Adaptation and application of the erosion potential method for tropical soils 1

- The water erosion process has a considerable negative effect on tropical soils, causes soil losses from arable land and reduces the capacity to support surrounding ecosystems. Estimating soil losses caused by water erosion is fundamental for evaluating the impacts of various production systems. Therefore, improving soil loss estimates via the adaptation of models for different edaphoclimatic environments is necessary for estimating local geographic and climatic differences. This study aimed to adapt, apply and evaluate the potentialities of the Potential Erosion Method for Latosols of the Hydrographic Subbasin of Caçús Stream, southern Minas Gerais State. Geological, topographic, pedological, climatic and land use and occupation data were processed via Geographic Information Systems and compared with those obtained by the Revised Universal Soil Loss Equation. The erosion intensity coefficient, Z, was 0.28, indicating weak erosion intensity, and the estimated average soil losses were 31 Mg ha -1 year -1 by the Potential Erosion Method and 36 Mg ha -1 year -1 by the Revised Universal Soil Loss Equation, which were both above the soil loss tolerance. The model results and comparisons indicated that the Potential Erosion Method has excellent performance and can be applied to estimate sediment production via water erosion in tropical soils.


INTRODUCTION
Water erosion is considered the primary cause of soil degradation, especially in tropical regions. The problem is enhanced by climate change, intensive land use, rainfall intensification, and runoff increases mainly in areas where conservationist management practices are neglected (LIMA et al., 2015). Dechen et al. (2015) estimated that the soil losses of temporary or annual crops in Brazil have reached 616.5 million Mg ha -1 year -1 , which is equivalent to a cost of US $1.3 billion.
Prediction models are essential for assessing environmental impacts, especially in the face of a growing world population and the associated increases in food, water, and energy consumption. Thus, studies on water erosion guide the adoption of mitigation measures and support soil and water conservation, as well as the restoration and repair of environmental impacts (SANTOS et al., 2017).
Soil loss estimates, however, should be compared to Soil Loss Tolerance (T) limits to determine whether they affect long-term agricultural sustainability. Conceptually, the T value corresponds to the soil formation rate. Therefore, sustainability is only possible if the losses are equal to the soil formation rate. However, obtaining the T boundary is still controversial due to the difficulties of accurately quantifying the factors and processes involved in soil formation.
In Brazil, the T calculation by Bertol and Almeida (2000) is the most frequently used method because it considers more attributes that reflect soil formation. Thus, T calculations complement the estimates of erosion rates and allow for the assessment of soil degradation stages. However, soil losses are cumulative, and even areas with losses below the T limit may require improved management practices (FOOD AND AGRICULTURE ORGANIZATION OF THE UNITED NATIONS, 2015) to prevent a lack of sustainability over time.
A comparison with benchmark models allows for the evaluation of the effectiveness of new soil loss estimation methods. In this context, the Revised Universal Soil Loss Equation (RUSLE) (RENARD et al., 1997) is the most frequently applied for estimating the erosion of Brazilian soils (BARRETTO; BARROS; SPAROVEK, 2008;OLIVETTI et al., 2015).

The
Erosion Potential Method (EPM) (GAVRILOVIC, 1988) is infrequently used in America and more commonly used in Europe, the Middle East and North Africa (KOUHPEIMA; HASHEMI; FEIZN, 2011;NIKOLIC et al., 2018;NYSSEN et al., 2014;SPALEVIC et al., 2013;VUJACIC et al., 2015). In Brazil, the EPM has only recently been implemented (SILVA; CELSO;SILVA, 2014;TAVARES et al., 2017) because it is inadequate for tropical edaphoclimatic conditions. Milanesi, Pilotti and Clerici (2014) adapted the EPM model for the Italian Alps region, which has a constant snow presence, and showed the good fit of the model after modifications and its reliable sediment production estimates.
This study aimed to adapt the EPM to estimate soil losses due to water erosion in tropical soils and apply the method in the Hydrographic Subbasin of Caçús Stream, which is located in the municipality of Alfenas, southern Minas Gerais State.

