# Prediction of Aboveground Biomass from Low-Density LiDAR Data: Validation over P. radiata Data from a Region North of Spain

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}) LiDAR flight conducted by the Basque Government in 2012 for cartographic production. We propose a linear regression model based on explanatory variables obtained from the LiDAR point cloud data. We calibrate the model using field data from the Fourth National Forest Inventory (NFI4), including the selection of the optimal model variables. The results revealed that the best model depends on two variables extracted from LiDAR data: One directly related with tree height and a second parameter with the canopy density. The model explained 80% of its variability with a standard error of 0.25 ton/ha in logarithmic units. We validate the predictions against the biomass measurements provided by the government institutions, obtaining a difference of 8%. The proposed approach would allow the exploitation of the periodic available low-density LiDAR data, collected with territorial and cartographic purposes, for a more frequent and less expensive control of the forestry biomass.

## 1. Introduction

^{3}/ha. The importance of P. radiata in Spain is due to its high productivity: It is only 0.7% of the national forested area; however, the outcome of this species is approximately 7% of the total wood production made in Spain [6].

^{2}).

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. The average altitude of the region is 465 m, with an average slope of 18.6°. High slope (30–45°) areas are frequent across the entire region.

#### 2.2. Field Data Collection

#### 2.3. Field Plot Positioning

#### 2.4. LiDAR Data

^{2}. The spatial localization of the points was obtained with a precision <10 cm. The reference system is the European Terrestrial Reference System 89 (ETRS89) and the coordinate system is UTM for the thirtieth time zone. The dataset was divided into sheets of 2 × 2 km of extension, classified into eight classes: Unclassified, Ground, Low Vegetation, Medium Vegetation, High Vegetation, Building, Low Points, and Reserved. The data are publicly available at: ftp://ftp.geo.euskadi.eus/lidar/LIDAR_2012_ETRS89/LAS/.

#### 2.5. Orthophotos

#### 2.6. Methods

#### 2.6.1. Biomass Field Calculation

#### 2.6.2. LiDAR Data Processing and Overall Process

^{2}/pixel. A digital surface model (DSM) was created with the highest returns of the point cloud over the sample plots, assigning the elevation of the highest return within each grid cell to the grid cell center. A canopy height model (CHM) was obtained by subtracting the DTM from the DSM. The CHM characterizes the tree canopy and it is able to give the canopy height directly. For each plot a large collection of metrics, that can be used as regressors for biomass prediction, was computed over all returns above a 2 m threshold [31,32], including height distributions, canopy density metrics, and descriptive statistics (these metrics are enumerated in Appendix A).

#### 2.6.3. Regression Analysis

^{2}adj) was used to assess the quality of the adjustment. R

^{2}adj represents the proportion of the variability explained by the adjusted model [35] after application of the correction factor described below. Additionally, standard error of the estimations (SEEs) were calculated in order to compare with other studies results. Akaike information criterion (AIC) is an index based on in-sample fit that can be used as an estimate of the likelihood of a model to predict the future values [36]. Our optimal feature selection corresponds to the model that has minimum AIC.

_{i}is a regressor model. The, S

_{i}is the contribution of regressor X

_{i}to the variance of the output Y as specified in the following:

_{i}) is the expectation of the output Y conditioned to input factor X

_{i}and V(Y) the unconditional variance of the model output, which can be decomposed into the conditional regressor variances V

_{i..}as follows:

_{i}is the first-order sensitivity index for regressor X

_{i}, and S

_{ij}is the second-order sensitivity index for the interaction between regressors X

_{i}and X

_{j}with j≠i. The total contribution of regressor X

_{i}to output Y variability is computed as follows:

_{Ti}is the total effect on the output variation due to factor X

_{i}, adding its first-order effect and all higher-order effects due to interactions with other regressors. When the sum of the first-order index and total-effect index of a variable is not equal to one, interactions among factors in the model may occur. Additionally, we compute the fraction of the output variance arising from the uncertainty of each regressor X

_{i}, and the complementary set of regressors, denoted D

_{1}and D

_{t}, respectively.

#### 2.6.4. Validation

_{i}is the natural logarithm of the values of the dependent variable, $\mathrm{ln}{\widehat{Y}}_{i}$ is the natural logarithm of the model estimations, N the number of cases of the sample. In fact, we will use the root of the MSE (RMSE) [41].

## 3. Results

#### 3.1. Results

^{2}adj = 0.81) in some cases, but introducing the third variable was not statistically significant in the models, hence, we discarded using more than two variables. Since the models presented in the table have very similar R

^{2}values, further statistical analysis was undertaken to decide which model better fulfilled the assumptions of the linear regression analysis.

