Detecting the presence of standing dead trees using airborne laser scanning and optical data

ABSTRACT Deadwood is an important indicator of biodiversity in forest ecosystems. Identifying areas with large density of standing dead trees through field inventory is challenging, and remotely sensed data can provide a more systematic approach. In this study, we used metrics derived from airborne laser scanning (ALS) data (7.1 points m−2) and vegetation indices from optical images (HySpex sensor VNIR-1800: 0.3 m, SWIR-384: 0.7 m) to predict the presence of standing dead trees over a 15.9 km2 managed forest in Southern Norway. The dead basal area (DBA) of 40 sample plots was computed and used to classify the plots into presence/absence of standing dead trees. An area-based approach (ABA) using logistic regression was initially tested, but due to limited ground reference information, no statistically significant models could be formulated. A tree-based approach (TBA) was used to overcome this limitation. It identified trees on the ALS point cloud with a local maxima function and used a vegetation index to determine if the trees were dead. Between 18% and 42% of the predicted area with standing dead trees intersected a field recorded validation dataset. The TBA provided a good alternative to area-based regression models in the context of few standing dead trees.


Introduction
Despite the widespread recognition of the critical significance of forest ecosystem services to human well-being and economic prosperity, services that do not have a direct monetary value are often undervalued in decision-making by governments, the private sector, and civil society (Costanza et al. 2017). This has led to the degradation of ecosystem condition and the loss in biodiversity, threatening the capacity of ecosystems to deliver services (IPBES 2019). In Fennoscandian forests, very few forests unaffected by human activity remain after centuries of forest exploitation (Gjerde et al. 2007). Thus, managed forests are important habitats for many species and play a central role in the management and preservation of biodiversity (Hansson 2001;Lindenmayer and Franklin 2002;Gjerde et al. 2004).
Deadwood serves as a significant structural element of forest ecosystems (Harmon et al. 1986;Franklin et al. 1987;Hansen et al. 1991;Siitonen 2001;Kuuluvainen 2002;Lonsdale et al. 2008). It provides a long-term source of organic matter and nutrients, increases site productivity, contributes to carbon sequestration, and controls soil erosion (Harmon et al. 1986;Franklin et al. 1987;Lonsdale et al. 2008). Many saproxylic species of fungi and insects, but also of plants, birds and mammals that depend on decaying and dead trees for habitat, are rare and/or threatened (Harmon et al. 1986;Esseen et al. 1997;Siitonen 2001;Stokland et al. 2012). The communities of saproxylic species vary depending on the type of deadwood, such as logs, snags, or stumps (Harmon et al. 1986). Although downed logs accommodate a larger diversity of fungi and epixylic bryophyte species, snags are important habitats for lichens, insects such as ants, pollinators and flies, and cavitynesting birds (Lõhmus and Lõhmus 2001;Humphrey et al. 2002;Laudenslayer 2002;Heilmann-Clausen and Christensen 2003;Dufour-Pelletier et al. 2020). Standing dead trees offer a range of microenvironments over a vertical gradient with different insulation, temperature, water content and aeration (Humphrey et al. 2004). The presence of standing dead trees is therefore a key ecological factor in forest ecosystems and can serve as an indicator for biodiversity monitoring (Humphrey et al. 2004;Stokland et al. 2004;Lassauce et al. 2011).
In Norway, forest owners have adopted a habitat inventory approach called Complementarity Hotspot Inventory (CHI) (Baumann et al. 2002a;Gjerde et al. 2007). The main goal of the CHI approach is to improve the knowledge base and management of biological diversity in forests by registering habitats presenting specific qualities associated with high biodiversity and considered vulnerable to impact from forest operations. In presence of key habitats such as standing dead trees, large density of snags are delineated, and the number of deciduous and coniferous snags together with their dimension and decaying stage are recorded (Baumann et al. 2002b). The information is subsequently used to define thresholds to guide the delineation of deadwood key habitats.
Remote sensing has the potential to provide a more systematic approach in the identification of areas with deadwood. A map of presence/absence of standing dead trees could provide a valuable tool in the context of CHI to more effectively allocate resources and time related to field inventory of standing deadwood key habitats.
Optical remotely sensed data, such as aerial photographs, have been used in forest management for decades to visually delineate stands, identify dominant tree species, and estimate stand volume, tree height and density. Wavelengths in the near-infrared (NIR) and shortwave infrared (SWIR) parts of the spectrum are more sensitive to chlorophyll and water content in the vegetation, respectively, and are therefore useful to discriminate between living and dead trees. Pasher and King (2009) used color infra-red (CIR) images at 0.2 m resolution to detect deadwood through a direct method combining unsupervised clustering, linear spectral unmixing and object-based segmentation and classification, and through regression-based modeling using spectral, spatial, and object-based image information. They obtained 90% accuracy on validation sites with the direct method, but no satisfactory results with the regression-based method. Adamczyk and Osberger (2015) calculated a variety of vegetation indices to identify different classes of forest disturbance, as well as the presence of deadwood, and concluded that deadwood was better assessed