# A Functional Analysis of Pedotransfer Functions Developed for Sri Lankan soils: Applicability for Process-Based Crop Models

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Meteorological Data

#### 2.2. Soil Data

^{3}as the true density (TD). BD denotes the bulk density in Equation (1).

#### 2.3. APSIM Simulation

#### 2.4. Sensitivity Analysis

_{i}is the true output for the ith training run, $\widehat{y}$ is the corresponding emulator approximation, s

_{i}is the standard deviation calculated with the ith training point removed, and n is the number of runs [59,62].

_{i}) was estimated by partitioning the output variance induced by the variations in all input parameters under the assumption that all input uncertainties are unknown but uniform. S

_{i}represents the expected reduction in the output variance if parameter x

_{i}is known [61,62], and the relative importance of each parameter in terms of its effect on output uncertainty can be ranked using the S

_{i}values of the selected parameters [67]. The main effect index (Si) is defined as

_{i}is known.

#### 2.5. Functional Analysis

_{i}is the simulated value, O

_{i}is the observed value, and $\overline{O}$ is the mean of the observations.

## 3. Results and Discussion

#### 3.1. Sensitivity Analysis

#### 3.2. Functional Analysis

^{2}values for WAGT and WRR, respectively (Table 2). This ensures no significant differences between PTF-based simulations and measurement-based simulations. A comparison between the outputs of the rice simulations (WAGT and WRR) under both simulation scenarios also confirmed the acceptability of PTF-based simulations, as no significant difference (p > 0.05) between both types of simulations under a t-test was observed (Table 2). The reported Nash–Sutcliffe efficiency was 0.89 and 0.90 for WAGT and WRR, respectively. Hence, we confirmed the similarity of PTF-based and measurement-based simulations. Wilmott’s index of agreement also confirmed the agreement of the results of PTF-based simulations with measurement-based simulations for both WAGT (d = 0.97) and WRR (d = 0.99). The RMSEs for WAGT and WRR were 811 and 445 kg/ha, respectively, which also confirmed the similarity of both simulation scenarios, which were assumed to be within the bounds (half of the standard deviation (SD) of the measurement-based simulations) (WAGT, SD = 2485 kg/ha; WRR, SD = 1424 kg/ha).

^{2}values for all selected soil module related daily outputs (SWS(1), Infiltration, Runoff, and EOS) (Table 2). This ensures that PTF-based simulations can perform as well as measurement-based simulations. Further, the comparison of soil module related outputs between both simulation scenarios also confirmed the acceptability of PTF-based simulations, as no significant difference (p > 0.05) was found between both simulation scenarios for infiltration and runoff (Table 2). The Nash–Sutcliffe efficiency showed a better agreement between the two simulation scenarios, as all outputs related to the soil module recorded an NSE over 0.85. Wilmott’s index of the agreement also confirmed the agreement of the results of the PTF-based simulation with the measurement-based simulation for all soil module related outputs, reporting over 0.95 for d. The RMSE for SWS(1), Infiltration, Runoff, and EOS were 0.05 mm/mm, 0.70 mm/day, 0.45 mm/day, and 0.35 mm/day, respectively, which also confirmed the similarity of both simulation scenarios, which were assumed to be within the bounds.

## 4. Conclusions

## 5. Limitations

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

**Table A1.**The accuracy of the emulators developed to estimate the total above-ground dry matter (kg/ha) of rice (WAGT) for different environments in Sri Lanka.

Year | Dry Zone Soil | Intermediate Zone Soil | Wet Zone Soil | ||||||
---|---|---|---|---|---|---|---|---|---|

Sigma sq | CV RMSE | CV RMSSE | Sigma sq | CV RMSE | CV RMSSE | Sigma sq | CV RMSE | CV RMSSE | |

