# Classification of Hydrological Relevant Parameters by Soil Hydraulic Behaviour

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. General Procedure

^{6}equally distributed numbers with the condition that the sum of (always three) numbers has to be one. The resulting three fractions were assigned to sand, silt, and clay content, while keeping the total sum at of these fractions at 100%. Subsequently, these particle triplets were passed to the software ROSETTA, (free of charge software, which is based on a hierarchical neural network, see e.g., [19,20,21]), by which the van Genuchten [15] parameters (VGP) for each of the triplets were created. These VGP were used to perform soil water simulations on the basis of the Richards equation [16]. 10

^{6}of these simulations were numerically solved with an impulse input as the upper boundary condition. A more complex dynamic upper boundary condition was applied to an additional simulation of a subset with 10

^{5}triplets. This was done in order to generate different unsaturated conditions throughout the simulation period. The deepness of the domains was assigned to 200 cm, respectively, 400 cm in order to have no influence of the lower boundary condition. We set this condition to constant pressure head, but also applied the free drainage condition with the same classification results. The outputs of these simulations were water fluxes at different soil depths. These time series were used to perform a classification with the help of a k-means cluster algorithm [17,18]. Each of the 10

^{6}triplets was thereby assigned to a soil cluster. The advantage of this procedure is that the classification is based on the hydraulic behaviour of the soils, which is an important characteristic for any hydrological model application.

#### 2.2. Soil Hydraulic Models

with: | |||

${\mathrm{S}}_{e}$ | Soil water saturation | (m³∙m^{−3}) | |

$h$ | Soil water pressure head | (m) | |

$\alpha $ | Van Genuchten parameter | (m^{−1}) | |

$\mathrm{n}$ | Van Genuchten parameter | (-) | |

$\mathrm{m}$ | Van Genuchten parameter | (-) |

with: | |||

$\Theta $ | Volumetric water content | (m³∙m^{−3}) | |

${\Theta}_{r}$ | Residual volumetric water content | (m³∙m^{−3}) | |

${\Theta}_{s}$ | Saturated volumetric water content | (m³∙m^{−3}) |

with: | |||

$\mathrm{K}\left(\Theta \right)$ | Unsaturated hydraulic conductivity | (m∙s^{−1}) | |

${K}_{s}$ | Saturated hydraulic conductivity | (m∙s^{−1}) | |

$\mathrm{l}$ | Empirical parameter (mostly l = 0.5) | (-) |

with: | |||

$t$ | Time | (s) | |

$\mathrm{z}$ | Flow length, positive upward | (m) |

#### 2.3. Soil Hydraulic Parameters

^{6}artificial samples of possible compositions of texture fractions were obtained. The large number of generated samples was empirically determined in order to obtain a representative population for the statistical analyses.

_{r}, Θ

_{s}, α, and n, as well as K

_{s}for each sample. ROSETTA is established in soil physical disciplines and it is used in several studies, see e.g., [7,26,27]. It is based on neural network analyses and was calibrated by means of a large database comprised of 2134 soil samples that consists of more than 20,000 measured pairs of Θ and h in total. 1306 soil samples were available for the saturated hydraulic conductivity. A total of 235 samples also contained data for the unsaturated hydraulic conductivity function K(Θ), including more than 4000 data points [28]. The database UNSODA [20,21] significantly contributes to these data points.

#### 2.4. Simulation of Soil Water Movement

- An “impulse” boundary condition (IBC), which provides 0.1 cm/d flux for 30 days.
- A “dynamic” boundary condition (DBC), which is a time series of measured precipitation in cm/h, with a length 89 days and a total amount of precipitation of approx. 14 cm.

^{6}simulation runs were conducted with the IBC, and another 10

^{5}simulations were conducted with the DBC. The results comprised time series of water flux for several depths.

#### 2.5. Soil Classification by Soil Hydraulic Response

^{6}(IBC), respectively, 10

^{5}(DBC) simulations. In this way, the hydraulic response of every possible combination in the texture triangle is considered in the classification. The time series of the simulations with IBC and DBC were individually treated.

^{6}and 10

^{5}time series and the objective was set to maximum correlation within the clusters.

