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Assessing rainfall erosivity indices through synthetic precipitation series and artificial neural networks

Abstracts

The rainfall parameter that expresses the capacity to promote soil erosion is called rainfall erosivity (R), and is commonly represented by the indexes EI30 and KE>25. The calculations of these indexes requires pluviographical records, that are difficult to obtain in Brazil. This paper describes the use of synthetic rainfall series to compute EI30 and KE>25 in Espírito Santo State (Brazil). Artificial neural networks (ANNs) were also developed to spatially interpolate R values in Espírito Santo. EI30 and KE>25 indexes values were close to those calculated on a homogeneous area according to the similarity of rainfall distribution; indicating the applicability of the use of synthetic rainfall series to estimate the R factor. ANNs had a better performance than Inverse Distance Weighted and Kriging to spatially interpolate rainfall erosivity values in the State of Espírito Santo.

interpolation; rainfall generator; soil conservation; universal soil loss equation


Dentre as características da precipitação aquela que expressa sua capacidade em promover a erosão do solo é denominada erosividade das chuvas (R), sendo comumente representada pelos índices EI30 e KE>25. A determinação destes indices requer a disponibilidade de series de dados pluviográficos, que são de difícil acesso no Brasil. O presente artigo descreve o uso de séries sintéticas de dados pluviográficos para calcular os índices EI30 e KE>25 no Estado do Espírito Santo (Brasil). Redes neurais artificiais (ANNs) também foram desenvolvidas para promover a interpolação espacial dos valores de R no Espírito Santo. Os valores calculados para os índices EI30 e KE>25 foram próximos àqueles encontrados em áreas pluviométricamente homegêneas próximas, indicando a aplicabilidade do uso de séries sintéticas de dados pluviográficos. As redes neurais artificiais consistiram em interpoladores espacial melhores que os métodos de inverso da potência da distância e krigagem para a espacialização dos índices de erosividade no Espírito Santo.

interpolação; gerador climático; conservação do solo; equação universal de perdas de solo


INTRODUCTION

Soil erosion is a widespread land degradation problem in many parts of the world. On-site and off-site costs of soil erosion reach about 44 billion dollars in the United States (Pimentel et al. 1995), 4.2 billion dollars in Brazil (Hernani et al. 2002Hernani LC, Freitas PL, Pruski FF, De Maria IC, Castro Filho C and Landers JC. 2002. A erosão e seu impacto. In: MANZATTO CV ET AL. (Eds), Uso agrícola dos solos brasileiros. Rio de Janeiro, EMBRAPA, p. 47-60. (in Portuguese).) and 45.5 billion dollars in the European Union (Telles et al. 2011Telles TS, Guimarães MF and Dechen SCF. 2011. The costs of soil erosion. Rev Bras Ci Solo 35: 287-298.). Assessing the risk of erosion, predicting erosion rates and designing and evaluating different soil protection strategies is an essential tool for selecting soil and watershed best management practices. Mathematical models are used to quantify and predict soil losses. The universal soil loss equation (USLE) (Wischmeier and Smith 1978Wischmeier WH and Smith DD. 1978. Predicting Rainfail Erosion Losses - A Guide to Conservation Planning, vol. 537 of Agriculture Handbook, USDA, Washington, DC, USA.) and the revised universal soil loss equation (RUSLE) (Renard et al. 1991Renard KG, Foster GR, Weesies GA and Porter JP. 1991. RUSLE: Revised Universal Soil Loss Equation. J Soil Water Conserv 46: 30-33.) have been the most widely used models in predicting soil erosion losses (Baskan et al. 2010Baskan O, Cebel H, Akgul S and Erpul G. 2010. Conditional simulation of USLE-RUSLE soil erodibility factor by geostatistics in a Mediterranean Catchment, Turkey. Environ Earth Sci 60: 1179-1187.).

Rainfall is the main climatic characteristic that influences soil erosion, given the extraordinary importance of soil detachment processes due to drop impact and runoff shear. Among USLE-RUSLE factors, the erosive capacity of rainfall is expressed as rainfall erosivity (R), commonly represented by the indices EI30 (Wischmeier and Smith 1958Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291.) or KE>25 (Hudson 1973Hudson NW. 1973. Soil conservation. Ithaca: Cornell University Press, 320 p.).

