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.     

A Simple Framework for Incorporating Seasonal Streamflow Forecasts into Existing Water Resource Management Practices1

Gong, Gavin, Lucien Wang, Laura Condon, Alastair Shearman, and Upmanu Lall, 2010. A Simple Framework for Incorporating Seasonal Streamflow Forecasts Into Existing Water Resource Management Practices. Journal of the American Water Resources Association (JAWRA) 46(3):574-585. DOI: 10.1111/j.1752-1688.2010.00435.x Abstract: Climate-based streamflow forecasting, coupled with an adaptive reservoir operation policy, can potentially improve decisions by water suppliers and watershed stakeholders. However, water suppliers are often wary of straying too far from their current management practices, and prefer forecasts that can be incorporated into existing system modeling tools. This paper presents a simple framework for utilizing streamflow forecasts that works within an existing management structure. Climate predictors are used to develop seasonal inflow forecasts. These are used to specify operating rules that connect to the probability of future (end of season) reservoir states, rather than to the current storage, as is done now. By considering both current storage and anticipated inflow, the likelihood of meeting management goals can be improved. The upper Delaware River Basin in the northeastern United States is used to demonstrate the basic idea. Physically plausible climate-based forecasts of March-April reservoir inflow are developed. Existing simulation tools and rule curves for the system are used to convert the inflow forecasts to reservoir level forecasts. Operating policies are revised during the forecast period to release less water during forecasts of low reservoir level. Hindcast simulations demonstrate reductions of 1.6% in the number of drought emergency days, which is a key performance measure. Forecasts with different levels of skill are examined to explore their utility.     

Multireservoir real-time operations for flood control using balanced water level index method

This paper presents a real-time simulation-optimization operation procedure for determining the reservoir releases at each time step during a flood. The proposed procedure involves two models, i.e., a hydrological forecasting model and a reservoir operation model. In the reservoir operation model, this paper compares two flood-control operation strategies for a multipurpose multireservoir system. While Strategy 1 is the real-time joint reservoir operations without using the balanced water level index (BWLI) method, Strategy 2 involves real-time joint reservoir operations using the BWLI method. The two strategies presented are formulated as mixed-integer linear programming (MILP) problems. The idea of using the BWLI method is derived from the HEC-5 program developed by the US Army Corps of Engineers. The proposed procedure has been applied to the Tanshui River Basin system in Taiwan using the 6h ahead forecast data of six typhoons. A comparison of the results obtained from the two strategies reveals that Strategy 2 performs much better than Strategy 1 in determining the reservoir real-time releases throughout the system during flood emergencies in order to minimize flooding, while maintaining all reservoirs in the system in balance if possible. Consequently, the proposed model using the BWLI method demonstrates its effectiveness in estimating real-time releases.     

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.     

THE VALUE OF STREAMFLOW FORECASTING IN RESERVOIR OPERATION1

ABSTRACT: The value of streamflow forecasts in reservoir operation depends on a number of factors and may vary considerably. Assessment of forecast benefits is presented here for three specific systems. Statistical streamflow models of increasing forecasting ability are coupled with a recently developed stochastic control method in extensive simulation experiments. The performance of the system is statisticafly evaluated with regard to energy generation and flood and drought prevention. The results indicate that forecast benefits are system specific and may range from quite substantial to fairly minimal.     

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.     

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.     

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.     

Joint operation rules considering the uncertainty of energy available for multiple cascaded hydropower system

Multi-reservoir operation rules have been widely used in practice operation. The operation rules are often derived from historical or simulated run-off information through implicit stochastic optimization or parameterization-simulation-optimization. The output decisions of operation rules are usually obtained without considering inflow forecasting or using perfect runoff forecast information, which is hardly implemented in practical applications. This paper proposes robust joint operation rules for multiple cascaded reservoirs considering the uncertainty of energy available. The rule parameters are optimized using multi-step genetic algorithm for minimum-power maximization. A case study for a three-cascaded-reservoirs system shows that, compared with deterministic joint operation rules, the accuracy of energy available estimation of joint operation rules is increased by 2.3%, considering inflow uncertainty. The simulated minimum-power decision of joint operation rules considering the uncertainty of energy available is 40.4% higher than that of determinate joint operation rules. Results indicate that there is a possibility of obtaining greater and more effective power decisions through the joint operation rules considering the uncertainty of available energy.     

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.     

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.     

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.     

