Application of wavelet empirical orthogonal function analysis to investigate the nonstationary character of Ethiopian rainfall and its teleconnection to nonstationary global sea surface temperature variations for 1900–1998
Mohamed Helmy Elsanabary,
Civil Engineering Department, Port Said University, Port Said, Egypt
Department of Civil and Environmental Engineering, University of Alberta, Edmonton, Canada
Correspondence to: Dr T. Y. Gan, PhD, PEng, FASCE, Department of Civil and Environmental Engineering, University of Alberta, 3-033 Markin/CNRL Natural Resources, Edmonton, Alberta T6G 2W2, Canada. E-mail: email@example.com
This study employed the wavelet empirical orthogonal function (WEOF) analysis to analyse the nonstationary variability of rainfall in Ethiopia and global sea surface temperature (SST) for 1900–1998. The study found that the nonstationary variations of both the June to September (JJAS) and February to May (FMAM) Ethiopian rainfall can be delineated into three zones: western half of Ethiopia north of the Great Rift Valley (GRV), southern Ethiopia south of the GRV and the GRV from southwestern Ethiopia to the Afar Triangle. The leading wavelet principal component (WPC) signals showed that Ethiopian rainfall had been in stagnation for most of 1900–1998, with major droughts in the 1940s and 1980s. The dominant frequencies of Ethiopian rainfall ranged between 2 and 8 years. In western Ethiopia, the 2–4-year rainfall frequencies dominated the rainfall variation, but their trends are modulated by 5–7-year frequencies, whereas in the Afar Triangle, the 5–7-year frequencies were dominant. Between 1900 and 1998, the Afar Triangle region experienced decreasing rainfall for 60 years (1900–1960). The seasonal global SST revealed that regardless of what time of the year, the strongest contributions to global SST variations occur in the Antarctic Ocean, the El Niño region of South America and in the southwestern Pacific Ocean, followed by the Atlantic and the Indian Oceans. Further, this study also shows annual migrations of SST variations in the El Niño region, the Antarctic and the Atlantic Oceans. The leading SST signal variations show that SST warming started in the Atlantic and Indian Oceans, from 1950 to 1975, and spread to the Antarctic Ocean between 1960 and 1990, which probably contributed to the melting of sea ice. Teleconnections between WPC1 of Ethiopian rainfall and SST scale-averaged wavelet power were found for the El Niño region and northern Atlantic, west of the Sahara desert.
Ethiopia's climate variation in particular that of rainfall is nonstationary (Segele et al., 2009). Because of the nonstationary characteristics inherent in rainfall data, nonstationary techniques are needed to analyse the variability of rainfall in space and time. To complement the nonstationary knowledge of Ethiopia's rainfall variability, it is also necessary to understand similar variations in global ocean sea surface temperatures (SSTs), known to be linked to Ethiopian's rainfall variations (Diro et al., 2011). As reaffirmed by Mwale et al. (2004, 2007) and Mwale and Gan (2005), an important by-product of the nonstationary analysis of rainfall and SST is the ability to teleconnect seemingly remote nonstationary spatial and temporal patterns of these climatic variations, making it possible to reliably predict rainfall from SST. The ability to understand and teleconnect the nonstationary variations of rainfall and SST should be useful to Ethiopia, a country where droughts and famines are notoriously endemic (Degefu, 1987). Droughts and famines are endemic because agriculture, which accounts for approximately 50% of Ethiopia's gross domestic product and employs 80% of Ethiopia's population, is heavily dependent on rainfall (Abegaz et al.., 2007), which has been found to exhibit considerable spatial and temporal variability (Shanko and Camberlin, 1998; Bewket and Conway, 2007). As nonstationary climatic information shows dominant events irregularly distributed in space and time (Torrence and Compo, 1998), the dominant events can reveal rainfall droughts and floods, and warming or cooling of ocean SST. As shown by Mwale et al. (2004), the complementary interaction of dominant events in rainfall and SST, simultaneous or lagged, evolves over time and space. Knowledge of this interaction would create the potential for Ethiopia to improve its rainfall prediction capabilities and adapt its agriculture practices wisely. Further, Ethiopia is also the headwaters of the Blue Nile River and its tributaries, which endow Egypt and Sudan with 60% of its streamflow (Seleshi and Demaree, 1995). The Blue Nile is the major tributary of the Nile River whose flow variability is strongly modulated by atmospheric circulations over the Atlantic, West Indian and Pacific Oceans (Jury, 2011), e.g. Yeshanew and Jury (2007) found that the Pacific thermocline oscillation and the Atlantic circulations modulate the convective polarity of North Africa. Understanding the nonstationary variations of rainfall across the Blue Nile basin has the potential to assist Egypt and Sudan, downstream of the Blue Nile, to understand the nonstationary character of streamflow and plan for their water supplies accordingly.
