Rainy Season Migration across the Northeast Coast of Brazil Related to Sea Surface Temperature Patterns

: Accurate regional seasonal forecasts of the rainy season are essential for the implementation of effective socioeconomic activities and policy. However, current characteristics of the period of occurrence of the rainy season in the Eastern Northeast Brazil (ENEB) region demonstrated that maximum precipitation varies substantially depending on the period analyzed. From 1972 to 2002, the rainy season occurred during the June–July–August (JJA) quarter, while from 1981 to 2011, it occurred in the April–May–June (AMJ) quarter. To access how these differences may be due to different patterns of sea surface temperature (SST), using observed precipitation and SST data from NOAA for the period from 1982 to 2018, this study identified the spatial patterns of inter-annual changes in Pacific and Atlantic SST related to the occurrence of the ENEB rainy seasons. We focus on the statistical method of symmetric mean absolute percentage error (sMAPE) for forecasting these periods based on SST information. Our results revealed five different quarterly periods (FMA, MAM, AMJ, MJJ, JJA) to the rainy season, in which MJJ is more prevalent. The sMAPE values of the SST patterns are inversely proportional to precipitation in the ENEB. Hence, it may be concluded that our climate analysis demonstrates that seasonal SST patterns can be used for forecasting the period of the rainy season.


Introduction
Oceanic regions cover more than two-thirds of our planet, being responsible for fundamental aspects of the Earth's climate system.Slowly evolving sea surface temperature (SST) anomalies act as heat sources or sink-altering atmospheric flow patterns [1], and studies that evaluated 20th-century SST trends found that global oceans warmed almost everywhere [2].This is worrying, since previous studies have suggested that El Niño-Southern Oscillation (ENSO) plays an important role in changes in hydrological processes at global [3][4][5][6] and regional scales [7][8][9].In addition, just as the seasonal cycle and inter-annual variability of SST influence the onset of the rainy season worldwide, climate change is also causing seasonality intensification, with rainy seasons becoming wetter, as already demonstrated by [10] for the ENEB region, using daily rainfall data during 1972 to 2002 to calculate the linear trend of rainfall events.A table of abbreviations is noted as Supplementary Materials (Table S1).
The rainy season is the time of the year when the majority of a country's or region's annual precipitation occurs.Unlike other parts of the world, where the rainy season is controlled by the monsoon, across Eastern Northeast Brazil (ENEB), the rainy season is mainly modulated by two meteorological systems fed by SST [11]: (1) Easterly Wave Disturbances (EWD); and (2) the Intertropical Convergence Zone (ITCZ).EWDs contribute at least 60% of the total rainfall over the east coast of ENEB throughout the rainy season, with the greatest occurrences from May to July being more (less) frequent during La Niña (El Niño) [12].On the other hand, the Atlantic ITCZ is the main rainfall atmospheric mechanism over the ENEB on submonthly time scales during the years of simultaneous occurrence of the La Niña and southward SST gradient in the intertropical Atlantic [13].
Studies have already shown that the occurrence period of the climatological rainy season in the ENEB region may vary depending on the period analyzed [10][11][12][13][14].These interval shifts for rainy season periods may be due to different patterns of SST, since several studies have shown that the ENEB precipitation is strongly dependent on SST patterns in the Pacific and Atlantic Oceans [15][16][17][18][19][20][21].However, although several studies have shown this strong connection, none of them take into account the seasonal variability of the global SST spatial patterns insofar as the occurrence of a specific rainy season is concerned.So, this is the first highlight of the work proposed here.
To fill this gap, the present study has the main aim of determining the spatial patterns of interannual changes of SST over the regions of the Pacific and Atlantic Ocean basins related to the occurrence of the ENEB rainy seasons, using observed precipitation and SST data for the period from 1982 to 2018.Furthermore, a new statistical method that uses only SST information as a proxy for forecasting the rainy season period is also proposed as an additional aim.So, this is the second highlight of this work, which demonstrates the novelty of the methodology here presented that proposes an approach that is less computationally demanding in comparison to the traditional dynamical downscaling method, and therefore more feasible operationally to be applied by regional meteorological services and to support the mitigation climate policy in the ENEB.
