**2.1 Study area**

206 Environmental Monitoring

shape (Morgan et al., 2010). The experience of the interpreters is critical and the results from manual interpretation are thus often more accurate than those from automated approaches. However, the manual approach may be time-consuming (Corona et al., 2004), subjective (interpreter-dependent) and considerable variation may occur between photo interpreters. The automated approach is sometimes unreliable, for instance, when land cover classes that are similar in terms of spectral reflectance should be separated (Wulder et al., 2008). In addition, overall time, including delineation and corrections may be large if an

Sample based approach is an interesting alternative to extract landscape data compared to complete mapping (Kleinn and Traub, 2003). The argument is that a sample survey takes less time; that it is possible to achieve more accurate result in a well-designed and wellexecuted sample survey; and that data can be acquired and analyzed more efficiently (Raj, 1968; Cochran, 1977). The efficiency and speed in delivering results is of particular interest in landscape–scale monitoring programs where stakeholders commonly are closely involved and expect outputs within reasonable time. Figure 1 shows examples of complete mapping and sample based approaches (point and line intersect sampling methods) over 1 km × 1 km

 Fig. 1. Examples of complete mapping and sample based approaches to extract landscape metrics in 1 km × 1 km aerial photo. A) Complete mapping, B) systematic point sampling with fixed buffer (40 m), C) point pairs sampling, and D) systematic line intersect sampling. Since aerial photos are important source of data for many ongoing environmental monitoring programs such as NILS (Ståhl et al., 2011), there is an urgent need to investigate the possibilities and limitations of both mapping and sample based approaches for estimating landscape metrics. The overall objective of this chapter is to compare the

inappropriate automated approach is chosen.

aerial photo from NILS.

The data was collected from aerial photographs and land cover maps from the NILS program (Ståhl et al., 2011), which covers the whole of Sweden. NILS was developed to monitor conditions and trends in land cover classes, land use and biodiversity at multiple spatial scales (point, patch, landscape) as basic input to national and international environmental frameworks and reporting schemes. NILS was launched in 2003 and has developed a monitoring infrastructure that is applicable for many different purposes. The basic outline is to combine 3-D interpretation of CIR (Color Infra Red) aerial photos with field inventory on in total of 631 permanent sample plots (5 km × 5 km) across all terrestrial habitats and the land base of Sweden (see Fig. 2).

Fig. 2. Illustration of systematic distribution of 631 NILS 1 km × 1 km sample plot across Sweden with ten strata. The density of plots varies among the strata (Ståhl et al., 2011).

Landscape Environmental Monitoring:

**2.2.2 Total edge length (E)** 

total length of all line transects, and *A* is the total area.

delineated aerial photograph for estimating edge length in practice.

be estimated without bias, for a given land cover class by

land cover class *j* is then estimated by

where *d* is buffer width (m) in one side.

monitoring and sustainable forest magament.

Sample Based Versus Complete Mapping Approaches in Aerial Photographs 209

where *ij l* is the intersection length of the *j* th land cover class with sampling line *i* , *L* is the

This metric refers to the amount of edge within landscape. An edge is defined as the border between two different land cover classes. Edge length is a robust metric and can be used as a measure of landscape fragmenattion (Saura and Martinez-Millan, 2001). In a highly fragmented landscape there are more edges and response to those depends on the species under consideration (Ries et al., 2004). The length is relevant for both biodiversity

Ramezani et al. (2010) demonstrated that total edge length in the landscape can be estimated using point sampling in aerial photographs without direct length measurement. In such procedure, estimation of the length is based on area proportion of a buffer around patch borders. In Fig. 3 is shown a rectangular buffer around patch border for simulation application. The proportion of sampling points within the buffer can be employed for estimating the buffer area and, hence, the edge length. In practice, however, if a photo interpreter observed a point within distance *d* from a potential edge, this would be recorded. Figure 2 shows a circular buffer (with fixed radius 40 m) around sampling points on non-

According to Ramezani et al. (2010), the buffer area *Bj* inside the landscape with area *A,* can

where ˆ *<sup>j</sup> p* is the estimator (1) of the buffer area proportion. The length *Ej* of the edge of the

<sup>ˆ</sup> <sup>ˆ</sup> <sup>ˆ</sup> 2 2 *j j j*

Fig. 3. Illustration of rectangular buffer with fixed width created in both sides of patch border for estimating edge length for simulation application (from Ramezani et al., 2010)

<sup>ˆ</sup> <sup>ˆ</sup> *B pA j j* (4)

*<sup>B</sup> <sup>A</sup> E p d d* (5)

The present study is based on a detailed aerial photo interpretation of a central 1 km × 1 km square in the sample plot. Landscape data was extracted from 50 randomly selected NILS 1 km × 1 km sample plots distributed throughout Sweden. The aerial photo interpretation is carried out on aerial photos with a scale of 1:30 000. The aerial photographs in which interpretations were made had a ground resolution of 0.4 m. Polygon delineation is made using the interpretation program Summit Evolution from DAT/EM and ArcGIS from ESRI. According to the NILS' protocol, homogenous area delineated into polygons which are described with regard to land use, land cover class, as well as features related to trees, bushes, ground vegetation, and soils (Jansson et al., 2011; Ståhl et al., 2011).

