### Calculation of rainfall energy

The concept of R was firstly put forward by American scholars Wischmeier W. H and Smith D. D et al [1], After comprehensive analysing the relationship among soil loss data and many rain physical parameters such as P, E, maximum time intensity (IN), antecedent precipitation (Pa) and other compound factors, a formula was established by they to calculate R value:

R=\sum E\cdot {I}_{30}

(1)

Where E is the total energy of a rainfall (MJ/hm^{2}), and I_{30} the maximum 30-min intensity (mm/h).

As the USLE has widely been used for predicting soil loss in countries all over the world, the formula (1) is generally recognized as one of the most classic calculation methods to predict R [12].

E is determined by quality and velocity of raindrop, as a result, a rain drop's energy can be calculated if quantity and velocity are known, an individual rainfall's energy is the sum of all drops. Energy of an individual rainstorm is the function of the total rainstorm quality and the various rain intensity [13], the following equation was used to calculate the energy of an individual rainstorm:

E=\underset{0}{\overset{T}{\int}}e\cdot idt

(2)

Where e is the energy of one unit rainfall (J), i is rainfall intensity of differential time (mm/min), t is differential time and T is the total time of one rain.

However, as the physical shape and velocity of one rain drop is hardly to measure, so far, energy of rainfall is still acquired by the relationship between energy and statistic rain intensity. In most cases, formula (2) can be replaced by this following discontinuous form:

Where E is the energy of a certain period rainfall (MJ/hm^{2}), e the energy of per unit rainfall (MJ/hm^{2} mm) and P the rainfall precipitation of one certain period. In the Wischmeier W. H's formula, e can be determined by the formula as follows:

Where e is the energy of per unit rainfall (J/m^{2} mm) and I the intensity of per unit rainfall (mm/h).

Through analyzing nature raindrops' characters, the calculation formula of Northwest, Northeast and Southern of China were established respectively by Zhongshan Jiang [14], Suyuan Liu [15], Fujian Zhou [16] to calculate the rainfall energy, which is express as, e=a+blogi or e=ai^{b}, where e is the energy of per unit rainfall(J/m^{2} mm), i is the rainfall intensity, a and b is calculating coefficients.

As a result, how to determine the rainfall energy (e) and intensity (I) of one unit period is the key to measure and calculate the energy. Between these two parameters, I is a common rainfall character value which can be obtained by measuring rainfall precipitation and rainfall duration, while the measurement and calculation of energy is relatively difficult.

### The traditional ways to measure raindrop's quantity and down velocity

One way to measure rain drop's quantity is called Stain method (or filter paper method) [17]. The precise process are as follows: firstly, a piece of filter was spread with water-solubled dyestuff, which doesn't show color when dry but a permanent rough circular stain will emerge when it was wetted by raindrops. Then, every stain's diameter was measured, raindrop's diameter can be determined according to a relationship between diameter of drops' and stain's. At last, their quantity can be calculated according to their volume if they are regard as sphere. The velocity of raindrops is distinguished by two situations [18], when a drop's diameter < 1.9 mm, velocity is calculated according to amendatory Sha Yuqing formula, when a drop's diameter ≥ 1.9 mm, calculated by amendatory Newton formula. An individual drop's energy can be computed based on moving object's energy formula when a drop's quantity and velocity are known, the unit area's rainfall energy of an individual rainfall is the sum of every single raindrop's energy.

From these above current classic rainfall energy calculation, it can be concluded that the R factor of an individual rain is determined by energy and intensity, intensity can be computed through measured data by self-restrainting hyetometers, while energy is usually calculated by regression models, which were obtained through typical measurements among rainfall energy, rainfall intensity and rainfall quantity.

Obviously, obtain rainfall physical parameters through stain method, calculate rainfall energy through a regression mode is unscientific when adopted in large region, because this method tends to neglect spatial and temporal variation of rain, will unavoidably reduce the measurement accuracy. Moreover, stain method's accuracy and efficiency are limited because it depends a lot on human measurement. As a result, there is still an urgent demand to develope an instrument which can measure rainfall physical parameters timely, thus creating a method to calculate rainfall energy rapidly in soil erosion subject.