# The Use of Remotely Sensed Data and Polish NFI Plots for Prediction of Growing Stock Volume Using Different Predictive Methods

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area

^{2}. According to the Central Statistical Office [20], forest covers 29.6% of the country’s area, which corresponds to 92,420 km

^{2}. Poor and moderately rich forest habitats predominate and cover 57% of the forested area which is reflected in the dominance of coniferous tree species, which dominate over 68% of the area of Polish forests [21]. According to the National Forest Inventory [22], Scots pine (Pinus sylvestris L.) is predominant in most Polish tree stands. Among the deciduous species, oaks (Quercus spp.), silver birch (Betula pendula Roth.) and black alder (Alnus glutinosa Gaertn) are the species with the largest share. In mountainous areas, the share of Norway spruce (Picea abies Karst.), silver fir (Abies alba Milland) and European beech (Fagus sylvatica L.) is more significant. Forest ownership also has an impact on its management. In Poland, public forests are predominant (80.7%), with most of them under the administration of the State Forests. The age structure is mainly represented by III and IV age classes (41–60 and 61–80 years old, respectively). As reported by the National Forest Inventory at the end of 2016, the timber resources in Polish forests reached 2587 million m

^{3}of gross merchantable timber, out of which almost 80% is in the State Forests [21]. The mean growing stock volume of Polish forests is 269 m

^{3}/ha, which is much higher than the average in European forests (163 m

^{3}/ha) [23].

#### 2.2. Polish National Forest Inventory Data

^{2}), 11.28 m (400 m

^{2}) and 12.62 m (500 m

^{2}) radii depending on the forest stand age. In the last recent cycle (2015–2019), a radius of 11.28 m (400 m

^{2}) was used for all plots. At each NFI sample plot, many tree and stand characteristics were measured. The diameter at breast height (DBH) was measured for all trees with a DBH ≥ 7 cm. The heights of the selected trees were measured to estimate the height curve. To obtain the GSV for a sample plot, first, the allometric models are used to predict individual tree volumes. Then, after aggregation from single trees, the plot-level GSV is calculated [25,26]. In this research, measurements from the second cycle of the NFI (2010–2014) were used since these measurements guaranteed the smallest difference between the time of the field measurements and the time of the ALS point cloud acquisition. For the analysis, 13,323 NFI sample plots were used, where the full area of the sample plot was located within the borders of a single forest stand and for which the ALS point clouds were available. The basic characteristics of the GSV at the plot level are presented in Table 1. The species share at the plot level was calculated using the volume of single trees.

#### 2.3. Landsat Images

#### 2.4. Airborne Laser Scanning Point Clouds

^{2}of Poland. In the following years (2015–2017), data collection for other areas of the country continued. ALS data were obtained in two standards: Standard I (mainly forest and rural areas outside cities), where the point density is at least four pulses per square meter (ppsm) and Standard II (94 cities in most without forests), with a density of at least 12 ppsm. The acquisition of ALS point clouds took place from mid-October to April, that is, in the leaf-off period, which at the transverse scan angle (allowed up to 25 degrees) guaranteed good penetration of the laser beams through the stand hood to the ground. Since the second cycle of the NFI (2010–2014) took place at nearly the same time as ALS data acquisition with the ISOK project (2011–2015), the absolute time difference between the two datasets was, in most cases (90.4%), less than three years (Table 2).

#### 2.5. Extraction of Predictor Variables

#### 2.6. Validation Data

#### 2.7. Predictive Methods

#### 2.7.1. Random Forests

_{tree}) with a certain depth (t

_{depth}), using a randomly chosen subset of predictors for each one (m

_{try}). To build trees, the out-of-bag samples (OOB) procedure is applied, where each tree is built independently based on bootstrap samples from the training dataset, while the remaining one-third of the samples are randomly left out. More details on the RF method can be found in the review of Belgiu and Drăgu [39] and in the article of Li et al. [32].