The main method to calculate rainfall erosivity values requires pluviographic records. This kind of information is difficult to obtain in Brazil due to the reduced number and inadequate spatial distribution of meteorological stations that are equipped to provide pluviographic data. This makes it very difficult to know an R factor for all of Brazil. On the other hand, some empirical equations can also estimate values of rainfall erosivity by using geographical coordinates or pluviometric records, such as annual and monthly rainfall averages (Silva 2004Silva AM. 2004. Rainfall erosivity map for Brazil. Catena 57: 251-259., Hoyos 2005Hoyos N. 2005. Spatial modeling of soil erosion potential in a tropical watershed of the Colombian Andes. Catena 63: 85-108., Aquino et al. 2008Aquino RF, Avanzi JC, Silva MLN, Sáfadi T and Curi N. 2008. Use of time series models for predicting monther erosivity in Lavras, MG. R Bras Agromet 16: 205-210. (in Portuguese)., Capolongo et al. 2008Capolongo D, Diodato N, Mannaerts CM, Piccarreta M and Strobl RO. 2008. Analyzing temporal changes in climate erosivity using a simplified rainfall erosivity model in Basilicata (southern Italy). J Hydrol 356: 119-130., Zhang et al. 2008aZhang Q, Wang L and Wu F. 2008a. GIS-based assessment of soil erosion at Nihe Gou Catchment. Agric Sci China 7: 746-753.).

Yu (2002)Yu B. 2002. Using CLIGEN to generate RUSLE climate inputs. Trans ASAE, 45: 993-1001. and Zhang et al. (2008bZhang Y, Liu B, Wang Z and Zhu Q. 2008b. Evaluation of CLIGEN for storm generation on the semiarid Loess Plateau in China. Catena 73: 1-9., 2010)Zhang YG, Nearing MA, Zhang XC, Xie Y and Wei H. 2010. Projected rainfall erosivity changes under climate change from multimodel and multiscenario projections in Northeast China. J Hydrol 384: 97-106. assessed the ability of stochastic weather generators to generate daily rainfall synthetic series used to calculate the R factor. These generators have the potential to be used in Brazil to extend the rainfall erosivity index database.

Many authors (Qi et al. 2000Qi H, Gantzer CJ, Jung PK and Lee BL. 2000. Rainfall erosivity in the Republic of Korea. J Soil Water Conserv 55: 115-120., Silva 2004Silva AM. 2004. Rainfall erosivity map for Brazil. Catena 57: 251-259., Hoyos et al. 2005Hoyos N, Waylen PR and Jaramillo A. 2005. Seasonal and spatial patterns of erosivity in a tropical watershed of the Colombian Andes. J Hydrol 314: 177-191., Moreira et al. 2006Moreira MC, Cecílio RA, Pinto FAC, Lombardi Neto F and Pruski FF. 2006. Estimates of rainfall erosivity in São Paulo state by an artificial neural network. Rev Bras Ci Solo 30: 1069-1076. (in Portuguese)., Yin et al. 2007Yin S, Xie Y, Nearing MA and Wang C. 2007. Estimation of rainfall erosivity using 5-to 60-minute fixed-interval rainfall data from China. Catena 70: 306-312., Men et al. 2008Men M, Yu Z and Xu H. 2008. Study on the spatial pattern of rainfall erosivity based on geostatistics in Hebei Province, China. Front Agric China 2: 281-289., Shamsad et al. 2008Shamsad A, Azhari MN, Isa MH, Wan Hussin WMA and Parida BP. 2008. Development of an appropriate procedure for estimation of RUSLE EI30 index and preparation of erosivity maps for Pulau Penang in Peninsular Malaysia. Catena 72: 423-432., Angulo-Martínez et al. 2009Angulo-Martínez M, López-Vicente M, Vicente-Serrano SM and Beguería S. 2009. Mapping rainfall erosivity at a regional scale: a comparison of interpolation methods in the Ebro Basin (NE Spain). Hydrol Earth Syst Sci 13: 1907-1920., Silva et al. 2010aSilva MA, Silva MLN, Curi N, Santos GR, Marques JJGSM, Menezes MD and Leite FP. 2010a. Evaluation and spatialization of rainfall erosivity in the Rio Doce Valley, central-eastern region of Minas Gerais, Brazil. Rev Bras Ci Solo 34: 1029-1039. (in Portuguese)., bSilva RB, Iori P, Armesto C and Bendini HN. 2010b. Assessing Rainfall Erosivity with Artificial Neural Networks for the Ribeira Valley, Brazil. Int J Agron 2010: 1-7., Alves Sobrinho et al. 2011) used spatial interpolation techniques like “inverse distance weighted”, “kriging” and “artificial neural networks” (ANNs) to create maps representing spatial distribution of R values. Since no single interpolation method among those available for spatial interpolation of R factor is optimal for all regions and all indices, it is very important to compare the results obtained through different methods, applied to each set of data (Goovaerts 1999Goovaerts P. 1999. Using elevation to aid the geostatistical mapping of rainfall erosivity. Catena 34: 227-242., Beguería and Vicente-Serrano 2006Beguería S and Vicente-Serrano SM. 2006. Mapping the hazard of extreme rainfall by peaks over threshold extreme value analysis and spatial regression techniques. J Appl Meteorol 45: 108-124., Angulo-Martínez et al. 2009Angulo-Martínez M, López-Vicente M, Vicente-Serrano SM and Beguería S. 2009. Mapping rainfall erosivity at a regional scale: a comparison of interpolation methods in the Ebro Basin (NE Spain). Hydrol Earth Syst Sci 13: 1907-1920.).

