**2. Methodology**

Michigan is located in the Great Lakes Region of the United States of America. It is the only state to consist of two peninsulas with the longest shoreline of any state of the lower 48 states. These two peninsulas are linked by the Mackinaw Bridge. The Straights of Mackinac separate the Upper Peninsula from the Lower Peninsula, whose shape looks like a mitten (**Figure 1**). The study area spans abundant agricultural lands in the south, hardwood forests in the middle portion, and mixed evergreen forests in the north. The study area also contains a large urban landscape comprised of metropolitan Detroit, plus numerous industrial sites, especially in the lower part of the state. The study area contains level glacial lake plains, hilly moraines, and ancient eroded mountain chains. The population of the state is only 10 million people (roughly the same population number as the Kingdom of Sweden but about half the size in overall land area).

The methodology used for this study was similar to that utilized by Lu et al., where land cover and visual/environmental quality covary [26]. A comprehensive explanation of this methodology can be found in Lu et al. [26]. Adhering closely to this method, images of various landscapes across the study area were collected and randomly sorted into two groups: one group to assist in making a prediction and another group to validate or refute the prediction. From the first group, scores for the images were generated by employing Eq. (1) developed by Burley [19]. The information presented by Burley is the formative paper in this line of work and investigators interested in understanding the fundamentals of this line of research are urged to examine this paper. Once the scores were obtained, they were applied to similar land-uses to form a map predicting environmental quality.

$$\begin{aligned} \text{mass to form a map preceding environment quantity.}\\ \text{(1) } &= 68.30 - (1.878 \, ^\circ \text{HEAD}) - (0.131 \, ^\circ \text{X1}) - (0.064 \, ^\circ \text{X6}) + (0.020 \, ^\circ \text{X9}) \\ &+ (0.036 \, ^\circ \text{X10}) + (0.129 \, ^\circ \text{X15}) - (0.129 \, ^\circ \text{X19}) - (0.006 \, ^\circ \text{X2}) \\ &+ (0.00003 \, ^\circ \text{X34}) + (0.032 \, ^\circ \text{X52}) + (0.0008 \, ^\circ \text{X1} \, ^\circ \text{X1}) + (0.00006 \, ^\circ \text{X6} \, ^\circ \text{X6}) \\ &- (0.0003 \, ^\circ \text{X15} \, ^\circ \text{X15}) + (0.0002 \, ^\circ \text{X19} \, ^\circ \text{X2} \, ^\circ \text{X14}) \\ &- (0.00003 \, ^\circ \text{X52} \, ^\circ \text{X52}) - (0.0000001 \, ^\circ \text{X52} \, ^\circ \text{X4}) \end{aligned} \tag{1}$$

where

HEALTH = environmental quality index (**Table 1**)

X1 = perimeter of immediate vegetation

X2 = perimeter of intermediate non-vegetation

X3 = perimeter of distant vegetation


Lothian presents the fundamentals and an overview of various approaches to constructing

These recent studies provide a setting for our investigation. As an extension of Lu's et al. and Jin's research, we were interested in applying this approach to all of Michigan (**Figure 1**) [26, 27].

Michigan is located in the Great Lakes Region of the United States of America. It is the only state to consist of two peninsulas with the longest shoreline of any state of the lower 48 states. These two peninsulas are linked by the Mackinaw Bridge. The Straights of Mackinac separate the Upper Peninsula from the Lower Peninsula, whose shape looks like a mitten (**Figure 1**). The study area spans abundant agricultural lands in the south, hardwood forests in the middle portion, and mixed evergreen forests in the north. The study area also contains a large urban landscape comprised of metropolitan Detroit, plus numerous industrial sites, especially in the lower part of the state. The study area contains level glacial lake plains, hilly moraines, and ancient eroded mountain chains. The population of the state is only 10 million people (roughly the same population number as the Kingdom of Sweden but about half the

The methodology used for this study was similar to that utilized by Lu et al., where land cover and visual/environmental quality covary [26]. A comprehensive explanation of this methodology can be found in Lu et al. [26]. Adhering closely to this method, images of various landscapes across the study area were collected and randomly sorted into two groups: one group to assist in making a prediction and another group to validate or refute the prediction. From the first group, scores for the images were generated by employing Eq. (1) developed by Burley [19]. The information presented by Burley is the formative paper in this line of work and investigators interested in understanding the fundamentals of this line of research are urged to examine this paper. Once the scores were obtained, they were applied to similar

visual quality maps and is a substantia update to the work of Taylor et al. [12, 28]

We wanted to make a validated map for all of Michigan.

land-uses to form a map predicting environmental quality.

