1 Introduction

East African countries, including Uganda, Kenya, Tanzania, Rwanda, and Burundi, depend heavily on rainfed agriculture. Rainfed agriculture remains the most significant contributor to the economy of these countries despite the effects of high spatial and temporal variability exhibited in rainfall over this region (Camberlin & Okoola, 2003; Mumo et al., 2019). The rains are highly variable and frequently associated with extreme events such as floods (Indeje et al., 2000) and droughts (Ayugi et al., 2020; Haile et al. 2020), which cause major disruption of food production and distribution chains. This is exacerbated by the impact of the unreliable weather pattern, such as variable onset and cessation, prolonged dry spells, and hailstone events (Adhikari et al., 2015; Ojara et al., 2020).

Most parts of the region receive bimodal rainfall patterns with the first season occurring during March–May (MAM) and the second season experienced in October–December (OND) associated with the north–south oscillation of the Intertropical Convergence Zone (ITCZ) (Yang et al., 2015; Ongoma et al., 2017). Additionally, the moist tropical oceanic air masses that move across the region from the Atlantic contribute to precipitation in the region (Nicholson, 2017), and the Indian Ocean contributes to the equatorial low-pressure zone near the equatorial belt (Danley et al., 2012). The influence of the southeast monsoon during the northern summer and the northeast monsoon in the southern summer also affects most parts of EA (Spinage, 2012). The rains are also regulated by many weather phenomena, including the Indian Ocean Dipole (IOD) (Behera et al., 2005; Ogwang et al., 2015; Ongoma, et al., 2015) and El Niño Southern Oscillation (ENSO) which is associated with the interannual rainfall variability over this region (Fer et al., 2017; Indeje et al., 2000).

Over the African continent, the strongest signal of ENSO modulating rainfall is experienced in eastern equatorial and southeastern Africa. Further, the ENSO mechanism is believed to be responsible for many prominent rainfall teleconnection patterns/systems over the continent, including the strong tendency for opposite anomalies in the equatorial and South Africa region (Nicholson & Kim, 1997). According to Nicholson and Kim (1997), there is a strong tendency for a positive anomaly during the first half of the ENSO cycle and a negative anomaly over the second half, corresponding to the cold and warm phases in the adjacent Atlantic and Indian oceans, respectively. In this regard, rainfall tends to be enhanced during the cold phase and reduced during the warm phase. In some parts of East Africa like Uganda, composite analysis revealed that the cool-phase ENSO supports increased May–October rainfall through zonal overturning of lower westerly/upper easterly atmospheric circulation, supported by the inflow of moisture from the west Indian Ocean (Jury, 2018).

Comprehensive studies on the influence of ENSO using spectral coherence by Nicholson and Entekhabi (1986) demonstrated a strong relationship between ENSO and rainfall on a timescale of 2.3–3.5 and 5–6 years in various parts of equatorial and South Africa. Similar observations were reported by Ropelewski and Halpert (1989) while employing a novel harmonic method based on individual station datasets. The modulation influences of ENSO over global weather systems are strongly linked to the recent increase in the frequency and amplitude of extreme events over the twenty-first century, adding to the already warming planet Earth. For example, the period between 2014 and 2016 is observed as the warmest in the recent past, which coincided with the strongest El Niño years (Byakatonda et al., 2019).

In addition, the Indian Ocean Dipole (IOD) mode, which refers to the zonal temperature gradient over the equatorial Indian Ocean, and the coupled IOD–ENSO influence have been prominent in causing some wet conditions over East Africa in recent years (Bowden & Semazzi, 2007; Owiti et al., 2008). The empirical orthogonal function (EOF) analysis revealed two dominant modes of intra-seasonal variability for the OND season over the Greater Horn of Africa which includes mixed interaction between ENSO–IOD and a decadal mode. Several case studies of intra-seasonal ENSO–IOD events over the last three decades revealed that the warm events are linked to consistently above-normal pentad rainfall during the entire rainfall season despite fluctuations. Meanwhile, other case studies analyzing the negative ENSO–IOD events showed that the negative cases do not present mirror images of the warm events (Bowden & Semazzi, 2007).

In terms of the actual rainfall received, changes in major variables causing the EA rains have also been linked to similar trends in seasonal rainfall. For example, the MAM rainfall season has been reported to decline (Lyon & Dewitt, 2012; Rowell et al., 2015; Williams & Funk, 2011; Nicholson et al., 2018). However, studies showed an increase during the OND rainy season is a response to the large-scale weakening of the Walker circulation (Liebmann et al., 2014; Tierney et al., 2015; Kebacho, 2021). The decline in rainfall observed in the 1980s in the East African region is linked to the abrupt change in rainfall after the year 1999 (Lyon & Dewitt, 2012). The increasing sea surface temperature (SST) in the south-central Indian Ocean and the western Pacific Ocean is reported to be responsible for reducing precipitation by providing resultant latent heat and altering the regional winds and moisture flux mechanisms which subsequently reduces the long rains over EA (Williams & Funk, 2011).

The reduction in seasonal rainfall in EA most likely contributed to severe drought events which were experienced in Kenya during 1973–1974 and 1983–1984 (Ayugi et al., 2022; Masih et al., 2014; Omolo, 2010). A recent study over Uganda revealed an upward tendency in the length of the maximum dry spell occurrence during March (Ojara et al., 2020). On the contrary, excessive rainfall has occurred in some parts of this region, mainly covering parts of eastern Uganda and northwestern Kenya, resulting in rainfall-related disasters, including flash floods and mudslides (Omolo, 2010; Onyutha, 2014). The period of exceptionally high rainfall amount in EA has been found to correspond to the rainy periods during the El Niño events such as those of 1997–1998 and 2015–2016 which brought much moisture and precipitation over the region.

