# Regional Scale Rain-Forest Height Mapping Using Regression-Kriging of Spaceborne and Airborne LiDAR Data: Application on French Guiana

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## Abstract

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## 1. Introduction

^{2}over French Guiana for example) and inhomogeneous spatial sampling (sampling lines along satellite tracks). Therefore, merging LiDAR data (spaceborne and/or airborne) with other data sources is essential in order to create forest canopy heights with complete land coverage and a good precision (e.g., [10,20]).

^{2}) of 0.67. A more recent study conducted by Simard et al. [10] improved on the work of Lefsky et al. [20] for global canopy height mapping using other ancillary data such as the annual mean precipitation, seasonal precipitation, annual mean temperature, seasonal temperature, data from a digital elevation model (DEM) and percentage tree cover provided from MODIS. Their global canopy height map validated against in-situ measurements showed moderate canopy height estimation precision with an RMSE of 6.1 m (R

^{2}of 0.5) on the estimation of canopy heights.

^{2}). The last 40% could be related to forest dynamic endogenous processes (i.e., gap processes). In addition, while the canopy height mapping from Simard et al. [10] and Lefsky et al. [20] provide somewhat good canopy height estimates at large scales with a medium/low spatial resolution, such precisions are not optimal when estimating forest biomass with allometries that only use canopy heights (e.g., [1,3]). In fact, an RMSE of about 6 m leads to a relative error on the estimation of biomass of about 25%. This precision on the estimation of biomass is more than the recommended relative error of 20% set by the United Nations programme on Reducing Emissions from Deforestation and Forest Degradation (REDD) (e.g., [21,22]). Hence, to satisfy the UN REDD recommendations on the precision of biomass, improved canopy height estimates are required.

## 2. Study Area and Datasets

#### 2.1. Study Area

^{2}. The forest is mostly old growth rainforest and vegetation types are of natural or anthropogenic origin (forests, swamps, savannas and agricultural crops). French Guiana’s terrain is mostly low lying rising occasionally to small hills and low altitude mountains with Altitudes ranging between 0 and 851 m and 67.8% of the slopes are below 5°.

#### 2.2. Datasets Description

#### 2.2.1. Spaceborne LiDAR Dataset

#### 2.2.2. Airborne LiDAR Dataset

#### Small Footprint Low Density LiDAR Dataset

^{2}. Low canopy heights (maximum of 20 m) can be observed in the northern parts of French Guiana on the coastal marsh areas.

#### Small Footprint High Density LiDAR Dataset

^{2}(between 0.9 and 5.6 points/m

^{2}). This dataset covers several small reference sites in the North of French Guiana (Figure 2). A comparison of the canopy height estimates of the LD and HD datasets showed a high correlation between LD and HD datasets (R

^{2}of 93%) with a root mean square error of 1.57 m [24].

#### 2.2.3. Ancillary Datasets

#### MODerate-Resolution IMAGING Spectroradiometer (MODIS) Data

#### SRTM Digital Elevation Model Data

#### Geological Map

#### Forest Landscape Types Map

- (1)
- LT8 represents dense closed-canopy forest with small crowns of the same canopy height and small gaps mixed with regular canopies with well-developed crowns of almost the same canopy height without large gaps interlaced with flooded savannas (10%).
- (2)
- LT9 is a closed canopy forest dominated by well-developed crowns of almost the same canopy height without large gaps.
- (3)
- LT10 is an irregular and disrupted-canopy forest where the trees have very different heights and different crown diameters with large gaps mixed with closed-canopy forest dominated by well-developed crowns at almost the same elevation without large gaps. LT10 is also interlaced with liana forests.
- (4)
- LT11 is similar to LT10 with more liana forest and non-forest land covers.
- (5)
- LT12 is an open forest associated with wetlands and bamboo thickets. The LT dataset was chosen for its correlation with canopy heights. Indeed, in Fayad et al. [24], the difference between SRTM and canopy top elevations from ICESat were found to be correlated with different LTs as well as different canopy heights.

#### Average Rainfall Map

## 3. Canopy Height Estimation Methods

#### 3.1. Canopy Height Trend Mapping Using Random Forest Regressions

#### 3.2. Canopy Height Mapping Using Regression-Kriging

**ẑ(s**is the predicted value at an unvisited location

_{0})**s**, $\widehat{\mathit{m}}\left({\mathit{s}}_{\mathbf{0}}\right)$ the fitted trend (the RF canopy height estimates), and

_{0}**ê(s**the kriged residual.

