Linear trend of occurrence and intensity of heavy rainfall
events on Northeast Brazil
Priscilla Teles de Oliveira,* Cl´audio Mois´es Santos e Silva and Kellen Carla Lima
Program of Post Graduation to Climatic Sciences, Federal University of Rio Grande do Norte, 59078-970 Natal, RN, Brazil
*Correspondence to:
P. T. de Oliveira, Program of Post Graduation to Climatic Sciences, Federal University of Rio Grande do Norte, Campus Universit´ario Lagoa nova, caixa postal 1524, 59078-970 Natal, RN, Brazil. E-mail: priskateles@yahoo.com.br Received: 21 March 2013 Revised: 29 October 2013 Accepted: 18 November 2013 Abstract
A comprehensive dataset of daily rainfall covering the period from 1972 to 2002 was used to compute the climatology and trend of occurrence and intensity of heavy, weak and normal events of rainfall on Northeast Brazil (NEB). For selection of rainfall events, we used the technique of quantiles and the trend was identified using the nonparametric Mann–Kendall test. The heavy events are modulated by La Ni ˜na and El Ni ˜no occurrences and in general they presented negative trend concerning to number of episodes and positive trend to daily rainfall.
Keywords: Mann–Kendall test; percentile; climatic variability; semi-arid
1. Introduction
The Northeast Brazil (NEB) exhibits high climatic variety since semi-arid regions (annual rainfall less than 500 mm), to rainy regions in the coastland (annual precipitation above 1500 mm), being influ-enced by extreme events on the weather scale (pre-cipitation excess) and climatic scale (dry episodes). The rainfall observed is heterogeneous in the spatial-temporal scales due to the main atmospheric systems that act in NEB: the Intertropical Convergence Zone (ITCZ) (Coelho et al., 2004); the Upper Tropospheric Cyclonic Vortex (Kousky and Gan, 1981); the East-erly Waves Disturbances (EWD) (Riehl, 1945) and the Squall Lines (SL) (Kousky, 1980). The South Bahia has actuation from the Front Systems (FS) (Kousky, 1979) and the South Atlantic Convergence Zone (SACZ) (Kodama, 1992). Climatologically, the rainy season occurs during the autumn (March–April–May) (Silva, 2004), although the variety of atmospheric sys-tems above all the NEB.
Several studies focusing on the climatological aspects of rainfall in NEB exist, but, studies con-cerning heavy rainfall events (HRE), with consider-able amount of rainfall data of good quality, have been scarce. There are little insights about climatol-ogy, trends, preferred areas of occurrence, character-istics of the formation, development and dissipation of HRE. Knowing the climatology of these events provides important informations that can be used for predictability purposes.
A trend analysis of extreme events of precipitation is very complex because there is a low degree of temporal and spatial correlation between the precip-itation events. Despite the difficulty, several studies were conducted in order to understand how far the
anthropogenic changes have interfered on the occur-rence of these events. For example, studies were conducted in China (Gemmer et al., 2011), Iberian Peninsula (Acero et al., 2011), United States (San-tos et al., 2011), Central Asia (Bothe et al., 2011) and Europe (Anagnostopoulou and Tolika, 2012).
There are few researches on the HRE climatology in Brazil, although there are important scientific efforts about the South America (Haylock et al., 2006) and about the regions South and Southeast Brazil (Teixeira and Satyamurty, 2011). On NEB, the researches are few (Oliveira et al., 2012, 2013) and the results are concerning to studies of global data analysis (Groisman et al., 2005) or in local scope studies (e.g. Santos and Manzi, 2011). In general, the results have shown positive trend in atmospheric moisture content and precipitation over some regions on south of the South America and negative trend of annual rainfall on NEB (Haylock et al., 2006; Groisman et al., 2005); however, there are evidences of positive trends of HRE occurrence on NEB.
