SWIM3: MODEL USE, CALIBRATION, AND VALIDATION N. I. Huth, K. L. Bristow, K. Verburg

ABSTRACT. SWIM3 is the latest release in the family of SWIM (Soil Water Infiltration and Movement) models that provides efficient solutions to the Richards and advection-dispersion equations for use in studies of soil water and solute dynamics. This version of the model has been designed specifically for use in farming systems simulation. Development within the APSIM (Agricultural Production Systems Simulator) framework enables SWIM3 to be combined with a wide range of soil and crop models to simulate a variety of agricultural systems. Other improvements in this release provide a new approach for specifying soil hydraulic properties from simple measures of soil water behavior. The simplicity of this new approach makes such a mechanistic numerical model more accessible to farming systems researchers. The effectiveness of this approach and the utility of SWIM3 for use in farming systems analysis is demonstrated using data from two long-term trials with different soils, climates, and cropping systems. These examples show how the design of SWIM3 allows model parameterization from consistent and well understood emergent soil properties in a simple but meaningful way. Access to the model and involvement in its ongoing development is welcomed via the APSIM Community Source Framework. Keywords. APSIM, Computer model, Hydrologic model, Soil physical properties, Soil water movement.

S

WIM3 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 of 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 one-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 convectiondispersion 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-

Submitted for review in September 2012 as manuscript number SW 9416; approved for publication by the Soil & Water Division of ASABE in April 2012. The authors are Neil Ian Huth, Senior Research Scientist, CSIRO Ecosystem Sciences, Toowoomba, Queensland, Australia; Keith Leslie Bristow, Senior Principal Research Scientist, CSIRO Land and Water, Townsville, Queensland, Australia; and Kirsten Verburg, Senior Research Scientist, CSIRO Land and Water, Canberra ACT, Australia. Corresponding author: Neil Ian Huth, CSIRO Ecosystem Sciences, P.O. Box 102, Toowoomba, Qld 4350, Australia; phone: +61-7-46881421; e-mail: [email protected].

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 and was redeveloped for use as a component within integrated modeling frameworks. While much of the numerical approach used within the APSWIMSWIM 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 on 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 feefor-service activity. However, all workshop materials, user documentation, and a model user support forum are freely available via the APSIM website (www.apsim.info).

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© 2012 American Society of Agricultural and Biological Engineers ISSN 2151-0032

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SWIM3 DESCRIPTION The APSIM modeling framework has been developed to simulate biophysical processes 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 has been used in a broad range of applications, including on-farm decision making, farming systems design, assessment of seasonal climate forecasts, analysis of agribusiness supply chains, development of waste management guidelines, risk assessment for government policy, and as a guide to research and education activities (Keating et al., 2003). APSIM’s component-based design allows individual models to interact via a common communications protocol (Moore et al., 2007). Models are available for over 30 major crop, pasture, and tree species (Robertson et al., 2002; Wang et al., 2002; Paydar et al., 2005b), as well as the main soil processes affecting agricultural systems (e.g., C, N, and P dynamics, water, and erosion) (Probert et al., 1998). APSIM also provides a flexible agricultural management capability enabling the user to specify complex crop rotations and land management regimes (Keating et al., 2003). 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. While 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 one-dimensional, lumped parameter, physically based model. Some submodels within SWIM3 capture simple spatial processes, so SWIM3 can also be described as a quasi two-dimensional model. SWIM3 provides a onedimensional simulation of water fluxes through a numerical solution to the Richards equation (Richards, 1931):

∂θ ∂  ∂ψ ∂z  = K (ψ)  + +S ∂t ∂x  ∂x ∂x 

(1)

where θ is volumetric water content (cm3 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 (cm3 cm-3 h-1). Solute fluxes are calculated using a solution to the convection-dispersion equation: ∂ ( θc ) ∂t

+

∂ ( ρs ) ∂t

=

∂  ∂c  ∂ ( qc ) +ϕ  θD  − ∂x  ∂x  ∂x

(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 (cm2 h-1), q is the water flux (cm h-1), 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 the Richards equation shown in equation 1 is highly non-linear, especially in dry soils, so it is solved using a hyperbolic sine transform of ψ (Ross, 1990a). A detailed description of the numerical methods used in solving equa-