_{0})#### 3.3. Ordinary Krigging of Regression Residuals

**γ**as a function of distance between samples

**h**using the following function:

**γ(h)**is the semivariance as a function of lag distance

**h**,

**N(h)**is the number of pairs of data separated by

**h**, and

**e**, the canopy height estimate residuals at locations

**s**and

_{i}**(s**[42]. Semivariograms have three main parameters: (1) the nugget which is the semivariance at a lag distance of zero; (2) the sill is the semivariance where there is no spatial correlation; and (3) the range is the distance at which the sill is reached. After plotting the sample semivariogram that describes the spatial autocorrelation of a given dataset, a mathematical function is fitted to this semivariogram in order to represent the range, the sill and the nugget. Thus, the datasets sample variogram can now be represented using a function. The sample semivariogram was plotted in R using the geoR package. The main parameters of the semivariograms were first roughly estimated, and the estimates corrected by an automated function provided by the geoR package. After model fitting of the sample semivariogram, ordinary krigging is then used, which estimates values

_{i}+h)**ê(s**at an unvisited location

_{0})**s**using the following equation:

_{0}**ê(s**is the kriged residual,

_{0})**λ**are the kriging weights determined by the spatial autocorrelation structure (variogram), and

_{i}**e(s**is the residual at location

_{i})**s**[42]. Ordinary kriging was implemented using ArcMap with the semivariogram parameters from the previous step, as well as the canopy height residuals.

_{i}#### 3.4. Effects of LiDAR Sampling Density on Precision of the Mapped Canopy Heights

^{2}), LD_10 (0.11 pts/km

^{2}), LD_20 (0.08 pts/km

^{2}), LD_30 (0.05 pts/km

^{2}), LD_40 (0.04 pts/km

^{2}), and LD_50 (0.03 pts/km

^{2}), a corresponding canopy height map was created. Canopy height maps were created using the same procedure described in Section 3.1 and Section 3.2, which consists of first creating a canopy height map using Random Forest regressions with each one of the LD_cal subsets as reference data and the ancillary variables as predictor variables for the model, and next each canopy height residual from each model were kriged and added to the corresponding canopy height map.

## 4. Results

#### 4.1. Canopy Height Trend Mapping Using Random Forest Regressions

^{2}of 0.55). The precision of the estimates slightly increased when using the RF model with the LD_cal dataset, with an RMSE on the canopy height estimates of 5.8 m (R

^{2}of 0.62). Finally, the bias (mean (verification canopy heights—estimated canopy heights)) for both the GLAS and LD_cal datasets was very low (<0.2 m).

#### 4.2. Canopy Height Estimation Using Regression-Kriging

^{2}is the nugget, σ

^{2}the sill, and a the range of the semivariogram (γ). For the different canopy height residual datasets, the fitted semivariograms presented similar nuggets (between 15 and 18 m

^{2}), sills (between 28 and 32 m

^{2}), and ranges (between 4421 and 4823 m). Next, the fitted semivariograms were used in the kriging of the canopy height residuals for each of the GLAS and LD_cal datasets. In total, two residual maps were obtained. Then, each residual-kriged map was added to the wall-to-wall map corresponding to that model (Figure 5). These maps were then validated using the verification datasets (LD_val and HD) (Figure 6, Table 2). Results showed that using the regression-kriging technique increased the estimation precision of these maps. Indeed, for the canopy heights map obtained using the GLAS dataset, the RMSE on the canopy height estimation decreased from 6.5 m with Random Forest regression to 3.6 m (R

^{2}of 0.76) with regression-kriging. For the canopy heights map obtained using the LD_cal dataset, the RMSE on the canopy height estimation decreased from 5.8 to 1.8 m (R

^{2}of 0.95) with regression-kriging. Moreover, the bias for the two datasets was very low (<0.2 m). These results show that the maps derived from the LD_cal datasets and using regression-kriging clearly captured finer local variations when estimating canopy heights. Finally, the canopy height estimates uncertainty from both maps appears to be correlated with the location of the reference dataset measurements (Figure 7). For the GLAS dataset, the standard deviation of canopy height estimates uncertainty ranged between 4 and 7 m (Figure 7a). In addition, standard deviation values appear to be lower near the location of the GLAS canopy height estimates, and increases with increasing distance until they reach 7 m. Similar results appear for the LD_cal dataset (Figure 7b), with lower standard deviations in areas with denser LiDAR acquisitions (i.e., north of French Guiana) and higher standard deviations with sparser LiDAR acquisitions (i.e., center of French Guiana). However, due to the generally denser dataset in comparison to the GLAS dataset, standard deviation of canopy height estimates uncertainty ranged between 1 and 4 m (Figure 7b).

