Assessment of The Spatial Structure of Windbreaks: What Optical Porosity Tells About Them

2. Materials and Methods

Model windbreaks

Our survey covers a total of 16 windbreaks A1 to D4 (Table 1) located in area with wind erosion risk in the southeastern part of the Czech Republic (Figure 2) with specific locations (Figure 3):

• Location A (GPS: 48.8135347N, 16.7514300E): A1 to A4
• Location B (GPS: 48.8322958N, 16.5939950E): B1
• Location C (GPS: 48.7647197N, 16.1589622E): C1 to C7
• Location D (GPS: 48.8500761N, 16.1760425E): D1 to D4

All windbreaks were superficially categorized according to [29] and [30] and then divided into 278 segments in total, with each segment representing a 30meter long section of the windbreak (see Figure 4) in order to meet software for OP evaluation requirements described by [31].

• Permeable (WB_P), 87 segments: A2 (16 segments), C1 (15 segments), C2 (22 segments), C5 (20 segments), D4 (14 segments)

• Semi-permeable (WB_SP), 59 segments: A1 (18 segments), C7 (6 segments), D1 (14 segments), D2 (8 segments), D3 (13 segments)

• Impermeable (WB_IP),132 segments: A3 (22 segments), A4 (21 segments), B1 (26 segments), C3 (19 segments), C4 (21 segments), C6 (23 segments)

The boundary points of individual segments were geodetically surveyed and marked with wooden stakes for future reassessment. The OP evaluation was conducted in two periods:

• Spring period (s) – when the windbreaks were without foliage

• Fully foliated period (f) – when the windbreaks were in full leaf

3. Results and discussion

One of the objectives of our study is to demonstrate how OP results vary depending on the methodology used to determine windbreak height (and consequently, the image size within which OP is assessed. There are several reasons for introducing such a complexity:

• Practical reasons – to ensure a simple and widely applicable approach.

• Research accuracy – to achieve the most precise measurements possible.

• Comparability – to allow for standardized comparisons across different windbreaks and study areas.

• Scalability – to facilitate the use of OP assessment in large-scale studies or remote sensing applications.

Figure 6 provides an overview of windbreak height parameters. With minor exceptions in WB_P, the mean, maximum and contour heights (MEAN, MAX, CONT) do not exceed 15 m. This justifies one of our approaches - assessing OP based on a fixed artificial height of 15 m (CUM₁₅_OP), regardless of the actual windbreak height. However, while a 15 m threshold may be appropriate for wind erosion control, other windbreak functions may require different height considerations. [1] emphasize that for odor mitigation in livestock operations, shelterbelts of 6–9 m may be optimal, as odor plumes tend to remain close to the ground. This suggests that OP assessment should be adapted depending on the specific function of a windbreak, whether for wind speed reduction, odor interception, or snow redistribution. Future research should explore how windbreak effectiveness varies across different height thresholds and how OP interacts with specific windbreak functions beyond erosion control. This will allow for more function-specific windbreak design and management strategies.

Another objective is to determine how well the detailed OP results correspond to the preliminary categorization of windbreaks based on their structure into WB_P, WB_SP, and WB_IP groups. These categories are generally recognized but only roughly distinguished, so our analysis aims to assess their validity with more precise OP measurements. For this purpose, the following Figures (8 to 11) evaluate windbreaks and their segments collectively based on their classification into one of these categories. We also look into the effect of state of foliage on OP.

Figure 7 presents the results of CUM₁₅_OP, highlighting differences in optical porosity (OP) across windbreak categories. WB_P exhibits the highest overall OP but also the greatest variability, particularly in the fully foliated state (CUM₁₅_OP_f ranging from 15.3 to 74.9). This suggests that individual segments differ in structure, likely due to species composition or irregular foliage distribution. WB_SP, despite having slightly lower OP than WB_P_s, shows reduced variability across segments, indicating a more uniform structure. WB_IP displays the widest range of CUM₁₅_OP_f, with some segments maintaining moderate permeability (up to 73.4) while others are nearly opaque (down to 2.7). This variability suggests heterogeneity within this category, possibly due to differences in tree density or canopy gaps.

Overall, WB_P consistently allows the most wind penetration, whereas WB_IP is the most effective at blocking wind, particularly during the fully foliated period. The seasonal contrast is most pronounced in WB_IP, where full foliage drastically reduces OP, reinforcing its function as a dense wind barrier. WB_SP maintains an intermediate role, offering a relatively stable level of permeability throughout the year.

Figure 8 illustrates the variability of MAX_OP across windbreaks’ categories and foliage conditions. WB_P exhibits the highest internal variability, with MAX_OP_s ranging from 49.3 to 95.9 and MAX_OP_f from 15.4 to 91.0. The wide range in MAX_OP_f suggests that foliage has an inconsistent impact across segments, leading to notable differences in OP within this group. WB_SP shows more stable MAX_OP values, with MAX_OP_s between 48.6 and 83.9 and MAX_OP_f ranging from 28.2 to 60.6. The reduction in porosity due to foliage is evident but less variable than in WB_P, suggesting that WB_SP has a more uniform internal structure. WB_IP has the lowest MAX_OP_s (42.0–81.1) and MAX_OP_f (8.3–59.3), with a sharp decline in porosity in the foliated state (median MAX_OP_f = 27.0). This confirms that foliage plays a crucial role in reducing permeability in this category.