The catastrophic nature of persistent droughts and famines across Ethiopia (see Tab1e 2.1 of Degefu, 1987, pp 29–31) has in the last three decades rekindled efforts aimed at understanding the nature of rainfall variability, so as to better prepare the population to these climatic extremes. Such efforts include those of Eklundh and Pilesjö (1990); Bekele (1997); Gissila et al. (2004); Bewket and Conway (2007); Segele et al. (2009) and Diro et al. (2011). Among all these studies, only Segele et al. (2009) applied the nonstationary techniques of wavelet analysis to analyse Ethiopian rainfall. Using pentad time series, Segele et al. (2009) showed that rainfall in Ethiopian is dominated by interannual cycles of 0.57–1.42, 1.41–3.04 and 3.04–4.6 years, which they determined were caused by local and regional atmospheric circulation mechanisms and global SST anomaly patterns. Segele et al. (2009)'s identification of rainfall oscillations and their variations in time and across Ethiopia was a valuable contribution to understanding the nonstationary character of Ethiopia's rainfall. However, their study utilized only 30 years of rainfall data (1979–2008). With longer datasets, there is a potential to uncover the temporal evolution and interaction of lower and higher frequencies in rainfall, which can reveal how droughts and floods evolve over long periods of time, which is not possible when short datasets are used. Hence, the first goal of this study is to re-analyse Ethiopian rainfall using 99 years of monthly rainfall and SST data (1900–1998).
As shown by Mwale and Gan (2005), although rainfall data before the Second World War was scarce for large parts of Africa, which include Ethiopia, the few datasets that were available (and have since been interpolated) give very meaningful results of rainfall variation in both space and time, especially when most of the noise is removed, such as through computing the scale-averaged wavelet power (SAWP) of rainfall data (Torrence and Compo, 1998). Further, instead of using composite analysis, this study employs a technique reported by Mwale et al. (2004) called wavelet-based empirical orthogonal function (WEOF) analysis to study simultaneous nonstationary variations of rainfall and SST and their teleconnectivity.
Besides understanding the spectral characteristics of Ethiopian rainfall, Ethiopia has also been delineated into several homogenous rainfall regions. For example, Diro et al. (2011) used composite analysis to divide Ethiopia into six homogenous zones of rainfall and showed that different mechanisms linked to SST control rainfall variations in various zones. Eklundh and Pilesjö (1990) applied the principal component analysis (PCA) and common factor analysis (CFA) to regionalize annual Ethiopian rainfall into seven homogeneous zones. Generally, these regions were identified as southern Ethiopia, south of the Great Rift Valley (GRV), western half of Ethiopia north of the GRV, eastern half of Ethiopia north of the GRV and the GRV. Further, Bekele (1997) regionalized Ethiopia into three zones of the rainy seasons and found that the central and eastern regions of Ethiopia had bimodal rainfall [i.e. February to May (FMAM) and June to September (JJAS)], the western part of the Ethiopia had unimodal rainfall and the southern and southeastern had rainfall almost all year round (i.e. December to February, March to May, June to August and September to November). On the other hand, Jury (2010) divided the Ethiopian Highlands (EH) into a northern zone with a unimodel rainy season that is linked to the tropical easterly jet and Atlantic multidecadal oscillation, and a southern zone with a bimodal rainy season enhanced by the Pacific decadal oscillation.
A delineation of Ethiopia into homogenous zones of rainfall helped the country to create a reliable database of rainfall. To our understanding, all the studies that delineated Ethiopian rainfall into homogenous zones did not use nonstationary approaches, and hence the zones identified are not dependent on nonstationary characteristics of rainfall. Further, these studies also did not relate the nonstationary rainfall zones to nonstationary zones of global SST variability, meaning that there is room to understanding Ethiopia's rainfall variations and its teleconnections to SST. In this study, not only is the dominant nonstationary characteristics of Ethiopian rainfall and global SST variations determined, but also their spatial and temporal patterns are teleconnected. Identifying dominant SST and rainfall patterns that are teleconnected has been shown to be critical for predicting spatial and temporal patterns of rainfall in eastern, central southern and southern Africa (e.g. Mwale et al., 2004, 2007; Mwale and Gan 2005). This is the second goal of this article.
2. Research objectives
To meet the above goals, the objectives of this study are the following:
Analyse the nonstationary variations of seasonal (JJAS and FMAM) Ethiopian rainfall by employing wavelet analysis and WEOF analysis.
