SST Indexes in the Tropical South Atlantic for Forecasting Rainy Seasons in Northeast Brazil

May-to-July and February-to-April represent peak rainy seasons in two sub-regions of Northeast Brazil (NEB): Eastern NEB and Northern NEB respectively. In this paper, we identify key oceanic indexes in the tropical South Atlantic for driving these two rainy seasons. In Eastern NEB, the May-to-July rainfall anomalies present a positive relationship with the previous boreal winter sea surface temperature anomalies (SSTA) in the southeast tropical Atlantic (20◦–10◦ S; 10◦ W–5◦ E). This positive relationship, which spread westward along the southern branch of the South Equatorial Current, is associated with northwesterly surface wind anomalies. A warmer sea surface temperature in the southwestern Atlantic warm pool increases the moisture flux convergence, as well as its ascending motion and, hence, the rainfall along the adjacent coastal region. For the Northern NEB, another positive relationship is observed between the February-to-April rainfall anomalies and the SSTA of the previous boreal summer in the Atlantic Niño region (3◦ S–3◦ N; 20◦ W–0◦). The negative remote relationship noticeable between the Northern NEB rainfall and the concomitant Pacific Niño/Niña follows cold/warm events occurring during the previous boreal summer in the eastern equatorial Atlantic. The southeastern tropical Atlantic and Atlantic Niño SSTA indexes may, then, be useful to predict seasonal rainfall over the Eastern and Northern NEB, respectively, for about a 6 month leading period. The ability of both southeastern tropical Atlantic and Atlantic Niño SSTA indexes to forecast the Eastern and Northern NEB rainfall, with about a 6 month lead time, is improved when these indexes are respectively combined with the Niño3 (5◦ S–5◦ N; 150◦–90◦ W) and the northeast subtropical Atlantic (20◦ N–35◦ N, 45◦ W–20◦ W), mainly from the 1970’s climate shift.


Introduction
The precipitation regime over Northeast Brazil (NEB) is known to be related to climatic variability in the tropical Atlantic [1][2][3][4][5][6][7][8][9][10][11][12]. The peak seasonal rainfall in Northern NEB (see black box in Figure 1a) is concomitant with the southernmost position of the intertropical convergence zone (ITCZ), which remains near the equator during February-March-April (FMA) (Figure 1a,c). The year-to-year variability of the seasonal rainfall in Northern NEB is affected by the inter-hemispheric mode of sea surface temperature (SST) in the tropical Atlantic, which is associated with the anomalous latitudinal displacement of the ITCZ [5,7,8,13] between February and May.
Atmosphere 2018, 9, x FOR PEER REVIEW 2 of 22 of sea surface temperature (SST) in the tropical Atlantic, which is associated with the anomalous latitudinal displacement of the ITCZ [5,7,8,13] between February and May. Several studies have also highlighted remote influence of the El Niño Southern Oscillation (ENSO) phenomena in the Pacific Ocean on the rainfall variability in NEB [14][15][16][17][18][19][20][21][22]. The ENSO phenomena, which reaches its mature phase during the boreal winter, and the inter-hemispheric mode of the tropical Atlantic are generally used to forecast the Northern NEB rainy season with a

Product Description Spatial and Temporal Resolutions Data Availability
Land area precipitation From the Global Precipitation Climatology Centre (GPCC). GPCC supplies the global land area precipitation calculated by objective analysis from dozens of thousands of rain gauge stations [41]. The full data reanalysis combined with monitoring (from 2014) version 7 is used in this work.
Monthly gridded data with 1 • × 1 • spatial resolution From 1901 to present and available at [42] Sea surface temperature (SST) From the Objectively Analyzed Air-Sea Fluxes Project-OAFlux of Woods Hole Oceanographic Institution (WHOI). The OAFlux product is synthesized using National Centers for Environmental Prediction (NCEP1, NCEP2), European Centre for Medium-Range Weather Forecasts (ECMWF) ERA40, and ERA-interim Re-analysis [43][44][45] Monthly data with 1 • × 1 • horizontal resolution Available from 1958 to present at [46] Reanalyzed Wind vectors, specific humidity, stream function, velocity potential and omega From the National Centers for Environmental Prediction/National Center for Atmospheric Research-NCEP/NCAR [47] Monthly data with regular horizontal grid of 2.5 • × 2.5 • and 17 pressure levels (mb) From 1948 to present at [48] Surface sea wind Combination of Quick Scatterometer (QuikSCAT) and Advanced Scatterometer (ASCAT) satellite measurements [49] Monthly data with 0.25 • × 0.25 • regular horizontal grid QuikSCAT data are available from July 1999 to November 2009 and ASCAT data from May 2007 to present. These data are supplied by CERSAT, Ifremer and are available at [50] The vertically integrated moisture flux convergence (MFC, in kg m −2 s −1 ) is calculated as follows: Atmosphere 2019, 10, 335

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where g is the gravitational acceleration (m s −2 ), Ps is the surface pressure (hPa), P 1 = 300 hPa, q is the specific humidity (g kg −1 ), V is the horizontal wind vector (m s −1 ), and dp is the change in pressure [51][52][53]. Monthly anomalies are estimated by removing the monthly climatology  from the monthly quantities.