Despite this study providing a comprehensive view of the regions of the Pacific and Atlantic Oceans basins across the ENEB, and the method being proposed and applied for that specific region, both the ease of methodology application and the clarity of the obtained SST spatial patterns associated with the occurrence of the rainy season indicate that the methodology might be expanded to other regions and has a global interest with importance for general readers with high international impact.
Finally, the consequences arising from the occurrence of extreme precipitation events from SST positive anomalies can be extremely harmful.For example, in June 2010, the SST positive anomalies above 1 • C in the western Tropical South Atlantic favored convection and intense rains in the ENEB region [21], which led to floods and consequently resulted in a total of 67 damaged cities, 20 deaths, approximately 30,000 homeless people, and economic loss of approximately USD 1 billion [22].Hence, considering that extreme precipitation events across the ENEB are more frequent during the rainy season, previous identification of the core period of the climatological rainy season becomes crucial for many regional weather services.It demonstrates the importance and the main contributions and applications of this work, mainly for planning socioeconomic activities where weather services are particularly relevant, i.e., agriculture, construction, energy, insurance, telecommunication, tourism, transport, logistics, and water availability [23].Furthermore, anticipation or delay of the rainy season concerning the climatological core period has a very strong impact on the livelihood of people because it can create water scarcity or surpluses outside the expected rainy season, affecting the livelihood of local people.

Materials and Methods
The ENEB region study area, with coordinates on land between 5.5 • to 9.5 • S and 34.5 • W to 36 • W (Figure 1), was selected for being characterized as the rainiest region of the Northeast of Brazil (NEB), with mean annual precipitation above 1000 mm, influenced by the orographic effect.

Results and Discussion
The seasonal precipitation path to identify the dominant months of the rainy season is initially investigated.The monthly variation of precipitation for ENEB region during the period 1982 to 2018 is shown in Figure 2. Monthly climatology shows that the highest amount of precipitation occurs in June (204 mm) and the lowest precipitation is observed in November (18 mm) (Figure 2a).These results are consistent with those shown by [20,31].
A simple three-point moving average is also calculated.This analysis in essence consists of replacing the actual values of time series with a calculated mean value for filtering noise and converting the data into a relatively smooth curve [32].Figure 2a (red line) demonstrates a precipitation pattern with a unimodal distribution for the 3-month moving average.This highlights that the maximum amount of precipitation concerning regional patterns occurs in the period of the rainy season, indicating that a unique maximum point does exist.June represents the maximum point of the curve that corresponds to the climatological average.Thus, the climatological core period of the rainy season occurs within the May-June-July (MJJ) quarter, corroborating with [20,31].This result is in line with the highest-frequency period of the EWD events in ENEB [12].However, our result differs from the rainy season periods of [10,14], which were identified to occur in June-July-August (JJA) and April-May-June (AMJ), respectively.Differences may be attributed to distinct analyzed periods.
It has to be mentioned that considering the climatological period, rainy seasons may occur at different seasonal periods, and in the current case with a frequency of about 38% (14 years) in MJJ quarter, 30% (11 years) in AMJ quarter, 13% (5 years) in JJA quarter, 11% (4 years) in FMA (February-March-April) quarter and 8% (3 years) in MAM (March-April-May) quarter (Figure 2b).Here, we do not focus on the duration of the rainy seasons, i.e., in date of the onset and demise of the rainy season, but rather on the wettest quarter, which was then used to define the mean period of occurrence of the specific rainy season.Therefore, precipitation climatology in the ENEB (1982-2018) allowed for the identification of five different seasonal periods for rainy seasons: FMA, MAM, AMJ, MJJ, and JJA.To examine the seasonality of precipitation in the ENEB region, we analyzed precipitation information extracted from daily precipitation data produced by the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) from their website at https://psl.noaa.gov(accessed on 29 May 2019) [24,25].This dataset was constructed from gauge reports from over 30,000 stations collected from multiple sources.Orographic effects were corrected, and the optimal interpolation objective analysis technique was used to interpolate the daily dataset on a 0.5-degree latitude and longitude grid over the global land areas for the period 1 January 1979 to 31 December 2018.
