# A Comparative Investigation of Various Pedotransfer Functions and Their Impact on Hydrological Simulations

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## Abstract

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## 1. Introduction

- Applied methods (e.g., statistical regression techniques, data mining and exploration techniques);
- The underlying database of measured soil moisture retention data used to fit van Genuchten model estimates; and
- Required input parameters or predictors (e.g., grain size distribution, bulk density, organic matter content) to derive PTF.

- The measurement methods and techniques used to obtain the complete soil moisture retention characteristic in the laboratory;
- The sample size used at different pressure heads is not the same;
- Variations in the number of data points, as well as the values of pressure heads used to determine the WRC [17].

## 2. Materials and Methods

#### 2.1. Study Area

^{2}and an elevation difference of 95 m (Figure 1a), resulting in an average terrain gradient of 4.7%. The soil types were derived from the Übersichtsbodenkarte Bayern (ÜBK25) and consist mainly of Cambisol (65%) and Gley (19%), which is located near the watercourse. These grain size compositions of the soil types are displayed in Figure 1b and cover 71% of the KA5-texture classes [32] and 85% of the FAO texture classes.

#### 2.2. Model Setup and Calibration

#### 2.3. Scenario Definition

_{sat}, θ

_{res}, α, n, which are required for the soil description in WaSiM, are specified by all selected PTFs. The PTFs of Wösten et al. (1999) [19], Renger et al. (2009) [35] and Zhang & Schaap (2017) [39] additionally contain a definition of the parameter K

_{sat}(saturated hydraulic conductivity). The key differences among the PTFs, apart from the underlying databases, are the number of considered soil samples and the selected predictors. While soil texture is included in all PTFs as a predictor, in some other PTFs, bulk density (BD), and organic matter content (OM) are not always taken into account.

#### 2.4. Evaluation Strategies

#### 2.4.1. Soil Hydraulic Properties

_{sat}). The FC corresponds to the pore volume which is filled with water at a matric potential of pF = 1.8. The AWC is the respective pore volume between pF = 1.8 and pF = 4.2. Values of FC and AWC were determined for each grid cell for the uppermost meter of the soil profile, and K

_{sat}was analyzed for individual soil horizons. The distribution of these values were statistically examined using box plots analysis, considering only cropland, grassland, and forest areas. In addition, demonstration of the spatial distribution of these three variables (AWC, FC, K

_{sat}) can be used to establish qualitative relationships between soil hydraulic properties and land use distribution or topography.

#### 2.4.2. Runoff Response

- %BiasRR: The percent bias in overall runoff ratio is a diagnostic signature index of the total water balance. It is expected to show primary sensitivity to model parameters that control evapotranspiration.
- %BiasMidslope: The percent bias of the mid-segment slope of the FDC (between 20% and 70% exceeding probability) indicates the reactivity of the catchment to the rainfall events and quantifies the rainfall-runoff response rate.
- %BiasFHV: The percent bias in high-segment volumes of the FDC (<2% exceeding probability) is related to the surface runoff and compares the peak discharges for heavy rainfall events.
- %BiasFLV: The percent bias in low-segment volumes of the FDC (>70% exceeding probability), that reflects the minimum discharge values and is related to the base flow.

#### 2.4.3. Water Balance Components

#### 2.4.4. Spatial Pattern Analysis

## 3. Results

#### 3.1. Soil Hydraulic Properties

_{sat}is presented for the top layer (horizon 1) and for the soil horizon 3, which accounts for a depth of about 75 cm. The thickness of the horizons, and consequently the depths of them, vary among the soil types. For AWC and FC, we included all PTFs, which have their own specific equation to estimate K

_{sat}, and those that consider the parametrization of Ad-hoc-AG Boden [32] for K

_{sat}.

_{sat}by the baseline scenario (defined according to Ad-Hoc AG Boden, 2006) [32] is within the values of the other PTFs for the considered horizons. The largest median of K

_{sat}was defined via Renger et al. (2009) [35]. This PTF is also the only one for which the median increases from horizon 1 to horizon 3. The distinctly smaller variability of K

_{sat}in Rosetta H2w compared to Rosetta H3w is due to the lack of consideration of the bulk density in Rosetta H2w.

_{sat}) were observed in Zhang and Schaap (2017), H3w [39]. Forest sites result in much higher values of K

_{sat}, while the increase is less distinct on grassland sites. On cropland, the K

_{sat}values of Zhang & Schaap (2017) [39], H3w are mostly lower than those of Ad-Hoc AG Boden (2006) [32]. The differences in Wösten et al. (1999) [19] are also attributed to the land use type but less distinguished. The dependency of K

_{sat}on the land use type is driven by the inclusion of bulk density and/or organic matter content in the PTFs.

