Microsoft Word - 1-Agra_21287.doc


536 
Original Article 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

10-DAY PROBABLE RAINFALL FOR UBERLÂNDIA, MINAS GERAIS 
STATE, BRAZIL 

 
PRECIPITAÇÃO DECENDIAL PROVÁVEL PARA UBERLÂNDIA, MINAS GERAIS, 

BRASIL 
 

Bruno Teixeira RIBEIRO1; Domingos da Costa FERREIRA JÚNIOR2; 
Cláudio Ricardo da SILVA1 

1. Professor, Doutor, Instituto de Ciências Agrárias - ICIAG, Universidade Federal de Uberlândia - UFU, Uberlândia, MG, Brasil. 
btribeiro@iciag.ufu.br ; claudio@iciag.ufu.br. 2. Discente do Curso de Agronomia, Bolsista PET-Agronomia, ICIAG - UFU, 

Uberlândia, MG, Brasil.  
 

ABSTRACT: The knowledge of probable rainfall can contribute substantially to farming activities, mainly in 
irrigation projects. This work was carried out aiming to determine the probable rainfall for Uberlândia, Minas Gerais State, 
Brazil. Daily precipitation data from 1975 to 2010 were summed in 10-day period (decennial) and applied to Gamma 
distribution. The probable rainfall was estimated to different probability levels (ranging 10% to 95%). The Gamma 
distribution was suitable to estimate the probable rainfall for 10-day period. During the wet season the historical average 
rainfall (10-day period) has 40% of probability of exceedance and during the dry season has 30%. From this work the 10-
day period rainfall can be estimated at different probability levels and contribute to farming activities, especially to 
irrigation. 

  
KEYWORDS: Irrigation. Gamma distribution. Agriculture planning. 

 
INTRODUCTION 
 

Uberlândia is located in Cerrado Biome – 
nowadays an important region of Brazilian 
agribusiness. Corn, soybean, citrus, vegetables, 
fruits, coffee, livestock and most recently sugarcane 
are intensively cultivated in this region (IBGE, 
2011). In this context, due to the irregular 
distribution of rainfall during the crop season and 
aiming to improve the production, irrigation area 
has increased every year. 

In many irrigation projects, the water supply 
has been planned in terms of total irrigation, 
disregarding the occurrence of rainfall. As rainfall 
has very spatial and temporal variability it can be 
suite for crop season with little rainfall. However, in 
years with more abundant rainfall could result in a 
highly uneconomic and wasteful project. Then, the 
estimative of probable rainfall is very important for 
an adequate and sustainable irrigation system 
planning (BERNARDO, 2005).  

The minimum precipitation to be overcome 
in a given probability level (probability of 
exceedance) is called probable rainfall 
(BERNARDO, 2005). The knowledge of probable 
rainfall may avoid the oversizing of irrigation 
systems when the water crop requirements are 
considered and also to contribute to reduce the water 
use from rivers and reservoirs. For example, in 
Barbacena, in southern of Minas Gerais State, it was 
found that the monthly probable rainfall during 

cropping season (summer) attend the most of water 
requirement of tomato, corn and bean (RIBEIRO et 
al., 2007). If the probable rainfall is taken account, 
the costs of irrigation projects can drop 
significantly. Additionally, the knowledge of 
probable rainfall may also contribute to farming 
planning as soil tillage, sowing, liming, fertilization, 
harvesting and application of pesticides. All these 
activities depend on rainfall distribution.            
 The probability of 75% to 80% is 
considered suitable in irrigation projects 
(BERNARDO, 2005). In general, the historical 
average rainfall has approximately 40% of 
probability of exceedance (MURTA et al., 2005; 
RIBEIRO et al., 2007; RIBEIRO; AVANZI, 2010). 
So, its use can lead to error in the designing fittest 
irrigation system (FIETZ et al., 1998). 
 To estimate the probable rainfall some 
distribution models (Gamma, Normal, Log-Normal 
2 and 3 parameters) have been applied to a historical 
series (decennial, monthly, annual) in different 
regions of Brazil. The Gamma distribution 
frequently has been considered more adequate 
(FIETZ et al., 1998; FIETZ et al., 2008; MARTINS 
et al., 2010; RIBEIRO et al., 2007; RIBEIRO; 
AVANZI, 2010; SOCCOL et al., 2010).         

This work aimed to determine the 10-day 
probable rainfall for the municipality of Uberlândia, 
State of Minas Gerais, Brazil, in order to contribute 
to a suitable irrigation projects in this region. 
 

