SWIM3: Model Documentation

N. I. Huth, K. L. Bristow, K. Verburg

**Information
taken from Huth, N.I., Bristow, K.L., Verburg, K., 2012. SWIM3: Model use,
calibration, and validation. Transactions of the ASABE 55, 1303-1313.**

SWIM3 is the
latest release in the family of SWIM (Soil Water Infiltration and Movement)
models developed for simulating water and solute movement within soils. These
models have been used predominantly for studies into management options for water
and solutes in agricultural systems or for evaluating alternate numerical
methods for efficiently solving complex systems of flow equations. SWIMv1 (Ross, 1990b) provided an efficient solution
to the 1-dimensional Richards’ equation for the simulation of water movement
and uptake by plants. SWIMv2 (Verburg* et al.*, 1996b) extended the
functionality of SWIMv1 through the provision of a wider range in boundary
conditions, the ability to specify soil hydraulic properties as the sum of
simple functions (Ross and Smettem, 1993) described using
piecewise cubic approximations (Ross, 1992), and a solution of the
convection-dispersion equation for solute transport. The utility of this model
code was further enhanced by its incorporation into the APSIM (Agricultural Production
Systems Simulator) framework (Keating* et al.*, 2003) to create the
APSIM-SWIM version of the model (McCown* et al.*, 1995; Huth* et al.*, 1996). With this move, SWIM ceased to be developed as a standalone
product, but was redeveloped for use as a component within integrated modeling
frameworks. Whilst much of the numerical approach used within the APSWIM-SWIM model
was retained from the parent SWIMv2 model, further enhancements were included
to facilitate application to various farming systems. These included the
simulation of multiple non-interacting solutes(Verburg* et al.*, 1996a), the effects
of surface residues on evaporation or surface sealing (Connolly* et al.*, 2002) and equations
for simulating subsurface drains (Malone* et al.*, 2007; Snow* et al.*, 2007) or local groundwater interactions (Paydar* et al.*, 2005b). SWIM3 builds
upon the work of APSIM-SWIM and provides a new approach to specify soil
hydraulic properties for a broad range of soil types from simple measures of
soil water behavior. The simplicity of this new approach makes this mechanistically-based
numerical model more accessible to farming systems researchers within the APSIM
modeling community who, until now, have limited their use of APSIM-SWIM due to perceived
difficulties of parameterization. SWIM3 is developed and maintained within the
APSIM Community Source Framework (www.apsim.info)
by the APSIM Initiative. This initiative provides a transparent and open-source
approach to combine broadly based collaborative science with best practice
software development and maintenance, and science quality control. APSIM is
freely available for research and development, extension or educational use.
APSIM training is provided via regular international workshops as a fee for
service activity. However, all workshop materials, user documentation and a
model user support forum are also freely available via the APSIM website (www.apsim.info).

The APSIM
modeling framework has been developed to simulate biophysical process in
farming systems, in particular where there is interest in the economic and
environmental outcomes of management practice in the face of climatic risk,
climate change or changes in policy. APSIM’s component-based design allows
individual models to interact via a common communications protocol (Moore* et al.*, 2007). The role of
SWIM3 within an APSIM simulation is to calculate fluxes and storage of soil
water and solutes and to communicate this information to other models within
the simulation. Whilst SWIM generally uses much smaller time steps in computing
its numerical solutions, most communications to other models within a
simulation occur on a daily frequency. SWIM3 is available for use in APSIM
Version 7.3 or later.

SWIM3 is a 1-dimensional lumped physically-based model. Some sub models within SWIM3 capture simple spatial processes and so it can also be described as a quasi 2-dimensional model. SWIM3 provides a 1-dimensional simulation of water fluxes through a numerical solution to Richards’ equation (Richards, 1931) (Eq. 1)

(1)

where θ is
volumetric water content (cm^{3}cm^{-3}), x and t describe
space (cm) and time (h), K is hydraulic conductivity (cm h^{-1}), z and
ψ are the gravitational and matric potentials (cm), and S is the
source/sink term for water (cm^{3}cm^{-3}h^{-1}).
Solute fluxes are calculated using a solution to the Convection-Dispersion
equation (Eq. 2)

(2)

where c and s
are solute concentrations (ppm) in solution or adsorbed to the soil surface, D
is the combined dispersion and diffusion coefficient (cm^{2} h^{-1}),
q is the water flux (cm h^{-1}) and ρ is the soil bulk density (g
cm^{-3}), and φ is the source/sink term for solute (ppm h^{-1}).
The mixed ψ and θ form of Richards’ equation shown in equation 1 is
highly non-linear, especially in dry soils, and so it is solved using a
hyperbolic sine transform of ψ (Ross, 1990a). A detailed description of
the numerical methods used in solving equations 1 and 2 is included in (Verburg* et al.*, 1996b).

