LWCt1 = LWCt 0 + dt(MELT_I ∆t + RAIN_IN_I ∆t - REFREZ ∆t - EXCESS_LWC∆t ).
(1)
The differential time step used in the numerical integration is represented by dt. The subscripts are as
follows:
t1 = present time
t0 = one dt in the past
∆t = the differential time step between period t0 and t1.
In eq 1 LWCt1 is the liquid water content evaluated at the present time. LWCt 0 is a the liquid water
content evaluated one dt in the past. MELT_I∆t, RAIN_IN_I∆t, REFREZ∆t and LWC_OUT∆t are rates
of mass movement that influence LWC evaluated between t0 and t1. Hence, eq 1 states that the mass of
liquid water in the snowpack at the present time ( LWCt1 ) is equal to the mass of liquid water in the
snowpack one dt in the past ( LWCt 0 ), plus the melting rate of solid ice (MELT_I∆t)) and the rainfall
rate (RAIN_IN_I∆t) that occurred between the present time and one dt in the past, minus the refreez-
ing rate of liquid water (REFREZ∆t)) and the rate of excess liquid water removed from the snowpack
(EXCESS_LWC∆t)) that occurred between the present time and one dt in the past.
The value of LWC in eq 1 will increase with above freezing air temperatures accompanied by rain
and snowmelt and decrease with below freezing temperatures accompanied by refreezing of liquid
water. The value of SWC in eq 2 will increase with freezing air temperatures accompanied by snow-
fall and decrease with above freezing air temperatures accompanied by snowmelt and sublimation.
The value of TOT_LIQ_WTR_REL in eq 3 will increase more rapidly with above freezing tempera-
tures accompanied by rainfall and snowmelt:
SWCt1 = SWCt 0 + dt(SNOWE ∆t + REFREZ ∆t - MELT_I ∆t - SUBLIM ∆t ).
(2)
TOT LIQ_WTR_RELt1 = TOT LIQ_WTR_RELt 0 +
(3)
dt(EXCESS_LWC∆t + RAIN_IN_II∆t - MELT_II∆t )
SWC is incremented by SNOWE and REFREZ and decremented by MELT_I, MELT_II, and
SUBLIM. SNOWE is the product of SNOW and NEWDEN. SWC is also decremented by SUBLIM
only in subzero or rain-free conditions (eq 4). SUBLM contains the value of SUBLIMP because
SUBLM and SUBLIMP are linked by a connector (Fig. 9).
If
TEMPs < 0
then
SUBLIMP = SUBLIM
If
TEMPs > 0 OR RAINs>0
then
SUBLIMP = 0
(4)
EXCESS_LWC, MELT_II, and RAIN_IN_II increment TOT_LIQ_WTR_REL.
When LWC is greater than LWCAP, all of the excess liquid water is routed directly out of the
snowpack via EXCESS_LWC. In Object-GAWSER, all excess liquid is accumulated within
TOT_LIQ_WTR_REL. Excess liquid water is routed by eq 5 and 6 below.
When LWC is greater than LWCAP, Object-GAWSER follows the following procedure. First,
EXCESS_LWC decrements LWC by the amount that LWC exceeds LWCAP. Second, LWC is no
longer incremented by MELT_I and RAIN_IN_I to prevent LWC from further exceeding LWCAP;
therefore, additional meltwater or rainwater is accounted for by incrementing TOT_LIQ_WTR_REL
with MELT_II and RAIN_IN_II. Once LWC is less than or equal to LWCAP, RAIN_IN_II and
MELT_II stop incrementing TOT_LIQ_WTR_REL and MELT_I and RAIN_IN_I begin increment-
ing LWC. Equations 5 and 6 are found within RAIN_IN_I, RAIN_IN_II, EXCESS_LWC, MELT_I,
and MELT_II of Figure 9, respectively.
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