Recent studies have only employed statistical approaches to highlight the trends and changes in precipitation over East Africa (Ayugi et al., 2016; Ongoma & Chen, 2017), the mechanism leading to trends and changes in rainfall have been examined using dynamic mechanisms (e.g., Ayugi et al., 2018), and general implications of the changing climatic trend explored (Ogwang et al., 2016).

This paper differs from previous studies as it employed relatively new advanced wavelet statistical analysis to combine rainfall data with atmospheric variables ENSO and IOD, showing their modulatory influence on extreme precipitation phenomena such as floods and drought over the EA region. The remaining sections of the paper are structured as follows: Section 2 describes the study domain, datasets, and methods. This is followed by Sect. 3, presenting the main results. Section 4 elucidates the discussions, conclusion, and recommendations based on the findings of this research.

2 Data and Methodology

2.1 Study Area

East Africa is enclosed within the geographical latitude 5.1° N to 11.74° S and longitude 28.86° E to 41.91° E. The main physical features in the region include some of the world’s highest mountains, Mt. Kilimanjaro, Rwenzori, and Elgon (Fig. 1b). EA generally experiences two main rainy seasons, namely, MAM and OND. MAM is usually referred to as the “long rains” (Camberlin & Philippon, 2002; Ongoma & Chen, 2017), and it is occasionally termed the Boreal spring. The first season follows the migration of the Intertropical Convergence Zone (ITCZ) to the Northern Hemisphere. OND, on the other hand, is usually referred to as “short rains” (Kizza et al., 2009), which results from the movement of the ITCZ from the north to the Southern Hemisphere. The rains are also influenced by atmospheric phenomena such as ENSO (Indeje et al., 2000; Ntale & Gan, 2004) and IOD (Behera et al., 2005). The ENSO phenomena are strongly associated with the inter-annual variability of rainfall in this region (Indeje et al., 2000).

Fig. 1
figure 1

Location of the study area: a map of Africa, b East Africa, c eight rainfall zones of EA (R1–R8), d selected meteorological stations (red dots) in different rainfall zones

Full size image

Studies showed that seasonal rainfall patterns in EA result from the interaction between the ITCZ and the complex atmospheric movement referred to as “perturbations” in climate circulation studies (Owiti & Zhu, 2012). The complex interplay of the ITCZ with other phenomena such as the quasi-biennial oscillation (QBO), large-scale monsoon winds, and extra-tropical weather events also influences seasonal variability (Ng’ongolo et al., 2014). Several other factors that affect EA rainfall are well described by other scientists (e.g., Indeje et al., 2000; Ogwang et al., 2014; Owiti & Zhu, 2012).

Rainfall characteristics of East Africa were delineated into eight homogenized rainfall zones (R1–R8) using the empirical orthogonal function (EOF), spatial cluster analysis, and simple correlation analysis with other related techniques (Indeje et al., 2000); see Fig. 1c. These rainfall zones have been adopted and widely used to describe the climate of the region (e.g., Ongoma et al., 2018). Other individual country zonation of EA includes those by Rourke (2011) where a clustering approach for rain gauge datasets over Kenya was done considering the topography of Kenya and the geographic proximity of the rain gauge stations following Gissila et al. (2004). Similarly, Uganda’s rainfall was zoned into 12 clusters (Basalirwa, 1995) and was later revised into 16 new clusters also appropriate for individual country situation analysis.

2.2 Data

2.2.1 In Situ Datasets

This study employed the in situ daily and monthly rainfall data from the national meteorological institutions in EA including the Uganda National Meteorological Authority (UNMA), Kenya Meteorological Department (KMD), Rwanda Meteorological Agency (Meteo Rwanda), Geographical Institute of Burundi (IGEBU), and Tanzania Meteorological Agency (TMA). All country datasets covered the period 1960–2017. The datasets were previously collected from more than 30 manual rain gauges. The stations were selected to represent the eight homogeneous rainfall zones (R1–R8) over EA after the preliminary quality test. Detailed geographical information of the meteorological stations selected from each rainfall zone (RF/Z) can be seen in Table 1

Table 1 Information for all meteorological stations (RF/Z represent rainfall zones)
Full size table

2.2.2 Atmospheric Indices

Two ocean-atmospheric indices, ENSO and IOD, were employed to assess the physics of the rainfall variability in EA. Monthly ENSO data represents the interaction between the atmosphere and the ocean in the Tropical Pacific, which periodically causes variations in below-normal or above-normal sea surface temperatures and dry and wet conditions over a few years. The dataset can be accessed from the official website (https://origin.cpc.ncep.noaa.gov).

The IOD is the anomalous SST difference between the western (50°–70° E and 10° S–10° N) and southeastern regions (90°–110° E and 10° S–0° N) of the Indian Ocean. It is an interannual climate pattern exhibited across the tropical Indian Ocean (Behera et al., 2005; Saji et al., 1999). Saji et al. (1999) suggested that cooler than normal and warmer than normal water in the tropical western Indian Ocean characterize the positive IOD period. On the other hand, a negative IOD period is shown by the positive conditions at the same location in the ocean. The monthly IOD time series data can be downloaded from the National Oceanic and Atmospheric Administration (NOAA) official website (https://www.esrl.noaa.gov). These two indices were selected based on the relevancy demonstrated in past studies explaining the variability of rainfall over EA (Behera et al., 2005; Indeje et al., 2000).

