Ground Surface Moisture Flux Boundary Conditions - Unsaturated Soil Mechanics in Engineering Practice - page 290

Table 6.3 Comparison of Computed Relative Humidity

RH RH August- RH

Dry Bulb Dew-Point Simplified Roche-Magnus Bosen

Temperature, ◦ C Temperature, ◦ C Equation, % Equation, % Equation, %

25.0 24.5 97.5 97.06 97.06

25.0 24.0 95.0 94.20 94.20

25.0 22.0 85.0 83.48 83.49

25.0 20.0 75.0 73.84 73.85

25.0 18.0 65.0 65.19 65.21

25.0 16.0 55.0 57.44 57.46

25.0 12.0 35.0 44.33 44.34

25.0 10.0 25.0 38.82 38.83

25.0 6.0 5.0 29.57 29.57

20.0 19.0 95.0 93.98 94.01

20.0 16.0 80.0 77.79 77.88

20.0 12.0 60.0 60.03 60.16

20.0 10.0 50.0 52.56 52.71

20.0 6.0 30.0 40.04 40.19

6.3.6.7 Comparison of Equations for Calculating
Relative Humidity
Table 6.3 contains calculated relative humidity values when
typical values are selected for the dry bulb temperature
and the dew-point temperature. The results show that the
proposed simplified equation provides reasonable estimates
of the relative humidity as long as the computed values
are above about 50%. The August-Roche-Magnus and the
Bosen (1958) equations give similar computed humidity val-
ues over the entire range of relative humidity.

Measured
precipit ation,
P

Actual
ev aporation,
AE

Soil surface

a 2

P , AE, and R are given
for a unit of surface area

P cos α 2

6.3.7 Runoff
Runoff R is defined as the rainwater that cannot gain
entrance into the soil during the period of rainfall. The
amount of moisture leaving the ground surface by actual
evaporation can also be taken into consideration. Rainfall is
generally assumed to fall vertically, and therefore the slope
of the ground surface should be taken into consideration.
The water balance equation at ground surface takes on the
general form shown below, and its meaning is illustrated in
Fig. 6.20:

Runoff, R

Figure 6.20 Ground surface moisture flux associated with runoff.

Equation 6.17 applies only during periods of rainfall and
does not represent a rigorous analysis of the runoff pro-
cess. Runoff has no functional relationship with precipitation
other than as part of the water balance at ground surface.
Rather, runoff appears as the missing term in the water
mass balance equation (i.e., the term that is not generally
measured). Runoff as presented in Eq. 6.17 is relevant only
during precipitation periods where there is excess water to
generate runoff. The assumption is sometimes made that
there is no evaporation from the ground surface during pre-
cipitation events (i.e., R

R = P cos α 2 − I − AE (6.17)

where:

I = net moisture infiltration, mm/day, I ).

Actual evaporation is a function of weather parameters
and the soil suction at the soil-atmosphere boundary. Actual
evaporation is discussed later and can be computed based on
one of several proposed procedures (Wilson et al., 1997a).

= P cos α 2 −

P = precipitation, mm/day,

α 2 = ground surface slope, deg,

AE = actual evaporation, mm/day, and

R = runoff, mm/day.