Year 1 | 0.13 | 615.7 | 1.12 | 0.17 | 1272.3 | 1.04 | 0.17 | 1272.3 | 1.04 |

Year 2 | 0.03 | 233.1 | 1.11 | 0.14 | 927.1 | 1.06 | 0.14 | 927.1 | 1.06 |

Year 3 | 0.10 | 732.6 | 1.01 | 0.28 | 1736.4 | 1.04 | 0.28 | 1736.4 | 1.04 |

Year 4 | 0.03 | 150.9 | 0.92 | 0.04 | 371.2 | 1.11 | 0.04 | 371.2 | 1.11 |

Year 5 | 0.05 | 450.2 | 1.10 | 0.24 | 1594.6 | 1.06 | 0.24 | 1594.6 | 1.06 |

Year 6 | 0.13 | 998.2 | 1.11 | 0.37 | 1742.5 | 1.04 | 0.37 | 1742.5 | 1.04 |

Year 7 | 0.05 | 284.1 | 1.18 | 0.26 | 1346.7 | 1.06 | 0.26 | 1346.7 | 1.06 |

Year 8 | 0.03 | 373.4 | 1.01 | 0.18 | 1056.5 | 1.09 | 0.18 | 1056.5 | 1.09 |

Year 9 | 0.06 | 438.5 | 1.08 | 0.11 | 919.4 | 1.03 | 0.11 | 919.4 | 1.03 |

Year 10 | 0.06 | 268.3 | 1.14 | 0.21 | 1358.2 | 0.96 | 0.21 | 1358.2 | 0.96 |

**Table A2.**The accuracy of the emulators developed to estimate the weight of rough rice (kg/ha) of rice (WRR) for different environments in Sri Lanka.

Year | Dry Zone Soil | Intermediate Zone Soil | Wet Zone Soil | ||||||
---|---|---|---|---|---|---|---|---|---|

Sigma sq | CV RMSE | CV RMSSE | Sigma sq | CV RMSE | CV RMSSE | Sigma sq | CV RMSE | CV RMSSE | |

Year 1 | 0.14 | 398.2 | 1.16 | 0.21 | 867.9 | 1.04 | 0.14 | 737.8 | 1.05 |

Year 2 | 0.07 | 182.5 | 1.26 | 0.19 | 631.4 | 1.03 | 0.11 | 546.2 | 1.00 |

Year 3 | 0.04 | 309.2 | 1.01 | 0.38 | 777.0 | 1.05 | 0.22 | 845.6 | 0.98 |

Year 4 | 0.12 | 108.3 | 0.99 | 0.11 | 303.1 | 1.04 | 0.09 | 197.1 | 1.13 |

Year 5 | 0.02 | 195.8 | 1.09 | 0.39 | 942.7 | 1.00 | 0.21 | 720.8 | 1.05 |

Year 6 | 0.04 | 383.5 | 1.04 | 0.44 | 752.7 | 1.02 | 0.42 | 1009 | 1.05 |

Year 7 | 0.08 | 169.0 | 1.10 | 0.38 | 970.3 | 1.01 | 0.20 | 584.3 | 1.07 |

Year 8 | 0.09 | 197.8 | 1.19 | 0.22 | 553.8 | 1.04 | 0.25 | 524.6 | 1.06 |

Year 9 | 0.12 | 180.5 | 1.13 | 0.26 | 815.3 | 1.06 | 0.11 | 315.1 | 1.10 |

Year 10 | 0.05 | 176.4 | 1.16 | 0.48 | 778.1 | 0.95 | 0.20 | 616.9 | 1.01 |

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**Figure 1.**A map of Sri Lanka showing the study sites and climatic zones defined based on the mean annual rainfall.

**Figure 2.**Variation of the the sensitivity index (Si) of selected soil parameters on the simulated total above-ground dry matter (WAGT) and simulated dry-weight of rough rice (WRR) for rice in Sri Lanka.

**Figure 3.**Relationship between use of measurement-based inputs and pedotrandfer functions derived (PTF-based) inputs on simulations of rice, (

**a**) Total above-ground dry matter (WAGT) (kg/ha) of rice; (

**b**) Dry weight of rough rice (WRR) (kg/ha); (

**c**) Soil water content of the topsoil layer (SWS(1)) (mm/mm); (

**d**) Daily infiltration (infiltration) (mm); (

**e**) Daily runoff (runoff) (mm); and f) Potential evapotranspiration after modifications of green cover and residue (EOS) (mm).

