<figure><img src="image_1.png" /></figure>

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# LiDAR mapping of forests in kanton Uri (Switzerland)

Jean-Matthieu Monnet

► To cite this version:

Jean-Matthieu Monnet. LiDAR mapping of forests in kanton Uri (Switzerland). LESSEM. 2024. [hal-05019687v2](https://hal.inrae.fr/hal-05019687v2)

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Distributed under a Creative Commons Attribution 4.0 International License
# LiDAR mapping of forests in kanton Uri

<figure><img src="image_3.png" /></figure>

Jean-Matthieu Monnet

2024-09-19

This report presents the forest resource mapping in kanton Uri with field data from the Swiss National Forest Inventory (NFI) and the LiDAR data from Swisstopo.

* Funding: Amt für Forst und Jagd of the Kanton Uri.

* NFI data: WSL, 2024: Schweizerisches Landesforstinventar LFI. Daten der Erhebung 2018-22. FabrizioCioldi-DL1624. Eidg. Forschungsanstalt WSL, Birmensdorf.

* Implementation: LESSEM, INRAE

The main work tasks are:

* LFI and LiDAR data preparation

* Tree-level comparison of LiDAR and LFI data for co-registration improvement and removal of plots with significant changes

* Calibration of estimation models for basal area, volume, mean and dominant diameter, stem density

* Production of raster maps for each forest parameter (estimate and confidence interval)

* Inference of estimates and confidence intervals for administrative entities

The project deliverables were:

* Rasters maps for each forest parameter (estimated value and confidence interval) within the forest area of kanton Uri.

* Project report, including description of data, methods and results.

* Scripts of R code used for analysis and processing are on https://forgemia.inra.fr/lidar/kanton_uri (https://forgemia.inra.fr/lidar/kanton_uri)

Contacts :

* Funding: Andreas Zurbringgen (Kanton Uri, Sicherheitsdirektion, Amt für Forst und Jagd, Klausenstrasse 2, 6460 Altdorf)

* Technical: Jean-Matthieu Monnet (Université Grenoble Alpes, INRAE, LESSEM, 2 rue de la Papeterie-BP 76, F-38402 St-Martin-d'Hères, France)

We would like to thank F. Cioldi from WSL for providing the data and advice on Swiss NFI.

## Table of content

* Data

* LiDAR data from swisstopo

* LFI data

* Forest maps

* Comparison of LFI data with LiDAR data

* Point clouds extraction

* Topography

* Tree positions

* Computation of LiDAR metrics

* Parameters

* LFI plots

* Map

* Additional variables

* Modelling

* LFI plot selection

* Global models

* Stratified models

* Mapping

* Metrics check

* Forest mask

* Map production

* Comparison of map and field distributions of values

* Statistics by management area

* Method

* Results
# LiDAR data from swisstopo

* home page, metadata and download (https://www.swisstopo.admin.ch/fr/geodata/height/surface3d.html),

* pdf doc (https://www.swisstopo.admin.ch/content/swisstopo-internet/fr/geodata/height/surface3d/_jcr_content/contentPar/tabs_copy/items/343_1554992725551/tabPar/downloadlist/downloadItems/

The tiles available on the swisstopo website as of May 5, 2024 are shown on the following map. Most of the data was acquired in 2019 (dark green). The main valley was acquired in 2020. Some acquisitions from other years (2017, 2018, 2020 and 2021) overlap at the borders.

<figure><img src="image_4.png" /></figure>

LiDAR tiles were downloaded from the swisstopo website in two steps:

* Creation of the tiles map: export of a csv file with download links from the swisstopo interface (https://www.swisstopo.admin.ch/fr/modele-altimetrique-swisssurface3d#swissSURFACE3D---Download) by selecting "Full dataset" and unchecking "Temporal state", before clicking on "Search" then "Export links". The resulting file is then used in the `load_classified ta_ch()` function in the R package `lidarHD` (https://forgemia.inra.fr/lidar/lidarHD) to create the tiles map.

* Download of tiles intersecting the canton of Uri with the `download_files_ch()` function. The tiles are then indexed with "lax" files for faster subsequent spatial queries.

The number of tiles per year is shown below.

<table><thead><tr><td>Year</td><td>Freq</td></tr></thead><tbody><tr><td>2019</td><td>1118</td></tr><tr><td>2020</td><td>79</td></tr></tbody></table>

## Computation of points heights

The height of each point relative to the ground is calculated and added to the original files as an additional H attribute ("Extra-Byte" format). Modified files are renamed by prefixed with "EB-" to ensure traceable changes. This step was carried out on a server for a total 300 hours. The resulting files are then indexed for faster access in subsequent steps (18 hours).

A few "ground" points may end up with non-zero height values in the case of interpolation errors in very hilly areas (e.g. cliffs and overhangs). Negative heights are set to zero for further processing, and all "ground" points have their height set to zero.

## Example file

This paragraph describes the characteristics of the point cloud contained in the file "swisssurface3d_2020_2693-1183_2056_5728.laz".
## class : LAS (v1.2 format 1)

## memory : 1.1 Gb

## extent : 2693000, 2694000, 1183000, 1184000 (xmin, xmax, ymin, ymax)

## coord. ref. : CH1903+ / LV95

## area : 1 km²

## points : 16.9 million points

## density : 16.9 points/m²

## density : 11.35 pulses/m²

The metadata contained in the file header are.

## File signature: LASF

## File source ID: 0

## Global encoding:

## - GPS Time Type: Standard GPS Time

## - Synthetic Return Numbers: no

## - Well Know Text: CRS is GeoTIFF

## - Aggregate Model: false

## Project ID - GUID: 00000000-0000-0000-0000-000000000000

## Version: 1.2

## System identifier:

Descriptive statistics for the points contained in the file are presented below.

## X Y Z

## Min. :2693000 Min. :1183000 Min. :483.2

## 1st Qu.:2693186 1st Qu.:1183225 1st Qu.:505.8

## Median :2693392 Median :1183455 Median :531.5

## Mean :2693438 Mean :1183473 Mean :557.8

## 3rd Qu.:2693692 3rd Qu.:1183729 3rd Qu.:601.6

## Max. :2694000 Max. :1184000 Max. :814.1

## gpstime Intensity ReturnNumber

## Min. :270218139 Min. : 5.00 Min. :1.0

## 1st Qu.:270285916 1st Qu.: 20.00 1st Qu.:1.0

The distribution of intensity values (log scale) is shown in the following figure.

Intensity

<figure><img src="image_5.png" /></figure>

The following table shows the distribution of points by order of arrival and the total number of echoes associated with the transmitted pulse.
We check that there are no points below the diagonal, and that the numbers are close for each column.
## TotalReturns

<table><thead><tr><th>ReturnOrder</th><th>1</th><th>2</th><th>3</th><th>4</th><th>5</th><th>6</th></tr></thead><tbody><tr><td>1</td><td>7928919</td><td>1881204</td><td>1043273</td><td>388959</td><td>89887</td><td>13650</td></tr><tr><td>2</td><td>0</td><td>1877364</td><td>1040921</td><td>388220</td><td>89742</td><td>13645</td></tr><tr><td>3</td><td>0</td><td>0</td><td>1037827</td><td>387149</td><td>89609</td><td>13628</td></tr><tr><td>4</td><td>0</td><td>0</td><td>0</td><td>385416</td><td>89323</td><td>13599</td></tr><tr><td>5</td><td>0</td><td>0</td><td>0</td><td>0</td><td>88865</td><td>13572</td></tr><tr><td>6</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>13482</td></tr><tr><td>7</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr></tbody></table>

The following table shows the distribution of points by scan direction and end of the scan line. It seems those attributes are not specified.