Various losses
from the overall water balance, such as canopy interception or losses from
irrigation infrastructure are calculated in other modules within APSIM. Potential
crop water use is calculated by each crop model using methods appropriate to
the crop being simulated as specified by each crop model developer. Evaporation,
drainage and runoff losses are calculated via sub-models within SWIM3 and
incorporated into the numerical solution through the sink term, S. Evaporation
is calculated using the approach of Campbell (1985) assuming isothermal vapor transport.
Potential evaporation rate is calculated using the method of Priestly and
Taylor (1972). Plant water uptake is calculated using the approach of Campbell
(1985) which treats the
soil-plant-atmosphere continuum as a resistance network. Uptake from each
layer is calculated using the analogue of a single cylindrical root surrounded
by a homogeneous cylinder of soil (Cowan, 1965). Partitioning of water uptake
between layers is obtained by calculation of a xylem potential, up to a
species-specific maximum value, required to meet daily plant water demand. Loss
via subsurface drainage networks is calculated using the steady-state Hooghoudt
equation (Malone* et al.*, 2007), formulated in
a way similar to that found in DRAINMOD (Skaggs, 1989). Vertical losses from the
soil profile are calculated depending on the chosen bottom boundary condition.
A zero matric potential gradient is assumed to exist below the bottom boundary
for simulations where no water table exists within the soil profile.
Otherwise, ground water flow is calculated from the simulated water potential
at the bottom boundary using a lumped parameter describing the rate of flow per
unit potential difference to capture ground water behavior (Paydar* et al.*, 2005b).

Runoff losses
were previously calculated in SWIMv1 and SWIMv2 using detailed models of
surface water storage and soil surface crust dynamics in response to detailed
data on storm rainfall intensity (Connolly* et al.*, 2002). These
approaches often required parameters and input data not available to many users.
SWIM3 makes use of the SCS Runoff Curve Number technique (Hawkins, 1996) for calculating daily runoff
losses from more readily available daily rainfall totals.

The
convection-dispersion equation (Eq.2) is used to calculate the fluxes of all
solutes within the APSIM simulation (usually NO_{3}, NH_{4},
Cl, and Urea). No interaction or competition for exchange surfaces by solutes
is considered. Adsorption of solute to soil surfaces is specified via a
Freundlich isotherm and soil pore space tortuosity effects on solute diffusion
are captured in a simple user-defined function of soil water content which can
reproduce many of the common forms (Moldrup* et al.*, 2005).

Simulations can be
applied to a field, or to a section within a field, depending on the intended use
of the model. Field variability is captured within the lumped parameterization
approach. If field variability is large, separate simulations are conducted
for the main soil types within the field and results are aggregated in an
appropriate manner. The timescale of an APSIM simulation generally ranges from
a few days to over a century in duration if suitable input data, such as
weather information, exists. The user selects the depth of the soil profile to
be simulated and the way in which this profile is discretized into soil layers
for numerical solution. Soil properties can be input at different levels of
spatial information (detailed spatial disaggregation *vs* simple soil
horizons) and these are mapped into the simulation layer structure by the user
interface, ensuring conservation of mass of water and solutes, and appropriate
interpolation of model parameters.

SWIM3 has been developed for use within the APSIM modeling framework and so the requirements for model parameterisation are set by the requirements for farming systems analysis. Soil water balance is a critical component in the simulation of many farming systems and the functional requirements of soil water models vary. Because of this, APSIM has provided both detailed (e.g. Richards’ equation) and simple (e.g. capacity or ‘bucket’) models to suit the various problem domains and uses of the model. Detailed models rely on information on soil hydraulic properties, which are often determined using laboratory techniques, pedotransfer functions or inverse methods. From these basic properties the hydraulic behavior is determined via solutions to the flow equations. However, history has shown that simple soil water models are more extensively used, despite their shortcomings, because they are easier to parameterize and provide a much simpler conceptual model of soil water behavior.

