Trends and Persistence of Dry–Wet Conditions in Northeast Brazil

: We analyze trend and persistence in Standardized Precipitation Index (SPI) time series derived from monthly rainfall data at 133 gauging stations in Pernambuco state, Brazil, using a suite of complementary methods to address the spatially explicit tendencies, and persistence. SPI was calculated for 1-, 3-, 6-, and 12-month time scales from 1950 to 2012. We use Mann–Kendall test and Sen’s slope to determine sign and magnitude of the trend, and detrended ﬂuctuation analysis (DFA) method to quantify long-term correlations. For all time scales signiﬁcant negative trends are obtained in the Sert ã o (deep inland) region, while signiﬁcant positive trends are found in the Agreste (intermediate inland), and Zona da Mata (coastal) regions. The values of DFA exponents show di ﬀ erent scaling behavior for di ﬀ erent time scales. For short-term conditions described by SPI-1 the DFA exponent is close to 0.5 indicating weak persistency and low predictability, while for medium-term conditions (SPI-3 and SPI-6) DFA exponents are greater than 0.5 and increase with time scale indicating stronger persistency and higher predictability. For SPI-12 that describes long-term precipitation patterns, the values of DFA exponents for inland regions are around 1, indicating strong persistency, while in the shoreline the value of the DFA exponent is between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion. These results should be useful for agricultural planning and water resource management in the region. weather stations, with incorporated topographic information. A.S.A.d.S.; Funding acquisition, A.S.A.d.S., M.C.F. R.S.C.M.; Investigation, A.S.A.d.S., M.C.F., T.S. B.S.; Methodology, A.S.A.d.S., M.C.F., T.S. B.S.; Software, A.S.A.d.S. and B.S.; Supervision, R.S.C.M., T.S. B.S.; Validation, A.S.A.d.S., M.C.F., R.S.C.M., T.S. and B.S.; Visualization, A.S.A.d.S. and T.S.; Writing—original draft, M.C.F., and


Introduction
Rainfall variability leads to a deficit or excess of water with respect to normal conditions at a given location. Severity and duration of these anomalies have a direct effect on availability of water resources and can compromise agricultural productivity, food security, water resource management, land use, human health and ecological equilibrium [1][2][3][4]. Extreme rainfall related events as severe floods and drought have been observed in many tropical countries and it is expected to increase in severity during this century [5]. Several indices have been developed to evaluate the severity of dry/wet conditions including the Palmer Drought Severity index (PDSI) [6], the Standardized Runoff Index (SRI) [7], the Standardized Precipitation Index (SPI) [8] and Standardized Precipitation Evapotranspiration Index (SPEI) [9]. Among them, the SPI stands out from the point of view that it only requires rainfall data for computations (and no other additional variables or empirical parametrizations), it can be compared among different regions with different climatic conditions [10], and it has already been widely applied to analyze dry/wet conditions in different parts of the world, in many different contexts [11][12][13][14][15]. The data used in this work are historical series of monthly precipitation for the state of Pernambuco, Brazil, provided by the Meteorological Laboratory of the Institute of Technology of Pernambuco (Laboratório de Meteorologia do Instituto de Tecnologia de Pernambuco-LAMEP/ITEP). The monthly series of precipitation, with time span from 1950 to 2012, corresponds to records obtained from 133 meteorological stations as shown in Figure 1, together with the digital elevation model (DEM) data. The missing data were filled using the trend surface analysis interpolation method [28]. The study period was selected as a trade-off between the series length and the number of stations, where stations with over 10% of missing data were discarded. The resulting interpolated mean annual precipitation is shown in Figure 2. All the analyses were performed in R [29], with the help of the contributed package trend [30].

