The Covariability of Sea Surface Temperature and MAM Rainfall on East Africa Using Singular Value Decomposition Analysis

The study assesses the covariability of Sea Surface Temperature (SST) and March to May (MAM) rainfall variability on East Africa (EA) from 1981 to 2018. Singular Value Decomposition (SVD) analysis reveals the significant influence of SST anomalies on MAM rainfall, with covariability of 91%, 88.61%, and 82.9% for Indian, Atlantic, and the Pacific Ocean, respectively. The Indian Ocean explains the variability of rainfall to the large extent followed by the Atlantic Ocean and the Pacific Ocean. The rainfall patterns over the EA correspond to SST variability over the western, central, and eastern Indian Ocean. Likewise, the variability of SST anomalies was observed over the central, south, and north of the Atlantic Ocean while the Pacific Ocean captured the El Nino Modoki (ENSO) like pattern in the SVD1 (SVD2). The heterogeneous correlation of Indian SST anomalies and rainfall over EA of the first (second) principal component (PC) shows a positive correlation over much of the domain (central region). The SST anomalies over the Pacific Ocean show higher correlation values with the rainfall over much of the study domain except over the southwestern highland and southern region of Tanzania. Over the Atlantic Ocean, the correlation result shows the patterns of positive (negative) values over the northern (southern) part for PC1, while PC2 depicts negative correlation values over much of the Ocean. SST anomalies over the Indian (Atlantic) Ocean are highly correlated with MAM rainfall when SST leads by 1(7) month(s). The Pacific Ocean shows a weak (strong) correlation across all (zero) lead seasons.


Introduction
Rainfall is a very important parameter of weather and climate system in the region of EA. This is particularly common in the countries whose economy relies on rain-fed agriculture (Thornton et al., 2010;Ongoma et al., 2015;Brigadier et al., 2016), that contribute about 40% of gross development product (GDP) and employs about 80% of the active population (Mikova, 2015;Ongoma & Chen, 2017). Due to rainfall variability, the region of EA is affected by extreme weather events, such as floods and droughts (Anyah & Semazzi, 2006;Ber-hane & Zaitchik, 2014;MacLeod, 2018) which have impacts to the environmental and socio-economic activity of the region (IPCC, 2007;Ongoma, 2013).
The inter-annual rainfall variability over the region is attributed to the zonal circulation of the Indian ocean (Mafuru & Guirong, 2018;Limbu & Guirong, 2019). Previous studies discussed the influence of SST on seasonal rainfall variability over the region (Hastenrath et al., 2010;Mikova 2015). The same results have been found by Ngarukiyimana et al. (2018) and Camberlin (2018). During MAM rainfall season, the region receives intense rainfall due to the warmer SST in the western Indian ocean (Yang et al., 2015). The dry phases during the MAM season are associated with warmer SSTs over the western tropical Pacific and cooler SSTs over the central and eastern tropical Pacific Lyon et al., 2014;Yang et al., 2015). Thus, correspond to the intensification of Mascarene and Saint Helen anticyclones which trans-port the humidity air from the Atlantic Ocean passing through the Congo basin and Lake Kivu bringing the moisture and enhance precipitation over the region (Anyah & Semazzi, 2006).
However, there are still many unresolved questions concerning the factors influencing MAM rainfall variability over EA meanwhile the prediction skill for MAM rainfall over the region is about 80% (Walker et al., 2019) which is not sufficient enough. This study aims to analyze how the SST varies with the rainfall over the region. The outcome of this study provides important information for climate services end users which help for reducing the vulnerability to the climate related destruction, damage, and losses.
The remaining parts are subdivided into the following sections: Data and methodology are detailed in section 2. The results and discussion are explained in the section 3. The final remarks of this study are addressed as the conclusion in section 4.

