Kenya Journal of Science and Technology (A) (1981) 2: 83-90

Trend of rainfall in East Africa

Laban Ogallo, Department of Meteorology. University of Nairobi. Nairobi. Kenya

ABSTRACT

Trends of rainfall in East Africa during the period 1922-1975 are examinedusing two independent approaches. namely the graphical and statisticalmethods. Under the graphical method the original and smoothed rainfallseries were displayed visually on a graph. while the Spearman rankcorrelation test and the analysis of variance approach were employed inthe statistical approach. The data used included the monthly. seasonal andannual rainfall records of about 100 stations during the period 1922-1975.

The results of the study indicate significant trends of annual rainfall atnine stations when the Spearman rank correlation test was used. Thesmoothed graphs indicated similar tendencies at these stations during theperiod of study. The use of analysis of variance technique. however.indicated no significant difference between long-term averages and theaverages of some standard periods at six of the nine stations. The onlythree stations where significant rainfall trends were indicated with bothmethods were Lodwar, Wajir and Magadi. All methods indicated anincreasing annual rainfall tendency at these stations during the period ofstudy. The results from the monthly. seasonal and regional rainfall recordsrevealed no significant trends on the regionally averaged annual rainfallrecords. or on the monthly and dry season records. The wet seasons hadcharacteristics close to those of the annual series.

INTRODUCTION

The economy of the East African countriesdepends largely on agricultural and pastoralproducts. The major factor which limits theseproducts is water from rainfall. This watersource also limits the water supply fordomestic' and industrial use and for hydro-electric production.

It is evident from both historical andinstrumental records that the global generalcirculation and climate have experiencedcertain fluctuations. These fluctuations haveranged from long-term changes of greatmagnitude to short-term regional anomalies.Such fluctuations have been observed in allweather elements including rainfall.

Short-term variations of the meteorologicalparameters are referred to as weather changes

while their long-term fluctuations constituteclimatic variations. The trend describes long-term movement of any time series. Suchmovements can be described by the use ofgraphical or statistical methods.

In East Africa Rodhe and Virji (1976) useda graphical technique in examining the natureof trend of annual rainfall of 35 stationsconcentrated mainly i~~Kenya and northernTanzania. Their graphical technique indicatedno significant rainfall trend except in thenortheastern region of Kenya where anincreasing annual rainfall tendency wasdisplayed. In this study both graphical andstatistical methods are employed to examinethe nature of trend of the East Africanmonthly. seasonal. annual and regionallyaveraged rainfall records during the period1922-1975. The distribution of the stationsused are given in table 1and figure 1.

~I

© The Kenya National A~ademy for Advancement of Arts and Sciencestit

84 Laban Ogallo

~TBR(49)

50"E

TANZANIA.00".(56) BGY(59)

.SWG(6U.MBY(62)

.MHG(63l·

• >.~(66)

/.TR,H69) .-/•......./---,,---/

o

.SNA(65)

Figure 1. Network of the rainfall stations (code name and number are given for each station)

GRAPHICAL METHODS

In graphical methods, the trend is visualisedfrom the graphical representation of thesmoothed and unsmoothed time series. In thesmoothed time series the trend at any givenpoint in time is represented by a weightedaverage of the observed values near that point.Several weighting functions have been usedin the smoothing of time series (WMO 1966;Shapiro 1975; Herrman 1971; Rabiner et al.1975; Julian and Stephens 1977; and manyothers). In this study five-term binomialcoefficients (WMO 1966) have been used tosmooth the rainfall series. The correspondingsmoothed and unsmoothed rainfall serieswere then displayed graphically. Some ofthese graphs are presented in figures 2-5.

STATISTICAL METHODS

The examination of trend by graphicalmethods has several disadvantages which mayderive from the facts that:

1. The methods are based on visualtechniques which depend highly on individualjudgement;

2. Some data set are lost by some smooth-ing techniques;3. Some smoothing techniques generatefluctuations which are not present in theoriginal data a good example is the Slutzky-Yule effect where systematic oscillations mayappear in the filtered series (WMO 1966;Kendall 1976);

4. Some smoothing techniques may havethe effect of altering the amplitude (and oftenthe ph e as well) of the fluctuations of thetim-e series.

An objective approach towards determ-ining the trend of any time series is to includesome statistical tests to examine the signific-ance of any trend observed in the time series.The most commonly used methods are theanalysis of variance techniques, the use ofpolynomial functionsand methods based onrank statistics.

