1.  Bowen ratio

The Bowen ratio is defined as follows (Ponce, 1989):

Qh                   Ts  -  Ta             p B  =   ______   =  γ   ____________   ________            Qe                   es  -  ea          1000

(1)

in which B = Bowen ratio; Q_h = sensible heat transfer from water body to the atmosphere by convection and conduction; Q_e = energy expended in the evaporation process; T_s = water surface temperature, in °C; T_a = overlying air temperature, in °C; e_s = saturation vapor pressure at the water surface temperature, in millibars (mb); e_a = 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:

cp p γ  =  __________              rMW λ

(2)

in which c_p = specific heat of air at constant pressure, in cal gr^-1 °C^-1; p = atmospheric pressure, in mb; r_MW = ratio of the molecular weight of water vapor to dry air: r_MW = 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: c_p = 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:

(0.24017) (1013.25) γ  =  ___________________________                       0.622 λ

(3)

which reduces to:

391.24 γ  =  ___________                  λ

(4)

with λ in cal gr^-1 and γ in mb °C^-1.

For any atmospheric pressure p (mb), the psychrometric constant is:

0.24017 p γ  =  ________________                0.622 λ

(5)

which reduces to:

0.3861 p γ  =  _______________                     λ

(6)

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).

Table 1.  Variation of psychrometric constant γ with temperature, at standard atmospheric pressure. T (°C) λ (cal gr-1) γ (mb °C-1) 0 597.3 0.655 5 594.5 0.658 10 591.7 0.661 15 588.9 0.664 20 586.0 0.668 25 583.2 0.671 30 580.4 0.674 35 577.6 0.677 40 574.7 0.681

Fig. 1  Variation of the psychrometric constant with temperature,
at standard atmospheric pressure.

4.  Summary

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.

References

Ponce, V. M. 1989. Engineering Hydrology: Principles and Practices. Prentice Hall, Englewood Cliffs, New Jersey.