#### 4.3. Relationship between LiDAR Flight Lines Spacing and the Precision on the Kriged Canopy Height

^{2}between 0.60 and 0.65). In order to add the kriged height residuals to the canopy height maps, the semivariograms of the canopy height residuals for each LD_cal subset were fitted. Similar sill, range and nuggets were obtained as those from the canopy height residuals from the GLAS and LD_cal datasets. When adding the kriged residuals corresponding to each of the LD_cal subsets (Figure 8), the precision on the canopy height estimate maps increased as expected (Figure S4, Table 2). This increase in the precision on canopy height estimation was found to be negatively correlated with LiDAR flight lines spacing of the LD subsets. For the LD_5 and LD_10 subsets, the precision on the canopy height estimates was similar to the results obtained with the LD_cal dataset (RMSE = 1.8 m, R

^{2}= 0.94). However, for the LD_20, LD_30, LD_40, and LD_50 subsets, the precision on the canopy height estimates decreased from RMSE = 3.3 m for LD_20 to RMSE = 4.8 m for LD_50.

## 5. Discussion

^{2}insignificant). This is mainly due to the canopy heights obtained in the study of Lefsky et al. [20] representing Lorey’s height while the canopy heights in our study represent maximum canopy height. Lorey’s heights are generally expected to be lower than maximum canopy heights [10].

^{2}) (Table 2), and in order to improve the precision of the canopy height product, canopy height estimation residuals (reference canopy heights—estimated canopy heights by RF) were kriged and used. This approach proved very efficient, although highly sensitive to the spatial sampling of the reference LiDAR dataset (flight line spacing). Indeed, for the French Guiana, the semivariograms indicated that the autocorrelation in the canopy height residuals did not go beyond 5 km, beyond this distance their contribution to the precision of the final canopy height maps started to decrease. In contrast, kriging only the LiDAR canopy heights without using the predictor variables with RF did not yield satisfactory results. For instance, by kriging directly the LD_cal canopy heights, we obtained a RMSE on the canopy height estimates of 5.1 m in comparison to the verification datasets against an RMSE of 5.8 for the RF technique with the LD_cal and 1.8 m for the regression-kriging technique. For the kriged GLAS canopy heights, the precision on the estimated canopy heights was 7.3 m in comparison to the verification datasets. The low precision of the kriged canopy heights from the GLAS dataset is due to the fact that the distance between the available canopy height estimates (~20 km) is higher than the range of their spatial autocorrelation (5 km), so a high smoothing occurred. This also explains the difference between the kriged canopy height estimates and the estimates from the verification datasets (bias of −4 m). To analyze the contribution of the regression-kriging technique on the canopy height precision, the kriging of the height residuals were replaced by the mean value of the height residuals in a 5 km radius. Results showed that for the LD_cal using the mean of the residuals, the R² decreases from 0.94 to 0.85 and the RMSE increases to 2.4 m in comparison to the kriging method (RMSE = 1.8 m).

## 6. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**Figure 1.**Location of French Guiana and map of canopy heights estimated from the GLAS dataset (in m).

**Figure 2.**Map of canopy heights calculated from the airborne LiDAR LD dataset for French Guiana. The locations of airborne LiDAR HD datasets are in delineated with circles.

