Erosive rainfall in Rio do Peixe Valley in Santa Catarina, Brazil: Part I-Determination of the erosivity index

Chuvas erosivas do Vale do Rio do Peixe: Parte I Determinação do índice de erosividade R E S U M O Este trabalho teve como objetivo determinar o índice de erosividade das chuvas para a região do Vale do Rio do Peixe, em Santa Catarina, Brasil. Foram usadas as séries de três estações pluviográficas para determinar a erosividade das chuvas baseado no índice EI30 e ajustar as equações para estimar o valor de EI30 a partir do coeficiente de chuva. Observouse que as chuvas erosivas representam em média de 81,4 a 88,5% da precipitação anual. As equações ajustadas podem ser usadas para estimar a erosividade da chuva em locais com somente dados pluviométricos, e a equação regional indicada para a estimativa da erosividade é EI30 = 74,23 Rc0,8087. O fator R é de 8704,8, 7340,8 e 6387,1 MJ mm ha-1 h-1 ano-1 respectivamente para Campos Novos, Videira e Caçador. Em Campos Novos e Videira a erosividade é classificada como Alta enquanto que em Caçador é classificada como Média.


Introduction
Mathematical and hydrological modeling have been used to predict soil erosion losses, evaluate soil conservation practices, and assist in agricultural planning (Amorim et al., 2010;Kinnell, 2010).The Universal Soil Loss Equation (USLE) model is the most notable, and it includes the rainfall erosivity factor (R).
Several indices were developed to determine rainfall erosivity, including the EI30 index (Wischmeier & Smith, 1978;Kinnell, 2010) and the KE > 25 index (Hudson, 1971;Morais et al. 1988).Carvalho et al. (1991) concluded that the equation for the calculation of kinetic energy does not differ significantly between those two indices.Morais et al. (1988), who studied the correlation of erosion with the loss of soil, stated that the EI30 index is considered to be the most adequate in the state of Rio Grande do Sul (RS) to estimate the erosive potential of rain.
Determining erosion of an individual rainfall is performed with the analysis of the pluviograms, which require a long series of data.Several authors comment on the difficulty of obtaining this data, both in Brazil and in other countries (Beskow et al., 2009;Mello et al., 2007).As a result, the most common method to use the average of the monthly and annual precipitation, which can be obtained based on rainfall records from rain gauges (Waltrick et al., 2015).This methodology is often used to estimate the annual erosivity and to generate erosivity maps, as done by Silva (2004), Oliveira et al. (2012) and Mello et al. (2013).
The objective of this study was to determine the Universal Soil Loss Equation (USLE) rainfall erosivity factor (R) by using the standard procedure based on pluviographic records and to adjust the equations to estimate the rainfall erosivity based on the rainfall data from the Valley of Rio do Peixe, in the state of Santa Catarina (SC), Brazil.

Material and Methods
Pluviographic data from three meteorological stations of the Company of Agricultural Research and Rural Extension of Santa Catarina (EPAGRI), located in the Valley of Rio do Peixe in the state of Santa Catarina, Brazil, were used for this study (Table 1).Daily pluviometric data were also used to obtain a series from the same period of observation because the pluviographic records have some missing data, and the series were not from the same period.According to the Köppen classification, the climate of the region is classified as humid and subtropical -without a dry season and with a mild summer (Cfb) (Alvares et al., 2014).
The hyetograph data (pluviograph data) were digitized.A computer program was developed to read the digitized data and to perform the calculations, as described by Valvassori & Back (2014).
A pluviometric precipitation of 10 mm or more, or rain precipitation of 6 mm or greater over a maximum interval of 15 min, is considered to be an erosive rain according to the criteria proposed by Wischmeier & Smith (1958) and modified by Cabeda (1976).The calculation of the kinetic energy units of each uniform segment of rain used in this study was proposed by Wischmeier & Smith (1978) and modified by Foster et al. (1981) wherein the EC is the kinetic energy (MJ ha -1 mm -1 ); and i is the rainfall intensity -given in mm h -1 in the segment under consideration.
The kinetic energy of the segment, expressed in MJ ha -1 , is calculated by multiplying the EC by the amount of rainfall in the respective uniform segment, i.e.:

ECs EC h =
wherein ECs is the kinetic energy of the segment (MJ ha -1 ); and h is the precipitation of the segment (mm).By summing up the kinetic energy of each uniform segment, the total kinetic energy of the rain is found, i.e.:

= ∑
The EI30 index, which represents the erosivity of each individual and erosive rainfall, is determined through the following expression, according to Cassol et al. (2007):

EI
ECt I 30 30 = wherein EI30 is the erosivity index of the individual erosive rainfall (MJ mm ha -1 h -1 ); ECt is the total kinetic energy of rainfall (MJ ha -1 ); and I30 is the maximum 30-minute intensity of storm (mm h -1 ).
The linear and potential relationships between the rainfall erosivity calculated by the EI30 Index and the rainfall coefficient were established from the values of the rainfall erosivity index and the monthly and annual rainfall by the following expressions: wherein EI30 is the rainfall erosivity index (MJ mm ha -1 h -1 ); a and b are the coefficients of adjustment; and Rc is the rainfall coefficient in mm, given by the following relation: R. Bras.Eng.Agríc.Ambiental, v.21, n.12, p.774-779, 2017.
wherein Pm is the average monthly rainfall; and Pa is the average annual rainfall in mm.
The values of EI30 were estimated for the data series of the respective rain gauges of each station by using the adjusted equations, and also a general equation with the data from the four seasons.

