# The Least Square Adjustment for Estimating the Tropical Peat Depth Using LiDAR Data

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. The Covariates

#### 2.2. Peat Depth Estimation

#### 2.3. Raster Operation

#### 2.4. Statistical Testing

_{α/2}is a critical value at the level of significance α and degree of freedom r, S

_{0}is a posteriori estimated variant factor, q

_{ii}is the variant residual value.

_{i}is the estimated parameter, μ

_{o}is the true value of the parameter, σ

_{ii}is the standard deviation of the estimated parameter, and n is the number of observation equations.

_{i}) is an estimated value based on the modeling result, x

_{i}is the true value of the field measurement, and n is the number of peat depth data.

## 3. Results

#### 3.1. Peat Depth and Mineral Soil Elevation

#### 3.2. Identification of the Characteristics

#### 3.3. Coefficients of Estimation Equation

#### 3.4. Accuracy Assessments

_{value}≤ t

_{table}. The result for 50% data is t

_{value}= 0.5001, or less than 1.96. It can be concluded that using 50% of the data in the determination of the estimation equation is statistically the same (insignificantly different) as using the entire dataset (100%) at the confidence level of 95%.

_{value}of 0.181 or less than a t

_{table}of 1.96, which confirmed that the use of 25% of the data can be said statistically to be equal to 100% data usage.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Cross-section view along the lines of Cross-section 1, Cross-section 2, and Cross-section 3 based on estimation 1, estimation 2, and estimation 3 results, which are overlaid on the real mineral soil surface and peat soil surface (topography).

**Figure A2.**Cross-section view of Cross-section 1, Cross-section 2, and Cross-section 3 lines of mineral soil elevation based on 25%, 50%, and 100% of the data, which are overlaid on the peat surface topography and the real mineral soil elevation.

## Appendix B

^{o}to 360

^{o}[59]. The slope usually is used to measure the level of change in elevation and the direction of each change in altitude.

^{o}; (5) upper slope if 0.5 SD <TPI ≤ 1 SD; and (6) ridge if TPI> 1 SD. The class is called the slope position classification [43].

^{SN}≤ −1 and TPI

^{LN}≤ −1; (2) midslope drainage if TPI

^{SN}≤ −1 and −1 < TPI

^{LN}< −1; (3) upland drainage if TPI

^{SN}≤ −1 and TPI

^{LN}≥ 1; (4) u-shape valleys if −1 < TPI

^{SN}< 1 and TPI

^{LN}≤ −1; (5) plains if −1 < TPI

^{SN}< 1 and −1 < TPI

^{LN}< −1 and slope ≤ 5°; (6) open slope if −1 < TPI

^{SN}< 1 and −1 < TPI

^{LN}≤ 1 and slope > 5°; (7) upper slope if −1 < TPI

^{SN}< 1 and TPI

^{LN}≥ 1; (8) local ridge/hills in valleys if TPI

^{SN}≥ 1 and TPI

^{LN}≤ −1; (9) midslope ridges, small hills in plains if TPI

^{SN}≥ 1 and −1 < TPI

^{LN}< 1; (10) mountain tops, high ridges if TPI

^{SN}≥ 1 and TPI

^{LN}≥ 1 [43].

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**Figure 1.**Aerial photograph visualization of the Peat Hydrological Unit (PHU) area of Tebing Tinggi Island with the river and stream (blue line) and street features (red line) added.

**Figure 3.**Condition of topographic (depressionless digital terrain model (DTM) above the local MSL) and distribution of peat measurements on file.

**Figure 4.**The condition of elevation mineral soil resulted in the estimation model by involving all covariates. Note: the elevation is above the local MSL.

**Figure 5.**Mineral soil position of estimation results by ignoring gravity parameters and outliers. Note: the elevation is above the local MSL.

**Figure 6.**Estimation results of the mineral soil elevation after eliminating four insignificant parameters and removing outliers. Note: the elevation is above the local MSL.

**Figure 7.**(

**a**) Positions of the profile line and (b) the longitudinal profile view along the profile line. Note: cross-section 1, cross-section 2, and cross section 3 can be seen in Appendix A.

**Figure 8.**Longitudinal profile of the estimation results of mineral soil elevation based on 25%, 50%, and 100% of data, which are overlaid onto the peat surface topography and the real mineral soil elevation.

**Table 1.**The calculation results of the coefficients by involving the entire dataset and all the parameters (estimation 1). Digital terrain model (DTM); slope position index (SPI); topographic positional index (TPI); topographic wetness index (TWI); standard deviation (SD).

Covariates | DTM | Gravity | Geology | SPI | Landform | Valley Depth | Vertical Distance | TPI | TWI | Nearest River | Constant |
---|---|---|---|---|---|---|---|---|---|---|---|

coefficient | 0.5326 | –0.1907 | –0.2993 | –1.09 | 0.4473 | 0.3322 | –0.0759 | 0.1952 | –0.0774 | –0.0165 | 10.942 |

SD | 0.0208 | 0.0576 | 0.0264 | 0.1366 | 0.1199 | 0.0855 | 0.0523 | 0.1665 | 0.0149 | 0.0041 | 0.3652 |

t-value | 25.6612 | –3.3086 | –11.3404 | –7.9821 | 3.7321 | 3.8863 | –1.4505 | 1.1722 | –5.1931 | –4.0165 | 29.9605 |

**Table 2.**The calculation results of the coefficient after eliminating gravity disturbance and outliers from the input data (estimation 2).

