Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

Pesquisas Agrárias e Ambientais

DOI: https://doi.org/10.31413/nativa.v10i3.13913 ISSN: 2318-7670

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Daniela CASTAGNA1, Adilson Pacheco de SOUZA1*, Laurimar Gonçalves VENDRUSCULO2,

Cornélio Alberto ZOLIN2

1Postgraduate Program in Environmental Sciences, Federal University of Mato Grosso, Sinop, MT, Brazil.

2Brazilian Agricultural Research Corporation (Embrapa Agrosilvopastoral), Sinop, MT, Brazil.

E-mail: pachecoufmt@gmail.com

ORCID: (0000-0002-6313-6437; 0000-0003-4076-1093; 0000-0002-3729-3455; 0000-0003-3028-8722)

Submitted on 05/31/2022; Accepted on 08/18/2021; Published on 08/19/2022.

ABSTRACT: The objective of this work was to estimate the rainfall erosivity in 101 municipalities in the

Brazilian Cerrado biome. First, a filling of missing data was carried out for 81 rain gauge stations, with a 20-

year historical series, in the states of Mato Grosso (MT), Mato Grosso do Sul (MS), Minas Gerais (MG), and

Goiás (GO). The corrected data were subjected to 16 regionally calibrated equations, which enabled the

determination of the rainfall erosivity. The results indicated that municipalities in northeastern MS present the

highest monthly erosivity indexes (El30m), reaching 2,796.5 MJ mm ha-1 h-1 year-1 in January, whereas the lowest

index for this same month was 733.0 MJ mm ha-1 h-1 in the eastern MT. The rainfall annual erosivity, or R

factor, varied between 3,713.1 and 12,345.6 MJ mm ha-1 h-1 year-1, with the lowest values for municipalities in

eastern MT and the highest values for those in northeastern MS. Although the municipalities studied are within

the same biome, the spatial distribution makes them present regional effects due to different climatic factors,

resulting in different rainfall volumes and intensities, which is reflected in the results of the monthly erosivity

index and R factor.

Keywords: rainfall stations; R fator; fill missing data; precipitation.

Erosividade da chuva em municípios do Cerrado brasileiro

RESUMO: O objetivo deste trabalho é estimar a erosividade da chuva em 101 municípios localizados no

bioma Cerrado. Para tanto, inicialmente foi realizado o preenchimento de falhas para 81 estações

pluviométricas, com série histórica de 20 anos, localizadas nos estados de Mato Grosso, Mato Grosso do Sul,

Minas Gerais e Goiás, posteriormente com os dados consistidos, foram aplicadas 16 equações calibradas

regionalmente, permitindo determinada a erosividade da chuva. Os resultados apontaram que os municípios

localizados na região Nordeste de MS, apresentam os maiores índices El30m, chegando a 2.796,5 MJ mm ha-1

h-1 ano-1 no mês de janeiro, enquanto para o mesmo mês, o menor índice foi de 733,0 MJ mm ha-1 h-1 no Leste

de MT. A erosividade da chuva anual ou fator R variou entre 3.713,1 a 12.345,6 MJ mm ha-1 h-1 ano-1, com os

menores valores para os municípios da região Leste de MT e o maiores para a região Nordeste de MS. Apesar

dos municípios estudados estarem localizados dentro do mesmo bioma, a distribuição espacial lhes confere

influências regionais de fatores climáticos diferentes, ocasionando volumes e intensidades pluviométricas

distintas, o que reflete no resultado no índice de erosividade mensal e no fator R.

Palavras-chave: estações pluviométricas; fator R; preenchimento de falhas; precipitação.

1. INTRODUCTION

Erosion is the process of soil disaggregation and

transport and deposition of this material in a new place

(BERTONI; LOMBARDI NETO, 2005). When it occurs

naturally and slowly, shaping the landscape and assisting in

soil formation, it is characterized as geological or natural

erosion (POESEN, 2018).

Erosion can be divided into hydric and eolic erosions,

which are caused by water and wind, respectively. Water

erosion varies according to local edaphoclimatic

characteristics and is dependent on factors connected to

rainfall, soil, topography, soil cover, and management and

conservationist practices, which have joint or isolated action

and provide detachment, drag, and deposition of soil

particles.

Losses from water erosion can be considered the main

form of soil degradation (BERTOL et al., 2007) and a serious

environmental and economic problem due to the

impoverishment of soils, decreases in agricultural yields,

aggradation of reservoirs and rivers, and pollution of water

resources (CASSOL et al., 2008).