_{tree}, m

_{try and}t

_{depth}(Table 5), searching for the combination that minimizes the Root Mean Square Error:

#### 2.7.2. k-Nearest Neighbours

#### 2.7.3. Deep Learning Fully Connected Neural Network

#### 2.7.4. Multiple Linear Regression

_{j}is the respective regression coefficient and ${\epsilon}_{i}$ denotes a random residual term with the distribution of $N\left(0,{\sigma}_{i}^{2}\right)$. LM does not have hyperparameters and does not require an optimization phase. However, we calculated the performance of LM with the same 5-fold-cross validation procedure used for RF, k-NN and DL.

#### 2.8. Models Training and Validation

^{2}, the bias and the relative bias for the bootstrap samples.

## 3. Results

#### 3.1. Set of Predictor Variables

#### 3.2. Optimization Results

#### 3.3. Performance Assessment

^{3}/ha and an RMSE% between 30.45% and 31.69% with the RF that achieved the highest accuracy (Table 7). Using the ALS predictors, we found that all the predictive methods achieved RMSE results between 81.43 and 83.90 m

^{3}/ha and RMSE% results between 24.30% and 25.03% with the DL that achieved the highest accuracy. Using the Landsat and ALS predictors, the evaluated predictive approaches achieved results for an RMSE between 80.98 and 84.41 m

^{3}/ha and an RMSE% between 24.16% and 25.18% with the RF that achieved the lowest accuracy and the DL the highest accuracy.

^{2}(Figure 5). Using Landsat, only the R

^{2}dropped to 0.01. Similarly, using only Landsat, the bias was large, ranging between 40.39 and 36.56 m

^{3}/ha. On the other hand, Landsat made an important contribution to DL when used together with the ALS. Indeed, when using DL with just the ALS, the bias was −11.64 m

^{3}/ha but while using both the Landsat and the ALS, the bias dropped to −7.31 m

^{3}/ha.

#### 3.4. Performance Assessment per Dominant Tree Species

^{3}/ha (20.99%) for oak-dominated stands with the DL method to 80.00 m

^{3}/ha (24.06%) for pine-dominated stands predicted with the RF model. A considerably larger RMSE was obtained for the beech-dominated stand varying from 106.94 m

^{3}/ha (DL) to 110.19 m

^{3}/ha (LM). For beech-dominated stands, large systematic errors (bias) were also observed for all evaluated predictive methods: from −20.19% (−66.62 m

^{3}/ha) for the DL model up to −23.71% (−78.55 m

^{3}/ha) for LM. The relative bias for pine, oak and fir varied from 0.70% (fir; RF) to −6.73% (oak, LM). The R

^{2}averaged through all predictive methods was the highest for beech-dominated stands (0.50) and the lowest for fir-dominated stands (0.30). The R

^{2}was also low for the group of 19 stands dominated by “other species” (0.13).

## 4. Discussion

^{2}values that we obtained. Nevertheless, our study shows that for coniferous species (Scots pine and silver fir), relatively low RMSE% (22%–23%) and bias% (1%) can be obtained for stand-level GSV predictions when combining ALS point clouds and Landsat images with NFI data, even when the positional errors of the field plots vary from several to about 15 m. It can be assumed that collecting accurate information about the plot centre coordinates in the next cycles of the Polish NFI may increase the accuracy of the predictive models of GSV. However, McRoberts et al. [53] observed only a small decrease in the standard error of the mean aboveground biomass in ALS-assisted estimates of aboveground biomass when using survey-grade GPS receivers with sub-meter accuracy compared to field grade GPS receivers with a 5–10 m accuracy. The aforementioned authors concluded that the high costs of acquiring a survey-grade GPS receiver are not justified in the case of ALS-assisted estimates of aboveground biomass at the national scale level in the USA.