Standardized Precipitation Index
The Standardized Precipitation Index (SPI), developed by McKee et al. [8] to quantify the precipitation deficit for multiple time scales (i.e., 1, 3, 6, 12, 24 and 48 months), is recommended by the World Meteorological Organization (WMO) as an index to characterize drought severity [31]. For calculation of the SPI, first it is necessary to adjust the probability density function (pdf) for the precipitation dataset. Among several distributions proposed in the literature [32,33], in this work we adopt the gamma distribution, which is the most widely used to fit precipitation time series [8,34]. The gamma pdf is given by  The data used in this work are historical series of monthly precipitation for the state of Pernambuco, Brazil, provided by the Meteorological Laboratory of the Institute of Technology of Pernambuco (Laboratório de Meteorologia do Instituto de Tecnologia de Pernambuco-LAMEP/ITEP). The monthly series of precipitation, with time span from 1950 to 2012, corresponds to records obtained from 133 meteorological stations as shown in Figure 1, together with the digital elevation model (DEM) data. The missing data were filled using the trend surface analysis interpolation method [28]. The study period was selected as a trade-off between the series length and the number of stations, where stations with over 10% of missing data were discarded. The resulting interpolated mean annual precipitation is shown in Figure 2. All the analyses were performed in R [29], with the help of the contributed package trend [30].

Standardized Precipitation Index
The Standardized Precipitation Index (SPI), developed by McKee et al.
[8] to quantify the precipitation deficit for multiple time scales (i.e., 1, 3, 6, 12, 24 and 48 months), is recommended by the World Meteorological Organization (WMO) as an index to characterize drought severity [31]. For calculation of the SPI, first it is necessary to adjust the probability density function (pdf) for the precipitation dataset. Among several distributions proposed in the literature [32,33], in this work we adopt the gamma distribution, which is the most widely used to fit precipitation time series [8,34]. The gamma pdf is given by

Standardized Precipitation Index
The Standardized Precipitation Index (SPI), developed by McKee et al.
[8] to quantify the precipitation deficit for multiple time scales (i.e., 1, 3, 6, 12, 24 and 48 months), is recommended by the World Meteorological Organization (WMO) as an index to characterize drought severity [31]. For calculation of the SPI, first it is necessary to adjust the probability density function (pdf) for the precipitation dataset. Among several distributions proposed in the literature [32,33], in this work we adopt the gamma distribution, which is the most widely used to fit precipitation time series [8,34]. The gamma pdf is given by where α > 0 is a shape parameter, β > 0 is a scale parameter, x is the amount of precipitation and Γ(α) is gamma function Γ(α) = ∞ 0 y α−1 e −y dy. The parameters α and β are estimated using maximum likelihood method, which yields estimateŝ Atmosphere 2020, 11, 1134 4 of 15 where x is the average value of precipitation quantity, notation A ≡ ln(x) − Σ ln x n is used to provide a more compact formula representation, and n is the number of observations [35]. Next, f (x) is integrated with respect to x, to obtain the cumulative probability The gamma function is undefined for x = 0, and as naturally precipitation data does contain zeros, the cumulative probability is taken to be where q is the probability of zero (null) precipitation, which is calculated as q = m/n, where m represents the number of zeros in a precipitation series and n is the number of observations. Finally, the SPI is generated by standardizing the values obtained in H(x) [36,37] with c 0 = 2.515517; c 1 = 0.802853; c 2 = 0.010328; and d 1 = 1.432788; d 2 = 0.189269; d 3 = 0.001308, and t is given by The 1-month SPI is related to meteorological types of drought together with short-term soil moisture and crop stress, SPI-3 reflects medium-term soil moisture conditions, while 6-month and 12-month SPI indicate seasonal to long-term precipitation temporal patterns and are associated with anomalous streamflows, and reservoir and ground water levels [10].
In this study, the 1-and 3-month SPI are used to represent short-term and seasonal drought, the 6-month SPI is used for intermediate-term drought, and the 12-month SPI is used for long-term drought. In all cases the whole period is used to adjust the gamma pdf.