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tions 1 and 2 is provided by 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 submodels 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 analog 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 in which no water table exists within the soil profile. Otherwise, groundwater 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 groundwater 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 NO3, NH4, 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, then separate simulations are conducted for the main soil types within the field, and results are aggregated in an appropriate manner. The time scale of an APSIM simulation generally ranges from a few days to over a century if suitable input data, such as weather information, exist. The user selects the

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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 CALIBRATION AND VALIDATION APSIM VALIDATION PROCESSES Software processes developed within the APSIM Initiative and its Community Source Framework provide an effective means for maintaining ongoing model testing and validation during widespread collaborative development of the model (Holzworth et al., 2011). This process makes use of an extensive range of detailed model tests that exercise the APSIM model at various levels (submodel, model, simulation) to determine model reliability, validity, and utility. Ongoing model validation is an important component of the continuous integration process (Duvall et al., 2007). The entire model test suite is run and compared after every change to the source code is committed to the APSIM version control system. This automated testing system includes the validation tests for each APSIM model provided by the developer. In many cases, it also includes datasets, similar to the case studies in this article, which APSIM users can provide to further enhance and broaden the overall test suite over time. The parameters used in this broad model testing approach are then distributed with the model to provide an official set of universally applicable parameters that are to be used across all simulations. These commonly include physical constants, parameters for soil organic matter dynamics, crop physiological parameters, chemical makeup of fertilizers or other amendments, or basic model parameters deemed to be simulation independent. This leaves only the simulation-dependent parameters, usually site- or problem-specific parameters, to have their values determined by measurement, prediction, or calibration. The APSIM user interface provides access to these, and publications are available to assist users in measuring parameters where possible (Dalgliesh and Foale, 1998; Probert et al., 1998; Robertson et al., 2002). SWIM3 CALIBRATION SWIM3 has been developed for use within the APSIM modeling framework; therefore, the requirements for model parameterization 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 provides both detailed (e.g., the 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 de-

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termined 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 (Ks). 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), 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., subsurface 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 15,000 cm respectively, although 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 6.09 × 106 cm, although 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 the Appendix for 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

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10-3 10-5 10-7 10-9 0.0

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Figure 1. Demonstration of how basic soil properties (SAT = 0.5 cm3 cm-3, DUL = 0.4 cm3 cm-3, LL = 0.12 cm3 cm-3, oven dry, Ks = 1000 mm d-1, and KDUL = 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 Kmatrix).

from the model user’s specification of DUL and Ks, where Ks describes the drainage rate at saturation. By definition, DUL describes the water content at which the drainage rate is reduced to some nominal low value, hereafter KDUL. This information then provides two points of 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 Ks at saturation. This approach ensures that drainage rates approach Ks 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, and 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-Ks and DUL-KDUL pairs (fig. 1b) representative of a silt loam soil. CALIBRATION PARAMETERS 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, 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).

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Alternatively, DUL and LL can be estimated from laboratory measurements of soil water content at 100 and 15,000 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 (Ks) 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 Ks by anchoring the conductivity curve at DUL. The model will still be sensitive to estimated Ks values near saturation, 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 are available as default values for the user. Defaults are also provided for parameters used in the numerical solution of the 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 user. 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 article. However,

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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).