^{2}adj value (0.79) and standard error (0.25 ton/ha in logarithmic units), the remaining columns reporting tests results had similar values too, including the detection of outliers according to Bonferroni´s test in all the models, where no outliers were detected. Regarding the normality of the residuals, it is not possible to reject this hypothesis in any model. The results are slightly better in the models using the 99% percentile of the height. In the case of the Breusch–Pagan test, the p-values values do not vary too much among regressor subsets, so it will be acceptable for all the models in the table, corresponding the best results (in the sense of non-rejection of null hypothesis) to the eighth model. The values obtained for the Durbin–Watson test and the variance inflation factor are very similar for all the models, concluding that no autocorrelation or collinearity problems were detected. The RESET linearity test results confirm the null hypothesis of a linear functional dependence of the biomass on the regressors for all tested models.

_{i}). The total-effect indices (ST

_{i}) show that only p95 is taking part in the interactions, because ST

_{i}> S

_{i}. D

_{1}represents the portion of the output variance arising from the uncertainty of factor i, while D

_{T}is the variance for the complementary set D(-i) [44]. First-order effect (S

_{i}) is bigger for the density metric than for the percentile of the height, which implies that this variable is more sensible in the model. D

_{1}and D

_{T}corroborates this tendency, pointing that the density metric contributes more than the height percentile to the output variance, because D

_{1}is bigger for the density metric than for the height percentile.

#### 3.2. Application of the Selected Model

#### 3.3. Validation of the Selected Model

## 4. Discussion

^{2}= 0.74; SE = 0.2) were reported by Hall et al. [48] in an area in Colorado, USA, for Pinus ponderosa and Pseudotsuga menziesii species. The density points in the American study were higher than the one used in our study (1.23 points/m

^{2}), but in their study the only variable introduced in the exponential model was a density metric, no metrics derived for the tree height were included.

^{2}values (0.88) than us with a very similar value for RMSE (0.25 in logarithmic units) in a Norwegian area composed primarily of Pinus sylvestris and Picea abies using a point density up to 1.2 points/m

^{2}. Their chosen regressors were a high percentile of the LiDAR measured tree height (90% percentile) and a low-density metric. The density metric was more statistically significant in the Norwegian model than in our study: They found that the partial value of R

^{2}for each variable was 0.61 and 0.21, respectively, while in our study the values were 0.74 and 0.15, respectively. The mean value of the estimated biomass was similar in both studies (150 ton/ha). Hence, differences in the model determination coefficient can be due to the geographical location, altitude, species composition, or site quality. Another relevant study [49] was carried out over the Taita Hills (55,000 ha), in southeast Kenya, with a pulse density of 3.1 points/m

^{2}. They used a boosted regression trees (BRT) technique for identifying regressors that better explain biomass distribution. Multilinear regression was used to predict aboveground biomass using LiDAR metrics (R

^{2}= 0.88 and RMSE = 52.9 Mg/ha) and the mean AGB was 123 ton/ha. In this case, the point density was significantly higher than in our study. It has been shown that pulse density below 1 pulse/m

^{2}has a negative influence on the quality of the prediction [50].

^{2}= 0.74, RMSE = 40.469 ton/ha). The study area was situated in the north of the peninsula too, with similar conditions to those found in the Arratia-Nervión (mean biomass = 150 ton/ha in both cases), but their point density was very high (8 points/m

^{2}). In the province of Zaragoza (Spain), the work reported in [26] estimated the biomass with good results (R

^{2}= 0.89, RMSE = 7326.12 kg/ha), but the mean and the maximum biomass measured in the field were much lower, along with the variability of the samples.

^{2}, due to the acquisition of several overlapped scans [51]. They report results from nine different point density values: 0.25, 0.5, 1, 1.5, 2, 3, 4, 5, and 6 points/m

^{2}, obtaining increasing values for R

^{2}ranging from 0.69 to 0.92 as the point density increased. Another work [52] analyzed the importance of the point density for biomass estimation in three different sites across Ontario, Canada. They concluded that even with a very low point density of 1/100, automated LiDAR scan (ALS) is a feasible option for assessing AGB in vast areas of flat, lowland peat swamp forest. Additionally it has been found [50] that the accuracy of predicted forest structure metrics decreases as the pulse density decreases, remaining relatively high until low densities (e.g., 1 pulse/m

^{2}). Due to the influence of all these factors, replication effects can be detected in the final AGB estimations. Magnussen et al. [53] found that a minimum point density of 1 point/m

^{2}was needed to reduce the replication variance in LiDAR-derived predictions. Known factors affecting extracted ALS-based predictors of forest inventory attributes are instrument errors, positional errors, and posts-capture data-processing errors. We must take into account that these factors limit the ability to replicate results of AGB estimation. However, the major conclusion of the reviewed studies is that useful AGB estimations can be obtained from low-density LiDAR data, as done in our study.