## Scan_Edge

Scanjaviruses

0 16900078

The swisstopo classification codes are as follows (Number / Object type / "ASPRS category") :

• 1 Unclassified and temporary objects "unclassifed"

• 2 Ground

• 3 Vegetation (low - medium - high) "Low Vegetation"

• 6 Buildings

• 9 water

• 17 bridges, footbridges, viaducts "Bridge Deck"

The distribution of points by class is given in the following table.

<table><thead><tr><th>Classification</th><th>Freq</th></tr></thead><tbody><tr><td>1</td><td>246656</td></tr><tr><td>2</td><td>9477569</td></tr><tr><td>3</td><td>6526587</td></tr><tr><td>6</td><td>415174</td></tr><tr><td>9</td><td>203457</td></tr><tr><td>17</td><td>30635</td></tr></tbody></table>

The distribution of height values by class is shown in the following boxplot. For the forest analysis, only points in class 3 (vegetation) will be used. Class 2 and 9 points are used to represent the terrain. Class 1 points appear to be located in a wide range of heights. The points in classes 1, 6 and 17 are not used.
<figure><img src="image_6.png" /></figure>

The distribution of scan angles is shown in the histogram below.

<figure><img src="image_7.png" /></figure>

The distribution of points in the different flight bands is as follows.

```
## flight strip
## 2207 2208 2209 2210 2211 2212 2213
## 630863 1677619 3018005 3616088 4350724 2245873 895408
## 2214 2259
## 396247 69251
```

GPS acquisition times are homogeneous for each flight strip. It seems that the points on this tile were acquired on two different days (two height levels on the figure).
<figure><img src="image_8.png" /></figure>

## Tiles content statistics

In order to map the characteristics of the LiDAR data, the following statistics of the point cloud are computed for each pixel of a 20 m grid:

* total density of points,

* density of emitted pulses,

* density of points classified as ground,

* density of points classified as 1,

* density of points classified as vegetation,

* start date of flight,

* flight end date,

* average altitude of points,

* maximum height of points,

* average intensity,

* standard deviation of intensity,

* mean scan angle,

* standard deviation of scan angle.

Polygons representing the flight strips are also reconstructed.

To calculate the flight date, GPS time is converted to absolute time by adding a delay of 1 billion seconds to the recorded value. The "leap" seconds are neglected. The machine time required to produce this data is around 150 hours.

The average pulse density is 18/m², with a slightly lower density in the valley and in the south-east part of the kanton. The following map shows the pulse density (scale from 0 to 40 and more per squared meter).
Pulse density (/m2)

<figure><img src="image_9.png" /></figure>

The valleys were flown from 28 March to 8 April 2020, and higher altitudes from 28 August to 12 October 2019. We can consider that no growth occured between those dates. However it is possible that some areas were flown in leaf-off state and others in leaf-on, which might add noise in the models, and local bias in the maps.

First flight

<figure><img src="image_10.png" /></figure>

Last flight

<figure><img src="image_11.png" /></figure>

As expected, intensity values are higher in non vegetated areas. Some patterns linked with flight strips can be observed. Intensity values are influenced by the acquisition geometry, and this effect is hard to correct. Intensity values will not be used in the models.

Mean scan angle displays some variability, so that it is important to check the robustness of the height metrics in relation to the acquisition configuration.
<figure><img src="image_12.png" /></figure>

## Digital Terrain Model computation

A digital terrain model (DTM) at 1 m resolution is calculated by bilinear interpolation of points classified as "soil" and "water". A 5 m resolution DTM is then calculated by averaging the 1 m resolution DTM cells per 5 m pixel. This represents around 200 hours of machine time.

## LFI data

The aim of the National Forest Inventory (NFI) is to assess the state and dynamics of Swiss forests. It is based on a network of field plots sampled on a 1.4 km grid (protocol (https://www.lfi.ch/en/publications/methods-and-models-NFI4)). 6600 plots are measured over a 9-year cycle. Data from LFI 4 (2009-2017) are available, while those of LFI 5 (2018-2026) are only partially available.

The trees inventoried are:

* dead or alive,

* standing or on the ground,

* with a diameter greater than 12 cm over a projected area of 200 m²

* with a diameter larger than 36 cm over a projected area of 500m².

Depending on the slope measured on the plot by the operators, the maximum ground distance is determined in order to assume the desired plot projected area. Assuming that the ground of the plot is a plane, this amounts to inventorying a disc on an inclined plane. The projected area of this disc is 200 or 500 m², but its shape projected onto the horizontal plane is an ellipse with its short axis in the direction of the slope. This information has to be taken into account in order to extract LiDAR point clouds on the same extent as the field inventory.

## Description

The data for 108 LFI 4 and 84 LFI 5 plots have been provided, including plot location information and tree-level data.

Plot data include:

* plot id ( CLNR ),

* coordinates: theoretical ( X, Y ) and GPS ( GPS_X, GPS_Y ) dans le système MN03 (CH1903),

* inventory date ( DATUMF ): dates are before the ALS flight, changes can be expected because of growth of trees, disturbances and harvest,

* slope ( SLOPE25 , percent), aspect ( ASPECT25 , degrees ) and altitude ( Z25 , m above sea level) extracted from a digital terrain model,

* development stage ( EST : -1 Wert nicht ermittelt, 1 Jungwuchs/Dickung, 2 Stangenholz, 3 schwaches Baumholz, 4 mittleres Baumholz, 5 starkes Baumholz, 6 gemischt)

* dominant diameter at breast height in cm ( DDOM )

* species mixture level ( MISCHG : -1 Wert nicht ermittelt, 1 91-100% Nadel, 2 51- 90% Nadel, 3 11- 50% Nadel, 4 0- 10% Nadel)

* stand structure ( STRUK : -1 Wert nicht ermittelt, 1 einschichtig, 2 mehrsch. regelm., 3 stufig, 4 Rottenstruktur)

* forest variables, available as total for all species (ALL), or by species (FICHT, TANNE, FOEHR, LARCH, ARVEN, UENDH, BUCHE, AHORN, ESCHE, EICHE, CASTA, UELBH); computed with standing AND lying trees.

* stem density, all stems ( GESTZ ), live only ( STZ ) or dead only ( T0STZ )

* volume, all trees ( GESV ), live only ( V ) or dead only ( T0V )

* basal area of live trees ( BAS ).

* maximum ground distance (m) for trees smaller than 36 cm ( PFRAKL ) and larger than 36 cm ( PFRAGR )
* slope measures (NEIG1, NEIG2), and mean slope used to compute the ground distance (NEIG, percent)

* plot azimuth (gradians) AZIEXPO.

