Matlab: Gravity Model for Some Value

Gravity Center

某指数的空间重心可以由以下公式直接算出：

\[X = \frac{{\sum\limits_{i = 1}^n {{W_i}{X_i}} }}{{\sum\limits_{i = 1}^n {{W_i}} }}\] \[Y = \frac{{\sum\limits_{i = 1}^n {{W_i}{Y_i}} }}{{\sum\limits_{i = 1}^n {{W_i}} }}\]

式中：X、Y为重心的经度（横坐标）、纬度（纵坐标）；W为某指数；n为参与计算的指数数量。

Movement Distance

重心转移距离可以由以下公式直接算出：

\[D = \sqrt {{{\left( {{X_{t1}} - {X_{t2}}} \right)}^2} + {{\left( {{Y_{t1}} - {Y_{t2}}} \right)}^2}} \]

式中：D为重心转移距离；t1、t2为前后两个时间。

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References

[1] Yingbin He, Youqi Chen, Huajun Tang, et al.. Exploring spatial change and gravity center movement for ecosystem services value using a spatially explicit ecosystem services value index and gravity model[J]. Environmental Monitoring and Assessment, 2011, 175:563–571.

[2] Caiyao Xu, Lijie Pu, Ming Zhu, et all.. Ecological Security and Ecosystem Services in Response to Land Use Change in the Coastal Area of Jiangsu, China[J]. Sustainability, 2016, 8(8): 1~24.

[3] 孙东琪, 张京祥, 朱传耿等. 中国生态环境质量变化态势及其空间分异分析[J]. 地理学报, 2012, 67(12): 1599~1610.