We consider the three consecutive months that correspond to the occurrence of the highest seasonal rainfall over Northern and Eastern NEB, i.e., February-March-April (FMA) and May-June-July (MJJ), respectively, to define the peak of the rainy season in these regions. Limiting the rainy seasons to FMA and MJJ, in Northern NEB and Eastern NEB respectively, allows us to consider two seasons with completely distinct months. These two regions present a clear year-to-year variability in rainfall with selected long periods of wet and dry events [38].
The normalized rainfall anomalies in Northern and Eastern NEB are split into three different groups using the threshold of ±0.5 std. From the 56 year period (i.e., 1960-2015), the normalized rainfall anomalies greater than +0.5 std are considered WET events in FMA and MJJ over Northern and Eastern NEB, respectively ( Table 2). In contrast, those with anomalies less than −0.5 std are considered DRY events. The other years with values close to the climatological (seasonal) mean are considered neutral events. Using these criteria, 15 WET events and 19 DRY events are selected for Eastern NEB, and 19 WET events and 20 DRY events are selected for Northern NEB ( Table 2). The composites used in this study are based on the years of WET and DRY events selected above.  Lagged linear relationships (spatial and temporal) are identified between anomalies of different climatic fields (e.g., SST, surface wind), and the rainfall anomalies in MJJ over Eastern NEB and in FMA over the Northern NEB. For the lagged relationships, the seasons (three consecutive months) corresponding to the year preceding the rainy season in Eastern NEB and Northern NEB are indicated by (−1), e.g., July-August-September(-1) (JAS(−1)), and those of the current year (related to the rainy season) are indicated by (0), e.g., May-June-July(0) (MJJ(0)).

Results
In this section, we investigate the most consistent spatial-temporal relationship between the oceanic climate variables and rainfall variability over Eastern NEB in MJJ and Northern NEB in FMA. Figure 2a illustrates the lagged linear regression coefficient between the gridded SST and surface wind anomalies in November-December-January(−1) (NDJ(−1)) and the MJJ(0) Eastern NEB rainfall anomalies for the period 1960-2015. The correlation/regression is shown for NDJ because our preliminary study indicated that this season corresponds to the highest lagged correlation between tropical South Atlantic SSTA and MJJ rainfall anomalies in the Eastern NEB. An area with a significant positive regression coefficient between the NDJ(−1) SSTA and the MJJ(0) Eastern NEB rainfall anomalies is clearly identifiable in the eastern portion of the tropical south Atlantic, with a value greater than 60 mm month −1 / • C (correlation coefficient higher than +0.5). A northwesterly wind anomaly signal, significantly related to Eastern NEB rainfall, is noted over the area of positive significant coefficients observed with the SSTA. No significant relationship is noticeable between the tropical North Atlantic surface climatic variables (i.e., the SST and surface wind) and MJJ rainfall in Eastern NEB. These results suggest that there is a several month (about 6 month) leading influence of the SST-wind interactions of the tropical South Atlantic on the variability of seasonal rainfall in Eastern NEB.

Results for Eastern NEB
The significant positive relationship between the tropical South Atlantic SSTA and the MJJ Eastern NEB rainfall moves westward from NDJ and concentrates only near the NEB coast just before or during the rainy season ( Figure 2b). This observation is consistent with results in [38]. The westward displacement of the SSTA relationship is confirmed in Figure 2c Atlantic exhibit higher interannual variability than negative SSTA for the study period. Contrarily, negative SSTA present higher variability than positive SSTA from April to August. Figure 2e shows the longitude-time diagrams of the differences between composites (WET-DRY) of standardized SST anomalies, corresponding to rainfall events in Eastern NEB. The difference between composites of SSTA is positive during a long period of the year ( Figure 2e). As noted previously, a positive SST signal propagates westward from the African coast to the western part of the basin. The positive values of the WET-DRY difference start in the eastern part of the basin during the boreal fall of the year preceding the Eastern NEB rainfall events; they reach the western part at the beginning of the next year and then remain there until MJJ(0). The strongest values for the differences between SSTA composites are centered near 10 • W in DJF(0). The significant positive relationship between the tropical South Atlantic SSTA and the MJJ Eastern NEB rainfall moves westward from NDJ and concentrates only near the NEB coast just before or during the rainy season ( Figure 2b). This observation is consistent with results in [38]. The westward displacement of the SSTA relationship is confirmed in Figure 2c,d, in which we show the longitude-time diagram of the WET and DRY composites of standardized SSTA along the diagonal band indicated in Figure 2a. However, the largest values of the positive and negative SSTA linked to WET and DRY events, respectively, in Eastern NEB are not symmetric during the westward propagation. The high positive SSTA linked to WET events in Eastern NEB start early in the eastern To illustrate how the variability of the surface oceanic-atmospheric conditions in the tropical South Atlantic can be linked to the rainfall in Eastern NEB, we perform a longitude-time diagram of the MFC anomalies ( Figure 3). Positive anomalies of MFC are observed near the coast for the composite of WET years from MAM to MJJ (Figure 3a). For the composite of the DRY years, large negative anomalies of the MFC are marked from MAM to MJJ, with the highest values observed in MJJ ( Figure 3b). The amplitude of the negative MFC anomalies is stronger than that of the positive MFC anomalies near the Eastern NEB coast during the period corresponding to the peak of the rainy season. This suggests that the deficit of the MJJ Eastern NEB rainfall is highly associated with negative MFC anomalies over the oceanic region near the coast. The large negative MFC anomalies observed near the NEB coast in MJJ during the DRY years are certainly linked to the negative SSTA, which are high during the peak of the rainy season ( Figure 2c). In the same way, the relatively weak positive MFC anomalies noted near the NEB coast in MJJ during the WET years are linked to weak positive SSTA observed during MJJ. The difference between the WET and DRY composites of anomalies of MFC is positive and high from MAM to MJJ in the western part of the tropical South Atlantic (Figure 3c). between composites (WET-DRY) of standardized SST anomalies, corresponding to rainfall events in Eastern NEB. The difference between composites of SSTA is positive during a long period of the year ( Figure 2e). As noted previously, a positive SST signal propagates westward from the African coast to the western part of the basin. The positive values of the WET-DRY difference start in the eastern part of the basin during the boreal fall of the year preceding the Eastern NEB rainfall events; they reach the western part at the beginning of the next year and then remain there until MJJ(0). The strongest values for the differences between SSTA composites are centered near 10° W in DJF(0).