Tree data include (tree with diameter larger than 12 cm):

* plot id (CLNR),

* tree id (BANR),

* species code (BART): two columns, the first one has more "999" values,

* coordinates (X03, Y03) in the coordinate system MN03 (CH1903),

* diameter at 1,3 m height (D13),

* diameter at 1,3 m, measure with a compass (BHD) of trees with diameter smaller than 60 cm,

* perimeter at 1,3 m, measure with a ruban tape (UMFANG) of trees with diameter larger than 60 cm,

* tree health condition (DUERR: -1 Wert nicht ermittelt, 1 Dürrständer, 2 stehend grün, 10 liegend dürr, 11 liegend grün, 20 liegend dürr) (lebend oder tot, verwertbar))

* sampling weight (RPSTZ): 50 for trees with D13 < 36 cm (200 m² area) and 20 for larger trees (500 m² area). Different values might occur in case of plots not fully covered by forest. In this case, weights should be set to 20 or 50 as models should be built with the tree list corresponding to the extracted point cloud (whole plot), (précisions de M. Cioldi du WSL "Facteur de représentation d'un arbre. Chaque arbre relevé sur une placette représente un certain nombre d'arbres par hectare. Ce facteur d'extrapolation n'est pas le même pour tous les arbres et sur toutes les placettes, mais dépend du diamètre de l'arbre (soit ≥ 36 cm, soit < 36 cm) et du fait que la placette a été ou non réduite par des lignes de "démarcation" (p. ex. dans le cas d'une lisière de forêt, d'une limite d'accessibilité, etc.) Le facteur de représentation est d'autant plus élevé que la surface de la placettes réduite par des lignes de "démarcation" est petite. Normalement, le facteur de représentation reste le même d'un inventaire à l'autre, sauf si la ligne de réduction en lisière de forêt a un tracé différent.")

* trunk volume (VMRD),

* total height (for a sample of trees) (HOEHE),

* FIELD YEAR: year of tree position measure?

Stand parameters

Stand parameters are computed from the tree-level data to check that the data have been correctly interpreted.

The following parameters are also computed for live standing trees by applying a *w* weight of 50 and 20 /ha respectively for trees under and over 36 cm in diameter respectively. The RPSTZ value is not applied, as it takes into account the fact that the plot is partially inventoried in the field (edge plot, for example), whereas the LiDAR point cloud will be extracted over the entire ellipse. The RPSTZ should be taken into account if the plot is partially inventoried due to inaccessibility, but this information is not known.

* basal area (m²/ha) G.m2ha = $\sum \pi \times (\frac{D13_i}{200})^2 \times w_i$,

* mean diameter (cm) D.cm = $\frac{\sum D13_i \times w_i}{\sum w_i}$,

* stem number (/ha) N.ha = $\sum w_i$,

* volume (m³/ha) VMRD.m3ha = $\sum VMRD_i \times w_i$,

* dominant diameter (cm) DDOM value is computed by the LFI,

* complete: was the plot fully inventoried (TRUE) or not (FALSE).

Descriptive statistics of the data obtained for the LFI 4 and LFI 5 surveys (plots with at least one tree surveyed) are shown below.

<table><caption>## [1] "LFI 4"</caption><thead><tr><th>G.m2ha</th><th>D.cm</th><th>N.ha</th><th>VMRD.m3ha</th><th>Complete</th></tr></thead><tbody><tr><td>Min.: 0.00</td><td>Min.: 12.00</td><td>Min.: 0.0</td><td>Min.: 0.0</td><td>Mode: logical</td></tr><tr><td>1st Qu.: 12.82</td><td>1st Qu.: 21.00</td><td>1st Qu.: 205.0</td><td>1st Qu.: 112.3</td><td>FALSE: 13</td></tr><tr><td>Median: 32.81</td><td>Median: 27.42</td><td>Median: 410.0</td><td>Median: 335.0</td><td>TRUE: 70</td></tr><tr><td>Mean: 31.30</td><td>Mean: 28.36</td><td>Mean: 452.9</td><td>Mean: 343.0</td><td>NA</td></tr><tr><td>3rd Qu.: 46.42</td><td>3rd Qu.: 33.68</td><td>3rd Qu.: 615.0</td><td>3rd Qu.: 522.9</td><td>NA</td></tr><tr><td>Max.: 85.55</td><td>Max.: 68.14</td><td>Max.: 1500.0</td><td>Max.: 946.5</td><td>NA</td></tr><tr><td>NA</td><td>NA's: 2</td><td>NA</td><td>NA</td><td>NA</td></tr></tbody></table>

<table><caption>## [1] "LFI 5"</caption><thead><tr><th>G.m2ha</th><th>D.cm</th><th>N.ha</th><th>VMRD.m3ha</th><th>Complete</th></tr></thead><tbody><tr><td>Min.: 0.6637</td><td>Min.: 13.00</td><td>Min.: 40.0</td><td>Min.: 2.805</td><td>Mode: logical</td></tr></tbody></table>
<table><thead><tr><th>G.m2ha</th><th>D.cm</th><th>N.ha</th><th>VMRD.m3ha</th><th>Complete</th></tr></thead><tbody><tr><td>1st Qu.:14.0146</td><td>1st Qu.:19.96</td><td>1st Qu.: 170.0</td><td>1st Qu.: 108.091</td><td>FALSE:13</td></tr><tr><td>Median :27.1041</td><td>Median :27.39</td><td>Median : 400.0</td><td>Median : 307.646</td><td>TRUE :52</td></tr><tr><td>Mean :31.1556</td><td>Mean :27.25</td><td>Mean : 447.4</td><td>Mean : 339.273</td><td>NA</td></tr><tr><td>3rd Qu.:45.1659</td><td>3rd Qu.:32.14</td><td>3rd Qu.: 690.0</td><td>3rd Qu.: 511.118</td><td>NA</td></tr><tr><td>Max. :93.1364</td><td>Max. :58.29</td><td>Max. :1170.0</td><td>Max. :1013.677</td><td>NA</td></tr></tbody></table>

## Conversion of coordinates from system 1903 to 1903+

Coordinates are converted from the CH1903 system to CH1903+ (EPSG code: 2056) in order to extract LiDAR point clouds, using the swisstopo interface (https://www.swisstopo.admin.ch/fr/cartes-donnees-en-ligne/calculation-services/reframe.html).

## Selection of the last measure

For each plot the measures of the last available LFI is used. For plots where no trees have been inventoried, the parameters are considered as "missing data". There are a total of 116 different plots, which were not necessarily measured in each campaign due to changes in forest area and because the LFI 5 inventory has not yet been completed.

<table><thead><tr><th>LFI</th><th>Freq</th></tr></thead><tbody><tr><td>LFI4</td><td>32</td></tr><tr><td>LFI5</td><td>84</td></tr></tbody></table>

## Vegetation periods

According to WSL, the method for computation of the number of vegetation periods between two dates is as follows: "Nombre de périodes de végétation (au 1/4 de période près) qui séparent les dates de relevés sur le terrain des placettes accessibles par le groupe de relevés sur le terrain lors des inventaires qu'on veut comparer. Par définition de l'algorithme, seuls les mois de mai à septembre sont considérés comme période de croissance, c'est-à-dire que les mois de janvier à avril comptent pour mai et les mois d'octobre à décembre pour septembre. Le jour d'enregistrement d'un mois n'est pas pris en compte."