Across all windbreaks, foliage decreases porosity, but the extent varies. The differences in MAX_OP between WB_P, WB_SP, and WB_IP support their classification by permeability. WB_P displays the greatest variability, WB_SP maintains moderate and stable MAX_OP values, while WB_IP remains the least permeable, particularly when fully foliated.

Figure 9 shows the range of MEAN_OP values across windbreaks. WB_P has the widest range, with MEAN_OP_s averaging 70.1 (38.2–91.1), indicating an overall open structure. In the foliated period, MEAN_OP_f drops significantly to an average of 49.0 (7.7–85.0), reflecting increased canopy density. The overall MEAN_OP_mean across both conditions is 55.9. WB_SP is more stable, with MEAN_OP_s between 39.8 and 76.2 (average 65.8), confirming a moderately open structure. In full foliage, MEAN_OP_f decreases to 26.5, showing a significant reduction in permeability. The overall MEAN_OP_mean of 46.7 highlights a more consistent structure compared to WB_P. WB_IP has the lowest MEAN_OP_s (36.9–74.9, average 56.4). In full foliage, MEAN_OP_f drops sharply to 15.7 (range 3.9–42.7), confirming their dense structure. The overall MEAN_OP_mean of 38.3 highlights their low permeability year-round.

These results suggest that WB_P exhibits high MEAN_OP variability, with an open structure in the leafless period and increased density in full foliage. WB_SP shows moderate porosity, maintaining openness without foliage but becoming denser when foliated. WB_IP remains the densest, ensuring limited permeability year-round.

Figure 10 presents CONT_OP values, showing seasonal porosity differences. WB_P exhibits a notable contrast, with CONT_OP_s averaging 62.9%, allowing significant light and air penetration. In full foliage, this drops to 34.4%, indicating increased density. The mean CONT_OP across both states is 50.0%, with a median CONT_OP_s of 63.9%, reinforcing the trend of high porosity within this group. WB_SP follows a similar pattern but with lower overall values. The mean CONT_OP_s (63.9%) is slightly lower than in WB_P, and CONT_OP_f decreases to 26.1%, suggesting reduced porosity even in full foliage. The overall mean CONT_OP is 48.5%, and the median CONT_OP_s is 64.3%, placing WB_SP between the other two categories. WB_IP shows the lowest values, with CONT_OP_s averaging 53.6% and dropping to 22.5% in the foliated period. The overall mean CONT_OP is 38.05%, confirming that WB_IP has the lowest porosity among all categories. The median CONT_OP_s of 53.0% supports their classification as the least permeable windbreak type.

Overall, WB_P shows high porosity variation, WB_SP maintains intermediate permeability, and WB_IP remains the most impenetrable, particularly in full foliage, ensuring strong wind protection.

Our findings confirm that OP is a critical parameter for assessing windbreak permeability and functional effectiveness. The high variability in OP observed in WB_P, particularly in the foliated state, aligns with [21], who also reported significant seasonal OP differences. Their assessment of "OP reduced" highlights the importance of considering windbreak height and structure when evaluating permeability, a factor that may influence the observed internal variability in our study.

A key practical implication of windbreaks OP is its relationship wind speed reduction. [33] demonstrated a strong negative correlation between OP and wind speed at various distances, reinforcing the role of OP in defining wind protection effectiveness. Our results further support this link, particularly with the differences observed across windbreak categories. The overlap of WB_SP with both WB_P and WB_IP suggests that permeability-based classification may not always directly correspond to wind reduction efficiency, as noted in [20]. Their findings suggest that OP, particularly in the lower portion of windbreaks, may serve as a reliable predictor of windspeed reduction, a factor that could be further refined in future studies.

Methodological differences in OP assessment also present challenges in comparability, as highlighted by [27]. Their introduction of 3D LiDAR for windbreak porosity estimation addresses a major limitation of 2D image-based analyses. While our MATLAB-based approach provides a standardized and automated evaluation method, it is limited to 2D data, which may not fully capture spatial OP variations. Future research could explore integrating 3D LiDAR to enhance accuracy in OP estimation, particularly in complex or heterogeneous windbreak structures.

The aerodynamic implications of OP were further explored by [34], who proposed a semiempirical model incorporating aerodynamic porosity and additional factors such as surface roughness and wind direction. Their model suggests that OP alone may not fully capture windbreak efficiency, emphasizing the need for a more holistic approach. Our results indicate that OP metrics such as MAX_OP and CUM₁₅_OP exhibit high internal variability, while MEAN_OP and CONT_OP provide more consistent classification. This suggests that combining OP metrics with aerodynamic modeling could refine windbreak performance assessments.