with vegetation indices using NIR and blue bands. Hyperspectral data were used to assess different levels of tree mortality caused by insect invasion (Lausch et al. 2013;Fassnacht et al. 2014). Although advanced mortality stages were more easily identified, confusion occurred between deadwood and background soil (Fassnacht et al. 2014). The misclassification problem associated with deadwood and bare ground classification was addressed by Zielewska-Büttner et al. (2020) by complementing random forest models with a "deadwooduncertainty" filter to quantify the deadwood probability from the neighborhood environmental and spectral conditions. Over the past few years, the utilization of deep learning and neural network techniques has increased for the classification of trees in varying stages of decay using images captured by unmanned aerial vehicles (Jiang et al. 2019;Deng et al. 2020). Thus, optical remotely sensed data provide valuable information about the reflectance of the trees and their condition as well as height information in case of photogrammetric point clouds (Gobakken et al. 2015).
Airborne laser scanning (ALS) data provide three-dimensional characterizations of the forest in the form of point clouds (Campbell and Wynne 2011). The analysis can be done following an area-based approach (ABA), by means of models dependent on ALS-derived metrics related to height and density of the canopy (Naesset 2002), or following a tree-based approach (TBA) (Morsdorf et al. 2003;Maltamo et al. 2004). The ABA is commonly used in operational management inventories to estimate forest attributes such as heights and volume at stand level (Magnussen and Boudewyn 1998;Naesset 2004). ABA have been used in conservation areas and in managed forests with large density of snags to estimate downed dead trees (Pesonen et al. 2008;Joyce et al. 2019) and standing dead trees (Pesonen et al. 2008;Bater et al. 2009;Kim et al. 2009;Martinuzzi et al. 2009). Using ALS data with a density of 4 points m −2 , Pesonen et al. (2008) concluded that the standard deviation of the first return heights adequately predicted the volume of downed dead trees (RMSE = 51.6%) but was less accurate to predict standing dead trees (RMSE = 78.8%). Bater et al. (2009) found that the distribution of standing dead trees was best predicted by the coefficient of variation of the ALS height data (r = 0.61, RMSE = 16.8%). Martinuzzi et al. (2009) combined canopy height and topographic metrics derived from ALS data to assess the presence of snags in regions with distinctive snag abundance. The classification accuracies ranged between 73% and 95% depending on the diameter at breast height (dbh) of the trees. Both studies were using ALS data with a density smaller than 1 point m −2 . Kim et al. (2009) used the intensity of ALS data, density of 6 points m −2 , to assess standing dead trees in Arizona, USA, and concluded that low intensity distribution peak frequency was a good predictor of standing dead trees. Poorer results were obtained in managed forests where the low occurrence of standing dead trees can even prevent the formulation of statistically significant models ). In such cases, the detection of standing dead trees could be performed following a TBA. With a TBA, individual trees can be located directly on ALS point clouds (Rahman et al. 2009;Li et al. 2012;Wing et al. 2015), ALS-based canopy height models (CHM) (Popescu and Wynne 2004;Solberg et al. 2006;Ene et al. 2012), or on high spatial resolution optical images (Wang et al. 2004). Wing et al. (2015) classified the ALS returns into dead or living trees based on their location, intensity, and three-dimensional neighborhood statistics, and identified individual snags using a local-maxima detection algorithm. They found that the canopy cover had a negative impact on the snag detection. Kamińska et al. (2018) performed a species-related single dead tree detection by combining intensity and structural variables from ALS data acquired under leaf-on and leaf-off conditions with spectral information derived from aerial imagery. They reached an overall accuracy of 90% using the three datasets, while the leaf-on ALS dataset alone was producing the lowest accuracies with an overall accuracy varying from 75 to 81%. The point density for both studies was around 6 points m −2 . The combination of optical and ALS data, by providing both spectral and structural information on the forest cover, was found to improve the prediction of forest canopy height (Hudak et al. 2002), tree species classification (Dalponte et al. 2012;Ørka et al. 2013;Vauhkonen et al. 2014) and deadwood (Pesonen et al. 2010).
Rare objects such as standing dead trees are not appropriately sampled using standard sampling inventory procedures based on field plot measurements due to their irregular and sparse distribution, especially in managed forests (Ducey et al. 2002). Although modified sampling procedures have been proposed to work around this limitation (Ducey et al. 2002;Kenning et al. 2005), they are seldom implemented because they often are more difficult to implement and time consuming to perform. To the authors' knowledge, no studies have yet assessed the feasibility of detecting standing dead trees in managed forests using remotely sensed data and standard field plot measurements. This study aimed to evaluate the potential of ALS and optical data in combination with plot measurements from standard sampling inventory procedures to detect standing dead trees in a managed forest in Norway. More specifically, the study objectives were: . to detect the presence of standing dead trees following an ABA using ALS-derived metrics and optical image-based vegetation indices; . to detect the presence of standing dead trees following a TBA using ALS data for tree identification and an optical image-based vegetation index to discriminate between dead and living trees.