MATERIAL AND METHODS
The EPM estimates the average soil loss (m 3 km -2 year -1 ) using variables and coefficients that represent soil physical characteristics as well as the land use and management, temperature, rainfall, slope, erosion resistance and erosion observed in the field at the subbasin scale. Each coefficient is obtained from the equations described in Table 1 (GAVRILOVIC, 1988).
The original parameters of the EPM, developed for the edaphoclimatic conditions of the Balkans, need to be adapted to tropical soils.

Adaptation of the method to tropical soils
The index Tables that simulate water erosion processes were adjusted for tropical soil conditions. For soil erosion resistance (Y), the EPM integrates water infiltration and percolation processes as well as structural resistance to particle breakdown. The Y value ranges from 0.20 to 2.00 and changes according to the soil type and its source material (SILVA; CELSO; SILVA, 2014) (Table 2). However, the same source material may generate different soils with distinct erosion resistance (RESENDE et al. , 2 0 1 9 ) d u e t o edaphoclimatic conditions. Thus, in addition to the source material, the soil class and respective Y values are described in Table 2.
The coefficient of erosion (Z) ( Table 3) represents the intensity of the erosive process at the subbasin scale considering the following parameters: average air temperature (°C year -1 ), soil erosion resistance coefficient, soil use and management, soil erosion features observed in the field and mean slope (%).

Soil protection coefficient (X a )
The soil protection coefficient (X a ) expresses the area that is less susceptible to erosion due to soil use and management. The X a value ranges from 0.05 for areas with dense vegetation to 1.0 for bare soils.   (2007) suggested changing the categorization of the X a based on different land use categories (Table 4), with urban areas considered potentially erosive and assigned a value higher than zero. These authors included urbanization variables as well as vegetation types.   The EPM parameters visible erosion (φ), Y, and X a were analyzed to determine the magnitude of the average soil losses. Small fluctuations in the values result in significant changes in soil loss estimates.
The potential and usual land uses in Brazil were considered to define the X a coefficient (Table 5) as well as the parameter sensitivity. The assigned coefficient should consider the degree of crop development and not just the phenological stages. The EPM should consider the various stages of agricultural development when determining the average annual soil loss.
The most traditional temporary crops in tropical soils include rice, beans, corn, cassava, soybeans, and sugar cane, and the permanent crops currently include orange, banana, cocoa, coffee, and coconut. Permanent crops retain their canopy structure throughout the year and over a long period, thus offering higher protection to the soil when compared to temporary or annual crops.

Erosion Potential Method application
The EPM was applied to the hydrographic subbasin of Caçús Stream (Figure 1), which was previously studied by Olivetti et al. (2015). However, these authors used the RUSLE model to evaluate soil losses. The subbasin occupies an area of 2,080 ha, extends between 21°26' to 21°29' S and 45°56' to 46°00' W along the southern plateau of Minas Gerais and is part of the Rio Grande River Basin. The climate is Tropical Mesothermal (CwB) (SPAROVEK; VAN LIER;DOURADO NETO, 2007). The geological framework is formed by biotite and garnet biotite polydeformed Proterozoic gneisses in Adaptation and application of the Erosion Potential Method for tropical soils the physiographic unit called mares de morros, which is translated as "seas of hills" and was formed by the union of several wavy elevations. After data acquisition and processing, the DEM was elaborated based on the contour lines of the topographic map and generated altimetric points. Using the DEM and the relief classes from Embrapa (2006), a slope map of the area was generated and the average inclination (%) was determined. The Digital Surface Model (MDS) was obtained by combining the slope map and soil classess, according to McBratney, Mendonça Santos and Minasny (2003). In order to determine the average slope (I sr ), the length of the contour lines and area between them were taken under consideration, as well as the highest and lowest altitude, the equidistance between contour lines, and the highest and lowest altitude of the contour lines, considering the variety of relief observed in the area.
The land use and management coefficient (X a ) was obtained adapting the coefficients of soil use and occupation from Gravilovic (1988). The soil losses estimates were performed using the software IntErO (Intensity of Erosion and Outflow) using the EPM algorithm (SPALEVIC et al., 2013).
To compare the results, the data were also calculated using GIS and EPM equation files, thus generating the spatial distribution of the soil losses.