Mann-Kendall Test
The Mann-Kendall test [38,39] is a non-parametric statistical method (it does not require that data follow any specific distribution) used to determine whether a time series has a monotonic upward or downward trend. It is a rank-based procedure, especially suitable for non-normally distributed data, data containing outliers, and nonlinear trends [40]. This test is based on the correlation between Atmosphere 2020, 11, 1134 5 of 15 the values of time series and their temporal order, the null hypothesis being that the observations are independent and identically distributed (no trend), and the alternative hypothesis being that there is a monotonic trend (upward or downward). For the times series x 1 , x 2 , . . . , x n the Mann-Kendall test uses the statistic where x i and x j are the sequential data values, n is the length of the dataset, and sgn(.) Stands for the sign of the argument, with Under the assumption that the data are independent and identically distributed (null hypothesis), the S statistics has mean zero, E(S) = 0, and variance given by in which q is the number of tied groups, and t p is the number of observations in the p-th group. The test statistic Z, which has a normal distribution, is computed based on the values S and Var(S) Positive values of Z indicate upward trends, while negative values of Z show downward trends. Finally, for testing purposes the p value (pv) is computed as where min(·, ·) stands for the minimum of the two arguments, and φ(·) is the cumulative distribution function of the standard normal distribution-the null hypothesis is rejected when the p value of the test standardized statistic Z is less than the chosen significance level α. Therefore, the trend is said to be downward if Z is negative and upward if Z is positive, and the pv is less than α. In this paper, we used the significance level α = 0.05. The Mann Kendall non-parametric test has been widely used to quantify the trends in hydro-meteorological times series [41][42][43].

Wilcoxon-Mann-Whitney Test
The Wilcoxon-Mann-Whitney test [44,45], is a non-parametric hypothesis test used to check whether or not two independent samples containing n 1 and n 2 elements correspond to the same distribution. It does not require the data normality assumption. The Wilcoxon-Mann-Whitney statistic W is computed as follows: the n 1 + n 2 observations of the two independent samples are combined in a single dataset. The elements of this dataset are sorted from smallest to largest. If there are ties in the combined dataset, the ranks for the observations in a tie are taken to be the average of the ranks for those observations. The Wilcoxon statistic, W, is calculated as the sum of ranks of the sample with the smaller sample size. Under this null hypothesis, the expectation and variance of W are, respectively µ W = n 1 (n 1 + n 2 + 1) 2 and σ 2 W = n 1 n 2 (n 1 + n 2 + 1) 12 .
Atmosphere 2020, 11, 1134 6 of 15 For n 1 and n 2 greater than 10, the distribution of the statistic T = (W − µ W )/σ W can be approximated by a normal distribution with zero expectation and variance equal to unity. In the case of ties the variance needs to be modified for the Gaussian approximation. Let n t be the number of groups with ties and t k the number of ties in group k then Under this assumption, the p value (pv) is calculated as where w denotes the value of the rank-sum statistic in the sample, and φ(·) is the cumulative distribution function of the standard normal distribution. For a specific significance level α ∈ (0, 1), the null hypothesis is rejected whenever pv < α.

Sen's Slope of Trend
The Mann Kendall test is an efficient method for identifying trends in time series, but it does not provide the magnitude of the trend. It can be complemented by the non-parametric method proposed by Sen [46] to estimate the true slope of an existing trend. The main strength of the Sen slope estimator is its robustness to the presence of outliers [47,48]. The slopes of all data value pairs are calculated as where x i and x j are the data values at times i and j (i < j), respectively. If the analyzed series has n values, then the number of pairs Q i,j is N = n(n − 1)/2. Finally, the slope median Q med (or Sen's slope estimator) is calculated: the sign of Q med reflects the data (upward or downward) trend, while its value indicates the steepness of the trend.

Detrended Fluctuation Analysis
Detrended fluctuation analysis (DFA) was introduced by Peng et al. [49] as a method for quantification of correlations in non-stationary time series [50,51]. This method represents a modified root-mean-square analysis of a random walk, and was successfully applied in physiological processes [52], geophysical signals [53], climatic records [54,55], hydrological time series [56] and financial data [57]. The implementation of the DFA algorithm is described as follows: of length n (here int(·) stands for the integer value of the argument), and in each segment s = 1, . . . , N n the local trend X n.s (k) (linear or higher order polynomial least square fit-termed DFA1, DFA2, DFA3, . . . , for polynomials of order 1,2, 3, . . . , respectively) is estimated and subtracted from X(k). In DFAm, trends of order m in the profile X(k), and of order m − 1 in the original record x(i) are eliminated.
(iv) Repeating this calculation for different window sizes provides the relationship between the fluctuation function F(n) and the window size n. If long-term correlations are present in original series, F(n) increases with n according to a power law The scaling exponent α is obtained as the slope of the linear regression of log F(n) versus log n. The value α = 0.5 indicates the absence of correlations (white noise), α > 0.5 indicates persistence of long-term correlations, meaning that large (small) values are more likely to be followed by large (small) values, while α < 0.5 indicates anti-persistent long-term correlations, meaning that large values are more likely to be followed by small values, and vice versa. The values α = 1 and α = 1.5 correspond to 1/ f noise and Brownian noise (integration of white noise), respectively [49].