Study area
The study was conducted in a managed forest in the municipality of Gjøvik (60°55 ′ N, 10°34 ′ E), Innlandet County, approximately 100 km north of Oslo, Norway ( Figure 1). The study area covers 15.9 km 2 and is located in a hilly terrain with elevation varying between 300 and 600 m above sea level. The area is characterized by a mosaic of forest stands in different development stages in a boreal forest dominated by Norway spruce (Picea abies (L.) Karst.).

Ground reference data
Two types of ground reference data were used in the current study. While sample plots provided field data to build models and adjust parameters, a CHI-based field survey was used as a reference dataset to assess the performance of deadwood detection approaches.

Sample plot inventory
Ground reference data were collected during summer and fall 2018. Within the study area, stands in old and mature spruce forests were identified according to an existing forest management plan, and 40 circular plots of size 250 m 2 (8.92 m radius) were systematically distributed within these stands.
The center of the sample plots was positioned using a Topcon Legacy E + Global Navigation Satellite System (GNSS) receiver, recording every 2 s for approximately 30 min. The GNSS data were postprocessed using a permanent geodetic base station in Moelv, approximately 7 km east of the study area. The positioning errors reported were less than 5 cm. The dbh, species and status, i.e. dead or living, were recorded for all trees located within a horizontal distance of 8.92 m of the center of the plots and with a dbh greater than 4 cm. In this study however, only the trees with a dbh greater than 10 cm were considered and were denoted ground reference trees. The status of the dead trees was set to "dead" without distinction between standing dead trees in early stage of decay, broken trees, or snags. The species of the dead trees was not recorded. Furthermore, the height was measured on approximately 10 selected sample trees per plot with a Vertex hypsometer. Sample trees were selected using a conventional relascope sampling method (see Maltamo and Packalen 2014, p. 378). The height of 421 trees, including eight dead trees, were measured. Most of the plots were dominated by Norway spruce, while four plots had a mixed cover consisting of Norway spruce and deciduous trees, mainly birch (Betula pendula Roth and B. pubescens Ehrh.). Dead trees were observed in 30 plots and five dead trees with a dbh greater than 30 cm were found in four of the plots. A summary of the sample plot characteristics is presented in Table 1. The dead basal area (DBA) was calculated per plot, by summing the basal area of the dead trees sampled. Presence of standing dead trees in the sample plots was determined using different thresholds of the dead basal area (DBA) in m 2 ha −1 . The thresholds were the 95 th , 90 th , 85 th and 80 th percentiles of the DBA (DBAth_95, DBAth_90, DBAth_85 and DBAth_80) computed from the sample plots, corresponding to 8.46, 8.28, 6.82, 5.01 m 2 ha −1 , respectively.

