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U.S. GEOLOGICAL SURVEY
Scientific Investigations Report 2008-5070

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Water-Temperature Model Calibration and Testing

A simulation period from April 1 through October 31, 2005, was used to calibrate the water-temperature model for the Roza–Prosser Reach. Daily mean water temperature data used to calibrate the model were obtained for Hydromet gaging stations at Parker, and at Grandview. Daily maximum water temperature data were obtained for sites maintained by the Bureau of Reclamation (fig. 12) where small temperature sensors (TidbiTs) were installed. Monthly distributions of weather variables measured at the AgriMet weather station (Harrah) that were used as model input during the calibration period are shown in figure 13. Weather coefficients in the SNTEMP program control file, which can be set to systematically increase or decrease the magnitude of SNTEMP climate input data (air temperature, wind speed, relative humidity, and solar radiation) by a user-specified percentage, were adjusted to obtain the best agreement between simulated and measured water temperature. The best agreement was obtained when the coefficients for air temperature, wind speed, and relative humidity were set to 1.0 and the coefficient for solar radiation set to 0.95. Because adjustments to Manning’s N did not produce better agreement between simulated and measured water temperatures, Manning’s N was left at the original value of 0.04.

The two statistics used for assessing the goodness-of-fit between simulated and measured water temperatures at the calibration and testing sites were root mean squared error (RMSE) and mean error. RMSE is the standard deviation of the simulated water-temperature values about the measured water-temperature values. For example, a RMSE value of 1.4°C for the Mabton site for the calibration simulation period indicates that approximately 68 percent of the simulated daily maximum water temperatures are within one standard deviation (+1.4°C) of the measured daily maximum water temperatures at Mabton, 95 percent are within two standard deviations (+2.7°C), and 99 percent are within three standard deviations (+3.6°C). RMSE is a measure of how accurately the model simulates water temperature; the lower the RMSE, the more accurate the simulations. The RMSE was calculated using the following steps: (1) subtracting simulated from measured water temperatures for each day of the period of interest (which could be a week, a month, or the entire simulation period) and squaring the differences (so that negative values do not cancel positive values), (2) sum all squared differences and divide by the number of days in the period of interest, and (3) take the square root of the value calculated in step 2 to get the RMSE.

Mean error is the average error of a number of observations by taking the mean value of the positive and negative errors without regard to sign. Therefore, mean error can be positive or negative and is an indicator of bias in simulation results. For example, if the mean error for the TidbiT site at Mabton is –0.8ºC, then on average, the model simulated daily maximum water temperatures that were 0.8ºC lower than the measured daily maximum water temperature at Mabton. Ideally, mean error should be zero, meaning that the model over-simulates and under-simulates water temperature equally and, therefore, has no bias. Possible reasons for bias in the calibration and testing simulations are discussed in section, “Limitations of Water-Temperature Model”. Mean error is calculated by subtracting the measured daily (mean or maximum) water temperature from the simulated daily (mean or maximum) water temperature for the period of interest, summing the differences, and then dividing the summed differences by the number of days in the period of interest. Table 7 shows the goodness-of-fit statistics for the five calibration sites of the final calibration simulation. Simulated and measured daily mean water temperatures for the calibration period at two Hydromet gaging stations are shown in figure 14. Simulated and measured daily maximum water temperatures at three TidbiT sites maintained by Bureau of Reclamation are shown in figure 15.

A simulation period from April 1 through October 31, 2006, was used to test the water-temperature model for the Roza–Prosser Reach. Daily mean water temperature data for testing were obtained from Hydromet gaging stations at Parker and Grandview, Washington, which were the same sites used to obtain data for the calibration simulation. Daily maximum water temperature data were obtained for three TidbiT sites maintained by the Bureau of Reclamation (fig. 12). The Mabton TidbiT site also was used to obtain data for the calibration simulations; however, data from TidbiT sites at Harlin Landing and Wapato were used only for the testing simulation. Monthly distributions of weather variables used as model input during the testing period measured at the AgriMet weather station (Harrah) are shown in figure 16. Model parameters were not adjusted for the testing simulation.

The goodness-of-fit statistics for the testing simulation at two Hydromet gaging stations and three TidbiT sites are shown in table 8. Graphs of simulated and measured daily mean water temperature for the calibration period at two Hydromet gages are shown in figure 17. Graphs of simulated and measured daily maximum water temperatures at three TidbiT sites maintained by the Bureau of Reclamation are shown in figure 18.

The graphs in figures 17 and 18 show that the Roza–Prosser Reach model simulates seasonal patterns in measured daily mean and maximum water temperatures at the testing sites indicating that flows generally are characterized correctly and the model is responding correctly to meteorological inputs. The RMSE for the testing simulation sites ranged from 1.6 to 2.2°C and mean error ranged from –1.3 to 1.6°C; whereas, RMSE for the calibration simulation sites range from 1.3 to 1.9°C and mean error ranged from 0.1 to 1.3°C, showing that the model is capable of simulating water temperature for growing seasons with differing flow and climate conditions with generally the same degree of accuracy.

Monthly RMSE and mean error values were calculated for the testing sites to investigate seasonal patterns in simulation error. Statistics were not generated for October because data for October from the TidbiT site contained errors. Monthly goodness-of-fit statistics for the testing sites are shown in table 9.

The mean error shows a general seasonal pattern where the model over-predicts water temperature from April through June of the simulation period and obtains greater accuracy or under-predicts water temperature from July through September (table 9). The seasonal pattern in error also can be seen in figures 17 and 18. This seasonal bias may indicate model sensitivity to air temperature, possibly caused by underestimating flow in the system resulting in less thermal buffering; overestimating stream width resulting in overexposure to solar radiation and air temperature input; or incorrect model-section lengths, resulting in errors in climate input. Errors and the effect on simulation results are discussed in section, “Limitations of Water-Temperature Model”.

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