Modeling of soil organic carbon loss by water erosion on a tropical watershed1

ABSTRACT Water erosion under tropical climate conditions is one of the main processes that change the balance between the inputs and outputs of soil organic carbon (SOC). Water erosion modeling using the Erosion Potential Method (EPM) can be used as an alternative to assist in understand soil carbon dynamics and its interaction with the erosive process. In this context, the objective of the study was to estimate carbon losses by water erosion in a watershed with a wide land-use diversity. The modelling was performed based on the soil organic matter content (SOM) of the area, and the estimated soil losses, according EPM. To the SOM determination, soil samples were collected 50 points (0-0.2 m) distributed in the watershed. The data analysis was performed using remote sensing techniques and a Geographic Information System, which was also used to interpolate the SOM content, through the use of the ordinary kriging. The results showed that from 126.53 Mg year-1 of the total eroded organic carbon estimated, 111.60 Mg year-1 were deposited in relief depressions, while 14.93 Mg year-1 reached the water body system. The applied methodology represents a cost-effective and relatively fast method to estimate the soil organic carbon loss by water erosion and allows the determination of the areas that most need intervention, aiming to decrease the impact of agriculture on greenhouse gas emissions. The main advantage of this method is the little input data requirement, which increases the possibility of application in poorly studied regions.


INTRODUCTION
The increased concentration of greenhouse gases in the atmosphere has drawn attention to soil organic carbon (SOC), as soils are the highest carbon reservoir of all terrestrial ecosystems (LAL, 2003). Thus, small variations in SOC stocks are very likely to have significant effects on the terrestrial carbon cycle, changing the CO 2 concentrations in the atmosphere, and influencing the greenhouse effect and global climate (ZHOU et al., 2019).
Water erosion under tropical climate conditions is one of the main processes that change the balance between the inputs and outputs of soil organic carbon (SOC) (LAL, 2019). This process causes soil loss, exposing the stabilized organic carbon inside the aggregates to the climatic elements and the microbial enzymes (DECHEN et al., 2015). Therefore, water erosion reduces the carbon stored in the soil, which can damage food production and promote environmental degradation.
Although several studies evaluate SOC losses in agricultural systems due to the soil organic matter (SOM) mineralization (PAUSTIAN et al., 2016;POKHAREL;CHANG, 2019;THANGARAJAN et al., 2013), data about the contribution of water erosion to carbon losses are scarce, especially in tropical soils (HANCOCK et al., 2019;NACHIMUTHU;HULUGALLE, 2016). The few studies found in the literature may be explicated to the fact of field assessments of soil organic carbon (SOC) loss by water erosion can be costly and consume much time. Moreover, data obtained from experimental plots are unable to represent an entire watershed due to the broad topographic and edaphic variations of the area (STARR et al., 2000). In this context, monitoring soil carbon removed by water erosion in the hydrographic basin scale can be realized using modeling techniques (HANCOCK et al., 2019;PARSONS, 2019;PRASANNAKUMAR et al., 2012). Starr et al. (2000) and Ya n et al. (2005) obtained satisfactory results by combining the Revised Universal Soil Loss Equation (RUSLE) (RENARD et al., 1997) with the SOC content in the topsoil to estimate the SOC loss by water erosion and wind erosion, respectively. In addition to RUSLE, there are several models, which can be used to predict erosion and combined with information on the SOC content in the study area, could be used to estimate carbon losses. However, models application is limited to areas with little available information, which is common in many tropical regions. In these cases, an alternative approach is the use of models that require little input data, such as the Erosion Potential Method (EPM) (GAVRILOVIC, 1962).
In addition to low data requirements, EPM parameters are obtained from tabulated values, which make it inexpensive and easy to apply (EFTHIMIOU et al., 2016;GAVRILOVIC, 1962). Another advantage of EPM over other models is the retention coefficient (R u ), which provides an estimate of the eroded sediment fraction that reaches the water body system and the fraction deposited along the watershed area.
Modeling the SOC loss is essential to understand the dynamics of soil carbon and its interaction with water erosion process, as well as support the planning of conservation measures to avoid environmental impacts. This study aimed to estimate the SOC loss in a watershed with a wide land-use diversity. We tested the hypothesis that the EPM combined with the spatial distribution of SOC content can be used to estimate the carbon loss by water erosion with satisfactory efficiency in a tropical region of Brazil.