TRENDS IN FRESHWATER INFLOW TO SAN FRANCISCO BAY FROM TUE SACRAMENTO-SAN JOAQUIN DELTA1

ABSTRACT: Outflow from the Sacramento-San Joaquin river system (Delta outflow) provides about 90 percent of the freshwater flow to San Francisco Bay. Because this river system also supplies most of the water used in California, some believed that annual freshwater flow to the Bay had declined by as much as 50 to 60 percent as water use increased. Consequently, we studied trends in actual Delta outflow and precipitation for the period 1921 to 1986, which is when Delta outflow data are available. We found that there has been no decrease in the annual Delta outflow over this period. In fact, a statistically significant increase in annual Delta outflow of 87 cfa/yr has occurred during the period 1921 to 1986. One reason that Delta outflow has increased is because precipitation has increased faster than water use. Other contributing factors include increased runoff from land use changes, water imports from other areas, and the redistribution of ground water. In addition, statistically significant seasonal trends in Delta outflow were found. Over the period 1921–1986 Delta outflow decreased in April and May and increased from July through November. Changes in other months were not statistically significant. These seasonal changes result primarily from the operation of upstream flood control and water development projects, which store water in the spring and release it in the summer and fall. These seasonal changes are also influenced by a climatic shift that has decreased spring snowmelt runoff and increased late summer through winter precipitation.     

A Streamflow Forecasting Framework using Multiple Climate and Hydrological Models1

Abstract: Water resources planning and management efficacy is subject to capturing inherent uncertainties stemming from climatic and hydrological inputs and models. Streamflow forecasts, critical in reservoir operation and water allocation decision making, fundamentally contain uncertainties arising from assumed initial conditions, model structure, and modeled processes. Accounting for these propagating uncertainties remains a formidable challenge. Recent enhancements in climate forecasting skill and hydrological modeling serve as an impetus for further pursuing models and model combinations capable of delivering improved streamflow forecasts. However, little consideration has been given to methodologies that include coupling both multiple climate and multiple hydrological models, increasing the pool of streamflow forecast ensemble members and accounting for cumulative sources of uncertainty. The framework presented here proposes integration and offline coupling of global climate models (GCMs), multiple regional climate models, and numerous water balance models to improve streamflow forecasting through generation of ensemble forecasts. For demonstration purposes, the framework is imposed on the Jaguaribe basin in northeastern Brazil for a hindcast of 1974‐1996 monthly streamflow. The ECHAM 4.5 and the NCEP/MRF9 GCMs and regional models, including dynamical and statistical models, are integrated with the ABCD and Soil Moisture Accounting Procedure water balance models. Precipitation hindcasts from the GCMs are downscaled via the regional models and fed into the water balance models, producing streamflow hindcasts. Multi‐model ensemble combination techniques include pooling, linear regression weighting, and a kernel density estimator to evaluate streamflow hindcasts; the latter technique exhibits superior skill compared with any single coupled model ensemble hindcast.     

APPLICATION OF A SINGLE RESERVOIR OPERATION POLICY TO A RAIN WATER CISTERN SYSTEM1

The operation policy for a single reservoir is applied to a rain water cistern system because the functions of a cistern are similar to a simple single reservoir. Since the cistern is a closed system, water loss is negligible. In this study, a dynamic programming analysis has been made to study the effects of the probable weekly rainfall and the water storage in the cistern towards the water consumption policy. The result of this study indicates that the water consumption rate should be adjusted into a lower rate when the water storage in the cistern is low and/or when the expected probable weekly rainfall is low if the owner of the cistern does not want to risk the chance of an empty cistern. The demand for a reliable method for forecasting weekly rainfall is evident in this study.     