For the Pacific and Atlantic Oceans, we focused our analysis on the observed SSTs obtained from the NOAA_OI_SST_V2 data provided by the NOAA/OAR/ESRL PSL, Boulder, Colorado, USA, from their Web site at https://psl.noaa.gov(accessed on 29 May 2019), and described by [26].These data provide monthly means of SSTs in the spatial resolution 1.0 degree (180 × 360) for the period 1981/12 to the present.For consistency, we used the precipitation and SST data for the common period of 1982-2018 (37 years).
The relationship between the SST variation and the period of the rainy seasons in ENEB was diagnosed from the statistical method of symmetric mean absolute percentage error (sMAPE) which can be calculated as follows: where Y t denotes the observation at time t and F t denotes the forecasts of Y t .The sMAPE is one of the most common percentage errors [27].The percentage error measures have the advantage of being scale-independent.Therefore, sMAPE is a kind of error that is more accurate and efficient in tracking the forecasting precision and performance evaluation, frequently when different scaled datasets are analyzed [28].Due to the error bounds defined, sMAPE is more resistant to outliers since it gives less significance to outliers compared to other measures that do not have bounds for errors.
Monthly data from the new global atmospheric reanalysis ERA5 were also used to examine the anomalies of zonal and meridional wind components associated with the rainy seasons between the period 1982-2018.ERA5 is the fifth-generation database produced by the European Centre for Medium-Range Weather Forecasts (ECMWF), available at https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5(accessed on 29 May 2019).ERA5 was produced using a sequential 4D-VAR data assimilation scheme with an improvement in horizontal resolution to ~30 km [29].
For rainy season forecast verification in ENEB, we chose a 2 × 2 contingency table, which is one of the most commonly used methods for dichotomous categorical verification of forecasts [30].

Results and Discussion
The seasonal precipitation path to identify the dominant months of the rainy season is initially investigated.The monthly variation of precipitation for ENEB region during the period 1982 to 2018 is shown in Figure 2. Monthly climatology shows that the highest amount of precipitation occurs in June (204 mm) and the lowest precipitation is observed in November (18 mm) (Figure 2a).These results are consistent with those shown by [20,31].Subsequently, with the identification of the five seasonal periods for rainy seasons, it is calculated the mean SST pattern associated with each quarterly period, and the anomaly concerning climatology (Figure 3).This is important to differentiate the SST distribution characteristic of these individual precipitation intervals (quarters).The warmest water is found in the western Pacific, with a maximum value of 29 °C.Concerning the FMA and MAM quarters, the central position of warm water ranged from the equator to about 15°S in the seasonal period during (or near) the austral autumn (Figure 3a,c).From AMJ to JJA, the highest SST region is featured by the movement from the Southern Hemisphere to the Northern Hemisphere (Figure 3e,g,i).In these seasons, the branch of warm water expands from the equator to about 20°N with a maximum value beyond 29 °C.
Seasonal SST over the Atlantic Ocean shows a similar pattern for the FMA and MAM quarters, with the highest values in the eastern equatorial region above 29 °C (Figure 3a,c).For the AMJ and MJJ quarters, a decrease in SST values is noted over the equatorial Atlantic (Figure 3e,g).During JJA, there is a weakening of the SST gradient east of the equatorial Atlantic in contrast to the increase in SST over the north Atlantic (Figure 3i).In general, each quarter related to the rainy season can be associated with a dominant SST response, which may be used to predict or anticipate the quarter of the rainy season each year.