CASE STUDIES Two case studies are provided to demonstrate the method for simple parameterization of SWIM3. The studies differ in soil and climate and include within them a range of cropping systems from which crop rotations with very different hydrology have been chosen for demonstration purposes. The simulations were performed using APSIM version 7.3. HUDSON ROTATION TRIAL The first experiment was conducted in the Liverpool Plains region of New South Wales, Australia (31° 45′ S, 150° 45′ E) to explore the water balance and productivity of nine different cropping systems including six treatments of continuous cropping of wheat (Triticum aestivum), sorghum (Sorghum bicolor), mungbeans (Phaseolus aureus), and chickpeas (Cicer arietinum) with differing cropping frequencies (Paydar et al., 2005a). The remaining three treatments involved continuous perennial pastures of lucerne (Medicago sativa), grass (Panicum coloratum), and a lucerne-grass mixture. Only the continuous wheat cropping and continuous grass treatments have been chosen for the demonstration purposes of this case study. The soil profile is classified as an endocalcareous, self-mulching, black vertosol (Isbell, 1996) or Ug5.15 (Northcote, 1979). The soil to around 1 m depth consists of colluvial material with 75% to 80% clay. This overlies >5 m of brown clay with variable amounts of calcium carbonate concretions. Groundwater occurs 15 m below the surface above basalt rock. Further detail on soil properties is provided by Ringrose-Voase et al. (2003). The mean annual rainfall for the site is approximately 684 mm year-1, with 56% of this falling within the April to November winter cropping season. Soil water content to 3.1 m depth was measured with a calibrated neutron moisture meter (CPN 503 DR Hydroprobe moisture gauge, Boart Longyear Co., South Jordan, Utah) at regular intervals from December 1994 until January 2000. Crop and pasture growth and development and soil and crop nitrogen contents were also monitored for the duration of the trial. All these data have been used in previous modeling of the trial by Ringrose-Voase et al. (2003) and Paydar et al. (2005a) with a configuration of the APSIM model using the Soilwat (Probert et al., 1998) water balance model. Model predictions are compared to measurements of soil water and naturally occurring soil chloride. Comparison of soil water data demonstrates the model’s ability to simulate the water balance of two contrasting farming systems, while the soil chloride data provide an inert environmental tracer for testing model predictions of solute transport.

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RUTHERGLEN ROTATION TRIAL The second experiment was conducted at Rutherglen in northeast Victoria, Australia (36° 6′ S, 146° 30′ E) to explore the water balance and productivity of eight different cropping systems consisting of continuous cropping of wheat (Triticum aestivum), canola (Brassica napus), lupins (Lupinus albus), lucerne (Medicago sativa), and a range of rotations varying in the timing and duration of a lucerne phase within a crop rotation (Hirth et al., 2001; Ridley et al., 2001). As for the Hudson case study, only the continuous wheat cropping and continuous lucerne treatments have been chosen for demonstration purposes. The soil at this site is classified as a mottled, sodic, eutrophic brown chromosol (Isbell, 1996) or Dy3.32. (Northcote, 1979). It is poorly drained, with a very fine sandy clay loam A horizon (approximately 15% to 20% clay content) overlying a light clay (approximately 35% clay content) B horizon. The mean annual rainfall for the site is 598 mm year-1, with 74% of this falling within the April to November winter cropping season. Soil water content to 2.7 m depth for the chosen treatments was measured with a calibrated neutron moisture meter (CPN Corp., Martinez, Cal.) at intervals of two to three weeks during the growing season and less frequently from harvest to the autumn break. Measurements were taken from September 1995 until December 1999. Crop growth and soil and crop nitrogen contents were also monitored for the duration of the trial. All these data have also been used in previous modeling of the trial by Verburg et al. (2007) with APSIM using the Soilwat water balance model. As with the Hudson trial, the soil water data are used to demonstrate the model’s ability to simulate the water balance of contrasting farming systems. CALIBRATION OF THE MODEL Both datasets contain detailed soil water data over several seasons. This allows simple deduction of soil hydraulic properties directly from the field data. This approach is regularly used in calibrating simple soil water models, as was the case for both datasets when previously modeled using the Soilwat model. This same approach is used here. The value of LL was inferred from dry soil profiles in treatments with continuous lucerne because it is a deeprooted perennial pasture with a strong ability to extract soil water. The value of LL for each soil depth was taken from measurements in the lucerne treatment when soil water content was low and not varying. DUL and SAT were inferred from the range in soil water content at each depth during periods of regular rainfall. In some cases, periods of saturation are followed by extended fallow periods during which the soil water content becomes stable, providing a good estimate of DUL. SAT was taken to be at the top of the range and DUL at the bottom of the range of soil water content during these periods using simple visual inspection of the time series data. Values of Ks were taken from published measurements at the Hudson site (Ringrose-Voase et al., 2003) and were estimated from the description above to be 100 and 10 mm d-1 for the surface and subsoil, respectively, at the Rutherglen site.

