Forest trees are opaque in the visible spectrum. Trunks, branches, leaves, and needles block the line of sight between the observer and the object. At the landscape level, forests substantially narrow viewscapes and increase the privacy of exurban homes (Vukomanovic
If a flat terrain is assumed, then the question of “How far can one see in a forest?” may be answered with exact formulas (Adiceam, 2016). For this it is necessary to assume a particular pattern of tree locations, additionally taking as known quantities the density
In contrast to gap probability (a well defined quantity, amenable to instrumental measurement), visibility within a forest, as recorded visually by a person, depends on several factors. Drummond & Lackey (1956) carried out visibility measurements by visually targeting a standard green cylinder 1.8 m in height and 45 cm in diameter. The authors defined continuous visibility
Anstey (1964) defines visibility
In the present study, we seek options for predicting field measurements of horizontal visibility
The Estonian forest resource register database was used to select forest stands for establishing field transects for visibility measurements. The database gives for each stand element within each stand its basic FI variables (age, density, mean tree height, and diameter at breast height). An element of a forest stand is defined as a combination of tree species, together with its membership in a tree layer. For each stand, visibility was first calculated using 1.5 / (
The observer was positioned at a point with medium visibility in each direction in the forest, thereby defining the starting point of a transect. The observed subject, wearing camouflage, then started pacing away from the observer, stopping when the observer could no longer see movement. The visibility determination was carried out in one direction. The direction was chosen more or less randomly. The observer point, on the other hand, was selected in an area for which the average density of forest was typical of the given stand. The location coordinates of the observer and the observed subject were determined with the Garmin GPSmap 60CSx receiver.
For the prediction of horizontal visibility with a theoretical model according to FI data, we subselected those stands that were inventoried in 2014 or later. To these we added some stands with age over 80 years, assuming in their case only minor changes, and slow growth, since the most recent inventory. These old stands were inventoried in or at some point subsequent to 2009, except four stands inventoried still earlier, in 2003, but growing on poor soil. The complete subsample comprised 70 stands, out of the original sample of 100 (Table 1).
Description of the 70 sampling transects that were used for visibility prediction based on the forest inventory data.
Dominant species | Age (yr) | Count of stands | ||
---|---|---|---|---|
85 (23–158) | 26 (2–45) | 24 (10–34) | 45 | |
49 (22–93) | 20 (5–33) | 28 (18–33) | 28 | |
60 (38–117) | 24 (11–30) | 30 (23–34) | 15 | |
58 (22–77) | 22 (9–29) | 27 (24–34) | 5 | |
33 | 24 | 40 | 1 | |
20 | 14 | 30 | 1 |
Let (x0, y0) be a random point in a forest comprising similar trees, at density
For each stand element, the height from ground to live crown base was predicted with a regression model (Lang, 2001). If the height to live crown base was below 1.5 m, then the crown radius (from model (14) in Lang
Airborne lidar data, from the Riegl VQ-1560i scanning system and a digital elevation model, were provided by the Estonian Land Board. The point density of the archived lidar data was on average between 0.15 m−2 and 2.0 m−2, with the pulse footprint at ground level about 50 cm, and the scanning nadir angle confined to within 30°. We used the FUSION toolbox (McGaughey, 2020) to calculate point heights over ground, to cut point clouds (with a 10 m buffer flanking the transect) out of ALS data, and to calculate point cloud metrics. The point cloud height distribution was calculated using all points, and then again using only the points with a height (over ground) greater than 1 m. The relative density of returns was calculated for horizontal layers with point heights over ground in the ranges 0.7 m ≤
In seeking predictor variables for regression models, we found, contrary to Drummond & Lackey (1956), that the upper height percentiles of the point cloud, used in FI practice to predict forest height, lack a correlation with
We excluded one outlier from the empirical dataset, a
The field observations from spring and from the end of summer were used as a joint empirical dataset. We tested a dummy variable, indicating season, in the multiple linear models. The parameter for the variable was found to be significant, showing the measured springtime
The residual standard error of the models was calculated as
An estimate of the determination coefficient
The relationship between the measured visibility and visibility as predicted from FI data was found to be somewhat scattered (Figure 1). The measured visibility
Observed visibility and the predicted 75th percentile of visibility using FI data. Transects were measured in April–May (black) and in September (green).
In the case of visibility predicted from ALS data, all the regression models (Table 2) were found significant. The variability explained lay in the range of 53–67%, and the residual standard error in the range of 21–28 m. The significance and values of parameters did not depend on the choice between summer and springtime ALS data. A cross-check of models on ALS data from vegetation periods other than those used for model fitting revealed almost no signs of the clustering that would be expected when mixing field measurements from springtime and summer (Figure 2), with the value of
Model (6), (a) as applied to 2019 springtime ALS data with parameters estimated from 2017 summer ALS data, and (b) conversely. Transects were measured in April–May (black) and in September (green).
