274 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
injury can cause yield loss to over-wintering crops, e.g. alfalfa Kanneganti et al., 1998.
Motivated by water supply and safety concerns, the snow literature is dominated by studies of relatively
deep snowpacks of mountainous or forested regions. Agricultural environments in the US Midwest more
commonly have relatively thin snowpack, and issues of practical importance can be significantly different
from those surrounding deeper snow. Compared to deep snowpacks, greater attention may be given to
dates of complete disappearance in agricultural set- tings. Early ablation, for instance, can have important
implications for alfalfa survival. Responses of envi- ronmental factors to thinner snow cover are more rapid
than in deep snow, e.g. to the diurnal cycles of surface energy fluxes Granger and Male, 1978.
Snow cover models vary in complexity. An early, essentially complete physically based model of snow
cover was that of Anderson 1976. This numerical model included physical descriptions of snowpack
accumulation, change of albedo, settling and com- paction, snowmelt, and meltwater retention and per-
colation as well as the snowpack energy balance. The major advantage of models of this type is that
they allow mechanistic understanding of snow cover processes and so should be transportable. However,
their use is limited by data needs and computational burden. Extensions to Anderson 1976 model ex-
panded the physical system to include the soil be- neath SNTHERM; Jordan, 1991, and vegetation and
residue SHAW; Flerchinger and Saxton, 1989.
The objective of this study is to test the validity of Anderson’s parameterizations for the snow depths
and dynamics of the relatively thin snowpacks of Wisconsin. Additionally, we needed to incorporate a
sophisticated snow routine into the atmosphere–land exchange ALEX model, which we use in several
agricultural modeling products Anderson et al., 1998; Bland et al., 1998; Diak et al., 1998. The speed and
simplicity of ALEX is suitable for landscape-to-global scale applications where calculations must be made
at thousands of locations. One such application is our project to assess the impact of landscape position and
time of year on optimizing wintertime disposal of an- imal manure. Additionally, ALEX is the land-surface
parameterization in the CRASS mesoscale forecast model personal communication; Diak, 1999, but
with only crude snow cover treatment. Finally, restruc- turing of the US National Weather Service during the
past decade eliminated many sites where professional observers recorded snow cover changes. The future
prospect is for fewer observations, so simulation will play an increasing role in real-time management
problems.
This study is unique in the extent of record used to demonstrate the validity of the model: four stations
totaling 61 site years of continuous hourly and daily weather observations. Detailed snow cover models
such as SNTHERM and SHAW have so far been ap- plied to only shorter records for verification purposes
typically extending 1–3 years. In contrast, snow cover routines subjected to longer-term verifications are
generally less sophisticated Motoyama, 1990; Yang et al., 1997. Additionally, the model created here
is both complete in process as defined by Anderson 1976 and numerically efficient enough to integrate
into a model suitable for mesoscale modeling projects. Because of computational limitations, snow submod-
els used in regional or climate studies so far exhibit low to intermediate complexity Slater et al., 1998,
typically lacking internal processes e.g. melt water retention and percolation Yang et al., 1997. In our
work, the snow cover parameters were successfully applied to the entire data set, covering a wide variety
of snow cover conditions. Results demonstrate that available parameterizations as implemented in ALEX
are robust.
2. The ALEX model and modifications for snow
2.1. The soil–vegetation system The ALEX model is a two-source soil and vege-
tation model of heat, water and carbon exchange between a vegetated surface and the atmosphere
Anderson et al., 1997; Anderson et al., 2000. Soil is represented by an arbitrary number of layers, whereas
vegetation is represented as a single layer. This single vegetation layer allows the model to be used in an in-
verse mode, for interpreting remotely-sensed temper- atures. Each layer is bounded by a pair of nodes and
defined by its unique physical properties with respect to the transport of heat and water. When vegetation
is present, the top node is at a height above the soil surface equal to roughness length plus displacement
C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287 275
height. Upper boundary conditions are specified at some measurement height above the top layer, whereas
lower boundary conditions are defined at some depth within the soil profile. Although the multi-layer struc-
ture so defined comprises different materials soil and vegetation as top layer, commonality of transport
processes among materials allows ‘binding’ of these layers into one single computational block. This block
is ‘routed’ into the numerical solution engine at the beginning of the time step with the new state variables
determined at the end of the time step. For instance, the soil–vegetation system is treated as one block with
respect to the transport of heat. Similarly, the soil is treated as another block with respect to infiltration of
water. The solution at the end of each time step is ob- tained after all the mass and energy balance closures
have been simultaneously satisfied. This structural simplicity allows addition of a manure layer, which, as
mentioned earlier, is a future improvement needed for simulations of wintertime disposal of animal waste.
