Comparison of Various Rainfall Erosivity Formulas in the Application of USLE for Erosion Cases in Indonesia

Erosion is a complex process that results in the movement of soil particles from one place to another through a series of processes of detachment, entrainment, transport, and deposition. Erosion can cause serious environmental problems, such as loss of soil fertility, and sedimentation of rivers, lakes, and reservoirs. Therefore, it is important to identify and mitigate erosion problems in the management of a watershed. The erosion prediction model that is popularly used, especially in Indonesia, is the Universal Soil Loss Equation (USLE). One of the parameters in the USLE formula is the rainfall erosivity factor (R). Many formulas have been developed to calculate the R-factor. However, not all formulas are suitable for application in Indonesia. In this study, a comparison of several R formulas from various countries in the Asia Region was carried out. From the results of the comparison, it was found that for Riam Kanan Sub-watershed, the appropriate formula for rainfall erosivity is the Merritt et al. (2003) formula, while for Brantas Sub-watershed erosivity formulas from Utomo (1994) and Babu et al. (2004) is the most suitable. The results of this study can be used as a consideration in determining the appropriate rainfall erosivity formula (R) for a particular case.


Introduction
Erosion is a natural process, in which the surface area of land is carried away by wind or water.In Indonesia, erosion is generally triggered by overland flow during rainfall.Erosion is a complex process that causes soil particles to move from one place to another through a series of processes of detachment, entrainment, transportation, and deposition.Erosion can cause serious environmental problems, such as land degradation, and sedimentation of rivers, lakes, and reservoirs.Land degradation (critical land) results in loss of soil fertility so productivity decreases and becomes highly dependent on the use of fertilizers, or even cannot be replanted, as found in Dieng High Land and North Bandung Area.The total area of critical land in Indonesia in 2018 is estimated about 14 million hectares [1].Sedimentation of lakes and reservoirs has resulted in ecosystem damage and decreases in reservoir operation performances.Considering these environmental serious problems, through Presidential Decree No. 60 of 2021, efforts are made to save 15 national priority lakes in Indonesia, namely Toba, Singkarak, Maninjau, Kerinci, Rawa Danau, Rawa Pening, Batur, Tondano, Mahakam Cascade, Sentarum, Limboto, Poso, Tempe, Mantano, and Sentani.Meanwhile, the reservoir revitalization program has been conducted as well to reduce the reservoir sedimentation effect.Bandung [2]; (b) Limboto Lake Sedimentation [3]; (c) PB.Soedirman Reservoir Sedimentation [4] In 2010 Badan Nasional Penanggulangan Bencana (BNPB) released a national erosion potential risk map (Figure 2), in which high-risk areas for erosion disasters including large parts of West Java, Central Java, and Nusa Tenggara, some high-risk areas found as well in North Sumatra, West Kalimantan, East Kalimantan, South Kalimantan, South Sulawesi, North Sulawesi, Maluku, and Halmahera.Erosion in Indonesia is predicted between 35-220 tons.ha - .yr - and annually increases from 7 to 14% or about 3 to 28 tons.ha - .yr - [5].Nature conditions that cause the soil in the Indonesia region to be highly susceptible to erosion are high amounts of rainfall, hilly/mountainous topography, and soil types that are sensitive to erosion [5].Rainfall is the triggering factor that detaches and transports soil particles downstream.Steep topography contributes to enhancing the flow, raising the velocity and so as the amount of runoff to transport the soil.Soil characteristics, especially related to its texture, contribute to its erodibility factor.Very fine sand and silt are more sensitive to erosion than soil texture dominated by clay.This unfavorable condition is exacerbated by the clearing of forests (deforestation) for farming and the agricultural practices on slopes that do not concern land conservation [6].
Considering the complexity of the problems, it is important to identify and mitigate erosion problems in watersheds as early as possible.Identification of erosion potential in an area can be done using various erosion prediction models that have been developed.In Indonesia, the most popular erosion model is the Universal Soil Loss Equation (USLE) which is an empirical formula based on erosion experiments on agricultural land in the USA.Various erosion studies in Indonesia apply this model [7,8,9,10], whether using USLE and so as a revision or modification version of it, namely Revised Universal Soil Loss Equation (RUSLE) and Modified Universal Soil Loss Equation (MUSLE).
One of the parameters in the USLE formula is the rainfall erosivity factor (R).The rain erosivity factor represents the capacity/ability of rainfall to peel off and transport soil particles downstream [11].Many formulas are available to calculate the R-factor [12,13,14,15,16,17,18,19,20].Those formulas emerged as the high variability of the rainfall characteristics in one place to another.Therefore, not all formulas are suitable for the Indonesian region.Determining the appropriate formula is very important to get the best erosion prediction.Regarding that, in this study, several rainfall erosivity formulas from different regions were applied to test their suitability for the environmental and climatic characteristics of Indonesia.

