Vol.2, No.12, 1407-1416 (2010)
doi:10.4236/ns.2010.212172
Copyright © 2010 SciRes. Openly accessible at http:// www.scirp.org/journal/NS/
Natural Science
The statistical prediction of East African rainfalls using
quasi-biennial oscillation phases information
Hashim K. Ng’ongolo, Sergei P. Smyshlyaev*
Department of Meteorology forecast, Russian State Hydrometeorological University (RSHU), Saint-Petersburg, Russia;
hngongolo@mail.ru, *Correspon ding Author: smyshl@rshu.ru
Received 22 September 2010; revised 25 October 2010; accepted 28 October 2010.
ABSTRACT
A simple correlation method and a quasi-biennial
oscillation (QBO)/rainfall composite analysis
were used to examine the teleconnections be-
tween the seasonal rainfall anomalies of March
through May (long-rains) over East Africa and
the different QBO phases in the stratospheric
zonal winds, and also explore the predictive
potential of the long rainy season using infor-
mation about the phases of the QBO for the pe-
riod 1979-2003. We study the spatial correlation
patterns statistically to understand the climatic
associations between the equatorial strato-
spheric zonal wind and regional rainfall at the
interannual time scale. The aim of this analysis
is to establish whether this global signal can be
employed as predictor variable in the long-range
forecasts. Principal component analysis (PCA)
is employed in the first instance to reduce the
large dimensionality of the predictant (monthly
rainfall data), to retain the time series of the
principal components ( P Cs ) and to delineate the
rain gauge network of East Africa into homo-
geneous zones. Spatial patterns of the factor
loading were used to delineate East Africa into
11 homogeneous zones.
Keywords: Principal Component Analysis (PCA);
Climatological Rainfall Zones;
QBO-Index; SOI-Index;
March to May Seasonal Rainfall in East Africa
1. INTRODUCTION
East Africa experiences two main rainy seasons,
namely the ‘long’ rains (March to May) and the ‘short’
rains (October to December). Significant evidence of the
relationships between short-rains over eastern Africa,
and SST and ENSO have been observed [1-3], and rela-
tively less attention has been directed at the predictive
potential of the long-rains season over th e region, which
is more critical than the short-rains in many parts of the
region for the agricultural industry and other social eco-
nomic activities. The long-rains season has been associ-
ated with complex interactions between many regional
and large-scale mechanisms which generally induce
large heterogeneities in the spatial rainfall distribution
[4,5] and virtually neglig ible co rrelations with ENSO [3].
Recent studies of interannual variability in the tropics
have largely focused on the ENSO, so much so that
other important long-term sources of climate variability
may have been overlooked. Therefore the objective of
this study is to investigate the relationships between the
different quasi-biennial oscillation (QBO) phases in the
stratospheric zonal wind and the long-rains season of
eastern Africa, and also explore the predictive potential
of the long rainy season using information about the
phases of the QBO. Several investigators have reported
the presence of the QBO in various atmospheric pa-
rameters and at different regions of the globe [5-7].
Studies by Holton and Lindzen, Plumb, Holton and Tan
[8-10] have indicated that the stratospheric equatorial
QBO is forced locally by alternating downward propa-
gating patterns of westerly and easterly mean zonal
winds which repeat with somewhat irregular period av-
eraging about 26 months. It has been pointed out that the
stratospheric QBO is excited primarily by vertically
propagating equatorial wave modes, and that these
modes excite a quasi-biennial mean zonal wind response
through the mechanism of radioactive damping which
causes the waves to decay in amplitude with height and
thus to transfer momentum to the mean zonal flow [8].
Lau and Sheu [11] have indicated that the fundamental
period of the Southern Oscillatio n (SO) is approx imately
double that of the QBO, which in turn twice that of the
annual cycle. QBO has been found to be strongly phase
locked with the annual cycle and it also tends to enhance
major negative swings in the SO associated with the El
Niño-Southern Oscillation (ENSO) events. Evidence
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suggests that the development of ENSO tends to be as-
sociated with the easterly phase of the lower strato-
spheric QBO [11]. Many attempts have been made to
examine the predictability potential of the QBO signals
because of its persistence and appearance in many at-
mospheric parameters [6,12,13]. Mukherjee et al. [6]
have identified a significant relationship between the
phases of the QBO in the zonal wind in the lower
stratosphere (30-mb) and the percentage departure of the
summer monsoon rainfall of India. They showed that the
strong easterly phase of the QBO is associated with
weak monsoons and weak easterly/westerly phases with
active monsoons. The weakening of the easterly winds is
generally a manifestation of westerly phases of the QBO
in the lower stratosphere, as the prevailing winds in the
stratosphere during summer monsoon are broadly east-
erly. Mason and Tyson [13] have analyzed the phases of
QBO and southern Africa rainfall and found a significant
correlation (+ 0.6) between QBO and regional rainfall
when the QBO is the west phase. Ogallo et al. [14] have
investigated the characteristics of QBO over tropical
eastern Africa using zonal wind composites from Nai-
robi, Kenya (1° 18´S, 36° 45´E) for the period 1 966-19 87.
