Mathematical View Point to the wind speed parameter role in the FAO PenmanMonteith Equation for Calculating ET0

From the mathematical point of view, the FAO Penman-Monteith equation shows a homographic function related to the wind speed. The homographic function has horizontal and vertical asymptotes. In this issue horizontal asymptote is applicable; because the vertical asymptote occurs for negative values of wind speed but the negative sign indicates the direction of the wind speed and only the absolute values of the quantities are used. By increasing wind speed from zero, evapotranspiration will increase until it reaches to a limited asymptote value. This value is the horizontal asymptote of the fractional function of FAO Penman Monteith equation. In this research the effect of wind speed variations on the evapotranspiration amounts was analyzed, with considering the mathematical framework of the Penman-Monteith equation. Meteorological data from three weather stations, including Tabriz, Isfahan and Rasht were used in this research. Results showed that in the FAO Penman-Monteith equation, wind speed effect on evapotranspiration is nonlinear and variation in evapotranspiration amounts is more at low wind speeds than high values of wind speeds. As a general result, evapotranspiration has tended to asymptote homographic function and the rate of increasing in evapotranspiration is reduced by wind speed increasing.