To illustrate how the variability of the surface oceanic-atmospheric conditions in the tropical South Atlantic can be linked to the rainfall in Eastern NEB, we perform a longitude-time diagram of the MFC anomalies ( Figure 3). Positive anomalies of MFC are observed near the coast for the composite of WET years from MAM to MJJ (Figure 3a). For the composite of the DRY years, large negative anomalies of the MFC are marked from MAM to MJJ, with the highest values observed in MJJ (Figure 3b). The amplitude of the negative MFC anomalies is stronger than that of the positive MFC anomalies near the Eastern NEB coast during the period corresponding to the peak of the rainy season. This suggests that the deficit of the MJJ Eastern NEB rainfall is highly associated with negative MFC anomalies over the oceanic region near the coast. The large negative MFC anomalies observed near the NEB coast in MJJ during the DRY years are certainly linked to the negative SSTA, which are high during the peak of the rainy season ( Figure 2c). In the same way, the relatively weak positive MFC anomalies noted near the NEB coast in MJJ during the WET years are linked to weak positive SSTA observed during MJJ. The difference between the WET and DRY composites of anomalies of MFC is positive and high from MAM to MJJ in the western part of the tropical South Atlantic ( Figure  3c). To define an oceanic index (i.e., SSTA) that could be used for forecasting the rainy season in Eastern NEB for a nearly 6 month leading time, we considered the oceanic zone and the season corresponding to the largest relationship with the SSTA (correlation coefficient > +0.5; Figure 2). Therefore, we chose the SETA limited oceanic region (10° S-20° S, 10° W-5° E) and the season NDJ (see Figure 2). To define an oceanic index (i.e., SSTA) that could be used for forecasting the rainy season in Eastern NEB for a nearly 6 month leading time, we considered the oceanic zone and the season corresponding to the largest relationship with the SSTA (correlation coefficient > +0.5; Figure 2). Therefore, we chose the SETA limited oceanic region (10 • S-20 • S, 10 • W-5 • E) and the season NDJ (see Figure 2).
To understand how the dynamic link between the SSTA in the SETA and subsequent rainfall events in Eastern NEB develop, we first analyzed the distribution of the lagged linear regression ( • C/ • C) of the SSTA in SETA during NDJ(−1), with the gridded SST and surface wind anomalies in MJJ(0) during 1960-2015 ( Figure 4a). This analysis highlights the link between the SSTA in SETA in NDJ(−1) and the gridded SST and surface wind anomalies over the entire tropical Atlantic basin in MJJ(0). It appears that this positive relationship passes through the oceanic portion near the eastern coast of Brazil, i.e., in the southwestern Atlantic warm pool [34,54,55], where the SITCZ signal is large (see Figure 1b). This observation supports the idea that a portion of the NDJ SSTA in SETA is transported westward to the coast of NEB. The interannual variability of the SITCZ should, then, be related to the westward propagating SSTA from the eastern part of the tropical South Atlantic. The NDJ SETA SSTA is also associated with an anomalous cyclonic surface atmospheric circulation (i.e., a convergence of surface winds) near the coast in MJJ. When located in the western part of the basin, the positive SSTA are also associated with anomalously low surface pressure and an upward vertical velocity at 500 hPa ( Figure 4b).
