# Combination of Multi-Temporal Sentinel 2 Images and Aerial Image Based Canopy Height Models for Timber Volume Modelling

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}in south-west Germany for (1) modelling the percentage of broadleaf tree volume (BL%) using Sentinel 2 time series and (2) modelling timber volume per hectare using 3D photogrammetric point clouds. Forest inventory plots were surveyed in the same years and regions as stereo photographs were acquired (2013–2017), resulting in 11,554 plots. Sentinel 2 images from 2016 and 2017 were corrected for topographic and atmospheric influences and combined with the same forest inventory plots. Spectral variables from corrected multi-temporal Sentinel 2 images were calculated, and Support Vector Machine (SVM) regressions were fitted for each Sentinel 2 scene estimating the BL% for corresponding inventory plots. Variables from the photogrammetric point clouds were calculated for each inventory plot and a non-linear regression model predicting timber volume per hectare was fitted. Each SVM regression and the timber volume model were evaluated using ten-fold cross-validation (CV). The SVM regression models estimating the BL% per Sentinel 2 scene achieved overall accuracies of 68%–75% and a Root Mean Squared Error (RMSE) of 21.5–26.1. The timber volume model showed a RMSE% of 31.7%, a mean bias of 0.2%, and a pseudo-R

^{2}of 0.64. Application of the SVM regressions on Sentinel 2 scenes covering the state of Baden-Württemberg resulted in predictions of broadleaf tree percentages for the entire state. These predicted values were used as additional predictor in the timber volume model, allowing for predictions of timber volume for the same area. Spatially high-resolution information about growing stock is of great practical relevance for forest management planning, especially when the timber volume of a smaller unit is of interest, for example of a forest stand or a forest district where not enough terrestrial inventory plots are available to make reliable estimations. Here, predictions from remote-sensing based models can be used. Furthermore, information about broadleaf and conifer trees improves timber volume models and reduces model errors and, thereby, prediction uncertainties.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Site and Reference Data

^{2}(Figure 2a) was used as study site. This comprises diverse topographic conditions with altitudes ranging from 87 m above sea level in the Rhine valley to 1493 m above sea level in the Black Forest mountain range. Therefore, the forest varies greatly in terms of tree species composition and is dominated by Norway spruce (Picea abies L., 34%), beech (Fagus sylvatica L., 21.8%), fir (Abies alba Mill., 8%), oak (Quercus sp. Thunb., 7.1%), pine (Pinus sylvatica L., 5.6%), ash (Fraxinus excelsior L., 4.9%), maple (Acer pseudoplatanus L., 3.7%), and Douglas fir (Pseudotsuga menziesii Mirb., 3.4%).

^{2}) were used. Plots cut off by intersecting borders such as forest roads or forest borders, were discarded. Also, plots in which forest management activities were conducted since the last inventory were removed. Furthermore, to detect errors in the data related to geolocation of inventory plots or in the 3D point clouds, maximum and mean heights from the inventory data and from the 3D point clouds were compared using linear models. For this purpose, all points from the 3D point cloud falling into the inventory plots were extracted, and maximum and mean heights for each plot were calculated. Linear models were fitted with maximum and mean height from the inventory data as response, and maximum and mean height from 3D point cloud values as predictor variables. 95% prediction intervals were calculated from these models, and all plots outside the 95% prediction intervals were removed. From this set of inventory plots two subsets were selected; for modelling BL% using Sentinel 2 data, all plots from the years 2013–2017 were used resulting in 24,788 plots (Figure 3a); for modelling timber volume using 3D photogrammetric point clouds from aerial stereo images, only those plots were selected, that were located in areas where aerial stereo photographs were collected in the same year as the forest inventory data, resulting in 11,554 plots (Figure 3b).

#### 2.2. Remote Sensing Data

#### 2.2.1. Sentinel 2 Satellite Images

#### 2.2.2. Aerial Image Based Canopy Height Model

^{2}). In areas without matching points, the pixel values were calculated via Triangular Irregular Network (TIN) streaming [37]. The CHMs with 1 m resolution were obtained by subtracting the ALS-DTM from the photogrammetric DSMs.

