**4.1 Rainfall intensity calibration**

To be effective in soil erosion experiments, a reliable rainfall simulator should have the capability to generate simulated rainfall events with a broad range of rainfall intensities. Typically, the rainfall intensity utilized in soil erosion experiments falls between 50 and 120 mm/hour, although it may be increased to 150 mm/hour for specific experiments or reduced to 30 mm/hour for less severe erosion studies [33]. The majority of present-day portable rainfall simulators, such as the QDPI rainfall simulator, manage the intensity of produced rainfall by manipulating two factors. First, the water flow/pressure from the primary water pump is regulated using a solenoid valve and pressure gauge. Second, the movement pattern of the nozzles is altered by employing a stepper motor controller and driver to modify the sweep and waiting time pattern. To verify the success of the apparatus (the rainfall simulator) in producing rainfall events with the desired intensities for the experiment or intended application, it must be calibrated using one of the following methods:


It is important to note that the calibration method used will depend on the specific rainfall simulator being used and the accuracy required for the experiment or application. The rainfall intensities generated by the "Port-RFS" were evaluated and adjusted by taking into account the average volume of water collected in the flume area using the pan method. Additionally, the water discharge from each Port-RFS nozzle was measured by enclosing polyvinyl chloride (PVC) tubes around each

*Using Rainfall Simulators to Design and Assess the Post-Mining Erosional Stability DOI: http://dx.doi.org/10.5772/intechopen.112240*

#### **Figure 5.**

*The Griffith University portable rainfall simulator (port-RFS) calibration curve for the rainfall intensities, relation between rainfall intensity, sweep and waiting times.*

nozzle individually and collecting the outflow for a duration of 5 min. To convert the collected data into flow rate in millimeters per hour, the recorded value was multiplied by 12.

**Figure 5** shows the calibration of the Port-RFS where rainfall intensity can be controlled at rates from 60 to 150 mm/h using combinations of waiting and sweep periods. It is evident that the Port-RFS has the capability to produce simulated rainfall storms ranging from a minimum intensity of 60 mm/h to a maximum intensity of 150 mm/h. The control of rainfall intensity in the simulated rainstorm was found to be straightforward and efficient using the digital control panel.

#### **4.2 Spatial uniformity over the flume area**

Obtaining a uniform distribution of rainfall across each section of the flume is crucial. Failure to achieve this can result in areas that receive more rainfall being more prone to erosion, compromising the accuracy of calculations based on the entire flume area. To ensure uniform rainfall distribution, the grid method is usually used to assess the spatial uniformity of simulated rainfall. It involves superimposing a grid with equidistant points onto the flume area and measuring the amount of rainfall that falls on each point using a rain gauge/graduated beaker. The gathered data for each point are then utilized to compute Christiansen's uniformity coefficient (CUC), as shown in Eq. (1) [57].

$$\text{CUC} = \mathbf{100} \left[ \mathbf{1} - \left( \frac{\sum (|D\_i - D\_m|)}{n \ast D\_m} \right) \right] \tag{1}$$

where CUC is the coefficient of uniformity (%); Di is the depth of water in the graduated beakers (cm); Dm is the mean depth of water in rain gages/graduated beakers (cm); and n is the number of rain gages/graduated beakers. When the rainfall


#### **Table 1.**

*The calculated uniformity coefficient % for portable rainfall simulator (port-RFS) under different rainfall intensities.*

**Figure 6.**

*The spatial distribution of the simulated rainfall over the flume/plot area for the Griffith University portable rainfall simulator (port-RFS) (100 mm/h rainfall intensity).*

pattern is more uniform, the CUC value approaches 100%. According to Sousa, Mendes [58], several researchers consider that any CU values above 80.0% are acceptable for the uniformity of the rainfall distribution. However, some other studies have accepted a CUC value of 70% for large plot areas, as demonstrated by Luk, Abrahams [59]. The uniformity coefficients of the Port-RFS at various rainstorm intensities are presented in **Table 1**. All the coefficients exhibit high values, ranging from 86.55% to 91.8%. These values indicate a high level of uniformity across the measured experimental area. **Figure 6** illustrates the distribution of rain intensities generated by the Port-RFS system for an average rain intensity of 100 mm/h across a flume area measuring 3 m 1 m. The figure demonstrates that the incident intensities vary between 90 and 110 mm/h, with an average uniformity coefficient of 89.8%.