transported westward to the coast of NEB. The interannual variability of the SITCZ should, then, be related to the westward propagating SSTA from the eastern part of the tropical South Atlantic. The NDJ SETA SSTA is also associated with an anomalous cyclonic surface atmospheric circulation (i.e., a convergence of surface winds) near the coast in MJJ. When located in the western part of the basin, the positive SSTA are also associated with anomalously low surface pressure and an upward vertical velocity at 500 hPa ( Figure 4b).  Figure 5a presents the linear regression/correlation coefficients (with lags) between the surface wind and SSTA in July-August-September(-1) (JAS(−1)) and Northern NEB rainfall anomalies in FMA(0) for the period 1960-2015. We show the JAS(−1) correlation/regression because our preliminary analysis indicated the highest lagged relationship between SSTA in the tropical Atlantic and FMA Northern NEB rainfall anomalies for this season. A significant positive relationship  Figure 5a presents the linear regression/correlation coefficients (with lags) between the surface wind and SSTA in July-August-September(-1) (JAS(−1)) and Northern NEB rainfall anomalies in FMA(0) for the period 1960-2015. We show the JAS(−1) correlation/regression because our preliminary analysis indicated the highest lagged relationship between SSTA in the tropical Atlantic and FMA Northern NEB rainfall anomalies for this season. A significant positive relationship between the SST and the rainfall anomalies is observed in the tropical South Atlantic several months before the rainy season in Northern NEB. This positive relationship is located mainly in the equatorial and the eastern portions of the tropical South Atlantic (Figure 5a). For this period, the largest positive regression coefficient (~+100 mm month −1 / • C) is centered near 20 • S, off the Angola-Namibia coast. However, the highest correlation coefficient (>+0.5) is marked in the eastern equatorial Atlantic and along the eastern coast of the basin. A relatively weak negative, but significant, relationship between the JAS(−1) SSTA and the FMA(0) Northern NEB rainfall anomalies is observed in the eastern equatorial Pacific. Other weak negative, but significant, relationships are observed between the JAS(−1) SSTA in the subtropical North Atlantic, the South Atlantic, and the Indian Ocean. Another region with a positive relationship is in the southeastern Pacific (near 50 • S). The significant relationship noted in the different tropical basins suggests their potential link with Northern NEB rainfall variability. No clear relationship is observed between the JAS(−1) surface wind over the study region and the FMA(0) Northern NEB rainfall.  During the Northern NEB rainy season, i.e., FMA(0), the positive relationship in the tropical South Atlantic is moved to the center of the basin immediately south of the equator, and the inter-hemispheric mode is established with a large negative relationship in the tropical North Atlantic in FMA(0) (Figure 5b). This SST meridional mode in FMA is associated with a strong meridional gradient of surface wind, namely, the northeasterly (northwesterly) signal in the northern (southern) hemisphere.

Results for Northern NEB
The negative coefficient of the SSTA and the associated anomalous southeasterly surface wind are also increased in the equatorial Pacific during Northern NEB's rainy season. We also note a weak negative relationship for SSTA, which is associated with an abnormal westward surface wind in the equatorial Pacific during this season. Therefore, the well-known influence of the negative/positive phase of the tropical Atlantic inter-hemispheric mode and/or the La Niña/El Niño in the equatorial Pacific on the positive/negative anomalies of Northern NEB rainfall [5,7,8,10,12,13] is clearly visible, with the strongest signal occurring during the first months of the year (Figure 5b). Furthermore, a negative signal is also observed with the SSTA in the Indian Ocean.
Because the Northern NEB rainfall variability is also associated with the inter-hemispheric mode in the tropical Atlantic, we constructed a time-latitude diagram of the WET and DRY composites of the west-east (60 • W-15 • E) averaged standardized SSTA, as illustrated in Figure 5c 1), they correspond to the negative relationship noted between the Northern NEB rainfall anomalies and SSTA in the northeastern tropical Atlantic (Figure 5a). In the composite of the DRY events, negative SSTA are present in the tropical South Atlantic for several months, but significant negative SSTA are only observed in the equatorial Atlantic from JJA(−1) to NDJ(−1) (Figure 5d). During the peak rainy season in Northern NEB, significant positive SSTA are observed in the tropical North Atlantic, which illustrates a positive phase of the tropical Atlantic inter-hemispheric mode. However, as in Eastern NEB, the positive and negative SSTA in the tropical South Atlantic, linked to positive and negative anomalies of Northern NEB, respectively, are not symmetric. Positive SSTA in the tropical South Atlantic associated with positive rainfall anomalies are higher than negative SSTA associated with negative rainfall anomalies in Northern NEB. Part of the positive SSTA marked in the tropical North Atlantic during the first month of the calendar year also originates from the subtropical North Atlantic in JAS(−1) through an equatorward propagation in the composite of DRY events (Figure 5d). The difference between WET and DRY composites of SSTA corresponding to Northern NEB rainy season has the same evolution, with significant positive SSTA noted in the WET composite (Figure 5e). This reinforces the observation that positive SSTA in the tropical South Atlantic linked to positive anomalies of Northern NEB's rainfall are larger than negative SSTA associated with negative anomalies of rainfall. The equatorward displacement of SSTA from the subtropical North Atlantic is also observed in the difference between the WET and DRY composites.