The ability of ANNs to use different input parameters makes them capable of solving complex problems from many areas (Sárközy 1999Sárközy F. 1999. Gis functions - Interpolation. Periodica polytechnica Ser Civ Eng 43: 63-86., Souza et al. 2006Souza ECB, Ribeiro SRA, Botelho MF, Krueger CP and Centeno JAS. 2006. Generation of isolines using GPR-L1L2 data and artificial neural network technique. Acta Scient Tech 28: 205-212. (in Portuguese).). The ANNs are cited as an alternative resource for estimating climatic variables that may replace the traditional interpolation methods (Bialobrzewski 2008Bialobrzewski I. 2008. Neural modeling of relative air humidity. Comput Electron Agric 60: 1-7., Sivapragasam et al. 2010Sivapragasam C, Arun VM and Giridhar D. 2010. A simple approach for improving spatial interpolation of rainfall using ANN. Meteorol Atmos Phys 109: 1-7.), including rainfall erosivity indexes as assessed by Moreira et al. (2006)Moreira MC, Cecílio RA, Pinto FAC, Lombardi Neto F and Pruski FF. 2006. Estimates of rainfall erosivity in São Paulo state by an artificial neural network. Rev Bras Ci Solo 30: 1069-1076. (in Portuguese). for São Paulo State, Brazil.

In this paper we aimed at: a) calculating rainfall erosivity indexes EI30 and KE>25 using synthetic rainfall series for several locations in Espírito Santo State, Brazil; b) developing ANNs to spatially interpolate rainfall erosivity in Espírito Santo State, Brazil; and c) comparing the developed ANNs performance to other spatial interpolators.

MATERIALS AND METHODS

Assessing Rainfall Erosivity Indexes

The stochastic weather generator ClimaBR 2.0, developed by Baena et al. (2005)Baena LGN, Pruski FF, Moreira MC, Souza VBC, Zanetti SS and Oliveira VPS. 2005. Software for Generating Synthetic Series of Climatic Data. Eng Agricult 13: 210-220. (in Portuguese). and validated by Zanetti et al. (2006)Zanetti SS, Oliveira VPS and Pruski FF. 2006. Validation of the model ClimaBR in relation to the number of wet days and to daily total precipitation. Eng Agríc 26: 96-102. (in Portuguese)., was used to generate daily synthetic rainfall series for 73 pluviometric stations in Espírito Santo State (Figure 1). Oliveira et al. (2005aOliveira VPS, Zanetti SS and Pruski FF. 2005a. CLIMABR part I: model for generation of synthetic series of precipitation. R Bras Eng Agríc Ambiental 9: 356-363. (in Portuguese)., b)Oliveira VPS, Zanetti SS and Pruski FF. 2005b. CLIMABR part II: generation of precipitation profile. R Bras Eng Agríc Ambiental 9: 348-355. (in Portuguese). describe all the method to generate synthetic rainfall precipitation series. The input data used to generate each synthetic rainfall series were the measured daily rainfall depth data series in the standardized format of the Brazilian National Water Agency (http:--hidroweb.ana.gov.br) with 15 or more years in extension. Each synthetic rainfall series had 100-year daily data of: rainfall depth, storm duration, peak storm intensity, time to peak and storm profile patterns.

