State-of-the-art hydrological applications require a process-based, spatially
distributed hydrological model. Runoff characteristics are demanded to be
well reproduced by the model. Despite that, the model should be able to
describe the processes at a subcatchment scale in a physically credible way.
The objective of this study is to present a robust procedure to generate
various sets of parameterisations of soil hydraulic functions for the
description of soil heterogeneity on a subgrid scale. Relations between
Rosetta-generated values of saturated hydraulic conductivity (

One of the major challenges in hydrological process modelling is to minimise
the discrepancy between model and data scale as described e.g. by

State-of-the-art hydrological applications require a process-based, spatially
distributed hydrological model. As the first objective, runoff characteristics
are demanded to be well reproduced by the model. Despite that, and even for
large-scale applications, the model should be able to describe the processes
at a subcatchment scale in a physically credible way. Following

The simulation of soil water movements and storages can be particularly
sensitive with respect to many model outputs (total runoff, infiltration,
groundwater recharge, actual evapotranspiration, etc.). Especially the water
content of the soil near the surface is a decisive factor for the runoff
generation

Hydrological models that rely on one effective (specific) parameterised set
of soil hydraulic functions for each soil type may not be able to describe
subgrid variation in an adequate way. Therefore, it can lead to a high
calibration effort and possibly to an inadequate process description.

Area-wide measured data of basic soil properties or even of soil hydraulic properties are not available for most hydrological model applications at the meso- and macroscale. However, in many cases rough information about the soil (e.g. soil maps) is available on a very coarse spatial resolution (1 : 50 000 at best). Using such rough input data does not allow direct parameterisation of any subgrid variability. In addition, soil maps are already products of regionalised input data. Consequentially, all soil hydraulic parameters based on soil maps can be interpreted (only) as effective parameters.

In this study, the subgrid spatial variability for the parameterisation of
soil hydraulic functions will be derived indirectly from soil map
information. To achieve this, three statements are formulated and will be
discussed below:

The spatial variability of saturated hydraulic conductivity of soils on a subgrid scale can be expressed by a lognormal distribution.

There are relationships between the saturated hydraulic conductivity and the parameters of soil hydraulic functions.

These relationships are mirrored in the parameters generated by the
software Rosetta

Besides the lack of measured soil samples, the effort of parameterisation by
means of sophisticated procedures that often require Monte Carlo applications
is very high even for models operating on the hill slope scale. This effort
is much higher for large areas and huge timescales as it is usual in
e.g. climate change hydrological modelling. Consequently, the use of effective
parameter sets and powerful calibration procedures is widespread. On the
other hand, some kind of calibration parameters are always needed in
hydrological modelling. Based on this, the third (innovative) statement was
formulated. Premised on profound analyses of the relationship between
Rosetta-generated

In this section, we shortly give the required theoretical background in soil
physics and statistics. Further, the creation of a database is presented by
means of the software Rosetta. The database contains the parameters and

Since the objective of this paper is the consideration of subgrid variability
of the parameterisation of soil hydraulic functions at the meso- and
macroscale, the model for the description of the soil hydraulic functions has
to be determined in the first place. The use of proxy information is one of
very few possibilities to parameterise soil hydraulic functions extensively
for large hydrological model areas. As the software Rosetta will be used for
this application (see Sect.

One objective is to investigate for correlations between Rosetta-generated
VGP and

The free-of-charge software Rosetta

Definitions of the used texture classes. The fractions of sand, silt
and clay is processed out of the soil map for Lower Saxony

The VGP sets (including

The complete database 0, which consists of the total of 10

A reduced database 1 based on the condition that

A reduced database 2 based on the condition that

Several selected databases 3

The final reductions to databases 3

Soil map of Lower Saxony, Germany

A flexible exponential regression model is used, since the modalities of the
relations between the

In addition to the univariate regression model shown above, a multivariate
regression will be performed by using a general multivariate model, which can
be denoted as

To evaluate the quality of the regressions, the coefficient of determination

For consideration of nonlinearities, Spearman's rank correlation coefficient

Regression analyses based on Eq. (

The

Generally, in some sections of the scatter diagrams there seem to be more
connections between the

Regression analyses based on Eq. (

Concerning

Concerning

Concerning

All statistical quality values from the univariate regression analyses are
listed in Table

Obtained coefficients of determination (

Subdivision of the soil texture by means of cluster analyses based
on 31 classes (blue coloured polygons). The classes were divided by similarity
of their soil hydraulic parameters (cf.