A key challenge in OP estimation is the reliance on different data sources. [26] demonstrated that OP estimation using remote sensing techniques showed weak correlations with commonly used vegetation indices. This is likely because OP is inherently a horizontally measured parameter, whereas satellite imagery provides a vertical perspective and lacks direct horizontal structural information [15]. In contrast, their study found strong linear relationships between OP and structural windbreak parameters, such as barrier height (h), average canopy length (CL), leaf area index (LAI), and windbreak width (w). These findings suggest that OP should be analyzed in conjunction with structural characteristics rather than relying solely on spectral vegetation indices, a consideration that further supports the need for precise, ground-based OP measurement techniques.

Structural descriptors such as crown density and vegetative surface area density, as discussed by [17], provide further insight into windbreak efficiency. Similarly, [35] proposed a three-dimensional crown (3D) density approach, which incorporates windbreak height, width, and crown/stem area ratios to assess its structure. This framework aligns with our findings, where OP values correlate with windbreak structure, but also emphasizes the need for more detailed 3D analysis to improve permeability classification.

Our study demonstrates that WB_IP consistently shows the lowest OP, reinforcing its function as the most effective wind barrier. However, the substantial seasonal OP changes in WB_P highlight the influence of canopy structure on permeability. The findings suggest that OP assessment methods should account for both spatial and seasonal variability to ensure accurate windbreak classification.

Overall, our study supports the use of OP as a key metric for windbreak evaluation but highlights the need for methodological consistency. While OP-based classification broadly aligns with structural expectations, the overlap of WB_SP with other categories suggests that permeability-based distinctions may require additional parameters, such as aerodynamic porosity or structural descriptors, to improve classification accuracy. Future research should explore integrating OP assessments with advanced 3D analysis and windflow modeling to enhance windbreak design and management strategies.

We confirmed that optical porosity (OP) is a key indicator of windbreak permeability, though its variability depends on the calculation method used. While WB_P generally exhibits the highest OP and WB_IP the lowest, the overlap of WB_SP with both categories suggests that permeability-based classification is not always clear-cut. Foliage significantly reduces OP across all windbreak types, particularly in WB_P.

While our analysis relies on frontal perspective OP assessment, future research will explore how these values compare with OP derived from aerial (satellite) imagery. Previous studies indicate that OP correlates more strongly with structural parameters than with vegetation indices [26]. However, the relationship between ground-based and satellite-derived OP remains largely unexamined. By integrating these perspectives, we aim to refine OP assessment methods and improve large-scale windbreak analysis. This future direction will enhance windbreak evaluation for landscape management, erosion control, and wind protection strategies, providing a more comprehensive framework for decision-making.

5. Conclusions

• The various OP expressions (MAX_OP, CUM₁₅_OP, MEAN_OP, CONT_OP) show differences in variability:

o MAX_OP generally has the highest values and the widest percentile range, indicating greater internal variability within each windbreak category.

o CUM₁₅_OP follows a similar trend but with slightly lower values and less variability than MAX_OP.

o MEAN_OP shows more stable differences between categories, with lower internal variability than MAX_OP and CUM_OP.

o CONT_OP has the lowest absolute OP values and the least internal variability, suggesting that it is the most conservative OP measurement method.

o Overall, different OP calculation methods produce consistent trends among windbreak types, but MAX_OP and CUM_OP display greater internal variability compared to MEAN_OP and CONT_OP.

• There are observable differences in OP values between the three types of windbreaks (permeable – WB_P, semi-permeable – WB_SP, and impermeable – WB_IP), but these differences are not always sharp:

o WB_P generally exhibit the highest OP values across all measurement methods, confirming their more open structure.

o WB_SP show intermediate OP values, but in some metrics (e.g., MAX_OP_s, CUM_OP_s), their values overlap with those of WB_P, making their distinction less clear.

o WB_IP tend to have the lowest OP values, in line with their denser structure. However, certain values (e.g. MAX_OP_s) indicate some overlap with WB_SP.

o Overall, while the differences between categories are noticeable, the WB_SP overlap with other types in some OP measures, suggesting that categorization based purely on permeability might not always be definitive.

• Foliage proved a significant impact on OP values:

o Across all windbreak categories and OP calculation methods, OP values are lower in the fully foliated state (f) compared to the leafless state (s), confirming that vegetation significantly reduces optical porosity.

o The most substantial OP decrease due to foliage occurs in WB_P, where, for example, median MAX_OP drops from 66 to 39.

o WB_IP, the OP reduction is less dramatic but still evident, such as in median CONT_OP_s: 53 vs. CONT_OP_f 12.

o In general, the higher the initial OP value in the leafless condition, the greater the observed decrease after foliage is present. This confirms that vegetation density plays a crucial role in determining windbreak OP.

• Evalutation of the spatial structure of windbreaks (optical porosity) by Windbreak software created in the Mathworks MATLAB R2024a allowed for automatic data analysis based on inserted photographs of windbreaks.