Non-Linear Operational Volumetric Forecasting
* Can nonlinear regressive forecasts improve volumetric water prediction and allow for quantitative uncertainty estimates about those predictions?
Reclamation regional and area office managers are often faced with decisions that rely on water availability information. Future water availability is a direct function of the hydrologic conditions that are present at the time of the forecast as well as what is going to happen in the future. The current state of the practice (within the Pacific Northwest (PN) Region, specifically) is to use linear regression models developed decades ago which often rely on assuming that everything that is going to happen in the future will be the "average" of the historical record.
Further, forecasts are made with respect to only one time interval at any site. This research will attempt to improve on current technology and will allow Reclamation to use water more effectively.
Need and Benefit
The PN Region currently relies on in-house linear regression models developed in the 1960s to make volumetric water supply forecasts. These methods use four or fewer independent variables to make forecasts. Each independent variable is itself a matrix of data comprised of snowtell sites, rain gages, and streamflow gages for various months during the year. If a forecast is being made before all of the information within the matrix is available the historical "average" conditions are used to fill in the matrix. The format of the independent variables violates independence assumptions inherent in the regression model.
Further, at any given forecast location, only one time period is forecast (e.g., October through July). If a volumetric forecast is needed in May, an October through July forecast is made and the water that has already run off up to May is subtracted from the forecast, resulting in a May through July forecast. For these two reasons, only one time period and assumed average conditions, the residuals produced by the forecasts are heteroscedastic, biased, and highly non-normally distributed; therefore, uncertainty estimates about the volumetric forecast are difficult to make. The tools in use to make forecasts that were developed approximately forty years ago are highly inflexible to adjust forecasts to a historical record which is, at most sites, twice as long as when the linear regression equations were initially developed. Credit is due to the operators of the models and managers whose personal experience leads to forecasts from which to make decisions. If, however, this experience is lost or quantitative assessments of uncertainty are desired (which they are), then a new forecast technique is necessary.
Reclamation water managers are forced to make decisions on water availability that will affect water users and stakeholders at various points throughout the water year. These decisions are based on forecasts of water availability. It is necessary that they be given an adequate, scientifically justifiable description of these forecasts which require characterizations of probabilities associated with the forecast estimates. The current procedure is incapable of providing these features even with the experience and judgment of the model operators and new tool development is required.
The PN Region desires further development of the forecast tools and has been intricately involved in the development of this proposal. There is a need for smooth transitions from the techniques which are currently in use and the next generation of forecast techniques. The end users and stakeholders must be comfortable with the new techniques and must understand the meaning and scope of probabilistic estimates of volumetric forecasts.
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