Thus, the objective of this study is to verify the general behaviour of HRE on NEB relating them to the normal rainfall events (NRE) and weak rainfall events (WRE) by analysing the variability and trends of these events in respect to the number of occurrence and intensity of the rainfall.
2. Methodology 2.1. Datasets
A comprehensive dataset of daily precipitation obtained from the 349 rain gauges management by the National Water Agency of Brazil (Agˆencia Nacional de ´Aguas – ANA) was used. The data
(a)
(b)
(c)
Figure 1. (a) Spatial distribution rain gauges. (b) Seasonal climatology of precipitation. (c) Seasonal climatology of the amount of
events.
covers from 1 January 1972 to 31 December 2002 (31 years) period. These data have undergone a process of quality control, resulting in 151 stations with 5.91% of missing data. The stations used are distributed according to Figure 1(a). In recent work, Oliveira et al. (2012) analysed the variability of precipitation and HRE on NEB; although, your analysis excluded the dataset of Bahia State, therefore in Oliveira et al. (2012) the total of rain gauges is 80. 2.2. Quantiles technique
The quantiles are points of a series of data organized in regular intervals. According to Wilks (2006) many statistical analyses were based on the quantiles tech-nique. The main advantage of this technique in relation to the traditional methods (mean and standard devia-tion) is the independency on normalization hypothesis, which is not necessarily satisfied in daily rainfall data. In addition, the quantiles technique considers the fre-quency distribution of precipitation to each rain gauge data. Therefore, the quantiles are immune to eventual asymmetry on the density function of probabilities that describe a random phenomenon.
Recent studies were developed over different regions, using the distribution of daily rainfall per-centiles to determine the HRE threshold. Groisman et al. (2005) used the 90th, 95th, 99th, 99.7th and 99.9th percentiles in a global study; Grimm and Tedeschi (2009) performed a study over South America, using the 90th percentile; Krishnamurthy et al. (2009) identified extreme events in the region
of India from the 90th and 99th percentiles; Jones et al. (2011) used the 90th percentile in a study over the United States; Lima et al. (2010) used the 99th percentile in a study over the Southeast of Brazil. Finally, Gemmer et al. (2011), with rainfall data over China used the 90th, 95th and 99th percentiles.
In this study, we selected extreme (weak and intense events) and the normal events only to nonzero daily rainfall. Each case is selected if at least one rain gauge was observed, based on previous works (Liebmann et al., 2001; Carvalho et al., 2002), thus: (1) the HRE presented precipitation≥95th percentile; (2) the NRE is identifying when the daily precipitation is between percentiles 45th and 55th; (3) the WRE presented precipitation ≤5th percentile. The dataset analyses was divided by seasons: summer DJF (December, January and February); autumn MAM (March, April and May); winter JJA (June, July, August) and spring SON (September, October and November).
2.3. Trend analyses
To analyse the trend of the number of events and rainfall intensity, the nonparametric Mann–Kendall (Mann, 1945; Kendall, 1975) test was applied. This test compares each value of the temporal series with the remaining values in sequential order, counting the number of times that the remaining terms are greater than the analysed value. The Mann–Kendall has been used to determinate climatic and hydrological tendencies (Silva, 2004; Cigizoglu et al., 2005; Sinha and Cherkauer, 2008; Santos et al., 2010; Acero et al.,
2011). To apply the Mann–Kendall test, the makesens spreadsheet developed by Salmi et al. (2002) was used; the calculations are performed as follows.
The S value is obtained by summing the counts of all the data series, xi and xj are the values of the series and i , j the years, being i= j + 1.