Received: 12/12/12 
Accepted: 19/03/13 



537 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

MATERIAL AND METHODS 
 

Daily precipitation data were acquired from 
the Brazilian National Water Agency – ANA 
(HIDROWEB, 2012) from a weather station located 
at 18°59’18’’S and 48°11’25’’W and altitude of 
800m. The data were summed in 10-day period 
(decennial) from 1975 to 2010 (36 years) and 
applied to Gamma distribution. This work evaluated 
the probable rainfall for 10-day period, considered 
suitable to crops with short and medium cropping 
seasons, while monthly periods would be more 
suitable to perennial or semi-perennial crops 
(ANDRADE; BASTOS, 1997). 

Gamma model is defined by the following 
integral equations (LANNA, 2001): 

( ) 0υdx,exαΓ x
0

1υ
>∫=

−∞ −
 (1) 

( ) ( ) dxexxα,P x
x

0

1υ −−
∫=  

(2) 

( ) ( ) dxexxα,P β
xx

0

1υ
−

−
∫=  

(3) 

The probability density function can be 
expressed as follows (BOTELHO, 1989): 

( )
( )

∞<<⋅⋅
γ⋅

=
−

−γ
γ

x,0ex
Γβ

1
xf:FDP β

x
1

 
(4) 

with γ > 0, β > 0, Γ (γ) > 0, where γ is dimensionless 
parameter, β is scale parameter and x is random 
variable (rainfall). 

The ν and β parameters can be estimated by 
Equations 5 and 6, respectively: 

2
x

2

S

x
=γ  

(5) 

x

S
β

2
x

=  
(6) 

where x  and Sx are the average and standard 
deviation of dataset, respectively. 

The Qui-Square Test (λ2) (α = 0.05) were 
used to evaluate the suitability of Gamma 
distribution, considering the degrees of freedom as 
being the number of classes minus one 
(FERREIRA, 2005). Once the Gamma distribution 
considered adequate, the decennial probable rainfall 
was estimated at different probability levels 
(ranging from 10% to 95%).  

 
RESULTS AND DISCUSSION 

 
The total annual historical average rainfall is 

1,472 mm spread out in two different periods: 

spring-summer or wet season (86% of total rainfall) 
and fall-winter or dry season (14%) (Figure 1). 
There is a serious period from June to August where 
the monthly rainfall does not reach 16 mm and 
could affect the growing and development of plant 
species, especially perennial or semi-perennial 
crops, suggesting the use of irrigation. This 
condition is one of the characteristics of Aw climate 
(Koppen’s classification) which dry season occurs 
during the winter because is under the influence of 
the subtropical highs and in the summer, as the 
intertropical convergence zone - ITCZ moves to 
south brings with it heavy precipitation (AHRENS,  
2009).  

In Table 1 are showed the descriptive 
statistics of decennial rainfall data, β and ν 
parameters from Gamma distribution, λ2 test results 
and the probability of occurrence of average rainfall 
for each period studied. Only to the third decennial 
of March, the Gamma distribution was not suitable 
(calculated λ2 > standard λ2). Many others studied 
have found that the Gamma distribution has been 
most well applied to studies of probability-
frequency rainfall distribution (FIETZ et al., 1998; 
ARAÚJO et al., 2001; RIBEIRO et al., 2007; 
MARTINS et al., 2010; RIBEIRO; AVANZI, 2010; 
SOCCOL et al., 2010).  

Considering each period studied, it was 
observed that the probability of occurrence of 
historical average rainfall decreases from wet season 
to dry season. In the wet season the probability of 
occurrence of historical average rainfall is 
approximately 40% while in the dry season is 30%. 
This observation is important when the average 
rainfall for a given period is taken account to 
irrigation project due to the fact that the level of 
suitable probability of occurrence is between 70% 
and 80% (BERNARDO, 2005). 

In general, the rainiest months had higher β 
and ν values. β values are related to variability of 
data and since it is directly proportional to the 
square of the standard deviation. This seems to be a 
characteristic of wet season and its inherent 
variability. At the same way, higher ν values were 
observed and this is related to asymmetry of data. 
The same results were found to Machado, southern 
of Minas Gerais State (RIBEIRO; AVANZI, 2010), 
for Tangará da Serra, Mato Grosso State 
(MARTINS et al., 2010) and for Lages, Santa 
Catarina State (SOCCOL et al., 2010). However, for 
Itapetinga and Vitória da Conquista, southwest of 
Bahia state, the higher ν values were found in driest 
months (MURTA et al., 2005). 