#### **4.3 The drop size distribution (DSD) and kinetic energy (KE)**

The ability of any rainfall simulator to generate raindrops that approximate the volumetric size distribution of the droplets that occur during rainstorms in nature is highly influential in our judgment of the efficiency and quality of the rainfall simulator design, as the distribution of grain size over the different classes of drop sizes (volume in mm3) affects the total kinetic energy generated from the simulated rainstorm, whereas the kinetic energy of a single drop is a function of a grain's mass, which is related to its size (volume) as well as its terminal velocity when it hits the ground [49, 60]. In general, the sizes of raindrops in nature range from 0.5 mm in diameter to the large drops associated with heavy rainfall and reaching up to 6 mm in diameter, with median droplet diameter varying depending upon the storm intensity but usually ranging from 2 mm to 3 mm [9, 46].

#### *Using Rainfall Simulators to Design and Assess the Post-Mining Erosional Stability DOI: http://dx.doi.org/10.5772/intechopen.112240*

There are numerous methods and instruments for measuring raindrops, which can be divided into two main groups: manual and automated techniques. These approaches are used to determine the raindrop size distributions and the average size of raindrops for simulated rainfall events.

Manual rain drop measurement techniques include the stain method that involves using dyed absorbent paper to measure the stains left by raindrops [61], the flour pellet method that uses finely sieved flour to create dough pellets from raindrops [62, 63], and the oil immersion method that measures raindrops in a vessel containing oil [64]. While these methods are simple and inexpensive, they are time consuming, the accuracy of the results obtained from it depends on the skills and experience of the researcher, and do not provide immediate data readings.

On the other hand, there are various automated techniques available for measuring raindrops, including but not limited to: the displacement disdrometers [65], the photographic method [66, 67], acoustic disdrometers [68], the radar technique [69, 70], and the optical spectra pluviometers [71].

While the disdrometer method has been particularly successful over the past decade due to its ability to generate a large number of measurements [72, 73] and its efficiency in measuring the impact of raindrop splash on soil detachment [74] and erosion caused by changes in soil cover [75], the old flour method [62] is a widely accepted, standardized test method [46, 49, 63]. Using the flour method, the mean diameter of the raindrops that came out of each examined rain event was measured and could be calculated using Eq. (2).

$$D\_r = \sqrt[3]{\left(\frac{6}{\pi}\right) W m\_R} \tag{2}$$

Where *Dr* is the mean raindrops' diameter (mm) and *W* is the mean weight of the raindrops (mg) and mR is the ratio of the mass of the raindrop to the mass of the pellet, which is obtained using the flour-calibration line [76].

Using Eq. (3), the kinetic energy of individual raindrops could be determined after the median size distribution (D50) of the rainfall simulator was easily estimated from the previous step:

$$\text{KE} = \text{\% } \text{mv}^2\tag{3}$$

where *KE* is the kinetic energy (Joule); *m* is the mass (kg) of the raindrop (calculated from the relation between the volume, density, and mass); and *v* is the terminal velocity (m/s) at which the drop hits the soil surface where the values for examined rainfall intensities by examined rainfall simulator could be obtained from the American Society for Testing and Materials (ASTM) [77] chart that correlates the fall velocity, fall height, and raindrop diameter.

The threshold kinetic energies needed to initiate soil detachment (erosion) by raindrop impact were listed and discussed by Salles, Poesen [78]; they stated that the threshold kinetic energy required to initiate the detachment of soil particles by raindrop impact declines with increasing median grain-sized diameters, starting from 0.001 mm until D50 reaches values near 0.1–0.2 mm. Once D50 becomes larger, the variation in the threshold kinetic energy changes and increases with median grain diameter of the soil.

By utilizing the flour method, the drop size distribution of the Port-RFS was examined, resulting in a median size distribution of 2.15 mm; **Figure 7** presents the

#### **Figure 7.**

*Raindrop size distribution for the Griffith University portable rainfall simulator (port-RFS) under different simulated rainfall intensities.*

drop size distribution pattern observed with the Port-RFS. In **Figure 8**, the relationship between the generated rainfall intensities and the corresponding kinetic energy (KE) per second per flume area is depicted. The measured KE values for rainfall intensities of 80, 90, and 100 mm/h were found to be 1.96, 2.2, and 2.45 Joule/Sec. flume area, respectively. Based on these calibration data, the kinetic energy and drop sizes generated by the Port-RFS were deemed satisfactory for initiating soil erosion in the range of 0.001 mm < D50 < 2.5 mm, which is considered suitable for most soil samples.

*The relation between rainfall intensity and the kinetic energy (KE) of the simulated rainfall events.*

*Using Rainfall Simulators to Design and Assess the Post-Mining Erosional Stability DOI: http://dx.doi.org/10.5772/intechopen.112240*
