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Oregon Water Science Center

An Analysis of Statistical Methods for Seasonal Flow Forecasting in the Upper Klamath River Basin of Oregon and California

By John C. Risley, Marshall W. Gannett, Jolyne K. Lea, and Edwin A. Roehl Jr.

Scientific Investigations Report 2005-5177

Prepared in cooperation with the Bureau of Reclamation
and the Natural Resources Conservation Service

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Lake of the Woods, upper Klamath River Basin, Oregon, with Mt. McLaughlin in the background.

 Photo: Lake of the Woods


Water managers in the upper Klamath Basin, located in south-central Oregon and northeastern California, use forecasts of spring and summer streamflow to optimally allocate increasingly limited water supplies for various demands that include irrigation for agriculture, habitat for endangered fishes, and hydropower production. Flow forecasts are made by the Natural Resources Conservation Service using statistical models that use current snow and precipitation data collected at nearby monitoring sites as input. The forecasts for five upper Klamath Basin sites (Williamson River, Sprague River, Upper Klamath Lake, Gerber Reservoir, and Clear Lake Reservoir) are made at the beginning of each month from January through June.

In 2003, the U.S. Geological Survey, the Natural Resources Conservation Service, and the Bureau of Reclamation began a collaborative study to reduce uncertainty and error in seasonal flow forecasting in the upper Klamath Basin. The main objectives included (1) evaluating nonregression statistical modeling approaches, such as artificial neural networks, for their efficacy in reducing model error, (2) finding and evaluating potential model variables that better described long-term climate-trend conditions, and (3) analyzing the efficacy of upper Klamath Basin snow-water equivalent and precipitation data in forecast models.

The modeling approaches evaluated included principal components regression, nonautoregressive artificial neural networks, and autoregressive artificial neural networks. For the Upper Klamath Lake forecast site, the nonautoregressive artificial neural network models had lower error than the other models for the January, February, and March forecasts. However,the principal components regression model performed better for the April forecast. Both models performed roughly the same for the May and June forecasts. For the Sprague River forecast site, the nonautoregressive artificial neural network models performed far better than the other models for the January, February, March, and June forecasts. However, the principal components regression models performed better for the April and May forecasts.

For the Williamson River and Gerber Reservoir forecast sites, the principal components regression models generally, but not always, performed better than the other models. For the Clear Lake Reservoir forecast site, the nonautoregressive artificial neural network models performed far better than the other models for the months of January, February, and March. However, the Clear Lake Reservoir autoregressive artificial neural network model performed better than the other models for the month of April. For the Williamson River, Upper Klamath Lake, and Gerber Reservoir forecast models, the inclusion of new long-term climate-trend variables reduced model error in many, but not all, instances.

The relationships between the upper Klamath Basin snow-water equivalent, precipitation, and flow data were analyzed to determine the ability and the extent to which currentsnow-water equivalent and precipitation conditions can be used to forecast future flow conditions. The analyses were made by decomposing the flow time series into annual periodic, long-term climatic, and chaotic components, and then lag correlating the snow-water equivalent and precipitation time series with the chaotic component time series. After 120 days (approximately 4 months), all of the snow-water equivalent and precipitation correlation coefficients were less than 0.4.

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Purpose and Scope
Study Area
Data Networks
Snow-Water Equivalent
Reservoir Net Inflow
Climate-Trend Variables
Principal Components Regression
Nonautoregressive Artificial Neural Networks
Autoregressive Artificial Neural Networks
Results and Discussion
Model Comparisons
Effect of Long-Term Climate-Trend Variables
Data Limitations in Forecast Modeling
References Cited

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