Data sources
The gridded observation monthly precipitation dataset produced by the Climatic Research Unit (CRU) at the University of East Anglia was used in this study. The dataset is of version 4.03 (CRU TS 4.03) for the period 1981-2018 covering the land surface at 0.5º x 0.5º resolution. The same dataset taken from http://data. ceda.ac.uk/badc/cru/data/cru_ts/cru_ts_4.03/data/ pre was successfully used by Harris et al. (2019). Moreover, previous researchers used the CRU dataset to investigate the variability of rainfall over the study region (Ogwang et al.,2015;King'uza and Limbu, 2019). The SST dataset used is the Extended Reconstructed Sea Surface Temperature version 5 (ERSSTv5) with a resolution of 2º x 2º from 1981 to 2018. The dataset is acquired from the National Oceanic and Atmospheric Administration/ National Climatic Data Center, NOAA NCDC (http://iridl.ldeo.columbia.edu/ SOURCES/.NOAA/.NCDC/.ERSST/. version5/. sst) and was used by Huang et al. (2017). These datasets were used to analyze how the SST varies with rainfall over EA.

Methodology
The SVD was used to analyze the covariability between MAM precipitation over EA and the SST in the Tropical Oceans (i.e. Atlantic, Indian, and Pacific). The SVD approach has the advantage of evaluating the cross-covariance matrix of two spatial-temporal fields to identify regions of similar behaviour (Aziz et al., 2010). The same technique was used by Ogou et al., 2016;Dubache et al. 2019;Li & Zhao, 2019;Quishpe-Vásquez et al. 2019;Li et al., 2020) to investigate the response of rainfall on SST. This technique is applied to two jointly analysed fields to identify couples of the coupled spatial pattern and their respective temporal variations. The decomposition allows the extraction of dominant modes of the coupled covariability between the two analysed fields.
Correlation analysis was employed to reveal the simple relationships between two variables (Wilks, 2006). The Pearson's correlation coefficient (r) is used as a good indicator of the strength of the relationship between the two fields. The same method was used by Cattani et al. (2018) and Kalisa et al. (2019) over the study region. From the SVD analysis, the heterogeneous correlation represents the correlation coefficients between the values of each grid point of the field and the expansion coefficients of the other field. In this study, the heterogeneous correlation indicates how well the pattern of the precipitation (SST) anomalies relates to the expansion coefficient of SST (precipitation). The anomaly was obtained by subtracting a value from its climatological mean (mean value from 1981 to 2010). The heterogeneous correlation was performed by projecting the temporal expansion series of each field onto the appropriate singular vector. The time lag correlation coefficient was used to find out in what time step the Atlantic, Indian and Pacific Oceans have a strong and significant linear relationship with East African's MAM rainfall. The same technique has been used by other researchers (Kug et al., 2006;Otte et al., 2017) in the region.

Study area
The EA region is located in the tropics bounded by a longitude of 280 E to 420 E and the latitude of 120 S to 50N (Fig. 1b). EA includes Tanzania, Kenya, Uganda, Rwanda, and Burundi. The climate of East Africa is characterized by two rainy seasons regimes, short rainy season, October to December (OND), and long rainy season, MAM (Nicholson, 2014;Rowell et al., 2015). This bimodal regime is due to the northward and southward movement of the Intertropical Convergence Zone (ITCZ) (Muhire et al., 2015;Camberlin, 2018). EA climate varies from one place to another in accordance with geographical location, altitude, relief, and vegetation cover.

Results
The first two dominant coupled modes of SVD ( Fig. 2) explain 88.61% of the total covariance, meaning that there is a good covariability between rainfall and SST over the Atlantic Ocean. The first SVD vector of precipitation in MAM ( Fig. 2a) indicates the highest positive values over the South-east of Tanzania, which may be associated with positive SVD values over the northern Atlantic Ocean (where the Azores high is located) as well as negative values over the sub-tropical Atlantic Ocean (Fig. 2c). For the second SVD (Fig. 2b), the lowest negative values are featured over the southeast of Tanzania instead, and this is complemented by the disappearance of positive SVD values over the northern Atlantic Ocean where negative values have now dominated. However, still, negative values are over the subtropical Atlantic Ocean (Fig. 2d).