 
 



538 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

 
Figure 1. Historical decennial average rainfall for Uberlândia, Minas Gerais State, Brazil (1975-2010). Error 

bars indicate the standard error (n=36). 
 
 
Table 1. Descriptive statistics, β and ν parameters and λ2 test for decennial rainfall data of Uberlândia, Minas 

Gerais State, Brazil. 
 Rainfall       

Period 
Average Median Maximum Minimum 

Standard 
Deviation 

β ν λ
2* 

λ
2** 

 
P 

(%) 
           

1/January 103.3 92.7 300.2 19.0 66.4 42.7 2.4 1.8 7.8 42 
2/January 84.1 63.0 268.1 1.4 67.9 54.8 1.5 0.7 7.8 39 
3/January 101.1 86.7 345.4 0.0 86.8 74.5 1.4 0.8 7.8 39 
1/February 85.5 71.4 305.1 0.0 68.9 55.6 1.5 0.8 6.0 39 
2/February 58.8 60.2 173.6 0.0 44.4 33.5 1.8 1.0 7.8 40 
3/February 49.5 44.7 154.7 0.0 37.7 28.8 1.7 2.7 7.8 40 
1/March 66.4 61.7 169.1 0.0 51.0 39.2 1.7 0.4 7.8 40 
2/March 70.2 65.5 167.5 0.0 47.0 31.5 2.2 1.9 7.8 41 
3/March 57.0 61.4 123.5 0.0 35.1 21.7 2.6 12.6 9.5 42 
1/April 36.9 37.6 90.8 0.0 27.6 20.7 1.8 6.0 7.8 40 
2/April 30.7 25.7 148.9 0.0 30.7 30.7 1.0 0.3 6.0 37 
3/April 14.8 6.7 102.2 0.0 22.3 33.5 0.4 0.06 3.8 31 
1/May 15.3 5.5 95.6 0.0 21.8 31.2 0.5 0.02 3.8 32 
2/May 9.6 4.1 46.2 0.0 11.4 13.7 0.7 0.5 6.0 34 
3/May 17.0 6.7 93.1 0.0 22.3 29.4 0.6 0.07 3.8 33 



539 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

1/June 9.9 1.0 65.5 0.0 16.4 27.2 0.4 0.02 3.8 29 
2/June 3.2 1.0 41.6 0.0 7.1 15.9 0.2 0.4 3.8 23 
3/June 4.1 1.0 29.2 0.0 7.2 12.6 0.3 0.06 3.8 28 
1/July 3.2 1.0 35.4 0.0 6.7 14.1 0.2 0.2 3.8 25 
2/July 4.5 1.0 60.0 0.0 10.6 24.8 0.2 10-3 3.8 23 
3/July 5.4 1.0 80.0 0.0 14.5 39.4 0.1 0.05 3.8 20 
1/August 3.5 1.0 52.9 0.0 9.7 26.9 0.1 1.0 3.8 20 
2/August 3.4 1.0 26.6 0.0 5.4 8.5 0.4 0.4 3.8 30 
3/August 10.5 1.0 76.0 0.0 19.1 34.9 0.3 0.02 3.8 27 
1/Sep. 14.3 3.6 89.7 0.0 21.2 31.6 0.5 4e-3 3.8 31 
2/Sep. 12.1 3.4 89.5 0.0 18.9 29.5 0.4 0.01 3.8 30 
3/Sep. 18.2 1.0 54.5 0.0 17.3 16.4 1.1 2.0 7.8 37 
1/October 34.5 16.9 179.1 0.0 44.8 58.2 0.6 0.3 6.0 33 
2/October 28.4 20.2 122.2 0.0 29.5 30.6 0.9 0.5 6.0 36 
3/October 41.0 35.7 115.9 0.0 33.5 27.3 1.5 2.8 7.8 39 
1/Nov. 55.3 52.8 229.4 0.0 46.2 38.7 1.4 2.1 6.0 39 
2/Nov. 64.1 60.6 154.7 0.0 39.3 24.1 2.7 0.8 7.8 42 
3/Nov. 73 59.4 268.1 0.0 58.6 47.0 1.6 0.4 6.0 39 
1/Dec. 82.7 82.8 227.0 0.0 50.5 30.8 2.7 0.9 6.0 42 
2/Dec. 97.1 92.6 308.0 6.0 65.3 43.9 2.2 0.02 6.0 41 
3/Dec. 113.0 111.0 275.2 20.6 65.4 37.9 3.0 3.5 7.8 42 

1/, 2/ and 3/ first, second and third decennial for each month; * and ** calculated and standard λ2, respectively; P: probability of 
occurrence of historical average rainfall for each period studied.       

