Quantifying how urban landscape heterogeneity affects land surface temperature at multiple scales

Table 5 Texture metrics as measures of spatial landscape heterogeneity

Metric	Value range	Expected relationship^a	Equation
First-order texture
Variance	≥ 0	H∼X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{\left(i-\upmu \right)}^2p\left(i,j\right) \)
Mean	≥ 0	H∼X	\( \sum \limits_k^{N_g}{kp}_{x-y}(k) \)
Second-order texture
Contrast	≥ 0	H∼X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{\left(i-j\right)}^2{p}_d\left(i,j\right) \)
Dissimilarity	≥ 0	H∼X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}p\left(i,j\right)\left\|i-j\right\| \)
Entropy	≥ 0	H∼X	\( -\sum \limits_i^{N_g}\sum \limits_j^{N_g}p\left(i,j\right)\mathit{\log}\left[p\left(i,j\right)\right] \)
Homogeneity	≥ 0; ≤ 1	H∼−X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}\frac{1}{1+{\left(i-j\right)}^2}{p}_d\left(i,j\right) \)
Correlation	≥ 0; ≤ 0	H∼−X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{p}_d\left(i,j\right)\frac{\left(i-{\mu}_x\right)\left(j-{\mu}_y\right)}{\sigma_x{\sigma}_y} \)
Energy	≥ 0; ≤ 1	H∼−X	\( \sum \limits_i^{N_g}\sum \limits_j^{N_g}{g}_{ig^2} \)

^aH∼X, larger values indicate greater heterogeneity; H ∼ –X, lower values indicate greater heterogeneity.

ISSN: 2288-1220