Procedure to obtain van Genuchten (VG) parameters and the saturated
hydraulic conductivity (

Average coefficient of determination (

Scatterplots of the van Genuchten parameters (

Scatterplots of the van Genuchten parameters (

Regression analyses based on Eq. (

Both the shape of the obtained fits of the multivariate method and the

Figure

Scatterplot of the van Genuchten parameter

Impact on the

In variant B, we concentrate on univariate regression analyses only. In
Fig.

Figure

Figure

The

It can be summarised that the modifications of the VGP caused by the
regression results of the databases 3

Spatial resolutions of hydrological models mainly depend on the resolutions of the input data of soil properties and land use, respectively. These input data are often not equally resolved in space and time (e.g. the German ATKIS database). If the model area is subdivided into polygons by the hydrological model, the spatial resolution is unequally distributed and given automatically by the input layers. If the model area is subdivided into raster cells, the spatial resolution is equally distributed and depends both on input layers and on the user's interests. For latter types of models, the spatial resolution may often induce a pseudo-accuracy, because the chosen grid size can be much smaller than most of the subdivisions of the input layers. In any case, the real spatial resolution of a hydrological model that has to be considered for the process description is given by the spatial resolutions of the input data. In most cases these spatial resolutions are rather coarse, causing many processes that are not directly resolved by the model.

To consider the spatial variability of soil water processes that are not
directly resolved by the hydrological model, the following procedure is
elaborated in order to generate parameterisations of soil hydraulic functions:

Acquisition of a soil map for the model area (or similar information).
In this study, a German soil map of Lower Saxony is used; see Fig.

Obtaining texture classes out of the soil map. For example, Sl with 65 %
sand, 25 % silt and 10 % clay (see Table

Random generation of trios of numbers within a range of 0–100 with the precondition that the sum of each trio has to be 100. The numbers of each trio are assigned to be a percentage fraction of sand, silt and clay.

Consideration of a boundary in each direction (sand, silt, clay). This
study used a

Generation of VGP sets with the software Rosetta for the obtained texture classes (categories).

Regression analyses between

At the next step, the obtained regression functions have to be applied in a
hydrological model. The following procedure is recommended:

Assumption of a lognormal distributions for the

Calculation of variations of the other VGP by using the regression functions
and the

Run the model by parallelly using the VGP sets that were obtained at the previous point 2.

These presented developments were implemented into the hydrological modelling
system PANTA RHEI

Application of different van Genuchten parameter sets on the soil
model of the hydrological modelling system PANTA RHEI. The different
parameterisations (domains) are parallel used at all spatial locations. The
domains are solved simultaneously and with interaction to each other. The
main input is given by the spatial precipitation (

The structure of the soil model of PANTA RHEI is shown in Fig.

The objective of this study was to present a robust procedure to generate
various sets of parameterisations of soil hydraulic functions for the
description of soil heterogeneity on a subgrid scale. To achieve this,
relations between

Our methodology can be connected to the work of

It is worth discussing the applicability of transferring Rosetta results to
a distributed hydrological model. An interchange of parameters between
different models can be cumbersome. This was e.g. found by

We thank the referees Yeugeniy Gusev, Anatoly Zeyliger and a anonymous referee as well as the editor Alexander Gelfan for their helpful comments and suggestions that significantly helped to improve the quality of the manuscript. Edited by: A. Gelfan