Determining the Optimal Sample Size for Assessing Crown Damage on Color Infrared (CIR) Aerial Photographs

Abstract

One of the priorities in sustainable forest management is monitoring the health status of trees and stands. From the aspect of remote sensing (RS), the best way of doing this is by interpreting color infrared (CIR) aerial photographs; however, this raises the issue of sample size. For this reason, to apply this method in practice, it is indispensable to determine an appropriate sample size to ensure sufficient reliability of the health status assessment of trees in CIR aerial photographs. This research was conducted in lowland forests of pedunculate oak in Croatia. To determine damage in the photographs of the main tree species, a systematic sample with varying dot grid densities—100 × 100 m, 200 × 200 m, 300 × 300 m, 500 × 500 m, 1000 × 1000 m—was used with combinations of different numbers of interpreted trees per sample. Damage indicators were also calculated based on tree distributions obtained by interpreting four trees, two trees and one tree in different sample sizes. The results of the testing showed that there were no statistically significant differences between different sample densities and numbers of interpreted trees in relation to mean damage assessment. Regardless of the fact that there were no statistically significant differences during damage assessment, it was found that by lowering sample densities, starting with 200 × 200 m, the number of trees and the number of sample points per particular sub-compartment significantly decreased, and so did the desired accuracy. Consequently, the participation (distribution) of particular species and damage degrees in the sample were lost, which significantly affected the overall tree health assessment. In contrast, grid densities of 100 × 100 m with one interpreted tree at the raster point proved to be the optimal sample size. This confirms the fact found in earlier research, that is, that the selected sample should have several spatially well-distributed points with a smaller number of trees in the point, and samples with larger numbers of trees in a smaller number of points should be avoided.

1. Introduction

Sustainable management of forests under conditions of climate change and natural disasters is necessary because forests, with their economic and social functions, are of immense importance in maintaining a healthy environment and mitigating climatic extremes. Forests in Croatia, as well as in Europe, are faced with many challenges such as the increasingly frequent dieback of trees, habitat degradation, the appearance of invasive species and climate change. Tree dieback is a complex process that involves a large number of sites, stands and biotic factors at different stages and different intensities [1,2,3,4,5,6]. We contribute to the stability and preservation of forest ecosystems through systematic monitoring of the state of ecological factors. Mapping, assessing and quantifying these effects is therefore of the most importance in order to understand disease progression and develop effective forest management plans [7].

The poor health condition of forests, caused by biotic and abiotic factors, usually leads to defoliation and/or leaf discoloration [8,9]. For this reason, defoliation of the crown is considered a key indicator of the health condition [10]. The negative consequences of tree dieback are being mitigated by monitoring the status of trees, primarily by assessing tree and crown damage [11,12,13,14]. The primary task is to assess the degree of forest damage and spatial distribution of damaged trees, which can be performed by terrestrial-monitoring or by applying RS methods [15,16], most commonly by interpreting color infrared (CIR) aerial images [15,17,18]. CIR films register the visible and near-infrared (IR) radiation of the Sun reflected from the surface of vegetation, and the amount of this radiation depends on the type of tree and its physiological condition, i.e., health status [19,20,21]. Damage to the crown of trees (loss of leaves, death of branches and parts of the crown, change in the color of leaves) causes significant changes in reflectance, especially in the infrared part of the spectrum (wavelengths 700–1100 nm), and because of this, damaged trees can be easily recognized on CIR aerial photographs [22,23,24,25,26,27,28].

To identify damage on aerial photographs, it is necessary to create a photo interpretation key for each type of tree, whereby the characteristics of the appearance of an individual tree species and the degrees of damage on aerial photographs are given descriptively and with a drawing or photograph [18].

Multispectral images have also been successfully used for mapping individual forest stands [29,30], for crown reconstruction and individual tree phenotyping [31,32], for identification of tree species [33,34] and for determining the health status [15,18,35,36,37,38,39,40,41,42].