Results and Discussion
In the rainfall data series from the Campos Novos station, an average of 1,790 mm of precipitation was recorded, and 81.4% of the precipitation was classified as erosive rain (Table 2).In Videira, the average precipitation was 1,765.7 mm with 82.2% erosive rains; while, in the Caçador Station, the average rainfall was 1,482.6 mm, and 88.5% classified as erosive rains.The lower values of precipitation observed in Caçador can be partly explained by greater missing pluviographic data.According to Alvares et al. (2014), in Campos Novos, Videira, and Caçador, the average annual precipitation measured with pluviometric rain gauges is 1,704; 1,730; and 1,738 mm; respectively.Similar percentage values of erosive rains were obtained by Back et al. (2016), who analysed pluviographic data from Chapecó SC, and by Valvassori & Back (2014), who analysed pluviographic data from Urussanga SC.
Precipitation ranged from 2,547.2 in 1990 to 1,229.0 mm in 2004 in Campos Novos (Figure 1A), while EI30 values ranged from 4,292.5 in 1984 to 11,711.6 MJ mm ha -1 h -1 in 1998.Similar variations were observed in Videira (Figure 1B).However, in Caçador (Figure 1C), the precipitation vary from 2,164 in 1997 to 948.2 mm in 2003, and the EI30 ranged from 2,484.1 in 2004 to 10,219.0MJ mm ha -1 h -1 in 2014.It is observed that there is a direct correlation between the precipitation and the EI30 index, but the total precipitation does not fully explain the erosivity variation.There are years with similar values for total annual precipitation, but with differences greater than 20% in EI30 values, as observed in the years 1992, 2005, and 2007 (Figure 1A).This finding is explained by the fact that erosivity depends not only on the total precipitated rain, but mainly on  Year the intensity of the rainfall.Another important observation in Figure 1 is that there is a large variation of rainfall erosivity; therefore, using an annual average value -which is used in many models to predict soil losses -may not be the best way to represent the soil losses over a long period of time.

Rc
According to Schick et al. ( 2014), the estimation of the erosivity index, especially its cumulative distribution over time, allows researchers to identify the time of year with the highest risk of water erosion; this helps to create a plan to control the water erosion more efficiently.
In the analysed stations, similar behaviors were observed.From January to March, the EI30 percentage values were slightly higher than the percentage values of precipitation.On the other hand, in the winter months from June to August, the opposite occured (Figure 2).However, the differences in monthly percentage values are less than 5%.
In Campos Novos (Figure 2A) from January to March, 25.1% rainfall and 29.70% EI30 values occurred, and in Videira, these values were 27.1 and 34.9%, respectively (Figure 2B).In Caçador (Figure 2C), a nearly uniform distribution of precipitation and EI30 values were observed.Valvassori & Back (2014) and Back et al. (2016) had already reported this (7) uniformity in rainfall distribution and erosivity index in rain gauge stations in Santa Catarina.However, in some Brazilian regions, there is a marked seasonal variation in erosivity.Almeida et al. (2012) reported a proportion equal to or greater than 94% erosivity occurring in the spring and summer seasons.Lombardi Neto (1977) found 90.7% of the erosivity index was from October to March, when the rainfall is at 80.1% of the total annual precipitation in the city of Campinas, in the state of São Paulo (SP).In Santa Catarina, especially in the Valley of Rio do Peixe, rainfall is well distributed throughout the year, so there is less ) Rc (mm) seasonal variation in the rainfall erosivity indices.Therefore, it is important to note that conservation practices of erosion control must be adopted throughout the year.

Figure 1 .
Figure 1.Annual rainfall values and EI30 index for Campos Novos (A), Videira (B), and Caçador (C) in the state of Santa Catarina, Brazil

Figure 2 .
Figure 2. Cumulative rainfall distribution and erosivity for Campos Novos (A), Videira (B) and Caçador (C) in the state of Santa Catarina, Brazil

Figure 3 .
Figure 3. Regression between erosivity index (EI30) and rainfall coefficient (Rc) for Campos Novos (A), Videira (B), Caçador (C), and for the Valley of Rio do Peixe in (D) in the state of Santa Catarina, Brazil

Table 1 .
; this expression is as follows: Location of the stations with the respective periods of the data used, in the state of Santa Catarina, Brazil

Table 2 .
Mean monthly rainfall and erosive rains measured by rain gauge stations in the Valley of Rio do Peixe in the state of Santa Catarina, Brazil

Table 3 .
Data of the estimated monthly precipitation (mm) and erosivity index (EI30) in the state of Santa Catarina, Brazil