Approximation of heat exchange at the air‐water interface

Abstract

The basic exchange equations for air-water interface are approximated by the Taylor series expansion around an undefined base temperature in order to calculate short-term heat exchanges. The expression 'short-term' is used here to indicate averaging over a period on the order of 1 hour. Numerical tests based on data from two shallow streams verify that the base temperature should be chosen so as to minimize deviations between the base temperature and the actual water temperature. The daily average natural temperature observed at a reference point is the most practicable base. The daily equilibrium temperature calculated from meteorologic data may be used as a base as long as it does not deviate excessively from actual water temperatures. Whereas the short-term natural temperature is the most accurate base, the short-term equilibrium temperature has no merit as a base temperature of linearization.Heat exchange at the air-water interface a deep body of water may be essentially conunder natural climatic conditions is a matter stant. When the assumption is so seriously of increasing concern to those who are engaged violated, can the equilibrium temperature in the abatement of thermal pollution as well method give reliable estimates of heat exas in the modeling of water temperature as change? N_o explicit reference to this problem an important element of water quality. Since has appeared in the papers devoted to the basic heat exchange equations are nonlinear equilibrium method. Recently Jobson [1972a] and complicated in form, approximations and raised this question in conjunction with his simplifications are often required. derivation of a linearization method based on A well-known method of approximation natural temperatures. among engineers is the equilibrium temperature The purpose of this report is to expand method [Edinger and Geyer, 1965], which is Jobson's derivation, which was limited to unhistorically derived for the calculation of daily natural excess temperatures, and to establish average heat exchange. As the modeling of general rules of approximation for the calculawater temperature has developed with the use tion of heat exchanges for time periods on the of digital computers, attempts have been made order of I hour. Simple Taylor series expansions to extend this method to the calculation of of the exchange equations are developed by the time intervals of less than I day [Federal use of an undefined base temperature. It is Water Pollution Control Administration, 1968]. argued that the natural temperature, definedSuch an extension should be undertaken with as the observed or predicted temperature at caution because it conflicts with a basic as-some reference point such as just upstream of sumption of the method, namely, that the dif-a waste heat discharge, is a better base temference between the equilibrium temperature perature than the equilibrium temperature as and the actual water temperature be small. far as the accuracy of approximation is con-Edinger et al. [1968] have shown that short-cerned. Nume...

Thermal mediation by littoral wetlands and impact on lake intrusion depth

“…Short-circuiting can be enhanced by station- Adams [1982]. This is a reasonable approximation except when the water temperature deviates substantially from the equilibrium temperature [Yotsukura et al, 1973], as occurs when the timescale of variation for Toe is short compared to theat , for example, over synoptic and diurnal timescales.…”

Benthic community dynamics during summer low‐flows in two rivers of contrasting enrichment 2. Invertebrates

“…Low flows can also place stress on invertebrates as a result of increases in temperature (Yotsukura et al 1973;Jobson 1977), and it is possible that some of the observed changes in invertebrate communities were a result of high temperatures. For example, Quinn et al (1994) found that taxa such as Deleatidium had a relatively low tolerance to warm waters, with over 50% of test organisms perishing at a 96-h exposure to temperatures >22.6°C.…”

Analysis and prediction of the water temperature of the McKenzie River, Oregon using the equilibrium temperature approach

“…correspond with recorded data more closely when computed values of equilibrium temperature are used. The assertion by Yotsukura, et al (1973) that "the short-term equilibrium temperature has no merit as a base ternperature of linearization" has been proven correct in this case. Since calculated equilibrium temperature performed poorly in modeling water temperature, no attempt was made to establish a relation between air and equilibrium temperatures.…”

“…Jobson's simplified model requires a minimum of meteorological data, using only equilibrium temperature and windspeed. According to Jobson (1980a, p. 27 (Edinger and Geyer, 1965;Dingman et al, 1968;Jobson, 1973;Paily et al, 1974;Hills and Viskanta, 1976;Jackman and Yotsukura, 1977) Other authors investigated the theoretical aspects of water temperature modeling (Edinger et al, 1968;Edinger, 1970;Dingman, 1972;Yotsukura et al, 1973;and Noble, 1981) as well as practical applications (Brown, 1969;Morse, 1970Morse, , 1972Brocard and Harleman, 1976;Jobson, 1980aJobson, , 1980bStang, 1982;Laenen and Hansen, 1985).…”