2.3 Methodology

2.3.1 Outlier, Normality, and Homogeneity Test

Monthly datasets were subjected to preliminary quality assessment that included control checks to identify the negative rainfall values, typing errors, missing gaps in the dataset, and false zeros. Two rainfall stations, Kiige and Serere, had less than 10 days of missing records throughout the monthly data. These stations were subsequently filled using datasets from nearby Jinja and Soroti stations, respectively. In this process, linear regression was employed after correlation showed that the data from each set of stations revealed a high correlation coefficient (r = 0.97 and r = 0.96, respectively). This was required as the linear regression method used required highly correlated rainfall records. The technique is non-complex, yet it gives good results (Kizza et al., 2009).

Datasets were also tested for outliers using the Grubbs (1969) test for outliers. This has been selected because it can identify outliers in all data values. The technique was recently used in a similar study on EA (Ojara et al., 2020). The data was found to have outliers in one station on two occasions. The enormous values recorded at the station correspond to the rainy periods during the El Niño events of 1997–1998 (Amissah-Arthur et al., 2002) and 2015–2016 in East Africa when the region received above-normal rainfall. The values were confirmed to be true after verification with World Meteorological Organization (WMO) form 49A for rainfall data entry. Then normality test was done using Shapiro–Wilk tests at a 5% significance level for the distribution type, on a null hypothesis that the data were normally distributed. The dataset was further tested for homogeneity using both the standard normal homogeneity test (SNHT) and Buishand’s test at a 5% significance level. The null hypothesis was that the data were homogeneous. The homogeneity test done was to ensure that variation in the data was due to climatic factors only (Costa & Soares, 2009).

Results for the homogeneity test using the SNHT showed that all the stations were fairly homogeneous (p > 0.05), while Buishand analysis showed that only two stations were inhomogeneous in two different months at a 5% significance level. These two stations, Kotido and Lodwar stations, were dropped from the analysis (Table S1). Decadal rainfall data for Jinja, Namulonge, Tororo, and Soroti were found to be homogeneous (Mugume et al., 2016). Table S1 shows the results for the normality test (htest), outlier test, and homogeneity test using both the SNHT and Buishand (BR) range test.

2.3.2 Variability and Trends of Rainfall in EA

Seasonal rainfall totals were computed based on 3-month totals for the main seasons in the region; March–May (MAM) and October–November (OND) (Kizza et al., 2009), and annual rainfall was derived by summing up all the monthly rainfall values for each station. Descriptive statistics were computed based on seasonal and annual rainfall.

The non-parametric Mann–Kendall (MK) test (Mann, 1945; Kendall, 1975) was performed at a 5% significance level to check the presence of any monotonic trend in the seasonal and annual rainfall. The null hypothesis for this test was that there is no trend in the dataset. To improve on the approximation of data, a continuity correction was applied to the analysis, and the autocorrelation was performed using the method advanced by Hamed and Rao (1998). The main advantage of the MK test is that it can be used for non-normally distributed data or even where datasets are approximately normally distributed (Modarres & Sarhadi, 2009). Similarly, the magnitude of missing data values and space–time monitoring does not affect the MK test statistic (Ongoma et al., 2018). The techniques give a more robust estimation of the trend, especially compared with other statistical techniques like regression. Over the current study area, the MK test has been used for detecting trends in climate-, hydrological-, and environmental-related datasets (e.g., Stern et al., 2011; Ongoma et al., 2018; Ngoma et al., 2021).

Sen’s slope estimator (SE) (Theil et al., 1950; Sen, 1968) was employed to estimate the rate of change of the slope of the trends in the rainfall time series. The positive results of the SE represent an increasing trend, while the negative values represent decreasing trends over a given time (Ongoma et al., 2018; Ayugi et al., 2018).

2.3.3 Wavelet Analysis

The wavelet transform (WT) is a recent technique used in signal processing analysis as an alternative to Fourier transform (FT) in preserving local, nonperiodic, multi-scaled phenomena, offering advantages over classical spectral analysis (Drago & Boxall, 2002). WT allows analysis over different scales of temporal variability, and it does not need a stationary series, making it appropriate to analyze irregularly distributed events and time series that contain nonstationary power at many different frequencies (Miao et al., 2012). WT analysis is considered to be more effective in studying the nonstationary time series as compared to the FT (Miao et al., 2012). The use of the WT acts as an effective method for analyzing and synthesizing the variable structure of a signal in time and is used to isolate different periodicities embedded in a time series (Drago & Boxall, 2002).

To highlight the theory of wavelet analysis, three main components of a wavelet, continuous wavelet transform (CWT), cross-wavelet transform (XWT), and wavelet transform coherence (WTC), are summarized (Grinsted et al., 2004; Torrence & Compo, 1998) and presented herein by Eq. (1):

$$\varpi \left( {\tau ,s} \right) = \frac{1}{{^{{S{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 2}}\right.\kern-\nulldelimiterspace} \!\lower0.7ex\hbox{$2$}}}} }}\int_{ - \infty }^{ + \infty } X \left( t \right)\varphi *\left( {\frac{t - \tau }{s}} \right)dt$$
(1)

where \(\varphi \left( t \right)\) is the mother wavelet defined by the transition parameter \(\tau\), corresponding to the position of the wavelet, and \(s\) is the scale dilation parameter that determines the width of the wavelet. The variability of the dominant mode with time is determined by a Morlet wavelet with a wave number equal to six (\(\omega 0 = 6\)) (Okonkwo, 2014). The criteria for selecting the Morlet wavelet are based on its localization in time and frequency, making it a good tool for extracting features (Grinsted et al., 2004). In wavelet analysis, information about the periodicity of the time series data is extracted from the CWT, while the XWT helps in determining whether the two time series are statistically significant by Pearson’s correlation coefficient (Okonkwo, 2014).

