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run to simulate the response of the soil system under constant
radiation, ambient air temperature and relative humidity conditions for
a period of 72 hours using various time steps to evaluate the numerical
stability and numerical error characteristics of the procedure.
Thermal and hydraulic properties of the soil were assumed to be
constant for the duration of the simulation for an Millhopper fine
sand. The water content and temperature profiles were assumed to have
a uniform initial distribution as were density and soil porosity.
Overall mass and energy balances were calculated for the soil
profile during the simulation. Any residual in these balances would
constitute error arising from the numerical algorithm and was
accumulated on an hourly basis for analysis purposes. The sum of the
squares of the residuals for the energy and mass balances for the
simulation period are presented in Figures 2-7 and 2-8, respectively,
for the different time steps. The sum of the squares of the residuals
(SSR) for the energy balance decreased when the time step of was
increased from 30 to 60 s then remained fairly constant for larger time
steps. The square root of the SSR represents an estimate of the
standard error of the estimate of the total heat flux. For the time
steps of 60, 120, 300 and 600 s, this represents approximately one
percent of the cumulative soil heat flux. The standard error of the
mass balance was approximately two percent of the cumulative
evaporation over the 72 h simulation (600 s time step). It is expected
that as properties are varied with time, that the standard error would
increase due to increased gradients in soil temperature and water
content particularly near the surface. Therefore, a time step of 60 s
was utilized in the model validation and sensitivity analysis.