It is found that the SST variability related to the rainy seasons in the seasonal periods over ENEB varies considerably over the Pacific and Atlantic Oceans (Figure 3b,d,f,h,j).Thus, a pattern of SST with positive anomalies in the Equatorial Western Pacific (EWP) and Equatorial Western Atlantic (EWA) and negative anomalies in the Equatorial Eastern Pacific (EEP), the Tropical South Atlantic (TSA), and the Tropical North Atlantic (TNA) produces precipitation patterns that promote a rainy season for the FMA period (Figure A simple three-point moving average is also calculated.This analysis in essence consists of replacing the actual values of time series with a calculated mean value for filtering noise and converting the data into a relatively smooth curve [32].Figure 2a (red line) demonstrates a precipitation pattern with a unimodal distribution for the 3-month moving average.This highlights that the maximum amount of precipitation concerning regional patterns occurs in the period of the rainy season, indicating that a unique maximum point does exist.June represents the maximum point of the curve that corresponds to the climatological average.Thus, the climatological core period of the rainy season occurs within the May-June-July (MJJ) quarter, corroborating with [20,31].This result is in line with the highest-frequency period of the EWD events in ENEB [12].However, our result differs from the rainy season periods of [10,14], which were identified to occur in June-July-August (JJA) and April-May-June (AMJ), respectively.Differences may be attributed to distinct analyzed periods.
It has to be mentioned that considering the climatological period, rainy seasons may occur at different seasonal periods, and in the current case with a frequency of about 38% (14 years) in MJJ quarter, 30% (11 years) in AMJ quarter, 13% (5 years) in JJA quarter, 11% (4 years) in FMA (February-March-April) quarter and 8% (3 years) in MAM (March-April-May) quarter (Figure 2b).Here, we do not focus on the duration of the rainy seasons, i.e., in date of the onset and demise of the rainy season, but rather on the wettest quarter, which was then used to define the mean period of occurrence of the specific rainy season.Therefore, precipitation climatology in the ENEB (1982-2018) allowed for the identification of five different seasonal periods for rainy seasons: FMA, MAM, AMJ, MJJ, and JJA.
Atmosphere 2024, 15, 713 5 of 13 Subsequently, with the identification of the five seasonal periods for rainy seasons, it is calculated the mean SST pattern associated with each quarterly period, and the anomaly concerning climatology (Figure 3).This is important to differentiate the SST distribution characteristic of these individual precipitation intervals (quarters).The warmest water is found in the western Pacific, with a maximum value of 29 • C. Concerning the FMA and MAM quarters, the central position of warm water ranged from the equator to about 15 • S in the seasonal period during (or near) the austral autumn (Figure 3a,c).From AMJ to JJA, the highest SST region is featured by the movement from the Southern Hemisphere to the Northern Hemisphere (Figure 3e,g,i).In these seasons, the branch of warm water expands from the equator to about 20 the EWP and TNA, and negative anomalies in the EEP and TSA (Figure 3h).The rainy season of the JJA period identified SST patterns with positive anomalies in the TSA and TNA, and negative anomalies in the EEP (Figure 3j).It is interesting to note that during the MJJ quarter, which corresponds to the most frequent period of the rainy season in the ENEB, the ENSO response is weak compared to other quarter periods, indicating that the rainy season is more related to the SST pattern in the Atlantic Ocean.Precipitation during austral autumn and winter in the ENEB are associated with southeast winds to the coast associated with the influence of the South Atlantic subtropical high (SASH) [16].Additionally, the AMJ quarter, which corresponds to about 30% occurrence of rainy seasons, is mainly linked to positive anomalies in the Tropical South Atlantic.According to [35], precipitation in the coastal region is influenced by the increase in the SST in the southwestern Atlantic, increasing the moisture flux convergence and convection.Seasonal SST over the Atlantic Ocean shows a similar pattern for the FMA and MAM quarters, with the highest values in the eastern equatorial region above 29 • C (Figure 3a,c).For the AMJ and MJJ quarters, a decrease in SST values is noted over the equatorial Atlantic (Figure 3e,g).During JJA, there is a weakening of the SST gradient east of the equatorial Atlantic in contrast to the increase in SST over the north Atlantic (Figure 3i).In general, each quarter related to the rainy season can be associated with a dominant SST response, which may be used to predict or anticipate the quarter of the rainy season each year.