S = n−1 j=1 n i=2 signal xi − xj (1) The signal function is performed as follows:
Signal= ⎧ ⎪ ⎨ ⎪ ⎩ 1, if xi − xj >0 0, if xi − xj = 0 −1, if xi − xj <0
To high values of n, the S parameter tends to normality with variance defined as:
VAR (S )= 1 18 n (n− 1) (2n + 5) − q p=1 tp tp− 1 2tp+ 5 ⎤⎦ (2) where tp is the number of data with equal values into the certain group, and q the number of groups having equal values in the series of data in one group p. Finally, the Z value of the Mann–Kendall test is determinated by the following equation:
ZMK= ⎧ ⎪ ⎨ ⎪ ⎩ S−1 √ Var(S ), if S > 0 0, if S = 0 S+1 √ Var(S ), if S < 0 (3)
The ZMK value determines the statistically
signifi-cant of trend. To test any trend (positive or negative) for a given level of significance, the null hypothe-sis is accepted if the value of Z is less than Z1−p
2,
which obtained from the standard normal cumulative distribution tables, then a positive ZMK indicates
pos-itive trend, whereas a negative value of ZMK indicates
a negative trend. In this article, we use the follow-ing significance levels: p= 0.001; p = 0.01; p = 0.05; p= 0.1.
3. Results and discussion
In the Figure 1(b), the seasonal climatology of rainfall is presented. The autumn (MAM) is the main rainy season with maximum precipitation of 400 mm and the dry season is the spring (SON) when the precipitation reaches 100 mm. The distribution of HRE, NRE and WRE (Figure 1(c)) is consistent with the rainfall climatology. The number of HRE, NRE and WRE occurrence is higher in MAM, but the distribution is relatively different. The NRE and WRE are ranging from 2000 to 2600 events whereas the HRE are
concentrated in DJF and MAM seasons. However, the HRE in JJA and SON is about 1000 cases resulting in an annual mean of 33 cases during the dry seasons and 65 cases in rainy seasons.
Table I shows the number of occurrence of HRE, NRE and WRE, annually and seasonally, and the occurrence of El Ni˜no and La Ni˜na events according to their intensity (weak, moderate or strong). The years with maximum occurrence of HRE were 1974, 1985, 1989, 1999 and 2000 and minimum in 1976, 1981, 1983, 1987 and 1993. Concerning the NRE, the years with maximum were 1973, 1974, 1975, 1985 and 2000, and minimum in 1982, 1987, 1993, 1995 and 1997. The years with maximum occurrence of WRE were 1998, 1999, 2000, 2001 and 2002 and minimum in 1990, 1991 1992, 1993 and 1994. The maximum and minimum occurrence of HRE, NRE and NRE coincide to years of La Ni˜na and El Ni˜no, respectively. According to Coelho et al. (2002), Grimm and Tedeschi (2009) and Rodrigues et al. (2011), El Ni˜no and La Ni˜na events have direct influence on the NEB rainy season and consequently on the HRE, NRE and WRE. For all seasons, the number of HRE showed low variability with negative trend from 1972 to 1991 and positive trend after 1991. However, this behaviour is not observed respecting to NRE and WRE, expect to the WRE during the DJF.
The precipitation intensity of HRE, NRE and WRE is presented in Figure 2. The HRE shows variation between 54 and 62 mm day−1(Figure 2(a)) to the rainy seasons, DJF and MAM. During dry seasons, JJA and SON, the rain rate varies between 41 and 60 mm day−1 (Figure 2(b)). The annual variation is between 53 and 58 mm day−1. There is a higher amplitude for the dry period which reaches 17 mm day−1 in JJA, with maximum in 1987 (59 mm day−1) and minimum in 1992 (41 mm day−1), whereas in the rainy season reaches a maximum amplitude of only 8 mm day−1, it is perceived that the dry season has more variability relatively to the rainy one.
The HRE does not show significant trend, except during autumn and spring, which shows a posi-tive trend. The NRE showed little variation around 1 mm day−1 for both dry (Figure 2(c)) and rainy sea-sons (Figure 2(d)). Annually the variation was also lower, about 0.6 mm day−1. In general, the NRE shows the positive or negative trend, excepting to the win-ter season (JJA), which shows a negative trend. The difference between the maximum and minimum WRE intensity during rainy and dry seasons do not exceeds 0.2 mm day−1; however presents a significant positive trend for all seasons. The intensity variability is cor-related with El Ni˜no and La Ni˜na occurrences, but this variation is less sensitive to these phenomena than the variation in the number of events.
