e-ISSN 1983-4063 - www.agro.ufg.br/pat - Pesq. Agropec. Trop., Goiânia, v. 47, n. 1, p. 15-21, Jan./Mar. 2017 Estimate of intense rainfall equation parameters for rainfall stations of the Paraíba State, Brazil1 Alcinei Ribeiro Campos2, João Batista Lopes da Silva3, Glenio Guimarães Santos4, Rafael Felippe Ratke5, Itauane Oliveira de Aquino2 ABSTRACT RESUMO Estimativa de parâmetros das equações de chuvas intensas Rainfall is the primary water source for hydrographic para estações pluviométricas do Estado da Paraíba, Brasil basins. Hence, the quantification and knowledge of its temporal and spatial distribution are indispensable in As chuvas constituem-se na principal fonte de água para dimensioning hydraulic projects. This study aimed at bacias hidrográficas. Por isso, a quantificação e o conhecimento assessing the fit of a series of rainfall data to different de sua distribuição temporal e espacial são indispensáveis para o probability models, as well as estimating parameters of dimensionamento de projetos hidráulicos. Objetivou-se avaliar a the intensity-duration-frequency (IDF) equation for rain aderência de séries de dados pluviométricos a diferentes modelos stations of the Paraíba State, Brazil. The rainfall data probabilísticos e estimar parâmetros da equação de intensidade- of each station were obtained from the Brazilian Water duração-frequência (IDF) para estações pluviométricas do Estado da Agency databanks. To estimate the maximum daily Paraíba. Os dados pluviométricos de cada estação foram obtidos a partir rainfall of each station and return period (5, 10, 15, 25, do banco de dados da Agência Nacional de Águas. Para estimar as 50 and 100 years), the following probability distributions precipitações máximas diárias de cada estação e o período de retorno (5, were used: Gumbel, Log-Normal II, Log-Normal III, 10, 15, 25, 50 e 100 anos), foram utilizadas as seguintes distribuições de Pearson III and Log-Pearson III. The estimation of rainfall probabilidade: Gumbel, Log-Normal II, Log-Normal III, Pearson III e in durations of 5-1,440 min was carried out by daily rainfall Log-Pearson III. A estimativa das chuvas nas durações de 5-1.440 min disaggregation. The adjustment of the IDF equation was foi realizada pela desagregação das precipitações pluviométricas performed via nonlinear multiple regression, using the diárias. O ajuste da equação IDF foi realizado por meio de regressão nonlinear generalized reduced gradient interaction method. múltipla não linear, com uso do método de interação de gradação When compared to the data observed, the intense rainfall reduzida generalizada não linear. As equações de chuvas intensas para equations for most stations showed goodness of fit with a maioria das estações, quando comparadas aos dados observados, coefficients of determination above 0.99, which supports apresentaram ajustes com coeficientes de determinação acima de 0,99, the methodology applied in this study. o que referenda a metodologia empregada neste trabalho. KEYWORDS: Hydrology; intensity-duration-frequency PALAVRAS-CHAVE: Hidrologia; equação intensidade-duração- equation; rainfall. frequência; pluviosidade. INTRODUCTION distributed are essential in studies related to irrigation needs, water availability for domestic and industrial Water is a natural resource with a wide range uses, soil erosion, flood control and water projects, of uses and is vital to the human development. among others (Oliveira et al. 2005, Araújo et al. 2008, Maintaining this finite resource at adequate standards of Santos et al. 2010, Castro et al. 2011). quality and quantity for its multiple uses is a challenge According to Mello et al. (2008), the 21st to society. Rainfall is the primary source of water for century should experience a great frequency of hydrographic basins. As such, its quantification and extreme temperature and rainfall events. These the knowledge of how it is temporally and spatially maximum rainfalls, also denominated intense rainfalls 1. Manuscript received in Oct./2016 and accepted for publication in Feb./2017 (http://dx.doi.org/10.1590/1983-40632016v4743821). 2. Universidade Federal do Rio Grande do Sul, Faculdade de Agronomia, Porto Alegre, RS, Brazil. E-mails: [email protected], [email protected]. 3. Universidade Federal do Sul da Bahia, Campus Paulo Freire, Teixeira de Freitas, BA, Brazil. E-mail: [email protected]. 4. Universidade Federal de Goiás, Escola de Agronomia, Goiânia, GO, Brazil. E-mail: [email protected]. 5. Universidade Federal do Piauí, Bom Jesus, PI, Brazil. E-mail: [email protected]. 