It is found that the SST variability related to the rainy seasons in the seasonal periods over ENEB varies considerably over the Pacific and Atlantic Oceans (Figure 3b,d,f,h,j).Thus, a pattern of SST with positive anomalies in the Equatorial Western Pacific (EWP) and Equatorial Western Atlantic (EWA) and negative anomalies in the Equatorial Eastern Pacific (EEP), the Tropical South Atlantic (TSA), and the Tropical North Atlantic (TNA) produces precipitation patterns that promote a rainy season for the FMA period (Figure 3b).The rainy season in the MAM period is associated with SST patterns in the eastern of TNA and EEP (i.e., characteristic of the El Niño event), and negative anomalies in TSA (Figure 3d).Negative anomalies in the TSA SSTs observed in the first months of the year can anticipate the rainy season in the ENEB [33].A detailed location of the area range of Pacific and Atlantic Oceans is highlighted as supplementary material (Figure S1).
The AMJ period is favored from the rainy season when there are SST conditions with positive anomalies in the TSA, and negative anomalies in the EEP, indicating the characteristic pattern of the La Niña event and negative phase of the Atlantic dipole, respectively (Figure 3f).When the TSA is warmer, the oceanic and atmospheric conditions are favorable to higher monthly precipitation near the ENEB [14].The TSA contributes to precipitation increase in the ENEB through the transport of water vapor by the southeast trade winds (e.g., [34]).For the MJJ season, the SST patterns show positive anomalies in the EWP and TNA, and negative anomalies in the EEP and TSA (Figure 3h).The rainy season of the JJA period identified SST patterns with positive anomalies in the TSA and TNA, and negative anomalies in the EEP (Figure 3j).
It is interesting to note that during the MJJ quarter, which corresponds to the most frequent period of the rainy season in the ENEB, the ENSO response is weak compared to other quarter periods, indicating that the rainy season is more related to the SST pattern in the Atlantic Ocean.Precipitation during austral autumn and winter in the ENEB are associated with southeast winds to the coast associated with the influence of the South Atlantic subtropical high (SASH) [16].Additionally, the AMJ quarter, which corresponds to about 30% occurrence of rainy seasons, is mainly linked to positive anomalies in the Tropical South Atlantic.According to [35], precipitation in the coastal region is influenced by the increase in the SST in the southwestern Atlantic, increasing the moisture flux convergence and convection.
The relationship between SST patterns and rainy seasons in the ENEB is further investigated to determine its occurrence during the seasonal period, through a statistical analysis of the patterns of variability.This spatial variation in SST is based on a series of measures of aggregating error including regular patterns of variability, within the study period.The sMAPE metric has been used to compute deviations between the average and observed values for all 37 years during the five seasonal periods for rainy seasons.Regions of sMAPE with a low degree of error may indicate an area with a high degree of regularity that usually influences the occurrence of the rainy season period (Figure 4).Accordingly, the spatial distribution of sMAPE demonstrates where low values are located.
