(*m*) and *h*s,melt (*m*) are the heads due to melting ice and snow, respectively, and ∆t (*sec*) is

the time step. If the ground is sloped, no water accumulates and any water that falls on

the surface, but which does not infiltrate, becomes runoff.

The evaporation and condensation rates depend on the moisture difference between the

air and the surface. They are quantified as the latent heat flux. Following the procedure

outlined in Chapter 4, Section 4.1.6, the modified surface energy balance is rearranged

such that

(1 - α ) *I * s ↓ +ε Ii↓ - εσ T 4 + ρac p,*a*CDW (*T*a - *T *)

.

(5.4)

∂*T*

+ *U * pc pTp + κ

∂*z*

Reference should be made to Chapter 6 for explanation of the individual terms. The

moisture flux to/from the surface is then

(5.5)

ρwl

and *l *(*J/kg*) is the latent heat of evaporation if the air temperature is above freezing and

the latent heat of sublimation otherwise. If the latent heat flux is positive, evaporation is

occurring, otherwise condensation is happening.

Equation (5.2) is solved numerically using an explicit scheme such that

θwj+1,*i *- θwj ,*i*

⎡ *v * j +1,*i*+1 - *v * j +1,*i *⎤

= -⎢

⎥ + *sources*(*i*) - *losses*(*i*)

(5.6)

∆*t*

∆*z*i

⎣

⎦

where

⎡*h *- *h *⎤

⎣ *z*i - *z*i-1 ⎦

.

(5.7)

⎡*h *-*h *⎤

⎣ *z*i+1 - *z*i ⎦

represent time and depth, respectively. The change in soil moisture content due to

changes in the ice content, i.e., freezing/thawing, is incorporated into the source and sink

terms. In Equation (5.2) it is the second term on the right-hand side. Equation (5.6) is

solved for ψi using a Newton-Raphson technique so that the final matrix equation

becomes

44