Covariates | DTM | Geology | SPI | Land Form | Valley Depth | Vertical Distance | TPI | TWI | Nearest River | Constant |
---|---|---|---|---|---|---|---|---|---|---|

Coefficient | 0.60140 | −0.24190 | −1.12370 | 0.50380 | 0.37550 | −0.03160 | 0.33200 | −0.05260 | 0.00760 | 7.13670 |

SD | 0.0176 | 0.0279 | 0.1407 | 0.1352 | 0.0951 | 0.056 | 0.1662 | 0.0158 | 0.0044 | 0.4681 |

t-value | 34.2421 | −8.6556 | −7.9886 | 3.7269 | 3.9467 | −0.5641 | 1.9976 | −3.3244 | 1.7253 | 15.2467 |

**Table 3.**Results of the coefficients and t-value by eliminating insignificant covariates and small effect parameters in the equation (estimation 3).

Covariates | DTM | Geology | SPI | Land Form | Valley Depth | TPI | Constant |
---|---|---|---|---|---|---|---|

Coefficient | 0.61340 | −0.22890 | −1.20190 | 0.60600 | 0.36950 | 0.45970 | 5.74200 |

SD | 0.0156 | 0.0265 | 0.1402 | 0.1339 | 0.0926 | 0.1576 | 0.4948 |

t-value | 39.3077 | −8.6298 | −8.5718 | 4.5265 | 3.9887 | 2.9172 | 11.6053 |

**Table 4.**Error Calculation of the different elevation between the real mineral soil line and the estimation results. Mean absolute error (MAE); minimum error (min error); maximum error (max error).

Estimation 1 | Estimation 2 | Estimation 3 | |
---|---|---|---|

MAE | 1.237 m | 1.010 m | 1.019 m |

Min Error | 0.002 m | 0.004 m | 0.002 m |

Max Error | 5.181 m | 3.614 m | 3.675 m |

SD | 1.076 m | 0.755 m | 0.746 m |

total data | 1109 | 971 | 971 |

Covariates | DTM | Geology | SPI | Land Form | Valley Depth | Vertical Distance | TPI | TWI | NearestRiver | Constant |
---|---|---|---|---|---|---|---|---|---|---|

Coefficient | 0.898 | 0.1037 | −0.5354 | 0.0159 | 0.0011 | −0.0447 | 0.8892 | −0.0168 | 0.263 | 1.7769 |

SD | 0.0233 | 0.0365 | 0.2164 | 0.1882 | 0.1106 | 0.0787 | 0.206 | 0.0214 | 0.0558 | 0.4445 |

t-value | 38.5058 | 2.843 | −2.474 | 0.0845 | 0.01 | −0.5679 | 4.3165 | −0.7841 | 4.7151 | 3.9978 |

Covariates | DTM | Geology | SPI | Land Form | Valley Depth | Vertical Distance | TPI | TWI | NearestRiver | Constant |
---|---|---|---|---|---|---|---|---|---|---|

coefficient | 0.8829 | 0.0141 | −0.4958 | −0.3635 | −0.0062 | −0.0836 | 1.3446 | −0.0249 | 0.3111 | −8.2318 |

SD | 0.0332 | 0.0508 | 0.3121 | 0.3281 | 0.1737 | 0.1069 | 0.2925 | 0.0321 | 0.0772 | 0.3071 |

t-value | −26.5681 | −0.2775 | 1.5885 | 1.1077 | 0.0355 | 0.7825 | −4.5964 | 0.7776 | −4.0291 | 26.8033 |

100% Data | 50% Data | 25% Data | |
---|---|---|---|

MAE | 1.010 m | 1.031 m | 1.020 m |

Min Error | 0.004 m | 0.001 m | 0.001 m |

Max Error | 3.614 m | 4.700 m | 4.688 m |

SD | 0.755 m | 0.819 m | 0.845 m |

total data | 971 | 524 | 274 |

**Table 8.**Volume comparison between the models resulted from the ordinary least square (OLS) method and the filed measurement.

Data | Volume (m^{3}) | Δ vol (%) |
---|---|---|

peat volume (original peat depth probe) | 8,299,347,092.475 | |

Δ vol. peat-probe vs. estimation1 | - 933,186,413.099 | 11.244 |

Δ vol. peat-probe vs. estimation2 | - 567,061,186.697 | 6.833 |

Δ vol. peat-probe vs. estimation3 | - 636,868,262.057 | 7.674 |

Δ vol. peat-probe vs. 50% data | - 542,225,677.094 | 6.533 |

Δ vol. peat-probe vs. 25% data | - 627,199,328.081 | 7.557 |

© 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**

Cahyono, B.K.; Aditya, T.; Istarno.
The Least Square Adjustment for Estimating the Tropical Peat Depth Using LiDAR Data. *Remote Sens.* **2020**, *12*, 875.
https://doi.org/10.3390/rs12050875

**AMA Style**

Cahyono BK, Aditya T, Istarno.
The Least Square Adjustment for Estimating the Tropical Peat Depth Using LiDAR Data. *Remote Sensing*. 2020; 12(5):875.
https://doi.org/10.3390/rs12050875

**Chicago/Turabian Style**

Cahyono, Bambang Kun, Trias Aditya, and Istarno.
2020. "The Least Square Adjustment for Estimating the Tropical Peat Depth Using LiDAR Data" *Remote Sensing* 12, no. 5: 875.
https://doi.org/10.3390/rs12050875