Tables II and III show the results of Mann–Kendall test applied to HRE, NRE and WRE, respectively, relatively to the quantity of events and intensity of daily precipitation. With respect to number of events, the WRE presents positive trend to the annual and
Table I. Number of occurrence to HRE, NRE and WRE and the occurrence of El Ni˜no and La Ni˜na events according to their
intensity (weak, moderate or strong).
1972 Strong Strong
298 333 199 Weak 71 85 57 79 67 Strong 75 81 35 73 77 40
1973 299 334 197 Strong 72 85 44 79 92 73 Strong 73 82 40 75 75 40
1974 Weak 289 334 218 Strong 64 82 65 82 92 84 Weak 81 87 32 62 73 37
1975 Strong 273 338 204 Weak 68 85 57 75 70 Strong 74 90 41 56 75 36
1976 Weak 245 321 151 Strong 69 79 43 68 46 Weak 57 75 18 51 79 44
1977 Weak 268 208 Weak 66 86 65 69 89 70 Weak 73 75 36 60 77 37
1978 256 332 203 Weak 65 85 61 69 89 79 − 60 83 32 62 75 31 1979 − − 274 323 187 − 66 80 65 77 87 63 − 67 80 19 64 76 40 1980 − 263 323 184 − 73 84 76 62 83 42 − 67 80 23 61 76 43 1981 − 272 320 159 − 64 83 51 64 87 63 − 75 80 16 69 70 29 1982 Strong 256 313 192 − 60 81 59 71 89 74 Strong 69 85 35 56 58 24 1983 242 314 155 Strong 66 84 51 67 83 51 Weak 58 76 14 51 71 39 1984 Weak Weak 267 319 200 Weak 62 78 46 74 89 79 Weak 68 84 37 63 68 38 1985 − 277 342 263 Weak 75 88 85 77 91 83 - 63 86 48 62 77 47 1986 Moderate 269 326 205 - 68 80 54 68 89 69 Moderate 63 80 38 70 77 44
1987 Moderate 272 164 Moderate 72 80 42 72 88 68 Moderate 73 72 26 55 62 28
1988 257 327 186 Moderate 68 86 55 70 85 68 Strong 56 83 38 63 73 25 1989 − 268 329 234 Strong 73 87 59 75 89 82 − 65 82 49 55 71 44 1990 − 214 318 177 − 61 77 55 53 85 45 − 43 81 41 57 75 36 1991 Strong 205 319 199 − 50 79 57 71 90 71 Strong 43 80 34 41 70 37 1992 215 320 186 Strong 65 80 74 52 86 51 44 88 31 54 66 30 1993 −− 238 306 162 − 62 82 51 69 85 54 − 47 69 29 60 70 28 1994 Moderate 230 330 198 − 57 82 54 68 91 76 Moderate 50 84 40 55 73 28 1995 265 309 184 Moderate 62 78 59 80 91 70 Weak 67 82 29 56 58 26 1996 − 296 320 195 Weak 75 74 50 82 88 66 − 76 85 36 63 73 43 1997 Strong 291 295 184 − 77 83 69 84 86 70 Strong 71 70 24 59 56 21 1998 307 326 188 Strong 80 84 60 79 90 50 Moderate 80 84 38 68 68 40
1999 Strong 307 331 214 Moderate 80 84 55 81 89 72 Strong 70 83 45 76 75 42
2000 Weak 320 335 221 Strong 77 87 71 87 89 64 Weak 79 84 50 77 75 36
2001 − 318 331 199 Weak 76 87 59 88 86 65 − 86 92 39 68 66 36 2002 Moderate 320 331 178 − 74 84 64 86 90 61 Moderate 83 89 32 77 68 21 327 302 Weak Strong Moderate
Annual DJF/MAM DJF MAM JJA/SON JJA SON
La Niñaa/El Niñob b b b b b b b b b b a a a a a a a a a a a b b b b b b b b b a a a a a a a a a
WRE NRE HRE
La Niñaa/El
Niñob WRE NRE HRE WRE NRE HRE
La Niñaa/El Niñob b b b b b b b b b b a a a a a a a a a a
WRE NRE HRE WRENRE HRE
90
88 88
Five largest values.