In general, different SST patterns related to sMAPE were identified during the five rainy seasons over ENEB.For the FMA season (Figure 4a), the Equatorial Eastern Atlantic (EEA), TNA and Western Tropical South Pacific (WTNP) regions showed low sMAPE values.The sMAPE index for the MAM season (Figure 4b) shows similar patterns to the FMA season; however, low sMAPE values were accompanied by an enlarged area over the EWA and WTNA regions.The high sMAPE values considerably decrease during the AMJ season (Figure 4c) over the tropical region, which presents the lowest sMAPE values in the TSA, EEA, and Western Tropical North Pacific (WTSP) regions.For the MJJ season (Figure 4d), there were widespread low sMAPE values, except for the Equatorial Eastern region of the Pacific and Atlantic.It is also seen for JJA season (Figure 4e), especially in the North Pacific, where there are branches of low sMAPE index expanding from western into eastern with below value beyond 1% between about 5 and 15 • N.
Atmosphere 2024, 15, x FOR PEER REVIEW 8 of 13 an increase in the rainfall in the ENEB, except in the northern region [42] might be expected.In the AMJ quarter, subtropical highs are completely absent over the Atlantic.This season is more related to the strengthening of trade winds (Figure 5d).As shown in Figure 3f, a warmer South Atlantic Ocean favors oceanic and atmospheric conditions which lead to higher monthly precipitation in the ENEB.The authors of [14] argue that this pattern represents more thermal energy and water vapor being transferred to the atmosphere.Once the wind field shows favorable conditions, this humidity may intensify the EWD, which is more frequent during the AMJ.Thus, we filter the regions with the sMAPE index below 1% and present the spatial distribution of ENEB rainy seasons (FMA, MAM, AMJ, MJJ, JJA) over the Atlantic and Pacific regions where the lowest value of sMAPE for each grid point is located (Figure 5a).It is found that there is no dominant rainy season when the lowest value of sMAPE happens over the whole Atlantic and Pacific.Therefore, the largest area of the spatial patterns of Pacific and Atlantic SST that favors the occurrence of the ENEB rainy seasons is for the JJA season (~2.465 × 10 7 km 2 )-followed by a gradual decline in MAM season with ~1.955 × 10 7 km 2 , FMA season with ~1.839 × 10 7 km 2 , MJJ season with ~1.694 × 10 7 km 2 and AMJ season with ~1.223 × 10 7 km 2 .
Anomalous winds in MJJ season are characterized by a strengthening of the SASH that favors the prevailing east and southeast winds over the east coast of NEB (Figure 5e).These atmospheric characteristics increase the advection of moisture from the ocean to the region enhancing atmospheric instabilities associated with the EWDs, which cause rain in the MJJ period [12].As documented by [31], during the months when the EWDs are active (MJJ) convergence areas located along the coastline of the ENEB region are noticed.For JJA, a high correlation exists between the northeast trade winds over the TSA (Figure 5f) and positive SST anomalies on the coast of NEB (Figure 3j).This rainy season is also influenced by the EWDs.According to [12], monthly EWD occurrence is higher between April and August.Additionally, we investigate the relation between the precipitation over ENEB and the sMAPE of the SST in the Atlantic and Pacific (Figure 6).We computed for each rainy season the average of the sMAPE and precipitation of all of the grid points within the region of the SST patterns and ENEB, respectively.Moreover, we analyze separately the data of the specific rainy season and climatological data.Our results indicate an inversely proportional relationship.More specifically, when the rainy season occurs, the value of sMAPE decreases and precipitation increases in the climatology of the region.
To verify the assumption of predicting the core period of the rainy season using only SST information through the statistical method, we examined the interannual variations of the relationship between the lowest sMAPE value and the highest precipitation that characterizes each rainy season (Figure 7).Our results confirm the aforementioned hypothesis, considering that during the 37-year analysis period, only 4 years (1993, 1994, The ocean-atmosphere interaction has a robust manifestation with the relationship between SST and surface wind stress in regions of strong SST gradients [36].Therefore, large-scale atmospheric characteristics delivered by surface wind anomalies also present a distinct pattern for each rainy season (Figure 5b-f).
