Soil moisture
A capacity approach was used to describe soil water dynamics (Wegehenkel, 2000). The capacity parameters are derived from the soil texture and modified by soil organic matter content and bulk density. Water contents at saturation, field capacity, and permanent wilting point for different bulk densities and correction values for different soil organic matter classes (Ad-hoc-AG Boden, 2005) are provided by Wessolek et al. (2009) and stored in the database.
If a crop is present, precipitation is partly intercepted and evaporates from the crop surface. Interception \(I\) is calculated as:
\(I\) Interception \([mm]\)
\(h_c\) Crop height \([m]\)
\(\beta\) Canopy closure \([m^2\,m^{-2}]\)
\(S_i\) Interception storage \([mm]\)
The remainder falls on the ground and is stored in a surface pond, from which water infiltrates into the soil. As long as the surface pond contains water, it is the only source of evaporation. The percolation of water volumes above field capacity is governed by an empirical, texture-dependent rate coefficient (\(\lambda\)):
\(\lambda\) Empirical percolation rate coefficient
\(f_s\) Soil sand content \([kg \, kg^{-1}]\)
\(f_c\) Soil clay content \([kg \, kg^{-1}]\)
\(f_u\) Soil silt content \([kg \, kg^{-1}]\)
If the groundwater level is located within the simulated soil profile, constant groundwater discharge can be adjusted to allow for the rising and falling groundwater level, depending on the soil water balance. The capillary rise from groundwater is considered according to empirical ascent rates (Ad-hoc-AG Boden, 2005). The groundwater level oscillates between given maximum and minimum levels with a period of one year.
Reference evapotranspiration \(ET0\) is calculated using the Penman-Monteith method, according to Allen et al. (1998). This method requires the diurnal minimum and maximum temperature, the water vapour pressure deficit, wind velocity, and total global radiation.
\(\Delta\) Slope of the vapour pressure curve \([kPa \, K^{-1}]\)
\(R_n\) Net radiation at the crop surface \([MJ \, m^{-2} \, d^{-1}]\)
\(G\) Soil heat flux density \([MJ \, m^{-2} \, d^{-1}]\)
\(T\) Mean daily air temperature at 2 m height \([^{\circ}C]\)
\(u_2\) Wind speed at 2 m height \([m\,s^{-1}]\)
\(e_s\) Saturation vapour pressure \([kPa]\)
\(e_a\) Actual vapour pressure \([kPa]\)
\(\gamma\) Psychrometric constant \([kPa\, K^{-1}]\)
\(r_s\) Atmospheric resistance \([s \, m^{-1}]\)
\(r_a\) Surface resistance \([s \, m^{-1}]\)
where
\(P\) Atmospheric pressure \([Pa]\)
The surface resistance for the reference evapotranspiration assumes a 12 cm cut grass crop and is calculated using:
\(r_1\) Stomata resistance; 100 s m-1 \([s \, m^{-1}]\)
The surface resistance for the actual crop is calculated in the crop growth module.
Pedotransfer Functions
A Pedotransfer Function (PTF) is a mechanism that transforms soil physical properties, mainly texture, into water retention capacity parameters. These parameters include pore space (PS, or saturation water capacity), field capacity (FC), and permanent wilting point (WP). They are required by the tipping-bucket water balance approach used in MONICA to simulate soil water content dynamics.
MONICA currently supports four PTFs, divided into two types:
Empirical PTFs
These methods use lookup tables or regression equations to directly relate soil properties to PS, FC, and WP.
Wessolek2009
This method uses a lookup table that relates categorical soil types to water retention parameters. The table is stored in SoilCharacteristicData.json, where airCapacity = PS and nFieldCapacity = WP. The implementation is based on Wessolek et al. (2009).
Toth
This method is based on the regression equations reported in Tóth et al. (2015), specifically equations 5, 9, and 12 of Table S1 in the Supplementary Material. It is implemented as fcSatPwpFromToth in soil.cpp, line 911.
Van Genuchten PTFs
These methods build a soil water retention curve using the Van Genuchten formula. Five parameters are estimated from soil texture and organic carbon content, from which PS, FC, and WP are derived at defined matric head values.
The Van Genuchten retention curve relates soil moisture (\(\theta\)) to matric head (\(h\)):
The pF values corresponding to FC and WP are used to derive the water retention parameters.
In its standard form, the Van Genuchten equation is used to calculate soil moisture from a given matric head. In MONICA, however, the current soil moisture (\(\theta\)) is already known at each time step. Therefore, the equation is inverted to compute the matric head (\(h\)), which can then be used in hydraulic calculations.
The pF scale is a logarithmic representation of soil suction, where \(h\) is expressed in centimeters of water column.
The workflow is therefore:
flowchart LR
A["Soil moisture (θ)"]
B["Inverse Van Genuchten"]
C["Matric head (h)"]
D["Hydraulic calculations"]
A --> B
B --> C
C --> DVanGenuchtenVereecken
This method is based on Vereecken et al. (1989). It assumes that \(\theta_r\) = WP, meaning that the residual water content is equal to the permanent wilting point, and fixes \(m = 1\). Because \(\theta_s\) = PS and \(\theta_r\) = WP are already known, only FC needs to be calculated. FC is not calculated at a single pF value. Instead, the pF value varies between 1.9 and 2.4 depending on clay and sand content. This method is implemented as fcSatPwpFromVanGenuchtenVereecken in soil.cpp, line 847.