Figure 1
Pluviometric stations in Espírito Santo State where synthetic rainfall series were generated.

A computational algorithm was developed to identify all the erosive precipitations on each rainfall series. The erosive precipitations were taken as all rainfall with depth equal or higher than 10 mm or lower than 10 mm in depth, but with a 15 minute depth equal or higher than 6 mm (Wischmeier and Smith 1958Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291., Wischmeier 1959Wischmeier WH. 1959. A rainfall erosion index for a universal soil loss equations. Soil Sci Soc Am Proc 23: 246-249., Cabeda 1976Cabeda MSV. 1976. Computation of storm EI value. West Lafayette: Purdue University, 6 p.). Two different rainfall erosivity indices were computed (EI30 and KE>25) using two different equations to calculate erosive precipitation kinetic energy (KE).

Before the calculation of EI30 (Wischmeier and Smith 1958Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291.) and KE>25 (Hudson 1973Hudson NW. 1973. Soil conservation. Ithaca: Cornell University Press, 320 p.) indices, it was necessary to estimate the erosive precipitation kinetic energy (KE). KE values were computed individually by the equations proposed by Wischmeier and Smith (1958)Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291. (equation 1) and Wagner and Massambani (1988)Wagner CS and Massambani O. 1988. Analysis of the Wischmeier and Smith rainfall intensity-kinetic energy relationship and its applicability for São Paulo (Brazil) region. Rev Bras Ci Solo 12: 197-203. (in Portuguese). (equation 2). Equation 1 is an universal accepted equation and Equation 2 is a local equation proposed to São Paulo State (Brazil). The two equations were used intending to make a comparison between their results on rainfall erosivity indices values.

where:

KE = kinetic energy, MJ.ha–1.mm–1; and

I = rainfall intensity, mm.h–1.

Equations 1 and 2 were used to compute KE of all the erosive rainfall with intensity equal to or lower than 76 mm.h–1. Erosive rainfall with greater intensities were assumed to have a KE equal to 0.283 MJ.ha–1.mm–1, as long as the raindrop diameter does not rise up to rainfall intensities greater than this limit (Foster et al. 1981Foster GR, McCool KG, Renard KG and Moldenhauer WC. 1981. Conversion of the universal soil loss equation to SI metric units. J Soil Water Cons 36: 355-359.).

The EI30 parameter for each specific event was calculated as the product of total kinetic energy (KE) computed individually by equations 1 and 2 and the maximum 30 min intensity, according to Wischmeier and Smith (1958)Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291.. The total KE of each event was computed using the one minute time step. Monthly values were determined as the sum of the individual events determined through the EI30 parameter (MJ.mm.ha–1.h–1), and annual values were determined in the same manner. Then mean monthly and annual values were computed using the 100-year values.

The KE>25 parameter for each specific event was calculated as the product of total kinetic energy (KE) computed individually by equations 1 and 2 and rainfall depth, according to Hudson (1973)Hudson NW. 1973. Soil conservation. Ithaca: Cornell University Press, 320 p.. The total KE of each event was computed by using one minute time step. Only rainfall intensities greater than 25 mm.h–1 were considered. Monthly values were determined as the sum of the individual events determined by the KE>25 parameter (MJ.ha–1) and annual values were determined in the same manner. Later mean monthly and annual values were computed using the 100-year values.

Since two different equations were used to compute KE (Wischmeier and Smith 1958Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291., Wagner and Massambani 1988Wagner CS and Massambani O. 1988. Analysis of the Wischmeier and Smith rainfall intensity-kinetic energy relationship and its applicability for São Paulo (Brazil) region. Rev Bras Ci Solo 12: 197-203. (in Portuguese).) and two different erosivity indices were calculated (EI30 and KE>25), final results consisted on four monthly and four annual values of R factors for each pluviometric station.