^{2}, 400 m

^{2}and 500 m

^{2}) and grids used for the model predictions (30 × 30 m; 900 m

^{2}). Nevertheless, we decided to use a 30 × 30 m resolution grid for prediction to avoid resampling and average the Landsat-derived predictors. Packalen et al. [54] reported that a resolution mismatch between the field plot size and grid cell size used for predictions caused only a small increase of bias in ABA. The authors indicated that a higher prediction resolution compared to training resolution caused an underestimation of AGB. However, in our study, overestimation of GSV was observed in most cases, even though the prediction grid was larger than the training sample size.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Localization of Poland in Europe (

**a**) with the distribution of the reference forest stands ((

**b**); black polygons) and the distribution of NFI (National Forest Inventory) plots in Poland ((

**c**); black dots).

**Figure 2.**Numbers of the images available for each of the Landsat Scenes (black dots represent the available images).

**Figure 3.**Importance ranking of Random Forests for each type of predictor: Landsat, ALS and Landsat and ALS. The graph reports the percentage increase in the mean square error (IncMSE%) of each type of predictor.

**Figure 4.**Results of the bootstrapping procedure for each considered approach (LM—multiple linear regression, KNN—k-nearest neighbours, RF—random forests and DL—deep learning) using different sets of predictor variables (Landsat, ALS and Landsat+ALS). The red line identifies the confidence interval.

**Figure 5.**Observed vs. predicted values of GSV (growing stock volume) for 360 validation stands for each considered predictive approach (LM—multiple linear regression, KNN—k-nearest neighbours, RF—random forests and DL—deep learning) for the best set of predictors (Landsat+ALS).

**Figure 6.**Observed vs. predicted values of GSV (growing stock volume) for validation stands obtained with the best set of predictors (Landsat+ALS) and grouped by dominant tree species and predictive approach (DL—deep learning, KNN—k-nearest neighbours, LM—multiple linear regression and RF—random forests).

**Table 1.**Characteristics of NFI plots used for the development of the GSV (growing stock volume) models (n = 13,323).

Dominant Tree Species | Number of Plots | Percentage of Plots (%) | Minimum GSV (m^{3}/ha) | Mean GSV (m ^{3}/ha) | Maximum GSV (m^{3}/ha) | Standard Deviation of GSV (m^{3}/ha) |
---|---|---|---|---|---|---|

Scots pine | 8334 | 62.6 | 0.2 | 300.7 | 935.1 | 139.6 |

silver birch | 904 | 6.8 | 0.3 | 192.8 | 708.4 | 119.8 |

Norway spruce | 731 | 5.5 | 0.4 | 309.3 | 1069.0 | 200.8 |

European beech | 708 | 5.3 | 0.1 | 351.8 | 1452.8 | 220.6 |

sessile oak | 680 | 5.1 | 0.2 | 296.0 | 1237.3 | 186.0 |

other species | 663 | 5.0 | 0.2 | 243.4 | 1347.1 | 174.0 |

common alder | 577 | 4.3 | 0.7 | 270.9 | 908.3 | 165.5 |

silver fir | 459 | 3.4 | 2.7 | 368.0 | 1338.0 | 217.5 |

European larch | 267 | 2.0 | 0.3 | 253.0 | 795.1 | 181.0 |

**Table 2.**Maximum absolute time difference between the time of the field measurements at the NFI plots and the time of the ALS (airborne laser scanning) point cloud acquisition.

Maximum Absolute Difference between NFI and ALS (Years) | Number of Plots | Percentage of Plots (%) |
---|---|---|

1 | 5209 | 39.1 |

2 | 4246 | 31.9 |

3 | 2588 | 19.4 |

4 | 1092 | 8.2 |

5 | 188 | 1.4 |

**Table 3.**Predictor variables calculated for the NFI plots and used for the development of the GSV (growing stock volume) models.

Description of Predictor Variables | Acronyms |
---|---|

Bottom of atmosphere reflectance of Landsat 7 ETM+ spectral bands | B1_30, B2_30, B_3_30, B4_30, B5_30, B6_30, B7_30 |

Mean value of point heights (m) | zmean |

Maximum value of point heights (m) | zmax |

Standard deviation of point heights (m) | zsd |

Skewness of point heights | Zskew |

Kurtosis of point heights | Zkurt |

Percentile values of point heights: 5th, 10th, 15th, …, 95th (m) | zq5, zq10, zq15, …, zq95 |

Entropy calculated as a normalized Shannon vertical complexity index | zentropy |

Percentage of all returns above 2 m (%) | pzabove2 |

Percentage of all returns above zmean (%) | pzabovezmean |

Cumulative percentage of returns from nine height layers. The height measurements were divided into 10 equal intervals according to Reference [31] (%) | zpcum1, zpcum2, zcum3, …, zpcum9 |

**Table 4.**Characteristics of stands used for model validation (n = 360; mean stand area = 1.1 ha; GSV—growing stock volume).