RESULTS AND DISCUSSION
The IntErO input and output values from 2016 are summarized in Table 6.
The subbasin area (F) is 20.80 km 2 , and it has a perimeter (O) of 24.96 km and minimum (H min ) and maximum (H max ) altitude of 765 m and 960 m, respectively. The length of the main stream (L v ) is 7.09 km, and it has an average width of 10 m, and the shortest distance among upstream and downstream (L m ) is 5.95 km. The shape coefficient (A) is 0.69, which represents a subbasin with low flood propensity. The average annual rainfall is 1,500 mm, which may favor water erosion. The energetic potential of the water flow during abundant rainfall (2gDF) 1/2 was 168 m km -1 s -1 , and the maximum flow rate in the river outflow (Q max ) was 69.83 m 3 s -1 .
Regarding the permeability of the rocky substrate, 78% of the subbasin area was classified as medium permeability and 22% was classified as low permeability. The average slope of the subbasin (I sr ) was 13.22%, which indicates a wavy relief domain.
The large-scale difference in land use mappings was also sensitive in the land use and occupation mapping.   The permeability coefficient (S 1 ) of 0.77 indicated that impermeable areas were not identified, while the cover vegetation coefficient (S 2 ) of 0.77 indicated high soil protection (Table 4). The EPM estimated the total soil losses (W yr ) as 23,118 m³ year -1 , and the value calculated by GIS (Figure 2) was 19,488.86 m³ year -1 ( Table 7). The difference between the EPM and GIS estimates was not significant.  The retention coefficient (R u ), which estimates the amount of sediment retained along the subbasin, was 0.154. The real soil loss (G yr ) was obtained by the total soil loss (W yr ) multiplied by the R u . To compare the soil density results between the EPM and RUSLE, data in m³ km-² year -1 were converted to Mg ha -1 year -1 , and the average density was 1.15 Mg m -3 .
The soil loss rate indicates the soil use and management under conservation practices and densified spacing. The X a coefficient was 0.47, and the subbasin land use classes were 44% pastures, 30% native forests, 10% coffee, 6% corn, 7% bare soil and 3% sugar cane ( Figure 2). Thus, the anthropogenic actions performed in the subbasin are not deleterious since the soils present high permeability, which indicates good soil structure preservation. In addition, the average slope of the area was not a hindering factor for land use and occupation.
The soil erodibility factor (K) of the RUSLE corresponds to the EPM soil resistance coefficient (Y). Indiscriminate Floodplain Soils (IFS) were not considered in the soil loss calculations since they are found in sediment deposition areas. To determine the Y coefficient, manual IFS polygonization was performed, and combined with the improved image spatial resolution, it generated more accurate soil loss spatial distributions (Figure 2). Soil loss rates estimates by RUSLE and EPM are usually consistent and can identify areas adopt conservation measures. However, the soil losses estimated by the EPM are generally lower than that of the RUSLE except for with coffee and pasture. The difficulties in obtaining the C and P factors of the RUSLE from experimental plots can explain these results. Therefore, the estimates consider the soil physical characteristics and land use and management characteristics of other areas.
In the comparison between the soil losses by the EPM and RUSLE, the average was 31.34 Mg ha -1 year -1 for the EPM and 36.36 Mg ha -1 year -1 for the RUSLE, and the difference is due to the greater detail of the EPM parameters.
The EPM coefficient visible erosion (φ), which is not considered in the RUSLE, was 0.41 (Table 3), which corresponded to 44% of the subbasin under non-apparent erosion; 30% protected by native vegetation; 9% under moderate laminar erosion; 6% under severe laminar erosion; 2% under weak erosion; and 6% with agricultural areas under non-apparent erosion features.
Previous studies have discussed the use of the φ coefficient in soil loss calculations, and it is used in the erosion intensity coefficient (Z) calculation and results in high variation in the total soil losses estimated by the EPM (DRAGIČEVIĆ; KARLEUŠA; OŽANIĆ, 2017). The φ coefficient is not used in similar methods of sediment yield evaluations despite its arbitrary use increasing the modeling sensitivity (DRAGIČEVIĆ; OŽANIĆ, 2016;KOUHPEIMA;HASHEMI;FEIZN, 2011). However, this parameter is not normally used in similar methods for sediment yield evaluations.
