Modeling of water temperatures based on stochastic approaches: case study of the Deschutes River

Water temperature is an important physical variable in aquatic ecosystems. It can affect both chemical and biological processes such as dissolved oxygen concentration and both the metabolism and growth of aquatic organisms. For water resource management, stream water temperature models that can accurately reproduce the essential statistical characteristics of historical data can be very useful. The present study deals with the modeling in the Deschutes River of average weekly maximum temperature (AWMT) series using univariate stochastic approaches. Autoregressive (AR) and periodic autoregressive (PAR) models were used to model AWMT data. The AR model consisted of decomposing water temperature data into a long-term annual component and a residual component. The long-term annual component was modeled by fitting a sine function to the time series, while the residuals representing the departure from the long-term annual component were modeled using a Markov chain process. The PAR model was applied to the standardized data obtained by subtracting the AWMT series from interannual mean of each period. To test the performance of the above models, the leave-one-out (Jackknife) technique was used. The results indicated that both models have good predictive ability for a relatively large system such as the Dechutes River. On an annual basis from 1963 to 1980, the average root mean square error varied between 0.81 and 0.90 degrees C for AR(1) and PAR(1), respectively, and the mean bias remained near 0 degrees C. Averaged Nash-Sutcliffe coefficient of efficiency (NSC) values obtained by AR (0.94) and PAR (0.92) models were close and comparable. Of the two models, the PAR(1) model seemed the most promising based on its performance and ability to model periodicity in autocorrelations. Since no exogenous variables such as air temperatures and streamflow were incorporated, the use of the PAR model limits the managerial decisions in natural streams and rivers.