The determination or estimation of losses due to water

erosion established in specific conditions of soil use,

occupation, and management depends on the application of

statistical and parametric models, such as the universal soil

loss equation (USLE) (WISCHMEIER; SMITH, 1978). This

is one of the most commonly used methods in the world for

studies on soil loss, and it estimates soil erosion based on

agents that cause or are determinants of erosion, such as soil

erodibility, topographic factors, factors related to soil use and

management, and rainfall erosivity.

Rainfall is the most important climatic factor among

those that promote water erosion due to the impact of water

drops and surface runoff, which are connected to interactions

of the soil surface with the different types of rainfall in terms

of rainfall volume and intensity (duration). Erosivity is the

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

374

factor that presents the greatest temporal and spatial

variations among those considered related to erosion by the

USLE (SHIN et al., 2019). This index represents the capacity

of rainfall to cause erosion in an area with no soil cover or

protection due to the impact of raindrops on the bare soil

(LOMBARDI NETO; MOLDENHAUER, 1992;

NEARING et al., 2017).

Studies on erosivity have been carried out in different

countries of the world (MEUSBURGER et al., 2012;

PANAGOS et al., 2017; TALCHABHADEL et al., 2020;

RIQUETTI et al., 2020). In Brazil, Oliveira et al. (2012)

conducted a bibliographic survey and found that the spatial

distribution of erosivity is lower in the Northeast region and

higher in the extreme North. Almagro et al. (2017) estimated

the erosivity for Brazil and developed predictions for climate

change situations and their possible impacts on erosivity.

Studies were also conducted at lower scales for state and

municipal levels (OLIVEIRA et al., 2012; AQUINO et al.,

2014). Di Raimo et al. (2018) estimated the erosivity for the

state of Mato Grosso and discussed the spatial distribution

and the potential correlation of rainfall with latitude and

phytophysiognomies of biomes in the state. Studies on

erosivity are usually designed according to political borders,

by countries, states, or municipalities, with no connection to

natural limits, such as biomes to which the area belongs.

Erosivity analyses demand homogeneous and consistent

rainfall data, which generate representative and reliable

results. In Brazil, there is a national hydrometeorological

network linked to official organs that make available rainfall

data, among other information, through public portals, such

as the Hidroweb, which shows information from 2,767

stations, and the Weather Databank for Teaching and

Research (BDMEP), which shows information from more

than 400 weather stations (HIDROWEB, 2021; BDMEP,

2021). However, the territorial distribution of these stations

was dependent on the socioeconomic importance of the

regions and access (logistics), resulting in a higher density of

rain gauges and pluviographic stations in the South,

Southeast, and Northeast regions of Brazil, whereas the

North and Central-West regions present a smaller number of

stations and shorter data period.

Moreover, the databases available on these portals may

present consistency errors and missing data because of

defects and calibration in the equipment and in the systems

of collection, streaming, and storage of data or because of

human errors, such as loss of records and errors of

compilation or communication (BERTONI; TUCCI, 2007).

These limitations can be solved through methodologies that

allow the filling of missing data to improve the database

consistency (OLIVEIRA et al., 2010).

In general, preliminary analyses of historical series of

hydrometeorological data include the filling of missing data

and verification of consistency, which denote the

homogeneity of the available data. The filling of missing data

in the temporal data series is based on correlations between

the data of surrounding stations, which can be done by

different methodologies, thus enabling the filling of gaps by

using the model with better regional fit (OLIVEIRA et al.,

2010; CARVALHO et al., 2017; IZZO et al., 2020).

The stations used for filling in missing data should be

established in places with similar climate, relief, and

vegetation characteristics, denoting hydrological similarity

(LEIVAS et al., 2006). Methodologies for the use of simple

or multiple linear regressions combined with regional

weighting have been highlighted due to their easy application

and satisfactory results for the filling of missing rainfall data

(MELLO et al., 2017; NOR et al., 2020; CORDEIRO;

BLANCO, 2021).

Brazil has a continental extension and, thus, has a high

climate variety, which is strongly determinant for the diversity

of soil, fauna, and flora, which determined the grouping of

areas with homogeneous characteristics into six

biogeographic zones or biomes: Amazon, Caatinga, Pampas,

Pantanal, Atlantic Forest, and Cerrado (MMA, [s.d.];

ICMBIO, 2017).