Note
Setting \(m = 1\) is a simplification that reduces the flexibility of the retention curve. This may affect the representation of soil water retention under dry conditions, as well as plant water availability, drying dynamics, and hydraulic conductivity calculations. The assumption that \(\theta_r\) = WP is also a simplification. Because \(m\) is fixed, the shape of the retention curve becomes more dependent on the parameter \(n\).
VanGenuchtenToth
This method is based on equation set 21 of the Supplementary Material in Tóth et al. (2015). WP is estimated at a matric head of −15,000 cm, while PS is assumed to be equal to \(\theta_s\). FC is calculated using the same approach as in VanGenuchtenVereecken. Unlike VanGenuchtenVereecken, the parameter \(m\) is not fixed at 1. Instead, it is derived from \(n\), resulting in a more flexible and physically realistic retention curve. This method is implemented as fcSatPwpFromVanGenuchtenToth in soil.cpp, line 881.
Summary of available PTFs
| PTF | Type | Based on | Key assumption |
|---|---|---|---|
Wessolek2009 |
Empirical | Wessolek et al. (2009) | Lookup table based on soil type |
Toth |
Empirical | Tóth et al. (2015) | Regression equations |
VanGenuchtenVereecken |
Van Genuchten curve | Vereecken et al. (1989) | \(\theta_r\) = WP, \(m\) = 1 |
VanGenuchtenToth |
Van Genuchten curve | Tóth et al. (2015) | WP at pF 4.2, \(m\) derived from \(n\) |
Configuration
The PTF used by MONICA is specified in site.json via the pwpFcSatFunction parameter:
"pwpFcSatFunction": "Wessolek2009"
Accepted values are: "Wessolek2009", "Toth", "VanGenuchtenVereecken", "VanGenuchtenToth"
Lambda Factor
Lambda (\(\lambda\)) is an empirical, texture-dependent percolation rate coefficient. It is multiplied by the amount of water exceeding field capacity in a soil layer to determine how much water is transferred to the layer below. A higher lambda value results in faster percolation.
Default formula in MONICA
The default lambda is calculated from sand, clay, and silt fractions. In the MONICA source code (soil_io3.py and mas_cpp_misc/soil/conversion.cpp, lines 78-82), it is implemented as:
def sand_and_clay_to_lambda(sand, clay):
return (2.0 * (sand * sand * 0.575)) + (clay * 0.1) + ((1.0 - sand - clay) * 0.35)
double Soil::sandAndClay2lambda(double sand, double clay) {
double lambda = (2.0 * (sand * sand * 0.575)) + (clay * 0.1) + ((1.0 - sand - clay) * 0.35);
return lambda;
}
where sand and clay are given as fractions (kg kg⁻¹).
Note
The code formula and the equation shown in the soil moisture description above are mathematically equivalent. Expanding the code: 2.0 * sand² * 0.575 = 1.15 * sand², clay * 0.1 = 0.1 * fc, and (1.0 - sand - clay) * 0.35 = 0.35 * silt. The code simply uses a different but equivalent notation.
Alternative lambda methods
Alternative methods for calculating lambda have been described in the literature, including those by Rawls et al. (1982) and Carsel & Parrish (1988). These methods generally produce lower lambda values and therefore lower percolation rates compared to the MONICA default.
Overriding the default lambda
A custom lambda value can be specified for individual soil layers through the Lambda parameter in the soil profile definition. If no value is provided, MONICA calculates a default value from the soil texture fractions.
Note
A known issue exists in the source code regarding low water percolation in loam soils. As a temporary workaround, a fixed value of lambda = 1.0 is noted in conversion.cpp.
References
- Ad-hoc-AG Boden (2005). Bodenkundliche Kartieranleitung (5th ed.). Hannover.
- Allen, R. G., Pereira, L. S., Raes, D., & Smith, M. (1998). Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56.
- Carsel, R. F., & Parrish, R. S. (1988). Developing joint probability distributions of soil water retention characteristics. Water Resources Research, 24(5), 755–769.
- Rawls, W. J., Brakensiek, D. L., & Saxton, K. (1982). Estimation of soil water properties. Transactions of the ASAE, 25(5), 1316–1320.
- Tóth, B., Weynants, M., Nemes, A., Makó, A., Bilas, G., & Tóth, G. (2015). New generation of hydraulic pedotransfer functions for Europe. European Journal of Soil Science, 66(1), 226–238.
- Vereecken, H., Maes, J., Feyen, J., & Darius, P. (1989). Estimating the soil moisture retention characteristic from texture, bulk density, and carbon content. Soil Science, 148(6), 389–403.
- Wegehenkel, M. (2000). Test of a modelling system for simulating water balances and plant growth using various different complex approaches. Ecological Modelling, 129(1), 39–64.
- Wessolek, G., Kaupenjohann, M., & Renger, M. (2009). Bodenökologie und Bodengenese: Bodenphysikalische Kennwerte und Berechnungsverfahren für die Praxis (40).