The continuous Morlet wavelet analysis allows the completion of a timescale representation of localized and transient phenomena occurring at different timescales. Timescale discrimination is achieved in a more satisfactory way than time–frequency decompositions such as the windowed Fourier method (Miao et al., 2012). The mother wavelet provides a good balance between time and frequency resolutions. The Morlet wavelet has been used successfully by many other researchers in identifying quasi-periodic fluctuations in a variety of geophysical time series. The preprocessing of data used was carried out by filtering the 1-year natural cycle of rainfall series before wavelet transform.

The continuous wavelet transform (CWT) of a discrete sequence x is defined as the convolution of xn with a scaled and translated version: \(\psi_{{\text{o}}} (\eta )\). Mathematically, the CWT is presented by Eq. (2) as follows:

$$W_{n} \left( S \right) = \sum\limits_{{n^{\prime} = 1}}^{N} {\left( {\frac{\delta t}{s}} \right)}^{1/2} x_{{n^{\prime}\psi^{*} }} \left[ {\frac{{\left( {n^{\prime} - n} \right)\delta t}}{s}} \right].$$
(2)

In this case, \(W_{n} \left( S \right)\) are the wavelet coefficients, n is the time index describing the location of the wavelet in time, s is the wavelet scale, and \(\delta t\) is the sampling interval. The function \(\psi\) is called the mother wavelet, and more elaborated information about the periodicity of the time series data can be decomposed from the CWT (Okonkwo, 2014). The phase difference between the atmospheric indices and rainfall is indicated by vectors, while the locally significant power of the red-noise spectrum at a 5% significance level is presented by the bold solid black contour lines or strips. A detailed methodology of the wavelet transform can be found in Grinsted et al. (2004) and Torrence and Compo (1998).

In this study, the cross-wavelet transform (XWT) was used to examine the relationship between interannual variability of precipitation and atmospheric indices by decomposing their time series into frequency space following the procedures of Torrence and Compo (1998). The wavelet analysis was applied to climate variables to detect the periodicity, phase change, and periodic intensity during the time series (Grinsted et al., 2004; Torrence & Compo, 1998). The relationship between the observed seasonal rainfall anomalies and different phases of ENSO was examined. Seasonal rainfall patterns associated with the various ENSO resonance cycles have been identified.

In a physical scenario, the XWT of two datasets in a time series such as seasonal rainfall and atmospheric teleconnection, xn and yn can be defined as \(W^{XY} = W^{X} W^{Y} *\), where * represents the complex conjugation. The current study defined the cross-wavelet power presented as the local relative phase between xn and yn in time as \(\left| {WXY} \right|\). The complex argument (\(W^{XY}\)) can be inter-frequency space. The theoretical distribution of the cross-wavelet power of two time series with background power spectra \(P_{k}^{X}\) and \(P_{k}^{Y}\) is given by Eq. (3) illustrated more comprehensively in Torrence and Compo (1998):

$$D\left( {\frac{{\left| {W_{n}^{X} \left( s \right)W_{n}^{X} *\left( s \right)} \right|}}{\partial X\partial Y} < P} \right) = \frac{{Z_{v} \left( p \right)}}{v}\sqrt {P_{k}^{X} P_{k}^{Y} }$$
(3)

where Zν(p) is the confidence level associated with the probability p for a probability density function defined by the square root of the product of two χ2 distributions.

3 Results

3.1 Climatology and Trends of Rainfall

The mean monthly rainfall cycle for the eight rainfall zones (R1–R8) of EA is presented in Fig. 2. Results showed high values of seasonal rainfall recorded during the months of March–May (MAM) and October–December (OND), coinciding with two main bimodal rainfall regimes, MAM and OND, over EA. Descriptive statistics for seasonal and annual rainfall are presented on the right-hand side of Table 2. The highest mean annual rainfall of 2070.7 mm was recorded at Bukoba station in rainfall zone 3 (R3) followed by Buginyanya station in rainfall zone 4 (R4) with 1953.4 mm. The two lowest mean annual rainfall values of 102.9 mm and 333.7 mm were recorded at the arid and semiarid land (ASAL) regions in Kenya at Garissa and Wajir stations represented by rainfall zone 1 (R1).

Fig. 2
figure 2

Mean monthly rainfall over eight rainfall regions (R1–R8) in EA for 1981–2017

Full size image
Table 2 The p value for Mann–Kendall trend analysis, Sen’s slope (SE), and statistics for annual and seasonal rainfall over eight rainfall zones of EA
Full size table

Table 2 presents the results of the MK) test for seasonal and annual rainfall. Results revealed varied trends in seasonal and annual rainfall at different stations in the regions. In terms of the annual rainfall trend, the results disclosed a negative trend at 58% of the stations, although only Songea station in southern Tanzania was statistically significant. The remaining 42% of the stations revealed a positive trend and were statistically significant at a few stations, including Namulonge, Jinja, Kiige, Buginyanya, Kasese, and Gisenyi. In this case, the highest rate of increase in annual rainfall is revealed at Buginyanya with 22.9 mm/year, followed by Namulonge station with 6.8 mm/year, while the remaining stations Kasese, Jinja, Gisenyi, and Kiige expressed an approximate increase rate in the range of 4.0–6.6 mm/year. Figure 3 presents the spatial representation of the MK test for annual and seasonal rainfall in MAM and OND for selected stations in EA during 1960–2017.

Fig. 3
figure 3

Spatial representation of MK trend results for selected stations over eight rainfall zones of EA

Full size image

Nearly 97% of the stations analyzed showed a decreasing trend in MAM seasonal rainfall. However, only two stations, Entebbe and Marsabit, were statistically significant, showing a decrease of almost 5.5 mm/year. For the OND rainy season, positive trends were exhibited in about 60% of the stations, although only a few stations revealed statistically significant trends, including Masindi, Kampala, Jinja, and Kasese stations. The rate of change at these four stations ranges between 1.9 and 4.2 mm/year.