#### 3.2. Runoff Response

#### 3.3. Water Balance Components and Spatial Pattern Analysis

_{sat}estimated by the respective PTFs leads to a reduction in interflow and an increase in baseflow (scenarios 5 and 6 compared to 9 and 10). This behavior is more pronounced between scenarios 5 and 9 (Rosetta, H2w) than between scenarios 6 and 10 (Rosetta, H3w).

## 4. Discussion

_{sat}determined for a quantitative comparison of the curves showed significant differences in their spatial distribution (Figure 2). These differences become particularly evident when comparing the individual scenarios with the baseline scenario. This issue is important because spatial variability of soil hydraulic properties is regarded as a significant factor to water distribution in the catchment [53].

_{sat}simulated by the scenarios and those of the baseline scenario could be attributed to the land use distribution as well as the proximity to watercourses (Figure 1 and Figure 3). AWC depends to a large extent on the bulk density and the silt content. Hence, PTFs that do not include BD typically result in lower AWC values in soils with lower bulk densities, such as those found in the upper soil horizons of forest soils in a study by [56,57]. They also identified the BD and soil texture as major factors explaining spatial variance in AWC for a study area in China.

_{sat}and AWC) and also the way water is being distributed across the landscape prior to the catchment outlet. As a result, owing to the fact that the spatial variability of K

_{sat}and AWC affects the temporal response of the catchment to precipitation and runoff concentration, one can consider that selection of a particular PTF makes evident changes in the distribution among groundwater infiltration, runoff and evapotranspiration in the catchment [53,62].

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Distribution of the soil hydraulic properties AWC, FC, and K

_{sat}for the land use types cropland, grassland and Forest in the Glonn catchment.

**Figure 3.**Spatial distribution of differences in soil hydraulic properties (∆AWC, ∆K

_{sat}). AWC is calculated for the first meter of the soil profile and the K

_{sat}at the uppermost horizon of the soil profiles.

**Figure 4.**Hydrographs of the baseline scenario and the 10 scenario runs for two exemplary events (scenario description: Table 3).

**Figure 5.**Frequency of occurrence of flow shares for all runoff components (scenario description: Table 3).

Parameter | Description |
---|---|

Horizon | ID for each soil horizon; one value per horizon. |

Layer | Number of numerical layers for each horizon. |

Thickness | Thickness of each single numerical layer in this horizon in m; one value per horizon. |

K_{sat} | Saturated hydraulic conductivity in m/s; one value per soil horizon. |

Θ_{sat} | Saturated water content (fillable porosity in 1/1); one value per soil horizon. |

Θ_{res} | Residual water content (in 1/1, water content which cannot be extracted by transpiration, only by evaporation); one value per soil horizon. |

α | van Genuchten Parameter α; one value per soil horizon. |

n | van Genuchten Parameter n; one value per soil horizon. |

K_{recession} | K_{sat} recession with depth: factor of recession per meter (only applied for the uppermost 2 m of the soil); one value per horizon. |

**Table 2.**Goodness of fit criteria and shares of water balance components for the calibration and validation period.

Parameter | Calibration | Validation |
---|---|---|

Time period | 1 November 1995–31 October 2004 | 1 November 2004–31 October 2013 |

NSE | 0.74 | 0.65 |

NSE_{log} | 0.61 | 0.67 |

PBIAS | 13.2 | −1.9 |

Volume share of | ||

Baseflow | 0.16 | 0.14 |

Interflow | 0.14 | 0.14 |

Surface runoff | 0.04 | 0.05 |

Evapotranspiration | 0.68 | 0.67 |

**Table 3.**Scenario definition: combinations of PTFs to determine the van Genuchten parameters (θ

_{sat}, θ

_{res}, α, n) and the saturated hydraulic conductivity (K

_{sat}).

Scenario | Van Genuchten Parameter | Saturated Hydraulic Conductivity |
---|---|---|

Baseline | Wösten et al. (1999) [19] | Ad-Hoc AG Boden (2006) [32] |

1 | Renger et al. (2009) [35] | Ad-Hoc AG Boden (2006) [32] |

2 | Weynants et al. (2009) [36] | Ad-Hoc AG Boden (2006) [32] |

3 | Zacharias & Wessolek (2007) [37] | Ad-Hoc AG Boden (2006) [32] |

4 | Teepe et al. (2003) [38] | Ad-Hoc AG Boden (2006) [32] |

5 | Zhang & Schaap (2017): Rosetta H2w [39] | Ad-Hoc AG Boden (2006) [32] |

6 | Zhang & Schaap (2017): Rosetta H3w [39] | Ad-Hoc AG Boden (2006) [32] |

7 | Wösten et al. (1999) [19] | Wösten et al. (1999) [19] |

8 | Renger et al. (2009) [35] | Renger et al. (2009) [35] |

9 | Zhang & Schaap (2017): Rosetta H2w [39] | Zhang & Schaap (2017): Rosetta H2w [39] |

