Developing and testing temperature models for regulated systems: A case study on the Upper Delaware River

Summary Water temperature is an important driver of many processes in riverine ecosystems. If reservoirs are present, their releases can greatly influence downstream water temperatures. Models are important tools in understanding the influence these releases may have on the thermal regimes of downstream rivers. In this study, we developed and tested a suite of models to predict river temperature at a location downstream of two reservoirs in the Upper Delaware River (USA), a section of river that is managed to support a world-class coldwater fishery. Three empirical models were tested, including a Generalized Least Squares Model with a cosine trend (GLScos), AutoRegressive Integrated Moving Average (ARIMA), and Artificial Neural Network (ANN). We also tested one mechanistic Heat Flux Model (HFM) that was based on energy gain and loss. Predictor variables used in model development included climate data (e.g., solar radiation, wind speed, etc.) collected from a nearby weather station and temperature and hydrologic data from upstream U.S. Geological Survey gages. Models were developed with a training dataset that consisted of data from 2008 to 2011; they were then independently validated with a test dataset from 2012. Model accuracy was evaluated using root mean square error (RMSE), Nash Sutcliffe efficiency (NSE), percent bias (PBIAS), and index of agreement ( d ) statistics. Model forecast success was evaluated using baseline-modified prime index of agreement (md) at the one, three, and five day predictions. All five models accurately predicted daily mean river temperature across the entire training dataset (RMSE = 0.58–1.311, NSE = 0.99–0.97, d  = 0.98–0.99); ARIMA was most accurate (RMSE = 0.57, NSE = 0.99), but each model, other than ARIMA, showed short periods of under- or over-predicting observed warmer temperatures. For the training dataset, all models besides ARIMA had overestimation bias (PBIAS = −0.10 to −1.30). Validation analyses showed all models performed well; the HFM model was the most accurate compared other models (RMSE = 0.92, both NSE = 0.98, d  = 0.99) and the ARIMA model was least accurate (RMSE = 2.06, NSE = 0.92, d  = 0.98); however, all models had an overestimation bias (PBIAS = −4.1 to −10.20). Aside from the one day forecast ARIMA model (md = 0.53), all models forecasted fairly well at the one, three, and five day forecasts (md = 0.77–0.96). Overall, we were successful in developing models predicting daily mean temperature across a broad range of temperatures. These models, specifically the GLScos, ANN, and HFM, may serve as important tools for predicting conditions and managing thermal releases in regulated river systems such as the Delaware River. Further model development may be important in customizing predictions for particular biological or ecological needs, or for particular temporal or spatial scales.

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