Estimating extreme stream temperatures by the standard deviate method

Abstract

It is now widely accepted that global climate warming is taking place on the earth. Among many other effects, a rise in air temperatures is expected to increase stream temperatures indefinitely. However, due to evaporative cooling, stream temperatures do not increase linearly with increasing air temperatures indefinitely. Within the anticipated bounds of climate warming, extreme stream temperatures may therefore not rise substantially. With this concept in mind, past extreme temperatures measured at 720 USGS stream gauging stations were analyzed by the standard deviate method. In this method the highest stream temperatures are expressed as the mean temperature of a measured partial maximum stream temperature series plus its standard deviation multiplied by a factor K E (standard deviate). Various K E-values were explored; values of K E larger than 8 were found physically unreasonable. It is concluded that the value of K E should be in the range from 7 to 8. A unit error in estimating K E translates into a typical stream temperature error of about 0.5 °C. Using a logistic model for the stream temperature/air temperature relationship, a one degree error in air temperature gives a typical error of 0.16 °C in stream temperature. With a projected error in the enveloping standard deviate dK E=1.0 (range 0.5–1.5) and an error in projected high air temperature d T a=2 °C (range 0–4 °C), the total projected stream temperature error is estimated as d T s=0.8 °C.