The first two dominant coupled modes of SVD explain 91% of the total covariance, meaning that there is a good covariability between rainfall and SST over the Indian Ocean (Fig. 3). There exist significant coupled modes of variability between SST in the Indian Ocean and the mean MAM rainfall over EA with the covariance of 83.9% of the first mode (SVD 1). SVD 1 ( Fig. 3a) shows that the East African region is dominated by homogeneous positive loading all over the region with strong rainfall variability over the eastern coast and over the Lake Victoria basin. This is associated with positive loading SST anomalies (Fig. 3c) over the western and southwestern Indian Ocean and negative loading of SST anomalies over the central Indian Ocean. SVD2 (Fig. 3b) depicts the presence of dipole patterns over the study area characterized by positive loading over the northern part extending towards the southwestern sectors, and negative loading over the eastern coast towards the southeastern and the western part of the Lake Victoria basin. The dipole pattern observed is associated with the dipole patterns of SST anomalies (Fig. 3d) over the Indian Ocean with positive loadings over the southeastern Indian Ocean and negative loadings over the remaining part of the Tropical Indian Ocean.
The first two dominant coupled modes of SVD explain 82.9% of the total covariance, meaning that there is a good covariability between rainfall and SST over the Pacific Ocean (Fig. 4). SVD 1 (Fig. 4a) depicts higher positive loading over bimodal rainfall regimes and the coastal belt of Tanzania. The same results persist in the southern region of Uganda including northern Lake Victoria while on the Kenyan side the loading occurs over the southwestern and coastal region. These loadings correspond with negative loadings over the central equatorial Pacific Ocean (160° -120° W) and other small SST anomalous over the Ocean (Fig. 4c). SVD 2 (Fig. 4b) re-veals diagonal positive loading of rainfall across EA and several positive loadings over the southern part of Tanzania, northern part, and the coast of Kenya. These loadings correspond with mixtures of weak positive and negative loadings over the Pacific Ocean (Fig. 4d). The remarkable feature is positive loading over the central eastern Pacific Ocean, which acts on opposite to SVD 1, this suggests the existence of a sea-saw pattern of SST anomalous over the region of El Nino Modoki. This gives a clue of a weak relationship between this region and rainfall over EA due to a weak correlation (0.41) on a temporal scale. Hence, Pacific Ocean SST is less related to MAM rainfall season over EA. Similar results were obtained by Preethi et al. (2015) which show that El Niño Modoki events are associated with suppressing of rainfall over eastern Africa.
The correlation between EA precipitation and PC1 and PC2 of SST anomaly shows that much of the central to northern parts of the region feature weak to moderate positive correlation (Fig. 5a&b). The strongest values are indicated over northern Kenya as well as localized areas in Northern Tanzania, with correlation values as high as 0.4. Otherwise, the rest of the region, mainly Southern parts, features very weak negative correlations. The correlation between SST over the Atlantic Ocean and PC1 of precipitation show positive values over the subtropical region of the Ocean and North of the Equator. Meanwhile, in the South of the Equator to the mid-latitude, there are negative values of correlation (Fig. 5c). However, further south, positive correlation values are evident. For PC2, there is hardly any clear pattern (Fig. 5d); a relatively high For the Indian Ocean, a heterogeneous correlation of PC1 of SST anomaly is positively correlated with the EA rainfall over the northeastern extending towards the southwestern parts of the study area (Fig.  6a). On the other hand, a negative correlation is observed over the remaining part. The PC2 of the SST anomaly is positively correlated with the EA rainfall almost all over the study area (Fig. 6b). Heterogeneous correlations of PC1 and PC2 of EA rainfall are negatively correlated with SST all over the Indian Ocean except the southeastern and maritime continent regions (Fig. 6c&d). This suggests the existing influence of western and southwestern parts of the Indian Ocean to MAM rainfall variability over the EA.