Using results from (i), delineate Ethiopia into homogenous zones of nonstationary rainfall variability, determine the leverage topographic terrain and other factors have on Ethiopian rainfall and understand the frequency of droughts and their spatial localization.
Using the nonstationary techniques of wavelet analysis and wavelet-based PCA (WPCA), analyse the nonstationary character of seasonal [January to March (JFM), April to June (AMJ), July to September (JAS) and October to December (OND)] global SST.
Using results from (iii), identify the spatial character of dominant nonstationary global ocean SST regions.
Using results from (iv), identify the nonstationary global SSTs that teleconnect with seasonal rainfall across Ethiopia, especially the region of the upper Blue Nile basin, the source of the Nile River.
Ethiopia has generally three rainy seasons. These are the JJAS rainy season, locally called the Kiremt, the February/March to June (F/MAM-J) rainy season, locally called the Belg, and the October to January (ONDJ) rainy season, locally called the Bega. Most of the rainfall occurs during the Kiremt rainy season, when 60–90% of rainfall occurs. Thus, 90–95% of all food is produced during the Kiremt rainy season. The Kiremt rainy season occurs in the western half of Ethiopia, central and most eastern parts, while the Belg and Bega rainy season mainly occurs in the south and southeastern parts of Ethiopia. The Belg rainy season is the main rainy season for southern Ethiopia and coincides with the MAM rainfall of East Africa (Mwale and Gan 2005).
4. Rainfall and sea surface temperature data
Historical monthly precipitation data (1900–1998), ‘gu23wld0098.dat’, Version 1.0, was supplied by Dr Mike Hulme at the Climatic Research Unit, University of East Anglia in the UK. The data, gridded at a resolution of 2.5° × 3.75° was extracted from the region 18°N–2°N to 33°–48°E over Ethiopia and the surrounding areas (Figure 1). Data was extracted for 35 grids. This data is part of an historical monthly precipitation dataset for global land areas from 1900 to 1998. These data were constructed from station data using Thiessen polygon weights. No topographic weighting has been applied to the interpolation scheme. Because the method interpolates anomalies and not precipitation values, it is reasonable to exclude the effects of elevation. The data quality control of these gridded data is described by Hulme (1992); Hulme (1994); Hulme and New (1997) and Hulme et al. (1998). Because this study focusses on the Belg and Kiremt seasons, the seasonal, averaged data for FMAM and JJAS were computed for each year. A longer (1900–2006) and more intense (0.5° × 0.5°) rainfall dataset was also collected from the University of Delaware in the United States. Comparison between the University of East Anglia and the University of Delaware data showed major disagreements, and the latter data was discarded (see Figure 2). The latter data was discarded in favour of the former because the former has been extensively used and shown to be reliable. Another gridded rainfall dataset (1901–2009), CRU 3.10.01, of higher resolution (0.5° ×0.5°) that covers the EH (Mitchell and Jones, 2005) was also tested. A preliminary comparison between both CRU datasets showed general similarities between them but there are major differences in the southeastern parts of EH where observed rainfall data are limited (Beyene and Meissner, 2010) and so results based on the newer, high-resolution CRU dataset may not necessarily be better.
In analysing a global mean monthly SST dataset of HadISST (Version 1.1), Rayner et al. (2003) attempted to improve the local SST by random sampling of measurement errors. In this study, we retrieved the same global SST dataset (1870–2008) of 1° ×1° grid resolution for about 65 000 grids from the Hadley Centre, United Kingdom Met Office. The monthly SST anomaly grid data were transformed into seasonal SST (OND, JFM, AMJ and JAS).
5. Research methodology
5.1. Wavelet analysis
Torrence and Compo (1998) defined the wavelet transform of an observed time series, o with respect to the mother wavelet, ψ, as a convolution integral:
where ψ* is the complex conjugate of ψ, n is the total length of the observation and Z(t,b) is a wavelet spectrum of the decomposed time series at scale b and time t. The quantity b− 1/2 in Equation (1) is an energy normalization term, which ensures that the energy of the mother and daughter wavelets remains the same over all scales, making it possible to directly compare wavelet transforms of one time series with another (Torrence and Compo, 1998).
The wavelet function (ψ) can be constructed so that it can easily be used to match a time series. For analysing rainfall or SST time series, Mwale et al. (2004) suggested using a Morlet wavelet. Convoluting a rainfall or SST time series with a Morlet wavelet over time gives a wavelet spectrum, whose coefficients show how well the wavelet matches with the time series. Therefore, at each scale the magnitude of the spectrum coefficients depicts the amplitude of a time series.