#### 2.3. SVM Regression Modelling of Percentage of Broadleaf Trees (BL%) Using Sentinel 2 Data

#### 2.4. Validation of SVM Regression Models

#### 2.5. Mapping Percentage of Broadleaf Trees

#### 2.6. Regression Modelling of Timber Volume Using 3D Metrics from Photogrammetric Point Clouds

_{K+2}, which is estimated from the sample data. Also, linear models were tested, and nonlinearity in the data was handled by adding some of the predictor metrics additionally as squared terms to the models, and by transforming the response variable.

#### 2.7. Application of Timber Volume Model

## 3. Results

#### 3.1. SVM Regression for Percentage of Broadleaf Trees

#### 3.2. Regression Model of Timber Volume

_{1}/(1 + exp(γ

_{2}+ γ

_{3}× CHMmean + γ

_{4}× CHMcv + γ

_{5}× DTMmean + γ

_{6}× CHMcc + γ

_{7}× BL%)),

^{3}/ha. This might be caused by trees from a certain age notably decreasing their height increment while stem diameters still increase, resulting in high timber volumes. However, stem diameters cannot easily be observed or modelled with airborne remote sensing data.

^{2}were 31.7, 0.22, 0.6, and 0.64, respectively. Standard deviation (SD) of bias% is larger than the mean bias% from the cross validation, indicating variation in bias% between the folds of the cross validation. A model fitted without the predictor BL% (model not presented) resulted in lower accuracies with RMSE%, bias%, and Pseudo R

^{2}of 35.8, 0.23, and 0.55, respectively. SD of bias% in this model was slightly better with 0.4. The final map of timber volume predictions is presented in Appendix B, Figure A2. A close-up of this map is presented in Figure 4b.

#### 3.3. Application of Timber Volume Model in Small Area

## 4. Discussion

^{2}of 0.64. This is similar to results of other studies, which used point clouds from stereo image matching and forest inventory data for the purpose of timber volume modelling. For example, RMSE% values of 31.92–37.89 were reported in a test area in Bavaria in Germany [11], 28.8–32.9 in four different study areas in Sweden [5], 31.43 in southeastern Norway [6], 43.5 in central Norway [48], and 36.87 in south-western Canada [49].

^{3}per hectare. Our errors still amounted to a bit more than 10%, however, our model assisted errors were 50% smaller than what in this case was possible with terrestrial field data only.

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

Sentinel 2 Bands Used in This Study | Sentinel 2A | Sentinel 2B | Spatial Resolution (m) | ||
---|---|---|---|---|---|

Central Wavelength (nm) | Bandwidth (nm) | Central Wavelength (nm) | Bandwidth (nm) | ||

Band 1—Coastal aerosol | 442.7 | 27 | 442.2 | 45 | 60 |

Band 2—Blue | 492.4 | 98 | 492.1 | 98 | 10 |

Band 3—Green | 559.8 | 45 | 559.0 | 46 | 10 |

Band 4—Red | 664.6 | 38 | 664.9 | 39 | 10 |

Band 5—Red edge | 704.1 | 19 | 703.8 | 20 | 20 |

Band 6—Red edge | 740.5 | 18 | 739.1 | 18 | 20 |

Band 7—Red edge | 782.8 | 28 | 779.7 | 28 | 20 |

Band 8—NIR | 832.8 | 145 | 832.9 | 133 | 10 |

Band 8A—Narrow NIR | 864.7 | 33 | 864.0 | 32 | 20 |

Band 9—Water vapour | 945.1 | 26 | 943.2 | 27 | 60 |

Band 10—SWIR-Cirrus | 1373.5 | 75 | 1376.9 | 76 | 60 |

Band 11—SWIR | 1613.7 | 143 | 1610.4 | 141 | 20 |

Band 12—SWIR | 2202.4 | 242 | 2185.7 | 238 | 20 |

## Appendix B

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**Figure 1.**Flow chart depicting the data sets and processing steps. BL%: percentage of broadleaf trees; SVM: support vector machine; CV: cross-validation.

**Figure 2.**Study area: (

**a**) Location of study area in south-west Germany, federal state of Baden-Württemberg; (

**b**) location of the field plots surveyed between 2012–2017; (

**c**) inventory design (100 m × 200 m grid) of 12 m radius plots; plots that were located on forest roads or were cut off due to borders were omitted.