During the FMA rainy season, there is a shift from the SASH to the coast of the South American continent and a strengthening of the North Atlantic subtropical high (NASH) favoring the trade wind strengthening in the Northern Hemisphere (Figure 5b).This results in the southward migration of the ITCZ, which is fed by warm and moist trade winds near the surface [37].As shown in Figure 3b, the tropical Atlantic SST anomalies are characterized by a typical north-south dipole-like pattern with negative anomalies on TNA and positive anomalies on TSA, primarily associated with weakened winds [2,[38][39][40][41].Therefore, the occurrence of the FMA rainy season in the ENEB can be associated with the anticipation of ITCZ's position on the furthest south.
In contrast with FMA, the MAM season has an intensification of the SASH favoring the trade wind strengthening in the Southern Hemisphere (Figure 5c).In addition, the Tropical Atlantic SST anomalies are in the positive phase of dipole mode in association with the ENSO pattern in the Tropical Pacific (Figure 3d).In this configuration of the Tropical Atlantic SST dipole and the Tropical Pacific SST, during austral autumn (MAM), an increase in the rainfall in the ENEB, except in the northern region [42] might be expected.
In the AMJ quarter, subtropical highs are completely absent over the Atlantic.This season is more related to the strengthening of trade winds (Figure 5d).As shown in Figure 3f, a warmer South Atlantic Ocean favors oceanic and atmospheric conditions which lead to higher monthly precipitation in the ENEB.The authors of [14] argue that this pattern represents more thermal energy and water vapor being transferred to the atmosphere.Once the wind field shows favorable conditions, this humidity may intensify the EWD, which is more frequent during the AMJ.
Anomalous winds in MJJ season are characterized by a strengthening of the SASH that favors the prevailing east and southeast winds over the east coast of NEB (Figure 5e).These atmospheric characteristics increase the advection of moisture from the ocean to the region enhancing atmospheric instabilities associated with the EWDs, which cause rain in the MJJ period [12].As documented by [31], during the months when the EWDs are active (MJJ) convergence areas located along the coastline of the ENEB region are noticed.For JJA, a high correlation exists between the northeast trade winds over the TSA (Figure 5f) and positive SST anomalies on the coast of NEB (Figure 3j).This rainy season is also influenced by the EWDs.According to [12], monthly EWD occurrence is higher between April and August.
Additionally, we investigate the relation between the precipitation over ENEB and the sMAPE of the SST in the Atlantic and Pacific (Figure 6).We computed for each rainy season the average of the sMAPE and precipitation of all of the grid points within the region of the SST patterns and ENEB, respectively.Moreover, we analyze separately the data of the specific rainy season and climatological data.Our results indicate an inversely proportional relationship.More specifically, when the rainy season occurs, the value of sMAPE decreases and precipitation increases in the climatology of the region.
Atmosphere 2024, 15, x FOR PEER REVIEW 10 of 13 2004, 2017) have not met our forecast criteria of the rainy season, which indicates a skill of 0.9.A perfect forecast has received a skill score of 1; therefore, our method indicates a relatively high accuracy for the prediction of the period of the rainy season in the ENEB.
In the four years that the maximum values of precipitation did not coincide with the minimum values of sMAPE, the highest precipitation occurred in the MJJ (Figure 7 × blue) while the lowest sMAPE occurred in two different rainy seasons periods: in JJA for 1993 and 2004 years and in AMJ for 1994 and 2017 (Figure 7 × red).In a study conducted by [43], the SST anomalies as the predictor field allowed for a reasonable predictability, with a 0.76 of correlation between the observed and the predicted precipitation time series for the FMA in the NEB.To verify the assumption of predicting the core period of the rainy season using only SST information through the statistical method, we examined the interannual variations of the relationship between the lowest sMAPE value and the highest precipitation that characterizes each rainy season (Figure 7).Our results confirm the aforementioned hypothesis, considering that during the 37-year analysis period, only 4 years (1993,1994,2004,2017) have not met our forecast criteria of the rainy season, which indicates a skill of 0.9.A perfect forecast has received a skill score of 1; therefore, our method indicates a relatively high accuracy for the prediction of the period of the rainy season in the ENEB.In the four years that the maximum values of precipitation did not coincide with the minimum values of sMAPE, the highest precipitation occurred in the MJJ (Figure 7 × blue) while the lowest sMAPE occurred in two different rainy seasons periods: in JJA for 1993 and 2004 years and in AMJ for 1994 and 2017 (Figure 7 × red).In a study conducted by [43], the SST anomalies as the predictor field allowed for a reasonable predictability, with a 0.76 of correlation between the observed and the predicted precipitation time series for the FMA in the NEB.

