**3. Results**

210 Environmental Monitoring

In the LIS method, the estimation of total edge length is based on the method of Matérn (1964). The edge length can unbiasedly be estimated by simply counting the number of intersections between patch border and the line transects. According to Matérn (1964), the

> 10000 ˆ 2 *<sup>m</sup> <sup>E</sup> n l*

where *m* is the total number of intersections, *n* is the sample size (number of lines) and *l*

Contagion metric was first proposed by O'Neill et al. (1988) as a measure of clumping of patches. Values for contagion range from 0 to 1. A high contagion value indicates a landscape with few large patches whereas a low value indicates a fragmented landscape with many small patches. Contagion metric is highly related to metrics of diversity and dominance and can also provide information on landscape fragmentation. This metric is originally defined and

Recently, however, a new (vector-based) contagion metric has been developed by Ramezani and Holm (2011a), which is adapted for point sampling. The new version is distance– dependent and allows estimating contagion metric using point sampling (point pairs). According to Ramezani and Holm (2011a), for a given distance *d* the (unconditional)

1 1

where the ( ) *ij p d* (unconditional probability) is estimated by the relative frequency of points in land cover classes *i* and *j* . The estimator ˆ ( ) *ij p d* is then inserted into the Eq. 7 to obtain

A vector based contagion metric has been developed by Wickham et al (1996), which is defined based on the proportion of edge length between land cover classes *i* and *j* to total edge length within landscape. This definition (i.e., Eq. 8) is more adapted to the LIS method.

*s s*

 

Similar to point based contagion (Eq. 7), component ˆ*ij p* should be estimated and then inserted into Eq. 8. The estimator ˆ*ij <sup>p</sup>* ( ˆ ˆ *E E ij <sup>t</sup>* ) is the proportion of the estimator of edge

*ii j <sup>C</sup>*

2

*s s*

*Eij* ) to the estimator of total edge length ( <sup>ˆ</sup>

ln(0.5( ))

ˆ ˆ ln( )

*p p*

*ij ij*

*s s*

ˆ() 1 2 ln( )

*i j*

According to Wickham et al (1996), contagion estimator can be written

ˆ

ˆ ˆ ( ) ln( ( ))

*ij ij*

*p d p d*

*s*

*C d*( ) the unconditional contagion function and *s*is the number of observed

calculated on raster based map (O'Neill et al., 1988; Li and Reynolds, 1993).

*C d*

*E* (m ha-1), using multiple sampling lines of equals length, is

(6)

(7)

(8)

*Et* )

total edge length estimator ˆ

is the length of the sampling line (m).

contagion estimator is defined as

land cover classes in sampling.

length between land cover classes *i* and *j* ( ˆ

estimator of ˆ

**2.2.3 Contagion (C)** 

given by

In this study, the statistical properties (RMSE and bias) of the estimators of the selected metrics were investigated for different sampling combinations. But some major results are presented here. In general, a systematic sampling design resulted in smaller RMSE and bias compared to simple random design, for all combinations.

#### **3.1 Shannon's diversity index**

In point sampling, both RMSE and bias of Shannon's diversity estimator tended to decrease with increasing sample size in both sampling designs. In Fig. 4 is shown the relationship between bias and sample size of Shannon's diversity estimator in systematic and random sampling designs.

Fig. 4. The relationship between bias and sample size of Shannon's diversity estimator using point sampling method in systematic and random sampling designs (from Ramezani et al., 2010).

Landscape Environmental Monitoring:

details in Ramezani and Holm (2011b).

rate of decrease in the contagion function.

bias for the contagion estimator despite its components (i.e., ˆ

differ as they are based on different equations (i.e., Eqs.7 and 8).

sampling design, straight line configuration and line length 37.5 m.

Sample Based Versus Complete Mapping Approaches in Aerial Photographs 213

if its component (i.e., ( ) *ij p d* ) was estimated without bias. The sources of bias discussed in

0.8 0.8 0.9 0.9 0.9 0.9

Contagion

Fig. 6. Example of two landscapes with different degree of fragmentation and their corresponding contagion function (Eq. 7). Top: a high fragmented landscape (four land cover class and nineteen patches) with large rate of decrease of the contagion function. Bottom: a homogenous landscape (three land cover class and three patches) with a small

Contagion

In line intersect sampling, both RMSE and bias of the contagion estimator (Eq.8) tended to decrease with increasing sample size and line transects length. Straight line configuration resulted in lower RMSE and bias than other configurations. We found a small and negative

0 0.2 0.4 0.6 0.8 1

without bias. The relative RMSE and bias of the contagion estimator through line intersect sampling (LIS) method (Eq.8) is shown in Fig. 7. Note that the two contagion estimators

A comparison was also made for variability in terms of range and mean in sample based estimates of Shannon's diversity, edge length and contagion metrics for sample sizes 16 and 100. In Table 1 is provided an example for line intersects sampling method, systematic

*Eij* and <sup>ˆ</sup>

0 100 200 300

0 100 200 300

Point distance (m)

Point distance (m)

*Et* ) can be estimated

In line intersect sampling, similar to point sampling, both RMSE and bias of Shannon's estimator tended to decrease with increasing sample size and line length. The longer line transect (here 150 m) resulted in lower RMSE and bias than shorter one (here 37.5 m), for a given sample size. We found a small and negative bias for the estimator in both point and the LIS methods. The magnitude of bias tended to decrease both with increasing sample size and line transects length. Straight line configuration resulted in lower RMSE and bias than other configurations.