Development of ANNs to Spatially Interpolate Rainfall Erosivity Indices

Neural modeling was carried out with MathWorks MatLab® software (MATLAB 2000Matlab Software. 2000. Version 6.0, The MathWorks, Inc., Natick, MA.). Pluviometric stations R values were randomly divided in two sub data-sets to develop 48 ANNs (four monthly R indices for 12 months): training sub data-set (60 stations) and test sub data-set (13 stations).

In the present study, a four-layer ANN model was used. The ANN architecture was 3-n1-n2-1 type, corresponding to one input layer with three variables (input parameters), two intermediate layers with n1 and n2 neurons and one neuron at the output layer representing output variable. The input variables were composed of the latitude and longitude values of each station (decimal degrees) and the altitude value (meters). A linear activation function was used in the output layer to obtain the rainfall erosivity value (R factor), in MJ.mm.h–1. ha–1.year–1 (EI30) or MJ.ha–1.year–1 (KE>25).

Before ANN's training all input and output data sets were standardized to values between -1 and 1. This procedure is essential to guarantee better training efficiency (Maier and Dandy 2000Maier HR and Dandy GC. 2000. Neural networks for the prediction and forecasting of water resources variables: a review of modeling issues and applications. Environ Modell Softw 15: 101-123.). The training algorithm feed forward back propagation was used. After each algorithm interaction the ANN's free parameters were refined by the Levenberg-Marquardt training rule. Different numbers of neurons at intermediate layers were tested (n1 and n2 varying from 1 to 12 neurons) as well as different total training epochs (50, 100, 200 and 500 epochs). The ANN's total number of neurons were limited by the number of samples (stations) used on the training sub dataset as suggested by Hagan et al. (1996)Hagan MT, Demuth HB and Beale M. 1996. Neural network design. Boston, PWS publishing company..

Considering that at the beginning of the ANN's training the free parameters are randomly generated, the ANNs resulted from each combination of n1 and n2 and training seasons were trained 20 times. For each month and each one of the four R factors, the ANNs that presented the highest correlation coefficient (r) obtained in the test sub data-set were selected to be the spatial interpolator ANNs.

The ANNs to spatially interpolate the annual R factor were not developed because their values were computed by the sum of the ANN's monthly interpolated R factors.

Evaluation of ANN and other Spatial Interpolator Performances

Aside from the selected ANN spatial interpolators, the following interpolators were evaluated: inverse distance weighted (IDW) – considering weights 2 (IDW2) and 3 (IDW3); and universal kriging – considering spherical (KSPH) and exponential (KEXP) semivariogram models.

Interpolators' evaluation was done using the cross-validation method (Robinson and Metternicht 2006Robinson TP and Metternicht G. 2006. Testing the performance of spatial interpolation techniques for mapping soil properties. Comput Electron Agric 50: 97-108.). For each station, observed (Oi) and interpolated (Si) R values were used to compute the agreement index (d) (Willmont 1981):

where:

d = agreement index;

O = observed R factor value;

S = observed R factor value; and

Ō = mean observed R factor value.

RESULTS AND DISCUSSION

Rainfall Erosivity Index Values

Table I presents the 73 values of mean annual EI30 and KE>25 rainfall erosivity indices computed by both equations to calculate rainfall kinetic energy: WS (equation 1 by Wischmeier and Smith 1958Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291.) and WM (equation 2 by Wagner and Massambani 1988Wagner CS and Massambani O. 1988. Analysis of the Wischmeier and Smith rainfall intensity-kinetic energy relationship and its applicability for São Paulo (Brazil) region. Rev Bras Ci Solo 12: 197-203. (in Portuguese).). It can be observed that EI30 index computed by the use of WM equation are about 3.0% higher than those computed by WS equation. On the other hand, KE>25 index values computed by WS equation are 1.1% higher than those computed by WM equation. According to Gonçalves et al. (2006)Gonçalves FA, Silva DD, Pruski FF, Carvalho DF and Cruz ES. 2006. Indices and spatialization of rainfall erosivity in Rio de Janeiro State, Brazil. R Bras Eng Agríc Ambiental 10: 269-276. (in Portuguese). this occurs only with KE>25 index, because the WS equation computes higher KE values when rainfall intensities are greater than 31 mm.h–1. The highest observed difference is equal to 6.2% on EI30 and 16.7% on KE>25, both at Santo Agostinho pluviometric station.

