Fig. 3.

Relationships between area and perimeter of soil moisture islands and the distribution of tree clusters. (A) Perimeter vs. area of soil moisture islands. Here $a_1=0.014$ ${\text{d}}^{-1}$ and $b_1=0.002$ ${\text{mm}}^{-1}$ for the case of average rain and threshold equal to 0.2. It shows that $P\propto A^{D/2}$ with $D=\mathrm{1.36.}$ Plots of perimeter vs. area with different rainfall and thresholds are similar and can be found in SI Appendix, Fig. S5. (B) The distribution function $P\left(A\prime \ge a\right)$ for tree clusters plotted at log–log scale, where $A\prime \propto A^{1-D/2}.$