10 | Zhang & Schaap (2017): Rosetta H3w [39] | Zhang & Schaap (2017): Rosetta H3w [39] |

PTF | Method | Database | Sample Size | Predictors |
---|---|---|---|---|

Wösten et al. (1999) [19] | Regression analysis | HYPRES [19] | 5521 | Clay, Silt, OM, BD, topsoil/subsoil |

Renger et al. (2009) [35] | Regression analysis | various sources | unknown | Sand, Silt, Clay |

Weynants et al. (2009) [36] | Regression analysis | Vereecken et al., 1989 [27] | 166 | Sand, Silt, Clay, BD, OM |

Zacharias and Wessolek (2007) [37] | Regression analysis | IGBP-DIS soil data (Tempel et al., 1996) [44]; UNSODA (Nemes et al., 2001) [43] | 676 | Sand, Silt, Clay, BD |

Teepe et al. (2003) [38] | Regression analysis | Teepe et al. (2003) [38] | 1850 | Lookup table: Sand, Silt, Clay, BD |

Zhang & Schaap (2017), Rosetta H2w [39] | Single Artificial Neural Network | Schaap et al. (2001) [45] | 2134 for WRC, 1306 for K_{sat} | Sand, Silt, Clay |

Zhang & Schaap (2017), Rosetta H3w [39] | Single Artificial Neural Network | Schaap et al. (2001) [45] | 2134 for WRC, 1306 for K_{sat} | Sand, Silt, Clay, BD |

**Table 5.**Peak changes (%) and volume changes (%) of the selected events in Figure 4 and the calibration and validation periods the event in June 2013 is evaluated separately for both peaks.

Scenario | Peak Change (%) | Volume Change (%) | ||||||
---|---|---|---|---|---|---|---|---|

06/2013 (1) | 06/2013 (2) | 09/2000 | 06/2013 (1) | 06/2013 (2) | 09/2000 | calib. | valid. | |

1 | 9.4 | −7.9 | 0.0 | 10.0 | −4.6 | 1.0 | −4.7 | −0.5 |

2 | −3.8 | −9.4 | −15.1 | −5.4 | −11.1 | −13.0 | −5.2 | −4.5 |

3 | 43.4 | 37.0 | 28.3 | 44.1 | 29.2 | 26.8 | −6.7 | −4.7 |

4 | −29.8 | −16.7 | −33.6 | −20.7 | −8.0 | −18.9 | −5.7 | −4.6 |

5 | −52.9 | −57.6 | −58.0 | −39.9 | −42.6 | −41.1 | −0.6 | −0.7 |

6 | −50.5 | −49.5 | −55.1 | −36.2 | −34.6 | −36.9 | −0.9 | −0.6 |

7 | −2.2 | −1.9 | −9.5 | −3.6 | −2.7 | −6.6 | 0.0 | 0.4 |

8 | −45.3 | −43.9 | −58.8 | −39.5 | −21.7 | −39.3 | −2.4 | 0.3 |

9 | −57.4 | −64.6 | −65.2 | −49.8 | −50.1 | −50.4 | −0.6 | −0.8 |

10 | −43.3 | −39.7 | −49.6 | −32.3 | −30.4 | −34.3 | −1.9 | −1.6 |

**Table 6.**Signature indices of the 10 scenarios compared to the baseline scenario; evaluation period: 1 November 1995–31 October 2013.

Scenario | %BiasRR | %BiasMidslope | %BiasFHV | %BiasFLV |
---|---|---|---|---|

1 | −2.6 | 7.5 | 10.1 | −16.8 |

2 | −4.8 | 1.0 | −3.9 | −11.2 |

3 | −5.7 | 87.5 | 43.5 | −47.2 |

4 | −5.1 | 43.3 | −11.8 | −25.4 |

5 | −0.6 | 20.2 | −24.6 | −11.1 |

6 | −0.7 | 38.1 | −20.8 | −25.7 |

7 | 0.2 | 1.0 | −2.5 | −0.3 |

8 | −1.0 | −0.1 | −23.5 | 6.1 |

9 | −0.7 | −3.6 | −34.7 | 14.1 |

10 | −1.7 | 27.1 | −18.0 | −21.3 |

**Table 7.**Mean annual amount of the water balance and infiltration components for the baseline scenario and the 10 scenarios.