Results and Discussion
Monthly precipitation data for representative stations of the three regions, together with the calculated SPI values on time scales 1, 3, 6 and 12 months are shown in Figure 3. iii) The detrended variance is now calculated as iv) Repeating this calculation for different window sizes provides the relationship between the fluctuation function ( ) and the window size . If long-term correlations are present in original series, ( ) increases with according to a power law ( ) ~ The scaling exponent is obtained as the slope of the linear regression of log ( ) versus log . The value = 0.5 indicates the absence of correlations (white noise), > 0.5 indicates persistence of long-term correlations, meaning that large (small) values are more likely to be followed by large (small) values, while < 0.5 indicates anti-persistent long-term correlations, meaning that large values are more likely to be followed by small values, and vice versa. The values = 1 and = 1.5 correspond to 1/ noise and Brownian noise (integration of white noise), respectively [49].

Results and Discussion
Monthly precipitation data for representative stations of the three regions, together with the calculated SPI values on time scales 1, 3, 6 and 12 months are shown in Figure 3.   scales. On the other hand, higher percentages of significant positive trends are found in Agreste and Zona da Mata, with the percentage obtained in Zona da Mata region (close to the coast) always higher than that obtained in the (inland) Agreste region.

Trend Analysis
The results of the trend analysis for the series of SPI values (time scale 1, 3, 6 and 12 months) for regions Sertão, Agreste and Zona da Mata are summarized in Figure 4. This figure shows the percentage of stations with significant trends ( < 0.05) for each of the SPI time scales and for each region. Higher percentages of significant negative trend are obtained in the Sertão region, for all time scales. On the other hand, higher percentages of significant positive trends are found in Agreste and Zona da Mata, with the percentage obtained in Zona da Mata region (close to the coast) always higher than that obtained in the (inland) Agreste region. For all time scales, percentage of non-significant trends ( ≥ 0.05) is lower than the percentage of significant trends. These percentages are 45% (26% Sertão, 14% Agreste, 5% Zona da Mata), 35% (18% Sertão, 12% Agreste, 5% Zona da Mata), 30% (17% Sertão, 11% Agreste, 2% Zona da Mata) and 28% (15% Sertão, 10% Agreste, 3% Zona da Mata) for time scales 1, 3, 6 and 12, respectively. Spatial distributions of trends (significant and non-significant) for the series of SPI values for time scales 1, 3, 6 and 12 months are shown in Figure 5. The downward oriented red triangles, and the upward blue triangles represent negative and positive trends, respectively, while filled triangles indicate significant trends. For all time scales, a general predominance of the negative tendencies (red triangles) can be seen in the Sertão region, indicating dominance of a drying tendency, while a predominance of positive trends (blue triangles) can be seen in Agreste and Zona da Mata, indicating the dominance of wetting tendency.
Cunha et al. [18] used high resolution adjusted SPI index, derived from regional empirical relationships between a remote sensing-based index (vegetation health index-VHI) and rain-gaugebased Standardized Precipitation Index (SPI) to study the spatial-temporal characteristics of drought in Northeast Brazil. For the period 1982-2016 they found negative SPI-adjusted trends in most of the study region, indicating a statistically significant shift towards drying conditions. However, in several spots positive SPI adjusted trends are observed, mostly in the coastal area and areas that have been undergoing an expansion of irrigation in recent years, such as São Francisco River valley in Sertão. We also found the predominance of positive SPI trend in Zona de Mata e several locations with positive SPI trend in semiarid Sertão region.