Their results, based on spectral analysis indicated the
dominance of a 28 months period in the zonal wind
component. The results also indicated some significant
(at 5% level) association between rainfall and QBO sig-
nal based on the reversal in zonal winds.
2. AREA OF STUDY
The domain of study is the eastern Africa region
which lies within longitude lines 29-42°E and by latitud e
lines 5-12°S. The region has complex topographical fea-
tures: East African highlands that include high moun
tains; Kilimanjaro 5895 m above sea level, Kenya 5199
m and Elgon 4321 m. Some of these mountains like
Kilimanjaro and Kenya have permanent glaciers at their
top throughout the year, which makes them very special
as potential indicators of regional or large-scale
long-term climate fluctuations. The complex mountains
are also the source watersheds for some of the major
rivers of the region [15], they therefore form an integral
component of the regional hydrological cycle. The other
unique physical characteristics of the region include the
water masses of Lake Tanganyika, Turkana, Albert, Vic-
toria and Indian Ocean. The total rainfall amount for
meteorological stations in East Africa varies from year-
to-year as well as having large seasonal variations. The
mean annual rainfall totals range from below 500 mm in
the semi-arid areas, which include the northern and east-
ern parts of Kenya and eastern and central Tanzania.
However, the areas around the Lake Victoria have a rela-
tively high mean annual rainfall of 1200-1600 mm [16].
The coastal areas receive over 1000 mm, the highlands
of central Kenya and southern Tanzania, much of
Uganda and western Tanzania also receive rainfall of
more than 800 mm. The region experiences bimodal and
unimodal rainfall seasons Figure 1.
Thus Uganda, Kenya and most of the locations in the
northern half of Tanzania experience two rainfall seasons
(bimodal) which includes March-May (MAM) long
rains’ and ‘short rains’ October-December (OND). The
southern half of Tanzania is characterized by a unique
unimodal rainfall pattern characteristic to the southern
Africa rainfall that occurs between November and April
in the subsequent year. These rainfall patterns are con-
trolled by the seasonal migration of the Inter-Tropical
Convergence Zone (ITCZ).
(a) (b)
F
igure 1. Annual cycle of rainfall for 2 selected stations, bimodal (a) Dagoretti and unimodal (b) Songea.
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3. DATA DESCRIPTION AND
METHODOLOGY
The data used as predictor variables in this study are
Southern Oscillation Index (SOI) and globally averaged
equatorial stratospheric 30-mb zonal wind index (QBO).
This data set was obtained from climate analysis center
(CPC/NOAA) database. The data used as the predictant
variables are long-term monthly rainfall records for 71
meteorological stations scatted over the East African
region Figure 2, and are supplied by the Tanzania Mete-
orological Agency (TMA) and, the Ugandan and Kenyan
Meteorological Departments. To ensure consistency with
the SOI and QBO-indices data; we extracted rainfall
records from the stations for the period from 1979 to
2003. A simple correlation method and a QBO/rainfall
composite analysis were used to examine the telecon-
nections between the seasonal rainfall anomalies of
March through May (long-rains) over East Africa and
the different QBO phases in the stratospheric zonal
winds, and also explore the predictive potential of the
long rainy season using information about the phases of
the QBO for the period 1979-2003. We study the spatial
correlation patterns statistically to understand the cli-
matic associations between the equatorial stratospheric
zonal wind and regional rainfall at the interannual time
scale. The aim of this analysis is to establish whether
this global signal can be employed as predictor variable
in the long-range forecasts. Principal Component Analy-
sis (PCA) is employed in the first instance to reduce the
large dimensionality of the predictant, to retain the time
series of the principal components (PCs) and to delineate
the rain gauge network of East Africa into homogeneous
zones. Spatial p atterns of the facto r loading were used to
delineate East Africa into 11 homogeneous zones Figure
3.