Dominant Tree Species | Number of Stands | Percentage of Stands (%) | Minimum GSV (m^{3}/ha) | Mean GSV (m ^{3}/ha) | Maximum GSV (m^{3}/ha) | Standard Deviation of GSV (m^{3}/ha) |
---|---|---|---|---|---|---|

Scots pine | 270 | 75.0 | 111.0 | 332.6 | 593.0 | 97.4 |

silver fir | 29 | 8.1 | 223.0 | 387.7 | 629.0 | 97.4 |

European beech | 22 | 6.1 | 158.0 | 336.0 | 590.0 | 116.3 |

sessile oak | 20 | 5.6 | 174.0 | 348.0 | 473.0 | 86.8 |

other species | 19 | 5.3 | 190.0 | 277.6 | 479.0 | 77.7 |

**Table 5.**Set of tested parameters for each nonparametric predictive approach (KNN—k-nearest neighbours, RF—random forests and DL—deep learning).

Model | Hyperparameter | Values | Tuning Method |
---|---|---|---|

KNN | K | 1–40 | Random Search |

Minkowski distance | Euclidean distance, Manhattan distance | ||

Distance metrics | Unweighted, Weighted, Inverse, Reciprocal | ||

RF | n_{tree} | 100–500 | Random Search |

m_{try} | 2—number of predictors | ||

t_{depth} | 2–10 | ||

DL | Hidden layers | Trial-and-error | |

Nodes | |||

Optimizer | |||

Learning Rate | |||

Dropout layers | |||

Dropout percentage | |||

Activation functions | |||

Regularization layers | |||

L1 regularization | |||

L2 regularization |

**Table 6.**The best hyperparameter configurations selected for each predictive approach and each set of predictors (RF—random forest, k-NN—k-nearest neighbours).

Predictive Approach | Predictors | Configurations | ||
---|---|---|---|---|

RF | m_{try} | t_{depth} | n_{tree} | |

Landsat | 2 | 9 | 500 | |

ALS | 2 | 6 | 500 | |

Landsat+ALS | 2 | 3 | 500 | |

k-NN | kmax | distance | kernel | |

Landsat | 36 | Manhattan | unweighted | |

ALS | 37 | Manhattan | inverse | |

Landsat+ALS | 35 | Manhattan | inverse |

**Table 7.**Performance of the developed growing stock volume models (DL—deep learning, KNN—k-nearest neighbours, LM—multiple linear regression and RF—random forests) assessed at the stand level (n = 360).

Model | Predictors | R^{2} | RMSE (m^{3}/ha) | RMSE% | Bias (m^{3}/ha) | Bias% |
---|---|---|---|---|---|---|

DL | Landsat | 0.01 | 106.24 | 31.69 | 40.39 | 12.03 |

DL | ALS | 0.39 | 81.43 | 24.30 | −11.64 | −3.48 |

DL | Landsat+ALS | 0.38 | 80.98 | 24.16 | −7.31 | −2.2 |

KNN | Landsat | 0.04 | 104.54 | 31.19 | 39.94 | 11.9 |

KNN | ALS | 0.38 | 83.24 | 24.85 | −16.77 | −5.02 |

KNN | Landsat+ALS | 0.38 | 83.19 | 24.83 | −16.94 | −5.06 |

LM | Landsat | 0.05 | 104.92 | 31.3 | 38 | 11.3 |

LM | ALS | 0.37 | 82.72 | 24.69 | −11.7 | −3.51 |

LM | Landsat+ALS | 0.37 | 82.57 | 24.64 | −12.01 | −3.6 |

RF | Landsat | 0.07 | 102.10 | 30.45 | 36.56 | 10.89 |

RF | ALS | 0.38 | 83.90 | 25.03 | −16.51 | −4.93 |

RF | Landsat+ALS | 0.39 | 84.41 | 25.18 | −17.81 | −5.32 |

**Table 8.**Performance of the developed growing stock volume models (DL—deep learning, KNN—k-nearest neighbours, LM—multiple linear regression and RF—random forests) assessed at the stand level for different dominant tree species (n = 360).