## 5. Conclusions

^{2}). The approach could be transferred to other areas, if LiDAR and forest inventory datasets are available, and could become a powerful tool for complimenting other traditional methods (e.g., NFI4), reducing significantly the high investment of time and money required by such methodologies.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Variable | Description | Variable | Description |
---|---|---|---|

count | number of returns above the minimum height | ccr | canopy relief ratio:((mean - min)/(max – min) |

densitytotal | total returns used for calculating cover | eqm | elevation quadratic mean |

densityabove | returns above height break | ecm | elevation cubic mean |

densitycell | density of returns used for calculating cover | r1count,…,r9count | count of return 1,…,9 points above the minimum height |

min | minimum value for cell | rothercount | count of other returns above the minimum height |

max | maximum value for cell | allcover | (all returns above cover height (h))/(total returns) |

mean | mean value for cell | afcover | (all returns above cover h)/(total first returns) |

mode | modal value for cell | allcount | number of returns above cover h |

stddev | standard deviation of cell values | allabovemean | (all returns above mean h)/(total returns) |

variance | variance of cell values | allabovemode | (all returns above h mode)/(total returns) |

cv | coefficient of variation for cell | afabovemean | (all returns above mean h)/(total first returns) |

cover | cover estimate for cell | afabovemode | (all returns above h mode)/(total first returns) |

abovemean | proportion of first (or all) returns above the mean | fcountmean | number of first returns above mean h |

abovemode | proportion of first (or all) returns above the mode | fcountmode | number of first returns above h mode |

skewness | skewness computed for cell | allcountmean | number of returns above mean h |

kurtosis | kurtosis computed for cell | allcountmode | number of returns above h mode |

AAD | average absolute deviation from mean for the cell | totalfirst | total number of first returns |

p01,…,p99 | 1st,…,99th percentile value for cell | totalall | total number of returns |

iq | 75th percentile minus 25th percentile for cell |

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**Figure 1.**Inset: Localization in the Spain country. Picture: Arratia-Nervión region (dashed) in Basque Country, Spain.

**Figure 2.**P. radiata distribution (in green) in the Arratia-Nervión region (ETRS89 UTM zone 30 North reference system).

**Figure 4.**Sample plots distribution of the National Forest Inventory 4 (NFI4) in Arratia-Nervión (ETRS89 UTM zone 30 North reference system).

**Figure 5.**Distribution of the diameter and height, respectively, of all the trees measured in the National Forest Inventory 4 (NFI4) that were taken into account for the estimation.

**Figure 6.**Representation of the simulated translation of the plot 443. Each color represents the gathered LiDAR data for the mentioned nine plots (ETRS89 UTM zone 30 North reference system).

**Figure 7.**(

**a**) Flow chart of the Light Detection and Ranging LiDAR data. (

**b**) Overall process carried out in the study.

**Figure 8.**Inset: Localization of the experiment area in Spain. Picture: Model application area shaded is Orozoko in Arratia-Nervión and model validation area is Gordexola in Encartaciones.

**Figure 9.**Dispersion diagrams between the logarithm of the biomass and the most correlated height percentile and canopy density metric.

**Figure 10.**Extensive diagnostics graphics for the chosen model, being Normal Q-Q the Quantile-Quantile plot.

**Figure 11.**(

**a**) Dispersion diagram between residuals and the fitted values of the logarithm of the biomass; and (

**b**) dispersion diagram between the diameter and the logarithm of the biomass in field.

**Figure 12.**Dispersion diagrams between the two regressors of the chosen model and the logarithm of the biomass.

**Figure 15.**Biomass estimations for Orozko municipality (Arratia-Nervión) by the application of the developed model.

**Table 1.**Cohen concordance test for plot 443. The concordance between the original plot (0) and the eight displaced plots according to the compass rose.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |
---|---|---|---|---|---|---|---|---|---|

0 | 1.00 | 0.99 | 0.99 | 0.97 | 0.96 | 0.98 | 0.98 | 0.98 | 0.98 |

1 | -- | 1.00 | 0.99 | 0.96 | 0.94 | 0.95 | 0.95 | 0.97 | 0.98 |

2 | -- | -- | 1.00 | 0.98 | 0.95 | 0.95 | 0.95 | 0.96 | 0.96 |

3 | -- | -- | -- | 1.00 | 0.98 | 0.98 | 0.94 | 0.93 | 0.91 |

4 | -- | -- | -- | -- | 1.00 | 0.98 | 0.94 | 0.93 | 0.91 |

5 | -- | -- | -- | -- | -- | 1.00 | 0.98 | 0.97 | 0.95 |

6 | -- | -- | -- | -- | -- | -- | 1.00 | 0.99 | 0.96 |

7 | -- | -- | -- | -- | -- | -- | -- | 1.00 | 0.98 |

8 | -- | -- | -- | -- | -- | -- | -- | -- | 1.00 |

**Table 2.**Accuracy values and test p-values obtained for the ten best models; p-values are shown for all the tests except VIF. p99, p95, and p90 are the 99%, 95%, and 90% percentiles of the laser canopy heights, respectively; tr_2, tr_3, and tr_4 are the canopy densities corresponding to the second, third, and fourth layers, respectively; allabovemean = (all returns above mean height)/(total returns). R