Conclusions
Since the period of the rainy season is of major interest for many regional weather services over the ENEB, it is important to find a reasonable way for its prediction.Our climate analysis demonstrates that seasonal SST patterns can be used for forecasting the period of the rainy season.It was found that the rainy season in ENEB is characterized by inter-annual SST variability, with five different seasonal periods (FMA, MAM, AMJ, MJJ, JJA) during 1982-2018.By analyzing the relationship between SST and precipitation from the statistical method, sMAPE, it has been identified the SST patterns in the regions of the Pacific and Atlantic oceanic basins for each quarterly period of the rainy season.This method is easily applicable since it depends solely on SST data.
The sMAPE values of the SST patterns were applied in the five different rainy seasons, showing an inversely proportional relationship with precipitation in the ENEB.This shows the importance of the studies related to the ocean-atmosphere interaction.Indeed, the lowest sMAPE value characterizes the highest precipitation in a given year, which determines the quarter of the rainy season.This method can be useful for predicting the period of the rainy season, with a forecast skill of 0.9.However, there may be limitations in their application such that it is necessary to know how this method will be used as a reference with prescribed SST simulations for future predictions.In general, the present study was conducted as a pioneer study that still needs to be further developed on different time scales.Nevertheless, this approach can help forecasters and assist decision making regarding the anticipation or delay of the rainy season in the ENEB.

Figure 1 .
Figure 1.Regional distribution of mean annual precipitation (mm•year −1 ) and location of the area of study (red).Database from National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center (CPC) [24,25].

Figure 3 .
Figure 3. Climatological seasonal SST ( • C) pattern (a,c,e,g,i); and SST ( • C) anomalies-differences between SST in the specific rainy season of the seasonal period years and SST climatological seasonal mean (b,d,f,h,j) in each quarterly period (FMA, MAM, AMJ, MJJ, JJA) from 1982 to 2018.

Figure 6 .
Figure 6.Bars showing data of mean precipitation (mm.monthly −1 ) over ENEB and seasonal mean sMAPE (%) of the SST over Pacific and Atlantic Oceans, for specific rainy season occurrence (black bars) and climatological 1982-2018 period data (grey bars).Values in bars are mean (white line), max and min variation.

Figure 6 .
Figure 6.Bars showing data of mean precipitation (mm•monthly −1 ) over ENEB and seasonal mean sMAPE (%) of the SST over Pacific and Atlantic Oceans, for specific rainy season occurrence (black bars) and climatological 1982-2018 period data (grey bars).Values in bars are mean (white line), max and min variation.

Figure 6 .
Figure 6.Bars showing data of mean precipitation (mm.monthly −1 ) over ENEB and seasonal mean sMAPE (%) of the SST over Pacific and Atlantic Oceans, for specific rainy season occurrence (black bars) and climatological 1982-2018 period data (grey bars).Values in bars are mean (white line), max and min variation.

Figure 7 .
Figure 7. Validation between maximum values of precipitation and minimum values of sMAPE during the five quarterly periods of the rainy seasons from 1982-2018.Green colors represent true; blue (precipitation) and red (sMAPE) colors represent false.
• N with a maximum value beyond 29 • C.