The Cerrado is the second largest biome in Brazil; it is

mainly in the Brazilian Central Highlands, encompassing

24% of the national territory, approximately 2,036,448 km²

(IBGE, 2004). It has significant importance in terms of water

contribution, encompassing river springs, such as those of

the São Francisco, Paraíba, and Tocantins Rivers

(OLIVEIRA et al., 2019), and contributes to eight of the

twelve main hydrographic basins in Brazil, representing 71%,

94%, and 71% of the water source of the Araguaia-Tocantins,

São Francisco, and Paraná-Paraguai basins, respectively

(FELFILI et al., 2005; OVERBECK et al., 2015), and is an

important recharge zone of the Guarani aquifer (OLIVEIRA

et al., 2014).

The Cerrado is the savanna-like biome with the highest

biodiversity in the world and high endemism; however, it is

one of the world hotspots, mainly due to the loss of natural

habitats because of changes in land cover and use connected

to agriculture (MYERS et al., 2000; NEWBOLD et al., 2015).

This biome encompasses most agricultural and livestock

production in Brazil; despite presenting unfavorable natural

soil characteristics (weathered and acidic soils with low

nutrient contents), this production is promoted by the

possibility of improving soil acidity and fertility and

mechanization, which is favored by favorable relief and

climate (KLINK; MACHADO, 2005).

The municipalities studied are in regions within the

Cerrado biome with intense agriculture due to the favorable

relief and climate conditions. In general, the climate in these

regions is characterized by two well-defined seasons: dry

(April to September) and rainy (October to March)

(ALVAREZ et al., 2013; BECK et al., 2018). The rainy

season peaks at the time that the soil is partially or completely

uncovered due to the sowing seasons and phenology of

agricultural crops and pastures, which, combined with the

lack of adequate planning and soil management, can trigger

erosive processes under intense rainfall and saturated soils.

Understanding the erosivity intensity over the year in

different places is important to avoid problems caused by

erosion in the Cerrado biome in Brazil.

Therefore, the objective of this work was to estimate the

rainfall erosivity for 101 municipalities in the states of Mato

Grosso, Mato Grosso do Sul, Goiás, and Minas Gerais,

according to data from rain gauge stations distributed

spatially in the study area and to erosivity equations calibrated

for each place.

2. MATERIALS AND METHODS

The study area encompasses 101 municipalities: 25 in the

state of Mato Grosso (MT), 25 in Goiás (GO), 25 in Minas

Gerais (MG), and 26 in Mato Grosso do Sul (MS) (Figure 1).

They are mostly in the Cerrado biome, between the latitudes

11°43'S and 22°45'S and longitudes 44°00'W and 59°06'W.

Castagna et al.

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

375

Figure 1. Location and spatial distribution of the studied municipalities in the Cerrado biome, Brazil.1

Figura 1. Localização e distribuição especial dos municípios estudados no bioma Cerrado, Brasil.

The municipalities were distributed in a region with

climate variation, enabling the assessment of six different

climates, according to the Köppen classification: tropical

humid or subhumid (Am), tropical with dry winter (Aw),

subtropical with hot summer (Cfa), temperate with mild

summer (Cfb), subtropical with dry winter (Cwa), and

subtropical highland (Cwb), with mean temperatures

between 20 and 26 °C and rainfall depths between 1,000 and

2,500 mm (ALVARES et al., 2013).

The studied municipalities are part of the Sustainable

Rural Project – Cerrado (SRP-Cerrado), whose objective is to

decrease poverty, increase production, and mitigate the

greenhouse gas effect through the adoption of low-carbon

technologies and prevention of deforestation in the

municipalities covered by the project (PRS, 2021). The SRP-

Cerrado has financial support through a Technical

Cooperation approved by the Inter-American Development

Bank (IDB) with the International Climate Financing of the

United Kingdom Government, whose institutional

beneficiary is the Brazilian Ministry of Agriculture, Livestock

and Food Supply (MAPA), the Brazilian Institute for

Development and Sustainability (IABS) is responsible for the

administration, and the Rede ILPF Association is responsible

for carrying out scientific coordination and technical support

through the Brazilian Agricultural Research Corporation

(EMBRAPA) (PRS, 2021).

2.1. Filling of missing data

Eighty-six rain gauge stations within the study area were

used: 81 of them were considered for estimating erosivity,

and five stations were used for support, i.e., the data were

used for filling the missing data from other stations and not

for erosivity estimation, as their location was in municipalities

that had a second station with a lower quantity of missing

data and that had a better data quality was chosen for

1The municipality corresponding to the identification number present in Figure 1 can be found in Anexo A.

estimating erosivity.