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RESULTS Simulation results for Hudson (fig. 2) and Rutherglen (fig. 3) farming systems trials show that the model captured the major differences in soil water content for cropping and pasture treatments. Seasonal variation in soil water is higher under annual crops than for perennial pastures, with deeper and more frequent wetting under the former. It should be noted that, for some periods, observed increases in soil water storage exceeded rainfall, suggesting preferential wetting of soil surrounding the neutron moisture meter tubes. As a result, simulated water storage is less than the measured values for these events. Extraction of deep soil water (>1 m) was too rapid in simulations for pasture at Hudson. This might be due to errors in predictions of root exploration at depth or to a cumulative error caused by consistent overprediction of excessive plant water use. In contrast to this, predicted surface soil water contents were too high for the cropping treatment at Rutherglen. Much of this occurred during the drying phase during crop growth, when

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Soil Water Content or Daily Rainfall (mm)

Information on the agronomic management of each site, including plant population, timing, and cultivars for sown crops and pastures, nitrogen fertilizer rates, tillage, harvesting, and spraying of weeds was incorporated into the model specifications. The rooting depth of each crop and pasture species was chosen according to the observed soil water extraction data at each site. Soil organic matter, mineral nitrogen, and naturally occurring chloride levels were input as specified for the previous modeling of these datasets described earlier. As stated earlier, soil water data for several soil depths are available in both datasets for use in evaluating the simulation results. These have been compared graphically to predictions of soil water distribution through time. The ability of the model to simulate the total water storage within the soil profile is very important for agronomic or environmental applications. For the Hudson trial, temporal variation in soil chloride levels indicates leaching of salts caused by deep drainage of water. Therefore, a range of statistical measures of model effectiveness in predicting total profile soil water and chloride were calculated. These include Nash-Sutcliffe efficiency (NSE) and root mean square error to standard deviation ratio (RSR) to express model error relative to data variance (Moriasi et al., 2007) and mean error (ME) and mean absolute error (MAE) to show bias and average error in simple water or chloride balance terms. None of these four measures accounts for uncertainty in observed data values. Therefore, the percentage of observed data that were predicted with an error of less than the 95% confidence interval of the measurement (% within CI) has been also calculated to account for instances in which poor model performance may be due to data quality. Finally, both NSE and RSR return lower values of model performance when temporal variation is low in a dataset. In many cases, predictions of treatment differences are as important as predictions of temporal variation, so the above statistics have been calculated for individual and combined treatment data for each trial.

200

c) 90-130 cm

160 120 240 200

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40

0 Jan-95

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Date

Figure 2. Predicted (lines) and observed (symbols) soil water content for various soil depths (a-f) for continuous pasture (black) and continuous cropping (gray) treatments at Hudson. SAT, DUL, and LL for the various depths are indicated on the right side of each graph. Daily rainfall totals (g) are shown for comparison.

canopy cover would be high. This suggests that the error here is likely to be related to underestimates of crop water use by some of the crop models. However, the range in water content in each section of the soil profile, drainage after saturation, and extraction by crops are all captured using the approaches described above for deriving the soil hydraulic properties from field data. Predictions of total soil water storage are good indications of a model’s ability to simulate the water balance of different cropping systems. Statistical evaluation of the results is shown for Hudson in table 1 and for Rutherglen in table 2. Moriasi et al. (2007) suggest that values of NSE greater than 0.65 indicate good to very good model performance for predictions of monthly hydrological data. Predictions of nearly all treatments at both sites fall into these categories if we assume that the same rating scale can be used for soil water data of similar frequency. Only the predictions for the cropping treatment at Rutherglen provided an unsatisfactory result using this rating scale. Moriasi et al. (2007) also suggest that values of RSR below 0.6 indicate good to very good performance, and once again only

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Figure 4. Predicted (lines) and observed (symbols) profiles of soil chloride concentration at the beginning of the trial in 1994 (solid lines, closed symbols) and at the end of the trial in 2000 (dashed lines, open symbols) at Hudson. Graphs show the results for (a) continuous pasture and (b) continuous cropping.

160 120

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Figure 3. Predicted (lines) and observed (symbols) soil water content for various soil depths (a-f) for continuous pasture (black) and continuous cropping (gray) treatments at Rutherglen. SAT, DUL, and LL for the various depths are indicated on the right side of each graph. Daily rainfall totals (g) are shown for comparison. Table 1. Statistical analysis of simulation results for total soil water (0-250 cm) for individual and combined treatment data for the years 1994 to 2000 in the Hudson trial. Total Profile Soil Water Statistic Cropping Pasture Combined NSE 0.86 0.70 0.86 RSR 0.37 0.55 0.37 ME (mm) -8.7 -2.9 -5.6 MAE (mm) 26.7 35.7 31.4 % within CI 71 45 57

