Mathematical Problems in Engineering Landscape Ecological Security Assessment and Ecological Pattern Optimization of Inland River Basins in Arid Regions: A Case Study in Tarim River Basin

Table 1

The methods of landscape pattern indices.

Index	Formula	Ecological meaning of landscape pattern index
Landscape fragment, Ci		Ci represents the fragmentation degree to which the landscape is segmented at a given time and nature, with higher values representing higher fragmentation of the landscape and greater human disturbance to the landscape. ni is the number of patches of landscape type i, Ai is the total area of landscape type i.
Landscape separation, Ni		Ni represents the degree of separation of patch distribution in the same landscape type, and the larger the value, the more complex the corresponding landscape spatial distribution and the higher the degree of fragmentation [36]. A is the total landscape area.
Landscape fractal dimension, Fi		Fi is a noninteger dimension value representing the geometric complexity of the patch or landscape mosaic. The value ranges from 1 to 2. The larger the value, the more complex the structure and change of the landscape patch. Pi is the perimeter of landscape type i.
Landscape interference, Ei		Ei represents the effect of human interference on the area. The smaller the value, the better the survival of the creature. a, b, and c are the weights of the corresponding landscape indices, and a + b + c = 1, assign a, b, and c to 0.5, 0.3, and 0.2, respectively [37, 38].
Landscape fragility, Vi	Expert consultation and normalization	Vi represents the sensitivity of different landscape types to external disturbances, and the larger the value, the higher the ecological risk. According to the actual situation of the study area, the desert and Gobi are assigned a value of 7. The saline-alkali land is assigned a value of 6. The water area is assigned a value of 5. The cropland land is assigned a value of 4. The grassland is assigned a value of 3. The forest is assigned a value of 2. The urban land in the oasis in the arid area is the main area of human activities, the most stable, and is assigned a value of 1. Then, the landscape fragility is calculated using normalization.
Landscape loss degree, Ri		Ri expresses the difference in the ecological loss suffered by various types of landscapes when disturbed, that is, the degree of loss of natural attributes. Through the comprehensive reflection of landscape disturbance index and landscape vulnerability index
Ecological risk index, ERI		Based on the landscape disturbance index and vulnerability index, the spatial pattern was transformed into ecological risk variables by sampling method, and the ecological risk index of land use was constructed. N is the number of landscape types, Axi is the area of the i-th type of landscape component in the x-th risk area, and Ax is the total area of the x-th risk area