When the wavelet spectrum coefficients at each scale are summed over the length of a time series, they give a new representation of a wavelet spectrum called a global wavelet spectrum. A global wavelet spectrum is similar to a Fourier spectrum. Both spectra show periodic cycles present in the time series, but not their occurrence in time.
Having computed the wavelet spectrum, the SAWP, which represents the mean variance of wavelet coefficients over a range of scales, may also be computed from the wavelet spectrum. This is done in order to examine the variation of rainfall and SST over a range of statistically significant oscillations, as follows:
where Cδ is 0.776 for the Morlet wavelet, δj is a factor for scale averaging and δt is the sampling period (Torrence and Compo, 1998). Because SAWP is a time series of average variance in a certain frequency band, SAWP can also be used to examine the modulation of one time series by another (e.g. variation of rainfall due to SST variations) or the modulation of one frequency by another within the same time series.
5.2. Wavelet empirical orthogonal function analysis
WEOF analysis or wavelet principal component analysis (WPCA) transforms an ‘n × k’ data of SAWP into another ‘n × k’ data of SAWP signals and noise. The signals and noise are called WPCs, designated here as U. U accounts for all the variability in the SAWP and some noise due to minor errors (i.e. extra energy introduced into the SAWP because δt the sampling period is discrete and may include spurious energy into the wavelet spectrum). If the rainfall or SST variability was the same at all grids, the matrix U would contain one SAWP signal (WPC1), which would account for all the variations of the SAWP. Mwale and Gan (2005) pointed out this is never the case because SST in different parts of the oceans will vary differently. Similarly, rainfall varies differently from place to place. Hence, there are usually a few U (or um) to account for the majority of the SAWP variation. The SAWP signals (um) are computed as follows:
where ekm are the eigenvectors, are the k SAWP anomalies and m represents a small subset of the k possible signals. The signals, um, are usually the major spatial and temporal patterns that account for the majority of the variations in the SAWP, and can be used to spatially delineate rainfall or SST variations into independent zones.
6. Data analysis and results
6.1. Dominant oscillations
Before the 1900–1998 SAWP was computed for each rainfall or SST grid, the range of dominant periodic cycles (i.e. oscillations above the 95% confidence level of a red noise process) in the rainfall and SST time series were identified using the time domain wavelet spectra and the frequency fixed global spectra. Figure 3(a) shows an example wavelet and global spectra of Ethiopian rainfall from 12°N and 41.25°E. Using this and other figures (not shown), statistically significant power in JJAS and FMAM Ethiopian rainfall was found to have occurred within the 2–8-year frequency band during 1950–1970 and 32-year frequency band during 1940–1960.
Equally, as there were 65 000 grids of SST data, we could not show wavelet and global spectra for all the SST data. An example wavelet spectrum of SST extracted at 0.5°N–98°W, which shows dominant oscillations of SST within the 2–8-year range during 1880, 1920 and 1970–2000, is given in Figure 3(b). However, some SST data (not shown) exhibited frequencies with the 2–16-year range. To be able to simultaneously analyse rainfall and SST, only the 2–8-year frequency range could be used. Hence, the SAWP for both the SST and rainfall was computed using the 2–8-year frequency range.
6.2. How many signals in rainfall or SST data?
It is generally useful to have an idea about the number of signals, or the leading eigenvectors present in a group of observed data which contains both signals and noise, and it is possible to separate them using empirical orthogonal function (EOF) analysis. Generally, the leading eigenvectors represent the underlying physical processes that give rise to the observed time series, which partly due to inherent limitations of data measurements, and also contain noise or the random component of observed data. In an EOF analysis, eigenvalues and eigenvectors of a time series are computed and eigenvalues are often presented in a scree plot. The relative size of the eigenvalues represents how ‘independent’ the eigenvectors are. The farther apart the eigenvalues, the more distinct their corresponding eigenvectors and vice versa. This is one subjective way to check how many signals are present in the time series. The other way is to look for an ‘elbow’ or sudden change in the gradient of the scree plot. Eigenvalues to the left of the ‘elbow’ are subjectively considered to represent eigenvectors that correspond to signals in the time series, while the ones to the right of the elbow are essentially ‘noise’. When using a filtered time series, such as the SAWP, a useful way to determine the number of signals present in a time series can be done by observing spatial patterns of the eigenvectors (Mwale et al., 2004). Mwale et al. (2004, 2009) found that rainfall spatial patterns may reflect the regional physiographic or topographic characteristics, localized climatic processes or warming and cooling of regional ocean current systems. Some eigenvectors, especially the ones that cover very small areas are discarded, because they are considered as ‘noise’ or meaningless. Figure 4 shows the scree plot of the Ethiopian rainfall (JJAS and FMAM) and Figure 5 shows the scree plot of global SST for the seasons of OND, JFM, AMJ and JAS. From Figures 4 and 5, Ethiopian rainfall (both JJAS and FMAM) may have up to four distinct signals and global SSTs appear to have three distinct signals.