The spatial distribution of the magnitude of SPI trend (Sen's slope) is shown in Figure 6. The signs of the slopes are consistent with the results of Mann-Kendall test: negative in Sertão, with decreasing magnitude from west to east towards the transitional Agreste region, where the trend For all time scales, percentage of non-significant trends (pv ≥ 0.05) is lower than the percentage of significant trends. These percentages are 45% (26% Sertão, 14% Agreste, 5% Zona da Mata), 35% (18% Sertão, 12% Agreste, 5% Zona da Mata), 30% (17% Sertão, 11% Agreste, 2% Zona da Mata) and 28% (15% Sertão, 10% Agreste, 3% Zona da Mata) for time scales 1, 3, 6 and 12, respectively. Spatial distributions of trends (significant and non-significant) for the series of SPI values for time scales 1, 3, 6 and 12 months are shown in Figure 5. The downward oriented red triangles, and the upward blue triangles represent negative and positive trends, respectively, while filled triangles indicate significant trends. For all time scales, a general predominance of the negative tendencies (red triangles) can be seen in the Sertão region, indicating dominance of a drying tendency, while a predominance of positive trends (blue triangles) can be seen in Agreste and Zona da Mata, indicating the dominance of wetting tendency.
Cunha et al. [18] used high resolution adjusted SPI index, derived from regional empirical relationships between a remote sensing-based index (vegetation health index-VHI) and rain-gauge-based Standardized Precipitation Index (SPI) to study the spatial-temporal characteristics of drought in Northeast Brazil. For the period 1982-2016 they found negative SPI-adjusted trends in most of the study region, indicating a statistically significant shift towards drying conditions. However, in several spots positive SPI adjusted trends are observed, mostly in the coastal area and areas that have been undergoing an expansion of irrigation in recent years, such as São Francisco River valley in Sertão. We also found the predominance of positive SPI trend in Zona de Mata e several locations with positive SPI trend in semiarid Sertão region.
The spatial distribution of the magnitude of SPI trend (Sen's slope) is shown in Figure 6. The signs of the slopes are consistent with the results of Mann-Kendall test: negative in Sertão, with decreasing magnitude from west to east towards the transitional Agreste region, where the trend becomes positive with increasing magnitude towards Zona de Mata. It is also seen that the Sen's slope increases with the increase in aggregation time scale.
Atmosphere 2020, 11, x FOR PEER REVIEW 9 of 15 becomes positive with increasing magnitude towards Zona de Mata. It is also seen that the Sen's slope increases with the increase in aggregation time scale.  In order to assess the difference in trend magnitudes between each of the regions, we construct boxplots of SPI's Sen's slopes and perform the Wilcoxon-Mann-Whitney test at the 5% significance level (Figure 7). For all time scales the Sertão region has negative Sen's slope, the Agreste region has a slightly positive Sen's slope, and Zona da Mata has a high positive Sen's slope. The test results indicate that there is a significant difference between the regions for all time scales. Atmosphere 2020, 11, x FOR PEER REVIEW 9 of 15 becomes positive with increasing magnitude towards Zona de Mata. It is also seen that the Sen's slope increases with the increase in aggregation time scale.  In order to assess the difference in trend magnitudes between each of the regions, we construct boxplots of SPI's Sen's slopes and perform the Wilcoxon-Mann-Whitney test at the 5% significance level (Figure 7). For all time scales the Sertão region has negative Sen's slope, the Agreste region has a slightly positive Sen's slope, and Zona da Mata has a high positive Sen's slope. The test results indicate that there is a significant difference between the regions for all time scales. In order to assess the difference in trend magnitudes between each of the regions, we construct boxplots of SPI's Sen's slopes and perform the Wilcoxon-Mann-Whitney test at the 5% significance level (Figure 7). For all time scales the Sertão region has negative Sen's slope, the Agreste region has a slightly positive Sen's slope, and Zona da Mata has a high positive Sen's slope. The test results indicate that there is a significant difference between the regions for all time scales.

Figure 7.
Sen's slope boxplots for each of the three regions for different time scales (SPI-1, SPI-3, SPI-6 and SPI-12). The star symbol "*" indicates that there is a significant difference between the regions at the 5% significance level ( < 0.05).