#### 2.6. Identification of Representative Parameter Sets

with: | |||

$R$ | Pearson correlation coefficient | (-) | |

$RMSE$ | Root mean squared error | (m∙s^{−1}) | |

$Nash$ | Model efficiency | (-) | |

$d$ | Index of agreement | (-) | |

$Offset$ | Shift of position between peak values | (s) | |

${x}_{i}$ | Entries of test time series | (m∙s^{−1}) | |

$\overline{x}$ | Average value of test time series | (m∙s^{−1}) | |

${y}_{i}$ | Entries of arithmetic mean time series | (m∙s^{−1}) | |

$\overline{y}$ | Average value of arithmetic mean time series | (m∙s^{−1}) | |

$n$ | Length of time series | (-) |

with: | |||

$C$ | Ideal number of classes | (-) | |

$N$ | Number of samples | (-) |

## 3. Results

#### 3.1. Number of Clusters

^{5}(DBC), a class number of 17–18 was calculated. A sample size of 10

^{6}(IBC) was yielded in 21 classes. We preferred the ideal number of 15 clusters to be more convenient although these numbers are slightly higher than the number that was obtained by the elbow criterion.

#### 3.2. Classification Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Blöschl, G.; Sivapalan, M. Scale issues in hydrological modelling: A review. Hydrol. Process.
**1995**, 9, 251–290. [Google Scholar] [CrossRef] - Hopmans, J.W.; Nielsen, D.R.; Bristow, K.L. How useful are small-scale soil hydraulic property measurements for large-scale vadose zone modeling? In Environmental Mechanics: Water, Mass and Energy Transfer in the Biosphere; AGU: Washington, DC, USA, 2002; ISBN 0-87590-988-4. [Google Scholar]
- Beven, K. Linking parameters across scales: Subgrid parameterizations and scale dependent hydrological models. Hydrol. Process.
**1995**, 9, 507–525. [Google Scholar] [CrossRef] - Bronstert, A.; Bárdossy, A. The role of spatial variability of soil moisture for modelling surface runoff generation at the small catchment scale. Hydrol. Earth Syst. Sci.
**1999**, 3, 505–516. [Google Scholar] [CrossRef] - Hasenauer, S.; Komma, J.; Parajka, J.; Wagner, W.; Blöschl, G. Bodenfeuchtedaten aus Fernerkundung für hydrologische Anwendungen. Österr Wasser- und Abfallw
**2009**, 61, 117–123. [Google Scholar] [CrossRef][Green Version] - Kreye, P. Mesoskalige Bodenwasserhaushaltsmodellierung mit Nutzung von Grundwassermessungen und Satellitenbasierten Bodenfeuchtedaten. Ph.D. Dissertation, Technische Universität Braunschweig, Braunschweig, Germany, 2015. [Google Scholar]
- Kreye, P.; Meon, G. Subgrid spatial variability of soil hydraulic functions for hydrological modelling. Hydrol. Earth Syst. Sci.
**2016**, 20, 2557–2571. [Google Scholar] [CrossRef][Green Version] - Davis, R.O.E.; Bennett, H.H. Grouping of Soils on the Basis of Mechanical Analysis; U.S. Department of Agriculture: Washington, DC, USA, 1927.
- Twarakavi, N.K.C.; Šimůnek, J.; Schaap, M.G. Can texture-based classification optimally classify soils with respect to soil hydraulics? Water Resour. Res.
**2010**, 46, W01501. [Google Scholar] [CrossRef] - Bormann, H. Towards a hydrologically motivated soil texture classification. Geoderma
**2010**, 157, 142–153. [Google Scholar] [CrossRef] - Diekkrüger, B.; Arning, M. Simulation of water fluxes using different methods for estimating soil parameters. Ecol. Model.
**1995**, 81, 83–95. [Google Scholar] [CrossRef] - Brooks, R.H.; Corey, A.T. Hydraulic Properties of Porous Media; Colorado State University: Fort Collins, CO, USA, 1964. [Google Scholar]
- Groenendyk, D.G.; Ferré, T.P.A.; Thorp, K.R.; Rice, A.K. Hydrologic-Process-Based Soil Texture Classifications for Improved Visualization of Landscape Function. PLoS ONE
**2015**, 10, e0131299. [Google Scholar] [CrossRef] [PubMed] - Šimůnek, J.; van Genuchten, M.T.; Šejna, M. HYDRUS 1D Software Package for Simulating the One-Dimensional Movement of Water, Heat, and Multiple Solutes in Variably-Saturated Media. IGWMC-TPS70 Version 4.08; Colorado School of Mines: Golden, CO, USA, 2009. [Google Scholar]
- Van Genuchten, M.T. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Soc. Am. J.