Remote sensing makes it possible to collect data on forest conditions quickly and reliably [43,44,45]. This procedure lessens the scope of fieldwork and saves time and money [44]. So far, there have been six forest damage assessments in the Republic of Croatia based on the photointerpretation of CIR aerial photographs. All the research was conducted by photo interpreting analogous aerial photographs using analytical stereo instruments. Trees to be interpreted were selected according to a randomly placed systematic sample, proportional to the stratum (sub-compartments) size, and with a systematic sample using the 100 × 100 raster method. The development of digital cameras has opened new possibilities for using digital CIR aerial photographs to assess damage to both single trees and stands on a digital photogrammetric station (DPS). However, this raises the problem of sample size; namely, in all previous research, a sample in the form of dot grids proved to be best because it is regularly distributed in space but interprets a much larger number of trees while achieving the same reliability in comparison to field assessments [46]. Thus, in order to apply the method in practice, it is necessary to determine the size of a sample that will ensure sufficient reliability in assessing the health status or tree damage in digital CIR aerial images.

Sample size has been much more extensively studied in the course of forest management assessment, during forest measurement rather than during damage assessment. The samples are taken from the entire population [47] with the aim of obtaining a cost-effective estimate of the entire population [48]. Sampling should be made for every measurement procedure since measuring the whole population would be impractical and unfeasible because of time constraints and liability for errors. For this reason, a well-conceived and executed sampling procedure efficiently substitutes total measurement as regards the quality of the acquired data and costs [49].

In their inventory of forest damage in the Spačva Basin, Kalafadžić et al. [50] tested different sampling methods and intensities in 10 randomly chosen compartments. They employed the point method and the raster method. The point method, with spacing ranging from 400 m, 200 m and 400 × 200 m, was used to interpret the same number of trees, while the raster method, depending on the size of the raster overlaid on the compartment, was used to interpret a different number of trees closest to the raster point. After testing, they concluded that samples with a larger number of trees in a smaller number of points should be avoided.

In all the research conducted to date, a dot grid sample proved best because it is well distributed in space. Since it interprets a much larger number of trees, it is as reliable as field assessment.

To apply the method in practice, it is necessary to determine the form and size of a sample in order to ensure sufficient reliability of tree health assessment in digital CIR aerial photographs.

The results obtained by interpreting CIR aerial imagery are most commonly presented in thematic maps using a geographic information system (GIS).

The primary goal of this study is to investigate the most appropriate sample size and the number of interpreted trees per sample in digital color infrared (CIR) aerial photographs to assess crown damage and tree health status for practical purposes. Therefore, it was necessary to carry out an inventory of damage on systematic samples with different density points (100 × 100 m, 200 × 200 m, 300 × 300 m, 500 × 500 m, 1000 × 1000 m) and a number of trees (1, 2 and 4 trees), analyze and process the data, interpret the results obtained, and based on this, determine the shape and size of the sample that would ensure sufficient reliability of crown damage assessment on CIR aerial photographs.

2. Materials and Methods

Research comprised the lowland forest area of pedunculate oak in Croatia, of the management unit (MU) “Josip Kozarac” (45°23′30″ N, 16°46′50″ E), Lipovljani Forest Office, and the Lipovljani Forest Training and Research Centre, the management unit of “Opeke” (45°22′00″ N, 16°49′45″ E) (Figure 1). The MU “Josip Kozarac” area is 5759.13 ha, while the MU “Opeke” area is 547.27 ha. In the management units, the lowest point is 94 m above sea level and the highest altitude is 96 m above sea level (MU “Opeke”), i.e., 105 m above sea level (MU “Josip Kozarac”). Four phytocoenoses are represented in the researched area in which, in addition to other species, the main types of trees are Pedunculate oak (Quercus robur L.) and Narrow-leaved ash (Fraxinus angustifolia Vahl).

The recording was carried out in surveyed strips using a multi-spectral digital camera-UCX-Vexcel, focal length f = 100.5 mm. Digital aerial photographs (122) were taken with a spatial resolution of 0.1 m, a longitudinal overlap of 60% and a transverse overlap of 36%.

Crown damage, and thus the health status of the trees, was assessed on digital CIR aerial photographs for the main tree species—Pedunculate oak and Narrow-leaved ash.

Digital aerial photographs were interpreted on a digital photogrammetric workstation (DPS) using the PHOTOMOD Lite 4.4. software package.

Before the interpretation of the DPS, it was necessary to determine the method for mapping crown damage so that they could classify trees into individual degrees of damage to create projects and code tables.

