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

Abstract

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.

A multicatchment analysis of headwater and downstream temperature effects from contemporary forest harvesting

“…Several studies have documented cooling gradients of warmed water flowing downstream from openings into reaches with closed forest canopies; however, the magnitude of cooling effects have been highly variable, ranging from 2.0 to 9.2 °C km −1 (Broadmeadow, Jones, Langford, Shaw, & Nisbet, ; Keith et al, ; Story et al, ). Davis et al () used Newton's law of cooling to develop an empirical model, which estimated that maximum stream temperature would decline ~50% at a distance ~300 m downstream from a harvest. They attributed the principal determinants of variability in the actual cooling gradient to the downstream width, depth, and channel gradient (Davis et al, ).…”

“…Studies from Oregon, California, British Columbia, and elsewhere have also demonstrated both natural stream cooling in a downstream direction (Fullerton et al, ; Madej, Currens, Ozaki, Yee, & Anderson, ) and cooling of warmed water flowing from a stream reach draining a clear‐cut back into a closed canopy (Keith, Bjornn, Meehan, Hetrick, & Brusven, ; McGurk, ; Story et al, ). Although there is growing recognition of the high degree of variability in longitudinal stream temperature dynamics (Davis, Reiter, & Groom, ; Ebersole, Liss, & Frissell, ; Fullerton et al, ), it is increasingly important to determine the magnitude, spatial extent, and drivers of the downstream transmission of warmer stream water following disturbances.…”

Evaluating Links Between Forest Harvest and Stream Temperature Threshold Exceedances: The Value of Spatial and Temporal Data

“…Davis et al . () developed a mechanistic model predicting changes in stream temperature downstream of harvest and predicted that 50% (range = 82% to < 1%) of the temperature increase would persist downstream after streams flowed through 300 m of unharvested riparian forest.…”

“…Post-harvest stream shade was an important variable for a statistical model of stream temperature increases; shade levels were positively related to the remaining riparian stand basal area and, more weakly, inversely related to tree height. Davis et al (2016) developed a mechanistic model predicting changes in stream temperature downstream of harvest and predicted that 50% (range = 82% to < 1%) of the temperature increase would persist downstream after streams flowed through 300 m of unharvested riparian forest.…”

Summer stream temperature changes following forest harvest in the headwaters of the Trask River watershed, Oregon Coast Range

“…Stream temperature response to natural and anthropogenic disturbances can be complex and nonlinear (Davis, Reiter, & Groom, ; Groom, Dent, & Madsen, ; Groom, Dent, Madsen, & Fleuret, ; Steel, Beechie, Torgersen, & Fullerton, ). However, the complexity of thermal responses to disturbance can be oversimplified when responses are represented by a single metric, such as a daily, weekly, or monthly maximum or minimum temperatures.…”