Trend of rainfall in East Africa 85

In the analysis of variance techniques thestudy period may be divided into somestandard subperiods, generally of at least 30years' records (WMO 1967). The averages ofthese standard periods may then be comparedby using statistical tests (WMO 1966;Parthasarathy and Dhar 1974; Jones 1975;Granger 1976).

Under the polynomial approach, the trendof the time series may be approximated byfitting to the time series a polynomial which isa function of time. The weakness, of thismethod is that, quite often the observed trendsin the climatic data are unknown functionsof time which generally move with time makingit difficult to represent them well with poly-nomial functions.

In the rank statistical methods, theapplication of the rank correlation tests aremore common. The rank correlation testsuse a nonparametric (distribution-free)measure of correlation based on ranks. Themost common ofthese methods are the Mann-Kendall and the Spearman rank tests (Kendall193~•..1945, 1948; Kendall and Stuart 1961;Si~el 1956; WMO 1966). The Spearmanrank correlation test has been used in thisstudy. '{'he Spearman rank correlation r8 is'defined from the equation,

r8= 1-(6~ d~ )IN(N2-1) (1)i=1 I

where d, = kl- i, k, is the rank of the timeseries XI with N number of observations.

The significance of the calculated r. aretested by computing the statistic I given by,

I = r, [(N - 2)/(1 - r;)]i (2)The computed I values are compared with

those of the theoretical r-distribution withN - 2 degrees of freedom. The results of thistest is presented in table 1 for the annualrainfall,

The nature of rainfall trend in East Africawas further examined using the r-test, Underthis method arithmetic averages for thecommon periods 1922-1951 and 1931-1960were compared with the long-term averages(averages for the period 1922-1975). Theresults are presented in the next section.

86 Laban Ogallo

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'18· I • LOOWA II --Orl,l •••• rl••--- •••• 1•••4 •• ,1 ••

•..........c...•c.,

'18·:5 'WA~III -- 0,1,1 •• 1 '.rl ••--- S_olh4 ••,I.,

l...a tHO te70

YEARS OF OBSEIIVATION

Figures 2 and 3. Observed rainfall trends at Lodwar and Wajir

-- Orl,I •• 1 , •• I"--- •••• lh4 , ••I••

•..........c...•

...••.~--- orl'I.~ ••• 1••--- •••• lh4 ••• 1••.c.,

YIAII. 0' O•• EIIVATIOII

Figures 4 and 5. Observed rainfall trends at Kasulu and Lushoto

Table 1. Statistical parameten

Trend of rain/all in East Africa 87

Country andstations

r,Code Mean(mm)

r, Country andstations

Code Mean(mm)

Kenya

GarissaGaziKarbanetKabeteKajiadoKakamegaKapsabetKerichoKiambuKilifiKisumuKitaleKituiKonzaLamuLodwarLondianiMachakosMagadiMakinduMakuyuMalindiMarsabitMeruMombasaMt. ElgonMoyaleNaivashaNakuruNanyukiNarokNgongN. KinangopNyeriRongaiSolaiSotikTambachVoiWajir

AmaniArusha

GRSGAZKBTNRBKJDKKGKPTKRCK.IBKLFKSMKTLKTIKNZLMULDRLNIMCKMGDMKDMKYMLIMSTMRUMBSMESMYLNVSNKRNYKNARNGNNKPNYNRGISOlSOTTBCVOlWJR r

AMNARS

31713151060970472

1829143517791290962

105610181026495

1023174

1134869411521927

1049843

134911841061693618

1040692732779

1086866982987

13391196525277

19471238

0.03-0.02-0.29

0.11-0.08-0.06-0.07-0.01

0.08-0.28-0.22-0.16-0.04

0.01-0.24

0.39·-0.08-0.07

0.42·0.120.14

-0.060.16

-0.01-0.22

0.2.80.250.050.240.190.34·0.090.020.240.230.110.010.170.060.38·

-0.08-0.29

BagamoyoBiharamuloBukobaDar es SalaamDodomaKigomaKilosaKagondoKilindoniKigomashaKasuluLindiLushotoMahengeMasasiMbeyaMorogoroMoshiMusomaMwanzaMkokotoniPanganiSongeaSumbawangaTaboraTangaTukuyuTunduruWete

Uganda..AruaEntebbePort FortalGuluKabaleKalagalaKitgumMasakaMasindiMbaleMbararaMoyoNgoraSerereTororo