Study Case
The observation and measurement data used for analysis in this study were obtained from two previous erosion studies conducted at the Riam Kanan Sub-watershed (Upstream Waduk Muhammad Nur) in 4 South Kalimantan and at the Brantas Sub-watershed in East Java.These two cases were chosen to represent the characteristics of soil and environmental conditions in various regions of Indonesia, as presented in Figure 3

Data Collecting
Erosion measurement data in this study is secondary data obtained from two case study locations as mentioned previously.The data used includes monthly rainfall data during the observation period, soil erosion data, soil type, plot geometry and dimensions, vegetation cover, and land utilization, as well as soil conservation management.
Erosion data from Riam Kanan Sub-watershed were measured during the rainfall season in two periods, the first period taken from February to April 1995 and the second period taken from January to April 1996 (see Figure 4).The highest erosion occurred at plot LU2 which is above 900 ton/ha in April at the first year and above 400 ton/ha in March at the second year, while the other observation plots were below 300 ton/ha at the first year and lower than 100 ton/ha at the second year.The rainfall amount in 1995 was greater than in 1996, the monthly rainfall was above 100 mm, except in February, while it was lower than 100 mm the following year.
Erosion data from Brantas Sub-watershed was collected from six experimental plots for four months from February to May 2017 (see Figure 5).The erosion amount of each plot was significantly different from one to another.The lowest erosion was recorded in Plot-1 ranging from 0 to 20 tons/ha/month, as the highest one reaching about 127.960 tons/ha/month, occurred in Plot-3.Similar to all plots, the rainfall graphics showed the peak rainfall happened in April, exceptional for Plot-3 which occurred in March.Soil characteristics in Riam Kanan Sub-watershed are classified as sandy loam which is dominated by clay with fractions of more than 50%, meanwhile, sand fractions range from 26.5 to 28.1%, and silt range from 17.5 to 19.4%.There are two soil types in Brantas Sub-watershed, loamy silt soil found at Plot-1 to Plot-4 and sandy silt soil at Plot-5 and Plot-6.Silt fractions in all plots are between 41 to 57%, clay fractions between 20-43% at Plot-1 to Plot-4 and 4-8% at Plot-5 and Plot-6, whilst sand fractions between 10-36% at Plot-1 to Plot-4 and 35-41% at Plot-5 and Plot-6.The organic material in Plot-1 to Plot-4 is about 2.36-3.68%while in Plot-5 and Plot-6 about 6.47-6.84%.Soil properties for both subwatersheds are given in Table 1.The size, slope, vegetation, land conservation, and management of the experimental plots are presented in Table 2.The plot sizes in Riam Kanan Sub-watershed were between 2200-4600 m 2 with a gentle slope of around 9 to 10%, while the plot areas in Brantas Sub-watershed were between 300-985 m 2 with a steep slope of between 15 to 43%.The vegetation in each plot in both cases varied including forest, apple tree, reed grass, groundnut, mustard green, and potato.