Model parameters (ALS) with
Model | Data | Parameters / | ||||||
---|---|---|---|---|---|---|---|---|
3 | 2017 | 2.59 | 0.023 | − | − | 28.3 | *0.64 | 97 |
2019 | 1.98 | 0.016 | − | − | 26.3 | *0.69 | 97 | |
4 | 2017 | 14.3 | 8.02 | − | − | 24.8 | 0.55 | 97 |
2019 | 18.5 | 8.11 | − | − | 25.1 | 0.53 | 97 | |
5 | 2017 | 4.59 | 6.08 | 0.362 | − | 23.9 | 0.59 | 96 |
2019 | 2.72 | 5.26 | 0.506 | − | 23.8 | 0.59 | 96 | |
6 | 2017 | 39.9 | 7.43 | 0.309 | −0.610 | 21.8 | 0.66 | 95 |
2019 | 28.4 | 7.73 | 0.438 | −0.655 | 21.3 | 0.67 | 95 |
Estimated with equation (9).
At the initial state of a forest stand after its establishment by planting or through natural regeneration, the trees are small, and their early growth is not limited by competition with other trees. The stems are small, with visibility blocked mainly by needles and leaves. As time passes, trees grow taller, the canopy closes, and competition for light and nutrients drives changes in crown shapes and in the location of canopy foliage. Lower branches die, while for some time remaining attached to trunks. With insufficient light, the mortality of trees increases, as does the height to the live crown base. These changes, in turn, create more open space. A point is eventually reached at which the amount of photosynthetic energy transmitted through the upper canopy layer is sufficient to support regrowth of shade-tolerant bushes and trees in the understorey. In the case of managed forests, thinning alters the canopy cover, increasing the light available for lower vegetation layers. The feedback process, driven by light availability, is probably the reason why forest height or canopy cover alone were found not to be sufficient variables for the prediction of horizontal visibility.
It was assumed that horizontal visibility determinations, as made by the human eye, would be best predicted by combining information on tree density, crown dimensions, and tree location patterns. The needed information is only partly available in FI databases: FI records are not updated each year, and information on regrowth is additionally limited by the concentration of FI interest on the dominant upper canopy. In our study, we found the 75th percentile of visibilities, as predicted by a theoretical model from FI data, to be in concordance with field measurements. However, in many stands the predicted visibility distance was found to substantially exceed the measured distance. The discrepancy was attributed to a lack of FI information on regrowth.
Field measurements of visibility using visual tracking are subject to many influences, including not only environmental conditions and stand structure, but also the observer's level of experience and the relative movement of observer and target. This combination of influences introduces random error, and also possibly systematic error, into the data, and is probably one reason why the field measurements from spring and summer did not form clusters in our analysis. We do not have repeated measurements on the same plots with leaf-on and leaf-off conditions. However, by using the measurement season as a factor in regression modelling, we were able to determine that on average the visibility distance was greater for the springtime measurements. The increase was probably driven on the one hand by the better illumination conditions under the forest when the upper canopy layer was without leaves, and on the other hand (in a particularly direct way) by the presence of shade-tolerant deciduous broadleaf tree species in the forest understorey.
The lack of FI database information regarding the forest understorey can be overcome by instead using ALS data. In ALS datasets, the pulse returns are triggered mainly by the upper dominant canopy layer and (because laser scanners are designed for measuring elevation of the terrain surface) by the ground. Properties of the point cloud are influenced by flight altitude, pulse incidence angle, and the extent to which the scanner is capable of recording multiple returns per emitted pulse, and also by canopy depth and canopy density. We found that up to 70% of variability in the measured horizontal visibility could be described by a regression model based on three variables: canopy cover, the relative proportion of returns in the lower layer of the point cloud, and the 10th percentile of the point cloud height distribution. The remaining variability is due to uncertainties both in lidar and in field measurements (including the definition and the recording of field-measured visibility; errors in tran-sect location coordinates; local variations in point cloud properties resulting from lidar scan nadir angle; and the phenological status of each given transect, whether at the time of lidar flight or at the time of fieldwork). Two factors decrease the probability of obtaining accurate data for a key determinant of horizontal visibility, the understorey vegetation: the interception of lidar pulse energy by the upper canopy, and the structure of the lidar-system internal software, which searches preferentially for the last possible return position near the ground surface. Nevertheless, our tests indicate that the proposed models based on ALS data are applicable both to measurements taken at leaf-off and leaf-on time, permitting the use of the models in practical applications where estimates of horizontal visibility within a forest are needed.