Using the same investigative methodology as in the Eastern NEB scenario, we now consider the most suitable oceanic zone and period to select an oceanic index (i.e., SSTA) that can help in forecasting the subsequent rainy season in Northern NEB. Based mainly on the SST vs. rainfall correlation/regression coefficient shown in Figure 5a, we consider the equatorial SSTA index during JAS(-1). For convenience and to connect our results with other historical studies, we chose the ATL3 region (3 • N-3 • S, 20 • -0 • W), which shows the highest lagged correlation coefficient with Northern NEB rainfall. This ATL3 region was previously defined in [56] and has been used by several other authors [26,57].
For the complete series of 1960-2015, the correlation between the JAS(−1) SSTA in the ATL3 and the FMA(0) rainfall anomalies in Northern NEB (i.e., the SSTA time series leads the rainfall anomaly time series by more than 6 months) is +0. 42. Considering the period in the 1980's , which corresponds to the period of the strengthening of the relationship between the boreal summer Atlantic Niño/Niña and the following boreal winter Pacific Niña/Niño [26], the correlation between the JAS(−1) ATL3/SSTA and the FMA(0) rainfall in Northern NEB reaches +0.60. No significant relationship is observed between the JAS(−1) ATL3/SSTA and the FMA(0) rainfall anomalies in Northern NEB for the period of 1960-1980. Figure 5f displays the 25 y (centered) running correlation between the JAS(−1) ATL3 SSTA and the FMA(0) rainfall anomalies in Northern NEB for the period 1960-2015. Although the correlation is significant along the study period, except the first point (period 1960-1984) where the correlation is not significant, a clear increase of the correlation can be observed from the 1980's to recent years. This increase in correlation could be linked to the 1970's climate shift discussed earlier. Therefore, the strengthening of the relationship between the summer equatorial Atlantic SSTA and the FMA rainfall anomalies in Northern NEB potentially emerges from the change in the Atlantic-Pacific Niño connection during recent decades. The increase in this relationship could also come from the better quality of the observations from the 1970's. This change in the relationship between oceanic-atmospheric variables and the rainfall anomalies, according to the study period, is also observed for the Eastern NEB case (not shown). Indeed, the spatial distribution of the correlation coefficient between the MJJ(0) Eastern NEB rainfall anomalies and the NDJ(−1) gridded SSTA exhibits high significant positive values (>0.5) in a wide part of the tropical South Atlantic, including the SETA and the ATL3, for the period 1980-2015 (not shown). A weak significant negative relationship is also observed between the Eastern NEB rainfall and SSTA in the eastern equatorial Pacific for the period 1980-2015. However, the likely physical mechanism that links the tropical South Atlantic SSTA to the Eastern NEB rainfall anomalies is the same for the reduced (1980-2015) and entire  study periods.
We also analyze the physical processes that link Accordingly, we now focus on the analysis of the Northern NEB case for all years of the period 1980-2015 that presents a highly positive relationship between JAS(−1) ATL3/SSTA and the FMA(0) rainfall anomalies in Northern NEB. Figure 6a is the latitude-time diagram of the linear correlation/regression of the west-east (60 • W-15 • E) averaged SSTA with FMA(0) rainfall anomalies in Northern NEB for the period 1980-2015. This figure displays a positive coefficient inside the tropical South Atlantic from MAM(−1) to SON(−1), i.e., more than 6 months before the FMA(0) rainy season in Northern NEB. Two regions with the strongest positive relationships (>+80 mm month −1 / • C) are noticeable during this period: the first one is in the 15 • -20 • S latitude band in JJA(−1), which is associated with the Benguela Niño, and the second one is in the equatorial band in JAS(−1), which is associated with the Atlantic equatorial mode (see Figure 5a). Previous studies have reported a connection between these two regions [57][58][59]. One of the principal mechanisms that connect these two regions are Kelvin waves, which are excited by zonal wind anomalies in the equatorial west Atlantic and propagate along the equator and the African coast [59,60]. The time lag between these regions with the largest positive relationships agrees with the results in [57,59], which indicated that the Benguela Niño precedes the equatorial Atlantic mode by an average of one to three months. During the first months of the following year, an inter-hemispheric mode pattern, negative coefficient in the northern hemisphere, and positive coefficient in the southern hemisphere, are observed, although with a small area of positive coefficients in the tropical South Atlantic that is centered approximately at 15 • S. These results, once again, suggest that the positive/negative SSTA in the tropical South Atlantic during the previous boreal summer were followed by positive/negative rainfall anomalies during the FMA(0) in Northern NEB.
the African coast [59][60]. The time lag between these regions with the largest positive relationships agrees with the results in [57,59], which indicated that the Benguela Niño precedes the equatorial Atlantic mode by an average of one to three months. During the first months of the following year, an inter-hemispheric mode pattern, negative coefficient in the northern hemisphere, and positive coefficient in the southern hemisphere, are observed, although with a small area of positive coefficients in the tropical South Atlantic that is centered approximately at 15° S. These results, once again, suggest that the positive/negative SSTA in the tropical South Atlantic during the previous boreal summer were followed by positive/negative rainfall anomalies during the FMA(0) in Northern NEB.   Like for the scenario in the Eastern NEB, we investigated the dynamical link between the SSTA in the ATL3 and the rainfall anomaly events in Northern NEB for the period 1980-2015.