The temporal data series of all rain gauge stations

evaluated covered a period of 20 years (1999 to 2019), except

for the station in Sete Lagoas (MG), which covered 16 years

(1999 to 2015). The rainfall data were acquired from the

following platforms and selected according to the availability

of data for each municipality (Figure 2 and Table 1):

HIDROWEB, managed by the Brazilian National Water and

Sanitation Agency (ANA); and BDMEP, databank of the

Brazilian National Institute of Meteorology (INMET).

The spatial distribution analysis of rain gauge stations was

carried out in the program QGIS v. 3.16.9, with the aid of the

experimental plugin ANA Data Acquisition v. 0.2, to assess

the proximity between stations.

According to the guide for instruments and weather

observation methods of the WMO (2014), the spacing

between stations should be 150 to 250 km to obtain good

representativeness of the data. Thus, a buffer with a radius of

200 km surrounding the station to be corrected was used to

assess the availability of support stations to obtain similar

data for the filling of missing data. Three support stations

were then selected to determine which data best represent the

area of interest.

The data were obtained, and monthly missing data over

the analyzed period were identified for each station; the

month corresponding to the missing data to be corrected was

also deleted in the support stations to obtain consistent,

synchronized datasets. These datasets were divided into two

groups: training/calibration of simple linear regression

models (70%) and test/validation (30%).

Training, or calibration, is the procedure adopted to

create the statistical model that will be applied. The test, or

validation, refers to the remaining data subjected to

application of the statistical model to assess its performance.

Linear regression is used to indicate the mathematical

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

376

correlation between two variables to carry out predictions

from this correlation (UYANIK; GÜLER, 2013;

HOFFMANN, 2016). The linear regression method was

used for filling the missing data due to the amount of data

analyzed and its easy application; the methodology presented

good results and was used with no need to test other

methods.

Stations with missing data (response variable) were

correlated to the respective support stations (predictor

variable), focusing on the coefficients a and b, thus

determining the equation (Equation 1):

y = a + b ∗ x (01)

where: y is the dependent or response variable, a is the intercept, b

is the angular coefficient, and x is the independent or predictor

variable.

Figure 2. Location of the rain gauge stations used for analysis of rainfall distribution, classified according to the BDMEP databank (Brazilian

National Institute of Meteorology - INMET) and HIDROWEB (managed by the Brazilian National Water and Sanitation Agency - ANA),

and location of pluviographic stations that present a calibrated equation for calculating erosivity.

Figura 2. Localização das estações pluviométricas, utilizadas para análise da distribuição da precipitação, classificadas conforme o banco de

dados BDMEP do INMET e HIDROWEB gerido pela ANA, e localização das estações pluviográficas que apresentam fórmula calibrada

para o cálculo da erosividade.

The equation found for the training data for each support

station was applied to the validation dataset, thus estimating

the response values for the station with missing data. The

statistical performance was evaluated following the

methodology used in studies on weather data by applying

statistical indicators: MBE (Mean Bias Error), RMSE (Root

Mean Square Error) and Willmott agreement index (d)

(WILLMOTT, 1981), to define statistical errors (over- or

underestimates) and apply them for the filling of missing data

(BADESCU, 2013; SOUZA et al., 2017).

MBE (Equation 2) shows the deviation of the mean of

the estimated data from the data found, presenting a negative

value when the estimated data are underestimated, a positive

value when the estimated data are overestimated, and zero

denotes a perfect simulation.

MBE = ∑()



  (02)

where: N is the number of observations, Pi is the estimated value

and Oi is the measured value.

RMSE (Equation 3) indicates the actual spreads of errors

of estimated values in relation to the values found and,

different from MBE, does not indicate the underestimation

or overestimation; however, the lower the value, or closer to

zero, the better the performance.

RMSE = 󰇣∑()



 󰇤



 (03)

where: N is the number of observations, Pi are the estimated values,

and Oi are the measured values.

The Willmott agreement index (Equation 4) indicates the

fit of estimated values to the measured ones, varying from 0

to 1, corresponding to the worst and best fit, respectively.

d = 1 − ∑()





∑(|󰆒||󰆒|)



 (04)

where: N is the number of observations, Pi are the estimated values,

Oi is the measured values, |𝑃′𝑖| is the absolute value of the

difference, Pi −Oi, and |𝑂′𝑖| is the absolute value of the difference

Oi −Oi.

Castagna et al.

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

377

A ranking of statistical indicators was carried out to

define which station presented the best filling of missing data

(MBE, RMSE, and Willmott agreement index); weights of 1

to 3 were attributed for each indicator: 3 for the best and 1

for the worst result; the weights were added (considering the

3 indicators), and the station that presented the highest sum

was defined as the best filling of missing data. In the case of

a tie in the performance, the criterion used was the lowest

distance between the station to be corrected and the support

stations.