CHI inventory
As part of a larger project on the identification of CHI habitats the study area was divided into three geographical sections: S1 on the western side of the study area (393 ha), S2 in the center (420 ha) and S3 on the eastern side (775 ha). Two experienced inventory companies, designated company A and company B, respectively, conducted a field survey and delineated areas between 0.2 and 3.9 ha in size where standing dead trees were found according to the practical CHI methodology adopted in Norway (Landbruksdirektoratet 2017). Company A has a long experience with vegetation mapping in general while company B has been mapping CHI habitats specifically. To comply with the CHI methodology, the delineated areas had to meet certain criteria, including a minimum size of 0.2 ha and a density of standing dead trees of 40 ha −1 for medium size dbh (≤ 30 cm) and 20 ha −1 for large size dbh (> 30 cm). Both companies did the field survey in S1, and company B also did the survey in S3. In S2, no field survey was conducted according to the CHI methodology. Company A delineated 13 polygons in S1 covering a total area of 9.4 ha, while company B had 38 polygons: 15 in S1 (12.5 ha) and 23 in S3 (20.7 ha). The overlap area between the two sets of polygons in S1 was 2.7 ha (14%). The CHI-based dataset A 1 B 1 combined the polygons from both companies in S1 (19.2 ha), while A 1 B 13 included in addition the polygons from company B in S3 (39.9 ha), corresponding to 16% and 11% of the area of old and mature forests for S1 and S3, respectively. Both A 1 B 1 and A 1 B 13 were used to assess the predictive performance of the deadwood detection approaches. Figure 1 shows the extent of the sections S1, S2 and S3, the CHI-based dataset A 1 B 13 and the sample plots.

Remotely sensed data
The data acquisition was performed on 5 th and 15 th of July, 2018, at approximately 17.30 and 15.30 (UTC +1), respectively, under similar weather conditions. Both ALS and hyperspectal sensors were mounted onboard a fixed-wing aircraft and were flown simultaneously at a maximum speed of 130 knots and at an altitude of approximately 900 m above ground level. The platform was equipped with an Inertial Motion Unit (Micro IRS IE-IPAS-uIRS) and a GNSS Topcon Legacy E.
The ALS data were acquired with a Leica ALS70-HP (Leica Geosystems, Heerbrugg, Switzerland) system, a discrete small-footprint laser scanner with a footprint diameter of approximately 20 cm using a Multiple Pulses in Air Technology and operating at a wavelength of 1064 nm, a pulse rate of two times 218.6 kHz and a scan angle of ±20°. It was flown with a side overlap of 44% and recorded up to four returns per pulse, resulting in an average point density of 7.1 points m −2 .
The ALS returns were classified as "ground", "unclassified" and "noise" by the contractor, Terratec AS. Terrain surface models were produced from the returns classified as ground, and the relative height of each return was calculated as the difference between the return height value and the terrain height. The ALS metrics were computed for each plot following the procedure described in Naesset (2004). Only the returns associated to the canopy (i.e. ≥ 2 m) were used to eliminate the effect of shrubs, stones, and other features on the ground (Naesset 1997). The ALS metrics, computed for first returns, included 14 height metrics: the 10 th , 20 th , … , 90 th percentiles (H 10 , H 20 , … , H 90 ), the mean (H mean ), standard deviation (H sd ), skewness (H skew ), kurtosis (H kurt ) and coefficient of variation (H cv ), and 10 density metrics calculated from the proportion of returns above 10 vertical layers to the total number of returns (D 0 , D 1 , … , D 9 ). The layers were of equal height, i.e. one-tenth of the height range between the 2 m threshold and the 95 th percentile (H 95 ). In addition, a canopy height model (CHM) was created with a spatial resolution of 0.3 m using Delaunay triangulation of first returns with a linear interpolation within each triangle.
The optical data were acquired with two hyperspectral HySpex sensors, VNIR-1800 and SWIR-384, operating in the visible and near-infrared (VNIR) and SWIR part of the electromagnetic spectrum, between 400 and 1000 nm, and 930 and 2500 nm, respectively. The VNIR images were composed of 186 spectral bands with a spatial resolution of 0.3 m, while the SWIR images had 288 bands and a resolution of 0.7 m.
The VNIR and SWIR images were mosaicked, and a relative radiometric normalization was applied to every band by performing a linear correction using the overlapping areas between two images. The SWIR mosaic was resampled to 0.3 m resolution and aligned on the VNIR mosaic. To eliminate the effect of background soil, the CHM was used to mask out the pixels corresponding to heights smaller than 2 m for both the VNIR and SWIR mosaics. A total of five vegetation indices (Table 2) were computed for their potential to discriminate between living and dead trees (Goodwin et al. 2008;Meddens et al. 2013;Adamczyk and Osberger 2015). Although the optical images used in this study were  hyperspectral, we computed vegetation indices from a selection of the hyperspectral bands to simulate multispectral images. Multispectral aerial images are commonly used in ordinary operational forest management inventory. The indices' description and formula were found on the Index Database (Henrich et al. 2012). As very little energy is stored in individual hyperspectral bands due to their narrow bandwidths, the indices were computed by averaging the reflectance values of three consecutive bands located at the center of each band, or bandwidth, constituting the indices. The indices' mean and standard deviation (sd) were calculated for every plot, for a total of ten variables based on vegetation indices. The stands of old and mature forests in the study area were tasseled into cells of 250 m 2 , i.e. the same area as the plots, for a total of 22 296 grid cells. The ALS metrics and the vegetation indices were computed for every grid cell.