6.3. Spatial patterns of June to September rainfall
Although Figure 4 showed that the JJAS rainfall appeared to have four signals that account for the majority of rainfall variability, only the first two leading WPCs, i.e. WPC1 and WPC2, were retained for analysis, because the other two WPCs could not be explained. The first two WPCs jointly accounted for 41% of the total rainfall SAWP variability, with WPC1 explaining 23% and WPC2 18%. Figure 6(a) and (b) shows the spatial patterns formed by correlating WPC1 and WPC2 to the rainfall SAWP at each of the 23 grids, with contours outside Ethiopia trimmed off. WPC1 is positively correlated to SAWP from the GRV to northern Ethiopia (excluding an area north of 12.5°N, between 37.5°N and 43°N) and negatively correlated to southern Ethiopia, south of the GRV. The strongest positive correlations were in the western half of Ethiopia. The correlations decrease northwards, eastwards and southwards, all towards the GRV. The tightness of contours along the GRV showed decreasing correlation between WPC1 and SAWP (i.e. variation of rainfall in the GRV is different), highlighting the leverage the topography of GRV has on the Ethiopian rainfall. In Ethiopia, GRV is a geographic trench 50–100 km wide (see Google maps), which cuts Ethiopia diagonally from the southwestern corner of the country. From the middle of the country and stretching northeastwards, the GRV funnels out into a triangular depression (the Afar Triangle) with its base stretching from the Gulf of Eden to the Red Sea (see Google maps). Rainfall variability in the Afar Triangle region and an area north of 12.5°N (between 37.5°N and 43°N) was not accounted for by WPC1, because the rainfall in this area varies independently of rainfall to the rest of Ethiopia. The variability of rainfall in the Afar Triangle and the area north of 12.5°N (between 37.5°N and 43°N) is shown in Figure 6(b). Figure 6(b) shows that WPC2 is negatively correlated to SAWP in the region (12.5°N–17.5°N and 37.5°N–44°N) and positively correlated to the Afar Triangle region, with a boundary at about 10°N–12°N, which separates the two regions.
Figure 6(c)–(f) shows the spatial patterns of Ethiopian rainfall's WPC1 and WPC2 using energy extracted from the 2–4- and 5–7-year frequency bands. Figure 6(e) appears more similar to Figure 6(a) than does Figure 6(c) to Figure 6(a), showing that spatially 5–7-year frequency periods are more dominant within the 2–8-year frequency band than the 2–4-year frequencies. Figure 6(c) shows that the 2–4-year frequency energy is dominant in the whole of Ethiopia, north of the GRV, and much weaker south of the GRV. The similarity of spatial patterns corresponding to WPC1, among all frequency bands, north of the GRV goes to show that, except along the GRV, where correlations between WPC1 and SAWP are weak or zero, all frequencies in the 2–8-year bands are important in the JJAS Ethiopia rainfall. Similarly, Figure 6(d) and (b) appears similar to Figure 6(b), showing also that the 2–4- and 5–7-year frequencies are dominant within the 2–8-year frequency band.
From the spatial patterns of three spectral bands (i.e. 2–4, 5–7 and 2–8 years), Ethiopia's JJAS rainfall may generally be delineated into three nonstationary rainfall zones. These zones are western Ethiopia north of the GRV, southern Ethiopia, south of GRV and the GRV from southwestern Ethiopian to the Afar Triangle. The steep gradient along the GRV shows that while JJAS rainfall occurs all over Ethiopia, its variability is attenuated by the valley, and it is out of phase between western Ethiopia and southern Ethiopia. As the rainfall pattern is negatively correlated to southern Ethiopia, WPC1 shows that when JJAS rainfall increases for the rest of Ethiopia, it decreases in southern Ethiopia and vice versa. Our results have some differences with that of Jury (2010) who separated Ethiopian rainfall into two zones, the northern and the southern zones but he missed the GRV zone. The differences between our results and that of Jury (2010) are likely because we used the CRU dataset while Jury used the monthly rainfall data of the World Climate Research Program Global Precipitation Climatology Center (GPCC) and partly because Jury used a 5-year running mean to filter the rainfall fields while we did not filter the rainfall data.