The procedures adopted allowed for the filling of missing

data according to rain gauge stations with higher similarity,

based on the statistical indicators used. A synthesis of the

methodology used is shown in the flowchart in Figure .

Table 1. Location and identification of rain gauge stations evaluated and percentage of missing data in the databases.

Tabela 1. Localização e identificação das estações pluviométricas avaliadas e percentual de falhas nas bases de dados.

Identification

Municipalities

States

Filling (%)

Latitude

Longitude

1853000

(A1)

Alto Taquari

811388

288888

1754000

(A1)

Itiquira

207222

138888

1653004

(A1)

Alto

Garças

943888

533055

1358005

(A1)

Sapezal

909722

897222

1256002

(A1)

Lucas do Rio Verde

979722

180555

1555005

(A1)

Campo Verde

836944

323055

1554006

(A1)

Jaciara

988333

967222

83358

(B2)

Poxoréu

827499

395555

83309

(B2)

Diamantino

406111

446944

1356002

(A1)

Nova Mutum

820555

084166

1255001

(A1)

Sorriso

674166

791666

1655001

(A1)

Santo Antônio do

Leverger

608055

206388

1654000

(A1)

Rondonópolis

470555

656388

1452004

(A3)

Água Boa

076388

150277

1358001

(A1)

Campo Novo do Parecis

641666

287500

83270

(B2)

Canarana

470833

271111

1654004

(A1)

Pedra Preta

842222

407222

83319

(B2)

Nova Xavantina

697917

350226

1457000

(A1)

Tangara

631944

468055

1554005

(A1)

Primavera do Leste

314722

175833

1552006

(A1)

Barra do Garças

035555

237499

2153003

(A1)

Nova Andradina

981944

439722

2155000

(A1)

Maracaju

617222

136388

1754002

(A1)

Sonora

586944

756666

2252000

(A1)

Anaurilândia

181666

716944

2152005

(A1)

Santa Rita do Pardo

295000

810277

83565

(B2)

Paranaíba

663611

191388

1951005

(A1)

Inocência

736388

932499

1954005

(A1)

Bandeirantes

917777

358611

1952001

(A1)

Água Clara

678055

896388

2054014

(A1)

Campo Grande

458333

604722

2154007

(A1)

Sidrolândia

181388

743888

2152001

(A1)

Bataguassu

715833

437222

2152014

(A1)

Brasilândia

248333

288055

1852002

(A1)

Chapadão do Sul

996666

587222

1853005

(A1)

Figueirão

673611

641388

2053000

(A1)

Ribas do Rio Pardo

443333

757500

1953004

(A1)

Paraíso das Águas

054444

014166

2052004

(A1)

Três Lagoas

598333

219444

1853004

(A1)

Costa Rica

546666

133888

1754004

(A1)

Pedro Gomes

830833

313055

2054019

(A1)

Jaraguari

101666

433611

1954006

(A1)

Camapuã

302499

172777

83536

(B2)

Curvelo

747435

454654

1944010

(A1)

Paraopeba

268055

401666

1944068

(A1)

Cordisburgo

028888

193888

1944049

(A1)

Papagaios

428333

719722

83586

(B2)

Sete

Lagoas

48454

173798

1847000

(A1)

Monte Carmelo

720555

524444

1847008

(A1)

Coromandel

471111

188333

1746007

(A1)

Lagoa Grande

502777

571666

83479

(B2)

Paracatu

244166

881666

83428

(B2)

Unaí

366286

889321

1945035

(A1)

Abaeté

163055

442500

1848000

(A1)

Monte Alegre de Minas

872222

869444

1949002

(A1)

Prata

359722

180277

1846015

(A1)

Vazante

004999

911111

1747005

(A1)

Guarda

Mor

772500

098611

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

378

Table 1. Location and identification of rain gauge stations evaluated and percentage of missing data in the databases. (CONTINUATION)

Tabela 1. Localização e identificação das estações pluviométricas avaliadas e percentual de falhas nas bases de dados. (CONTINUAÇÃO)

Identification

Municipalities

States

Filling (%)

Latitude

Longitude

1947026

(A1)

Uberaba

535833

811111

1846019

(A1)

Patos de

Minas

373611

914999

1948006

(A1)

Uberlândia

988333

190277

1849000

(A1)

Ituiutaba

941111

463055

1746001

(A1)