**1980**, 44, 892–898. [Google Scholar] [CrossRef] - Richards, L.A. Capillary conduction of liquids through porous mediums. Physics
**1931**, 1, 318–333. [Google Scholar] [CrossRef] - Lloyd, S. Least squares quantization in PCM. IEEE Trans. Inf. Theory
**1982**, 28, 129–137. [Google Scholar] [CrossRef][Green Version] - Arthur, D.; Vassilvitskii, S. K-means++: The advantages of careful seeding. In Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, USA, 7–9 January 2007. [Google Scholar]
- Schaap, M.G.; van Leij, J.F.; van Genuchten, M.T. ROSETTA: A computer program for estimating soil hydraulic parameters with hierarchical pedotransfer functions. J. Hydrol.
**2001**, 2001, 163–176. [Google Scholar] [CrossRef] - Leij, F.; William, J.; van Genuchten, M.; Williams, J. The UNSODA Unsaturated Soil Hydraulic Database: User’s Manual; National Risk Management Research Laboratory, Office of Research and Development, U.S. Environmental Protection Agency: Cincinnati, OH, USA, 1996.
- Nemes, A.; Schaap, M.; Leij, F.; Wösten, J. Description of the unsaturated soil hydraulic database UNSODA version 2.0. J. Hydrol.
**2001**, 251, 151–162. [Google Scholar] [CrossRef] - Jury, W.A.; Horton, R. Soil physics, 6th ed.; J. Wiley: Hoboken, NJ, USA, 2004; ISBN 9780471059653. [Google Scholar]
- Wösten, J.H.M.; van Genuchten, M.T. Using Texture and Other Soil Properties to Predict the Unsaturated Soil Hydraulic Functions. Soil Sci. Soc. Am. J.
**1988**, 52, 1762–1770. [Google Scholar] [CrossRef] - Van Genuchten, M.T.; Nielsen, D.R. On Describing and Predicting the Hydraulic Properties of Unsaturated Soils. Ann. Geophys.
**1985**, 615–628. [Google Scholar] - Mualem, Y. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res.
**1976**, 12, 513–522. [Google Scholar] [CrossRef] - Børgesen, C.D.; Iversen, B.V.; Jacobsen, O.H.; Schaap, M.G. Pedotransfer functions estimating soil hydraulic properties using different soil parameters. Hydrol. Process.
**2008**, 22, 1630–1639. [Google Scholar] [CrossRef] - Pérez-Cutillas, P.; Barberá, G.G.; Conesa-García, C. Effects of the texture and organic matter values in the estimation of the soil water content at a regional scale. Cuadernos de Investigación Geográfica CIG
**2018**, 44, 697–718. [Google Scholar] [CrossRef] - Schaap, M.G.; Leij, F.J.; van Genuchten, M.T. Neural Network Analysis for Hierarchical Prediction of Soil Hydraulic Properties. Soil Sci. Soc. Am. J.
**1998**, 62, 847–855. [Google Scholar] [CrossRef] - Skeel, R.D.; Berzins, M. A Method for the Spatial Discretization of Parabolic Equations in One Space Variable. SIAM J. Sci. Stat. Comput.
**1990**, 11, 1–32. [Google Scholar] [CrossRef] - Sturges, H.A. The Choice of a Class Interval. J. Am. Stat. Assoc.
**1926**, 21, 65–66. [Google Scholar] [CrossRef] - Pearson, K. Note on Regression and Inheritance in the Case of Two Parents. Proc. R. Soc. Lond.
**1895**, 58, 240–242. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River Flow Forecasting through Conceptual Models. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] - Legates, D.R.; McCabe, G.J. Evaluating the use of “goodness-of-fit” Measures in hydrologic and hydroclimatic model validation. Water Resour. Res.
**1999**, 35, 233–241. [Google Scholar] [CrossRef][Green Version] - Hall, M.J. How well does your model fit the data? J. Hydroinform.
**2001**, 3, 49–55. [Google Scholar] [CrossRef][Green Version] - García-Gutiérrez, C.; Pachepsky, Y.; Martín, M.Á. Saturated Hydraulic Conductivity and Textural Heterogeneity of Soils. Hydrol. Earth Syst. Sci. Discuss.
**2018**, 22, 3923–3932. [Google Scholar] [CrossRef] - Shannon, C.E. The Mathematical Theory of Communication; University of Illinois Press: Baltimore, MD, USA, 1948; ISBN 9780252725463. [Google Scholar]

**Figure 2.**Number of Clusters in relation to standardized objective functions. All criteria were set to the same range (0 = no agreement, 1 = perfect agreement). (

**a**) Impulse boundary condition; (

**b**) Dynamic boundary condition. Correlation = Pearson correlation coefficient, RMSE = root mean square error, Nash = model efficiency [32], Agreement = Index of agreement, Mean OF = arithmetic mean out of all objective functions. “Std” denotes for standard deviation.