16 A. R. Campos et al. (2017) (Silva et al. 2012, Souza et al. 2012, Aragão et al. Pfafstetter (1957), who used rainfall records from 2013), produce a large volume of water in a short stations located in the cities of João Pessoa and São period of time. As such, they are apt to cause large Gonçalo. For these areas, Pfafstetter (1957) adjusted surface flows and considerable damage in both urban the parameters of the relationship between rainfall and agricultural areas in the form of floods, dam and return period for different durations. In other ruptures, inundation of cultivated land, soil erosion, study, Souza (1972) used data from João Pessoa to silting and contamination of water bodies (Cecílio et develop the IDF equation for this station. Since these al. 2009, Santos et al. 2009). The knowledge of rainfall outdated reports were the only ones available for volume at a specific time and space is important for Paraíba, a State that depends greatly on the efficient planning soil and water conservation practices and use of water for its cropping activities, it is required hydrographic basin management, in order to establish to update and estimate them for other locations in the flow used in different types of hydraulic projects this region. (Back 2009, Cecílio et al. 2009, Santos et al. 2009). Due to the significant lack of information To characterize rainfall, it is necessary to know about rainfall intensity-duration-frequency (IDF) for its duration, intensity and frequency of occurrence. most locations in Paraíba, and given the importance These relationships are commonly denominated of knowing such information for the design of intensity-duration-frequency (IDF) curves, one of irrigation projects, this study aimed at estimating the the most widely used methodologies in rainfall-flow parameters of the IDF equation for rainfall stations transformation processes (Damé et al. 2008). Intense in this State. rainfall is determined by empirical adjustments of IDF equation parameters, derived from rainfall data MATERIAL AND METHODS for each of the stations (Santos et al. 2009, Back et al. 2012). The parameters of the intense rainfall The study was carried out in 2014, at the equation can be obtained via nonlinear multiple Universidade Federal do Piauí, in Bom Jesus, Piauí regression, based on information extracted from the State, Brazil. Daily rainfall data were collected from series of rainfall data (Campos et al. 2014), which 132 stations in the Paraíba State, obtained from the do not always contain duration, but are composed of Brazilian Water Agency databank (Brasil 2012). daily records. However, it is necessary to know which First, the consistency of the data series of rainfalls lasted less than 24 h, in order to adjust IDF each station was analyzed, and those with less than equations (Aragão et al. 2013). One alternative is 16 years of observation were excluded, leaving only disaggregation based on proportionality factors, which one per municipality, and a total of ninety stations makes possible to obtain rainfall duration in minutes (Figure 1). (Cetesb 1986, Garcia et al. 2011, Aragão et al. 2013). A series of mean maximum 1-day rainfalls was In the Brazilian Paraíba State, pioneering obtained for the following return periods: 5, 10, 15, studies on intense rainfall were conducted by 25, 50 and 100 years. The probability distributions Figure 1. Location of ninety rainfall stations used to estimate the intensity-duration-frequency (IDF) equations for the Paraíba State. Source: Brasil (2012). e-ISSN 1983-4063 - www.agro.ufg.br/pat - Pesq. Agropec. Trop., Goiânia, v. 47, n. 1, p. 15-21, Jan./Mar. 2017 17 Estimate of intense rainfall equation parameters for rainfall stations of the Paraíba State, Brazil 17 used were: Gumbel, Log-Normal II, Log-Normal III, ∑(x - x) . (y - ӯ) 2 (2) r2 = Pearson III and Log-Pearson III (Santos 2010). For ( √∑(x - x) . (y - ӯ)) each station, the maximum rainfall in which the data series showed the best fit to the probability model was where x is the observed values; x the observed mean selected, i.e., the distribution model with the lowest values; y the estimated values; and ӯ the estimated standard error. All these stages were conducted using mean values. the SisCAH software (Sousa et al. 2009). Afterwards, Goodness of fit was also evaluated using the the probability model that best fitted the data series regression equation of data observed in relation to the was determined to estimate the maximum daily estimated data, considering, in this case, the angular rainfall, and the number of occurrences of each model coefficient of the straight line. was counted. After the parameters (K, a, b and c) were Once the maximum daily rainfalls had been adjusted, they were used to estimate the maximum established, 1-day rainfall disaggregation was rainfall intensity for the return period of 25 years, as performed at 5, 10, 15, 20, 25, 30, 60, 360, 480, 600, well as duration of 5, 30, 60, 360, 720 and 1,440 min. 720 and 1440 min, using the coefficients from the Next, these data were regionalized for all the Paraíba rainfall disaggregation method proposed by Cetesb State, using the kriging method and ArcGis 10 software. (1979) (Table 1). Once the fit of distribution data to the probability RESULTS AND DISCUSSION model had been assessed and disaggregation was achieved at shorter times, the parameters K, a, b and From the probability models that exhibited c of the intensity-duration-frequency equation were the best fit for the series of rainfall data, the highest established (Equation 1), according to Pfafstetter standard error observed was 41.83.