Five lowest values. Source: http://ggweather.com/enso/oni.htm.
Figure 2. Distribution of daily precipitation mean of HRE, NRE and WRE. Parts (a), (c) and (e) have the rainier seasons (MAM
Table II. Trend statistical of the Mann–Kendall test applied in variation of quantity events.
WRE NRE HRE
Test Z Significance Slope Test Z Significance Slope Test Z Significance Slope
Annual 1.99 * 0.143 −1.00 −0.176 −0.32 −0.160 DJF 1.36 0.222 −0.27 0.000 0.77 0.182 MAM 1.86 + 0.357 −0.38 0.000 −0.99 −0.200 JJA 0.19 0.059 1.25 0.115 1.24 0.235 SON 0.75 0.133 −2.76 ** −0.250 −1.79 + −0.200 *Trend is significant at p= 0.05. **Trend is significant at p= 0.01. +Trend is significant at p = 0.1.
Table III. Trend statistical of the Mann–Kendall test applied in variation of mean daily rainfall.
WRE NRE HRE
Test Z Significance Slope Test Z Significance Slope Test Z Significance Slope
Annual 2.33 * 0.003 0.00 0.000 0.51 0.016 DJF 1.15 0.001 1.29 0.006 −0.48 −0.015 MAM 2.86 ** 0.003 0.95 0.003 2.31 * 0.092 JJA 3.06 ** 0.002 −1.70 + −0.009 −1.12 −0.113 SON 1.46 0.001 0.58 0.003 2.31 * 0.147 *Trend is significant at p= 0.05. **Trend is significant at p= 0.01. +Trend is significant at p = 0.1.
autumn season (MAM) at 95 and 90% confidence level, respectively. The annual NRE presented nega-tive tendency. All seasons, with exception in the win-ter (JJA), presents positive trend, but only the spring (SON) presents statistical significance at 99%. The spring also shown significant trend in relation to the HRE, with confidence level at 90%.
Concerning to the rainfall intensity, the WRE pre-sented a positive trend at 95% significance level to the variation annual and 99.9% significance level to the season’s autumn and winter. The NRE presented positive trend in majority cases, with exception in the winter, which shows a negative trend with sta-tistical significance at 90% level. The HRE showed positive trend in variation annual, autumn (MAM) and spring (SON), however only autumn and spring presents trend significance at 95% level. Negative trend was observed during the summer (DJF) and win-ter (JJA), but without statistical significance. In gen-eral, the quantity of events presented a negative trend over the NEB, whereas the rainfall intensity shows positive trend.
4. Conclusions
A dataset composed of 151 rain gauges provides daily rainfall that was used to define HRE, NRE and WRE, in order to perform the climatology of the number of occurrence and intensity of daily precipitation, as well as analyse her trend. The following results were obtained:
• Concerning to the climatology aspects, the number of events is modulated by La Ni˜na and El Ni˜no
occurrences, which were verified strong and weak events, being the rainfall intensity variation less sensitive to the El Ni˜no and La Ni˜na occurrence comparatively to the numbers of events.
• The difference between the maximum and min-imum rainfall is higher during the dry season (17 mm day−1) in comparison with rainy season (8 mm day−1), shown that the dry season is less homogeneous that the rainy season.