**Figure 3.**Wall-to-wall map of French Guiana with Random Forest regressions using as reference data the canopy height estimates from: (

**a**) GLAS dataset; and (

**b**) LD_cal dataset.

**Figure 4.**Comparison between the reference canopy heights of the verification datasets and the canopy height trend estimates using Random Forest: (

**a**) GLAS dataset; and (

**b**) LD_cal dataset.

**Figure 5.**Wall-to-wall map of French Guiana with regression-kriging using as reference data canopy height estimates from: (

**a**) GLAS dataset; and (

**b**) LD dataset.

**Figure 6.**Comparison between the reference canopy heights of the verification datasets and the canopy height estimates using Random Forest regressions and residual-kriging: (

**a**) GLAS dataset; and (

**b**) LD_cal dataset.

**Figure 7.**Wall-to-wall standard deviation map (STD_DEV) of the canopy height estimates uncertainty for: (

**a**) GLAS dataset; and (

**b**) LD_cal dataset.

**Figure 8.**Examples of wall-to-wall maps of French Guiana with regression-kriging using as reference data the canopy height estimates from: (

**a**) LD_5; (

**b**) LD_20; and (

**c**) LD_50.

**Figure 9.**Comparison between the canopy heights of our verification datasets (LD_val and HD) and the canopy height estimates from the study of [10].

Short Name | Full Name | Source | Resolution |
---|---|---|---|

MIN_EVI | Minimum value of EVI time series data | MODIS | 250 m |

MEAN_EVI | Mean value of EVI time series data | ||

MAX_EVI | Maximum value of EVI time series data | ||

PC1 | 1st principal component of EVI time series data | ||

PC2 | 2nd principal component of EVI time series data | ||

PC3 | 3rd principal component of EVI time series data | ||

Slope | Terrain slope in 3 × 3 cells | SRTM | 90 m |

Roughness | Terrain roughness in 3 × 3 cells | ||

ln_drain | Log of drainage surface | ||

GEOL | Geological map (no units, arbitrary shapes) | [27] | Vector |

LTs | Forest landscape type (no units, arbitrary shapes) | [28] | 1 km (Vector) |

Rain | mean value of rainfall | TRMM | 8 km |

**Table 2.**Comparison between the canopy heights of the verification datasets (LD_val and HD) and the canopy height estimates using regression kriging.

Using RF Only | Using Regression Kriging | |||||
---|---|---|---|---|---|---|

Dataset | Bias (m) | RMSE (m) | R² | Bias (m) | RMSE (m) | R² |

GLAS | 0.14 | 6.5 | 0.55 | 0.09 | 4.2 | 0.75 |

LD_cal | 0.15 | 5.8 | 0.62 | 0.12 | 1.8 | 0.94 |

LD_5 | 0.06 | 5.7 | 0.65 | 0.12 | 1.8 | 0.94 |

LD_20 | 0.09 | 6.0 | 0.63 | 0.14 | 3.3 | 0.75 |

LD_30 | 0.14 | 6.2 | 0.60 | 0.05 | 3.9 | 0.75 |

LD_40 | 0.11 | 6.1 | 0.62 | 0.09 | 3.9 | 0.74 |

LD_50 | 0.07 | 6.2 | 0.60 | 0.13 | 4.8 | 0.66 |

© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons by Attribution (CC-BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fayad, I.; Baghdadi, N.; Bailly, J.-S.; Barbier, N.; Gond, V.; Hérault, B.; El Hajj, M.; Fabre, F.; Perrin, J. Regional Scale Rain-Forest Height Mapping Using Regression-Kriging of Spaceborne and Airborne LiDAR Data: Application on French Guiana. *Remote Sens.* **2016**, *8*, 240.
https://doi.org/10.3390/rs8030240

**AMA Style**

Fayad I, Baghdadi N, Bailly J-S, Barbier N, Gond V, Hérault B, El Hajj M, Fabre F, Perrin J. Regional Scale Rain-Forest Height Mapping Using Regression-Kriging of Spaceborne and Airborne LiDAR Data: Application on French Guiana. *Remote Sensing*. 2016; 8(3):240.
https://doi.org/10.3390/rs8030240

**Chicago/Turabian Style**

Fayad, Ibrahim, Nicolas Baghdadi, Jean-Stéphane Bailly, Nicolas Barbier, Valéry Gond, Bruno Hérault, Mahmoud El Hajj, Frédéric Fabre, and José Perrin. 2016. "Regional Scale Rain-Forest Height Mapping Using Regression-Kriging of Spaceborne and Airborne LiDAR Data: Application on French Guiana" *Remote Sensing* 8, no. 3: 240.
https://doi.org/10.3390/rs8030240