#### **2.2 Landscape metrics**

Landscape metrics are defined based on measurable patch (landscape element) attributes where these attributes first should be estimated. In this study, point (dot grid) and line intersect sampling (LIS) methods were separately applied in (vector-based) land cover map from aerial photos for estimating three landscape metrics: Shannon's diversity, total edge length and contagion. Riitters et al. (1995) demonstrated that these metrics are among the most relevant metrics in landscape pattern analysis. Definition and estimators of the selected metrics are briefly described below.

#### **2.2.1 Shannon's diversity index (H)**

This metric refers to both the number of land cover classes and their proportions in a landscape. The index value ranges between 0 and 1. A high value shows that land cover classes present have roughly equal proportion whereas a low value indicates that the landscape is dominated by one land cover class. The index, *H* , is defined as

$$H = -\frac{\sum\_{j=1}^{s} p\_j \cdot \ln(p\_j)}{\ln(s)}\tag{1}$$

where *<sup>j</sup> p* is the area proportion of the *j* th land cover class and *s* is the total number of land cover classes considered (assumed to be known). For 0, ln( ) *jjj ppp* is set to zero. The estimator *H*<sup>ˆ</sup> of *H* is obtained by letting the estimator ˆ *<sup>j</sup> <sup>p</sup>* for land cover class *<sup>j</sup>* in Eq. 2 (for point sampling) and in Eq. 3 (for line intersect sampling) take the place of *<sup>j</sup> p* in formula (1). With point sampling, *<sup>j</sup> p* is estimated without bias by

$$
\hat{p}\_{\dot{j}} = \frac{1}{n} \sum\_{i=1}^{n} y\_i \tag{2}
$$

where *<sup>i</sup> y* takes the value 1 if the *i* th sampling point falls in certain class and 0 otherwise and *n* is the sample size (total number of points).

With the line intersect sampling (LIS) method (Gregoire and Valentine, 2008), *<sup>j</sup> p* can unbiasedly be estimated by

$$
\hat{p}\_j = \frac{A}{L} \cdot \sum\_{i=1}^n I\_{ij} \tag{3}
$$

where *ij l* is the intersection length of the *j* th land cover class with sampling line *i* , *L* is the total length of all line transects, and *A* is the total area.

### **2.2.2 Total edge length (E)**

208 Environmental Monitoring

The present study is based on a detailed aerial photo interpretation of a central 1 km × 1 km square in the sample plot. Landscape data was extracted from 50 randomly selected NILS 1 km × 1 km sample plots distributed throughout Sweden. The aerial photo interpretation is carried out on aerial photos with a scale of 1:30 000. The aerial photographs in which interpretations were made had a ground resolution of 0.4 m. Polygon delineation is made using the interpretation program Summit Evolution from DAT/EM and ArcGIS from ESRI. According to the NILS' protocol, homogenous area delineated into polygons which are described with regard to land use, land cover class, as well as features related to trees,

Landscape metrics are defined based on measurable patch (landscape element) attributes where these attributes first should be estimated. In this study, point (dot grid) and line intersect sampling (LIS) methods were separately applied in (vector-based) land cover map from aerial photos for estimating three landscape metrics: Shannon's diversity, total edge length and contagion. Riitters et al. (1995) demonstrated that these metrics are among the most relevant metrics in landscape pattern analysis. Definition and estimators of the

This metric refers to both the number of land cover classes and their proportions in a landscape. The index value ranges between 0 and 1. A high value shows that land cover classes present have roughly equal proportion whereas a low value indicates that the

1

where *<sup>j</sup> p* is the area proportion of the *j* th land cover class and *s* is the total number of land cover classes considered (assumed to be known). For 0, ln( ) *jjj ppp* is set to zero. The estimator *H*<sup>ˆ</sup> of *H* is obtained by letting the estimator ˆ *<sup>j</sup> <sup>p</sup>* for land cover class *<sup>j</sup>* in Eq. 2 (for point sampling) and in Eq. 3 (for line intersect sampling) take the place of *<sup>j</sup> p* in formula (1).

*j*

*s*

ln( )

(1)

(2)

(3)

*j j*

*p p*

ln( )

1

1

where *<sup>i</sup> y* takes the value 1 if the *i* th sampling point falls in certain class and 0 otherwise

With the line intersect sampling (LIS) method (Gregoire and Valentine, 2008), *<sup>j</sup> p* can

<sup>ˆ</sup> *<sup>n</sup> j ij i*

*A p l L*

<sup>1</sup> <sup>ˆ</sup> *<sup>n</sup> j i i p y n*

*s*

bushes, ground vegetation, and soils (Jansson et al., 2011; Ståhl et al., 2011).

landscape is dominated by one land cover class. The index, *H* , is defined as

*H*

**2.2 Landscape metrics** 

selected metrics are briefly described below.