3.2 Rainfall Periodicity

The monthly rainfall time series is presented in Fig. 4a, and its subsequent wavelet power spectrum (WPS) in Fig. 4b. The highest monthly rainfall received, which ranged between 2010.0 and 2760.4 mm, was experienced in the years 1961, 1964, 1970, 1977, 1978, 1985, 1986, and 2006. With exception of 1961 and 2006 when the highest monthly rainfall was registered in November, the rest of the years recorded their highest monthly values in April. Above the 95% confidence level, the WPS showed more concentration between 0.25- and 0.5-year band cycles as a dominant period of variability, which shows that these times have a strong annual signal. This corresponds to bimodal rainfall seasons in EA, which occurred in MAM and OND. Similarly, the results in the cone of influence (COI) (Fig. 4b) revealed the presence of a 1-year cycle as a dominant period of variability over the entire period of analysis (1960–2017).

Fig. 4
figure 4

Variation of monthly rainfall for an area with typical MAM and OND rainfall seasons (a). The wavelet power spectrum (WPS) was derived from the Morlet mother wavelet (b). The region enclosed by the thin black line is the cone of influence (COI), where zero paddling has reduced the variance (mm2). The global wavelet spectrum (mm2) (c). The dashed line is the 5% significance level for the global wavelet spectrum. Scale-average wavelet power over a 1–2-year band (d). The red dashed line is 95% confidence

Full size image

In the wavelet power spectrum (WPS) (Fig. 4b), the dark contour lines denote a 95% confidence level with respect to the red-noise background spectrum, and the region below the U-shaped curve denotes the cone of influence (COI).

In light of the global wavelet power spectrum, the result revealed only one significant peak above the 95% confidence level for the global wavelet spectrum, represented by the red dashed lines (Fig. 4c). Figure 4d presents scale-average wavelet power of the time series of average variance in a certain 1–2-year band. This was used to examine the modulation of one time series by another within the same time series. It shows the average overall scales between 1 and 2 years, i.e., a measure of the average year versus time. The plot was used to show distinct periods when monthly rainfall variance was low/high over EA (Fig. 4d). The dry years include 1965–1967, 1971–1974, 1981–1982, and 2010–2012 with some important peaks in the scale-average time series identified for 1963, 1969, 1988, 2000–2001, and 2007–2009, indicating a period of wetter years. EA has 2-year wet/dry or 4-years oscillating wet/dry in its bimodal rains (Liebmann et al., 2014; Ongoma & Chen, 2017).

3.3 Continuous Wavelet Transforms (CWT) Analysis of ENSO/IOD and Seasonal Rainfall

Figure 5 shows the continuous wavelet transform (CWT) of ENSO and IOD during MAM and OND. Results show major periodicity in the power spectrum range of a 2–6-year band. For example, a 2–4-year band and a 3–5-year band were revealed for ENSO and MAM (Fig. 5a), while a 4–5-year band and a 3–4-year band were shown as the main periodicity between ENSO and OND (Fig. 5b). For the IOD and MAM, the periodicity was indicated at a 1–6-year band (Fig. 5c). Conversely, a 4–6-year band and a 1–6-year band are indicated as two bands for IOD and OND seasonal rainfall, respectively (Fig. 5d).

Fig. 5
figure 5

Continuous wavelet transform for a ENSO–MAM, b ENSO–OND, c IOD–MAM, and d IOD–OND. The thick contour-enclosed regions are greater than 95% confidence for a red-noise process. The thin solid black line indicates the 5% significance level against the red-noise “cone of influence” (COI) where edge effects become important

Full size image

In all these cases, the interannual cycles have time scales of approximately 6 years (Fig. 5). Besides, the region that is statistically significant at 95% confidence for the IOD is important regarding the wet conditions and drought events of the 1980s in the regions which were influenced by El Niño and La Niña events. These first steps of identifying key spots on the continuous wavelet transform allows the time series to be expanded into frequency space by application of the CWT as a band filter to the time series to help find the localized periodicities and feature extraction (Grinsted et al., 2004; Okonkwo, 2014).

3.4 Cross-Wavelet Transform (XWT) Analysis Between ENSO and MAM Seasonal Rainfall

Figure 6 shows the results of XWT analysis between ENSO and MAM seasonal rainfall over EA. For nearly all the occasions and rainfall zones (R1–R8), when and where significant resonance was revealed, the results showed the cause-and-effect relationship in the XWT analysis, indicating phase lock oscillation events, as shown by the left-pointing arrow (antiphase) in a significant resonance band (Fig. 6a–h).

Fig. 6
figure 6

Cross-wavelet transforms of ENSO and MAM rainfall over eight rainfall zones-regions of East Africa (R1–R2). The thick black contours depict enclosed regions greater than 95% confidence for a red-noise process, and the black line is the cone of influence. Right-pointing arrows indicate that the two signals are in phase, while left-pointing arrows indicate antiphase signals; down-pointing arrows indicate that the extreme indices are ahead of the atmospheric index, while up-pointing arrows indicate that the extreme indices lag behind the atmospheric index

Full size image
Fig. 7
figure 7

Wavelet transform coherence (WTC) between atmospheric index ENSO and MAM seasonal rainfall over eight rainfall zones-regions of East Africa (R1–R2) (see Fig. 6 for more description)

Full size image

Over the rainfall zone 1 (R1), results showed an antiphase relationship with a significant resonance cycle of 2–4 years, 3–5 years, and 12–16 years during 1965–1975, 1979–1988, and 1973–1993, respectively (Fig. 6a). Meanwhile, over the rainfall zone 2 (R2), a positive correlation (in-phase) between the ENSO index and MAM seasonal rainfall is shown with the first significant resonance cycle of 2–4 years between 1979 and 1990, and 12–16 years occurring between 1972 and 2002 (Fig. 6b). Similarly, rainfall zone 3 (R3) showed a significant antiphase resonance cycle of 2–4 years which stretches from 1979 to 1991, and 12–16 years during 1975–1989 (Fig. 6c). This antiphase (negative) relationship also extends to rainfall zone 4 (R4) which displayed two significant resonance cycles of 2–4 years between 1965 and 1972, followed by a 4–5-year band during 1978–1999 (Fig. 6d).