Photointerpretation of the degree of crown damage was carried out using a carefully created photointerpretation key of the research area, and the health statuses of trees (crowns) were classified into damage degrees based on the following scale [18,35]:

Damage degree	Damage percentage
0	0–10%
1	11–25%
2.1 (2A)	26–40%
2.2 (2B)	41–60%
3.1 (3A)	61–80%
3.2 (3B)	81–100%
4	Snags

After that, the projects or sequences (strips) of two or more adjacent digital aerial photographs were created in the module PHOTOMOD Montage Desktop in four steps:

• Block forming: digital aerial photographs were uploaded into the project; the direction of the block was determined and so was the position of aerial photographs in the block.
• Aerial triangulation: camera parameters were defined, and the internal orientation of aerial photographs was conducted.
• Block adjustment: external orientation of aerial photographs.
• Block processing: the last step in the project design in which a module was selected for further use in photointerpretation.

Aerial triangulation was performed automatically on the photogrammetric workstation (in the second step) using the ray bundle method and the GPS/IMU (inertial measurement system) measurements that were recorded during aerial surveys.

A total of five projects were created in four steps—block forming, aerial triangulation, block adjustment and block processing—for photointerpretation.

After the projects were created, a code table was generated for each stereopair within the project. The table was generated in order to collect data in the PHOTOMOD Stereo Draw module. In the code table, the interpreted objects (trees) were described by a code name, number of stereopairs in which they were collected, shape (point), color, symbol and additional attributes (number of trees, position, species, damage). A total of 32 code tables were created for the needs of the research.

After the projects and code tables were created, a photointerpretation key was used to interpret digital CIR aerial photographs. In a systematic 100 × 100 m sample, the four closest crowns were interpreted in every raster point laid over the aerial photographs (Figure 2).

Data collected by interpreting digital aerial images on DPS were exported in .DXF format for further statistical processing, and in .SHP format for geospatial analyses and construction of thematic maps.

Past research shows that a randomly placed systematic sample, in which a uniform distribution of interpreted crowns is achieved with the raster method, is best for damage assessment.

In previous studies, trees to be interpreted were selected according to the randomly placed systematic sample, which was proportional to the stratum size, while the health condition was assessed using the crown closest to the raster point. In more recent research, damage was assessed using the dot grid raster method (100 × 100). In each point (sample), four crowns closest to the raster point in the top left and right corners and in the bottom left and right corners were interpreted.

Compared with earlier research, this method resulted in a much higher number of trees in the same area; therefore, a question arises as to the optimal sample size and the optimal number of interpretable trees per sample that will ensure statistically sufficient reliability of tree health assessment.

For this reason, to define the most appropriate sample sizes that will ensure statistically sufficient reliability of tree health assessment, systematic samples with different dot grid densities—200 × 200 m, 300 × 300 m, 500 × 500 m and 1000 × 1000 m—were set up (Figure 3) with combinations of different numbers of interpreted trees per sample: 1 (A), 2 (AD) and 4 (ABCD) trees (Figure 4).

Based on the results of digital aerial imagery photointerpretation, damage indicators (damage, D; mean damage, MD; damage index, DI; mean damage of significantly damaged trees, MD₁) were calculated using Formulas (1)–(4) [15,35,50,51] for single tree species and all the interpreted species together, both for individual survey strips and overall for the entire surveyed area (compartments and sub-compartments covered by surveying).

• Damage (D) is an indicator that is calculated according to the formula:

$$\mathrm{D} (\%)=\frac{{\sum f}_{(1-4)}}{{\sum f}_{(0-4)}} ·100$$

(1)

For the calculation, only the total number of damaged trees is taken into account, not include the number of damaged trees in a particular damage degree.

2.

Mean Damage (MD) is calculated according to the formula:

$$\mathrm{MD} (\%)=\frac{{\sum f}_{i }·{ x}_i}{{\sum f}_i}$$

(2)

where f_i is the number of trees in i- damage stage

x_i–i- stage interval center in the damage stage scale for single trees

0 = 5%, 1 = 17.5%, 2.1 = 32.5%, 2.2 = 50%, 3.1 = 70%, 3.2 = 90%, 4 = 100%

To calculate the mean damage in the observed area (sample), a complex arithmetic mean is used with the number of trees in a particular damage class.