6.4. Temporal patterns of June to September rainfall
Figure 7 shows the temporal variations of the leading eigenvector time series of JJAS Ethiopian rainfall (i.e. WPC1 and WPC2) for frequency bands, 2–8, 2–4 and 5–7 years. Because SAWP was created from a convolution of rainfall by a periodically adjusted wavelet, the positive gradients in the SAWP are interpreted as increasing rainfall and vice versa.
Figure 7(a) shows that apart from the two periods of 1910–1917 and 1990–1998, which showed positive gradient in WPC1, Ethiopian rainfall was in ‘stagnation’ for much of the 20th century, with the lowest rainfall in the 1980, followed by 1941–1942. Decreasing rainfall leading up to 1980 and 1941–1942 is shown as low energy troughs in WPC1. Table 2.1 of Degefu (1987) chronicles droughts in Ethiopia, as depicted by famines and levels of the river Nile from 253 BC. The table documented droughts during 1913–1914, 1921–1922, 1932–1934, 1953, 1957–1958, 1960, 1964–1966, 1968–1978, 1982–1985 and 1991–1992. Those periods are depicted in WPC1 as troughs or plateaus. The three ‘peaks’ of WPC1 (i.e. 1917, the two decades of 1945–1965 and 1990) do not show any regularity, espousing the fact that Ethiopian rainfall exhibits a truly nonstationary character. Hence, by looking at WPC1, it is not possible to predict when the next anomalously wet or dry rainfall period will occur. Although data was limited for most of global land areas before 1945, including in Ethiopia, the few data that was available and interpolated for 1900–1998 by Hulme (1992) appears to have captured the variation of Ethiopian rainfall and validated the use of this data in Ethiopia for periods before 1945. Figure 7(b) shows the temporal variations of WPC2. This figure shows that rainfall consistently decreased from 1900 to about 1963, with a brief increase between 1963 and 1975 and exhibited strong regular variations between 1965 and 1998. WPC2 is positively correlated to the Afar Triangle region of Ethiopia and represents the calamitous regime of rainfall variability for this region.
A closer look at the narrower bands of frequency energy in the SAWP (i.e. 2–4 and 5–7 year of Figure 7(c)–(f)) showed that the JJAS 2–8-year WPC1 was largely dominated by the 2–4-year cycles and modulated by 5–7-year cycles, while WPC2 was dominated by 5–7-year cycles and modulated by 2–4-year cycles. The correlation between the 2–4-year WPC1 and 2–8-year WPC1 is 0.62 (i.e. the 2–4-year frequency band explains 0.622 = 38% variance in the 2–8-year band), while WPC2 (5–7 years) explained 57% of WPC2 (2–8 years). This means that in western Ethiopia, the 2–4-year rainfall frequencies dominate rainfall variation within the 2–8-year frequency band (see Figure 7(a) and (c)), but their trends are dominated by the 5–7-year frequency band (see Figure 7(a), (c) and (e)), which explains the suppression of the 1940–1965 peak in the WPC1 of the 2–8-year frequency band. This result re-affirms that when low frequency energy is propagating towards the trough, the 2–4-year (interannual) rainfall variations appear to not have enough energy to offset the 5–7-year energy propagation of the Ethiopian rainfall. This result is similar to that of Segele et al. (2009) who found that major climatic system processes contributing to the annual mode get augmented or suppressed by seasonal, quasi-biennial and El Nino Southern Oscillation (ENSO) time-scale variability. Hence, when analysing Ethiopian rainfall, it is necessary to simultaneously look at both low (5–7) and high (2–4) frequency bands to figure out the direction of propagation of the composite 2–8-year rainfall.
On the other hand, in northeastern Ethiopia, the 5–7-year frequencies dominate the rainfall (see Figure 7(b) and (f)), while the 2–4-year frequencies have limited influence in the variation of the 2–8-year frequency band (see Figure 7(b), (d) and (f)). This means that between 1900 and 1998, northeastern Ethiopia (Afar Triangle) experienced decreasing rainfall for over 60 years (1900–1963).
6.5. Spatial patterns of February to May rainfall
Figure 8 shows the spatial patterns of FMAM rainfall. Figure 8(a) shows that WPC1 is positively correlated to southern Ethiopia and negatively correlated elsewhere in Ethiopia, while Figure 8(b) shows that WPC2 is negatively correlated to almost all parts of Ethiopia, except the northernmost region. The two spatial patterns resemble those of JJAS rainfall and also divide Ethiopia into three zones. Because of the similarity between the FMAM and JJAS rainfall patterns, the former are not discussed further.
Figure 8(c)–(f) shows spatial patterns of WPC1 and WPC2, computed from 2–4- and 5–7-year frequency bands. These figures show similar patterns as that of WPC1 of 2–8 years. Similar to the JJAS rainfall, energy within the 2–4 and 5–7 years for FMAM rainfall also dominated the Ethiopian rainfall.