HEALTH = environmental quality index (**Table 1**)

X2 = perimeter of intermediate non-vegetation

X1 = perimeter of immediate vegetation

X3 = perimeter of distant vegetation

Y = 68.30 − (1.878 \* HEALTH) − (0.131 \* X1) − (0.064 \* X6) + (0.020 \* X9)

− (0.0003 \* X15 \* X15) + (0.0002 \* X19 \* X19) − (0.0009 \* X2 \* X14)

<sup>+</sup> (0.00003 \* <sup>X</sup>34) <sup>+</sup> (0.032 \* <sup>X</sup>52) <sup>+</sup> (0.0008 \* X1 \* X1) <sup>+</sup> (0.00006 \* X6 \* X6)

+ (0.036 \* X10) + (0.129 \* X15) − (0.129 \* X19) − (0.006 \* X32)

− (0.00003 \* X52 \* X52) − (0.0000001 \* X52 \* X34)

(1)

**2. Methodology**

116 Land Use - Assessing the Past, Envisioning the Future

size in overall land area).

where


Next, the second group of images was compared to predictions made by the map through the use of Kendall's Concordance, a statistical technique that examines and tests for significant agreement/similarity [29, 30]. If the scores statistically agree, it is possible to create a reliable visual quality prediction map. This step in the methodology used here is explained in great detail by Jin [31]. Investigators interested in applying this methodology are advised to obtain copies of Lu et al. and Jin for a complete explanation [26, 31].

The test statistics were determined by applying Eqs. (2) and (3) to the data. The results are based upon rankings of treatment scores across rows. In this case, the rows are pairs of images between two treatments: (1) the predicted score for a randomly chosen site in the study area and (2) the actual score from a photograph taken at that location. There are 30 rows (pairs of scores) for this study (n = 30). The treatments are the columns (m = 2). The rankings are summed and squared, to compute Kendall's W value (Eq. 2). (Rj)2 is the sum of the squares of the rankings for a column in computing the Kendall's W value [29, 30].

$$\mathcal{W} = 12\sum\_{j=1}^{n} \text{(Rj)}^2 - \left[ \Im \,\text{m}^2 \,\text{n} \,(\text{n}+1)^2 \right] / \left[ \text{m}^2 \,\text{n} (\text{n}^2 - 1) \right] \tag{2}$$

Kendall's W value is a number ranging between 0 and 1. When W is near 0, there is no strong overall trend of agreement among the respondents. If W is near 1, then the responses could be


**Table 1.** Variables for the environmental quality/health index in Eq. (1).

regarded as close to unanimous in their agreement. The W test statistic approximates a Chisquare distribution with n−1 degrees of freedom (Eq. (3)). If computed values for Chi-square (results of (Eq. (3)) are greater than significant values in a Chi-square table for n−1 degrees of freedom (in this case 29 = 30–1), then there is a high level of agreement/concordance—the predicted scores and the actual scores are in agreement.

$$\mathbf{X}^2 = \mathbf{m(n-1)W} \tag{3}$$

**Figure 2.** Image of sample number 67 of a forested landscape in the upper peninsula of Michigan (visual score of 38.548).

A Visual Quality Prediction Map for Michigan, USA: An Approach to Validate Spatial Content

http://dx.doi.org/10.5772/intechopen.79490

119

**Figure 3.** Image of sample number 80 of a farmland landscape in north-east of the lower peninsula of Michigan (visual

**Figure 4.** An image of a residential landscape (urban savanna with visual quality score of 46.587), sample number 12 in

score of 44.09).

the northwest of the lower peninsula.