Brasilândia de Minas

030833

013611

1944063

(A1)

Pompeu

087222

947222

83481

(B2)

João Pinheiro

740277

176944

1948003

(A1)

Veríssimo

673055

309722

1651000

(A1)

Caiapônia

948888

810277

83526

(B2)

Catalão

170277

958055

1852001

(A1)

Chapadão do Céu

406666

532499

1850001

(A1)

Goiatuba

104722

031388

83522

(B2)

Ipameri

724527

171916

1849016

(A1)

Itumbiara

338888

610833

83464

(B2)

Jataí

923611

717499

1752002

(A1)

Mineiros

688055

882777

1751004

(A1)

Montividiu

328333

260833

1749003

(A1)

Morrinhos

732500

115277

1749005

(A1)

Piracanjuba

307222

025555

1850002

(A1)

Quirinópolis

498333

528611

83470

(B2)

Rio Verde

785277

964722

1753002

(A1)

Santa Rita do Araguaia

351944

091388

1851005

(A1)

Serranópolis

305000

965833

1358002

(A1)

Sapezal

466666

975000

1357001

(A1)

Campo Novo do Parecis

697777

885277

1257000

(A1)

Brasnorte

116944

999166

1846007

(A1)

Patos de Minas

841111

550833

83423

(B2)

Goiânia

673055

263888

Platform A for HIDROWEB and B for BDMEP, operator 1 CPRM, 2 INMET, and 3 UFC.¹ The identification of the municipalities studied is presented in

Figure 1. ² Identification number of rain gauge stations in the databanks to which they belong. ³ Rain gauge stations used only as support.

Plataforma “A” para HIDROWEB e “B” para BDMEP, operador “1” CPRM, “2” INMET e “3” UFC. ¹ Identificador dos municípios estudados apresentados

na Figure 1. ² Número de identificação das estações pluviométricas nos bancos de dados as quais pertencem. ³ Estações utilizadas apenas como apoio.

Figure 3. Flowchart of the methodological procedures adopted for the filling of missing data.

Figura 3. Fluxograma que ilustra os procedimentos metodológicos adotados para o preenchimento de falhas.

2.2. Erosivity

Wischmeier (1959) proposed estimating rainfall erosivity

using the rainfall characteristics total kinetic energy (E) and

maximum intensity in a 30-minute period (I30) and their

correlations with soil loss. The result of this interaction was

termed the erosivity index (EI30) since the monthly sum of

the index for each rainfall event generates the monthly EI30,

and the sum of monthly values results in the annual EI30. The

mean of the annual erosivity indexes results in rainfall

erosivity, i.e., the R factor of the universal soil loss equation

(USLE) (WISCHMEIER; SMITH, 1978).

Data on rainfall intensity collected through pluviographic

stations are needed to calculate rainfall erosivity. However,

due to limitations of this type of data and the slowness of the

process, some researchers calibrate the equations to use data

from rain gauge stations, resulting in rainfall data with a

longer interval (days, months, and years) and in a higher

spatial availability of monitoring stations. Such equations

were developed from the correlation between pluviographic

and rainfall data, according to Lombardi-Neto (1977).

Castagna et al.

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

379

Bibliographical research was carried out to obtain

equations already published and calibrated that can be

applied to the areas covered by the present study (Table 3).

Figure presents the spatial distribution of the rain gauge

stations (represented by lozenges) that enabled the definition

of the equations shown in Table 3.

Table 3. Erosivity equations available for applications in different municipalities of the Cerrado biome in Brazil.

Tabela 3. Equações de Erosividade disponíveis para aplicações em diferentes municípios do Cerrado brasileiro.

Municipalities

States

Equations

References

Canarana

El30 = 12.18 (Rc

0.622

)

Di Raimo et al (2018)

Cuiabá

El30 = 244.47 (Rc

0.508

)

Diamantino

El30 = 51.46 (Rc

0.883

)

Vera (Gleba Celeste)

El30 = 171.29 (Rc

0.605

)

Nova

Xavantina

El30 = 96.36 (Rc

0.517

)

Poxoréu

El30 = 156.38 (Rc

0.552

)

Rondonópolis

El30 = 167.16 (Rc

0.567

)

São José do Rio Claro

El30 = 126.76 (Rc

0.464

)

Dourados

El30 = 80.305 (Rc

0.8966

)

Oliveira et al. (2012)

Coxim

El30 =

138.33 (Rc

0.7431

)

Campo Grande

El30 = 139.44 (Rc

0.6784

)

Goiânia

El30 = 215.33 + 30.23 (Rc)

Silva et al. (1997)

Lavras

El30 = 85.672 (Rc

0.6557

)

Aquino et al. (2014)

Sete Lagoas

El30 = 25.3 + 43.35 (Rc)

–

0.232 (Rc

)

De Sá et al.