TABLE I
Mean annual rainfall erosivity indices EI30 and KE>25 computed by kinectic energy equations presented by Wischmeier and Smith (1958)Wischmeier WH and Smith DD. 1958. Rainfall energy and its relationship to soil loss. Trans Am Geophys Union 39: 285-291. (WS) and Wagner and Massambani (1988)Wagner CS and Massambani O. 1988. Analysis of the Wischmeier and Smith rainfall intensity-kinetic energy relationship and its applicability for São Paulo (Brazil) region. Rev Bras Ci Solo 12: 197-203. (in Portuguese). (WM) at pluviometric stations of Espírito Santo State.

The low values of percentage differences on Table I indicate that both WS and WM equations compute very similar values to both R indices in Espírito Santo State. Gonçalves et al. (2006)Gonçalves FA, Silva DD, Pruski FF, Carvalho DF and Cruz ES. 2006. Indices and spatialization of rainfall erosivity in Rio de Janeiro State, Brazil. R Bras Eng Agríc Ambiental 10: 269-276. (in Portuguese). had found the same result in Rio de Janeiro, a state limiting with Espírito Santo and located on a homogeneous area according to similarity of rainfall distribution (Keller Filho et al. 2005). This was also observed in other homogeneous rainfall areas in Brazil, like the Brazilian Savanna (Marques et al. 1997Marques JJGSM, Alvarenga RC, Curi N, Santana DP and Silva MLN. 1997. Rainfall erosivity índices, soil losses and erodibility factor for two soils from the Cerrado region – first approximation. R Bras Ci Solo 21: 427-434. (in Portuguese)., Silva et al. 1997Silva MLN, Freitas PL, Blancaneaux P and Curi N. 1997. Rainfall erosivity indices in the Goiânia region, Goiás State, Brazil. Pesq Agropec Bras 32: 977-985. (in Portuguese).).

The EI30 index ranged from 2,123 (Santo Agostinho station) to 9,885 MJ.mm.ha–1.h–1. year–1 (Burarama (DNOS)). The KE>25 index ranged from 5.0 to 105.0 MJ.ha-1.year-1 on the same stations. The lowest R index values were observed at higher latitudes, where annual pluviometric depths are also the lowest. On the other hand, the higher values were observed on lower latitudes and higher longitudes (near the Brazilian coast), in regions characterized by orographic precipitations and maritime influence (Castro et al. 2010Castro FS, Pezzopane JEM, Cecílio RA, Pezzopane JRM and Xavier AC. 2010. Evaluation of the performance of the different methods of interpolaters for parameters of the climatologic water balance. R Bras Eng Agríc Ambiental 14: 871-880. (in Portuguese).). Silva et al. (2010c)Silva SA, Lima JSS, Souza GS and Oliveira RB. 2010c. Variability of rainfall erosive potential for Espírito Santo State, Brazil. Irriga 15: 312-323. (in Portuguese). had used pluviometric data of Espírito Santo to calculate EI30 indices and had found values ranging from 5,091 to 7,958 MJ.mm.ha–1.h–1.year–1.

Average EI30 e KE>25 were 5,592 MJ.mm.ha–1.h–1.year–1 and 58.0 MJ.ha–1.year–1, respectively. These values are very close to those found by Carvalho et al. (2005)Carvalho DF, Montebeller CA, Franco EM, Valcarcel R and Bertol I. 2005. Rainfall patterns and erosion indices at Seropédica and Nova Friburgo, Rio de Janeiro - Brazil. R Bras Eng Agríc Ambiental 9: 7-14. (in Portuguese). and Gonçalves et al. (2006)Gonçalves FA, Silva DD, Pruski FF, Carvalho DF and Cruz ES. 2006. Indices and spatialization of rainfall erosivity in Rio de Janeiro State, Brazil. R Bras Eng Agríc Ambiental 10: 269-276. (in Portuguese). in Rio de Janeiro, located on a homogeneous area according to the similarity of rainfall distribution (Keller Filho et al. 2005).

