Modelling temperature change downstream of forest harvest using Newton's law of cooling

We adapted Newton's law of cooling to model downstream water temperature change in response to stream‐adjacent forest harvest on small and medium streams (average 327 ha in size) throughout the Oregon Coast Range, USA. The model requires measured stream gradient, width, depth and upstream control reach temperatures as inputs and contains two free parameters, which were determined by fitting the model to measured stream temperature data. This model reproduces the measured downstream temperature responses to within 0.4 °C for 15 of the 16 streams studied and provides insight into the physical sources of site‐to‐site variation among those responses. We also use the model to examine how the pre‐harvest to post‐harvest change in daily maximum stream temperature depends on distance from the harvest reach. The model suggests that the pre‐harvest to post‐harvest temperature change approximately 300 m downstream of the harvest will range from roughly 82% to less than 1% of that temperature change that occurred within the harvest reach, depending primarily on the downstream width, depth and gradient. Using study‐averaged values for these channel characteristics, the model suggests that for a stream representative of those in the study, the temperature change approximately 300 m downstream of the harvest will be 56% of the temperature change that occurred within the harvest reach. This adapted Newton's law of cooling procedure represents a highly practical means for predicting stream temperature behaviour downstream of timber harvests relative to conventional heat budget approaches and is informative of the dominant processes affecting stream temperature. Copyright © 2015 John Wiley & Sons, Ltd.