 

From Figure 2, it is possible to observe that 
as the probability of exceedance increases the 
probable rainfall decreases, in other words, the 
increase in the accuracy level implies the reduction 
of the estimated value. Graphically it is possible to 
estimate the probable rainfall desired at a given 
probability level (MARTINS et al., 2010; 
RIBEIRO; AVANZI, 2010; SOCCOL et al., 2010). 

Considering the wet-season, in October, for 
a given probability level, is expected more rainfall 
for the third decennial, as well for November and 
December. At January, the first decennial seems to 
concentrate most part of rainfall. This observation is 
clear for February and April months. The evaluation 
of distribution of rainfall considering the probability 
of occurrence may play an important role to farming 
planning, for example, to soil tillage, sowing, 
liming, fertilization, harvesting and application of 
pesticides. 

For irrigation planning, considering the 
water requirement for a given crop in a given 
period, from Figure 2 it is possible to estimate the 
contribution of natural rainfall. In irrigation projects, 
the probability level considered suitable is between 
75% and 80% (BERNARDO, 2005).  

In Table 2 is summarized the rainfall 
expected for each period at 75% of probability of 
exceedance. Considering 75%, at January (for 
example) is expected 54, 34 and 38 mm for first, 
second and third 10-day period, respectively. 
Considering theses periods, if the water requirement 

for a given crop is higher than the natural rainfall 
expected, the complementary irrigation is 
recommended. For example, in Barbacena County, 
Minas Gerais State, the monthly rainfall expected in 
the wet season at 75% probability of exceedance 
attend the most of water requirement of tomato, 
corn and bean (RIBEIRO et al., 2007). On the other 
hand, the simple use of historical average rainfall 
(without probabilistic studies) can lead to oversizing 
or designing fittest of the irrigation systems and also 
to lead an unnecessary use of water from rivers and 
lakes – this late aspect may play an important 
environmental impact. 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 



540 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

 
Figure 2. Probable rainfall for 10-day period (decennial) for Uberlândia, Minas Gerais State, Brazil.  

 
 
 



541 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

Table 2. 10-day probable rainfall at 75% probability of exceedance of Uberlândia, Minas Gerais State, Brazil. 
Period Rainfall (mm) 

1/January 54.45 
2/January 34.51 
3/January 38.01 
1/February 35.17 
2/February 26.28 
3/February 21.82 
1/March 29.00 
2/March 35.64 
3/March 31.14 
1/April 16.67 
2/April 8.81 
3/April 1.14 
1/May 1.48 
2/May 1.77 
3/May 2.28 
1/June 0.45 
2/June 0.01 
3/June 0.13 
1/July 0.02 
2/July 0.01 
3/July 0.00 
1/August 0.00 
2/August 0.21 
3/August 0.24 
1/September 1.14 
2/September 0.77 
3/September 5.80 
1/October 4.87 
2/October 7.56 
3/October 16.62 
1/November 21.60 
2/November 35.22 
3/November 30.24 
1/December 45.57 
2/December 49.15 
3/December 64.86 

1/, 2/ and 3/ first, second and third decennial, respectively. 
 

CONCLUSION 
 

The Gamma distribution was suitable to 
estimate the probable rainfall for 10-day period. 
During the wet season the historical average rainfall 
(10-day period) has 40% of probability of 

exceedance and during the dry season has 30%. 
These values are below that considered ideal (75-
80%). From this work, the 10-day period rainfall 
can be estimated at different probability levels. This 
can contribute substantially to farming planning.   

 
RESUMO: O conhecimento da precipitação provável pode contribuir substancialmente para as atividades 

agrícolas, principalmente em projetos de irrigação. Este trabalho foi realizado com o objetivo de determinar a precipitação 
provável para o município de Uberlândia, MG. Dados diários de precipitação de 1975 a 2010 (36 anos de observação) 
foram organizados em períodos decendiais e ajustados à distribuição Gamma. A precipitação provável foi estimada em 
diferentes níveis de probabilidade (10% a 95%). A distribuição Gamma foi adequada para estimativa da precipitação 
provável. Durante a estação chuvosa, a precipitação média histórica decendial teve uma probabilidade de excedência de 
40% e, na estação seca, de 30%. A partir deste trabalho, a precipitação decendial pode ser estimada em diferentes níveis de 
probabilidade de ocorrência. Isso pode contribuir substancialmente para o planejamento das atividades agrícolas da região, 
especialmente irrigação. 



542 
10-Day probable... RIBEIRO, B. T.; FERREIRA JÚNIOR, D. C.; SILVA, C. R. 