6.6. Temporal patterns of February to May rainfall
Figure 9 shows the temporal variations of WPC1 and WPC2 for the FMAM rainfall, for 2–8-, 2–4- and 5–7-year frequency bands. Figure 9(a) shows that WPC1 exhibited highly irregular variations, generally with less energy between 1900 and 1943, positive energy between 1944 and until about 1980, and after which it shows a dramatic decrease in energy. As WPC1 is positively correlated to southern Ethiopia and negatively correlated to all other areas of the country, the variations in energy show that southern Ethiopia suffered from a serious decrease of rainfall for 1920–1945 and 1980–1998.
WPC2 (Figure 9(b)) also shows an irregular variation of energy, which generally decreases from 1900 to 1998 with the worst being 1965 and 1998. Decreases in the FMAM rainfall have impacted southern Ethiopia, where it is the main rainy season.
When the power within the 2–4-year (Figure 9(c) and (d)) and 5–7-year (Figure 9(e) and (f)) bands is examined, it is clear that the temporal variation of WPC1 computed using 2–8-year frequency bands was dominated by power in the 2–4-year range, but not by the 5–7-year cycles. WPC1 (WPC2) of the 2–4-year band explains 88% (86%) of the energy variation in 2–8-year frequency band, while the 5–7 WPC1 (WPC2) bands explain 11% (41%) of the energy variation in the 2–8-year frequency band. This means that for FMAM rainfall the 2–4-year frequencies are more important in the rainfall variations than the 5–7-year variations.
6.7. Global sea surface temperature variations
SST spatial and temporal patterns were computed for JFM, AMJ, JAS and OND. Only the first two WPCs were retained for further analysis. The JFM SST was chosen to see if there was a 3-month lead time to help with future prediction of JJAS Ethiopian rainfall from SST variations.
6.8. Spatial patterns of global SST
Figure 10(a), (c), (e) and (g) shows the leading SST SAWP spatial variations as represented by WPC1 of global SST for OND, JFM, AMJ and JAS, respectively, while Figure 10(b), (d), (f) and (h) shows similar variations represented by WPC2. Of the total seasonal SST SAWP variability, WPC1 (WPC2) accounted for 30% (15%) in OND, 29% (14%) in JFM, 31% (13%) in AMJ and 27% (13%) in JAS. Figure 10(a), (c), (e) and (g) shows that regardless of what time of the year, the strongest contributions to global SST variations occur in the Southern Ocean region (50°S–70°S), the El Niño region of South America and the southwestern Pacific Ocean region. As expected, in the Southern Ocean, the widest (Figure 10c) and strongest variations occur during JFM and narrowest variations (Figure 10g) occur during JAS. WPC2 shows that the second leading global SST variations are dominant in the Atlantic and Indian Oceans and part of the Pacific (i.e. ocean areas located on either side of the El Niño region in South America).
Figure 10(a), (c), (e) and (g) shows the nonstationary, migratory patterns of ocean SST variations of the El Niño, Atlantic and Southern Ocean basins. The figures show that during the OND period, SST variations show El Niño developing from the Pacific Ocean towards the South American coast (i.e. 140°W–100°W and 5°N–5°S). By JFM, SST variations intensify and develop along the South American coastlines, extending roughly from 80°W to 160°W and 10°N to 10°S and by AMJ, SST variations are fully developed both along the coastline and extend to 160°W. By JAS, variations in the El Niño region begin to dissipate, starting at 160°W. The SST variations and migration patterns in the Atlantic Ocean are similar to that found by Mwale and Gan (2005) and so are not discussed further.
6.9. Temporal patterns of sea surface temperature
Figure 11(a), (c), (e) and (g) shows the temporal variations of the leading eigenvectors of global SST from 1900 to 1998 for OND, JFM, AMJ and JAS, respectively. These figures show that generally between 1900 and 1960, low energy variations dominated the nonstationary characteristics of the global SST. However, between 1960 and 1998 there was a sharp increase in the energy of WPC1, which peaked in 1980 for OND, 1985 for JFM, 1985 for AMJ and 1990 for JAS. As WPC1 is positively correlated to the Southern Ocean, it shows that the Southern Ocean underwent considerable warming for about four decades (1960–1998). However, after 1998, there appears to be a dramatic decrease in SST for this region of the earth.