#### **3.2 Total edge length**

In point sampling, the magnitude of RMSE of estimator is highly related to buffer width, for a given sample size and a wide buffer resulted in lower RMSE than narrow one. The edge length estimator had bias since parts of buffer close to the map border were outside the map. Bias of estimator tended to increase with increasing buffer width whereas it was independent on sample size. To eliminate or reduce the bias of estimator three corrected methods were suggested which have been discussed in detilas in Ramezani et al. (2010).

In LIS, the magnitude of RMSE of estimator is dependent on the length of the line transect, for a given sample size and the longer transect resulted in lower RMSE than short one. Furthermore, straight line configuration resulted in lower RMSE compared to other configurations (e.g., L and square shape). In Fig. 5 is shown the relationship between relative RMSE and sampling line lengths of total edge length estimator.

Fig. 5. Relative RMSE of total edge length estimator for different sampling line lengths and configurations of line intersect sampling, for a given sample size (from Ramezani and Holm, 2011c).

#### **3.3 Contagion**

Point based contagion (i.e., Eq. 7) is a distance–dependent function that delivers a contagion value that decreased with increasing point distance. The rate of decrease of the contagion value was faster in a fragmented landscape compared to a more homogenous landscape. Examples of such landscapes are shown in Fig. 6. The contagion estimator was biased even

In line intersect sampling, similar to point sampling, both RMSE and bias of Shannon's estimator tended to decrease with increasing sample size and line length. The longer line transect (here 150 m) resulted in lower RMSE and bias than shorter one (here 37.5 m), for a given sample size. We found a small and negative bias for the estimator in both point and the LIS methods. The magnitude of bias tended to decrease both with increasing sample size and line transects length. Straight line configuration resulted in lower RMSE and bias than

In point sampling, the magnitude of RMSE of estimator is highly related to buffer width, for a given sample size and a wide buffer resulted in lower RMSE than narrow one. The edge length estimator had bias since parts of buffer close to the map border were outside the map. Bias of estimator tended to increase with increasing buffer width whereas it was independent on sample size. To eliminate or reduce the bias of estimator three corrected methods were suggested which have been discussed in detilas in Ramezani et al. (2010). In LIS, the magnitude of RMSE of estimator is dependent on the length of the line transect, for a given sample size and the longer transect resulted in lower RMSE than short one. Furthermore, straight line configuration resulted in lower RMSE compared to other configurations (e.g., L and square shape). In Fig. 5 is shown the relationship between

> straight line L - shape Y - shape Triangle shape Square shape

Fig. 5. Relative RMSE of total edge length estimator for different sampling line lengths and configurations of line intersect sampling, for a given sample size (from Ramezani and Holm,

Sampling line length per configuration (m)

25 75 125 175

Point based contagion (i.e., Eq. 7) is a distance–dependent function that delivers a contagion value that decreased with increasing point distance. The rate of decrease of the contagion value was faster in a fragmented landscape compared to a more homogenous landscape. Examples of such landscapes are shown in Fig. 6. The contagion estimator was biased even

relative RMSE and sampling line lengths of total edge length estimator.

other configurations.

**3.2 Total edge length** 

2011c).

**3.3 Contagion** 

RMSE (%)

if its component (i.e., ( ) *ij p d* ) was estimated without bias. The sources of bias discussed in details in Ramezani and Holm (2011b).

Fig. 6. Example of two landscapes with different degree of fragmentation and their corresponding contagion function (Eq. 7). Top: a high fragmented landscape (four land cover class and nineteen patches) with large rate of decrease of the contagion function. Bottom: a homogenous landscape (three land cover class and three patches) with a small rate of decrease in the contagion function.

In line intersect sampling, both RMSE and bias of the contagion estimator (Eq.8) tended to decrease with increasing sample size and line transects length. Straight line configuration resulted in lower RMSE and bias than other configurations. We found a small and negative bias for the contagion estimator despite its components (i.e., ˆ *Eij* and <sup>ˆ</sup> *Et* ) can be estimated without bias. The relative RMSE and bias of the contagion estimator through line intersect sampling (LIS) method (Eq.8) is shown in Fig. 7. Note that the two contagion estimators differ as they are based on different equations (i.e., Eqs.7 and 8).

A comparison was also made for variability in terms of range and mean in sample based estimates of Shannon's diversity, edge length and contagion metrics for sample sizes 16 and 100. In Table 1 is provided an example for line intersects sampling method, systematic sampling design, straight line configuration and line length 37.5 m.