(1998)

Caratinga

El30 = 321.63 (Rc

0.48

)

Silva et al. (2010)

Teodoro e Sampaio

El30 = 106.8183 + 46.9562 (Rc)

Colodro et al. (2002)

All the equations found require the rainfall coefficient

(Rc), which was determined according to the equation

proposed by Lombardi-Neto (1977):

𝑅𝑐 = ²

 (05)

where: p is the mean monthly rainfall (mm month-1) and P is the

mean annual rainfall (mm year-1).

The definition of the erosivity equation to be used for

each rain gauge station was based on the methodology used

by Di Raimo et al. (2018). The correlation (R) was carried out

for the following data: (i) monthly rainfall, (ii) mean monthly

rainfall, and (iii) rainfall coefficient (RC), comparing data

from the rain gauge station with those from the three closest

pluviographic stations using the calibrated equation.

The correlations between the mean monthly rainfall and

rainfall coefficient (RC) were classified by attributing weights

of 1, 2, and 3: 3 representing the best and 1 the worst result.

Monthly rainfall had a higher quantity of factors for

correlation because it corresponds to all months over the

studied period; thus, it was attributed higher weights (2, 4,

and 6): 6 representing the best, and 2 the worst result.

The weights attributed to the correlations were added,

resulting in a performance factor that determined which

equation to use. In the case of a tie in the performance, the

criterion used was the shortest distance between the rain

gauge and the pluviographic station.

The distribution of erosivity over the entire study area

was determined by interpolating the values found for the

stations using the inverse distance weighted (IDW) method,

which consists of attributing weighted values according to

the distance from the sampled points, as an area closer to the

sample has higher weight than more distant areas

(ANGULO-MARTÍNEZ et al., 2009; ZHU et al., 2019).

3. RESULTS

The filling of missing data, determined by calculating the

coefficients of determination (R²) and coefficients a and b

and using the statistical indicators between the correlations

generated among the support stations, is shown in Annex B.

The coefficients of determination of 81 rain gauge

stations varied, in general, from 0.7 to 0.9, except for the

station in Anaurilândia, which presented a coefficient of

correlation higher than 81%. Regarding the MBE indicator,

45% of the models underestimated the total monthly rainfall,

with variations between -0.001 and -19.3 mm; overestimates

were generated by 55% of the simple linear regressions, with

variations between 0.04 and 11.1 mm. The RMSE indicator

showed variations from 20.8 to 56.4 mm, whereas the

Willmott agreement index showed variations from 0.90 to

0.98.

The mean annual rainfall, according to the 81 rain gauge

stations, was 1,445.0±173.0 mm. The mean for the rainy

period (October to March) was 1,219.1±159.5 mm, and the

mean for the dry period (April to September) was 225.9±82.3

mm.

When the stations were segmented according to the states

in which they were installed, the data showed similarity in

rainfall distribution over the year, with a period of greater

rainfall volume between October and March and a period of

lower rainfall volume between April and September,

presenting higher dispersion of data in the rainy period than

in the dry period. However, they presented differences in

rainfall distribution and volume over the months (Figure 4).

According to the rainfall data by state, Minas Gerais had

the lowest mean annual rainfall, 1,300.3 mm, followed by

Mato Grosso do Sul, Goiás, and Mato Grosso, which

presented 1,429.6, 1,454.5, and 1,612.9 mm, respectively

(Figure 4).

Despite having the second lowest mean annual rainfall,

Mato Grosso do Sul was the state with the highest rainfall

volume (329.0 mm) in the dry season (April to September),

when approximately 23% of the total annual rainfall occurs,

while this percentage is between 11% and 13% of the total

annual rainfall in the other states studied (Figure 4).

Variations in monthly rainfall reflect erosivity, indicating

a higher data dispersion in the rainy period and a lower

dispersion in the dry period. In addition, the erosivity in

February and March presented a difference of only 14.9 MJ

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

380

mm ha-1 h-1 year-1 in the means, and the outliers in these

months reached similar values; it resulted in greater rainfall

volume for the states of Goiás and Minas Gerais in March

than in February, and the opposite occurred for the states of

Mato Grosso and Mato Grosso do Sul, which presented the

greatest rainfall volume in February (Figure 4 and Figure 5).