Detrended Fluctuation Analysis
We apply DFA analysis on SPI time series for all the 133 Pernambuco stations, and perform spatial interpolation of obtained scaling exponents, resulting in maps shown in Figure 8. The values of DFA exponents are greater than 0.5 and increase with SPI time scale, indicating stronger persistency and higher predictability of medium-term conditions in precipitation (SPI-3 and SPI-6), while for short-term conditions described by SPI-1, the DFA exponent is closer to 0.5 indicating weak persistency and low predictability. Long-term precipitation patterns described by SPI-12, show different behavior: in Sertão and Agreste, the values of DFA exponents are around 1, indicating strong persistency, while in Zona da Mata the value of the DFA exponent is found to be between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion (H = α − 1), meaning that SPI-12 increments exhibit anti-persistent long-term correlations. It can also be observed from Figure 6 that for short and medium conditions (SPI-1, SPI-3 and SPI-6), DFA exponents increase with decreasing distance to the ocean, indicating the weakest persistence (lowest predictability) in Sertão, and the strongest persistence (highest predictability) in Zona da Mata. The results obtained by DFA provide information about the existence of long-term correlations (predictability) of dry/wet conditions at different accumulation scales and is useful for agricultural planning and water resource management in the region. The DFA box plots for each region and all accumulation scales are shown in Figure 9. The verification of a significant difference between the regions was performed using the Wilcoxon-Mann-Whitney test at the 5% significance level. The test results shown in Figure 9 demonstrate that there is a significant difference between DFA exponents of the regions on all time scales. Recently Adarsh et al. [58] applied multifractal detrended fluctuation analysis-MFDFA (which is a generalization of DFA method) on SPI series from 30 meteorological subdivisions of India. They found that SPI time series exhibit persistence properties, with stronger persistence for higher time scales. Tatli et al. [59] applied DFA on Palmer drought severity index (PDSI) from 212 meteorological stations in Turkey and found that the values of scaling exponents were between 0.5 and 1, indicating the persistence of meteorological drought, which varies across the region. Qualitatively, our results are similar to those reported in these studies. . The star symbol "*" indicates that there is a significant difference between the regions at the 5% significance level (pv < 0.05).

Detrended Fluctuation Analysis
We apply DFA analysis on SPI time series for all the 133 Pernambuco stations, and perform spatial interpolation of obtained scaling exponents, resulting in maps shown in Figure 8. The values of DFA exponents are greater than 0.5 and increase with SPI time scale, indicating stronger persistency and higher predictability of medium-term conditions in precipitation (SPI-3 and SPI-6), while for short-term conditions described by SPI-1, the DFA exponent is closer to 0.5 indicating weak persistency and low predictability. Long-term precipitation patterns described by SPI-12, show different behavior: in Sertão and Agreste, the values of DFA exponents are around 1, indicating strong persistency, while in Zona da Mata the value of the DFA exponent is found to be between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion (H = α − 1), meaning that SPI-12 increments exhibit anti-persistent long-term correlations. It can also be observed from Figure 6 that for short and medium conditions (SPI-1, SPI-3 and SPI-6), DFA exponents increase with decreasing distance to the ocean, indicating the weakest persistence (lowest predictability) in Sertão, and the strongest persistence (highest predictability) in Zona da Mata. The results obtained by DFA provide information about the existence of long-term correlations (predictability) of dry/wet conditions at different accumulation scales and is useful for agricultural planning and water resource management in the region. The DFA box plots for each region and all accumulation scales are shown in Figure 9. The verification of a significant difference between the regions was performed using the Wilcoxon-Mann-Whitney test at the 5% significance level. The test results shown in Figure 9 demonstrate that there is a significant difference between DFA exponents of the regions on all time scales. Recently Adarsh et al. [58] applied multifractal detrended fluctuation analysis-MFDFA (which is a generalization of DFA method) on SPI series from 30 meteorological subdivisions of India. They found that SPI time series exhibit persistence properties, with stronger persistence for higher time scales. Tatli et al. [59] applied DFA on Palmer drought severity index (PDSI) from 212 meteorological stations in Turkey and found that the values of scaling exponents were between 0.5 and 1, indicating the persistence of meteorological drought, which varies across the region. Qualitatively, our results are similar to those reported in these studies.  boxplots for each region for SPI at different time scales (SPI-1, SPI-3, SPI-6 and SPI-12). The star symbol "*" indicates that there is a significant difference between the regions at the 5% significance level ( < 0,05)

