residual values unless the user provides a value. The bottom soil moisture is assigned the
average value of the residual and maximum moisture contents for the USCS soil type
present in Table 9.2.2.
If the temperature of the soil is frozen at any depth, the volumetric ice content at that
position equals 0.95*(soil moisture)*(water density)/(ice density).
10.3 Node Position and Number
FASST requires a minimum soil depth of 1.0 m. If the user-specified depth is less than
this, FASST extends the bottom soil layer until the total thickness is 1.0 m.
Node spacing is determined by both the number of soil temperature and moisture
observations as well as the number of soil layers. If measured temperature and/or
moisture values exist, a node is placed at each observation location. Nodes also occur at
any layer boundary if there are different soil types as well as the soil surface and bottom.
If no initial measurements are provided, 10 nodes are equally spaced through the total
soil thickness and at any layer boundaries, the surface, and bottom. Soil type dependent,
temperature and moisture independent, parameters are assigned to the nodes depending
on which layer they are in. Nodes located at layer boundaries have the properties of the
upper layer.
10.4 Time Step Determination
Once the soil type, temperature, and volumetric moisture content are known at a node,
the corresponding hydraulic and thermal properties of the soil are calculated. The thermal
model calculation time step, ∆t (sec), is then calculated based on the numerical stability
requirement for the soil temperature. Namely for each node,
⎡ 0.45 ( ∆zi )2 ⎤
∆t
< 0.5 → ∆t = min ⎢
⎥
kth,i
(10.1)
( ∆zi )
2
kth,i
⎢
⎥
⎣
⎦
where kth,i (m2/s) is the thermal diffusivity of the soil and ∆zi (m) is the nodal spacing and
the subscript i refers to the node. Since the thermal diffusivity varies with soil type and
temperature, the time step also varies. As indicated in Equation (10.1), the minimum
value needed to satisfy all nodal conditions is used.
With the determination of the number of nodes and their placement, as well as the
assignment of nodal properties, initialization of FASST is complete.
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