Erosion Model
For the last 50 years, many erosion models have been developed, whether conceptual, empiric, physical, or even a combination of them.So far, the empiric model still dominates the erosion model in Indonesia, especially the USLE model because its formula is simple to apply in various conditions.The USLE model defines erosion amount or soil loss as a function of five parameters as follows [12]: where A is soil loss (ton ha -1 yr -1 ); R is rainfall erosivity (MJ mm ha -1 hr -1 yr -1 ); K soil erodibility index (ton ha -1 yr -1 ); LS adalah length and slope factor; C adalah vegetation or crop factor; and P is land management and conservation practices.
Rainfall erosivity (R) is the capacity of rainfall to detach soil particles and transport them downstream [11].Rainfall erosivity is highly influenced by rainfall and climate characteristics.Thus, there are many formulas for determining the R-factor.Several formulas use the linear function below [14,15,17,18,22,23]: Others applied the power function as follows [19,24,25]: Meanwhile, fewer others define it as an exponential function [26]: Several Rainfall Erosivity Formulas (R) applied in the Asia Region are presented in Table 3.The soil erodibility factor (K) represents the inherent susceptibility of the soil to erosion, which is influenced by organic matter content, soil texture, soil structure, and permeability [21].The value of K in this study was calculated by using the following formula [12]: where  = [(  −   ) 100 ⁄ ] −   ; a = soil organic matter content; b = soil structural code; c = soil permeability class; St = silt fraction (%); Svf = very fine sand fraction (%); and Cf = clay fraction (%).
Land geometry, such as slope steepness and length, is an important factor that also determines the erosion process.The effect of the length and steepness of the slope on erosion by water is represented by the slope length and steepness factor (LS).The formula for determining the LS factor is as follows [12]: where ℓ = slope length (m); a = slope steepness (degrees); and m = exponent determined by slope steepness.
The crop management factor (C) shows the overall effect of vegetation, soil surface conditions, and land management on the amount of soil lost [21].The C-factor was determined based on the attached Table A-1 [13,16].Meanwhile, the soil conservation factor (P) is the ratio between the average eroded soil from land receiving certain conservation treatment to the average eroded soil from land treated without conservation action.The P-factor is determined as shown in Table A-2 attached [13].
Differences in environmental and climatic characteristics where an empirical erosion model is developed result in limitations on its application.The prediction accuracy of an empirical model is determined by the similarity of the conditions of the case area to the location where the formula is built.The discrepancy in the prediction results has prompted several researchers to develop or modify the previous model by making adjustments to the characteristics of the particular region.Therefore, in this study, several rain erosivity formulas (R) were compared to see the suitability of their application in two cases of soil erosion in Indonesia.

Rainfall Erosivity Analysis
The erosion process in the Indonesian region is dominated by rainwater erosion.High rainfall is accused as the reason for its high potency erosion.Therefore, the erosivity factor plays a significant role in determining the erosion rate in this region.The erosivity of rainfall in this study is calculated using the six formulas in Table 1.Those erosivity equations were developed based on the characteristics of the Asian region.The calculation results of the rainfall erosivity are plotted against the total rainfall during observation as presented in Figure 6 and Figure 7. From the calculation results, the erosivity of both cases is highly varied.The erosivity from Utomo and Nakil & Khire obtained the highest values, which are above 1000 MJ.mm/ha/hr in Riam Kanan Sub-watershed and above 600 MJ.mm/ha/hr in Brantas Sub-watershed.For the Riam Kanan Subwatershed, the highest R-factor was obtained from the [27] which is above 1500 MJ.mm/ha/hr, while for the Brantas Sub-watershed, the [26] gives the R-factor above 900 MJ.mm/ha/hr.The other formulas give lower R-factors which are below 700 MJ.mm/ha/hr for Riam Kanan Sub-watershed and less than 200 MJ.mm/ha/hr for Brantas Sub-watershed.The lowest R-factor was obtained from the [24] formula at both locations.
This high variability of erosivity is influenced by the differences in the characteristics of rainfall from one region to another.The R-factor produced by the [15] formula is much lower than the R-factor of the [26] formula, even though both formulas are developed in the Indian region.Likewise, the erosivity value of the formula [24] has a much lower value than the [27] and [14] formula despite being in the Southeast Asian region.This is due to differences in the regional climate of the study location which can have a significant effect on the characteristics of rainfall in the region, especially in relatively mountainous or contoured areas.