Species | Number of Stands | Method | R^{2} | RMSE (m^{3}/ha) | RMSE% | Bias (m^{3}/ha) | Bias% |
---|---|---|---|---|---|---|---|

European beech | 22 | DL | 0.46 | 106.94 | 32.13 | −66.62 | −20.19 |

KNN | 0.51 | 108.39 | 32.59 | −74.39 | −22.5 | ||

LM | 0.53 | 110.19 | 33.11 | −78.55 | −23.71 | ||

RF | 0.49 | 109.92 | 33.03 | −74.21 | −22.45 | ||

Scots pine | 270 | DL | 0.42 | 76.02 | 22.86 | −2.80 | −0.86 |

KNN | 0.42 | 78.6 | 23.64 | −12.08 | −3.65 | ||

LM | 0.40 | 77.79 | 23.40 | −6.13 | −1.86 | ||

RF | 0.42 | 80.00 | 24.06 | −13.18 | −3.98 | ||

sessile oak | 20 | DL | 0.33 | 72.61 | 20.99 | −10.91 | −3.32 |

KNN | 0.31 | 77.22 | 22.34 | −20.19 | −5.99 | ||

LM | 0.36 | 73.38 | 21.24 | −22.78 | −6.73 | ||

RF | 0.32 | 77.62 | 22.45 | −20.27 | −6.01 | ||

silver fir | 29 | DL | 0.28 | 87.74 | 22.63 | 18.01 | 4.53 |

KNN | 0.3 | 83.32 | 21.49 | 6.78 | 1.63 | ||

LM | 0.29 | 84.08 | 21.68 | 12.81 | 3.18 | ||

RF | 0.32 | 84.53 | 21.82 | 3.15 | 0.70 | ||

other species | 19 | DL | 0.13 | 103.23 | 37.11 | −37.98 | −14.17 |

KNN | 0.12 | 109.53 | 39.45 | −51.86 | −19.19 | ||

LM | 0.14 | 108.51 | 39.04 | −45.55 | −16.91 | ||

RF | 0.12 | 109.09 | 39.27 | −47.89 | −17.74 |

© 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/).

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**MDPI and ACS Style**

Hawryło, P.; Francini, S.; Chirici, G.; Giannetti, F.; Parkitna, K.; Krok, G.; Mitelsztedt, K.; Lisańczuk, M.; Stereńczak, K.; Ciesielski, M.;
et al. The Use of Remotely Sensed Data and Polish NFI Plots for Prediction of Growing Stock Volume Using Different Predictive Methods. *Remote Sens.* **2020**, *12*, 3331.
https://doi.org/10.3390/rs12203331

**AMA Style**

Hawryło P, Francini S, Chirici G, Giannetti F, Parkitna K, Krok G, Mitelsztedt K, Lisańczuk M, Stereńczak K, Ciesielski M,
et al. The Use of Remotely Sensed Data and Polish NFI Plots for Prediction of Growing Stock Volume Using Different Predictive Methods. *Remote Sensing*. 2020; 12(20):3331.
https://doi.org/10.3390/rs12203331

**Chicago/Turabian Style**

Hawryło, Paweł, Saverio Francini, Gherardo Chirici, Francesca Giannetti, Karolina Parkitna, Grzegorz Krok, Krzysztof Mitelsztedt, Marek Lisańczuk, Krzysztof Stereńczak, Mariusz Ciesielski,
and et al. 2020. "The Use of Remotely Sensed Data and Polish NFI Plots for Prediction of Growing Stock Volume Using Different Predictive Methods" *Remote Sensing* 12, no. 20: 3331.
https://doi.org/10.3390/rs12203331