The EI30 values on the west side of Espírito Santo (lower longitudes) were close to those found by Mello et al. (2007)Mello CR, Sá MAC, Curi N, Nello JM, Viola MR and Silva AM. 2007. Monthly and annual rainfall erosivity for Minas Gerais State. Pesq Agropec Bras 42: 537-545. (in Portuguese). near the limit to the State of Minas Gerais. It indicates the applicability of the use of synthetic rainfall series to estimate the R factor, corroborating Zhang et al. (2010)Zhang YG, Nearing MA, Zhang XC, Xie Y and Wei H. 2010. Projected rainfall erosivity changes under climate change from multimodel and multiscenario projections in Northeast China. J Hydrol 384: 97-106..

In Espírito Santo State there is one value of EI30 calculated by using pluviographic data from 1998 to 2003 on Aracruz station. This value is equal to 6,500 MJ.mm.ha–1.h–1.year–1 (Martins et al. 2010Martins SG, Avanzi JC, Silva MLN, Curi N, Norton LD and Fonseca S. 2010. Rainfall erosivity and rainfall return period in the experimental watershed of Aracruz, in the coastal plain of Espírito Santo, Brazil. Rev Bras Ci Solo 34: 999-1004.) and is relatively close to the one found on the present paper (about 5,000 MJ.mm.ha–1.h–1.year–1), once again indicating the applicability of the use of synthetic rainfall series to estimate the R factor.

ANNs Developed to Spatially Interpolate Rainfall Erosivity Indices

Table II presents the architecture (number of neurons on the intermediate layers and training seasons) of the ANNs developed to spatially interpolate monthly values of EI30 and KE>25 at Espírito Santo State, considering WS and WM equations. According to the criteria taken from Hagan et al. (1996)Hagan MT, Demuth HB and Beale M. 1996. Neural network design. Boston, PWS publishing company., the maximum number of neurons on the intermediate layers of the ANNs would be 12. The low number of neurons on the developed ANNs (Table II) indicates a lower complexity, better ability to generalization and estimation (Bernardos and Vosniakos 2007Bernardos PG and Vosniakos GC. 2007. Optimizing feedforward artificial neural network architecture. Eng Appl Artif Intell 20: 365-382.) and had a lower probability of “memorizing” answers (Sinha and Wang 2007Sinha SK and Wang MC. 2007. Artificial neural network prediction models for soil compaction and permeability. Geotech Geol Eng 26: 47-64.).

TABLE II
Number of neurons on intermediate layers and training seasons of the ANN developed to spatial interpolation of monthly EI30 e KE>25 erosivity indices (computed considering WS and WM equations) at Espírito Santo.

ANN with increased numbers of neurons were only those for the spatial interpolation of EI30 for the months of October, November and December (KE computed by WS equation) and for February and October (KE computed by WM equation). The same happened to the ANNs developed for spatial interpolation of KE>25 for May (KE computed by WM equation).

Evaluation of ANN and other Spatial Interpolators' Performance

Table III presents the agreement index (d) used to evaluate the ability of the interpolators to estimate spatially KE>25 and EI30 erosivity indices. Considering each erosivity index separately (EI30 and KE> 25), the values of “d” for conventional interpolators (IDW and kriging) are very similar for each month. Thus the performance of conventional interpolators doesn't depend on the equation taken to compute KE (WS or WM). This behavior was expected since, as previously shown in this paper, WS and WM equations compute very similar values to both R indices for Espírito Santo State. Thus, the performance of conventional interpolators only depends on the distance between stations, which are weighting factors in mathematical models used for conventional interpolation. This did not occur on the ANNs because trained architectures (Table II) are different for each month and each situation (WS or WM equations), resulting in different performances. In general, the conventional interpolation methods evaluated had similar performances. These interpolators have advantages and disadvantages that depend on various factors such as the amount of data available and regularity of the spatial distribution. If the distribution of observed data is not favorable, the results may be unsatisfactory.

TABLE III
Agreement index (d) used to evaluate the ability of the interpolators to estimate spatial KE>25 e EI30 erosivity indexes (computed considering WS and WM equations) at Espírito Santo.