Erosion Potential Method (EPM)
The Erosion Potential Method (EPM) was used to estimate the annual soil loss and the rate of sediment delivered to the water bodies. The EPM takes into account factors related to climate, geology, surface, Modeling of soil organic carbon loss by water erosion on a tropical watershed soil properties, topographic characteristics, geometric features, type and distribution of land use and the watershed erosion degree (EFTHIMIOU; LYKOUDI; KARAVITIS, 2017;GAVRILOVIC, 1962). The model was calculated by the equations described in Table 1.
Notes: dimen. = dimensionless. * Parameter incorporated into the original formula for conversion of m 3 year -1 to Mg year -1 . Source: Gavrilovic (1962) Soil resistance to erosion (Y) values range from 0.20 (soils with high resistance to erosion) to 2.0 (soils with low resistance to erosion), differing according soil type (GAVRILOVIC, 1962). The soil was classified as a dystrophic Red Latosol.  The soil use and management coefficient (X a ) expresses the protection of an area against soil aggregates breakdown. Its values range from 0.05 (areas with dense vegetation) to 1.0 (areas without vegetation cover). The erosion degree is characterized by the coefficient of visible erosion features (φ), which is obtained from visual characterization. The values range from 0.1 (areas with no evident erosive processes) to 1 (areas with severe erosion processes) (GAVRILOVIC, 1962).
The parameters Y, X a , and φ were calculated based on tabulated values adapted to Brazilian edaphoclimatic conditions by Sakuno et al. (2020).
The mean slope of the area (I sr ) was obtained based on the watershed declivity Map ( Figure 2B). In order of that, a Digital Elevation Model (DEM) (Figure 2A The coefficient of retention (R u ) was quantified based on physical parameters of the area previously described (O, D, L). The R u value represents the fraction of the eroded soil that was lost from the watershed area (G yr ) (GAVRILOVIC, 1962).
The coefficient of erosion (Z) expresses the watershed susceptibility to erosion: values close to 0 indicate lower tendency. The input parameters of the model are expressed in Table 2.
Using the Raster Calculator tool from ArcGIS 10.3 (ENVIRONMENTAL SYSTEMS RESEARCH INSTITUTE, 2015), all the parameters were combined in the EPM equation, mapping the estimated erosion, that present the spatial distribution of the soil losses.

Validation
The soil losses estimated by the EPM were validated using data of the total solids that achieve the water bodies -daily flow -, according to Batista et al. (2017).
Initially, we build a water discharge curve relating to total sediments transported with water discharge (Figure 3). To construct this, we used data of total solids in the water and respective discharge from 2008 to 2018, which are monitored by a weather station operated by "Instituto Mineiro de Gestão das Águas" (IGAM) and located near the Coroado Stream exutory at coordinates 45°53'35" W and 21°39'55" S.
Moreover, the actual soil loss, given by the sediment that leaves the watershed per year, was calculated based on the water discharge curve and the dataset of the daily flow rate in 2019, obtained from the "Agência Nacional de Águas". The results were then compared to the estimates of generated sediment acquire from EPM.  Notes: Y = Average of soil resistance to erosion; X a = Average coefficient of soil use and management; φ = Average coefficient of visible erosion features; I sr = mean slope; Z = Average coefficient of erosion; t 0 = Mean air temperature; F = watershed area; O = perimeter; D = average elevation difference; L = length of the area, which was measured from the main watercourse; R u = retention coefficient and; dim. = dimensionless

Soil organic carbon loss estimation
The carbon soil loss by water erosion was estimated using Equation 6, based on methodologies proposed by Starr et al. (2000) and Ya n et al. (2005), combined with the parameters of the EPM. C erosion = W yr . SOM . 0,58 Equation 6 Where C erosion = eroded SOC (Mg year -1 ); W yr = annual erosion (Mg year -1 ); SOM = soil organic matter content (%) and 0.58 = van Bemmelen constant, used for the conversion of SOM to SOC (0.58 kg C kg SOM -1 ).
The retention coefficient (R u ) estimate the rate of eroded carbon that was deposited at lower relief positions and the fraction lost by the subbasin area.
C loss = C erosion . R u Equation 7 Where C loss = SOC loss (Mg year -1 ); C erosion = eroded SOC (Mg ano -1 ) and R u = retention coefficient.
To determine soil organic matter (SOM) content, soil from the surface layer (0-0.2 m) was sampled, in 50