Figure 2. The location of stations used in the study.
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Figure 3. The homogeneous climatological zones over eastern Africa derived from PCA.
The stratification of the QBO indices was based on
four seasons: March to May (MAM), June to August
(JJA), September to November (SON), and December to
February (DJF). The standardized departures of the
rainfall for East Africa from 71 meteorological stations,
normals were calculated for the long-rains season of
MAM based on the relation:

YY
, where Y is
MAM rainfall in a year, Y and
are mean and
standard deviation respectively, based on the 1979-2003
period.
3.1. Principal Component Analysis
The following is PCA procedures [17]. Consider the
matrix
M
XN , whose elements mn
F
f
are standardized
values, when m = 1, 2, 3, …M (stations) or grid points
and n = 1, 2, 3, …N (time i.e. months, years, seasons
etc).
1) Compute the covariance matrix
M
XM
1T
F
F
N
 (1)
2) Determine the eigenvectors
12
,...
M
ee e and
eigenvalues
12
,.... M
 
from the characteristics
equation of Z, where I is a unit matrix
0I
 (2)
3) Compute the principal component time series, C
such that its elements
M
N
C, are the projection of mn
f
on
M
e given by
T
CEF (3)
Each of the PCs will be orthogonal to the other, the
(PC1) will be the most dominant pattern and it explains
most of the variances, then (PC2) will be second fol-
lowed by PC3, etc. The Kaiser criterion was used to de-
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termine the number of significant factors retained in the
PCA varimax rotation [18]. The magnitude of the load-
ing of each variable (station) on each of the common
factors is the index, which is used to assign the variable
(station) to its group or type. Finally other verification
method which included the use of relief and physical
processes playing role in rainfall generation over East
Africa were used to determine the reality of the deline-
ated PCA rainfall pattern s.
3.2. Correlation Analysis
In view of the large variability of distribution of rain-
fall over the region, the analysis was based on the 11
homogeneous climatological zones as can be seen in
Figure 3, in order to examine the relation ship of rainfall
of those zones with QBO. Each of the 71 rainfall indices
and the regional rainfall index time series for 11 zones
were first correlated with the equatorial averaged strato-
spheric zone wind in order to identify the spatial extent
of the associations between QBO and rainfall. The zones
that significantly correlated with QBO were identified
and were cross-correlated with the SOI to test the con-
tribution of each of the two glob al climate indices on the
long-rains season. These zones time series were then
generalized into categories using contingency tables
based on the west and east phases of the QBO. Zero and
non-zero lag correlation analysis were used in this study
and the statistical significance of the correlation coeffi-
cient (R) is tested based on the Z-transformation of
Fisher and criterion student. The student’s t-statistic was
used to decide the significance of the correlation from
the matrices [19]. The space and time patterns of the
significant correlations were then used to investigate the
relationships between QBO and SOI, and regional rain-
fall. Simple correlation coefficient (R) can be expressed
as follows.


1
22
11
N
ii
NN
ii
XXYY
R
X
XYY



(4)
where ,
ii
X
Y are predictors and predictants, and ,
X
Y
are the mean values respectively; is the sample size,
positive and negative values of (R) are in-
dicative of the positive or negative relationship respec-
tively. The statistical sign ificance of the correlation coef-
ficient () is tested based on the Z-transformation of
Fisher.
N
1R 1,
R
11
21
R
In R

(5)
and criterion student, zKP
Z
where
K
P
coin-
cide with 5, 1 or 0.1% level of significance. The stan-
dard deviation of parameter Z can be estimated using the
relationships:
1
3
ZN
(6)
3.3. Composite Analysis
In the composite analysis we used the years with
above normal rainfall and coinciding with west phases of
the QBO and years with below normal rainfall and coin-
ciding with the east phase of the QBO. The years having
a standardized rainfall index of were classified
as high-rainfall and the years having a standardized
rainfall index
0.12
0.12
, classified as low-rainfall years.
The choice of this range of the standardized rainfall in-
dex is based on a student t-test applied on a sample size
of 25 years. The t-scores on the high- and low-rainfall
indices indicate that the two series are significantly dif-
ferent at 95% significance level.
