1. Bowen ratio
The Bowen ratio is defined as follows (Ponce, 1989):
in which B = Bowen ratio; Qh = sensible heat transfer from water body to the atmosphere by convection and conduction; Qe = energy expended in the evaporation process; Ts = water surface temperature, in °C; Ta = overlying air temperature, in °C; es = saturation vapor pressure at the water surface temperature, in millibars (mb); ea = vapor pressure of the overlying air, in mb; p = atmospheric pressure, in mb; γ = psychrometric constant, in mb °C-1 (Note that 1000 has the units of mb).
2. The psychrometric constant γ
The psychrometric constant γ is expressed as follows:
in which cp = specific heat of air at constant pressure, in cal gr-1 °C-1; p = atmospheric pressure, in mb; rMW = ratio of the molecular weight of water vapor to dry air: rMW = 0.622, and λ = latent heat of water vaporization, in cal gr-1.
The specific heat of air between 0°C and 40°C is: cp = 1.005 J gr-1 °C-1 = 0.24017 cal gr-1 °C-1. The mean sea-level atmospheric pressure is: p = 1013.25 mb. Therefore, at sea level, the psychrometric constant is:
which reduces to:
with λ in cal gr-1 and γ in mb °C-1.
For any atmospheric pressure p (mb), the psychrometric constant is:
which reduces to:
with p in mb, λ in cal gr-1 and γ in mb °C-1.
3. Variation of γ with temperature
Since λ varies with temperature, γ also varies with temperature. Table 1 shows the variation of the psychrometric constant γ with temperature, at standard sea-level atmospheric pressure (p = 1013.25 mb) (Fig. 1).
Fig. 1 Variation of the psychrometric constant with temperature,
at standard atmospheric pressure.
The slight variation of the psychrometric constant γ with temperature has been explained and clarified. The aim is to increase the accuracy of online evaporation calculations (http://onlinecalc.sdsu.edu)
Fig. 2 Ira Sprague Bowen.
Ponce, V. M. 1989. Engineering Hydrology: Principles and Practices. Prentice Hall, Englewood Cliffs, New Jersey.