Simple ‘cascading’
water balance models, such as the Soilwat model (Probert* et al.*, 1998), make use of
well known properties of soils such as the Drained Upper Limit (DUL) or Field
Capacity, the Lower Limit (LL) of plant water extraction, and the saturated water
content (SAT) and saturated hydraulic conductivity (K_{S}). The
difference between DUL and LL is referred to as the Plant Available Water (PAW)
content and is a very important soil property in agronomic assessment. The
first advantage of this way of describing soils is that these parameters align
very closely to the conceptual model employed by many users of farming systems
models (Gardner, 1988; Dalgliesh and Foale, 1998).
The second advantage is that long standing and geographically broad usage of
these simple models provides a very large database of readily accessible soil
data for use with these simple models. Furthermore, options exist for deriving
properties from simple *in situ* field measurements (Dalgliesh and Foale, 1998) and so many
modelers are continually adding to the information available for future model
users. However, the simulation of some problem domains requires more detailed
hydrological models to describe certain boundary conditions (e.g. fluctuating
water tables), detailed solute fluxes (e.g. salt or nitrate leaching), complex
flow processes (e.g. sub-surface drains), or processes occurring at much
smaller time and spatial scales. There is therefore an advantage to be gained
from providing a means for farming systems modelers to use a Richards’ equation
model within their agronomic understanding of soil function. SWIM3 provides
such an approach.

The values of
SAT, DUL and LL are used to describe three points on the soil water retention
curve, θ(ψ). These three water contents are assumed to correspond to
soil matric potentials of 1 cm, 100 cm and 15000 cm respectively, though the
user can choose to vary the value used at DUL. A fourth and very important
point on the retention curve is the zero water content assumed in oven drying
of soil samples for determination of soil water content. The nature of the
retention curve approaching dryness is important for simulating evaporation
from the soil surface (Ross* et al.*, 1991). The
corresponding matric potential for oven dry soil, assuming air of 25° C and 50%
relative humidity, is 6.09x10^{6} cm, though the impact of these
assumptions is likely to be low (Ross* et al.*, 1991). Two further
assumptions are made from general observations of soil water retention data.
The slope of the retention curve is assumed to be zero at saturation and almost
constant between LL and oven dry. From these six pieces of information a
series of monotonic cubic Hermite splines are constructed for describing the
retention curve across the entire water range (See Appendix for more details).
The use of splines ensures that the retention curve exactly matches the model
user’s specification of ranges of water contents for near saturation, plant
available and near dry conditions.

The hydraulic
conductivity function, K(θ), is inferred from the model user’s
specification of DUL and K_{S}. K_{S} describes the drainage
rate at saturation. By definition, DUL describes the water content at which
drainage rate is reduced to some nominal low value, hereafter K_{DUL}.
This information then provides two points on the soil hydraulic conductivity
function with which we develop a two-region model of hydraulic conductivity
incorporating the effect of macropores and micropores. This approach is very
similar to the three-region model of Poulsen* et al.*(2002). Both this model, and that of
Poulsen* et al.* (2002), avoid errors caused by extrapolating
a single function from saturation to dry soil by anchoring and interpolating
the function at intermediate water contents using extra information. Here, we
assume that the conductivity function is related to the retention curve when
the soil water content is below DUL and that the conductivity is a notional
value of 0.1 mm d^{-1} at DUL. A function for macropore contribution to
K is calculated such that it is significant only above DUL, and results in
total conductivity equaling K_{S} at saturation. This approach ensures
that drainage rates approach K_{S} at saturation and that water content
approaches DUL after drainage (Gardner, 1988). A more detailed description
of the method is included in the Appendix.

Figure 1
illustrates how the four moisture contents (SAT, DUL, LL, Oven Dry) are used to
create a continuous soil water retention curve (Fig. 1a) and how the two-region
conductivity function is constructed from the SAT-K_{S} and DUL-K_{DUL}
pairs (Fig. 1b) representative of a silt-loam soil.

