The non-linear influence of wind-speed variability on gas transfer in lakes

Abstract

The analytical representation of wind-speed probabilities by the Weibull distribution allows the empirical characterization of a scalar wind field on the basis of two Weibull parameters. Such a parameterization obviates the necessity of including wind data in time-series form explicitly in air-water interaction models when accounting for non-linear wind effects. By combining the Weibull wind-speed distribution with commonly employed trilinear and power-law expressions for the dependence of the gas transfer velocity on wind speed, analytical expressions for the mean value of the transfer velocity are obtained. These expressions predict the non-linearity of the dependence of gas transfer velocity on wind speed to be responsible for an increase in the mean transfer velocity which will normally not exceed 100% of the value obtained when non-linear wind effects are neglected. In the specific case of the winter oxygenation of a typical subalpine Swiss lake (Aegerisee), the commonly employed trilinear and power-law expressions are found to underestimate the mean O₂ transfer velocity considerably. It is evident that such expressions cannot be employed to determine gas transfer velocities in sheltered lakes without considerable modification at low wind speeds. The extent of the modification required, however, suggests that the role played by the instantaneous wind speed in determining the gas transfer velocity in such lakes may be much less significant than is usually assumed.