3.

Damage index (DI) provides the percentage share of trees in the sample, which is classified as damage degree 2.1 (2A) or higher, i.e., severely damaged trees.

$$\mathrm{DI} (\%)=\frac{{\sum fx}_{(2-4)}}{{\sum f}_{\left(0-4\right)}}$$

(3)

4.

Mean Damage1 (MD1) is the value of the mean degree of damage of trees classified into damage level 2.1 (2A) or more.

$${\mathrm{MD}}_1=\frac{{\sum f}_{(2-4)}}{{\sum f}_{(0-4)}} ·100$$

(4)

The calculated damage indicators and the number of interpreted trees provided input variables for statistical data processing. According to Pranjić and Lukić [52], the sample size was determined based on the variability (s_x) of the estimated mean damage and the desired accuracy (s͞_x), as well as the reliability coefficient (t).

An χ² test was used to test different sample point densities and numbers of interpreted trees per sample with regard to tree health assessment, with 95% reliability [53].

In addition, binomial distribution was used to obtain the desired accuracies (B) for different dot grid densities and numbers of interpreted trees per sample (N).

In line with the results obtained from interpreting tree health conditions on the raster of varying dot grid densities using a combination of interpreted trees per raster point, thematic layers containing a spatial distribution of mean damage (MD) were constructed for all the species along particular survey strips and the research area (compartments/sub-compartments). Based on the acquired results, thematic maps of mean damage can also be constructed for the main tree species as well as for other damage indicators.

3. Results

The results of crown damage interpretations for 4 trees (ABCD), 2 trees (AD) and 1 tree (A) (Figure 4) for different sample sizes (100 × 100 m, 200 × 200 m, 300 × 300 m, 500 × 500 m and 1000 × 1000 m) (Figure 3) provided tree distributions per damage degree (

Table 1. Tree distribution per specific damage degree for different sample densities and different numbers of interpreted trees.

Sample Density	Degree of Damage	Number of Trees			Sample Density	Degree of Damage	Number of Trees
		ABCD (4)	AD (2)	A (1)			ABCD (4)	AD (2)	A (1)
100 × 100	0	90	46	30	500 × 500	0	6	3	1
	1	1782	931	473		1	75	48	24
	2A	1536	752	363		2A	67	27	17
	2B	973	475	225		2B	30	12	3
	3A	454	217	122		3A	11	5	3
	3B	401	199	112		3B	22	11	5
	4	22	12	5		4	2	1	0
	∑	5258	2632	1330		∑	213	107	53
200 × 200	0	25	12	7	1000 × 1000	0	2	1	0
	1	435	235	118		1	23	14	8
	2A	368	171	79		2A	13	3	1
	2B	261	130	65		2B	12	5	2
	3A	122	54	34		3A	3	2	1
	3B	108	57	31		3B	7	5	3
	4	5	4	2		4	0	0	0
	∑	1324	663	336		∑	60	30	15
300 × 300	0	11	6	2
	1	194	92	47
	2A	185	99	45
	2B	119	60	26
	3A	43	21	15
	3B	35	16	11
	4	3	2	2
	∑	590	296	148

).

By interpreting a particular sample size and number of interpreted trees per sample, different tree distributions were obtained per damage degree. It was therefore necessary to determine whether there was a significant difference among the assessed damage degrees with regard to the inclusion of different numbers of trees in the sample. Testing was performed using the χ² test and the results are given in

Table 2. Values of χ² test frequency distributions for particular sample sizes and combinations of interpreted trees in relation to the 100 × 100 m sample size and 4 interpreted trees (ABCD), with 95% reliability at a limit of 12.59.

Sample Sizes/Combinations of Numbers of Trees	Values for χ2 Test (Total)
100 × 100 AD	2.96
100 × 100 A	8.49
200 × 200 ABCD	3.67
200 × 200 AD	5.15
200 × 200 A	6.52
300 × 300 ABCD	5.64
300 × 300 AD	6.37
300 × 300 A	3.93
500 × 500 ABCD	10.63
500 × 500 AD	11.81
500 × 500 A	7.90
1000 × 1000 ABCD	4.97
1000 × 1000 AD	9.23
1000 × 1000 A	7.90

.