HYDROLOGIC ENGINEERING TECHNIQUES FOR REGIONAL WATER RESOURCES PLANNING1

The emphasis upon comprehensive regional water resources planning in the past decade has encouraged the hydrologic engineer to take advantage of improvements in technology to develop new hydrologic engineering techniques for use in regional planning studies. The new techniques are necessary because the traditional hydro-logic engineering techniques are not always consistent with the increased scope and diversified objectives of regional planning studies. The Hydrologic Engineering Center has been involved in aiding in the development of some of these new techniques as the result of studies that have been made in cooperation with other Corps of Engineers offices. Most of the new techniques being developed emphasize computational procedures developed specifically for use with electronic computers. Applications of new techniques range from framework studies to planning of day-to-day operation criteria. Studies recently completed or in progress include: (1) development of a regional flood control site screening plan for the North Atlantic Region study; (2) use of streamflow simulation for planning and operation of the Missouri River mainstem projects; (3) development of an operation plan for the Arkansas-White-Red Rivers Reservoir System; (4) standard project flood and flood frequency estimates for the Colorado River Basin Framework Study; and several other projects which are described in more detail in the following paragraphs. One of the initial efforts in regional analysis was the formulation of procedures for determining standard project flood estimates for southern California coastal streams using generalized criteria. Techniques were developed that were readily adaptable to the computer and which would determine representative unit hydrographs, losses and standard project precipitation for any location in the study area. The resulting standard project flood estimates were consistent with the accuracy required for framework studies; however, they could be refined easily for design studies. As a result of the recent drought in the Northeastern United States, a study was made to evaluate both present and future water supply reservoirs in that region. The study consisted of computerized studies of the hypothetical operation of a large number of reservoirs as a system. The reservoirs were on many different streams throughout the region and had varying constraints, depending upon the stream and the state in which the reservoir was located. Since only preliminary data was available on the proposed reservoirs, it was not possible to refine the studies to a large degree. However, the models of each system can be easily refined as more accurate design data become available. The development of a computer-aided screening procedure for use in evaluating several hundred potential reservoir sites for the Missouri River Basin Comprehensive Framework Study is a third example of regional analysis. The adopted procedures used available physical, hydrologic, and climatologic data in estimating reservoir storage requirements throughout the basin. Because the procedure is based upon the techniques often used in more refined studies, it is expected that the results of the screening study will be very useful in future planning and design work. Shortcomings of some of the traditional techniques have helped in the development of new techniques. For maximum usefulness the new techniques should: (1) be consistent with the scope, objectives, and requirements of the overall study; (2) use all available physical, hydrologic, and climatologic data without requiring extensive data which may not be available; (3) take full advantage of the capabilities of the computer and associated data processing systems; and (4) produce results which form a firm basis for future, more detailed, planning and design studies instead of being limited in usefulness largely to the study at hand.     

RESERVOIR OPERATION ANI EVALUATION OF DOWNSTREAM FLOW AUGMENTATION1

ABSTRACT: Operation of a storage‐based reservoir modifies the downstream flow usually to a value higher than that of natural flow in dry season. This could be important for irrigation, water supply, or power production as it is like an additional downstream benefit without any additional investment. This study addresses the operation of two proposed reservoirs and the downstream flow augmentation at an irrigation project located at the outlet of the Gandaki River basin in Nepal. The optimal operating policies of the reservoirs were determined using a Stochastic Dynamic Programming (SDP) model considering the maximization of power production. The modified flows downstream of the reservoirs were simulated by a simulation model using the optimal operating policy (for power maximization) and a synthetic long‐term inflow series. Comparing the existing flow (flow in river without reservoir operation) and the modified flow (flow after reservoir operation) at the irrigation project, the additional amount of flow was calculated. The reliability analysis indicated that the supply of irrigation could be increased by 25 to 100 percent of the existing supply over the dry season (January to April) with a reliability of more than 80 percent.     

A STOCHASTIC DYNAMIC PROGRAMMING MODEL FOR THE OPTIMUM OPERATION OF A MULTI-PURPOSE RESERVOIR1

ABSTRACT: The main objective of this paper is to present a stockastic dynamic programming model useful in determining the optimal operating policy of a single multipurpose surface reservoir. It is the unreliability of forecasting the amount of future streamflow which makes the problem of a reservoir operation a stochastic process. In this paper the stochastic nature of the streamflow is taken into account by considering the correlation between the streamflows of each pair of consecutive time intervals. This interdependence is used to calculate the probability of transition from a given state and stage to its succeeding ones. A dynamic programming model with a physical equation and a stochastic recursive equation is developed to find the optimum operational policy. For illustrative purposes, the model is applied to a real surface water reservoir system.     

PREDICTING FECAL COLIFORM BACTERIA LEVELS IN THE CHARLES RIVER,MASSACHUSETTS, USA1

In Massachusetts, the Charles River Watershed Association conducts a regular water quality monitoring and public notification program in the Charles River Basin during the recreational season to inform users of the river's health. This program has relied on laboratory analyses of river samples for fecal coliform bacteria levels, however, results are not available until at least 24 hours after sampling. To avoid the need for laboratory analyses, ordinary least squares (OLS) and logistic regression models were developed to predict fecal coliform bacteria concentrations and the probabilities of exceeding the Massachusetts secondary contact recreation standard for bacteria based on meteorological conditions and streamflow. The OLS models resulted in adjusted R²s ranging from 50 to 60 percent. An uncertainty analysis reveals that of the total variability of fecal coliform bacteria concentrations, 45 percent is explained by the OLS regression model, 15 percent is explained by both measurement and space sampling error, and 40 percent is explained by time sampling error. Higher accuracy in future bacteria forecasting models would likely result from reductions in laboratory measurement errors and improved sampling designs.     

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.