4. RESULTS AND DIS CUSSION
4.1. Relationships between Seasonal
Rainfall and the QBO-Index
The basis for using the lower equatorial stratospheric
zonal wind index in seasonal prediction is based on its
tendency to persist for several months after the phase
change from easterly to westerly and vice versa. Figure
4 shows plots of simultaneous and lag correlations be-
tween the long-rains over homogeneous rainfall zones in
eastern Africa and 30-mb QBO-index for the period
1979-2003. Based on the criterion student on a sample
size of 25 years, correlation coefficients [r] 0.51 are
above 5% confidence level. Table 1 gives a summary of
the seasonal and monthly correlation indices between the
two variables.
Figure 4. The mean correlation patterns of three seasons lag,
two seasons lag, one season lag and zero lag between QBO-
index and MAM seasonal rainfall over East Africa. Correlation
alues above 5% significant level area also indicated. v
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Ta bl e 1. Simultaneous and lag correlations coefficient between the QBO-index and MAM seasonal rainfall over 11 homogeneous
zones over East Africa based on a sample size of 25 years.
Period Zone A Zone B Zone C Zone D Zone E Zone F Zone G Zone H Zone I Zone J Zone K
JJA 0.58** 0.54** –0.42* 0.55** 0.11 0.60** 0.32 0.42* 0.41* 0.45* 0.20
SON 0.52** 0.53** –0.34 0.17 -0.19 0.53** 0.35 0.30 0.26 0.12 0.09
DJF 0.09 0.11 –0.15 0.40* 0.45* 0.32 0.33 0.41* 0.28 0.44* 0.25
MAM 0.46* 0.26 –0.21 0.43* 0.41* 0.46* 0.20 0.21 0.35 0.42* 0.23
JUNE –0.04 0.47* –0.34 0.40* 0.16 0.56** 0.23 0.41* 0.40* 0.43* 0.20
JULY –0.50* 0.54** –0.43* 0.46* 0.13 0.59** 0.33 0.40* 0.41* 0.40* 0.19
AUG –0.49* 0.57** –0.41* 0.37 0.03 0.57** 0.38 0.42* 0.36 0.29 0.18
SEPT –0.39 0.55** –0.38 0.26 –0.08 0.55** 0.38 0.42* 0.30 0.19 0.13
OKT –0.51** 0.52** –0.35 0.17 –0.19 0.52** 0.35 0.43* 0.26 0.13 0.10
NOV –0.55** 0.50* –0.29 0.07 –0.29 0.46* 0.31 0.40* 0.20 0.05 0.03
DEC –0.51** 0.44* –0.25 0.02 –0.35 0.32 0.20 0.41* 0.12 –0.02 –0.04
JAN 0.39 –0.20 0.04 0.27 0.52** 0.23 0.17 0.03 0.09 0.40* 0.17
FEB 0.36 –0.09 0.02 0.31 0.53** 0.29 0.15 0.12 0.18 0.31 0.29
MAR 0.18 0.08 –0.08 0.40* 0.48* 0.38 0.16 0.16 0.28 0.47* 0.26
APR –0.04 0.20 –0.23 0.43* 0.44* 0.46* 0.19 0.21 0.35 0.44* 0.24
MAY –0.27 0.35 –0.29 0.40* 0.30 0.51** 0.22 0.42* 0.38 0.32 0.18
**Significant at 99 % level. *Significant at 95% level.
Results indicate significant simultaneous and lag cor-
relations between the QBO-index and rainfall over zone
F, which covers the Lake Victoria region (+0.6), the
southern region of Tanzania (zone A) of about +0.6, the
western region of Tanzania (zone D) of about +0.6, the
central region of Tanzania (zone B), the eastern, central
and western of Uganda (zone J) and, central rift valley
and Nairobi area (zone H). The QBO/rainfall correla-
tions in these zones are significantly high for at least five
months prior to the MAM rainfall season. The highest
significant correlation between seasonal rainfall and
QBO-index is +0.6 observed between the MAM rainfall
index and the JJA QBO-index of the previous year and
decreases towards the target rainfall season (MAM).
These lagged relationships between the two variables
indicate high prospects for using them in the develop-
ment of prediction methodology. However, the correla-
tions suddenly collapse between 3 and 2 seasons lag for
zones D, H and J. The sudden collapse in correlations
suggests that long-term prediction (of two seasons or in
advance) may not be feasible in these three zones. The
observed areas of significant lag correlations suggest
that seasonal prediction may be feasible in those areas.