Water Balance Components (mm/a) | Infiltration Components (mm/a) | ||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Surface Runoff | Interflow | Base Flow | Transpiration | Evaporation | Snow Evaporation | Interception Evaporation | Change in Soil Storage | Change in Snow Storage | Infiltration Excess | Macropore infiltration | Matrix Infiltration | Interception Evaporation | Snow Evaporation | ||

Baseline | 39 | 117 | 121 | 99 | 302 | 14 | 163 | 4 | 0 | 39 | 19 | 625 | 163 | 14 | |

Scenario | 1 | 42 | 121 | 108 | 98 | 303 | 14 | 163 | 10 | 0 | 42 | 19 | 622 | 163 | 14 |

2 | 41 | 113 | 110 | 99 | 316 | 14 | 163 | 4 | 0 | 41 | 19 | 624 | 163 | 14 | |

3 | 50 | 117 | 95 | 99 | 323 | 14 | 163 | 0 | 0 | 50 | 18 | 615 | 163 | 14 | |

4 | 37 | 89 | 136 | 99 | 322 | 14 | 163 | 0 | 0 | 37 | 19 | 627 | 163 | 14 | |

5 | 34 | 120 | 122 | 97 | 310 | 14 | 163 | 0 | 0 | 34 | 19 | 630 | 163 | 14 | |

6 | 34 | 135 | 106 | 97 | 310 | 14 | 163 | 0 | 0 | 34 | 19 | 630 | 163 | 14 | |

7 | 39 | 121 | 119 | 99 | 302 | 14 | 163 | 4 | 0 | 39 | 19 | 625 | 163 | 14 | |

8 | 36 | 123 | 117 | 99 | 299 | 14 | 163 | 10 | 0 | 36 | 19 | 628 | 163 | 14 | |

9 | 35 | 107 | 133 | 97 | 309 | 14 | 163 | 1 | 0 | 35 | 19 | 629 | 163 | 14 | |

10 | 35 | 133 | 108 | 97 | 311 | 14 | 163 | 0 | 0 | 35 | 19 | 629 | 163 | 14 |

**Table 8.**Spatial correlation (correl) and histogram overlap (histo) of the 10 scenarios compared to the baseline scenario, for spatial mean of direct runoff, Interflow, baseflow, and ETa.

Scenario | Correl | Histo | Correl | Histo | Correl | Histo | Correl | Histo |
---|---|---|---|---|---|---|---|---|

Direct Runoff | Interflow | Baseflow | ETa | |||||

1 | 0.997 | 0.804 | 0.942 | 0.893 | 0.996 | 0.985 | 0.997 | 0.819 |

2 | 0.999 | 0.697 | 0.975 | 0.892 | 0.998 | 0.976 | 0.998 | 0.727 |

3 | 0.992 | 0.423 | 0.782 | 0.769 | 0.978 | 0.970 | 0.988 | 0.349 |

4 | 0.997 | 0.786 | 0.500 | 0.381 | 0.976 | 0.987 | 0.997 | 0.744 |

5 | 0.997 | 0.653 | 0.835 | 0.829 | 0.990 | 0.966 | 0.996 | 0.652 |

6 | 0.995 | 0.473 | 0.916 | 0.874 | 0.995 | 0.965 | 0.998 | 0.653 |

7 | 0.999 | 0.683 | 0.962 | 0.898 | 0.999 | 0.994 | 1.000 | 0.827 |

8 | 0.997 | 0.758 | 0.913 | 0.910 | 0.997 | 0.988 | 0.997 | 0.846 |

9 | 0.997 | 0.712 | 0.795 | 0.746 | 0.990 | 0.975 | 0.995 | 0.626 |

10 | 0.996 | 0.782 | 0.900 | 0.909 | 0.994 | 0.965 | 0.997 | 0.618 |

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**MDPI and ACS Style**

Mohajerani, H.; Teschemacher, S.; Casper, M.C. A Comparative Investigation of Various Pedotransfer Functions and Their Impact on Hydrological Simulations. *Water* **2021**, *13*, 1401.
https://doi.org/10.3390/w13101401

**AMA Style**

Mohajerani H, Teschemacher S, Casper MC. A Comparative Investigation of Various Pedotransfer Functions and Their Impact on Hydrological Simulations. *Water*. 2021; 13(10):1401.
https://doi.org/10.3390/w13101401

**Chicago/Turabian Style**

Mohajerani, Hadis, Sonja Teschemacher, and Markus C. Casper. 2021. "A Comparative Investigation of Various Pedotransfer Functions and Their Impact on Hydrological Simulations" *Water* 13, no. 10: 1401.
https://doi.org/10.3390/w13101401