Soil infiltration is one of the key factors that has an influence on soil erosion caused by rainfall. Therefore, a well-represented infiltration process is a necessary precondition for successful soil erosion modelling. Complex natural conditions do not allow the full mathematical description of the infiltration process, and additional calibration parameters are required. The Green–Ampt-based infiltration module in the EROSION-2D/3D model introduces a calibration parameter “skinfactor” to adjust saturated hydraulic conductivity. Previous studies provide skinfactor values for several combinations of soil and vegetation conditions. However, their accuracies are questionable, and estimating the skinfactors for other than the measured conditions yields significant uncertainties in the model results. This study brings together an extensive database of rainfall simulation experiments, the state-of-the-art model parametrisation method and linear mixed-effect models to statistically analyse relationships between soil and vegetation conditions and the model calibration parameter skinfactor. New empirically based transfer functions for skinfactor estimation significantly improving the accuracy of the infiltration module and thus the overall EROSION-2D/3D model performance are provided in this study. Soil moisture and bulk density were identified as the most significant predictors explaining 82 % of the skinfactor variability, followed by the soil texture, vegetation cover and impact of previous rainfall events. The median absolute percentage error of the skinfactor prediction was improved from 71 % using the currently available method to 30 %–34 % using the presented transfer functions, which led to significant decrease in error propagation into the model results compared to the present method. The strong logarithmic relationship observed between the calibration parameter and soil moisture however indicates high overestimation of infiltration for dry soils by the algorithms implemented in EROSION-2D/3D and puts the state-of-the-art parametrisation method in question. An alternative parameter optimisation method including calibration of two Green–Ampt parameters' saturated hydraulic conductivity and water potential at the wetting front was tested and compared with the state-of-the-art method, which paves a new direction for future EROSION-2D/3D model parametrisation.

Soil erosion modelling is a common and efficient approach to analyse and
understand the soil erosion process and propose solutions to minimise its impact. Therefore, development and improvement of soil erosion
modelling tools are of crucial interest among soil scientists, state
land offices, or landscape architects. EROSION-2D and EROSION-3D are
soil erosion modelling tools based on the same physical descriptions of
soil erosion processes on hillslopes (2D) or in catchment areas (3D) for
single rainfall events. In this paper EROSION-2D/3D shall refer to both
versions, where shared algorithms are discussed. These tools are able to
predict erosion patterns, as well as deposition areas, on agricultural
fields, infrastructure, and settlement areas

EROSION-2D/3D includes two submodules. The first submodule is an
infiltration module used to calculate infiltration rates over time. The
second submodule uses the infiltration rates to calculate excess water,
surface runoff, and detachment, as well as the transport and deposition
of particles. The infiltration submodule is based on the Green–Ampt approach

Previous studies have focused on estimating skinfactors for those other than measured conditions. The studies are based on 116 rainfall experiments conducted in Saxony (Germany) between 1992 and 1995, which
are published in the EROSION-3D Catalogue of Input Parameters (Parameter
Catalogue)

For this study, an R package, toolbox.e3d, was developed to enable automatic and batch determination of the skinfactors for multiple rainfall-runoff infiltration experiments. An extensive rainfall-runoff experiment database was processed by the package, creating a sufficient amount of data to statistically analyse the relationships between the skinfactor and other parameters describing the soil and vegetation conditions of the experiments. The aim of this study is to improve the performance of EROSION-2D/3D by providing easy-to-use transfer functions to calibrate the infiltration module of the model.

The infiltration model used in EROSION-2D/3D was developed by

List of symbols used in infiltration model equations.

The infiltration rate is a function of the wetting front penetration
depth and is calculated as mass flux by

This value can be divided by the density of infiltrating fluid to obtain infiltration rate as volume flow rate.