Cross-correlation between the QBO-index, rainfall and
SOI was computed and the resulting indices are summa-
rized in Table 2. These results show some good associa-
tions between QBO-index and the region rainfall with
significant simultaneous and lag correlations of +0.5
(explained about 25% of variance) and +0.6 (explained
about 36% of the variance) respectively. The fact that the
two global climate indices (QBO and SOI) are statisti-
cally unrelated at both simultaneous and lagged time,
gives more confidence of using them as predictors of the
seasonal rainfall with low risk of introducing artificial
skill.
Table 2. Simultaneous and lag cross-correlation matrix for
Rainfall, QBO and SOI index for the period (1979-2003).
Rainfall
index zone F QBO-index
(MAM) SOI-index
(MAM) QBO-index
(July)
QBO-index (MAM)0.46*
SOI-index (MAM)–0.15 0.15
QBO-index (July) 0.59** 0.78** 0.10
SOI-index (July) 0.07 0.21 0.44* –0.04
** Significant at 99% level. *Significant at 95% level.
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4.2. Predictability Potential of Seasonal
Rainfall Using the QBO-Index
Figure 5 shows the time evolution of the QBO-index
and SOI for the period 1979-2003. The figures show
years with westerly and easterly phases of the QBO-
index and SOI. iii. The west phases of the QBO-index
were observed during 1980, 1983, 1985, 1986, 1988,
1990, 1993, 1995, 1997, 1999 and 2002 while east
phases of QBO-index occurred in 1979, 1982, 1984,
1987, 1989, 1992, 1994, 1996, 1998, 2000, 2001 and
2003. On the other hand, frequent negative phases have
been dominant by the SOI for the analysis period. Dur-
ing the years: 1982, 1984, 1987, 1992, 1994, 1998 and
2003, the east phases of the QBO-index coincided with
the low (negative) phases of the SOI. All these years
with exceptio n of 1984 and 1994 have been classified as
ENSO years [20]. This observation is consisted with the
notion that ENSO tends to be associated with east phases
of the QBO.
Ta b le 3 shows three homogeneous zones of East Af-
rica that we have identified to have significant correla-
tion with the QBO-index. Generalizations of the sea-
sonal rainfall in these three zones into categories using
contingency tables and the west and east phases of the
QBO are also summarized in Table 3. Based on these
three zones, stratospheric westerly wind phases corre-
sponding to above normal rainfall, were observed 7 out
of 11 cases for zone A, 7 out of 11 for zone B, and, 8 out
of 11 for zone F, giving conditional probabilities of
about 0.6, 0.6 and 0.7 for the associations of above nor-
mal rainfall during the long-rains over eastern African
region and west phase of the QBO. Below normal rain-
fall coinciding with the westerly phase of the QBO were
observed during 1983 for the period of analysis. This
(a)
(b)
Figure 5. Annual mean time series for QBO-index (a) and SOI index (b).
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Table 3. Contingency table for zonal wind phases at 30-mb
level and the March to May seasonal rainfall anomalies over
three homogeneous zones of East Africa.
Rainfall anomaly
QBO-index phases AN NN BN TOTAL
West phases 7 2 2 11
East phase 3 1 8 12 ZONE A
TOTAL 10 3 10 23
West phases 7 1 3 11
East phase 3 2 7 12
ZONE B
TOTAL 10 3 10 23
West phases 8 1 2 11
East phase 2 2 8 12 ZONE F
TOTAL 10 3 10 23
AN-above Normal rainfall (
0.12
imean
XX
 ;
-The standard deviation;
BN-below Normal rainfall (
0.12
imean
XX
 ;i
X
-Denotes an observa-
tion; NN-near Normal rainfall (
0.12
mean
X0.12
mean
XX
i
 .
year has been classified as prolonged ENSO year [20].
Stratospheric east wind phases and below normal
rainfall shows 8 out of 12 for zone A, 7 out 12 for zone
B, and, 8 out of 12 for zone F, giving conditional prob-
abilities of ab out 0.7, 0.6 and 0.7 fo r below normal rain-
fall in the three regions and the east phase of the strato-
spheric zonal wind. The results obtained in this study
support the notion that above/below normal rainfall is
associated with the stratospheric westerly/easterly zonal
wind phases. These good associations between phases of
QBO and seasonal rainfall indicate encouraging poten-
tial for rainfall predictability using th e information abou t
the QBO phases. Significant correlations between rain
fall in Zones A, B and F and, QBO-index persists for
two seasons prior to the long-rains season, but collapses
in Zones D, H and J. In the rest of the analyses, we use
the rainfall index for zone F as an example for testing
the prediction poten tial of rainfall using the QBO-index.
