River Res. Applic. 32: 1355–1364 (2016)
A nonlinear regression model was used to estimate mean daily stream water temperature in 11 rivers of the North of the Iberian Peninsula employing as the only predictor variable the air temperature. The weighted mean value of air temperature of a variable number of preceding days was used as a predictor variable.
To obtain the weight of air temperature of each preceding day, initially, we calculate the weight of air temperature of current day. For this, we have included in the model the air temperature of current day and the water temperature of preceding day—representative of long-term effects of air temperature on current water temperature. Subsequently, the weight of remaining days was calculated by a negative exponential function.
The weight of air temperature of current day ranges between 0.28 and 0.10, and it was correlated to length of river (R2 = 0.69) and to time of concentration (R2 = 0.66). This fact implies that the number of preceding days required to obtain a good estimation differs across the rivers. The results show that the mean root mean square error (RMSE) between observed and estimated water temperatures was 1.23 °C (±0.30 °C), employing a number of days so that the sum of their weights was 0.65. For the validation period, RMSE was 1.20 °C (±0.18 °C).
For the period 1986–2013, estimated temperature of water was 0.6 °C higher than that estimated for the period 1950–1986. This increase value is slightly lower than that observed in the air temperature (0.8 °C). On the other hand, during the period 1986–2013, water temperature showed a rate of increase of 0.16 °C/decade, similar to the increase of air temperature (0.15 °C/decade).