Figure 4. Boxplot for monthly rainfall considering 81 rain gauge stations in areas in the Cerrado biome, grouped according to the state in

which they were installed. The box represents the interquartile interval, the line inside is the median, the bars are the lower and upper limits,

and the dots outside the box are the outliers.

Figura 4. Boxplot referente a precipitação pluvial mensal considerando 81 estações pluviométricas localizadas em área de Cerrado, agrupados

de acordo com o estado em que está instalada. A caixa representa o intervalo interquartil, a linha no interior é a mediana, as hastes são os

limites inferiores e superiores e os pontos externos à caixa são os outliers.

According to the erosivity data (Figure 5), 87.2% of all

erosivity occurs in the rainy season, mainly in January and

December, when 38.1% of the annual erosivity occurs with

means of 1,533 and 1,389.6 MJ mm ha-1 h-1 year-1,

respectively. July and August were the months with the

lowest erosivity means, presenting the same value: 76.2 MJ

mm ha-1 h-1 year-1 (Figure 5).

The outliers found in 5, referring to January, February,

March, and November, are also shown in the spatial

distribution of erosivity data in Figure 6 e Figure 7.

Figure 6 e Figure 7 show the distribution of monthly

erosivity indexes (El30m) for the municipalities studied.

January (Figure 66) showed higher erosivity in the

municipalities in northeastern Mato Grosso do Sul and

southwestern Goiás and lower erosivity in those in eastern

Mato Grosso. February (Figure 66) showed a decrease in

these indexes and lightening of higher erosivity points, and

the municipalities of the central-north region of Mato Grosso

presented the highest values.

Figure 5. Boxplot for the monthly erosivity index (El30m) in 101

Brazilian municipalities in the states of MS, MT, MG, and GO

within the Cerrado biome. The box represents the interquartile

interval, the line inside is the median, the bars are the lower and

upper limits, dots outside the box are the outliers, and the dot inside

the box is the mean.

Figura 52. Boxplot referente ao Índice de erosividade mensal (El30m)

em 101 municípios do Cerrado brasileiro nos estados de MS, MT,

MG e GO. A caixa representa o intervalo interquartil, a linha no

interior da caixa é a mediana, as hastes são os limites inferiores e

superiores, os pontos externos à caixa são os outliers e o ponto

interno é a média.

Castagna et al.

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

381

Figure 6. Spatialization of the monthly erosivity index (El30m) for 101 Brazilian municipalities in the Cerrado biome from January to July.

Figura 6. Espacialização do índice de erosividade mensal (El30m) em 101 municípios do Cerrado brasileiro, de janeiro à julho.

April to September showed a homogenization of El30 m

for all regions studied (Figure 66 and Figure7), with decreases

over the dry period. September showed increases in erosivity

in municipalities in the central-north region of Mato Grosso

and the central region of Mato Grosso do Sul when

compared to the other municipalities. The erosivity increased

from November onward, with the highest values found for

the central and western regions of Minas Gerais and eastern

Goiás (Figure7).

4. DISCUSSION

The lowest annual erosivity in the region studied was

found for eastern Mato Grosso, and the highest was found

for northeastern Mato Grosso do Sul (Figure 8). The

Rainfall erosivity in municipalities of the Brazilian Cerrado Biome

Nativa, Sinop, v. 10, n. 3, p. 373-386, 2022.

382

municipalities in Mato Grosso do Sul showed a variation of

6,725.09 to 12,323 MJ mm ha-1 h-1 year-1, with the highest

erosivity found for the northeastern region of the state

(between 10,000 and 12,323 MJ mm ha-1 h-1 year-1) and the

lowest for the municipalities in the east; the other

municipalities in the state present values between 9,000 and

8,000 MJ mm ha-1 h-1 year-1. These results are consistent with

those found by Oliveira et al. (2012).

The spatialization of the values found for the

municipalities in Mato Grosso, with higher indexes for the

central-north and lower indexes for the east region, is

consistent with the results found by Di Raimo et al. (2018);

however, there were differences in the actual values, as the

lowest index found by them was 4,904 MJ mm ha-1 h-1 year-

1, whereas that found in the present work was 3,713.12 MJ

mm ha-1 h-1 year-1 (for Barra do Garças).

Figure 7. Spatialization of the monthly erosivity index (El30m) in 101 Brazilian municipalities of the Cerrado in Brazil from July to December.

Figura 7. Espacialização do índice de erosividade mensal (El30m) em 101 municípios do Cerrado brasileiro, de julho à dezembro.