Figure 1.
Demonstration of how basic soil properties (SAT = 0.5 cm^{3}cm^{-3},
DUL= 0.4 cm^{3}cm^{-3}, LL= 0.12 cm^{3}cm^{-3},
Oven Dry, K_{S}=1000 mm d^{-1}, K_{DUL}=0.1 mm d^{-1})
are mapped into continuous hydraulic property functions for a) water content
and b) hydraulic conductivity. See appendix for definition of K_{matrix}.

The main parameters used in calibrating SWIM3 are therefore SAT, DUL, LL and Ks. Several methods are commonly used to determine these parameters. SAT is often estimated as a fixed proportion of the total porosity of the soil calculated from the soil bulk density. Bulk density is a mandatory parameter for several APSIM models and so it is not a data requirement particular to SWIM3. DUL and LL are often determined in the field: DUL via measurement of soil water content after an extended period of drainage following saturation and LL after maximal drawdown of soil water content by plants (Dalgliesh and Foale, 1998). Alternatively DUL and LL can be estimated from laboratory measurements of soil water content at 100 cm and 15000 cm matric suctions respectively (Gardner, 1988). Finally, SAT, DUL and LL can all be estimated from regular observations of soil water content including periods of wetting up and drainage, and periods of drying down by plants. Soil water content will often vary between SAT and DUL during periods of frequent rewetting, and decrease to LL during periods of high crop water use and minimal water input. In cases where long term information on soil water variation is available, rapid estimates of soil hydraulic properties can be obtained from direct interpretation of soil behavior. This approach will be demonstrated in the two case studies below.

The saturated
conductivity of the soil, K_{S}, can be estimated from infiltration
studies, laboratory measurements or relationships based on soil texture. As
stated above, the method used to derive the conductivity function within SWIM3
removes some of the sensitivity of the model to errors in estimates of K_{S}
by anchoring the conductivity curve at DUL. The model will still be sensitive
to estimated K_{S} values near saturation and so the parameter will be
important under situations of high water input. Under dry land conditions,
parameters for soil water holding capacity are likely to be more important.

The following
remaining parameters are of some importance. The runoff curve number (Hawkins, 1996), used in partitioning
rainfall between infiltration and runoff, is usually derived from guidelines
based on soil texture and soil surface characteristics (Ringrose-Voase* et al.*, 2003). Many
of the parameters for the convection-dispersion equation are taken from the
literature or physical tables and so are available as default values for the
user. Defaults are also provided for parameters used in the numerical solution
of Richards’ equation. These include error tolerances, limits for the
magnitude in iterative increments, space weighting factors and user selections
for handling numerical dispersion and oscillations. In most cases the
recommended default values can be adopted by the model users.

It should be
noted that a great number of other parameters are required by other models
within an APSIM simulation. These are outside the scope of this paper.
However, the reader can refer to other publications for information on
parameters for crop growth (Robertson* et al.*, 2002; Wang* et al.*, 2002), soil organic matter and nutrient dynamics (Probert* et al.*, 1998; Huth* et al.*, 2010), rules for agronomic management (Keating* et al.*, 2003) and various climatic
data (Jeffrey *et al.*, 2001).

The strength in
SWIM3 comes from the mechanistic numerical model based on solutions of the 1-dimensional
Richards’ and Convection-Dispersion equations. The main advantages of SWIM3 over
the early versions of the model come from its implementation within the APSIM
framework. The large number of crop and soil modules available to the user
allows the SWIM water balance to be used in model applications across a wide
range of problem domains. These benefits have been used in many previous
studies using the earlier APSIM-SWIM model as mentioned in the introduction to
this paper. However, this new implementation of the SWIM model brings with it
new benefits arising from the approach used for soil parameterization. SWIM3
can now be parameterized using fairly simple measures of soil attributes for
which formalized techniques are readily available (Dalgliesh and Foale, 1998). These
attributes, which describe the plant available water holding capacity of a
soil, are also very important determinants of the productivity of a soil,
especially for dry land farming systems (Dalgliesh and Foale, 1998). It is
therefore logical that these parameters will also be very important
determinants of modeled crop production. Previous studies have shown that
grain yield changes in response to water supply by an average 20 kg ha^{-1}
mm ^{-1} for wheat in southern Australia (French and Schultz, 1984).
Responses from crop models are likely to be comparable and so errors in
predictions of soil water supply will likely cause significant errors in crop
production. However, parameterization of SWIM3 directly from data on plant
available water contents provides the user with close control of modeled water
balance and the resulting crop production.