**Figure 3.**(

**a**,

**b**): Texture triangle with classification results for 15 classes (coloured patterns) based on hydraulic response in comparison to the established United States Department of Agriculture (USDA) classification [8]. (

**a**): Impulse boundary condition (IBC); (

**b**): Dynamic boundary condition (DBC). (

**c**,

**d**): Representative time series of water flux for the 15 classes based on IBC (

**c**) and DBC (

**d**). The legend numbering is in consistence with Table 1.

**Figure 4.**(

**a**) Representative time series of cluster 1 of the classification based on hydraulic behaviour (blue line) for the dynamic boundary condition. Further, the minima and maxima out of all class members are shown for each time step (grey area). (

**b**) The same analyse for the class members of “silt loam” of the USDA classification.

**Figure 5.**Standard deviation of van Genuchten Parameters and Ks values within the classes (blue = evaluation based on hydraulic response classes; grey = based on USDA classes). The horizontal black lines show the median. The boxes show the 25% and 75% percentiles and the whiskers symbolise the minima and maxima.

**Figure 6.**Bandwidth of the quality criteria Nash, RMSE (standardized), PBIAS (percentage error) and Offset (blue = evaluation based on hydraulic response classes; grey = based on USDA classes). The optimal value of Nash is one; the optimal values of RMSE, PBIAS, and Offset are zero. The horizontal black lines show the mean quality values of all classes. The boxes show the mean values ± two times standard deviation (cut at a value of one) and the whiskers symbolise the minimum and maximum values.

**Table 1.**Representative van Genuchten parameters of the 15 classes of the classification based on hydraulic response with dynamic boundary condition.

Nr | Θ_{r} (m³∙m^{−3}) | Θ_{s} (m³∙m^{−3}) | α (m^{−1}) | n (-) | Ks (m∙s^{−1}) |
---|---|---|---|---|---|

1 | 0.049 | 0.448 | 0.005 | 1.721 | 5.09 × 10^{−6} |

2 | 0.051 | 0.479 | 0.006 | 1.694 | 4.98 × 10^{−6} |

3 | 0.065 | 0.463 | 0.006 | 1.660 | 2.55 × 10^{−6} |

4 | 0.069 | 0.468 | 0.006 | 1.636 | 2.08 × 10^{−6} |

5 | 0.075 | 0.469 | 0.007 | 1.612 | 1.50 × 10^{−6} |

6 | 0.087 | 0.471 | 0.008 | 1.539 | 1.27 × 10^{−6} |

7 | 0.093 | 0.479 | 0.010 | 1.453 | 1.50 × 10^{-6} |

8 | 0.101 | 0.499 | 0.015 | 1.300 | 2.43 × 10^{−6} |

9 | 0.103 | 0.505 | 0.020 | 1.158 | 1.97 × 10^{−6} |

10 | 0.108 | 0.511 | 0.018 | 1.153 | 2.08 × 10^{−6} |

11 | 0.074 | 0.399 | 0.024 | 1.300 | 1.04 × 10^{−6} |

12 | 0.073 | 0.384 | 0.027 | 1.263 | 1.50 × 10^{−6} |

13 | 0.071 | 0.372 | 0.025 | 1.276 | 1.62 × 10^{−6} |

14 | 0.053 | 0.376 | 0.032 | 2.582 | 4.12 × 10^{−5} |

15 | 0.056 | 0.373 | 0.031 | 3.347 | 8.61 × 10^{−5} |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Kreye, P.; Gelleszun, M.; Somasundaram, M.; Meon, G. Classification of Hydrological Relevant Parameters by Soil Hydraulic Behaviour. *Geosciences* **2019**, *9*, 206.
https://doi.org/10.3390/geosciences9050206

**AMA Style**

Kreye P, Gelleszun M, Somasundaram M, Meon G. Classification of Hydrological Relevant Parameters by Soil Hydraulic Behaviour. *Geosciences*. 2019; 9(5):206.
https://doi.org/10.3390/geosciences9050206

**Chicago/Turabian Style**

Kreye, Phillip, Marlene Gelleszun, Manickam Somasundaram, and Günter Meon. 2019. "Classification of Hydrological Relevant Parameters by Soil Hydraulic Behaviour" *Geosciences* 9, no. 5: 206.
https://doi.org/10.3390/geosciences9050206