^{2}adj

**=**adjusted coefficient of determination; SE = Standard Error; AIC = Akaike information criterion; SW = Shapiro-Wilk residuals normality test; BP = Breustch–Pagan residuals homoscedasticity test; DW = residuals autocorrelationi test; VIF = Variance Inflation Factor; reset = Ramsey´s RESET linearity test; B = Bonferroni outlier test.

Regressors | R^{2}adj | SE | AIC | SW | BP | DW | VIF | RESET | B |
---|---|---|---|---|---|---|---|---|---|

{p99,abovemean} | 0.79 | 0.25 | 7.70 | 0.76 | 0.09 | 0.40 | 1.28 | 0.75 | 0.02 |

{p99,allabovemean} | 0.79 | 0.25 | 7.69 | 0.76 | 0.09 | 0.40 | 1.28 | 0.75 | 0.02 |

{p99,tr_3} | 0.79 | 0.25 | 8.38 | 0.68 | 0.10 | 0.34 | 1.12 | 0.83 | 0.02 |

{p99,tr_4} | 0.79 | 0.25 | 8.50 | 0.64 | 0.09 | 0.29 | 1.15 | 0.81 | 0.02 |

{p95,allabovemean} | 0.79 | 0.25 | 8.59 | 0.40 | 0.16 | 0.41 | 1.26 | 0.64 | 0.02 |

{p95,abovemean} | 0.79 | 0.25 | 8.61 | 0.40 | 0.16 | 0.40 | 1.27 | 0.64 | 0.02 |

{p99,tr_2} | 0.79 | 0.25 | 8.97 | 0.76 | 0.10 | 0.39 | 1.12 | 0.84 | 0.02 |

{p95,tr_3} | 0.79 | 0.25 | 9.18 | 0.48 | 0.19 | 0.35 | 1.11 | 0.74 | 0.02 |

{p99,allcover} | 0.79 | 0.25 | 9.36 | 0.81 | 0.08 | 0.45 | 1.14 | 0.82 | 0.01 |

{p95,tr_2} | 0.79 | 0.25 | 9.47 | 0.53 | 0.18 | 0.41 | 1.10 | 0.76 | 0.02 |

Variables | Estimated Value | Lower Bound | Upper Bound |
---|---|---|---|

Constant | 3.774 | 3.500 | 4.048 |

p_95 | 0.548 | 0.111 | 0.984 |

tr_3 | 0.67 | 0.056 | 0.078 |

**Table 4.**Sensitivity analysis results. Si = first-order effects; STi = total-effect index; D

_{1}= the portion of the output variance arising from the uncertainty of factor i; D

_{T}= variance for the complementary set D(-i).

Variables | Si | STi | Variance | D1 | Dt |
---|---|---|---|---|---|

p95 | 0.8128 | 0.9453 | 0.1314 | 0.1068 | 0.0072 |

tr_3 | 0.8513 | 0.8404 | 0.1426 | 0.1214 | 0.0228 |

© 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**

Tojal, L.-T.; Bastarrika, A.; Barrett, B.; Sanchez Espeso, J.M.; Lopez-Guede, J.M.; Graña, M.
Prediction of Aboveground Biomass from Low-Density LiDAR Data: Validation over *P. radiata* Data from a Region North of Spain. *Forests* **2019**, *10*, 819.
https://doi.org/10.3390/f10090819

**AMA Style**

Tojal L-T, Bastarrika A, Barrett B, Sanchez Espeso JM, Lopez-Guede JM, Graña M.
Prediction of Aboveground Biomass from Low-Density LiDAR Data: Validation over *P. radiata* Data from a Region North of Spain. *Forests*. 2019; 10(9):819.
https://doi.org/10.3390/f10090819

**Chicago/Turabian Style**

Tojal, Leyre-Torre, Aitor Bastarrika, Brian Barrett, Javier Maria Sanchez Espeso, Jose Manuel Lopez-Guede, and Manuel Graña.
2019. "Prediction of Aboveground Biomass from Low-Density LiDAR Data: Validation over *P. radiata* Data from a Region North of Spain" *Forests* 10, no. 9: 819.
https://doi.org/10.3390/f10090819