The calculation method will be used to verify the effect of the delay between the LiDAR flight and the field inventories on the models.

## Forest maps

The forest extent map is provided by kanton Uri.

The mixture map from OFEV (https://opendata.swiss/fr/dataset/waldmischungsgrad-lfi) is also considered. This layer has a spatial resolution of 10 m and values ranging from 0 (pure coniferous stand) to 100 (pure broadleaf stand).

The Normalized Difference Vegetation Index is computed from bands B08 and B04 of a Sentinel-2 L2A image acquired on August, 7 (https://browser.dataspace.copernicus.eu/?zoom=11&lat=46.72668&lng=8.64006&themeId=DEFAULT-THEME&visualizationUrl=U2FsdGVkX19waMfrGU2Y%2BEYdgCMw95UVvZfT7%2FF3TwIbzGETAvDUNMGiv%2FAc0me7YIPI7WEHBAp1j9>08-07T00%3A00%3A00.000Z&toTime=2020-08-07T23%3A59%3A59.999Z&demSource3D=%22MAPZEN%22&cloudCoverage=6&dateMode=SINGLE#), as $NDVI = \frac{(B_{08} - B_{04})}{(B_{08} - B_{04})}$. NDVI

might add information about land cover, and in particular regarding vegetation type.
NDVI from S2 image 2020-08-07

<figure><img src="image_13.png" /></figure>

# Comparison of LFI data with LiDAR data

## Point clouds extraction

Point clouds are extracted around the location of each plot within a 25 m radius of the GPS coordinates of the center. Topographical indices (slope, azimuth, altitude) are calculated by fitting an inclined plane to the cloud of points classified as "ground" located within less than 12.62 m from the plot center in horizontal distance.

## Topography

The information extracted from the DTM is consistent with that measured in the field. Points in the following plots are colored according to the number of the last inventory carried out on the plot.

Azimuth (gradians)

<figure><img src="image_14.png" /></figure>

Field

Slope (%)

<figure><img src="image_15.png" /></figure>

Field

## Tree positions

In order to check the position of the plots and the consistency between field measurements and the LiDAR flight, tree positions are displayed on the canopy height model (CHM) calculated by taking the height of the highest LiDAR point in each cell, at 0.5 m resolution. The elliptical plot border is also displayed. Trees may appear outside the ellipse, as the topography is not necessarily regular.
# Semi-automatic co-registration

An algorithm is applied to estimate a translation of the plot center (maximum 5 m distance around the original position) that best adjusts the position of the trees to the CHM values.

The maps for each plot are visually examined and the following criteria are evaluated:

* plot position: CORRECT / APPLY TRANSLATION / DOUBTFUL / BAD / EVALUATION NOT POSSIBLE

* missing trees: YES / NO

* additional trees: YES / NO

# Validation of co-registration

Following these checks, the translation proposed by the algorithm is applied when validated by the operator. The results of the verification are shown below.

<table><thead><tr><td>Position</td><td>Arbre_Manquant</td><td>Arbre_en_Trop</td></tr></thead><tbody><tr><td>APPLIQUER DECALAGE:21</td><td>Mode:logical</td><td>Mode:logical</td></tr><tr><td>CORRECT:41</td><td>FALSE:114</td><td>FALSE:113</td></tr><tr><td>DOUTEUX:15</td><td>TRUE:1</td><td>TRUE:2</td></tr><tr><td>EVALUATION IMPOSSIBLE:38</td><td>NA</td><td>NA</td></tr></tbody></table>

# Computation of plot extent

Once the coordinates have been adjusted, the ellipses of plot extent are recalculated and the information is added to the point clouds.

# Computation of LiDAR metrics

To calibrate the estimation models linking LiDAR data to forest parameters, three types of LiDAR variables (metrics) are calculated:

* statistical indices calculated directly from the point cloud,

* metrics describing the objects (trees) that can be extracted from the LiDAR data,

* topography metrics (slope, azimuth, altitude) calculated by fitting a plane to points classified as ground within the plot extent.

# Parameters

The parameters used to build the models are as follows:

* LiDAR points: ground and vegetation classes,

* height threshold of 60 m to remove outliers,

* pixel size of 22.4 m for the maps, so that the area (approx. 502 m²) is consistent with that of the LFI plots (500 m²).

* resolution for MNH calculation (tree detection): 0.8 m.

# LFI plots

The following steps are performed.

* Point filtering: points of interest (ground and vegetation classes) with a height of less than 60 m are selected.

* Extraction on the extent: points are extracted inside the ellipse.

* Computation of topography metrics from this point cloud.

* Computation of point cloud metrics: statistical indices describing the point cloud are calculated. Negative height values are first set to 0.

* Calculation of tree metrics: for the point cloud with a buffer zone, trees are detected. Trees detected whose apex is included in the ellipse are retained, and statistics describing their number and dimensions are calculated.

* Aggregation of metrics: statistics calculated on the plots are assembled in a table to be used for calibration.

# Map

* Forest metrics: statistical indices describing the LiDAR cloud and detected trees are also calculated for each pixel of the final map (approx. 150 h machine time).
# Additional variables

The following additional variables are calculated:

* number of vegetation periods between the inventory date and the date of the first and last LiDAR flights,

* cosine of exposure: indication of North (1) / South (-1) exposure,

* sine of exposure: indicates East (1) / West (-1) exposure,

* The Normalized Difference Vegetation Index from the S2 image.

LFI 5 field dates are always closer to LiDAR flight in vegetation periods than the LFI 4. For modeling, LFI 5 plots are thus always preferred when both campaigns are available.

# Modelling

For each forest parameter, the linear regression that best estimates field values from a subset of LiDAR metrics is selected.

## LFI plot selection

The plots used for calibration are those that meet the following criteria:

* non-zero or missing basal area,

* at least one tree detected in the LiDAR data,

Plots whose coordinates remain uncertain or impossible to assess have been retained. These plots are usually closed-canopy deciduous stands. By excluding them from the analysis, there is a risk of overestimating the model performance. Conversely, by including them, it is possible to obtain models that are slightly biased, but whose performance will be rather underestimated.

The forestry statistics for the selected plots are presented below.