Soil Loss
The calculated coefficient of the intensity of erosion (Z = 0.29) indicates that the watershed mainly presents lower erosion susceptibility areas. The good vegetation cover (X a = 0.43) provided by conservationist practices adopted in the coffee cultivation zones and the presence of native and reforested forests contributed to this result. Besides that, the local Latossolos are resistant to erosion (Y = 0.08), contributing to the overall low susceptibility of the watershed, once X a and Y are the most sensitive parameters to the variations of Z (DRAGIČEVIĆ; KARLEUŠA; OŽANIĆ, 2017).
The total soil loss (W yr ) estimated was 11,132.63 Mg year -1 . Considering the retention coefficient (R u = 11.80%), it was estimated the total sediment delivery rate, that is, the amount of soil that actually reaches the water bodies, which corresponds to the area actual soil loss (G yr ), was estimated in 1,175.00 Mg year -1 .
The average G yr estimated by EPM was 2.10 Mg ha -1 year -1 , with a maximum value of 12.72 Mg ha -1 year -1 . The soil loss calculated using the flow versus sediment ratio and the daily runoff dataset was 2.52 Mg ha -1 year -1 . Thus, the EPM showed an error of 16.67%, underestimating the soil losses at 0.42 Mg ha -1 year -1 . According to Pandey, Chowdary and Mal (2007), errors of less than 20% is acceptable. Thus, the EPM model presented acceptable efficiency and reliability it is possible to validate the erosion simulation, process based on the application of EPM for the Coroado Stream Watershed conditions. Efthimiou et al. (2016), applied EPM in a watershed in Greece and reported underestimation of results regarding field-observed sediment generation, with an error of 38%.
Around 90% of the watershed presented soil loss under 5 Mg ha -1 year -1 , which is considered low (PANDEY;CHOWDARY;MAL, 2007;PRASANNAKUMAR et al., 2012), and only 1.60% of the area present losses higher than 7.5 Mg ha -1 year -1 . Areas with steeper slope and bare soil had the highest soil erosion rates (Figure 4).
The areas with bare soil (access roads) exhibited the highest soil losses (average of 8.91 Mg ha -1 year -1 ), while the forest displayed the lowest rates (average 0.07 Mg ha -1 year -1 ), which highlight the role of vegetal density to provide soil protection against the raindrop impact and runoff detachment. Coffee crop was the agricultural-crop with the lowest soil loss rate (average of 2.47 Mg ha -1 year -1 ), likely due to the adoption of conservation practices such as vegetation management between rows, containment basins in the steeper slope and catchment areas. However, the soil loss rate for eucalyptus (5.03 Mg ha -1 year -1 ), also a permanent crop, was higher than the temporary crops, due to the absence of conservationist management practices, such as planting following the contour lines, and also the temporary crops being mainly located in the steepest sites. The sugarcane and corn areas presented soil loss of 3.35 Mg ha -1 year -1 and 4.15 Mg ha -1 year -1 , respectively. Facilities and drainage were not considered in the calculation, once they do not participate in sediment generation.

Carbon Loss
The SOM contents ranged from 2.10 to 3.00% with the highest values observed in the areas with lower altitudes and the northeast portion of the watershed. The spatial distribution is represented in Figure 5A.
The spatial distribution of SOM showed higher carbon contents in the low relief areas, which may be related to the SOC deposition. However, it is complex to determine the final destination of the eroded carbon since it depends on several factors, including the type and stage of erosion and the fractions removed (LAL, 2019).
The total eroded carbon (C erosion ) estimated was 126.53 Mg year -1 . According to the retention coefficient (R u ), 88.20% of the C erosion was deposited and redistributed on the area relief (111.60 Mg year -1 ). Thus, the estimated carbon content that reaches the water bodies (C loss ) was 14.93 Mg year -1 (11.80%), with rates ranging from 0.16 kg ha -1 year -1 to 109.50 kg ha -1 year -1 , with an average of 26.67 kg ha -1 year -1 ( Figure 5B). The lower rates were found in forest areas (1.73 kg ha -1 year -1 ), followed by coffee (36.29 kg ha -1 year -1 ), sugarcane (50.41 kg ha -1 year -1 ), corn (57.96 kg ha -1 year -1 ), and eucalyptus (76.75 kg ha -1 year -1 ). The access roads was not considered in carbon losses calculation due to imprecision in determining soil organic matter content in such location.
The values estimated are close to those found by Roose and Bartches (2006), which compared data from numerous experiments concerning the contribution of water erosion to carbon losses in different climatic, relief, soil type, and management conditions. These authors found values from 1 to 50 kg C ha -1 year -1 in soils protected by plant remains and 50-500 kg C ha -1 year -1 in harvested fields.
In the entire watershed, the controlling of the water erosion is essential to keep or even increase soil carbon sequestration. Even low rates of carbon loss by water erosion, in the long term, restrict carbon sequestration and damage the soil quality as a whole (HUA et al., 2016). The carbon loss by water erosion could be mitigated by the adoption of better management practices, such the maintenance of crop residues on the soil surface, cultivation of eucalyptus along the contour lines and vegetation management between rows. No-tillage should be introduced in temporary crops, Modeling of soil organic carbon loss by water erosion on a tropical watershed as this practice provides greater accumulation of SOC and improves the physical indicators of the soil, such as water infiltration (SALES et al., 2016).
The estimation of the carbon losses caused by water erosion in large areas using EPM and geostatistical techniques allows us to evaluate the sustainability of a productive system and to determine the areas that most need intervention, concerning to decrease the impact of agriculture on greenhouse gas emissions.

CONCLUSION
1. The results support the hypothesis that the applied methodology represents a cost-effective and relatively fast method to estimate the soil organic carbon loss by water erosion and to identify priority areas that need intervention. The main advantage is the little input data requirement, which increases the possibility of application in poorly studied regions; 2. Soil loss estimates could provide valuable information for the creation of strategies to cope with the effects of water erosion on soil carbon loss and the construction of measures to mitigate the agricultural contribution to the greenhouse gases emissions.