The heterogeneous correlation between EA rainfall and Principal components of Pacific Ocean SST was also analyzed. PC1 (Fig. 7a) shows the domination of positive correlation over much of the domain region except the southwestern highland and southern region of Tanzania where negative correlation is observed. PC2 (Fig. 7b), shows quite similar patterns to PC1; however, over portions of northeastern Tanzania, a positive correlation is replaced by a negative correlation which makes the area to resemble the dipole structure. Otherwise, in PC1, there are general-ly higher correlation values over much of the domain. Likewise, the heterogeneous correlation between the Pacific Ocean SST and PC 1 and 2 of EA rainfall (Fig.   Figure 5. Heterogeneous correlation between precipitation over the study area and PC 1 and 2 of Atlantic SST (a and b) and heterogeneous correlation between Atlantic Ocean and PC 1 and 2 of precipitation (c and d) Figure 6. Heterogeneous correlation between precipitation over the study area and PC 1 and 2 of Indian SST (a and b) and heterogeneous correlation between Indian Ocean and PC 1 and 2 of precipitation (c and d) Figure 7. Heterogeneous correlation between precipitation over the study area and PC 1 and 2 of Pacific SST (a and b) and heterogeneous correlation between Pacific Ocean and PC 1 and 2 of precipitation (c and d) 7c&d) shows a sea-saw pattern of SST anomalies over the central east Pacific Ocean (ENSO like pattern). The opposite SST patterns over the Pacific Ocean have a little relationship on changing rainfall patterns over East Africa but the figures give us the clue on which region over the Pacific Ocean has a stronger correlation to EA precipitation.
Looking into the lead-lag relationship between MAM precipitation over the EA and spatially averaged SST over the Atlantic Ocean, the results indicate that most significant correlation values are found in 7-month lead time i.e. during JJA (Fig. 8a). This is evident with negative values as low as around -0.3 observed over some Southern areas of the Lake Victoria while positive correlation values as high as 0.3 observed over the area just north of the Lake Victoria over Uganda. In addition, along the coastal areas, mainly over Tanzania, negative values of correlation of down to -0.4 have been observed. The lead-lag correlation shows that the Indian Ocean SST has a fairly high correlation with MAM rainfall over EA when SST leads by 1 month i.e. during JFM (Fig. 8b), characterized by positive correlation all over the region except the eastern coastal region. As for the Pacific Ocean, the results generally show that the magnitude of positive correlation decreases slowly until replaced with negative correlation while moving toward previous seasons. The correlation coefficient values were weak across all leads; hence, we may say that SST over the Pacific Ocean has a little contribution to EA rainfall during MAM.

Discussion
The global Oceans SST has been found to have an influence on interannual and interdecadal variability of rainfall over different regions in the world. Changes in global SST over different regions may lead to intense rainfall or suppressed rainfall. The results from SVD analysis confirmed the complexity variability of rainfall over EA during the MAM rainfall season. SVD results have shown more insight into the modes of interannual rainfall variability over the region. The dominant modes representing zonal SST variability in the Indian Ocean which is consistent with other studies including Okoola (1996), Goddard and Graham (1999), Mutai (2003), Nyakwada (2009) among others. The study showed that MAM rainfall variability over EA is associated with warmer SST over the western Indian Ocean. The same result was found by Yang et al. (2015), where they documented that intense rainfall corresponds to warmer SST over the western Indian Ocean. It is also found that intense MAM rainfall is related to warmer SST over the northern Atlantic Ocean and vice versa. Moisture influx from the ocean is associated with an enhanced westerly circulation that also favours the incursions of moisture from the always wet tropical forests of Congo, Zaire, and other central African countries. The SST variability in the Atlantic Ocean reaches its maximum in the period from January to May (Wu et al., 2007). This may be due to the relaxation of Azores' high, which in turn, more moisture is pushed to the region with the aid of St. Helena high (Manatsa et al., 2014). Over the Pacific Ocean, the existence of El Nino Modoki over the central Pacific Ocean corresponds to positive rainfall anomalies over EA, especially over the bimodal regions. The result agrees with the study of Preethi et al. (2015) which explained that El Niño Modoki is associated with suppressing rainfall over eastern Africa. On the other hand, an ENSO-like pattern was captured in SVD 2 similar to that was shown by Kijazi and Reason (2005).
