skill.     

APPLICATION OF GREY MODEL TOWARD RUNOFF FORECASTING1

ABSTRACT: A reliable forecasting model is essential in real‐time flood forecasting for reducing natural damage. Efforts to develop a real‐time forecasting model over the past two decades have been numerous. This work applies the Grey model to forecast rainfall and runoff owing to the model's relative ability to predict the future using a small amount of historical data. Such a model significantly differs from the stochastic and deterministic models developed previously. Ten historical storm events from two catchment areas in northern Taiwan are selected to calibrate and verify the model. Results in this study demonstrate that the proposed models can reasonably forecast runoff one to four hours ahead, if the Grey error prediction method is further used to update the output of the model.     

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.     

LONG-RANGE STREAMFLOW FORCASTING USING NONPARAMETRIC REGRESSION1

ABSTRACT: A class of nonparametric procedures is developed for producing long-range streamflow forecasts. The forecasting procedures, which are based solely on daily streamflow data, utilize nonparametric regression to relate a forecast variable to a covariate variable. The forecast variable is a function of future streamflow and can take a wide variety of forms. The covariate variable is a function of antecedent streamflow. The forecasting procedures are quite flexible, both in terms of the duration of the forecast period and the types of forecast variables that can be considered. The procedures are used to develop long-term (1–4 months) forecasts of minimum daily flow of the Potomac River at Washington, D.C. This forecast information is an integral component of water management activities for the Washington, D.C. metropolitan area.     

Mid‐Range Streamflow Forecasts Based on Climate Modeling – Statistical Correction and Evaluation1

Abstract: Mid‐range streamflow predictions are extremely important for managing water resources. The ability to provide mid‐range (three to six months) streamflow forecasts enables considerable improvements in water resources system operations. The skill and economic value of such forecasts are of great interest. In this research, output from a general circulation model (GCM) is used to generate hydrologic input for mid‐range streamflow forecasts. Statistical procedures including: (1) transformation, (2) correction, (3) observation of ensemble average, (4) improvement of forecast, and (5) forecast skill test are conducted to minimize the error associated with different spatial resolution between the large‐scale GCM and the finer‐scale hydrologic model and to improve forecast skills. The accuracy of a streamflow forecast generated using a hydrologic model forced with GCM output for the basin was evaluated by forecast skill scores associated with the set of streamflow forecast values in a categorical forecast. Despite the generally low forecast skill score exhibited by the climate forecasting approach, precipitation forecast skill clearly improves when a conditional forecast is performed during the East Asia summer monsoon, June through August.     

ANN OUTPUT UPDATING OF LUMPED CONCEPTUAL RAINFALL/RUNOFF FORECASTING MODELS1

ABSTRACT: Artificial neural networks (ANNs) are tested for the output updating of one‐day‐ahead and three‐day‐ahead streamflow forecasts derived from three lumped conceptual rainfall/runoff (R‐R) models: the GR4J, the IHAC, and the TOPMO. ANN output updating proved superior to a parameter updating scheme and to the ‘simple’ output updating scheme, which always replicates the last observed forecast error. In fact, ANN output updating was able to compensate for large differences in the initial performance of the three tested lumped conceptual R‐R models, which the other tested updating approaches were not able to achieve. This is done mainly by incorporating input vectors usually exploited for ANN R‐R modeling such as previous rainfall and streamflow observations, in addition to the previous observed error. For one‐day‐ahead forecasts, the performance of all three lumped conceptual R‐R models, used in conjunction with ANN output updating, was equivalent to that of the ANN R‐R model. For three‐day‐ahead forecasts, the performance of the ANN‐output‐updated conceptual models was even superior to that of the ANN R‐R model, revealing that the conceptual models are probably performing some tasks that the ANN R‐R model cannot map. However, further testing is needed to substantiate the last statement.     

Near-term forecasts of stream temperature using deep learning and data assimilation in support of management decisions

Deep learning (DL) models are increasingly used to make accurate hindcasts of management-relevant variables, but they are less commonly used in forecasting applications. Data assimilation (DA) can be used for forecasts to leverage real-time observations, where the difference between model predictions and observations today is used to adjust the model to make better predictions tomorrow. In this use case, we developed a process-guided DL and DA approach to make 7-day probabilistic forecasts of daily maximum water temperature in the Delaware River Basin in support of water management decisions. Our modeling system produced forecasts of daily maximum water temperature with an average root mean squared error (RMSE) from 1.1 to 1.4°C for 1-day-ahead and 1.4 to 1.9°C for 7-day-ahead forecasts across all sites. The DA algorithm marginally improved forecast performance when compared with forecasts produced using the process-guided DL model alone (0%–14% lower RMSE with the DA algorithm). Across all sites and lead times, 65%–82% of observations were within 90% forecast confidence intervals, which allowed managers to anticipate probability of exceedances of ecologically relevant thresholds and aid in decisions about releasing reservoir water downstream. The flexibility of DL models shows promise for forecasting other important environmental variables and aid in decision-making.     

WATER RESOURCE MANAGEMENT AND DROUGHT FORECASTS IN SOUTH CAROLINA1

ABSTRACT: Despite potential benefits for resource planning, community water systems managers have not used seasonal climate forecasts extensively. Obstacles to forecast use include a lack of awareness of their existence, distrust of their accuracy, perceived irrelevance to management decisions, and competition from other technological innovations. In this paper, ways in which seasonal forecasts might be extended to address more directly some concerns of South Carolina community water systems managers are explored. From May 1998 through August 2002, this group experienced drought conditions that threatened water quality and supply and required restrictions on water consumption. Methods for incorporating long lead forecasts with joint probabilities of monthly temperature and precipitation to produce drought forecasts are demonstrated. When tailored to specific places, such forecasts show the likelihood of exceeding drought thresholds that would trigger water use restrictions. The methods illustrate how long lead forecasts can be extended and customized into secondary products that address issues of greater relevance to water resource managers.     

A MONTHLY TIME SERIES MODEL OF MUNICIPAL WATER DEMAND1

A multivariate time series model is formulated to study monthly variations in municipal water demand. The left hand side variable in the multivariate regression model is municipal water demand (gallons per connection per day) and the right hand side contains (explanatory) variables which include price (constant dollars), average temperature, total precipitation, and percentage of daylight hours. The application of the regression model to Salt Lake City Water Department data produced a high multiple correlation coefficient and F-statistic. The regression coefficients for the right hand side variables all have the appropriate sign. In an ex post forecast, the model accurately predicts monthly variations in municipal water demand. The proposed monthly multivariate model is not only found useful for forecasting water demand, but also useful for predicting and studying the impact of nonstructural management decisions such as the effect of price changes, peak load pricing methods, and other water conservation programs.