Table 2. Statistical analysis of simulation results for total soil water (0-240 cm) for individual and combined treatment data for the years 1995 to 2000 in the Rutherglen trial. Total Profile Soil Water Statistic Cropping Pasture Combined NSE 0.40 0.89 0.93 RSR 0.78 0.33 0.26 ME (mm) 18.9 -9.9 6.4 MAE (mm) 22.2 15.3 19.0 % within CI 55 53 54

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the predictions of the cropping treatment at Rutherglen returned unsatisfactory results based on this index. However, ME and MAE values for all treatments at both sites are low, showing that bias and average error is mostly less than 30 mm. These values represent less than 5% of mean annual rainfall. Furthermore, the magnitude of these errors is likely to be comparable to the accuracy of the measurement protocol. For most simulations, over half of all observations were predicted to within the 95% confidence interval of their measurement. This is even true for predictions of the cropping treatment at Rutherglen, suggesting that uncertainty in the observed data may be at least partly responsi ble for the lower performance indicated by NSE and RSR. The range of observed data is also lower for cropping at Rutherglen than for the other treatments, and this would result in lower indices of model performance using NSE and RSR even if the model error is comparable to that of other simulations. Finally, analysis of predictions for the combined treatment data for each site provides values for NSE and RSR that all indicate very good performance using the rating system of Moriasi et al. (2007). This shows that the model is able to describe these conditions where treatment variation can be as significant as temporal variation. Finally, it is important to gain confidence that the model has been configured to get the right results for the right reasons. Further evaluation of the calculated water balance was undertaken using the soil chloride data for the Hudson trial. At this site, the leaching of naturally occurring soil chloride was monitored for use as an environmental tracer of water movement. SWIM3 predicted differences in the redistribution and leaching of naturally occurring soil chloride under continuous cropping and pastures (fig. 4). The frequent and deeper wetting of soils in cropping systems Table 3. Statistical analysis of simulation results for total soil chloride (0-250 cm) for individual and combined treatment data for the years 1994 to 2000 in the Hudson trial. Total Profile Chloride Cropping Pasture Combined NSE 0.61 -0.93 0.4 RSR 0.62 1.39 0.77 ME (% of mean) -9.9 -12.4 -11.8 MAE (% of mean) 14.5 12.5 13.4 % within CI 83 58 71

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results in leaching of salts, whereas the drier soil conditions under pasture minimize the likelihood of these events. Statistical evaluation of the predicted total soil chloride gives mixed results (table 3). Evaluation of the predictions of total soil chloride using NSE and RSR suggests that predictions for the cropping treatment are satisfactory, whereas predictions for the pasture treatment were unsatisfactory. However, in the case of the pasture treatment, spatial variation in soil chloride is greater than temporal variation, given the very small amount of leaching under the perennial vegetation. In situations such as these, indicators such as NSE and RSR become compromised by the error in the measurement, and other statistical or graphical methods should be considered. A large proportion of the soil chloride data from both treatments (83% for cropping, 58% for pasture) was simulated to within the 95% confidence intervals of the measurement. This, and agreement between measured and simulated chloride distribution at the end of the trial (fig. 4), gives confidence that the model’s prediction of soil water content was obtained via accurate simulation of appropriate processes.

DISCUSSION The strength of SWIM3 comes from the mechanistic numerical model based on solutions of the one-dimensional Richards and convection-dispersion equations. The main advantages of SWIM3 over the earlier 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 article. 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 waterholding 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, 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 article, 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 “cas-

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cading” 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 it with a more robust physically based numerical model. One consequence of this approach is a reduced number of soil parameters compared 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 the 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 nonlinear 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 article 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, 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 DEVELOPMENTS 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 by contacting the authors or through involvement in the APSIM Community Source Framework (www.apsim.info).

TRANSACTIONS OF THE ASABE

ACKNOWLEDGEMENTS Peter Ross provided much of the specialist design of the numerical methods used in SWIMv2 and hence SWIM3. Rick Young and Anna Roberts provided the data used for the Hudson and Rutherglen case studies.