Likewise, rainfall zone 5 (R5) revealed antiphase signals in three significant cycles of 2–4 years, 3–4 years, and 10–12 years occurring between 1962 to 1971, 1982 to 1993, and 1995 to 2002, respectively (Fig. 6e). The negative pattern is maintained in rainfall zone (R6) where two similar significant resonance cycles of 2–4 years and 4–6 years were revealed during 1966–1971 and 1989–1994, respectively. Further, rainfall zone 6 (R6) showed a third significant resonance cycle of 3–4 years between 1996 and 2002, but MAM seasonal rainfall was ahead of the ENSO atmospheric index (Fig. 6f). In the case of rainfall zone (R7), two antiphase significant resonance cycles of 3–5 years around 1978–1987 and a 1–4-year cycle during 1996–1999 in which MAM seasonal rainfall lagged behind the atmospheric index (ENSO) cycle were revealed (Fig. 6g). Lastly, in rainfall zone 8 (R8), the first significant resonance cycle of 3–4 years happened over 7 years starting from 1966 to 1973, but the seasonal rainfall was ahead of the atmospheric index as indicated by down-pointing vectors. The second significant resonance cycle of 3–6 years during the period 1978–1988 showed an antiphase relationship between ENSO and MAM seasonal rainfall (Fig. 6h).

Statistically significant coherence between MAM seasonal rainfall and the ENSO index is prominent at different bands for each rainfall zone (Fig. 6). For instance, in R1, statistically significant coherence of the 4–5-year band is shown during 2003–2016 (Fig. 6a). Meanwhile, R2 revealed statistically significant coherence at a 3–4-year band during 1980–2016, then at a 1–4-year band concentrated around 2005–2008, 16-year band concentrated in1981–1991, and a 10–12-year band during 1990–2011 (Fig. 6b).

In a more divergent case, R3 presented statistically nonsignificant coherent bands between MAM and ENSO over the years, as R4 and R5 presented their second statistically significant coherence bands in the 6–7-year band over the period 1991–1997 (Fig. 6d, e). Conversely, R5 showed another more pronounced statistically significant coherence at a 7–16-year band covering the entire period from 1966 to 2001. In the latter, the change in phase angle indicates MAM seasonal rainfall was ahead of atmospheric index ENSO (Fig. 6e). Rainfall zone 7 (R7) showed a 1–4-year band of statistically significant coherence during 1995–2002 and a 2–3-year band concentrated between 2007 and 2011 (Fig. 6g).

As for the final rainfall zone, R8, a strong statistically significant coherent band which originates as a 4–5-year band during the 1980s bulges to 4–8 years over the period 1991–2000. The most common statistically significant coherence localized around 1964–1975 is revealed in nearly all the rainfall zones (except in R2 and R7) at different bands (Fig. 6a, c–g). Apart from rainfall zone 2 and 7, the six remaining rainfall zones indicated a phase lock oscillation during the early parts of the study period (1965–1975) and from 1980 to 1986.

3.5 Cross-Wavelet Transform Analysis (XWT) Between ENSO and OND Seasonal Rainfall

Results of the cross-wavelet transform analysis between the atmospheric index ENSO and OND seasonal rainfall for the eight rainfall zones (R1–R8) of EA is displayed in Fig. 8.

Fig. 8
figure 8

Cross-wavelet transforms of seasonal ENSO and OND rainfall over eight rainfall zones (R1–R8) of East Africa (see Fig. 6 for more description)

Full size image

Results showed that the two variables ENSO and OND were in phase relationship (positive correlation) in all the regions (R1–R8). This is indicated by the right-pointing vector arrows in all the significant resonance for each cycle. In this case, rainfall zone 1 (R1) showed a significant resonance. For the second rainfall zone, R2, a significant resonance cycle of 4–5 years between ENSO and OND occurred during 1970–1981, and another cycle of 1–4 years was revealed between 1993 and 1999; the change in the phase angle shows that OND seasonal rainfall lagged behind ENSO in the region (Fig. 8b).

The third rainfall zone (R3) experienced a significant resonance cycle of a 1–3-year band between ENSO and OND over the period 1995–1999 (Fig. 8c). Meanwhile, rainfall zone 4 (R4) had on two separate occasions experienced significant cycles of 3–6 years and 1–5 years during 1965–1979 and 1994–2001, respectively (Fig. 8d). A single significant resonance cycles of 1–5 years occurred in region 5 (R5) from 1974 to 1986 (Fig. 8e), but the next closely located rainfall zone 6 (R6) showed two significant resonance cycles of 3–5 years and 5–6 years during 1974–1997 and 1986–1997, respectively (Fig. 8f). For rainfall zone 7 (R7), the results indicated two significant resonance cycles of 4–5 years and 1–3 years between ENSO and OND during 1971–1979 and 1994–1999, respectively, and the change in the phase angle shows that OND lagged behind ENSO in the region (Fig. 8g). Region 8 showed only one significant resonance cycle of 1–3 years concentrated around 1993–1997 (Fig. 8h).