• Analyzing the different seasons, we obtain a neg-ative trend in number of occurrence of HRE (at 90% confidence level) and NRE (at 99%) during the spring (SON) and a positive trend in the inten-sity of HRE (at 95%) during autumn (MAM). These results suggest alterations on the temporal rain dis-tribution over the NEB, resulting in an increase of the seasonality amplitude.
References
Acero FJ, Gallego MC, Garc´ıa JA. 2011. Multi-day rainfall trends over the Iberian Peninsula. Theoretical and Applied Climatology 108: 411–423.
Anagnostopoulou C, Tolika K. 2012. Extreme precipitation in Europe: statistical threshold selection based on climatological criteria.
Theo-retical and Applied Climatology 107: 479–489.
Bothe O, Fraedrich K, Zhu X. 2011. Precipitation climate of Central Asia and the large-scale atmospheric circulation. Theoretical and
Applied Climatology 108: 345–354.
Carvalho LMV, Jones C, Liebmann B. 2002. Extreme precipitation events in southern South America and large-scale convective patterns in the South Atlantic Convergence Zone. Journal of Climate 15: 2377–2394.
Cigizoglu HK, Bayazit M, ¨On¨oz B. 2005. Trends in the maximum, mean, and low flows of Turkish Rivers. Journal of
Coelho CAS, Uvo CB, Ambrizzi T. 2002. Exploring the impacts of the Tropical Pacific SST on the precipitation patterns over South America during ENSO periods. Theoretical and Applied Climatology
71: 185–197.
Coelho MS, Gan MA, Conforte JC. 2004. Estudo da variabilidade da posic¸˜ao e da nebulosidade associada `a ZCIT do atlˆantico, durante a estac¸˜ao chuvosa de 1998 e 1999 no Nordeste do Brasil. Revista
Brasileira de Meteorologia 19: 23–34.
Dee DP, Uppala SM, Simmons AJ, Berrisford P, Poli P, Kobayashi S, Andrae U, Balmaseda MA, Balsamo G, Bauer P, Bechtold P, Beljaars ACM, Van De Berg L, Bidlot J, Bormann N, Delsol C, Dragani R, Fuentes M, Geer AJ, Haimberger L, Healy SB, Hersbach H, H´olm EV, Isaksen L, Kallberg P, K¨ohler M, Matricardi M, Mcnally AP, Monge-Sanz BM, Morcrette JJ, Park BK, Peubey C, De Rosnay P, Tavolato C, Th´epaut JN, Vitart F. 2011. The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Quarterly Journal of the Royal Meteorological Society 137: 553–597.
Gemmer M, Fischer T, Jiang T, Su B, Liu LL. 2011. Trends in precipitation extremes in the Zhujiang River Basin, South China.
Journal of Climate 24: 750–761.
Grimm AM, Tedeschi RG. 2009. Enso and extreme rainfall events in South America. Journal of Climate 22: 1589–1609.
Groisman PY, Knight RW, Easterling DR, Karl TR, Hegerl GC, Razuvaev VN. 2005. Trends in intense precipitation in the climate record. Journal of Climate 18: 1326–1350.
Haylock MR, Peterson TC, Alves LM, Ambrizzi T, Anunciac¸˜ao YMT, Baez J, Barros VR, Berlato MA, Bidegain M, Coronel G, Corradi V, Garcia VJ, Grimm AM, Karoly D, Marengo JA, Marino MB, Moncunill DF, Nechet D, Quintana J, Rebello E, Rusticucci M, Santos JL, Trebejo I, Vincent LA. 2006. Trends in total and extreme South American rainfall in 1960–2000 and links with sea surface temperature. Journal of Climate 19: 1490–1512.
Jones C, Gottschalck J, Carvalho LMV, Higgins W. 2011. Influence of the Madden–Julian oscillation on forecasts of extreme precipitation in the contiguous United States. Monthly Weather Review 139: 332–350.
Kendall MG. 1975. Rank Correlation Methods. Charles Griffin: London; 120.
