Stream temperature‐equilibrium temperature relationship

Abstract

Equilibrium temperature is the water temperature at which the sum of all heat fluxes through the water surface is zero. It can be calculated from weather data. Mean weekly stream temperature was found to be linearly related to mean weekly equilibrium temperature above 0°C. The slopes and intercepts of the linear relationship were used to identify effects of shading, sheltering, cold water inputs (groundwater, meltwater, and deep reservoir releases) and warm water inputs (wastewater, cooling water, and lake surface water). The linearity hypothesis was confirmed for data from 596 U.S. Geological Survey stream gaging stations in the eastern and central United States. For approximately 15% (89 of 596, NSC ≥ 0.90) of stream gaging stations, weekly equilibrium temperature was a good estimator of weekly stream temperature with zero wind sheltering and sun shading. With sheltering and shading the number rose to 26% (156 of 596). For these streams the heat exchange through the water surface has the most controlling effect on stream temperatures. For the remaining 74% of streams the relationship between weekly stream temperature and weekly equilibrium temperature was also linear, but its slope was significantly less than 1.0 (even after calibration for shading and sheltering), indicating that processes other than surface heat exchange have an influence. Cold water inflows were dominant for 8% (46 of 596) of stream gaging sites. Less than 5% of all stream gaging stations showed evidence of unnatural heat inputs. Fitting an equilibrium temperature linearly to recorded stream temperatures, e.g., at a weekly timescale, can be of use to project stream temperatures under different weather‐climate scenarios or to identify both natural and anthropogenic heat and hydrologic inputs to streams.