Soil Loss Analysis
Besides the erosivity of rainfall (R), four other parameters must be determined first before calculating soil loss using the USLE formula.Those parameters are soil erodibility factor (K), slope and length factor (LS), crop management factor (C), and soil conservation factor (P). K and LS factors were calculated using Eq. ( 5) and (6), while C and P factors C and P factors are defined based on the coefficient values for certain types of vegetation and land management by [13] and [16].The value of the K and LS factors in Riam Kanan Sub-watershed is relatively homogenous because the slope, length, and soil type of the four plot areas are similar, while the K and LS factor in Brantas Sub-watershed has wider range values between 0.23 to 0.38 as the soil type a bit varies.The values of those four parameters in the two case locations are presented in Table 4 below.After obtaining all the parameters of the USLE formula, the soil loss estimation can be calculated using Eq.(1).Then, the results of soil loss are compared with the measured erosion values to find out the predictions that are closest to the measured values, as shown in Figures 8 and 9. Figure 6 shows that the best fit for Riam Kanan Sub-DAS is the soil loss prediction resulting from the [14] erosivity formula, which is based on rainfall characteristics in Thailand.The soil erosion regression line from [14] is the closest to the 1:1 line (black line) with a correlation value (R 2 ) of about 0.74.Whilst, the soil loss prediction with [15,19,26,27] erosivity formulas provide greater erosion values than the measured values (over-estimated), which are 17 times, 7.6 times, 4.4 times, and 1.5 times the actual erosion respectively.Meanwhile, only Sholagberu et al. erosivity formula results lower erosion value than the measured values (under-estimated), which is 0.2 times the actual erosion value.
For Brantas Sub-watershed, the best prediction was obtained from the soil loss that used the [27] formula, with soil loss estimation of around 0.8 times the measured values.It was not surprising because the erosivity formula by [27] was constructed through rainfall observations in Brantas Watershed.Meanwhile, the soil loss with the [26] erosivity formula has the highest results, which is around 1.2 times the measured values (over-estimated).On the contrary, the soil loss estimation with other erosivity formulas gives much lower (under-estimated) results.The soil loss with [15] erosivity formula is only about 0.2 times the measured value, while other formulas even give estimations of less than 1 %.
Many factors affect the erosivity of rainfall, not only influenced by the amount of rainfall but also by the size of the raindrops and the wind direction during rain.Even though the amount of rain that falls is the same, the difference in the size and inclination of the raindrops will affect the kinetic energy of the rainfall which plays an important role in the beginning process of the soil detachment process.However, in the current formula, the only variable represented is the amount of rain, either daily, monthly, or annual.Therefore, it is necessary to be careful in choosing an erosivity formula according to the rainfall characteristics of the region.

Conclusion
As the greatest archipelago country, Indonesia has diverse climate and rainfall variability, so the characteristics of rainfall between regions are varied as well.This study proved that the rainfall erosivity formula had a significant effect on the results of calculating the USLE soil erosion value.Therefore, applying the erosivity formula according to the characteristics of the rainfall the area studied plays an important role in the correct erosion prediction value.As in the case location of the Riam Kanan Sub-watershed, the appropriate formula for rain erosivity is the [14], while for the Brantas Subwatershed the appropriate erosivity formula is [27].
The current erosivity formulas only represent the amount of rainfall, while its kinetic energy, which causes the soil detachment, is also influenced by other variables, such as the size of the raindrops and wind direction.Further studies are necessary to find out the appropriate formula that also considers those parameters.The last but not the least, as this research only covers a small region of Indonesia, we also encourage further research for mapping the rainfall erosivity formula that is suitable for various other regions of Indonesia.

3 Figure 2 .
Figure 2. Erosion Risk Map in Indonesia below.

Figure 8 .
Figure 8.The soil loss in Riam Kanan Sub-watershed during observation

Figure 9 .
Figure 9.The soil loss in Brantas Sub-watershed during observation

Table 3 .
Rainfall Erosivity Formulas (R) applied in the Asia Region