<table><thead><tr><th></th><th>G.m2ha</th><th>VMRD.m3ha</th><th>D.cm</th></tr></thead><tbody><tr><td>Min.</td><td>0.6637</td><td>2.805</td><td>13.00</td></tr><tr><td>1st Qu.:</td><td>15.8376</td><td>137.190</td><td>21.51</td></tr><tr><td>Median:</td><td>28.0898</td><td>307.646</td><td>27.71</td></tr><tr><td>Mean</td><td>31.7360</td><td>347.342</td><td>28.56</td></tr><tr><td>3rd Qu.:</td><td>48.1017</td><td>528.199</td><td>32.31</td></tr><tr><td>Max.</td><td>93.1364</td><td>1013.677</td><td>68.14</td></tr><tr><td>DDOM</td><td>N.ha</td><td></td><td></td></tr><tr><td>Min.</td><td>13.00</td><td>20.0</td><td></td></tr><tr><td>1st Qu.:</td><td>32.90</td><td>170.0</td><td></td></tr><tr><td>Median:</td><td>43.00</td><td>400.0</td><td></td></tr><tr><td>Mean</td><td>41.67</td><td>435.2</td><td></td></tr><tr><td>3rd Qu.:</td><td>53.20</td><td>610.0</td><td></td></tr><tr><td>Max.</td><td>76.40</td><td>1170.0</td><td></td></tr></tbody></table>

The number of vegetation periods between the LiDAR flight and the field survey for the 85 plots selected is shown in the following figure.

with first day of flight

<figure><img src="image_16.png" /></figure>
The year and month for the first day of flight for the selected plots are presented below:

<table><thead><tr><th></th><th>03</th><th>04</th><th>08</th><th>09</th><th>10</th></tr></thead><tbody><tr><td>2019</td><td>0</td><td>0</td><td>18</td><td>27</td><td>11</td></tr><tr><td>2020</td><td>1</td><td>28</td><td>0</td><td>0</td><td>0</td></tr></tbody></table>

# Global models

## Calibration

When included in the variables (trials not shown), the mixture variable is always selected in the models, showing that the information about species composition is valuable to increase estimation precision. Unfortunately, the mixture layer does not fully covers the forest extent. So alternative models are built without this variable. It noteworthy that such information would help improve estimations. The *NDVI* slightly improves the models for basal area and volume, but does not improve the bias dependency on mixture (see next section). This variable is not included in the final models.

The following figures show the values measured in the field compared with the values estimated by the LiDAR model. In the case of a perfect model, all values would be aligned on the diagonal. The root mean square error is 11 m²/ha for basal area, 129 m³/ha for volume, 6.1 cm for mean diameter, 6.9 cm for dominant diameter and 180 /ha for stem density.

Dashed lines are the 95% confidence interval of the prediction error associated to each fitted value.

<figure><img src="image_17.png" /></figure>

<figure><img src="image_18.png" /></figure>

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

The selected estimation models are presented below (accuracy statistics are computed in leave-one-out cross validation):

* metrics: LiDAR statistics used in the model,

* R2_prcent : R² value obtained (percentage of variability explained by the model),

* RMSE : root mean square error (same unit as variable),

* CVRMSE : coefficient of variation of the RMSE (RMSE divided by the mean value of the variable, expressed in percent).

<table><thead><tr><th>variable</th><th>metrics</th><th>R2_prcent</th><th>RMSE</th><th>CVRMSE_prcent</th></tr></thead><tbody><tr><td>G.m2ha</td><td>mCH + TreeInf10_density + TreeCanopy_cover_in plot + altitude + expoNS</td><td>74</td><td>11.0</td><td>35</td></tr><tr><td>VMRD.m3ha</td><td>p_hmin + Tree_meanH + Tree_meanCrownSurface + expoNS</td><td>77</td><td>128.5</td><td>37</td></tr></tbody></table>
<table><thead><tr><th>variable</th><th>metrics</th><th>R2_PrCent</th><th>RMSE</th><th>CVRMSE_PrCent</th></tr></thead><tbody><tr><td>D.cm</td><td>pzabove2 + zq5 + Tree_meanH + TreeCanopyCover_in Plot + altitude</td><td>67</td><td>6.1</td><td>21</td></tr><tr><td>DDOM</td><td>zq5 + zq95 + Tree_giniH + altitude + slope_gr + expoNS</td><td>80</td><td>6.9</td><td>17</td></tr><tr><td>N.ha</td><td>zsd + pzabovezmean + Tree_sdH + TreeInf10_density + TreeCanopyCover_in Plot</td><td>61</td><td>182.3</td><td>42</td></tr></tbody></table>

## Residuals check

The error ($r_i = y_i - \hat{y}_i$) is difference between the field measured value $y_i$ and the value estimated by the model $\hat{y}_i$ on plot i. Errors (or residuals) of the models should be checked for dependencies with other variables, in order to avoid local biases during mapping. In particular, we evaluate the relationship between residuals and variables such as:

* the number of vegetation periods between the flight and the inventory (positive values: inventory occurred after the flight, negative values: inventory was performed before the flight),

* year of flight,

* month of flight (presence or absence of leaves),

* stand dendrometric parameters,

* mixture.

The link with altitude is not tested as this variable is already included in the estimation models if relevant.

When checking the link between residuals and the number of vegetation periods, one could expect:

* when field inventory are performed before the flight (negative values of vegetation periods):

* some large positive errors on harvested plots (trees inventoried but cut before the flight),

* many small negative errors on harvested plots (tree growth),

* when field inventory is performed after the flight (negative values of vegetation periods):

* some large negative errors (trees in the LiDAR but cut before the inventory),

* many small positive errors (tree growth).

When checking for the link between the absolute value of residuals with the absolute value of vegetation periods, one could expect a positive relationship.

In turns out that the slope of a linear regression of residuals against the number of vegetation periods is hardly significant, showing that the effect is small compared to other sources of errors.

<figure><img src="image_22.png" /></figure>

<figure><img src="image_23.png" /></figure>

<figure><img src="image_24.png" /></figure>

<figure><img src="image_25.png" /></figure>

<figure><img src="image_26.png" /></figure>

<figure><img src="image_27.png" /></figure>

<figure><img src="image_28.png" /></figure>

<figure><img src="image_29.png" /></figure>

<figure><img src="image_30.png" /></figure>

<figure><img src="image_31.png" /></figure>

Estimation errors do not seem to be influenced by year or month of flight. The graphs below show the distribution of errors according to year (first line) and month (second line) of flight. Statistical tests of comparison of means are not significant (values are displayed in the tiles of graphs).
<figure><img src="image_32.png" /></figure>

Graphs below display the link between the errors and the degree of mixture. It seems that coniferous stands have slightly underestimated values whereas broadleaved stands have slightly overestimated values, although the slope is not significantly different from 0.

<figure><img src="image_33.png" /></figure>

The error at the plot level is relatively high, which can be explained by several factors.

* The error is probably slightly overestimated because plots are not perfectly coregistrated, and the effects of time lag have not been corrected (growth, cut trees).

* Edge effects add noise to the models: for example, if a trunk is just outside the plot, it is not inventoried in the NFI, but part of its crown may extend over the plot and be part of the LiDAR point cloud. This generally induces a smoothing effect with the neighborhood, i.e. an overestimation of small values and an underestimation of large values, whatever the forest parameter.

* The fact that small stems are only inventoried in the 200 m² disc means that values measured in the field can be poorly extrapolated for the 500 m² zone (the one used for modelling), when their distribution is not homogeneous over the 500 m² disc.

With regard to the usefulness of the models, one should consider that:

* models account for much of the variability in forest parameters,

* when results are aggregated over larger areas, local errors tend to compensate each other, even if this cannot be quantified. Indeed estimation errors are linked to forest structure and LiDAR acquisition parameters, thus they are spatially correlated.

## Stratified models

If one considers that LiDAR flights from 2019 and 2020 are different, it might be relevant to calibrate separate models for the areas covered in each year.