Wavelet transform coherence (WTC) analysis demonstrated statistically significant coherence at several bands during OND rainfall seasons over the eight rainfall zones (R1–R8) in EA (Fig. 9). The three most closely geographically located rainfall zones R1, R2, and R3 showed strong statistically significant coherent signals between ENSO and OND seasonal rainfall in a 1–4-year band during 1991–2008 (Fig. 9a–c). This perhaps signifies the spatial relatedness of rainfall based on closed proximity of distance of separation (Ogwang et al., 2014; Owiti & Zhu, 2012).

Fig. 9
figure 9

Wavelet transform coherence (WTC) between atmospheric index ENSO and OND seasonal rainfall over eight rainfall zones-regions of East Africa (R1–R2) (see Fig. 6 for more description)

Full size image

Rainfall zone 4 (R4) showed statistically significant coherence bands on various events that show a greater influence of OND seasonal rainfall in the region. The first of these incidences is confined between 1973 and 1977 in 1–2-year bands. The second statistically significant coherent relationship happened around 1970–1977 in the 2–5-year band (Fig. 9d). Additionally, R4 showed statistically significant coherent bands towards the end of the analysis period in 1–5-year bands and in 8–9-year bands from around 2006 to 2011 (Fig. 9d). R5 and R6 presented statistically significant coherent results in small isolations, in a 4–5-year band and a 2–3-year band during 1996–1997 and 2005–2006 (Fig. 9e and f, respectively).

Similar to R4, R7 showed statistically significant coherence on four distinctive occasions, symbolizing the influence of OND seasonal rainfall in the region. The first coherence is confined between 1970 and 1974 in 4–5-year bands, followed by a more pronounced statistically significant coherence covering a period of 1982–2001 in 1–3-year bands. The third and fourth statistically significant coherent relationships happened around 2005–2011 in the 2–3-year band and in 1996–2011 in the 7–12-year band (Fig. 9g). The last rainfall zone R8 showed statistically significant coherence at only one point from 1995 to 2001 in 1–3-year bands (Fig. 9h).

3.6 Cross-Wavelet Transforms (XWT) of the IOD and OND Seasonal Rainfall

Results showed an in-phase relationship between the two variables, as indicated by the right-pointing arrows of the vectors for all the regions at different bands (Fig. 10). For example, all the first seven rainfall zones (R1–R7) showed a significant resonance cycle of a 4–5-year band occurring at nearly the same period of 1965–1979, 1968–1977, 1963–1981, 1968–1981, 1965–1981, 1968–1980, 1971–1982 for R1–R7, respectively.

Fig. 10
figure 10

Cross-wavelet transforms of IOD and OND seasonal rainfall over eight rainfall zones (R1–R8) of East Africa (see Fig. 6 for more description)

Full size image

Secondly, all the regions (R1–R8) revealed a significant resonance cycle of varying bands at the nearly same time from 1992 to 2001; this cycle occurs in nearly a similar band for each region of 1–5 years. This is supported by the strong coherence between OND seasonal rainfall and the IOD (Fig. 11), which showed statistically significant high common powers in these bands. The period 1974–1981 was characterized by strong La Niña and subsequently weak El Niño event that was followed by severe droughts in EA (Masih et al., 2014; Omolo, 2010).

Fig. 11
figure 11

Wavelet transform coherence (WTC) between atmospheric index IOD and OND seasonal rainfall over eight rainfall zones (R1–R2) of East Africa (see Fig. 6 for more description)

Full size image

Results showed very strong coherence between OND seasonal rainfall and the IOD (Fig. 11) during these second significant cycles which cover relatively wide periods. Generally, very strong 1–5-year statistically significant coherence during 1991–2011 is observed for R1 (Fig. 11a), while R2 showed similar statistically significant coherence in 1–5-year bands during 1999–2016 (Fig. 11b).

For the case of R3, two strong statistically significant coherence events of 1–4-year bands and 1–5-year bands occurred over the period 1992–1998 and 1997–2016, respectively. However, the latter coherence event reduces to 2–4-year bands from 2010 to 2016 (Fig. 11c). Rainfall zone (R4) presented statistically significant coherence in the 5–6-years band towards 1995–2001 (Fig. 11d), while R5 and R6 showed statistically significant coherence in the 8–9-year band towards 2011–2016 (Fig. 11e, f, respectively).

For each of the remaining two rainfall zones, R7 and R8 showed statistically significant coherence occurring at varying bands. For R7, statistically significant coherence of 1–4 years occurred around 1990–2001, where it was reduced to 2–4 years towards 2016. R7 again showed statistically significant coherence in a 4–5-year bands from 2000 to 2007 (Fig. 11g). Similarly, R8 showed two statistically significant coherence events at 1–4-year bands from 1992 to 2005 and a second coherence cycle at 4–5-year bands from 2001 to 2011 (Fig. 11h).

4 Discussions of Results

The main rainfall seasons of MAM and OND were revealed for most parts of the region as reported (Camberlin & Philippon, 2002; Kizza et al., 2009; Ongoma & Chen, 2017). Seasonal rainfall variations are associated with the ITCZ movement in the north–south direction, allowing low-level moisture convergence over the equator (Basalirwa, 1995). The additional rainfall in the northwestern and western parts of the study area in the months of June–July–August (JJA) is associated with the advection of mid-level tropospheric moist air from the Congo basin transported to the East African region by westerly winds (Owiti & Zhu, 2012).