BGYBHLBKBDESDDMKGMKLSKGDKNMKGMKSLLNDLSTMHGMSSMBYMGRMSHMSMMWZMKNPGNSNASWGTBRTNGTKYTRNWET

ARUETBFPLGULKBLKLLKTMMSKMSNMBLMRRMOYNGRSRRTRR

1051974

20441027562971

10091690189016021066896

11241906900911883871812

1049172112621123817921

1299250510351907

1376153714741505993

21211228111212981140925

1265134813301424

-0.06-0.07

0.25-0.16

0.060.32·0.180.30·

-0.190.210.32·

-0.10-0.31·-0.12

0.250.28

-0.01-0.12

0.32·0.240.24

-0.18-0.03

0.260.15

-0.180.080.02

-0.12

-0.04-0.11-0.12-0.15-0.05-0.26-0.11-0.08-0.01

0.100.09

-0.16-0.02

0.010.15

• Significant trend: ~

RESULTS AND DISCUSSION

Table 1 gives some results of the Spearmanrank test. It can be observed from these resultsthat nine annual rainfall series indicatedsignificant trends. These stations wereLodwar, Wajir, Narok and Magadi in Kenya,and Musoma, Kasulu, Kigoma, Lushoto and

Kagondo in Tanzania. No station in Ugandaindicated any significant trends. The resultsalso indicate that the significant valuesof the rank correlation coefficients werepositive during years of study except atLushoto. This indicates a general increasingrainfall tendency at the eight stations witha decreasing tendency. at Lushoto. These

88 Laban Ogallo

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..• ....

10 10

02• .,,'r" .......",r --

-...,,"' .•... ,.---,'-30 ·E 35 40

* INDICATE SIGNIFICANT TREND AT 5 °/. LEVEL.

Figure 6. The spatial distribution of the spearman rank correlation coefficient (r.)

patterns could be confirmed from the graphic-al approach. Figures 2-5 present graphs ofsome of the smoothed and unsmoothed rain-fall time series. The smoothed graphs indicatetendencies close to those observed from theSpearman rank statistics.

Figure 6 presents the spatial distributionof the rank correlations. It can be observedfrom this map that the spatial distribution ofthe nine stations with significant rainfalltrends forms no organized pattern. Althougheight of the stations are located in the dryregions of East Africa which have high yearto year rainfall variability, the rainfallstations adjacent to the nine stations showedno significant trends.

When the arithmetic averages of thestandards periods are compared, no signific-ant differences can be detected between theaverages of the standard subperiods and thelong-term average, except at Lodwar, Wajirand Magadi. Two of these stations (Lodwarand Wajir) are located in the dry northernregion of Kenya.

The results from the monthly, seasonaland regional annual rainfall records indicate:

1. no statistically significant trend on the:regionally averaged rainfall series;

2. no significant trend in the monthly anddry season records;

3. that the records of wet seasons hadresults close to those of the annual rainfallrecords. This is due to the strong seasonalityof rainfall in East Africa (Trewartha 1961;EAMD 1962; Potts 1971; Griffiths 1972;Brown and Cocheme 1973).

Many authors have observed no establishedpatteliQs of rainfall trends over various partsof Africa (Landsberg 1975; Bunting et al.1975; Tyson et al. 1975; Ogallo 1979). Theregional annual rainfall graphs presented byRodhe and Virji (1976) indicated someincreasing rainfall tendency in the north-eastern region of Kenya during the period1922-72. Their regional series was definedusing the yearly averages of Lodwar,Marsabit and Wajir. The results of the presentstudy indicate some significant increasing

Trend of rainfall in East Africa 89

rainfall tendency at two of these three stations(Lodwar and Wajir) during the period 1922-75. Hence any rainfall series defined usingthe yearly rainfall averages of Lodwar,Wajir and Marsabit will show some increasingrainfall tendency. The regional series usedhere were defined from empirical orthogonalanalysis (Ogallo 1980).

CONCLUSIONS

Fluctuations in rainfall are manifestationsof certain characteristics of the generalcirculation over the globe. The results of thisstudy indicate that of the about 100 rainfallstations examined, only nine show somesignificant annual rainfall trend during theperiod 1922-75. Comparison of the averagesof some standard periods using the r-test,however, declared only three rainfall seriessignificant. These were the annual rainfallseries at Lodwar.Wajir and Magadi._.....Mucheffort has been made to study the:muses of the 8uctuations which are observedin the climatic elements, but the majordrawback has been that the role of thephysical factors that govern climate are notfully understood, making it difficult tounderstand fully the actual causes of theobserved climatic fluctuations.