Based on the results of the χ² test, there are no statistically significant differences between different sample densities and numbers of interpreted trees in relation to mean damage assessment.

In the entire research area, the interpretation of 4 trees in a 100 × 100 grid resulted in the interpretation of a total of 5258 trees per strip (

Table 3. Determining the necessary sample size.

Survey Strip	Number of Trees	sx	s2	sx × s2
8527	2144	0.40	267.98	107.05
8528	1524	0.27	225.67	61.23
8531	1590	0.33	464.09	152.80
Total	5258	1		321.07

s_x, sx = t_α/2²/s͞_x² (t, distribution value for the desired confidence limit (1 − α); s͞_x, standard error of the estimate of mean damage; s², the variance of the sample.

). Since no statistically significant differences were found even though a large number of trees were interpreted, the next step was to determine the required sample size, i.e., the optimal number of trees required for interpretation to achieve identical assessment accuracy (

Table 4. Number of trees needed for interpretation to achieve identical assessment accuracy.

z	1.96	1.96	1.96	1.96
p	0.3104	0.3104	0.3104	0.3104
1 − p	0.6896	0.6896	0.6896	0.6896
B	0.01	0.012506	0.015162	0.049994
N	8223	5258	3577	329

z, table value for 95% reliability; p, assessment accuracy of mean damage; B, desired accuracy; N, number of trees.

).

According to Table 4, a total of 8223 trees should be interpreted in order to achieve the desired accuracy of 1% in the study area. The table also shows that an accuracy of 1.3% was achieved with 5258 interpreted trees. Therefore, along with the defined desired accuracy of 1.5%, the necessary number of trees for crown damage assessment was also determined in the study area.

In order to obtain mean damage of 31.04% in the surveyed area (sample of 100 × 100 m and 4 trees) at 1.5% accuracy and 95% reliability, 3577 trees should be interpreted. The desired accuracy of 5% was also tested, and the results obtained show that 329 trees should be interpreted. This number of trees was achieved in the 200 × 200 m sample by interpreting one tree per point (Table 1). Based on tree distribution per damage degree for different sample densities and different numbers of interpreted trees, an optimal sample size and number of interpreted trees per point was determined.

Figure 4 shows that at different sample densities and four interpreted trees per point, the same distribution trend was retained per particular damage degrees, while the total number of trees to be interpreted was significantly reduced.

During interpretation, the analysis of sample densities and numbers of interpreted trees per sample provided distribution per particular damage degree for the necessary number of trees (3577) (Figure 5).

In contrast, Figure 6 shows that the above trend changes as sample density reduces, starting from 200 × 200 m, if 2 or 1 tree per point is interpreted. This is why a limit threshold of 5% was taken to determine the optimal number of trees for interpretation to achieve the desired accuracy.

Damage indicators were also calculated based on tree distribution obtained by interpreting four trees (ABCD), two trees (AD) and one (A) tree for different sample sizes (

Table 5. Calculated damage indicators (damage, D; mean damage, MD; damage index, DI; mean damage of significantly damaged trees, MD₁).

Sample	Damage Indicator (%)	Total
		ABCD	AD	A
100 × 100 m	D	98.29	98.25	97.74
	DI	64.40	62.58	61.59
	MD	38.09	37.62	38.04
	MD1	49.81	49.84	50.99
200 × 200 m	D	98.11	98.19	97.92
	DI	64.63	61.56	60.51
	MD	38.90	38.52	39.55
	MD1	50.66	51.36	53.02
300 × 300 m	D	98.14	97.97	98.65
	DI	63.86	64.10	61.59
	MD	37.07	37.05	39.43
	MD1	47.85	47.11	50.53
500 × 500 m	D	97.18	97.20	98.11
	DI	58.52	47.15	43.48
	MD	37.42	35.26	33.73
	MD1	50.21	52.10	48.66
1000 × 1000 m	D	96.67	96.67	100.00
	DI	48.68	36.96	29.03
	MD	37.92	39.58	40.83
	MD1	53.21	55.00	67.50

).

Table 5 shows that the mean crown (stand) density (MD) has the same degree -2a (26–40%), regardless of the sample size and the number of interpreted trees per sample.