The penetration depth of the wetting front is the integral function of
the infiltration rate divided by the fillable pore space. An
approximation of this integral function is used in EROSION-2D/3D:

Parameters matrix potential and fillable pore space in Eq. (

Because Eqs. (

According to

In case the input value of soil moisture

The equations used for estimation of saturated hydraulic conductivity
are the following

Skinfactor in EROSION-2D/3D is a calibration factor to the saturated
hydraulic conductivity calculated by Eq. (

Two methods of deriving the skinfactors from rainfall-runoff experiments were established in previous studies, both yielding slightly different values, resulting in different surface runoff rates. The first
established method uses the skinfactor to adjust the amount of cumulative runoff from the plot area (skinfactor

Modelled infiltration rates resulting from different methods of skinfactor determination. Calculated infiltration rate is limited by rainfall intensity (0.933 mm min

An open database for storing, maintaining, and sharing protocols from
rainfall-runoff experiments is being developed in parallel to this study

Parameters included in statistical analysis for skinfactor prediction.

The determined skinfactor values range from 0.001 to 100 in the dataset. The assumption of normally distributed residuals in the linear mixed-effect models used in this study is violated when using untransformed skinfactors. Logarithmic transformation of skinfactors produces a near-normal distribution for the residuals. Therefore, this transformation was used for all skinfactor values in the statistical analysis.

To determine the transfer functions for the skinfactor, linear
mixed-effect models

Various models were fitted using the experimental dataset. Model ORIG,
with factorial predictors originally used in the Parameter Catalogue
(crop, management practice, dry/wet experiment, soil texture class,
plant development), was fitted to statistically evaluate the current
skinfactor prediction method available for model users

To examine the statistical reliability of the fitted models, a 10-fold cross-validation approach was followed. The experimental dataset was divided into the training subset, containing 90 % of the randomly selected
experiments, and the validation subset, containing the remaining 10 % of the experiments. For the training subset coefficients of the functions were
determined. The validation subset was then used to predict skinfactors.
This procedure was repeated 10 times, ensuring that each experiment was used for validation once. For each repetition model performance was
evaluated by commonly used indicators. The overall quality of the
transfer functions was calculated as average values of the indicators
plus/minus standard deviation. The indicators are coefficient of determination (

In the second step, an error propagation of the predicted skinfactors for surface runoff and sediment mass was analysed. Soil and vegetation conditions from the experiments were applied on a hypothetical 400 m long and 9 % steep slope. Surface runoff and sediment mass simulated with the experimentally derived skinfactor were compared to those simulated with the skinfactors predicted by the presented models. The results were evaluated by the same indicators as in the first validation step.

The last step of the validation was performed on real data collected on
three 40 cm

Rainfall events used for the skinfactor validation.

Saturation dry or wet was decided according to antecedent precipitation.

Four models were fitted to evaluate the skinfactor estimation method
given in the Parameter Catalogue and determine new transfer functions
for predicting skinfactors using the most significant predictors (Fig.

Experimentally derived versus predicted skinfactors (log values) for the selected validation dataset.

The dependency of the skinfactor on the bulk density and soil moisture. Point data represent the whole dataset with experimentally derived skinfactors. Line data represent skinfactor prediction by STRONG for three different initial soil moisture conditions. ISM: initial soil moisture.

All the new transfer functions performed well according to the
interpretation of the RSR indicator by

Linear mixed-effect models for skinfactor prediction: model evaluation based on the validation dataset using common statistical indicators, model variables, and their coefficients.

– indicates not included in the model.

Error propagation of the predicted skinfactors to the surface runoff and
sediment mass simulated by EROSION-3D was evaluated on the hypothetical
400 m long slope. Table

Surface runoff simulated with the derived
skinfactor versus the ORIG skinfactor

Sediment mass simulated by EROSION-3D with
the experimentally derived skinfactor versus skinfactor predicted by the ORIG model

Error propagation of skinfactor prediction in
the surface runoff

Error propagation of the skinfactor prediction models for the surface runoff and sediment mass evaluated by commonly used statistical indicators.

Real rainfall-runoff events were modelled using the new transfer
functions. To account for the potential error in the functions, each
event was simulated with the predicted skinfactor and the skinfactor
corrected by

Runoff volume (mL) from real rainfall events, measured versus simulated with the skinfactors predicted by the new transfer functions.