The spatial distribution of the lagged linear correlation/regression between the gridded SST ( • C/ • C) and surface wind (u and v, m s −1 / • C) anomalies over the global ocean in FMA(0), and the SSTA inside ATL3 in JAS(−1), for the period 1980-2015 is presented in Figure 7a. This figure displays the link between the JAS(−1) SSTA in the ATL3 and the gridded SST and surface wind anomalies over the global ocean during the peak of the rainy season in Northern NEB. The signal of SSTA regression is largely negative throughout the central and eastern equatorial Pacific, indicating a high link between the JAS(−1) Atlantic Niño and the FMA(0) Pacific Niña. This observation is consistent with previous results by [26], who suggested a relationship between the boreal summer ATL3 and the boreal winter Pacific Niño for the period 1979-2001. No significant relationship is observed in the tropical Atlantic from SSTA, suggesting that the positive anomalies of the ATL3/SSTA in JAS(−1) is not generally linked to the SSTA in the tropical Atlantic during the following FMA. With respect to the response of surface atmospheric circulation, northeasterly wind anomalies are especially marked in the tropical North Atlantic. The signal observed with the surface winds suggests that the response of the tropical North Atlantic to the boreal summer ATL3/SSTA is more significant through the surface atmospheric circulation than through the SSTA. This indicates that the SST inter-hemispheric mode associated with Northern NEB rainfall variability in FMA(0) is not significantly related to the JAS(−1) ATL3 SSTA. The weak (no significant) relationship observed between the JAS(−1) ATL3/SSTA and the FMA(0) SST inter-hemispheric mode in the tropical Atlantic, mainly in the tropical North Atlantic, indirectly suggests a weak relationship between the FMA ENSO and the FMA tropical North Atlantic SSTA, at least for the period 1980-2015. The analysis of the correlation between the FMA(0) Niño3 (5 • S-5 • N; 150 • W-90 • W) SSTA and the FMA(0) gridded SST and surface winds anomalies also indicates a weak significant positive correlation value (less than +0.5) with SSTA. However, a high significant northward surface wind relationship is observed in the tropical North Atlantic (not shown). Note that no significant correlation is observed between the FMA(0) Niño3 SSTA and the FMA(0) tropical South Atlantic SSTA. Accordingly, the ENSO influence in the tropical North Atlantic is more significant on the surface atmospheric circulation than on the SSTA for the period 1980-2015. The weak positive relationship between the ENSO and the tropical North Atlantic SSTA could be associated with the early conditions of SSTA in the tropical Atlantic. These results are coherent with previous results [5,24,61], who indicated a preconditioning role of tropical Atlantic variability on the development of the ENSO teleconnection. Additionally, a recent study in [62] indicated that the positive relationship between the El Niño and the tropical North Atlantic SSTA is not stationary and depends on the Atlantic multi-decadal oscillation. The distribution of the lagged linear regression between the JAS(−1) ATL3/SSTA and the gridded velocity potential and stream function anomalies at 200 hPa over the global ocean in FMA(0) exhibits two cyclonic motions on both sides of the equator and convergent motion over the tropical Pacific (Figure 7b). In the Atlantic, a convergent motion is observed at 200 hPa over the Northern Hemisphere with two anticyclonic motions on both sides of the equator at 200 hPa. These results support a teleconnection between the JAS(−1) Atlantic Niño and the FMA(0) Pacific Niña by affecting the Walker circulation [26,28], which, in turn, significantly influences the northern hemisphere's atmospheric circulation in the Atlantic. Although no significant relationship has been observed between the JAS(−1) ATL3/SSTA and the FMA(0) tropical Atlantic SSTA (or the inter-hemispheric mode), the atmospheric circulation in the tropical North Atlantic induces anomalous latitudinal displacement of the ITCZ. This agrees with the results in [17], who suggested that a part of the seasonal rainfall over Northern NEB is directly influenced by the Walker circulation anomalies induced in the eastern tropical Pacific by modulating the ITCZ position in the tropical Atlantic.  [26,28], which, in turn, significantly influences the northern hemisphere's atmospheric circulation in the Atlantic. Although no significant relationship has been observed between the JAS(−1) ATL3/SSTA and the FMA(0) tropical Atlantic SSTA (or the inter-hemispheric mode), the atmospheric circulation in the tropical North Atlantic induces anomalous latitudinal displacement of the ITCZ. This agrees with the results in [17], who suggested that a part of the seasonal rainfall over Northern NEB is directly influenced by the Walker circulation anomalies induced in the eastern tropical Pacific by modulating the ITCZ position in the tropical Atlantic.

Forecast Ability of the Southeastern Tropical Atlantic and Atlantic Niño Indexes
In this section, we test the ability of the southeastern tropical Atlantic (SETA; 10 • S-20 • S, 10 • W-5 • E) and the Atlantic Niño (ATL3; 3 • N-3 • S, 20 • W-0 • ) indexes to forecast, respectively, the Eastern and Northern NEB rainfall with a 6 month lead time using cross-validation for the period 1980-2015. The cross-validation method consists in calculating the amount of rainfall using the linear regression coefficients obtained after excluding from the series the year for which the rainfall is predicted.