In Figure 6, we present the Ju ly QBO-index prior to the
onset of the long-rains which indicated a high significant
correlation with the MAM seasonal rainfall over the
Lake Victoria region of eastern Africa. It is evident from
this figure that about 70% of the large positive/negative
anomalies in the rainfall were observed during the period
of large positive/negative QBO-index. Some of the ex-
treme rainfall anomalies were however, not related to the
QBO-index. The correlation coefficient between the
QBO-index and sub-region rainfall is found to be 0.59,
which is at 99% significant level based on criterion stu-
dent. This highly significant correlation indicates some
robust associations between the seasonal rainfall and the
QBO. The shown robust relationship between the
long-rains and the QBO-index shows high predictive
potential.
For the purpose of predicting the regional rainfall, the
most useful index appears to be the trend for QBO-index
before the rainfall season. The positive October to De-
cember (OND) minus JJA QBO trend could be a good
indicator for the non-occurrence of drought over eastern
Africa. Similarly, a negative trend could be a good indi-
cator for the non-occurrence of high rainfall over the
region. Figure 7 shows a scatter diagram between March
to May seasonal rainfall anomaly around Lake Victoria
region and the July 30-mb equatorial zonal wind (a) and,
the October to December minus June to August trend in
the QBO-index (b). The correlation coefficient between
the East African rainfall anomaly from zone F and the
difference between OND and JJA QBO-index is 0.63
Figure 6. Time series of rainfall over Lake Victoria region (zone F) and previous year July
QBO-index.
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141
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(a)
(b)
Figure 7. Scatter diagram between MAM seasonal rainfall anoanomaly over Lake Victoria re-
gion and the July 30-mb equatorial zonal wind (a), and the October to December minus June
to August trend in the QBO-index (b).
(explaining about 40% of the rainfall variance) which is
higher than that for JJA seaso n (0.6). As shown on Figure
7, most of the severe drought years are in the lower left
quadrant, and most of the very heavy rainfall years are in
the upper right quadrant of the scatter diagram. The near
absence of points in the lower right corner of this scatter
diagram suggests that a positive QBO-index trend should
be a very useful predictor for non-occurrence of droughts
over equatorial eastern Africa.
5. CONCLUSIONS
After analyzing the results obtained from the rela-
tionships between the different QBO phases in the
stratospheric zonal wind and long-rains season of eastern
Africa we are able to reach the following conclusions:
1) The relationship between the MAM seasonal rain-
fall and El Niño applies to limited number of years, the
ones when El Niño occurs, whereas the relationship be-
tween the QBO-index and seasonal rainfall is applicable
in all years. Therefore monitoring of both the parameters
can provide very useful guidance for the long-range
forecasting of seasonal rainfall in the region.
2) It is shown that, above/below normal rainfall in
eastern Africa is associated with the stratospheric west-
erly/easterly zonal wind phases.
3) It is shown that the phase of the QBO prior to the
MAM seasonal rainfall is a useful predictor index for the
seasonal rainfall. This is particularly the case for the
long-rains for which ENSO prov ides only limited skill in
the predictability of th e rains. This observatio n sh ould be
explored further in the search for more effective seasonal
climate predictors over eastern Africa and the other re-
gions of Africa.
4) In order to improve prediction of the MAM sea-
sonal rainfall in East African countries, which has a
foremost impact on all sectors of the economy in cluding
agriculture, water supply and hydropower generation
across much of the region we recommended using QBO
H. K. Ng’ongolo et al. / Natural Science 2 (2010) 1407-1416
Copyright © 2010 SciRes. Openly accessible at http:// www.scirp.org/journal/NS/
1416
signals as predictors.
6. ACKNOWLEDGEMENTS
The authors wish to thank the Tanzania Meteorological Agency
(TMA), the Ugandan and Kenyan Meteorological Departments for
providing the rainfall data. The work was supported by the Russian
Oriented Program ‘‘Scientific Teaching Personnel in Innovative Rus-
sian’’ (Kadryi).
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