Detection of standing dead trees
The detection of standing dead trees was carried out with both the ABA and the TBA. Figure 2 presents the workflow for the detection of standing dead trees with both approaches.

Area-based approach
The presence/absence of standing dead trees was predicted using GLM models with a binomial logit link function. Models were built for the four different thresholds of DBA, using ALS-derived metrics and variables derived from vegetation indices computed at plot level. From these models, the presence/absence of standing dead trees was predicted for the entire study area using the variables computed at grid-cell level.
The models were fitted on the 40 plots to calculate the accuracy metrics used for evaluating the models' performance. Accuracy metrics were derived directly from the models, such as the Akaike criterion (AIC), or calculated from the confusion matrices, like the area under the receiver operating characteristic curve (AUC-ROC), the area under the precision-recall curve (AUC-PR) and Cohen's kappa index. AIC is a measure of goodness of fit that favorizes models achieving high goodness-of-fit while using a minimum number of parameters. Smaller values are associated with better models. The AUC-ROC and the AUC-PR are threshold-independent metrics that calculate the area under the curve for, respectively, the plot of true positive rate versus false positive rate and the plot of precision versus recall. Because AUC-ROC integrates all the quadrants of the confusion matrix, it is sensitive to prevalence in presence/absence datasets (Sofaer et al. 2019). AUC-PR ignores the quadrant true negative and is therefore not affected by the prevalence, thus more appropriate for rare objects (Davis and Goadrich 2006). The values of AUC-ROC and AUC-PR vary between 0 and 1, with larger values associated with stronger relation between the predicted and observed values. The kappa index is a measure of agreement beyond randomness between two classifications, varying from slight (< 0.2) to nearly perfect (0.8-1) agreement (Landis and Koch 1977). It can be calculated from the observed sample matrix and from the estimated population matrix. The estimated population matrix represents the entire study area and can therefore compute unbiased statistics. It was calculated following the equation presented by Pontius and Millones (2011) (Eq. 1), where p ij is the estimated proportion of the study area that is classified as category (dead or living) i for the grid cells and category j for the reference plots, n ij is an entry in the observed sample matrix and N is the population total in number of pixels for every category i: In this study, we explored the use of prior knowledge regarding the expected density of standing dead trees for a specific area. Four different expected proportion of standing dead trees were tested, i.e. 0.05, 0.10, 0.15 and 0.20 of the old and mature forest stands area, by binarizing the predicted probabilities of standing dead trees into presence/absence using the percentile-based thresholds 95 th , 90 th , 85 th and 80 th , respectively.

Tree-based approach
A local maxima filter was applied on the relative heights of the ALS point cloud to identify trees. Window sizes from 1.5-2.0 m diameter were tested and the number of trees identified for each plot were compared to the number of trees measured in field. The NDVI value at the location of the trees was extracted, and based on preliminary visual assessment, trees with a NDVI value smaller than 0.5 were classified as dead. A diameter-height relationship was used to predict the dbh of the identified trees. A non-linear model was built from the measured heights and dbh of all the sample trees, including sample trees with dbh between 4 and 10 cm (421 observations), to predict the dbh of the identified trees from the height derived from the ALS data (Eq. 2), where c is the difference between the height (h) and breast height The subscripts correspond to the center wavelengths used to compute the indices.
(Eq. 3) and a and b are estimated parameters (Bi et al. 2012): The DBA of the identified dead trees was computed using Eq. 2 and was summarized for each grid cell. The grid cells were classified into presence/absence of standing dead trees when the DBA reached the DBA thresholds.