The statistics obtained by combining the estimation models by year are presented below. Performance is slightly improved compared to the global models, however the number of plots used to calibrate each model is rather small (approx. 40). Compared to global models, the year-specific models:

* should better take into account the heterogeneity of year-specific flights,

* might be less able to account for other sources of heterogeneity (forest structure) because the number of reference plots used to calibrate each model is quite low.

Global models will thus be preferred to produce the maps.

<table><thead><tr><td>variable</td><td>R2_PrCent</td><td>RMSE</td><td>CVRMSE_PrCent</td></tr></thead><tbody><tr><td>G.m2ha</td><td>77</td><td>10.2</td><td>32</td></tr></tbody></table>
<table><thead><tr><th>variable</th><th>R2_PrCent</th><th>RMSE</th><th>CVRMSE_PrCent</th></tr></thead><tbody><tr><td>VMRD.m3ha</td><td>80</td><td>119.8</td><td>34</td></tr><tr><td>D.cm</td><td>75</td><td>5.3</td><td>18</td></tr><tr><td>DDOM</td><td>84</td><td>6.2</td><td>15</td></tr><tr><td>N.ha</td><td>56</td><td>195.4</td><td>45</td></tr></tbody></table>

<figure><img src="image_34.png" /></figure>

<figure><img src="image_35.png" /></figure>

<figure><img src="image_36.png" /></figure>

<figure><img src="image_37.png" /></figure>

<figure><img src="image_38.png" /></figure>

# Mapping

## Metrics check

The metrics selected in the global models are presented in the table below.

<table><thead><tr><th></th><th>G.m2ha</th><th>VMRD.m3ha</th><th>D.cm</th><th>DDOM</th><th>N.ha</th></tr></thead><tbody><tr><td>mCH</td><td>X</td><td></td><td></td><td></td><td></td></tr><tr><td>TreeInf10_density</td><td>X</td><td></td><td></td><td></td><td>X</td></tr><tr><td>TreeCanopy_cover_in_plot</td><td>X</td><td></td><td>X</td><td></td><td>X</td></tr><tr><td>altitude</td><td>X</td><td></td><td>X</td><td>X</td><td></td></tr><tr><td>expoNS</td><td>X</td><td>X</td><td></td><td>X</td><td></td></tr><tr><td>p_hmin</td><td></td><td>X</td><td></td><td></td><td></td></tr><tr><td>Tree_meanH</td><td></td><td>X</td><td>X</td><td></td><td></td></tr><tr><td>Tree_meanCrownSurface</td><td></td><td>X</td><td></td><td></td><td></td></tr><tr><td>pabove2</td><td></td><td></td><td>X</td><td></td><td></td></tr><tr><td>zq5</td><td></td><td></td><td>X</td><td>X</td><td></td></tr></tbody></table>
<table><thead><tr><th></th><th>G.m2ha</th><th>VMRD.m3ha</th><th>D.cm</th><th>DDOM</th><th>N.ha</th></tr></thead><tbody><tr><td>zq95</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>Tree_giniH</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>slope_gr</td><td></td><td></td><td></td><td>X</td><td></td></tr><tr><td>zsd</td><td></td><td></td><td></td><td></td><td>X</td></tr><tr><td>pabovezmean</td><td></td><td></td><td></td><td></td><td>X</td></tr><tr><td>Tree_sdH</td><td></td><td></td><td></td><td></td><td>X</td></tr></tbody></table>

Some of the statistics extracted from LiDAR data may depend on the acquisition configuration (LiDAR hardware, flight parameters such as height and speed), or even the classification strategy. A visual inspection of the maps of these metrics is carried out to ensure that they display no apparent variability other than that linked to forest structure. In particular, it turns out that variables linked with the maximum height of the point cloud (quantiles close to 100, height of detected trees) exhibit too large values in steep terrains. It is due to the fact that vegetation height might be overestimated in such terrains, especially when branches hang over cliffs.

## Forest mask

Global models calibrated from LFI data are applied to each pixel of the metric map calculated at 22.4 m resolution to produce forest parameter maps. Outliers may occur due to extreme values in the LiDAR data, in cases where the model is extrapolating outside its calibration range. The maps are therefore thresholded to ensure that the values remain within the range of the values observed on the field plots (below).

Values are predicted at every point on the territory, and the forest mask defined by the "Forest_Extent_Map.shp" layer is applied to remove values outside of forest areas. Two methods are tested to handle pixels lying on the border of the forest polygons.

Method 1 "pixel center":

* pixels whose center is outside the mask have their values set to "missing data",

* pixels with missing values whose center is inside the mask have their values set to 0.

Method 2 "pixel proportion":

* pixels not touching the forest mask have their values set to "missing data",

* pixels with missing values that touch one or more polygons have their values set to 0.

* a layer is added, containing the percentage of the cell surface covered by polygons. The 0 values are replaced by "missing data".

In both cases, there are edge effects.

* Method 1: the total forest area is respected, but in the edge zones there may be a slight underestimation of the wood stock, because when the center of the pixel is in the mask, the counted pixel partly covers a non-forested zone, whereas when the center is outside the mask, the wooded part is not counted.

* Method 2: the total forest area is not respected, unless the pixel area is weighted by the cover proportion. It is not trivial to know how to integrate the case of pixels on edges (percentage value different from 100) into the calculations. For example, the stock value of a pixel should be entirely assigned to the wooded part if the edge is with a field. This is not the case if the pixel also contains a small group of trees that is not part of forest mask.

These effects do exist, mainly in areas of high forest fragmentation, but it is difficult to quantify them precisely. One solution would be to apply the mask directly to the LiDAR point cloud, but the tools are not designed to do this.

The maps for modality 1 are shown below.

## Map production

The maximum value measured on LFI plots used for calibration is shown in the table before the maps.

<table><thead><tr><th></th><th>x</th></tr></thead><tbody><tr><td>G.m2ha</td><td>93.1</td></tr><tr><td>VMRD.m3ha</td><td>1010.0</td></tr><tr><td>D.cm</td><td>68.1</td></tr><tr><td>DDOM</td><td>76.4</td></tr><tr><td>N.ha</td><td>1170.0</td></tr></tbody></table>
G.m2ha

<figure><img src="image_39.png" /></figure>

VMRD.m3ha

<figure><img src="image_40.png" /></figure>

D.cm

<figure><img src="image_41.png" /></figure>

DDOM

<figure><img src="image_42.png" /></figure>

N.ha

<figure><img src="image_43.png" /></figure>

Comparison of map and field distributions of values

The following histograms compare the distribution of values from :

* most recent LFI plots which extents intersect the forest mask (their center is not necessarily inside). Plots with no inventoried trees have their forest parameter values set to 0.

* map values (touched pixels).
The mean values are very close, but LFI plots tend to have more spread values. The title of the graph displays the mean value for the map (blue vertical line on the graph), followed by the 95% confidence interval for the mean based on field data (white vertical lines on the graph).

In the case of heterogeneous forests, two sources of error could explain this trend:

* Small trees are surveyed on a smaller circle than large trees, which may lead to their number on the whole plot being under- or over-estimated in field measurements.