**Figure 3.**Remote sensing data in study area and corresponding forest inventory data: (

**a**) Coverage of nine Sentinel 2 tiles; forest inventory data from the years 2013–2107 as used for modelling percentage of broadleaf trees are depicted as well (n = 24,788); (

**b**) coverage of the aerial surveys in the years 2012–2106; corresponding forest inventory plots from the same years as aerial surveys and as used for timber volume modelling are depicted as well (n = 11,554).

**Figure 5.**Observed versus predicted timber volume (m

^{3}/ha) of the non-linear logistic regression model from Equation (11).

**Figure 6.**Mean timber volume (m

^{3}/ha) of 100 forest departments estimated using simple random sampling (SRS) and forest inventory plots (y-axis), and model assisted (MA) predictions using the non-linear logistic regression model (x-axis). Horizontal lines are MA based standard errors, and vertical lines are SRS standard errors.

**Table 1.**Equations for regression models, Root Mean Square Error (RMSE), RMSE%, bias%, and Pseudo-R

^{2}, and simple random sampling (SRS) and model assisted (MA) statistics. In each equation, i indexes sample plots, X

_{ik}is the k

_{th}predictor, β are model parameters, ŷ

_{i}and y

_{i}represent predicted and observed timber volume for sample plot i, respectively, and n is the number of samples; ӯ represents the mean of observed values, and ε is a residual error term.

Description | Equation | Index |
---|---|---|

Non-linear logistic regression model | ${y}_{i}=\text{}\frac{{\beta}_{K+2}}{1+\mathrm{exp}({\beta}_{K+1}+\text{}{{\displaystyle \sum}}_{k=1}^{K}{\beta}_{k}{X}_{ik})}+\text{}{\epsilon}_{i}$ | (1) |

Linear regression model | ${y}_{i}=\text{}{\beta}_{0}+\text{}{\beta}_{1}{X}_{1i}+\dots +\text{}{\beta}_{K}{X}_{Ki}+\text{}{\epsilon}_{i}$ | (2) |

RMSE (m^{3}/ha) | $\sqrt{\frac{1}{n}\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left({y}_{i}-\text{}{\widehat{y}}_{i}\right)}^{2}}$ | (3) |

RMSE (%) | $100\times \text{}\frac{RMSE}{\frac{1}{n}\text{}{{\displaystyle \sum}}_{i=1}^{n}\left({y}_{i}\right)}$ | (4) |

Bias (%) | $100\times \text{}\frac{{{\displaystyle \sum}}_{i=1}^{n}\left({\widehat{y}}_{i}-\text{}{y}_{i}\right)}{{{\displaystyle \sum}}_{i=1}^{n}\left({y}_{i}\right)}$ | (5) |

Pseudo-R^{2} | $1-\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\widehat{y}}_{i}-\text{}{y}_{i}\right)}^{2}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-\text{}\overline{y}\right)}^{2}}$ | (6) |

SRS mean | ${\widehat{\mu}}_{SRS}=\text{}\frac{1}{n}\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{y}_{i}$ | (7) |

SRS variance | $\widehat{Var}\left({\widehat{\mu}}_{SRS}\right)=\text{}\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({y}_{i}-\text{}{\widehat{\mu}}_{SRS}\right)}^{2}}{n\left(n-1\right)}$ | (8) |

MA mean | ${\widehat{\mu}}_{MA}=\text{}\frac{1}{N}\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{\widehat{y}}_{i}-\text{}\frac{1}{n}\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}\left({\widehat{y}}_{i}-\text{}{y}_{i}\right)$ | (9) |

MA variance | $\widehat{Var}\left({\widehat{\mu}}_{MA}\right)=\text{}\frac{1}{n\left(n-1\right)}\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\left(\left({\widehat{y}}_{i}-\text{}{y}_{i}\right)-\text{}\overline{\u03f5}\text{}\right)}^{2}$ | (10) |

**Table 2.**Number and dates of multi-temporal Sentinel 2 tiles used in the final model, and number of forest inventory plots located in each tile. Note that in areas where S-2 tiles are overlapping inventory plots are counted multiple times; therefore, the sum of plots in this table is larger than the true number.