With point sampling, *<sup>j</sup> p* is estimated without bias by

and *n* is the sample size (total number of points).

unbiasedly be estimated by

**2.2.1 Shannon's diversity index (H)** 

This metric refers to the amount of edge within landscape. An edge is defined as the border between two different land cover classes. Edge length is a robust metric and can be used as a measure of landscape fragmenattion (Saura and Martinez-Millan, 2001). In a highly fragmented landscape there are more edges and response to those depends on the species under consideration (Ries et al., 2004). The length is relevant for both biodiversity monitoring and sustainable forest magament.

Ramezani et al. (2010) demonstrated that total edge length in the landscape can be estimated using point sampling in aerial photographs without direct length measurement. In such procedure, estimation of the length is based on area proportion of a buffer around patch borders. In Fig. 3 is shown a rectangular buffer around patch border for simulation application. The proportion of sampling points within the buffer can be employed for estimating the buffer area and, hence, the edge length. In practice, however, if a photo interpreter observed a point within distance *d* from a potential edge, this would be recorded. Figure 2 shows a circular buffer (with fixed radius 40 m) around sampling points on nondelineated aerial photograph for estimating edge length in practice.

According to Ramezani et al. (2010), the buffer area *Bj* inside the landscape with area *A,* can be estimated without bias, for a given land cover class by

$$
\hat{B}\_j = \hat{p}\_j \cdot A \tag{4}
$$

where ˆ *<sup>j</sup> p* is the estimator (1) of the buffer area proportion. The length *Ej* of the edge of the land cover class *j* is then estimated by

$$
\hat{E}\_j = \frac{\hat{B}\_j}{2d} = \hat{p}\_j \cdot \frac{A}{2d} \tag{5}
$$

where *d* is buffer width (m) in one side.

Fig. 3. Illustration of rectangular buffer with fixed width created in both sides of patch border for estimating edge length for simulation application (from Ramezani et al., 2010)

Landscape Environmental Monitoring:

**2.2.4 Monte-Carlo sampling simulation** 

*Eij* and <sup>ˆ</sup>

simple random sampling designs were employed for all cases above.

compared to simple random design, for all combinations.

within landscape. Both ˆ

**3. Results** 

sampling designs.

2010).

**3.1 Shannon's diversity index** 





Bias (%)



0

Sample Based Versus Complete Mapping Approaches in Aerial Photographs 211

In this study, Monte-Carlo sampling simulation was used to assess statistical performance (bias and RMSE) of estimators of the selected metric. Bias (or systematic error) is the difference between the expected value of the estimator and the true value. RMSE is the square root of the expected squared deviation between the estimator and the true value. In point sampling, simulation was conducted for four sample sizes (49, 100, 225, and 400) for both Shannon's diversity and total edge length and five buffer widths (5, 10, 20, 40, and 80 m) for total edge length. In line intersect sampling, simulation was conducted for four sample sizes (16, 25, 49, and 100), three line transect length (37.5, 75, and 150 m), and five transect configurations (Straight line, L, Y, Triangle, and Square shapes). In point pairs sampling (i.e., using Eq.7) simulation was conducted for nine point distances (2, 5, 10, 20, 30, 60, 100, 150, and 250 m) and five sample sizes (25, 49, 100, 225, and 400). Systematic and

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

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

0 100 200 300 400

Systematic design

Random design

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.,

Sample size

a value of 1 from Eq. 8 indicates a fragmented landscape with many small patches.

*Et* can unbiasedly be estimated by Eq. 6. In contrast to Eq. 7,

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 total edge length estimator ˆ *E* (m ha-1), using multiple sampling lines of equals length, is given by

$$
\hat{E} = \frac{10000 \cdot \pi \cdot m}{2 \cdot n \cdot l} \tag{6}
$$

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

#### **2.2.3 Contagion (C)**

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

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) contagion estimator is defined as

$$\hat{\mathbf{C}}(d) = 1 + \frac{\sum\_{i=1}^{s} \sum\_{j=1}^{s} \hat{p}\_{ij}(d) \cdot \ln(\hat{p}\_{ij}(d))}{2 \ln(s)}\tag{7}$$

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 estimator of ˆ *C d*( ) the unconditional contagion function and *s*is the number of observed land cover classes in sampling.

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

$$\hat{C} = -\frac{\sum\_{\vec{i}}^{S} \sum\_{\vec{i} \neq \vec{j}}^{S} \hat{p}\_{\vec{i}\vec{j}} \cdot \ln(\hat{p}\_{\vec{i}\vec{j}})}{\ln(0.5(s^2 - s))}\tag{8}$$

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 length between land cover classes *i* and *j* ( ˆ *Eij* ) to the estimator of total edge length ( <sup>ˆ</sup> *Et* ) within landscape. Both ˆ *Eij* and <sup>ˆ</sup> *Et* can unbiasedly be estimated by Eq. 6. In contrast to Eq. 7, a value of 1 from Eq. 8 indicates a fragmented landscape with many small patches.