Measured sumQ: min–max value measured in three trap devices.
Predicted sumQ: predicted

The joint rainfall simulation dataset of TUBAF and RISWC provides a
sufficient amount of data to statistically analyse the relationships between the skinfactor calibration parameter and commonly measured soil
and vegetation conditions as well as to derive the transfer functions for the skinfactor. It is however important to consider the spatial
limitation of the transfer functions given by the dataset, which
consists of data representing soils of the Czech Republic and Saxony (state of Germany). Other open databases of rainfall-runoff experiments
covering bigger spatial variability exist (e.g.

The current skinfactor prediction method published in the Parameter
Catalogue is based on easily and accurately measurable factorial
variables, i.e. crop, management practice, soil saturation, development stage of vegetation, and soil texture class. The results of model ORIG
show that out of these variables, only soil saturation had a statistically evident influence on the skinfactor. This parameter distinguishes only
two categories of soil saturation, dry soils (no antecedent precipitation) and wet soils (shortly after precipitation), indicating
rather impact of previous rainfall than the soil moisture itself. The relationship was explained by stability of aggregates

Further studies using numerical variable initial soil moisture observed a relationship of skinfactor and soil moisture corresponding to our
results. It was however again explained by the state of the soil before and after rainfall.

This study followed the state-of-the-art parametrisation method
established with EROSION-3D and used linear mixed-effect models to find relationships between the parameter and soil and vegetation conditions.
The derived pedotransfer functions showed a strong logarithmic relationship between skinfactor and soil moisture, which indicates drastic overestimation of infiltration of dry soils by EROSION-2D/3D. This raises questions regarding the used method of parametrisation. The
established approach fits infiltration curves by scaling only one of the
Green–Ampt parameters – saturated hydraulic conductivity. This value is estimated by Eq. (

The Green–Ampt parameter water potential at the wetting front is assumed to be equal to matrix potential of the soil at antecedent water content
in EROSION-2D/3D and is calculated by Eq. (

Comparison of parameter fitting
strategies:

To get better insight into the parameter-fitting strategy, Monte Carlo parameter optimisation

Nevertheless, the parametrisation method behind this study is not optimal: the presented functions to estimate the skinfactor indicate significant improvement in the infiltration module performance in comparison with the values presented in the parameter catalogue (compare results of model ORIG with the new pedotransfer functions). The
validation on real data indicates good model performance for rainfalls with higher intensity and volume. Model users should use the functions
carefully and with the awareness of an error introduced in the
parametrisation phase. At the same time results of the study are opening
a way for further EROSION-2D/3D development which can be approached
either through the algorithms implemented in the source code of
EROSION-3D or through a different method of model parametrisation. The very basic approach to optimise parameters of the Green–Ampt approach in EROSION-3D applied in this study can be seen as a first step towards the use of advanced parameter optimisation algorithms (e.g. the SPOTPY package,

This study aimed to increase the accuracy of the infiltration module of
the EROSION-2D/3D soil erosion simulation tool by introducing new
transfer functions to estimate the calibration parameter adjusting
saturated hydraulic conductivity called “skinfactor”. The relationship of the skinfactor with soil, vegetation, and farm management parameters was analysed using the linear mixed-effect models based on 273
rainfall-runoff experiments. The initial soil moisture and bulk density
were found to be the most important predictors, together explaining
82 % of the skinfactor variability. These parameters are not considered in currently available prediction methods provided in

This paper was compiled using the RMD template (

The supplement related to this article is available online at:

AR, JD, MM and AB made rainfall experiments, HB, JL and JD processed rainfall experiment data, JL automatised skinfactor determination, HB, JL and JD carried out the statistical analysis, IG provided data for validation of real events, HB and JL wrote the code and prepared the manuscript, and AR and JK consulted the whole process.

The authors declare that they have no conflict of interest.

This study was supported by the Ministry of Agriculture of the Czech Republic (grant nos. QK1810341 and MZE-RO0218) and by the European Social Fund in the Free State of Saxony (Förderbaustein: Promotionen).

This paper was edited by Jan Vanderborght and reviewed by Mehdi Rahmati and one anonymous referee.