Biosci. J., Uberlândia, v. 29, n. 3, p. 536-542, May/June 2013 

PALAVRAS-CHAVE: Irrigação. Distribuição Gama. Planejamento da agricultura.     
 
 

REFERENCES 
 
AGÊNCIA NACIONAL DE ÁGUAS - ANA. Hidroweb – Sistema de Informações Hidrológicas. Accessed 
in: April 12. 2012. Available at: www.hidroweb.ana.gov.br.   
 
ANDRADE JÚNIOR, A. S. DE; BASTOS, E. A. Precipitação pluviométrica provável em municípios do 
cerrado piauiense. Teresina: EMPRABA-CPAMN, 1997. 22p.  
 
AHRENS, D. C. Meteorology today: an introduction to weather, climate, and the environment. 9th ed. 
Belmont: Brooks Cole, 2009. 621p.  
 
ARAÚJO, W. F.; ANDRADE JÚNIOR, A. S.; MEDEIROS, R. D.; SAMPAIO, R. A. Precipitação 
pluviométrica mensal provável em Boa Vista, Estado de Roraima, Brasil. Revista Brasileira de Engenharia 
Agrícola e Ambiental, Campina Grande, v. 5, n. 3, p. 563-567, 2001. 
 
BERNARDO, S.; MANTOVANI, E. C.; SOARES, A. A. Manual de irrigação. Viçosa: UFV, 2005. 611p. 
BOTELHO, V. A. Ajuste da distribuição de probabilidade gama aos dados de precipitação para a região 
de Lavras, MG. 1989. 98p. Dissertação (Mestrado em Engenharia Agrícola) – Universidade Federal de 
Lavras. 
 
FERREIRA, D. F. Estatística Básica. Lavras: Editora UFLA, 2005. 654p. 
 
FIETZ, C. R.; FRIZZONE, J. A.; FOLEGATTI, M. V.; URCHEI, M. A. Precipitação esperada, em diferentes 
níveis de probabilidade, na região de Dourados, MS. Ciência Rural, Santa Maria, v. 28, n. 1, p. 29-34, 1998. 
 
FIETZ, C. R.; COMUNELLO, E.; CREMON, C.; DALLACORT, R. Estimativa da precipitação provável 
para o Estado de Mato Grosso. Dourados: Embrapa Agropecuária Oeste, 2008. 237p. 
 
INSTITUTO BRASILEIRO DE GEOGRAFIA E ESTATÍSTICA – IBGE. IBGE Cidades. Accessed in: April 
12, 2012. Avaiable at: http://www.ibge.gov.br/cidadesat/link.php?codmun=317020.  
 
LANNA, A. E. Elementos de estatística e probabilidade. In: TUCCI, C. E. M. Hidrologia: ciência e aplicação. 
2nd ed. Porto Alegre: ABRH/Editora UFRGS, 2001. p. 79-176.  
 
MARTINS, J. A.; DALLACORT, R.; INOUE, M. H.; SANTI, A.; KOLLING, E. M.; COLETTI, A. J. 
Probabilidade de precipitação para a microrregião de Tangará da Serra, estado do Mato Grosso. Pesquisa 
Agropecuária Tropical, Goiânia, v. 40, n. 3, p. 291-296, 2010.  
MURTA, R. M.; TEODORO, S. M.; BONOMO, P.; CHAVES, M. A. Precipitação pluvial mensal em níveis de 
probabilidade pela distribuição Gama para duas localidades do sudoeste da Bahia. Ciência e Agrotecnologia, 
Lavras, v. 29, n. 5, p. 988-994, 2005. 
 
RIBEIRO, B. T.; AVANZI, J. C.; MELLO, C. R.; LIMA, J. M.; SILVA, M. L. N. Comparação de distribuição 
de probabilidades e estimativa da precipitação provável para a região de Barbacena, MG. Ciência e 
Agrotecnologia, Lavras, v. 31, n. 5, p. 1297-1302, 2007. 
 
RIBEIRO, B. T.; AVANZI, J. C. Precipitação mensal provável para o município de Machado, Sul de Minas 
Gerais. Revista Agrogeoambiental, Inconfidentes, v. 2, n. 2, p. 117-122, 2010.  
 
SOCCOL, O. J.; CARDOSO, C. O.; MIQUELLUTI, D. J. Análise da precipitação mensal provável para o 
município de Lages, SC. Revista Brasileira de Engenharia Agrícola e Ambiental, Campina Grande, v. 14, n. 
6, p. 569-574, 2010.