The characteristics of the SVD modes are closely related to some climate extremes affecting the region. These could be associated with the behaviour of these modes on the circulations, energy, and moisture induced by the ocean, and other inland generating systems. Barnston et al. (1996) explained that the time-space behaviour of the SST field alone influences the seasonal rainfall over the region both on different time-scales. This suggests that the large-scale changes in the global basins' SSTs have a significant influence on regional climate variability. To emphasize the importance of Oceans on regional climate variability, many studies have been done on the strong relationship between ocean currents and regional climate (Cai and Cowan, 2007;Keller et al., 2007;Valsala and  Ikeda , 2007). The results in this study provide important information for improving the prediction skills of MAM rainfall over EA. Improvement in prediction skills will help to reduce the vulnerability to climaterelated destruction, damage, and losses. According to previous studies such as , and Ongoma and Chen (2017), MAM rainfall over EA shows a declining trend in the late 1990s. Therefore, we recommend future studies to focus on assessing the linkage of change in global SST especially on the regions identified with the declining trend of MAM rainfall over EA.

Conclusion
Results from this study point out the significant influence of SST anomalies over Indian, Pacific, and Atlantic Oceans on EA MAM rainfall seasonal variability. Indian, Atlantic, and the Pacific Ocean show good covariability of 91%, 88.61%, and 82.9% with EA rainfall respectively. This indicates that the Indian Ocean explains the variability of rainfall to the large extent followed by the Atlantic Ocean and the Pacific Ocean. The first two modes of SVD between SSTs and rainfall show similar rainfall patterns over eastern, eastern highlands, and Lake Victoria basin except SVD 2 which corresponding to the Pacific Ocean. The rainfall patterns over EA correspond to SST variability over the western, central, and eastern Indian Ocean. Additionally, the Atlantic Ocean depicts negative (positive) loading over central (south and north). However, the Pacific Ocean shows negative (positive) loading over central and eastern (eastern and western) in SVD1 and SVD2 respectively. SVD 1 (SVD 2) captured the El Nino Modoki-like (ENSO-like) pattern.
The heterogeneous correlation of Indian SST anomalies over EA rainfall of the first (second) PC shows positive correlations over much of the domain (central region). The PC's of EA rainfall anomalies were negatively correlated with SST anomalies over much of the Indian Ocean. Generally, the correlation between PC1 of Pacific SST anomalies and EA rainfall shows higher correlation values over much of the domain except over the southwestern highland and southern region of Tanzania. PC2 depicts a similar pattern with a northward extension of negative correlation. The correlation between the first and second PC of rainfall anomalies over the Pacific Ocean shows the EN-SO-like pattern. Meanwhile, flip-flop patterns of correlation values were observed over the northern and southern Pacific Ocean. Over the Atlantic Ocean, the correlation result shows the dipole patterns of positive (negative) values over the northern (southern) part for PC1, while PC2 depicts negative correlation values over much of the Ocean. The lead correlation between the Indian Ocean SST shows high correlations with East Africa MAM rainfall when SST leads by 1 month. Meanwhile, the results indicate the most significant correlation values when SST leads by 7 months (during JJA) for the Atlantic Ocean. The Pacific Ocean shows a weak correlation across all lead seasons.