For the Eastern NEB, the correlation between the MJJ rainfall predicted from the NDJ SETA and the observed MJJ rainfall is 0.51, with a root mean square error (rmse) of 109 mm (Table 3). We also evaluate the forecast ability of the NDJ NINO3 (5 • N-5 • S, 150 • W-90 • W) index that shows a significant weak negative relationship with the MJJ Eastern NEB rainfall for the period 1980-2015. The correlation between the MJJ Eastern NEB rainfall predicted from NDJ NINO3 and the observed MJJ rainfall is weak (0.29). However, when we combine the SETA and NINO3 indexes (multiple linear regression), the prediction skill is significantly increased with a correlation of 0.76 and a rmse of 83 mm. The correlation between the NDJ SETA and the NDJ NINO3 indexes is 0.23 (not significant at 95% confidence level), i.e., these two indexes can be considered independent. For the Northern NEB case, we use the JAS ATL3, the JAS NINO3 and the JAS northeastern subtropical Atlantic (NESTA; 20 • N-35 • N, 45 • W-20 • W) indexes because the three regions are significantly (at 95% confidence level) correlated with the FMA Northern NEB rainfall. The correlation between JAS ATL3 and JAS NINO3 indexes is −0.32 and the correlation between JAS ATL3 and JAS NESTA indexes is 0.14 (not significant at a 95% confidence level). The FMA Northern NEB rainfall predicted from the JAS ATL3 and the FMA observed rainfall present a correlation of 0.52 with a rmse of 137 mm. The correlation of the JAS NINO3 prediction of the FMA rainfall with the observed FMA rainfall is 0.27, and the rmse is 154 mm. When combining the ATL3 and NINO3 indexes, the prediction skill is not different from the skill obtained using the ATL3 index alone. However, the combination of the JAS ATL3 and JAS NESTA improves the prediction skill of the FMA Northern NEB rainfall. The correlation coefficient is 0.65 and the rmse is 121 mm. Therefore, a very high skill is reached when the NDJ SETA and NDJ NINO3 are combined to predict the MJJ Eastern NEB, although the NDJ SETA alone already shows a good result for the period 1980-2015. For the prediction of the FMA Northern NEB rainfall, the highest skill is achieved when we combine ATL3 and the NESTA, though ATL3 alone also presents a good skill.

Summary and Conclusions
The tropical South Atlantic is a key region that fully contributes to the seasonal and interannual variability of the rainy seasons over Northeast Brazil. The climatic impact of the tropical South Atlantic on Eastern NEB is a determining factor related to abnormal episodes during the rainfall season, i.e., in MJJ. Several months before this rainy season, and particularly during the previous austral summer, SSTA appeared in the southeastern tropical Atlantic near the African coast. Then they propagated northwestward (associated with a coherent modulation of the trade winds), modifying the convective system above the southwestern Atlantic warm pool near the Northeast Brazilian coast and contributing to abnormal episodes during the subsequent rainy season in Eastern NEB. The relationship with SSTA is positive, i.e., a warm/cold SST event is associated with wet/dry episodes in Eastern NEB. Interestingly, positive and negative SSTA that were linked to the WET and DRY episodes, respectively, are not symmetric in terms of the westward propagation of the anomalies. The high positive SSTA start during the last six months (boreal summer and fall) of their previous calendar year in the eastern portion of the basin and reached the western portion during the first months of the following year. Moreover, the negative anomalies spread from east to west during the boreal winter and spring of the calendar year. The convective activities over the southwestern Atlantic warm pool, which are maintained by the seasonal development of the southern ITCZ during the rainy season in Eastern NEB, appear to be the predominant component linked to the seasonal rainfall. This scenario between the SSTA in the tropical South Atlantic and the rainfall anomalies in Eastern NEB is essentially confined to these two regions, even if a weak negative relationship exists with ENSO events. Figure 8a displays the seasonal evolution of the linear correlation between MJJ rainfall anomalies in Eastern NEB and the SETA, moving SSTA from JJA(−1) to MJJ(0) for the period 1980-2015. This Figure illustrate that the highest significant positive correlation (~+0.6) is observed in NDJ. The positive relationship is also significant in NDJ when we consider the entire tropical South Atlantic SSTA. However, the tropical North Atlantic does not present any significant relationship with the MJJ rainfall anomalies in Eastern NEB. Therefore, the SSTA index in the southeastern tropical Atlantic appears as a valuable index that should be used by climate centers for forecasting the MJJ seasonal rainfall in Eastern NEB with about a 6 month lead time (Figure 8a). Interestingly, the combination of the southeastern tropical Atlantic SSTA index with the Niño3 index clearly improves the nearly 6 month forecast of Eastern NEB, especially since the 1970's climate shift.