The results of this study also indicate thatthe spatial distribution formed by the ninestations with some significant rainfall trendsformed no organized pattern. This make itdifficult for any climatological explanationsto be given for the observed significant rain-fall trends. Considering the limited dataused (54 years), it may be that these observedsignificant trends could form part of largeperiod fluctuations which could not bedetected with the available records. Thefluctuations in the microclimate around thestations showing significant trends have notbeen examined here, but the results fromhomogeneity analysis indicate that the rain-fall records from the nine stations withsignificant trends were not heterogeneous(Ogallo 1981).

90 Laban Ogallo

REFERENCES

[1] Brown, L. H. and Cocheme, J. (1973). A study of the agroclimatology of thehighlands of Eastern Africa. WMO Tech. Note. 125, Geneva: World Meteoro-logical Organization.

[2] Bunting, A. H., Dennet, M. D., Elston, J. and Milford, J. R. (1975). Rainfalltrends in West African Sahel. Q. J. R. Meteorol, Soc. 102: 59--64.

[3] EAMD, (1962). Climatic season of East Africa. East African Institute for Meteoro-logical Research Memo no. 8. Nairobi: East African Meteorological Department(EAMD). .

[4] Granger, C. W. J. (1976). Aspects of analysis and interpretation of temporal andspatial data. Statistician 24: 197-211.

[5] Griffiths, J. F. (1972). Climates of Africa. World Survey of Climatology Vol. 10.Amsterdam: Elsevier.

[6] Herrman, O. (1971). On the approximation problem in nonrecursive digitalfilter design. IEEE, 18: 411-413.

[7] Jones, R. H. (1975). Estimating the variance of time averages. J. App], Meteorol.14: 159-163.

[8] Julian, P. R. and Stephens, J. J. (1977). A simple technique for nonrecursivedigital filter design. 5th Conference on Problems of Statistics on AtmosphericScience. American Meteorological Society. pp. 272-277.

[9] Kendall, M. G. (1938). A new measure of rank correlation. Biometeorology . 30: 81-93.

[10] --. (1945). The treatment of ties in ranking problems. Biometeorology, 33:297-298.

[11] --. (1948). Rank Correlation Methods. London: Charles Griffin.[121 --. (1976). Time Series. London: Charles Griffin.[13] Kendall, M. G. and Stuart, A., (1961). Advanced Theory of Statistics. London:

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Meteorol. Geophs. B23: 193-200.[15] Ogallo, L. J. (1979). Rainfall variability in Africa. Mon. Weather. Review, 107:

1133-1139.[16] --. (1980). Regional Classification of East African rainfall stations into

homogeneous groups using the method of principal component analysis. Statist.Climatology Developments in Atmospheric Science, Amsterdam: Elsevier. 13: 255-261.

[17] --. (1981). Homogeneity of rainfall records over East Africa. East AfricanInstitute for Meteorological Research and Training Report. 4/1981.

[18] Parthasarathy, B. and Dhar, O. D. (1974). Secular variations of regional rainfallover India. Q.J.R. Meteorol. Soc., 102: 245-257.

[19] Potts, A. (1971). Application of harmonic analysis to the study of East Africanrainfall data. J. Trop. Geog. 34: 31-42.

[20] Rabiner, L. R., Mclellan, C. and Parks, T. W. (1975). FIR digital filter designtechniques using weighted Chebychev approximation, Proc. IEEE. 63: 593-610.

[21] Rodhe, H., and Virji, H. (1976). Trends and periodicities of East African rainfalldata. Mon. Weather Review 104: 307-315.

[22] Shapiro, R. (1975). Linear filtering. Math Compo 29: 1094-1097.[23] Siegel, S., (1956). Nonparametric Statistics for the Behavioural Sciences. London,

Toronto: McGraw-Hill.[24] Trewartha, C. (1961). The Earth's Problem Climates. Methuen: University of

Wisconsin Press, pp. 91-138.[25] Tyson, P. D., Dyer, T. G. J. and Mametse, M. N. (1975). Secular changes in

South African rainfall. Q. J. R. Meteorol, Soc. 101: 817-833.[26] WMO (1966). Climatic change. WMO Tech. Note 79. Geneva: WMO:[27] WMO (1967). A note on climatological normals. WMO Tech. Note 84. Genevaj, __

W~ ~~Laban Ogallo,Department of Meteorology,University of Nairobi,P.O. Box 30197,Nairobi, Kenya

. ,.

Acceptance date: 11 November 1981.