Native forest areas showed similar soil losses in both models because approximate values were assigned for natural factors. The bare soils presented the highest estimates of soil losses, with rates above the T limit. However, lower rates were observed in the EPM, which considers the mean value of the coefficient of erosion observed in the field (φ). Corn cultivation also presented similar soil loss rates in both methods, although the results were below the T, which allows us to infer that crops with conservationist management do not damage the sustainability of agricultural soils.
The soil loss rates estimated by the EPM and RUSLE were 4.69 Mg ha -1 year -1 and 1.43 Mg ha -1 year -1 for pasture, respectively, and 3.97 Mg ha -1 year -1 and 1.72 Mg ha -1 year -1 for coffee, respectively. For pasture, lower C factor values were assigned in the RUSLE compared with the X a coefficient values in the EPM. Even considering the high P factor values, the low C factor values reduced the estimates by the RUSLE. For sugar cane, the lower losses in the EPM were obtained due to the lower φ values compared to the P factor values of the RUSLE.
The Z coefficient of 0.28 reflects the abundance of erosive features observed on the ground and indicates that the subbasin belongs to the erosion intensity category IV or low. However, the erosion intensity was pronounced in intensive use areas, which has X a values close to 1.0, which is considered bare soil.
The EPM and RUSLE showed equivalent soil losses when considering land use and land management. Both methods consider different coefficients and parameters that represent factors related to soil cover. A list of land use and management coefficients used to determine the loss spatialization is presented in Table 8.
An indirect relationship is observed between the conservation practice parameters (P) from the RUSLE and erosive features observed in the field (φ) from the EPM. However, the values of these parameters used in the soil loss calculations have been tabulated. In the case of the C factor, the values were obtained from Olivetti et al. (2015). However, several authors disregard these parameters (BAHADUR, 2009).
The X a of the EPM corresponds to the C factor of the RUSLE, although a similar comparison to φ cannot be made. However, a relationship is observed between P and φ because P represents conservationist practices, which reflect a higher or lower propensity for erosion, and φ also represents the area susceptible to erosion. Therefore, for pasture, sugar cane, and bare soil, the maximum value of P (1.00) was assigned (OLIVETTI et al., 2015), which increases the soil losses in these areas.
The EPM is characterized by a high degree of security in the calculation of sediment production, transport, and accumulation. The method can quickly and effectively estimate the potential erosion rates and sediment production at the river basin scale. The accuracy of the estimates obtained by the models is directly related to the researcher's knowledge in setting the factors and parameters used in the model calculations (BAHADUR, 2009;OŽANIĆ, 2017;NYSSEN et al., 2014).
Gavrilovic's method is advantageous because is a fast and effective method of estimating soil losses by water erosion. In addition, the EPM can be applied even when physical and edaphoclimatic data are lacking and in areas without previous soil erosion research. Amorim et al. (2010) evaluated the soil loss estimates by several methods and concluded that the errors associated with the estimates are higher for the lowest loss rates and smaller for the highest loss rates. Moreover, studies have also indicated that areas with losses below the TPS may require constant management improvements to reduce soil losses and promote agricultural and environmental sustainability as recommended by Food and Agriculture Organization of the United Nations (2015).
When applying the EPM, the model sensitivity must be considered by assessing the responses caused by changes in each parameter and their contributions to the results. Accordingly, because the parameters are adjusted to the model, the EPM is an effective tool for performing socioeconomic and environmental planning and proposing conservationist land use and occupation policies in tropical regions.

The Erosion Potential Method is effective, and because
it is a conceptual model, it is less expensive and can be used in subbasins with limited available data; 2. Although the Erosion Potential Method was not validated by geostatistical models, experimental plot data or sedimentological data, its application, which was performed simultaneously with the Revised Universal Soil Loss Equation, showed that the model was able to point out areas with soil losses above the soil loss tolerance limits in tropical regions; 3. Estimations of soil loss and erosion intensity by the EPM contributes to risk assessments of the degradation of tropical and subtropical soils and represents a tool for assessing the socioeconomic sustainability of agricultural activities.