The Northern NEB scenario is different from that of Eastern NEB, although relevant similarities exist. Indeed, for both regions, strong SSTA occur in the center and eastern portions of the tropical South Atlantic during the boreal summer and fall of the previous calendar year. The Northern NEB scenario is positive (i.e., warm/cold SST associated with more/less rainfall). Here, again, the amplitudes of the composites of warm and cold SSTA are not symmetric. Warm events in the ATL3 in JAS are more marked than cold events. This suggests that positive ATL3 SSTA are better associated with more Northern NEB rainfall than negative ATL3 SSTA are associated with less rainfall. Furthermore, a progressive establishment of the wind/SST gradient over the entire tropical Atlantic was observed (during its positive phase) with a warm SST/relaxation of the southeasterly winds and a cold SST/intensification of the northeasterly winds. The inverse occurs during the negative phase. These dynamics respond to the wind/SST mechanism throughout the tropical Atlantic. This inter-hemispheric mode (already well known for its impact on rainfall in NEB) is directly linked to the meridional displacement of the ITCZ, i.e., an abnormal southward (northward) displacement that favors strong (weak) rainfall in NEB, particularly in Northern NEB. Our results support the idea that both ATL3 (or the tropical South Atlantic) and the inter-hemispheric mode in the tropical Atlantic (highest negative correlation coefficient in FMA(0)) are valuable for the predictability of seasonal rainfall in Northern NEB. However, the predictive skill, more than 6 months in advance, comes mainly from tropical South Atlantic (or ATL3) SSTA, whereas shorter lead time predictions may better benefit from the Atlantic SST inter-hemispheric mode (Figure 8b). The highest relationship between the inter-hemispheric mode and the Northern NEB rainfall, noticed for shorter lead time, is mainly associated with SSTA in the tropical North Atlantic (Figure 8b). It is shown that the July-September ATL3 and the December-March inter-hemispheric mode are not significantly correlated. Therefore, these two indexes will be of great importance in predicting Northern NEB rainfall. Moreover, the present study confirms that the climate variability in Northern NEB is strongly linked to ENSO events. Although the Niño3 index is negatively correlated with the Northern NEB rainfall from a long leading time, the largest negative relationship is observed just before and during the rainy season (Figure 8b). These observations agree with the results of earlier studies [5,13,24], which showed a negative relationship between the SSTA in the tropical South Atlantic and the opposite phase of ENSO events in the Pacific several months later. However, the teleconnection between the boreal summer Atlantic Niño and the boreal winter Pacific Niño and their influence on the rainfall in Northern NEB is remarkably high since the recent 1970's climate shift. Significant weak negative relationship is also noted between the FMA(0) Northern NEB rainfall and the JAS(−1) SSTA in the northeast subtropical Atlantic, suggesting a potential leading influence of this region on the rainfall. The combination of the JAS Atlantic Niño SSTA index with the JAS northeast subtropical Atlantic SSTA enlarges the 6 month forecast ability of the Northern NEB rainfall. It is important to note that our study does not show significant relationship between the SSTA in the Atlantic Cold Tongue region (i.e., ATL3) during the boreal summer and the inter-hemispheric mode of SST in the following boreal spring. Nonetheless, the relationship, which transits through the central-eastern tropical Pacific, is significant for the surface and high level (200 hPa) atmospheric circulation in the tropical North Atlantic.
Atmosphere 2018, 9, x FOR PEER REVIEW  17 of 22 austral summer, SSTA appeared in the southeastern tropical Atlantic near the African coast. Then they propagated northwestward (associated with a coherent modulation of the trade winds), modifying the convective system above the southwestern Atlantic warm pool near the Northeast Brazilian coast and contributing to abnormal episodes during the subsequent rainy season in Eastern NEB. The relationship with SSTA is positive, i.e., a warm/cold SST event is associated with wet/dry episodes in Eastern NEB. Interestingly, positive and negative SSTA that were linked to the WET and DRY episodes, respectively, are not symmetric in terms of the westward propagation of the anomalies. The high positive SSTA start during the last six months (boreal summer and fall) of their previous calendar year in the eastern portion of the basin and reached the western portion during the first months of the following year. Moreover, the negative anomalies spread from east to west during the boreal winter and spring of the calendar year. The convective activities over the southwestern Atlantic warm pool, which are maintained by the seasonal development of the southern ITCZ during the rainy season in Eastern NEB, appear to be the predominant component linked to the seasonal rainfall. This scenario between the SSTA in the tropical South Atlantic and the rainfall anomalies in Eastern NEB is essentially confined to these two regions, even if a weak negative relationship exists with ENSO events. Figure 8a displays the seasonal evolution of the linear correlation between MJJ rainfall anomalies in Eastern NEB and the SETA, moving SSTA from JJA(−1) to MJJ(0) for the period 1980-2015. This Figure illustrate that the highest significant positive correlation (~ +0.6) is observed in NDJ. The positive relationship is also significant in NDJ when we consider the entire tropical South Atlantic SSTA. However, the tropical North Atlantic does not present any significant relationship with the MJJ rainfall anomalies in Eastern NEB. Therefore, the SSTA index in the southeastern tropical Atlantic appears as a valuable index that should be used by climate centers for forecasting the MJJ seasonal rainfall in Eastern NEB with about a 6 month lead time (Figure 8a). Interestingly, the combination of the southeastern tropical Atlantic SSTA index with the Niño3 index clearly improves the nearly 6 month forecast of Eastern NEB, especially since the 1970's climate shift.  Correlations higher than ± 0.32 are significant at a 95% confidence level, according to the t-test, for (a,b).