Conclusions
We analyze temporal fluctuations of Standardized Precipitation Index (SPI) for the period from 1950 to 2012 (calculated from monthly rainfall records from 133 gauging stations located in Pernambuco state, Brazil) by using three complementary methods: the Mann-Kendall test, Sen's slope, and detrended fluctuation analysis (DFA). The results are interpolated over the entire study area to investigate spatial distribution of trend and persistence of SPI time series at different time scales. Our main findings are: (i) for all time scales significant negative trends were obtained in the (deep inland) Sertão region (with decreasing magnitude from west to east) while significant positive trends are found in Agreste and Zona da Mata regions, with increasing magnitude towards the coast; (ii) SPI-1 series that describe short-term dry/wet conditions (related with meteorological types of drought along with short-term soil moisture and crop stress) exhibit values of DFA exponents close  boxplots for each region for SPI at different time scales (SPI-1, SPI-3, SPI-6 and SPI-12). The star symbol "*" indicates that there is a significant difference between the regions at the 5% significance level ( < 0,05)

Conclusions
We analyze temporal fluctuations of Standardized Precipitation Index (SPI) for the period from 1950 to 2012 (calculated from monthly rainfall records from 133 gauging stations located in Pernambuco state, Brazil) by using three complementary methods: the Mann-Kendall test, Sen's slope, and detrended fluctuation analysis (DFA). The results are interpolated over the entire study area to investigate spatial distribution of trend and persistence of SPI time series at different time scales. Our main findings are: (i) for all time scales significant negative trends were obtained in the (deep inland) Sertão region (with decreasing magnitude from west to east) while significant positive trends are found in Agreste and Zona da Mata regions, with increasing magnitude towards the coast; (ii) SPI-1 series that describe short-term dry/wet conditions (related with meteorological types of drought along with short-term soil moisture and crop stress) exhibit values of DFA exponents close Figure 9. DFA exponents α boxplots for each region for SPI at different time scales (SPI-1, SPI-3, SPI-6 and SPI-12). The star symbol "*" indicates that there is a significant difference between the regions at the 5% significance level (pv < 0.05).

Conclusions
We analyze temporal fluctuations of Standardized Precipitation Index (SPI) for the period from 1950 to 2012 (calculated from monthly rainfall records from 133 gauging stations located in Pernambuco state, Brazil) by using three complementary methods: the Mann-Kendall test, Sen's slope, and detrended fluctuation analysis (DFA). The results are interpolated over the entire study area to investigate spatial distribution of trend and persistence of SPI time series at different time scales. Our main findings are: (i) for all time scales significant negative trends were obtained in the (deep inland) Sertão region (with decreasing magnitude from west to east) while significant positive trends are found in Agreste and Zona da Mata regions, with increasing magnitude towards the coast; (ii) SPI-1 series that describe short-term dry/wet conditions (related with meteorological types of drought along with short-term soil moisture and crop stress) exhibit values of DFA exponents close to 0.5, indicating weak persistency and low predictability, while for medium-term conditions (SPI-3 and SPI-6, which are related with medium-term soil moisture conditions and seasonal to medium-term trends in precipitation) DFA exponents are greater than 0.5 and increase with accumulation period, indicating stronger persistency and higher predictability; (iii) for SPI-12 series that describe long-term precipitation patterns which are relevant for streamflows, reservoir levels, and groundwater levels, the values of DFA exponents for Sertão and Agreste are around 1, indicating strong persistency, while in the coastal Zona da Mata region the value of the DFA exponent is found to be between 1.0 and 1.5, indicating anti-persistent fractional Brownian motion; (iv) for both trend and persistence of SPI, we find a significant difference between the regions. While trend analysis of SPI was extensively studied for different parts of the world, much less is known about persistent properties of dry/wet conditions, at different time scales. Our results should be useful for agricultural planning and water resource management in the NEB and indicate that more studies should be dedicated to investigate long-term correlations in temporal series of various drought indices, in order to deepen the understanding of long-term predictability of dry/wet conditions of regions that are most vulnerable to extreme climatic episodes.
In conclusion, in order to assess different aspects of the phenomenon, we use a suite of complementary methods that are capable of revealing both tendencies and persistence (predictability) of the SPI index, at different time scales, in a geographically explicit setting. Therefore, the current work should not be seen as just a local case study, but rather as a contribution to establishing guidelines for a multi-dimensional approach, that may be used in other regions of the world.