REFERENCES Campbell, G. S. 1985. Soil Physics with BASIC. New York, N.Y.: Elsevier. Connolly, R. D., M. Bell, N. Huth, D. M. Freebairn, and G. Thomas. 2002. Simulating infiltration and the water balance in cropping systems with APSIM-SWIM. Australian J. Soil Res. 40(2): 221-242. Cowan, I. R. 1965. Transport of water in the soil-plantatmosphere system. J. Applied Ecol. 2(1): 221-239. Dalgliesh, N. P., and M. A. Foale. 1998. Soil matters: Monitoring soil water and nitrogen in dryland farming. Toowoomba, Queensland, Australia: Agricultural Production Systems Research Unit. Duvall, P. M., S. Matyas, and A. Glover. 2007. Continuous Integration: Improving Software Quality and Reducing Risk. Boston, Mass.: Pearson Education. French, R. J., and J. E. Schultz. 1984. Water use efficiency of wheat in a Mediterranean-type environment: II. Some limitations to efficiency. Australian J. Agric. Res. 35(6): 765775. Fritsch, F. N., and R. E. Carlson. 1980. Monotone piecewise cubic interpolation. SIAM J. Numerical Analysis 17(2): 238-246. Gardner, E. A. 1988. Soil water. In Understanding Soils and Soils Data, 153-186. I. F. Fergus ed. Brisbane, Queensland, Australia: Australian Society of Soil Science. Hawkins, R. H. 1996. Runoff curve number: Has it reached maturity? J. Hydrol. Eng. 1(1): 11-19. Hirth, J. R., P. J. Haines, A. M. Ridley, and K. F. Wilson. 2001. Lucerne in crop rotations on the Riverine Plains: 2. Biomass and grain yields, water use efficiency, soil nitrogen, and profitability. Australian J. Agric. Res. 52(2): 279-293. Hochman, Z., Y. P. Dang, G. D. Schwenke, N. P. Dalgliesh, R. Routley, M. McDonald, I. G. Daniells, W. Manning, and P. L. Poulton. 2007. Simulating the effects of saline and sodic subsoils on wheat crops growing on vertosols. Australian J. Agric. Res. 58(8): 802-810. Holzworth, D. P., N. I. Huth, and P. G. deVoil. 2011. Simple software processes and tests improve the reliability and usefulness of a model. Environ. Modelling and Software 26(4): 510-516. Huth, N. I., B. A. Keating, K. L. Bristow, K. Verburg, and P. J. Ross. 1996. SWIMv2 in APSIM: An integrated plant, soil water, and solute modelling framework. In Proc. 8th Australian Agron. Conf., 667. Toowoomba, Queensland, Australia: Australian Agronomy Society. Huth, N. I., P. J. Thorburn, B. J. Radford, and C. M. Thornton. 2010. Impacts of fertilisers and legumes on N2O and CO2 emissions from soils in subtropical agricultural systems: A simulation study. Agric. Ecosystems and Environ. 136(3-4): 351-357. Isbell, R. F. 1996. The Australian Soil Classification: Australian Soil and Land Survey Handbook. Melbourne, Victoria, Australia: CSIRO Publishing. Jeffrey, S. J., J. O. Carter, K. M. Moodie, and A. R. Beswick. 2001. Using spatial interpolation to construct a comprehensive archive of Australian climate data. Environ. Modeling and Software 16(4): 309-330. Keating, B. A., P. S. Carberry, G. L. Hammer, M. E. Probert, M. J.