Kodama Y. 1992. Large-Scale common features of subtropical pre-cipitation zones (the Baiu Frontal Zone, the SPCZ and the SACZ), part I: characteristics of subtropical frontal zones. Journal of the
Meteorological Society of Japan 70: 813–836.
Kousky VE. 1979. Frontal influences on northeast Brazil. Monthly
Weather Review 107: 1140–1153.
Kousky VE. 1980. Diurnal rainfall variation in Northeast Brazil.
Monthly Weather Review 108: 488–498.
Kousky VE, Gan MA. 1981. Upper tropospheric cyclonic vortices in the tropical South Atlantic. Tellus 33: 538–551.
Krishnamurthy CKB, Lall U, Know HH. 2009. Changing frequency and intensity of rainfall extremes over India from 1951 to 2003.
Journal of Climate 22: 4737–4746.
Liebmann B, Jones C, Carvalho LMV. 2001. Interannual variability of daily extreme precipitation events in the State of S˜ao Paulo, Brazil.
Journal of Climate 14: 208–218.
Lima KC, Satyamurty P, Fern´andez JPR. 2010. Large-scale atmo-spheric conditions associated with heavy rainfall episodes in Southeast Brazil. Theoretical and Applied Climatology 101:
121–135.
Mann HB. 1945. Nonparametric Tests Against Trend . Econometrica
13: 245–259.
Oliveira PT, Santos e Silva CM, Lima KC. 2012. Trend of rain in Northeast Brazil. In Rainfall: Behavior, Forecasting and
Distribu-tion, Mart´ın OE, Roberts TM (eds). Nova Science Publishers: New
York, NY; 155–166.
Oliveira PT, Santos e Silva CM, Lima KC. 2013. Synoptic environment associated with heavy rainfall events on the coastland of Northeast Brazil. Advances in Geosciences 35: 73–78.
Riehl H. 1945. Waves in the Easterlies and the Polar Front in
the Tropics. Department of Meteorology, Chicago University:
Chicago; 79.
Rodrigues RR, Haarsma RJ, Campos EJD, Ambrizzi T. 2011. The impacts of inter-El Nino variability on the Tropical Atlantic and Northeast Brazil climate. Journal of Climate 24: 3402–3422. Salmi T, M¨a¨att¨a A, Anttila P, Ruoho-Airola T, Amnell T. 2002.
Detecting trends of annual values of atmospheric pollutants by the Mann–Kendall test and Sen’s Slope estimates – The Excel Template Application MAKESENS. Publication on Air Quality, Finnish Meteorological Institute 31.
Santos CAC, Manzi AO. 2011. Eventos extremos de precipitac¸˜ao no estado do cear´a e suas relac¸˜oes com a temperatura dos oceanos tropicais. Revista Brasileira de Meteorologia 26: 157–165. Santos CAC, Neale CMU, Rao TVR, Silva BB. 2011. Trends in indices
for extremes in daily temperature and precipitation over Utah, USA.
International Journal of Climatology 31: 1813–1822.
Santos DS, Silva VPR, Sousa FAZ, Silva RA. 2010. Estudos de Alguns Cen´arios Clim´aticos para o Nordeste do Brasil. Revista Brasileira
de Engenharia Agr´ıcola e Ambiental 14: 492–500.
Silva VPR. 2004. On climate variability in Northeast of Brazil. Journal
of Arid Environments 58: 575–596.
Sinha T, Cherkauer K. 2008. Time series analysis of soil freeze and thaw processes in Indiana. Journal of Hydrometeorology 9: 936–950.
Teixeira MS, Satyamurty P. 2011. Trends in the frequency of intense precipitation events in Southern and Southeastern Brazil during 1960–2004. Journal of Climate 24: 1913–1921.
Wilks DS. 2006. Statistical Methods in the Atmospheric Sciences. Academic Press: San Diego, CA; 627.