* LiDAR estimates may take into account part of the crown of trees in the neighboring pixel, leading to smoother values.

Morover, due to the diameter census threshold of 12 cm, plots with smaller trees have forest parameters set to 0, whereas the LiDAR models might estimate non-zero values as vegetation is present in the point clouds.

On should bear in mind the fact that the reference forest area is not necessarily the same between forest mask applied to the LiDAR map and the map used for sampling the LFI plots.

### G.m2ha

<figure><img src="image_44.png" /></figure>

Map: 24.2 (LFI: 21.2-30.3)

### VMRD.m3ha

<figure><img src="image_45.png" /></figure>

Map: 265 (LFI: 228-337)

### D.cm

<figure><img src="image_46.png" /></figure>

Map: 24.8 (LFI: 19.8-25.7)

### DDOM

<figure><img src="image_47.png" /></figure>

Map: 36.2 (LFI: 29.1-37.7)

### N.ha

<figure><img src="image_48.png" /></figure>

Map: 328 (LFI: 291-416)
# Statistics by management area

## Method

For each administrative entity, the average value of volume per hectare and basal area per hectare is calculated, on the one hand from the LFI data, and on the other from LiDAR mapping. Each pixel is attributed to the polygon which contains its center.

From *n* LFI plots contained in an area of interest, we use the following formula to calculate the estimate of the mean *M* and the error *E* corresponding to the interval [*M* − *E*, *M* + *E*] with a 95% chance of containing the true value.

$$ \bullet M_{LFI} = \frac{1}{n} \sum_{i=1}^{n} y_i $$

$$ \bullet E_{LFI} = t(0.975, n - 1) \times \frac{\sigma_y}{\sqrt{n}} $$

with *t*(0.975, *n* − 1) the 0.975 quantile of a Student distribution with *n* − 1 degrees of freedom and *σ*<sub>y</sub> the standard deviation of the *n* LFI values.

From the *N* LiDAR estimates contained in this same area, we calculate the simple regression estimate (SRE) by averaging the LiDAR estimates ŷ<sub>j</sub> contained in each entity.

$$ \bullet M_{SRE} = \frac{1}{N} \sum_{j=1}^{N} \hat{y}_j $$

LiDAR estimates are an indirect but exhaustive measure of the study area, while the LFI plots are a direct but partial measure. The uncertainty of the LFI estimate is linked to sampling, whereas the uncertainty of the LiDAR estimate is due to model error. The model may be biased for all or part of the study area because the calibration data is not necessarily representative of all forest stands. LiDAR estimates are therefore corrected by stratum to take into account the average error (bias) observed in the LFI plots contained in each administrative entity. This is the GREG (Generalized Regression Estimator) estimate.

$$ \bullet M_{GREG} = M_{SRE} - \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i) $$

$$ \bullet \text{the associated error is } E_{GREG} = t(0.975, n - 1) \times \frac{\sigma_r}{\sqrt{n}} $$

with *σ*<sub>r</sub> the standard deviation of the *n* prediction residuals on the LFI plots

The bias and *σ*<sub>r</sub> for each entity may be poorly estimated, if the number of field plots is not large enough (i.e. smaller than 15), leading to a wrong bias correction in the *GREG* estimator. Besides, due to their own sampling strategy it is not certain that LFI plots are representative of woodland areas. In the case of administrative entities with less than 10 LFI plots, the *LFI* and *GREG* estimates of the mean and the associated errors may be badly estimated. The *SRE* estimator may be preferred in those cases.

## Results

In this section, the barplots display:

* as a green bar the *SRE* value, bar width is proportional to the forest area (number of pixels),

* as a dark green square and whiskers the *GREG* mean and its 95% confidence interval,

* as a red square and whiskers the *LFI* mean and its 95% confidence interval.

### Kanton

## [1] "Volume (m3/ha)"

<table><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Uri</td><td>283 ± 54</td><td>294 ± 23</td><td>294</td><td>103</td></tr></tbody></table>

## [1] "Basal area (m2/ha)"

<table><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Uri</td><td>25.7 ± 4.6</td><td>27.1 ± 1.9</td><td>26.9</td><td>103</td></tr></tbody></table>
<figure><img src="image_49.png" /></figure>

Districts

## [1] "Volume (m3/ha)"

<table><thead><tr><td>Name</td><td>LFI</td><td>GREG</td><td>SRE</td><td>n</td></tr></thead><tbody><tr><td>Forstkreis 1</td><td>362 ± 116</td><td>381 ± 58</td><td>397</td><td>27</td></tr><tr><td>Forstkreis 2</td><td>331 ± 100</td><td>325 ± 41</td><td>311</td><td>31</td></tr><tr><td>Forstkreis 3</td><td>202 ± 77</td><td>229 ± 31</td><td>228</td><td>45</td></tr></tbody></table>

## [1] "Basal area (m2/ha)"

<table><thead><tr><td>Name</td><td>LFI</td><td>GREG</td><td>SRE</td><td>n</td></tr></thead><tbody><tr><td>Forstkreis 1</td><td>33.4 ± 9.8</td><td>33.7 ± 5.4</td><td>35.4</td><td>27</td></tr><tr><td>Forstkreis 2</td><td>29.6 ± 8</td><td>29 ± 3.5</td><td>28.3</td><td>31</td></tr><tr><td>Forstkreis 3</td><td>18.4 ± 6.5</td><td>22.5 ± 2.3</td><td>21.5</td><td>45</td></tr></tbody></table>
## Volume

<figure><img src="image_50.png" /></figure>

## Basal area

<figure><img src="image_51.png" /></figure>

## Management areas

For management areas the number of LFI plots for some entities is quite small, making the LFI and GREG estimates less reliable.

### [1] "Volume (m3/ha)"

<table><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Erstfeld</td><td>187 ± 114</td><td>296 ± 87</td><td>269</td><td>10</td></tr><tr><td>Altdorf/Flüelen/Sisikon</td><td>351 ± 214</td><td>363 ± 107</td><td>391</td><td>12</td></tr><tr><td>Spiringen/Unterschächen</td><td>322 ± 146</td><td>319 ± 56</td><td>274</td><td>12</td></tr><tr><td>Silenen</td><td>199 ± 142</td><td>319 ± 74</td><td>283</td><td>15</td></tr><tr><td>Seelisberg</td><td>541 ± 2937</td><td>330 ± 834</td><td>436</td><td>2</td></tr><tr><td>Uri Süd</td><td>204 ± 98</td><td>190 ± 30</td><td>207</td><td>30</td></tr><tr><td>Isenthal</td><td>272 ± 215</td><td>473 ± 163</td><td>420</td><td>6</td></tr><tr><td>Seedorf/Bauen/Attinghausen</td><td>405 ± 277</td><td>342 ± 101</td><td>370</td><td>7</td></tr><tr><td>Schattdorf/Bürglen</td><td>502 ± 266</td><td>368 ± 91</td><td>410</td><td>9</td></tr></tbody></table>