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Robertson, D. Holzworth, N. I. Huth, J. N. G. Hargreaves, H. Meinke, Z. Hochman, G. McLean, K. Verburg, V. Snow, J. P. Dimes, M. Silburn, E. Wang, S. Brown, K. L. Bristow, S. Asseng, S. Chapman, R. L. McCown, D. M. Freebairn, and C. J. Smith. 2003. An overview of APSIM, a model designed for farming systems simulation. European J. Agron. 18(3-4): 267288. Malone, R. W., N. Huth, P. S. Carberry, L. Ma, T. C. Kaspar, D. L. Karlen, T. Meade, R. S. Kanwar, and P. Heilman. 2007. Evaluating and predicting agricultural management effects under tile drainage using modified APSIM. Geoderma 140(3): 310-322. McCown, R. L., G. L. Hammer, J. N. G. Hargreaves, D. Holzworth and N. I. Huth. 1995. APSIM: An agricultural production system simulation model for operational research. Math. and Computers in Simulation 39(3-4): 225-231. Moldrup, P., T. Olesen, S. Yoshikawa, T. Komatsu, A. M. McDonald, and D. E. Rolston. 2005. Predictive-descriptive models for gas and solute diffusion coefficients in variably saturated porous media coupled to pore-size distribution: III. Inactive pore space interpretations of gas diffusivity. Soil Sci. 170(11): 867-880. Moore, A. D., D. P. Holzworth, N. I. Herrmann, N. I. Huth, and M. J. Robertson. 2007. The common modelling protocol: A hierarchical framework for simulation of agricultural and environmental systems. Agric. Systems 95(1-3): 37-48. Moriasi, D. N., J. G. Arnold, M. W. Van Liew, R. L. Bingner, R. D. Harmel, and T. L. Veith. 2007. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 50(3): 885-900. Mualem, Y. 1976. A new model for predicting hydraulic conductivity of unsaturated porous media. Water Resources Res. 12(3): 513-522. Northcote, K. H. 1979. A Factual Key for the Recognition of Australian Soils. Glenside, South Australia: Rellim Technical Publishers. Paydar, Z., N. Huth, A. Ringrose-Voase, R. Young, T. Bernardi, B. Keating, and H. Cresswell. 2005a. Deep drainage and land use systems. Model verification and systems comparison. Australian J. Agric. Res. 56(9): 995-1007. Paydar, Z., N. Huth, and V. Snow. 2005b. Modelling irrigated eucalyptus for salinity control on shallow water tables. Australian J. Soil Res. 43(5): 587-597. Poulsen, T. G., P. Moldrup, B. V. Iversen, and O. H. Jacobsen. 2002. Three-region Campbell model for unsaturated hydraulic conductivity in undisturbed soils. SSSA J. 66(3): 744-752. Priestley, C. H. B., and R. J. Taylor. 1972. On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review 100(2): 81-92. Probert, M. E., J. P. Dimes, B. A. Keating, R. C. Dalal, and W. M. Strong. 1998. APSIM’s water and nitrogen modules and simulation of the dynamics of water and nitrogen in fallow systems. Agric. Systems 56(1): 1-28. Richards, L. A. 1931. Capillary conduction of liquids through porous mediums. Physics 1(5): 318-333. Ridley, A. M., B. Christy, F. X. Dunin, P. J. Haines, and K. F. Wilson. 2001. Lucerne in crop rotations on the Riverine Plains: 1. The soil water balance. Australian J. Agric. Res. 52(2): 263277. Ringrose-Voase, A. J., R. R. Young, Z. Paydar, N. I. Huth, A. L. Bernardi, H. P. Cresswell, B. A. Keating, J. F. Scott, M. Stauffacher, R. G. Banks, J. F. Holland, R. M. Johnston, T. W. Green, L. J. Gregory, I. Daniells, R. Farquharson, R. J. Drinkwater, S. Heidenreich, and S. G. Donaldson. 2003. Deep drainage under different land uses in the Liverpool Plains catchment: Report 3. Agricultural Resource Management