**Figure 4.**Relationship between the measured and PTF-estimated soil hydraulic parameters (whole soil profile) of the selected soil profiles; (

**a**) lower limit (LL15) and (

**b**) drainage upper limit (DUL).

**Figure 5.**Relationship between measurement-based and PTF-based simulations of average yields (2000–2010); (

**a**) The total above-ground dry matter of rice (kg/ha); WAGT, (

**b**) dry weight of rough rice (kg/ha); WRR.

**Figure 6.**The error variation of PTF-based simulations of average yield (2000–2010) in different locations; (

**a**) total above-ground dry matter (kg/ha); WAGT and (

**b**) weight of rough rice kg/ha; WRR; LL15: Lower limit (mm/mm), DUL: drainage upper limit (mm/mm); The size of the bubble represents the magnitude of the error of the estimated yield.

Parameter | Description | Unit | Range | |
---|---|---|---|---|

Min | Max | |||

BD | Bulk density | g/cm^{3} | 0.8 | 2.0 |

LL15 | Drained lower limit (equals the permanent wilting point) | mm/mm | 0.05 | 0.30 |

DUL | Drained upper limit (equals the field capacity) | mm/mm | 0.0 * | 1.0 * |

SAT | Saturation | mm/mm | 0.0 ** | 1.0 ** |

KS | Saturated hydraulic conductivity | mm/day | 0.1 | 10,000 |

OC | Organic carbon | % | 0.1 | 1.5 |

pH | 4.0 | 9.0 | ||

SWCON | Drainage coefficient | 0 | 1 |

**Table 2.**Performance evaluation of the simulation accuracies of the measurement-based and PTF-based simulations.

Criteria | WAGT | WRR | SWS(1) | Infiltration | Runoff | EOS |
---|---|---|---|---|---|---|

R^{2} | 0.90 | 0.90 | 0.91 | 0.99 | 0.98 | 0.95 |

RMSE | 811 kg/ha | 445 kg/ha | 0.05 mm/mm | 0.74 mm | 0.45 mm | 0.35 mm |

NSE | 0.89 | 0.90 | 0.85 | 0.99 | 0.98 | 0.95 |

d | 0.97 | 0.97 | 0.95 | 1.00 | 1.00 | 0.99 |

CCC | 0.94 | 0.95 | 0.91 | 1.00 | 0.98 | 0.99 |

SD | 2485 kg/ha | 1424 kg/ha | 0.12 mm | 7.84 mm | 3.47 mm | 1.63 mm |

P(T <=t) | 0.42 | 0.60 | 0.06 | 0.83 | 0.74 | 0.02 |

^{2}: Coefficient of determination, RMSE: Root mean square error, NSE: Nash–Sutcliffe efficiency, d: Index of agreement, CCC: Lin’s concordance correlation coefficient, SD: Standard deviation, P: Probability of t-test.

© 2020 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**

Gunarathna, M.H.J.P.; Sakai, K.; Kumari, M.K.N.; Ranagalage, M.
A Functional Analysis of Pedotransfer Functions Developed for Sri Lankan soils: Applicability for Process-Based Crop Models. *Agronomy* **2020**, *10*, 285.
https://doi.org/10.3390/agronomy10020285

**AMA Style**

Gunarathna MHJP, Sakai K, Kumari MKN, Ranagalage M.
A Functional Analysis of Pedotransfer Functions Developed for Sri Lankan soils: Applicability for Process-Based Crop Models. *Agronomy*. 2020; 10(2):285.
https://doi.org/10.3390/agronomy10020285

**Chicago/Turabian Style**

Gunarathna, M. H. J. P., Kazuhito Sakai, M. K. N. Kumari, and Manjula Ranagalage.
2020. "A Functional Analysis of Pedotransfer Functions Developed for Sri Lankan soils: Applicability for Process-Based Crop Models" *Agronomy* 10, no. 2: 285.
https://doi.org/10.3390/agronomy10020285