### [1] "Basal area (m2/ha)"

<table><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Erstfeld</td><td>18.3 ± 9.6</td><td>26.6 ± 7</td><td>25.5</td><td>10</td></tr><tr><td>Altdorf/Flüelen/Sisikon</td><td>32.6 ± 18.3</td><td>30.8 ± 9.5</td><td>34.1</td><td>12</td></tr><tr><td>Spiringen/Unterschächen</td><td>31.3 ± 12.1</td><td>26.7 ± 5.7</td><td>25.3</td><td>12</td></tr><tr><td>Silenen</td><td>18.5 ± 12.1</td><td>30.5 ± 6.5</td><td>26.1</td><td>15</td></tr><tr><td>Seelisberg</td><td>55.9 ± 275.5</td><td>25.4 ± 67.3</td><td>37.7</td><td>2</td></tr><tr><td>Uri Süd</td><td>18.4 ± 8.2</td><td>18.9 ± 1.2</td><td>19.6</td><td>30</td></tr><tr><td>Isenthal</td><td>24.6 ± 15.7</td><td>43.6 ± 14.9</td><td>38.9</td><td>6</td></tr><tr><td>Seedorf/Bauen/Attinghausen</td><td>35.8 ± 21</td><td>31.7 ± 10.2</td><td>33.2</td><td>7</td></tr><tr><td>Schattdorf/Bürglen</td><td>40 ± 21.6</td><td>34.8 ± 8.2</td><td>35.5</td><td>9</td></tr></tbody></table>
<figure><img src="image_52.png" /></figure>

<figure><img src="image_53.png" /></figure>

## Municipalities

For municipalities the number of LFI plots for is small, *LFI* and *GREG* estimates are not reliable. The figure is not displayed because of the very large error whiskers.

## [1] "Volume (m3/ha)"

<table><thead><tr><td>Name</td><td>LFI</td><td>GREG</td><td>SRE</td><td>n</td></tr></thead><tbody><tr><td>Erstfeld</td><td>187 ± 114</td><td>296 ± 87</td><td>269</td><td>10</td></tr><tr><td>Silenen</td><td>199 ± 142</td><td>319 ± 74</td><td>283</td><td>15</td></tr><tr><td>Andermatt</td><td>9 ± 115</td><td>43 ± 38</td><td>46</td><td>2</td></tr><tr><td>Schattdorf</td><td>621 ± 2603</td><td>421 ± 621</td><td>344</td><td>2</td></tr><tr><td>Seelisberg</td><td>541 ± 2937</td><td>330 ± 834</td><td>436</td><td>2</td></tr></tbody></table>
<table><caption>## [1] "Basal area (m2/ha)"</caption><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Altdorf</td><td>684 ± 987</td><td>229 ± 667</td><td>438</td><td>3</td></tr><tr><td>Attinghausen</td><td>442 ± 902</td><td>290 ± 325</td><td>325</td><td>3</td></tr><tr><td>Flüelen</td><td>271 ± 128</td><td>449 ± 271</td><td>388</td><td>3</td></tr><tr><td>Hospental</td><td>48 ± 208</td><td>29 ± 14</td><td>32</td><td>3</td></tr><tr><td>Realp</td><td>4 ± 18</td><td>35 ± 5</td><td>36</td><td>3</td></tr><tr><td>Göschenen</td><td>153 ± 486</td><td>183 ± 10</td><td>186</td><td>4</td></tr><tr><td>Seedorf</td><td>378 ± 475</td><td>388 ± 177</td><td>411</td><td>4</td></tr><tr><td>Unterschächen</td><td>346 ± 295</td><td>385 ± 135</td><td>301</td><td>5</td></tr><tr><td>Isenthal</td><td>272 ± 215</td><td>473 ± 163</td><td>420</td><td>6</td></tr><tr><td>Sisikon</td><td>225 ± 326</td><td>387 ± 42</td><td>369</td><td>6</td></tr><tr><td>Bürglen</td><td>467 ± 345</td><td>377 ± 101</td><td>452</td><td>7</td></tr><tr><td>Spiringen</td><td>304 ± 222</td><td>268 ± 58</td><td>251</td><td>7</td></tr><tr><td>Gurtnellen</td><td>293 ± 234</td><td>285 ± 50</td><td>293</td><td>9</td></tr><tr><td>Wassen</td><td>298 ± 201</td><td>172 ± 104</td><td>215</td><td>9</td></tr></tbody></table>

<table><thead><tr><th>Name</th><th>LFI</th><th>GREG</th><th>SRE</th><th>n</th></tr></thead><tbody><tr><td>Erstfeld</td><td>18.3 ± 9.6</td><td>26.6 ± 7</td><td>25.5</td><td>10</td></tr><tr><td>Silenen</td><td>18.5 ± 12.1</td><td>30.5 ± 6.5</td><td>26.1</td><td>15</td></tr><tr><td>Andermatt</td><td>1.2 ± 15.7</td><td>6.5 ± 2.5</td><td>6.7</td><td>2</td></tr><tr><td>Schattdorf</td><td>49.6 ± 127.8</td><td>31.7 ± 71.1</td><td>30.4</td><td>2</td></tr><tr><td>Seelisberg</td><td>55.9 ± 275.5</td><td>25.4 ± 67.3</td><td>37.7</td><td>2</td></tr><tr><td>Altdorf</td><td>61 ± 82.1</td><td>16.2 ± 49.7</td><td>37.9</td><td>3</td></tr><tr><td>Attinghausen</td><td>36.4 ± 53.1</td><td>32.1 ± 3.3</td><td>30.4</td><td>3</td></tr><tr><td>Flüelen</td><td>29.3 ± 21.2</td><td>37.6 ± 29</td><td>34.3</td><td>3</td></tr><tr><td>Hospental</td><td>6.5 ± 27.9</td><td>5.8 ± 3.1</td><td>5.0</td><td>3</td></tr><tr><td>Realp</td><td>0.8 ± 3.3</td><td>6 ± 1.5</td><td>5.6</td><td>3</td></tr><tr><td>Göschenen</td><td>13.5 ± 43</td><td>18 ± 0.9</td><td>18.3</td><td>4</td></tr><tr><td>Seedorf</td><td>35.4 ± 43</td><td>31.9 ± 23.9</td><td>35.8</td><td>4</td></tr><tr><td>Unterschächen</td><td>34.1 ± 20.1</td><td>33.6 ± 12.1</td><td>26.6</td><td>5</td></tr><tr><td>Isenthal</td><td>24.6 ± 15.7</td><td>43.6 ± 14.9</td><td>38.9</td><td>6</td></tr><tr><td>Sisikon</td><td>20.1 ± 27.5</td><td>34.6 ± 3.1</td><td>31.8</td><td>6</td></tr><tr><td>Bürglen</td><td>37.3 ± 29</td><td>37.6 ± 10.9</td><td>38.8</td><td>7</td></tr><tr><td>Spiringen</td><td>29.4 ± 20.4</td><td>21.6 ± 6.1</td><td>24.1</td><td>7</td></tr><tr><td>Gurtnellen</td><td>25.9 ± 18</td><td>25 ± 2.4</td><td>25.4</td><td>9</td></tr><tr><td>Wassen</td><td>26.7 ± 17.2</td><td>19.3 ± 3.9</td><td>21.3</td><td>9</td></tr></tbody></table>