Sentinel 2 Tiles | n Scenes | Acquisition Date of Sentinel 2 Tiles | n Inventory Plots | RMSE of Best Model |
---|---|---|---|---|

32UNA | 4 | 19 June 2017, 19 July 2017, 24 August 2016, 14 September 2016 | 622 | 22.2 |

32UMV | 4 | 05 May 2016, 10 May 2017, 19 June 2017, 24 August 2016 | 7234 | 23.5 |

32UNV | 3 | 28 March 2017, 27 May 2017, 14 October 2017 | 3560 | 21.5 |

32ULU | 3 | 05 May 2016, 24 June 2016, 24 August 2016 | 592 | 24.4 |

32UMU | 3 | 10 May 2017, 19 June 2017, 23 August 2017 | 10511 | 22.6 |

32UNU | 3 | 27 May 2017, 26 June 2017, 14 October 2017 | 4626 | 26.1 |

32TLT | 4 | 30 April 2017, 05 May 2016, 24 June 2016, 24 August 2016 | 929 | 24.1 |

32TMT | 3 | 24 June 2016, 24 August 2017, 10 May 2017 | 3360 | 25.7 |

32TNT | 4 | 28 March 2017, 17 May 2017, 27 May 2017, 25 August 2017 | 783 | 23.9 |

**Table 3.**Confusion matrix and accuracies for the whole area generated by validation based on reference inventory data. b = broadleaf, m = mixed forest, c = conifer, UA = user’s accuracy, PA = producer’s accuracy, OA = overall accuracy.

Reference | ||||
---|---|---|---|---|

Prediction | b | m | c | UA [%] |

b | 7253 | 1649 | 243 | 79.3 |

m | 2206 | 3644 | 2142 | 45.6 |

c | 29 | 914 | 6708 | 97.7 |

PA [%] | 76.4 | 58.7 | 73.8 | |

OA [%] | 71.0 | |||

Kappa | 0.77 |

**Table 4.**Confusion matrix and accuracies for the whole area generated by validation based on the forest management plans. b = broadleaf, m = mixed forest, c = conifer.

Reference | ||
---|---|---|

Prediction | b | c |

b | 3202 | 233 |

m | 971 | 2110 |

c | 12 | 7250 |

PA [%] | 76.5 | 75.5 |

Parameter | Estimate | Std. Error | t-Value |
---|---|---|---|

γ_{1} | 1528 | 85.52 | 17.866 |

γ_{2} | 3.87 | 0.117 | 33.072 |

γ_{3} | −0.08706 | 0.002412 | −36.098 |

γ_{4} | −0.514 | 0.05414 | −9.494 |

γ_{5} | −0.0003507 | 0.00002185 | −16.053 |

γ_{6} | −0.8352 | 0.1038 | −8.044 |

γ_{7} | 0.006064 | 0.0001953 | 31.052 |

**Table 6.**Evaluation of the final non-linear logistic regression model from Equation (11); SD = standard deviation.

Model from Equation (11) | |
---|---|

RMSE% | 31.7 |

bias% | 0.22 |

SD of bias% | 0.6 |

Pseudo R^{2} | 0.64 |

© 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**

Schumacher, J.; Rattay, M.; Kirchhöfer, M.; Adler, P.; Kändler, G. Combination of Multi-Temporal Sentinel 2 Images and Aerial Image Based Canopy Height Models for Timber Volume Modelling. *Forests* **2019**, *10*, 746.
https://doi.org/10.3390/f10090746

**AMA Style**

Schumacher J, Rattay M, Kirchhöfer M, Adler P, Kändler G. Combination of Multi-Temporal Sentinel 2 Images and Aerial Image Based Canopy Height Models for Timber Volume Modelling. *Forests*. 2019; 10(9):746.
https://doi.org/10.3390/f10090746

**Chicago/Turabian Style**

Schumacher, Johannes, Margret Rattay, Melanie Kirchhöfer, Petra Adler, and Gerald Kändler. 2019. "Combination of Multi-Temporal Sentinel 2 Images and Aerial Image Based Canopy Height Models for Timber Volume Modelling" *Forests* 10, no. 9: 746.
https://doi.org/10.3390/f10090746