Area-based approach
Two methods were used to select the best model for each DBA threshold. The first method involved pre-selecting a set of variables using a stepwise selection procedure, followed by a best subset model selection using AIC (ABA AIC ). A maximum of three variables were chosen, and models with multicollinearity, i.e. with a variance inflation factor (VIF) greater than 5, were discarded. The second method aimed to select the model that best agreed with the CHIbased datasets (ABA ag , see section ("Validation")). For each DBA threshold, all possible combination of two variables derived from ALS data and from vegetation indices were modeled, for a total of 240 models per DBA threshold. The model achieving the best agreement with the CHI-based dataset while avoiding multicollinearity was selected.

Tree-based approach
The tree identification accuracy was assessed using the number of trees sampled at plot level. The classification as dead or living was validated with 200 identified trees randomly selected amongst eight classes of NDVI (< 0.2, 0.2-0.3, 0.3-0.4, 0.4-0.5, 0.5-0.6, 0.6-0.7, 0.7-0.8, > = 0.8) for a total of 25 trees per class, further denoted as reference trees. Using all aerial images available from the hyperspectral HySpex sensors and from web map services (www. norgeibilder.no), visual assessment of the trees' status (dead, living or unknown) and their exposure (exposed or in the shade of other trees) was performed.

Agreement with CHI-based dataset
The presence of standing dead trees from both the ABA and the TBA was validated against the CHI-based datasets A 1 B 1 and A 1 B 13 . The agreement was calculated as the proportion of area identified as standing dead trees intersecting the CHI-based datasets.

Area-based approach
There is an absence of relation between the accuracy metrics and the performance of the ABA models against the CHIbased datasets (Table 3). For example, for DBAth_90 the model based on NDVI mean and NDVI sd yielded the smallest values of AIC and the greatest values of AUC-ROC and kappa from both the observed sample matrix and the estimated population matrix. However, only a proportion of 0.22 and 0.13 of the predicted area agreed with the CHIbased datasets A 1 B 1 and A 1 B 13 , respectively, while the model based on H 90 and NDVI sd achieved the greatest proportion of agreement with A 1 B 1 (0.32) but yielded a larger AIC value and a small AUC-PR value. Concerning the thresholds of DBA, the proportion of agreement was larger with DBAth_95 and decreased towards DBAth_80.

Tree-based approach
Although the local maxima filter with a window size of 1.7 m had the smallest RMSE (339 trees ha −1 ), it underestimated the total density of trees by 106 trees ha −1 . Thus, a window size of 1.6 m (RMSE: 343 trees ha −1 , Pearson correlation coefficient: 0.51) was chosen to perform the analysis because it overestimated the total density of trees by just 46 trees ha −1 (Figure 3).
The dbh of the identified trees were predicted with the diameter-height model (Eq. 2) using the coefficients a = 0.533 and b = 0.054. Figure 4 suggests an overprediction of the model for small dbh and an underprediction for larger dbh with a saturation around 40 cm. In addition, the dbh of the spruce and pine trees was predicted with greater accuracy (RMSE: 6.24 cm, R 2 : 0.556) than for deciduous trees (RMSE: 7.09 cm, R 2 : 0.339), and for dead trees (RMSE: 7.03 cm, R 2 : 0.517).
Among the reference trees that could be visually determined, all living trees were classified correctly and only 6% of the dead trees (3 trees) where wrongly classified (Table 4). Table 5 displays the comparison between the performance of the TBA and the ABA. The TBA yielded greater agreement with both CHI-based datasets than ABA AIC across all DBA thresholds. Moreover, the TBA showed greater agreement with A 1 B 1 for the DBAth_90, DBAth_85 and DBAth_80, and a smaller agreement with A 1 B 13 than the ABA ag . In most cases, a larger proportion of agreement was observed for larger DBA thresholds, and with A 1 B 1 compared to A 1 B 13 .