Landscape Environmental Monitoring:

a (buffer 40 (m)) b (line 150 (m))

and lines)

**4. Discussion** 

Sample Based Versus Complete Mapping Approaches in Aerial Photographs 215

Table 2. Average time consumption of data collection on five NILS plots for point sampling and complete mapping for deriving the Shannon's index (from Ramezani et al. (2010))

Edge length estimator Shannon' s diversity estimator

Method Time needed (h)

Complete mapping 3.5

9 0.4 100 0.8 225 1.9 400 3.3

Sampling method Time needed (min)

time is independent on line configuration in the aerial photo.

Point sampling 25 a 28.3 LIS 18.3 b 60 b

Table 3. Average time needed for point and line intersect sampling (LIS) methods for deriving Shannon's diversity and total edge length. For sample size 100 (number of point

The time needed to collect data was highly related to landscape complexity and the classification system applied. We also found that in a coarse classification system the time needed was less than in a more detailed system. This issue becomes more serious in complete mapping approaches where all potential polygons should be delineated. Furthermore, time was also dependent on sampling method the chosen. With a point sampling method less time was needed for estimating Shannon's diversity compared with other metrics. With line intersect sampling; it was more time efficient to use edge-related metrics. For a given sample size, the time depended on the length of line transect (in LIS) and the buffer width (in point sampling). With the former method it is indicated that the

This study addresses the potential of sampling data for estimating some landscape metrics in remote sensing data (aerial photo). Sample based approach appears to be a very promising alternative to complete mapping approach both in terms of time needed (cost) and data quality (Kleinn and Traub, 2003; Corona et al., 2004; Esseen et al., 2006). However, some metrics may not be estimated from sample data regardless of chosen sampling method since currently used landscape metrics are defined based on mapped data. To describe landscape patterns accurately, a set of landscape metrics is needed since all aspect of landscape composition and configuration cannot be captured through a single metric. On the other hand, all metrics cannot be extracted using a single sampling method. Thus, in a sample based approach a combination of different sampling methods is needed, for instance, a combination of point and line intersect sampling. In such combined design, the

Point sampling (number of points)

Fig. 7. Relative RMSE (top) and bias (bottom) of contagion estimator (Eq. 8) for different sampling line lengths and configurations, a sample 49 and systematic sampling design


a according to Eq.8

Table 1. Variability (mean) in sample based estimates of Shannon's diversity, edge length and contagion in fifty random landscapes (NILS plots) in Sweden for sample sizes 16 and 100. Data collected using line intersects sampling method, systematic sampling design, straight line configuration and 37.5 m length of sampling lines. Ranges are given in parentheses.

#### **3.4 Time study (cost needed for data collection)**

A time study was conducted on non-delineated aerial photos from NILS employing an experienced photo interpreter. The results of the time study for Shannon's diversity and total edge length are summarized in Tables 2 and 3.


Table 2. Average time consumption of data collection on five NILS plots for point sampling and complete mapping for deriving the Shannon's index (from Ramezani et al. (2010))


a (buffer 40 (m))

214 Environmental Monitoring

25 75 125 175

Sampling line length per configuration (m)


Fig. 7. Relative RMSE (top) and bias (bottom) of contagion estimator (Eq. 8) for different sampling line lengths and configurations, a sample 49 and systematic sampling design

Sampling line length per configuration (m)

Shannon' diversity 0.398 (0.019-0.747) 0.423 (0.026-0.784) Contagion a 0.188 (0.006-0.478) 0.407 (0.226-0.758)

Total edge length (m ha-1) 92.2 (12.2-197.6) 92.1 (10.5-194.6)

Table 1. Variability (mean) in sample based estimates of Shannon's diversity, edge length and contagion in fifty random landscapes (NILS plots) in Sweden for sample sizes 16 and 100. Data collected using line intersects sampling method, systematic sampling design, straight line configuration and 37.5 m length of sampling lines. Ranges are given in parentheses.

A time study was conducted on non-delineated aerial photos from NILS employing an experienced photo interpreter. The results of the time study for Shannon's diversity and

16 100

Straight line L shape Y shape

Triangle shape square shape

Square shape

Landscape metrics Sample size

**3.4 Time study (cost needed for data collection)** 

15






Bias (%)



0

30

45

RMSE (%)

60

75

45

35

25

15

5

total edge length are summarized in Tables 2 and 3.

a according to Eq.8

b (line 150 (m))

Table 3. Average time needed for point and line intersect sampling (LIS) methods for deriving Shannon's diversity and total edge length. For sample size 100 (number of point and lines)

The time needed to collect data was highly related to landscape complexity and the classification system applied. We also found that in a coarse classification system the time needed was less than in a more detailed system. This issue becomes more serious in complete mapping approaches where all potential polygons should be delineated. Furthermore, time was also dependent on sampling method the chosen. With a point sampling method less time was needed for estimating Shannon's diversity compared with other metrics. With line intersect sampling; it was more time efficient to use edge-related metrics. For a given sample size, the time depended on the length of line transect (in LIS) and the buffer width (in point sampling). With the former method it is indicated that the time is independent on line configuration in the aerial photo.