2.2. The modified atmosphere–snow–soil system Building on the structure of ALEX, we introduced
a snow cover overlaying the soil profile. Similar to the soil profile, the snow cover consists of an arbitrary
number of layers bounded by pairs of nodes. The vegetation layer was removed and the series–parallel
resistance network associated with this layer was replaced with the aerodynamic resistance R
a
. Two major modifications were made to accommo-
date snow cover processes. One involved represen- tation of processes unique to snow layers e.g. snow
melt and the other involved mimicking of a contin- uously changing snow cover while maintaining the
structural consistency and conceptual simplicity of ALEX. For the snow layers, soil heat transport equa-
tions were modified to include melt energy Q
m
as a source, computed as the energy excess above 0
◦
C. The second major modification involved simulation of
an unstable material as part of a multi-layer structure; unlike soil, snow undergoes significant accumulation,
metamorphosis, compaction and ablation. As a result, layers of snow are added, expanded, contracted or
disappear continuously. Similarly, nodes associated with snow layers are added, left out, and reordered
continuously. When no snowpack is present, the sys- tem consists of the soil profile and the overlying air.
The model updates changes in layers overlying the soil profile at the end of each time step hourly.
2.3. Main snow cover routines Important snow-related equations are discussed in
this section. Values of most of the various empirical parameters were taken from the literature, as indicated
in Table 3. Parameters that we found necessary to adjust are discussed later.
The density of new snow is computed according to a formula given by LaChapelle 1969:
ρ
ns
= 50 + 1.7T
w
+ 15
1.5
, T
w
− 15
◦
C 50,
T
w
− 15
◦
C 1
where ρ
ns
is new snow density in kg m
− 3
and T
w
is the wet bulb temperature in
◦
C. Compaction of each layer of snowpack is based on a relationship reported
by Kojima 1967 and Mellor 1964: 1
ρ
sp
∂ρ
sp
∂t =
C
1
exp[−0.08T −
T ]W
s
exp−C
2
ρ
sp
] 2
where W
s
is the weight of the overlying snow, ρ
sp
the density of the solid phase of snow, T the snow temp-
erature in
◦
C, C
1
and C
2
are the constants, and T
=
◦
C. Destructive metamorphism is computed by the ex-
pressions Anderson, 1976 1
ρ
sp
∂ρ
sp
∂t =
C
3
exp[−C
4
T
c
− T
] for
ρ
sp
≤ ρ
d
3 1
ρ
sp
∂ρ
sp
∂t =
C
3
exp[−C
4
T
c
− T
]exp−46ρ
sp
− ρ
d
] for
ρ
sp
≥ ρ
d
4 where C
3
and C
4
are the empirical parameters and ρ
d
is a threshold density. If melting is under way, Eqs. 3 and 4 is multiplied by a parameter C
5
to account for the effect on metamorphism of liquid water contained
in the snow layer. Albedo of the snow is assumed to be independent
of sun angle, and is computed from Anderson 1976: α
sp
= 1 − 0.206C
v
d
s −
12
5
276 C.E. Kongoli, W.L. Bland Agricultural and Forest Meteorology 104 2000 273–287
where C
v
is an empirical extinction coefficient and d
s
is the grain size diameter of ice crystals mm. Grain size is calculated from Anderson 1976:
d
s
= G
1
+ G
2
ρ
s
ρ
l 2
+ G
3
ρ
s
ρ
l 4
6 where G
1
, G
2
and G
3
are the empirical coefficients, ρ
s
the density of snow at the surface and ρ
l
is the density of liquid water. The albedo of snowpacks less
than 4 cm thick is adjusted based on the albedo of the underlying material.
Melt water percolation in the snow is estimated us- ing the ‘lag and route’ approach originally adopted
by Anderson 1976 and incorporated into the SHAW model by Flerchinger 1995, 1997. Melt water pro-
duced in a snow layer begins to percolate after its wa- ter liquid holding capacity, often called the irreducible
water saturation, is satisfied. The irreducible water sat- uration is analogous to the so-called field capacity of
soil physics. The value of W
e
is assumed to be at a minimum W
e
min
if snow density exceeds a threshold value ρ
e
. If snow density is less than this threshold value, W
e
is computed using the expression W
e
= W
e
min
+ W
e
max
− W
e
min
ρ
e
− ρ
sp
ρ
sp
7 where W
e
max
is the maximum liquid water holding capacity Anderson, 1976.
3. Data collection and weather inputs