Discussion
The identification and delineation of areas with a large density of standing dead trees poses challenges. We built area-based models using up to three variables derived from ALS and optical data, with NDVI sd , NDVI mean , H mean , H sd and H 90 being the most commonly selected variables. Large values of NDVI sd and low values of NDVI mean suggest greater contrast in the canopy reflectance, which may indicate an open canopy with a mix of forest cover and background soil, or the presence of dead trees. Dead trees and bare ground tend to reflect poorly in the NIR part of the spectrum compared to living trees. Large values of H mean and H 90 are often associated with old and mature forests, particularly in managed forests. Conversely, larger values of H sd suggest a more complex vertical forest structure. Old managed forests are more likely to contain standing dead trees compared to younger forests, and forests with gaps or with a more complex vertical structure are typically older.
To evaluate the possibility of detecting the presence of standing dead trees using plot measurements from standard sampling inventory procedures, this study performed a logistic regression modeling using approximately the same number of field plots as used in operational forest management inventories in Norway, i.e. 40 plots per stratum (Naesset 2014). In the current study, these plots correspond to a single stratum in old and mature spruce forests and are expected to have similar biophysical Table 3. Summary of the statistics for the best performing ABA models. Best performing ABA models in terms of AIC (ABA AIC ), ABA models with the largest proportion of agreement with the CHI-based datasets (ABA ag ), probability value defined as threshold (TH), Akaike index (AIC), area under the receiver operating characteristic curve (AUC-ROC), area under the precision-recall curve (AUC-PR), true positive (TP), false positive (FP), false negative (FN), true negative (TN), kappa index (K), CHI-based datasets (CHI: company A and B in S1 (A 1 B 1 ), company A and B in S1 combined with company B in S3 (A 1 B 13 )), predicted area in hectare with standing dead trees (P), predicted area in hectare with standing dead trees in agreement with the CHI-based datasets (P CHI ), proportion of predicted area with standing dead trees in agreement with the CHI-based datasets (Prop). The estimated population matrix and the kappa index derived from the estimated population matrix are presented in parentheses. properties and thus similar distribution of ALS returns. King and Zeng (2001) reported that logistic regression produces scores biased towards the larger group and proposed an alternative method called rare event logistic regression. Rare event logistic regression accounts for the small occurrence of an event by incorporating three corrections: (1) selection of a sample that includes 1-5 times more absence than presence of the event, (2) prior correction of the intercept, and (3) correction of the probabilities. The sampling strategy adopted in this study, i.e. systematic sampling within old and mature spruce forest stands, did not capture a sufficient number of plots with deadwood.
Consequently, too few observations with presence of standing dead trees were available to select a sample to perform a rare event logistic regression. As an alternative, we looked for accuracy metrics that accounted for unbalanced datasets such as AUC-PR and the kappa index calculated from the estimated population matrix. Despite the use of unbiased accuracy metrics, no relations were found between the statistic values obtained for the best performing models and the extent of the agreement with the CHIbased datasets. In addition, a disadvantage of kappa and the estimated population matrix is that they cannot be computed when there are no predicted standing dead trees in the observed sample matrix. The small occurrence of standing dead trees in managed forests is clearly a limitation for using plot measurements from standard forest    Table 5. Agreement between the CHI-based datasets and the presence of standing dead trees derived from the TBA, the best performing ABA models in terms of AIC (ABA AIC ) and the ABA models with the greatest proportion of agreement with the CHI-based datasets (ABA ag ). CHI-based datasets (CHI: company A and B in S1 (A 1 B 1 ), company A and B in S1 combined with company B in S3 (A 1 B 13 )), predicted area in hectare with standing dead trees (P), predicted area in hectare with standing dead trees in agreement with the CHI-based datasets (P CHI ), proportion of predicted area with standing dead trees in agreement with the CHI-based datasets (Prop management inventory to build relation between DBA and ALS-derived and optical images-derived variables. To overcome the limited availability of appropriate field information, we proposed a TBA that used both an ALS point cloud and optical images-derived vegetation indices. Although the approach yielded similar agreement with the CHI-based datasets compared to ABA ag , it is more reliable as it is independent from the occurrence of standing dead trees in an area. The method identified trees from an ALS point cloud without going through a full crown segmentation, saving considerable processing time. Information from sample plots or existing models can be used to adjust the parameters for the tree identification or the dbh prediction. In previous studies, a priori information about area-based stem number (Ene et al. 2012) and crown size (Chen et al. 2006) estimates were used to guide the tree crown delineation. In addition, a priori knowledge of the standing dead trees proportion in an area can guide the determination of the DBA percentile-based threshold to produce a map showing the presence of standing dead trees. This study used stem density, along with the dbh and height of sample trees, to determine the appropriate window size to identify local maxima, and to construct dbh predictive models based on diameter-height relationship. However, using a fixed window size may have resulted in the exclusion of snags and severely defoliated trees entangled in adjacent tree crowns. Furthermore, predicting dbh based on a model built using all measured trees, including living trees, may have led to the underestimation of the dbh of identified trees with reduced heights such as broken trees and snags.
NDVI is convenient to determine the tree status as it can be computed from different types of multi-or hyperspectral data, provided that a NIR band is available, and the spatial resolution is fine enough to distinguish individual trees. Following the findings of Hengl (2006) who suggested that objects larger than four pixels can be identified, 0.5 m resolution images would be needed to detect standing dead trees with a crown larger than 1 m in diameter. The combination of ALS data for tree identification and spectral data to determine their status might give more flexibility, allowing the use older ALS data on the condition that recent optical data are available.
In this study, the CHI-based datasets A 1 B 1 and A 1 B 13 cover 16% and 11% of the old and mature forests, respectively. However, the intersecting area between the polygons delineated by both companies A and B corresponds to only 2% of the old and mature forests in S1. Figure 5 presents three different examples of agreement between the CHI-based dataset A 1 B 13 and the predicted area with large density of standing dead trees. First, a good agreement between the CHI-based dataset (Figure 51a), the TBA (Figure 51b) and the ABA (Figure 51c) is observed. However, the CHI-based dataset covers an area larger than the visible presence of standing dead trees from the available imagery, on the western side of the delineated area. Field surveys are susceptible to errors due to the subjective assessments by the surveyors (Eriksen et al. 2018;Haga et al. 2021), and the reduced accuracy of the GPS under canopy cover (Ørka et al. 2022). This can have resulted in delineation of areas smaller or larger than the actual extent where standing dead trees are found. A second example presents sparse dead trees delineated in the CHI-based dataset that were not identified by any of the approaches using DBAth_95 (Figure 52a) but identified with the TBA and DBAth_85 (Figure 52b). Thus, lowering the threshold leads to an increase in the total area detected as containing standing dead trees. A third example presents standing dead trees identified by both approaches (Figure  53b,c) but not delineated in the CHI-based dataset ( Figure  53a). Based on the small agreement between companies A and B, it is reasonable to think that many areas with large density of standing dead trees were missed during the field survey or were left out for other reasons. In addition, the CHI-based dataset did not contain any delineated area on the eastern side of S3 whereas the presence of standing dead trees was identified in several areas by both approaches. Both companies have extensive experience with forest inventory. The small agreement between them emphasis the challenges faced when performing a deadwood inventory for key habitat delineation.
The density of standing dead trees, as well as other CHI habitats such as rock walls or trees with pending lichen, varies across regions in Norway. Therefore, a single threshold for the entire country to determine the total area to preserve per CHI habitat is not desirable. Currently, thresholds for preserving CHI habitats in a region are determined subjectively. However, remote sensing offers the potential to develop a more standardized procedure for determining flexible thresholds based on regional conditions.

