5. Limitations

[48] Several limitations are apparent in this study. Certain spatial and temporal characteristics limit the accuracy of results when the convolution integral is applied to compute fluxes of stored heat energy. Also, the use of water temperature at only two depths to derive a mean vertical water column temperature change is questionable. Finally, the bias in computing water temperature changes with the convolution integral is problematic.

[49] Spatial and temporal characteristics limit the accuracy of results when the convolution integral is applied to compute fluxes of stored heat energy. Spatially, the results are more accurate at sites where water temperature changes are mostly controlled by air temperature changes. Although air temperature changes explain most of the variability in water temperature changes (Figure 4), other heat exchange processes also impact water temperature, including water management activities (site 1), evaporative cooling, rainfall, and perhaps surface water and groundwater interactions. Temporally, accuracy increases at daily time steps at all sites (Tables 2 and 3), because the errors at 30 min time steps are mostly normally distributed with a zero mean and unbiased. If the 30 min errors were nonnormal and highly biased, errors statistics at daily time steps likely would increase.

[50] The use of water temperature at only two depths to derive a mean vertical water column temperature change is questionable. Data availability necessitated this approach for sites 2 to 5 and 7 to 9. At other sites, water temperature was measured vertically every 10 cm [Schaffranek and Riscassi, 2004] at 30 min intervals. Changes in the mean vertical water column temperature were computed from August of 2000 through March 2001 using (1) the high-frequency data, and (2) assuming only the top and bottom water column temperatures were available. The mean absolute error between these two alternatives was about 0.3°C. This translates into an difference of greater than 300 W m^-2 at 30 min time steps assuming the water column is 50 cm deep. The water temperature changes measured with the high-resolution data may be more reliable. Thus, if reliable data are available, it seems prudent to compute fluxes of stored heat energy with high vertical resolution measurements of surface water temperature. When reliable data are not available, air temperature changes can be applied to the convolution integral as outlined in this paper to estimate fluxes of stored heat energy.

[51] The bias in computing water temperature changes also is problematic. The convolution site models compute a decrease in water temperature more precisely than an increase in water temperature at 30 min time steps. If the underlying mechanism for the bias could be resolved, the R² values and standard errors for water temperature change and fluxes of stored heat energy (Tables 2 and 3) likely would improve.