Simple non-linear models for the cooling of well-mixed rivers

Abstract

Using the presently known data of the temperature dependence of the coefficient of heat exchange at an air-water interface, the non-linear equation governing the one-dimensional cooling of a well-mixed river is solved analytically. It turns out that the effects of non-linearity are negligible within the small parameter range occurring in hydrological applications, justifying the use of linear models in one-dimensional river temperature calculations (e.g., exponential method). It is shown that the frequently used assumption of an exponential decay of excess temperature represents an acceptable approximation.