Conclusion
In forest ecosystems, deadwood is an important indicator of biodiversity. Using remotely sensed data combined with the use of sample plots from an ongoing operational forest management inventory to detect areas with large density of standing dead trees in the CHI context seems appealing. However, using approximately the same number of field plots as in operational forest management inventories in Norway to perform prediction following an ABA was not successful. On the other hand, utilizing sample tree information together with tree detection in a TBA provides greater agreement with the field survey. The TBA could be used with different types of remotely sensed data and has therefore the potential to be implemented for larger areas to support operational forest management planning and identification of key habitats at municipality level or to update existing CHI information.

Disclosure statement
No potential conflict of interest was reported by the author(s).

Funding
This study was funded by PreMiNa, "Evaluation of remote sensing data as pre-information for woodland key habitat mapping according to the EcoSyst framework" and the project NOBEL, "Novel business models and mechanisms for the sustainable supply of and payment for forest ecosystem services". The PreMiNa project is funded by the private research fund, Skogtiltaksfondet, the Forest Trust Fund (Utviklingsfondet for skogbruket), and private forest owners' associations in Norway. The project NOBEL is supported under the umbrella of ERA-NET Cofund For-estValue. ForestValue has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement N°773324. Furthermore, the study was supported by the Norwegian Research Council (Norges Forskningsråd) (project number 297883).

Data availability statement
The data presented in this study are available on request from the corresponding author. Restrictions apply to the availability of the CHI-based dataset. Data were obtained from the Norwegian Agricultural Agency and are available from the authors with the permission of the Norwegian Agricultural Agency.