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Report Series. Tamworth, New South Wales, Australia: NSW Agriculture. Robertson, M. J., P. S. Carberry, N. I. Huth, J. E. Turpin, M. E. Probert, P. L. Poulton, M. Bell, G. C. Wright, S. J. Yeates, and R. B. Brinsmead. 2002. Simulation of growth and development of diverse legume species in APSIM. Australian J. Agric. Res. 53(4): 429-446. Ross, P. J. 1990a. Efficient numerical methods for infiltration using Richards equation. Water Resources Res. 26(2): 279-290. Ross, P. J. 1990b. SWIM: A simulation model for soil water infiltration and movement. Reference manual to SWIMv1. Canberra, New South Wales, Australia: CSIRO Division of Soils. Ross, P. J. 1992. Cubic approximation of hydraulic properties for simulations of unsaturated flow. Water Resources Res. 28(10): 2617-2620. Ross, P. J. 2011. Numerical solution of the continuity equation for soil water flow using precomputed steady-state fluxes. Vadose Zone J. 10(2): 760-766. Ross, P. J., and K. R. J. Smettem. 1993. Describing soil hydraulic properties with sums of simple functions. SSSA J. 57(1): 2629. Ross, P. J., J. Williams, and K. L. Bristow. 1991. Equation for extending water retention curves to dryness. SSSA J. 55(4): 923-927. Skaggs, R. 1989. DRAINMOD User’s Manual. Interim Tech. Release. Raleigh, N.C.: North Carolina State University, Department of Biological and Agricultural Engineering. Snow, V. O., D. J. Houlbrooke, and N. I. Huth. 2007. Predicting soil water, tile drainage, and runoff in a mole-tile drained soil. New Zealand J. Agric. Res. 50(1): 13-24. Verburg, K., B. A. Keating, K. L. Bristow, N. I. Huth, P. J. Ross, and V. R. Catchpoole. 1996a. Evaluation of nitrogen fertiliser management strategies in sugarcane using APSIM-SWIM. In Sugarcane: Research Towards Efficient and Sustainable Production, 200-202. J. R. Wilson, D. M. Hogarth, J. A. Campbell, and A. L. Garside, eds. Brisbane, Queensland, Australia: CSIRO Division of Tropical Crops and Pastures. Verburg, K., P. J. Ross, and K. L. Bristow 1996b. SWIM V2.1 user manual. Divisional Report No. 130. Canberra, New South Wales, Australia: CSIRO Division of Soils. Verburg, K., W. J. Bond, J. R. Hirth, and A. M. Ridley. 2007. Lucerne in crop rotations on the Riverine Plains: 3. Model evaluation and simulation analyses. Australian J. Agric. Res. 58(12): 1129-1141. Wang, E., M. J. Robertson, G. L. Hammer, P. S. Carberry, D. Holzworth, H. Meinke, S. C. Chapman, J. N. G. Hargreaves, N. I. Huth, and G. McLean. 2002. Development of a generic crop model template in the cropping system model APSIM. European J. Agron. 18(1-2): 121-140. Williams, J., P. J. Ross, and K. L. Bristow. 1991. Perspicacity, precision, and pragmatism in modeling crop water-supply. In Climatic Risk in Crop Production: Models and Management for the Semiarid Tropics and Subtropics, 73-96. R. C. Muchow and J. A. Bellamy, eds. Wallingford, U.K.: CAB International.

APPENDIX DESCRIBING THE SOIL WATER RETENTION CURVE USING HERMITE SPLINES 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,

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(3) lower limit, and (4) oven dry. The method is as follows: 1. Calculate the slope of the secant lines between each successive point: Δi =

θi +1 − θi logψ i +1 − logψ i

(A1)

2. Calculate the slope at each successive point as the average of the secants either side of this point: m1 = 0, m2 =

Δ 2 + Δ3 , 2

Δ + Δ4 m3 = 3 , m4 = Δ 4 2

(A2)

3. The resultant cubic spline will not be monotonic if either of the following is true: αi =

mi m = 0, β = i +1 = 0 Δi Δi

(A3)

If so, set mi = τiαiΔi and mi+1 = τiβiΔi, where: τi =

3 αi2 + βi2

4. Interpolate the value of θ following the standard method for evaluating a cubic Hermite spline for the relevant region between ψi and ψi+1 within the interpolation set: θ ( ψ ) = θi h00 ( t ) + hmi h10 ( t )

+θi +1h01 ( t ) + hmi +1h11 ( t )

(A4)

where h = (logψi+1 – logψi), t = (logψ – logψi)/h, and the basis functions for the cubic Hermite spline are: 2

2

h00 = (1 + 2t )(1 − t ) , h10 = t (1 − t ) , h01 = t 2 ( 3 − 2t ) , h11 = t 2 ( t − 1)

DESCRIBING HYDRAULIC CONDUCTIVITY FROM BASIC DRAINAGE INFORMATION 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:  θ  K ( θ ) = K matrix    θs 

2b + 3

 θ  + ( K s − K matrix )    θs 

P

(A5)

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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 KDUL:

ψ  −log  DUL   ψ LL  where b = θ  log  DUL   θ LL 

The contribution of the micropore component is calculated from the assumption that the conductivity at DUL (KDUL) is almost entirely due to the soil matrix. Thus, the conductivity of the soil matrix component at saturation is: K matrix =

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K DUL  θ DUL     θs 

 0.01× K DUL  log   K s − K matrix   P= θ  log  DUL  θ  s 

(A7)

2b + 3

(A6)

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