As a mean damage (MD) of 31.04% (sample of 100 × 100 m and 4 trees) at 1.3% accuracy and 95% reliability was achieved in the surveyed area, the desired accuracy (B) for other grid densities and numbers of interpreted trees per point (N) were also tested (

Table 6. Numbers of interpreted trees (4 (ABCD), 2 (AD) and 1 (A) trees) and accuracies achieved for different samples.

Sample	100 × 100 m		200 × 200 m		300 × 300 m		500 × 500 m		1000 × 1000 m
	N	B	N	B	N	B	N	B	N	B
ABCD	5258	1.25	1324	2.49	590	3.73	213	6.21	60	11.7
AD	2632	1.76	663	3.52	296	5.27	107	8.77	30	16.56
A	1330	2.49	336	4.95	148	7.45	53	12.46	15	23.41

).

The results obtained show that the scope for the desired accuracies ranges within limits of up to 5%. This limit value is achieved at 200 × 200 m grid density and one interpreted tree per point, as confirmed using GIS analysis (Figure 7 and Figure 8).

Regardless of the fact that there is no statistically significant difference in damage assessment, it is noted that the number of sample points per particular sub-compartment decreases, whereas it is within the 5% limit for the entire surveyed area and density raster of 300 × 300 m.

This way, the participation of particular species and damage degrees in the sample is lost, or in other words, particular sub-compartments are assessed based on one or two sample points, which significantly affects the health status assessment.

The results obtained confirm that it is best to use a 100 × 100 m grid with one interpreted tree per raster point since raster points are optimally spatially distributed over the sub-compartments.

4. Discussion

To define the optimal sample size that should provide statistically sufficient accuracy for crown damage assessment, different dot grid densities (100 × 100 m, 200 × 200 m, 300 × 300 m, 500 × 500 m and 1000 × 1000 m) were tested in combination with different numbers of interpreted trees per sample (1 (A), 2 (AD) and 4 (ABCD) trees).

The testing results showed that there were no statistically significant differences between different sample densities and numbers of interpreted trees in relation to mean damage assessment. Regardless of the fact that there is no statistically significant difference in damage assessment, it was found that by lowering sample densities, starting with 200 × 200 m, the number of trees and the number of sample points per particular sub-compartment significantly decreases, and so does the desired accuracy. Consequently, the participation (distribution) of particular species and damage degrees in the sample are lost, which significantly affects the overall tree health assessment. In contrast, 100 × 100 m grid densities with one interpreted tree at the raster point proved to be the optimal sample size. This confirms the fact found in earlier research, that is, that the selected sample should have several spatially well-distributed points and a smaller number of trees in the point, and samples with larger numbers of trees in a smaller number of points should be avoided [50].

It was determined that the differences in damage indicators between terrestrial data and photointerpretation data are not significant. At the same time, field damage assessments were obtained with 10.84% precision, and according to the results obtained from the recordings, this corresponds only to the 1000 × 1000 m sample. For other sample densities, the precision is much higher in favor of photointerpretation, i.e., with the same precision and number of interpreted trees per systematic sample, significantly more time and estimators need to be invested in the field.

Identifying and monitoring the spatial distribution of damaged trees and snags is one of the priorities of sustainable management. Therefore, timely location of stands with poorer health is necessary so that appropriate measures can be applied to maintain their vitality and productivity at an optimal level. CIR aerial photographs allow an insight into the field condition over a short period [36].

5. Conclusions

Crown damage assessment and determination of the optimal sample size and number of trees per sample were conducted using digital CIR aerial photographs of the MU Josip Kozarac and MU Opeke areas.

Based on the research conducted and the results obtained, the following conclusions can be drawn:

• Interpretation of different sample point densities and numbers of interpreted trees per sample showed that the optimal systematic sample size is 100 × 100 m with one interpreted tree per point, and samples with larger numbers of trees in smaller numbers of points should be avoided.
• The research contributes to the development and application of the most favorable interpretation method to be used in practice. This ensures statistically sufficient reliability of tree health status assessment on CIR aerial photographs, combined with optimal sample size and number of interpreted trees.
• The existing methods for health status assessment are thus improved and new possibilities for applying digital CIR aerial photographs to enable sustainable management of forests under conditions of climate change.