Table III data shows that “d” index was higher on 44 of the 48 developed ANNs, which indicates better performance of ANNs for spatial interpolation of the R factor compared to conventional interpolators, as also seen by Moreira et al. (2006Moreira MC, Cecílio RA, Pinto FAC, Lombardi Neto F and Pruski FF. 2006. Estimates of rainfall erosivity in São Paulo state by an artificial neural network. Rev Bras Ci Solo 30: 1069-1076. (in Portuguese)., 2009)Moreira MC, Pruski FF, Oliveira TEC, Pinto FAC and Silva DD. 2009. Artificial Neural Networks for Monthly Estimates of Rainfall Erosivity in the Minas Gerais State. Eng Agricult 17: 75-83. (in Portuguese). in the States of São Paulo and Minas Gerais, respectively. According to Akkala et al. (2010)Akkala A, Devabhaktuni V and Kumar A. 2010. Interpolation techniques and associated software for environmental data. Environ Prog Sustainable Energy 29: 134-141., ANN interpolators work well with sparse data irregularly distributed, just as for the data presented (Figure 1). The ANNs, in order to have better performance, need consistent training and the data-set used must represent the nuances of the terrain to be modeled (Teegavarapu 2007Teegavarapu RSV. 2007. Use of universal function approximation in variance dependent surface interpolation method - an application in hydrology. J Hydrol 332: 16-29., Miranda et al. 2009Miranda F, De Freitas S and Faggion P. 2009. Integration and interpolation free air anomalies with basis in an ANN and kriging. Bol Ci Geod 15: 428-433. (in Portuguese)., Sivapragasam et al. 2010Sivapragasam C, Arun VM and Giridhar D. 2010. A simple approach for improving spatial interpolation of rainfall using ANN. Meteorol Atmos Phys 109: 1-7.), as was the case in this study.

Another important factor that led to the superiority of ANNs consisted in considering the altitude to interpolate the R factor (Goovaerts 1999Goovaerts P. 1999. Using elevation to aid the geostatistical mapping of rainfall erosivity. Catena 34: 227-242., Moreira et al. 2006Moreira MC, Cecílio RA, Pinto FAC, Lombardi Neto F and Pruski FF. 2006. Estimates of rainfall erosivity in São Paulo state by an artificial neural network. Rev Bras Ci Solo 30: 1069-1076. (in Portuguese)., Silva et al. 2010bSilva RB, Iori P, Armesto C and Bendini HN. 2010b. Assessing Rainfall Erosivity with Artificial Neural Networks for the Ribeira Valley, Brazil. Int J Agron 2010: 1-7.). This is a very important variable to explain the behavior of precipitation, especially in regions of great orographic influence on the climate, as for Espírito Santo State (Keller Filho et al. 2005; Melo Júnior et al. 2006).

The ANNs developed to spatially interpolate EI30 and KE>25 indices with KE computed by the use of WM equation showed always better performance than traditional interpolation, so they are recommended for use in spatial of rainfall erosivity in Espírito Santo State. Figure 2 presents the spatial distribution of the annual EI30 and KE>25 indices calculated with KE computed by the use of WM equation and interpolated using the developed ANNs.

Figure 2
Spatial distribution of the annual EI30 (A) and KE>25 (B) indices calculated with KE computed by the use of WM equation and interpolated using the developed ANNs.

CONCLUSIONS

Based on the presented results we can conclude that:

  1. The use of synthetic rainfall series is a promising alternative to estimate the rainfall erosivity at locations without pluviographic data availability;

  2. There were no significant differences in EI30 and KE> 25 rainfall erosivity indices estimated using two rainfall kinetic energy equations that were evaluated;

  3. Artificial neural networks presented better performance than IDW and Kriging to spatial interpolate rainfall erosivity values in Espirito Santo State.

The authors thanks Fundação de Amparo à Pesquisa do Espírito Santo (FAPES) for the financial support of (Process number 35613165-06.).

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Publication Dates

  • Publication in this collection
    11 Oct 2013
  • Date of issue
    2013

History

  • Received
    12 Mar 2012
  • Accepted
    15 Mar 2013
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