The results revealed a decreasing trend in seasonal rainfall which confirms the findings that MAM rainfall was decreasing (Gebrechorkos et al., 2019; Lyon & Dewitt, 2012; Rowell et al., 2015). The decreasing trend of rainfall in MAM is found to be associated with decadal natural variability which corresponds to sea surface temperature (SST) variations over the Pacific Ocean (Yang et al., 2014). The reduction in seasonal rainfall in rainfall zone R1, R2, and R3 regions covering Kenya most likely contributed to severe drought events experienced in those years, including 1973–1974 and 1983–1984 (Ayugi et al., 2020; Omolo, 2010).

Conversely, OND seasonal rainfall was found to be increasing throughout the analysis period. This is in agreement with the findings of most studies on OND seasonal rainfall which related the increase in OND seasonal rainfall to the large-scale weakening of the Walker circulation (Liebmann et al., 2014; Tierney et al., 2015). From this study, the influence of ENSO on MAM seasonal rainfall showed statistically significant coherence over bands and the period of analysis. This is consistent with the findings of previous studies which suggest that magnitude, seasonal timing, duration, and consistency of the rainfall response to ENSO vary among the sectors and from region to region in Africa (Nicholson & Kim, 1997).

Notably, statistical coherence was revealed to coincide with the 1972/1974 severe drought events reported in many parts of EA (Masih et al., 2014; Omolo, 2010). This most likely confirmed the cause and effect phenomena indicated by XWT in phase-locked oscillations. MAM and ENSO showed a weak correlation for all the regions, as indicated by the weak coherence results for the period analyzed. This is in good agreement with several studies that have investigated the influence of ENSO over EA and noted a lack of significant influence of ENSO on the “long rains” (Hastenrath et al., 1993; Camberlin & Philippon, 2002).

ENSO and OND showed very strong statistically significant coherence bands in nearly all the rainfall zones, implying that its influence is more robust during OND rainfall seasons than in MAM. Results revealed both negative and positive associations between the two variables; particularly, El Niño events appear to be associated with positive rainfall anomalies, while La Niña is associated with negative rainfall anomalies. For example, the OND season of 1997, which is demonstrated as the wettest season in all the rainfall zones, coincides with a strong El Niño event. These wet conditions during El Niño events are found to be associated with more enhanced convection activities and low-level easterly anomalies over the equatorial western Indian Ocean, implying enhanced advection of moisture from the Indian Ocean, while the reverse is true for La Niña years (Kijazi & Reason, 2012). Further, the results also showed a phase lock oscillation (antiphase) in a significant resonance at several bands concentrated around the 1990s; perhaps this is another cause-and-effect phenomenon between ENSO/La Niña and drought events that resulted in more widespread severe droughts over Africa during 1991–1992 regarded as continental in origin because of its expansive coverage over Africa (Masih et al., 2014).

Results showed that OND seasonal rainfall and the Indian Ocean Dipole (IOD) were strongly correlated over different bands and periods. This strongly confirms the findings of correlation analysis used to quantify the relationship between the IOD index and OND rainfall (Ogwang et al., 2015; Ongoma, et al., 2015). A strong positive IOD is associated with enhanced rainfall and extremely wet conditions over the region. The results support the justification of the previous study by Behera et al. (2005), which proposed that the influence of the IOD on OND seasonal rainfall in East Africa overwhelms those exerted by ENSO. In this case, the positive and negative phases of the IOD are associated with floods and drought events in EA, respectively (Saji et al., 1999). The OND seasonal rainfall in EA is influenced, among other factors, by the variation in strength of the equatorial surface westerlies which originates from the Indian Ocean and the zonal pressure gradient across the basin (Hastenrath & Polzin, 2004). In addition to these, other forces such as the Indian Ocean Zonal Mode or tropical dipole mode greatly impact East African OND seasonal rainfall (Saji et al., 1999).

4.1 Conclusion and Recommendations

This study examined periodicity in monthly rainfall and changes in seasonal and annual rainfall over East Africa, linking the two main seasons of MAM and OND with the two main atmospheric teleconnections, ENSO and IOD. This was achieved by employing statistical approaches: the Mann–Kendall (MK) test, Sen’s slope estimator (SE), and Morlet wavelet and transform analysis techniques. Results revealed the presence of a 1-year cycle as a dominant period of variability over the entire period of analysis (1960–2017). Nearly 97% of the stations showed a decreasing trend in MAM rainfall, which is the main growing season in EA. Meanwhile, OND and the annual rainfall presented an increasing trend in nearly 60% of the stations. Wavelet transform analysis revealed a statistically significant negative correlation between ENSO and MAM rainfall in a phased lock oscillation, confirming a cause-and-effect phenomena between the ENSO cold phase (La Niña) and drought events during 1973–1974 and 1983–1984. However, a strong positive statistically significant correlation was revealed between the IOD and OND seasonal rainfall which coincided with the two common occurrences of 1997–1998 and 2004–2005 El Niño episodes that caused extremely wet (floods) events over most areas of EA.

Rainfall remains one of the most important drivers of many socioeconomic activities like agriculture and hydroelectricity generation, but such variability in rainfall and occurrence of droughts and floods impose greater risks to most socioeconomic sectors. The implication of such observed trends and rainfall characteristics is an uneasy economic situation as a result of farmers' failures to cope because of low adaptive capacity. Knowledge of variability in rainfall, extremes, and its regulation mechanisms may be considered in improving national rainfall forecasting for individual countries. Future studies on the influence of atmospheric teleconnections on extreme events may include other variables such as the North Atlantic Oscillation (NAO) index and several high-pressure systems (e.g., Mascarene, St. Hellena, Azores and Arabian Ridge, etc.) whose influence is not well known, especially under the current changing climate.