**Appendix A**

Table A1 shows different fitting formulas of KE-*R* relationships in different research areas. KE-*R* formulas obtained in different regions vary, including polynomial, exponential, logarithm and other forms. In order to reflect the universality of the theoretical formulas introduced in this paper, KE-*R* relationships are obtained by changing equations based on Equation (18) to approximate the formulas given in different studies. The deterministic coefficient is used as the index to evaluate the approximation results, and the fitting results ensure that the deterministic coefficient of the two is greater than 0.99 for each reference listed in Table A1. The scatter points obtained by the KE-*R* relationship obtained by Equation (18) are described, and then, the linear fitting is performed with the points traced based on the original equation; results are shown in Figure A1. The abscissa is the KE obtained by changing different equations in this paper, and the ordinate is the relation obtained by different researchers. The red line is the fitting result. The rainfall intensity corresponding to the horizontal and vertical coordinates of each point on the line is the same. Figure A1 shows that the deterministic coefficients of different results are all above 0.99, indicating that Formula (18) can approximate the KE-*R* results obtained in different studies by changing the parameter values. Since the equation can be fixed only by determining the parameters, it has the value of further generalization.



**Figure A1.** The approximated results of KE-*R* relationships derived by different studies are as follows: (**a**–**f**) are the linear relationships between KE-*R* obtained by this paper and KE-*R* obtained by different studies shown in Table A1, respectively.

#### **References**


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