Figure 11(b), (d), (f) and (h) also shows the variations of the second leading eigenvectors (WPC2) of global SST from 1900 to 1998 for OND, JFM, AMJ and JAS, respectively. Similar to Figure 11(a), (c), (e) and (g), these figures show that between 1900 and 1940, low energy dominated the nonstationary characteristics of global temperature, which sharply increased between 1940 and 1975, peaking in 1970 for all seasons of OND, JFM, AMJ and JAS, and sharply decreasing between 1975 and 1998, confirming Mwale et al. (2004)'s finding. This means that ocean regions positively correlated to WPC2 experienced warming between 1940 and 1975 and experienced cooling between 1975 and 1998. A comparison of WPC1 and WPC2 shows that increase in SST started in the Atlantic and Indian Oceans spread to the Southern Ocean region, which had probably contributed to the melting of sea ice in the Southern Ocean because of the large specific heat capacity of the oceans.
6.10. Teleconnecting rainfall and sea surface temperature
Figure 12 shows the spatial, 5-month lagged correlation patterns between WPC1 and WPC2 of gridded JJAS precipitation and each of the 65 000 SAWP of gridded global SST for JFM. Figure 12(a) shows the 5-month lagged correlation between WPC1 of JJAS rainfall to SST of the El Niño region and the northern Atlantic Ocean (west of the Sahara desert), and also to other areas which include east and west of South America and south of Indian Ocean. Figure 12(a) shows that SST SAWP in the El Niño region only explains up to 16% of the rainfall variability of EH but SST SAWP in other areas could explain up to 64% of the rainfall variability of EH. As expected, the degree of correlation between them also depends on the lag time and the locations (Özger et al., 2009).
7. Observations and conclusions
Ethiopia's climate variation, in particular rainfall, is known to be nonstationary. Because of its nonstationarity, nonstationary analyses techniques of WEOF analysis were employed to analyse the variability of rainfall in space and time. To complement the nonstationarity of Ethiopia's rainfall variability, the techniques were also applied to global ocean SST variations, which are known to be linked to Ethiopian's rainfall variations. Other than examining the nonstationarity of Ethiopian rainfall and global SST variations, the aim is to teleconnect the two climatic variations.
The study revealed that both the JJAS and FMAM global SST variations espouse nonstationary characteristics. From a nonstationary perspective, rainfall variability in Ethiopia was delineated into three zones. These are western half of Ethiopia north of the GRV, southern Ethiopia south of the GRV and the GRV from the south west to the Afar Triangle.
Temporal characteristics of the leading WPC signals showed Ethiopian rainfall had been in “stagnation” for most of the 20th century (1900–1998), with major periods of drought during the 1940s and 1980s. The temporal characteristics also showed that despite the three peaks in the rainfall data (1913–1917, 1945–1955 and 1990–1998), these peaks were so irregular that Ethiopian rainfall exhibits a strong nonstationary character.
The dominant frequencies in the Ethiopian rainfall ranged between 2 and 8 years. In western Ethiopia north of the GRV, the 2–4-year rainfall frequencies dominated the rainfall variation within the 2–8-year frequency band, but their trends are modulated by the 5–7-year frequency band. Hence, when analysing Ethiopian rainfall, it is necessary to simultaneously examine both the low (5–7 years) and the high (2–4 years) frequency regimes to understand its nonstationary behaviour. On the other hand, in northeastern Ethiopia (Afar Triangle region), the 5–7-year frequencies dominate the rainfall but the 2–4-year frequencies have limited influence in the variation of the 2–8-year frequency band. This means that between 1900 and 1998, the northeastern Ethiopia experienced decreasing rainfall for 60 years (1900–1960), following the 5–7-year cycles of drought.
The nonstationary character of seasonal global SST (JFM, AMJ, JAS and OND) revealed that regardless of what time of the year, the strongest contributions to global SST variations occur in the Southern Ocean region, the El Niño region of South America and the southwestern Pacific Ocean region. The next dominant oceanic regions were the Atlantic and the Indian Oceans. Interesting findings of this study include the annual migration patterns of SST variation in the El Niño ocean region, the Southern and the Atlantic Oceans, which show the varying predictor data locations throughout the year. A comparison of leading signals in the oceans showed that increase in SST started in the Atlantic and Indian Oceans, which spread to the Southern Ocean, which probably contributed to the melting of Antarctic sea ice because of the large specific heat capacity of the oceans.
It was also found that the correlation between rainfall WPC1 and SST-SAWP in the El Niño region was comparatively weak, which means a weak relationship between El Niño SST and the Ethiopian rainfall, and so it will be difficult for us to relate individual El Niño events to the rainfall deficits or droughts in Ethiopia.
This research was funded by the Egyptian Ministry of Higher Education (MHE). The Wavelet software was provided by Torrence and Compo. It may be downloaded from the following website. http://atoc.colorado.edu/research/wavelets/