As has been
shown in this paper, the model can also be very easily parameterized from very
simple data on soil water behavior such as observed ranges in soil water
content. These approaches have been used with simple ‘cascading’ water balance
models such as SoilWat (Probert* et al.*, 1998) in APSIM. In
this case, we use this same approach of parameterization from simple observations
of soil water behavior but combine this with a more robust physically-based numerical
model. One consequence of this approach is a reduced number of soil parameters
to that required by the cascading water balance for some soil processes. For
example, two parameters used in Soilwat to describe evaporation, two for
unsaturated flow, and one for near-saturated water flow are not required when
we parameterize SWIM3 from the same basic field observations because these processes
are now captured by the solution of Richards’ equation.

One weakness of
SWIM3 when compared to the simpler soil water balance models is the increased
execution time required for the iterative solution of a series of highly
non-linear differential equations. In many applications this computation
overhead is of little consequence and the benefit of the extra model
capabilities outweighs this cost. However, this will be a limitation to its
use for large scale spatial analyses or large suites of long term simulations,
as is increasingly required of modern farming systems models. Solutions to this
constraint are available (Ross, 2011) and will be explored for a future release
of the model. A second weakness of the model is the lack of any consideration
of the impact of soil chemistry on soil hydraulic properties. Chemical impacts
on hydraulic properties, as is the case in sodic subsoils, are captured using
empirical relationships in simple water balance models (Hochman *et al.*,
2007). The effects of soil chemistry on the assumptions used in describing
soil hydraulic properties in SWIM3 will be considered in future work.

This paper also highlights the issues in model parameterization. While there is much value in efforts to provide laboratory measurement or numerical optimization of soil hydraulic properties, we have demonstrated that simple logic applied to soil water behavior can be used in a similar way. Soil properties can be deduced from soil behavior. Both approaches, measurement or rational deduction, are valid (Williams et al., 1991). A soil’s water content after drainage, and its plant available water holding capacity, are often consistent and well understood emergent properties of a soil and so model parameterization should take these into account in a simple but meaningful way. The method employed in this model, and the case studies shown above, provides such a framework.

Future development of SWIM3 will address the deficiencies identified above to provide increased numerical efficiency and the effect of soil chemistry on soil hydraulic processes. There are also efforts underway to allow rapid laboratory or field measurements to further inform model parameterization using commercially available apparatus. Modelers interested in assisting further development of SWIM3 can do so via contacting the authors or involvement in the APSIM Community Source Framework (www.apsim.info).

Peter Ross provided much of the specialist design of the numerical methods used in SWIMv2 and hence SWIM3.

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Appendix

SWIM3 uses a series of monotonic cubic Hermite splines (Fritsch and Carlson, 1980) to describe the soil water retention curve. Values for θ are interpolated between the four points for 1) Saturation, 2) Drained Upper Limit, 3) Lower Limit, and 4) Oven Dry. The method is as follows:

i) Calculate the slope of the secant lines between each successive point.

ii) Calculate the slope at each successive point as the average of the secants either side of this point.

iii) The resultant cubic spline will not be monotonic if either of the following is true

If so set

Where

iv)
Interpolate the value of θ following the
standard method for evaluating a cubic Hermite spline for the relevant region between
ψ_{i} and ψ_{i+1} within the interpolation set.

Where

and the basis functions for the cubic Hermite spline are:

** **

SWIM3 describes hydraulic conductivity as the sum of two functions describing the conductivity of the soil matrix and macropores (Ross and Smettem, 1993). The function for the soil matrix is related to the shape of the soil water retention curve (Mualem, 1976) as expressed by Campbell (1985). A simple power function is used for the contribution of macropores.

where

The contribution
of the micropore component is calculated from the assumption that the
conductivity at DUL (K_{DUL}) is almost entirely due to the soil matrix.
Thus, the conductivity of the soil matrix component at saturation is

The value of P
is calculated using the assumption that, at the drained upper limit, the
conductivity of the macropores is negligible. A value of P is therefore
determined such that the conductivity of the macropores at DUL contributes only
1% of the overall value of K_{DUL}.