Towards the prediction of the East Africa short rains based on sea-surface temperature–atmosphere coupling

INTERNATIONAL JOURNAL OF CLIMATOLOGY

Int. J. Climatol. 18: 975–997 (1998)

TOWARDS THE PREDICTION OF THE EAST AFRICA SHORT RAINSBASED ON SEA-SURFACE TEMPERATURE–ATMOSPHERE

COUPLINGC.C. MUTAIa,*, M.N. WARDb,c and A.W. COLMANb

a Kenya Meteorological Department, Drought Monitoring Centre, PO Box 30259, Nairobi, Kenyab Hadley Centre for Climate Prediction and Research, Meteorological Office, London Road, Bracknell, RG12 2SY, UK

c Cooperati6e Institute for Mesoscale Meteorological Studies, The Uni6ersity of Oklahoma, 100 E. Boyd, Norman,OK 73019-0628, USA

Recei6ed 22 August 1996Re6ised 26 September 1997

Accepted 30 September 1997

ABSTRACT

It is shown that the July–September sea-surface temperature (SST) pattern contains moderately strong relationshipswith the October–December (OND) seasonal rainfall total averaged across East Africa 15°S–5°N, 30°–41.25°E. Therelations can be described by using three rotated global SST empirical orthogonal functions (EOFs), mainly measuringaspects of SST patterns in the tropical Pacific (related to El Nino/Southern Oscillation), tropical Indian and, to a lesserextent, tropical Atlantic. Confidence in the relationships is raised because the three EOFs correlate significantly withOND near-surface divergence over the tropical Pacific, Indian and Atlantic Oceans (extending into Northernmid-latitudes), as well as with the rainfall in East Africa and also with rainfall across southern and western tropicalAfrica.

For the East African region, multiple linear regression (MLR) and linear discriminant analysis prediction modelsare tested. The predictors are pre-rainfall season values of the three rotated SST EOFs. The predictors use informationthrough September. Validating MLR hindcasts using a 1945–1966 (1967–1988) training period and a 1967–1988(1945–1966) testing period between 30 to 60% of the area-averaged rainfall variance is explained. To achieve unbiasedestimates of the expected skill of a forecast system, it is safest to keep model training and testing periods completelyseparate. The above strategy achieves this in the most important step of ensuring that the models fit the SST predictorsto the rainfall predictand using years independent of the testing period. However, the EOFs were calculated over1901–1980, so for hindcasts prior to 1981, the EOFs describe the SST variability a little better than could be achievedin real-time, which could inflate skill estimates. Tests in the years 1981–1994, independent of the 1901–1980 eigenvectoranalysis period, do produce similar levels of skill, but a few more forecast years are needed to confirm this result. Itis shown that the mean verification at each individual location within East Africa is somewhat lower, which is importantto consider for some applications. The need to monitor the prediction relationships and update the models isemphasised. Furthermore, these forecasts only become available as the OND season is underway, though some evidenceis found for one of the EOF predictors having skill as early as June. © 1998 Royal Meteorological Society.

KEY WORDS: East Africa short rains; seasonal forecasting; multiple linear regression; sea-surface temperature; regional andplanetary scale teleconnections; linear discriminant analysis; empirical orthogonal functions; skill

1. INTRODUCTION

1.1. General

Following Walker and Bliss (1932), many studies in recent years have proposed that seasonal rainfalltotals in the tropics have strong relationships with pre-rainfall season elements of the climate system,

* Correspondence to: Kenya Meteorological Department, Drought Monitoring Centre, P.O. Box 30259, Nairobi, Kenya; e-mail:[email protected]

Contract grant sponsor: WMO VCP FellowshipContract grant sponsor: UK Department of Environment, Transport and the Regions (DETR); Contract grant number: EPG 1/1/48

CCC 0899–8418/98/090975–23$17.50© 1998 Royal Meteorological Society

C.C. MUTAI ET AL.976

including sea-surface temperature anomalies (SSTAs), the Southern Oscillation Index (SOI), large-scaleatmospheric patterns and land surface characteristics (Nicholls, 1983, 1984, 1989; Hastenrath, 1984, 1987,1988; Parthasarathy and Pant, 1985; Farmer, 1988; Parker et al., 1988; Ogallo, 1988; Ogallo et al., 1989;Folland et al., 1991; Ward and Folland, 1991). Many of the associations are believed to result from theinfluence of global and regional sea-surface temperature (SST) on the tropical atmosphere. The idea thatSST variations can control some seasonal rainfall variability in the tropics has been strongly supported byresults from comprehensive general circulation models (GCMs) of the atmosphere forced with idealisedSSTs (Rowntree, 1972; Folland et al., 1986; Palmer, 1986) and more recently with the full globaldistribution of observed SSTs (examples include Lau, 1985; Folland et al., 1991; Graham et al., 1994;Rowell et al., 1995; Stern and Miyakoda, 1995; Kumar et al., 1996). The strongest large-scale SST-forcedsignals in the atmosphere are related to the El Nino/Southern Oscillation phenomenon (ENSO) (Walkerand Bliss, 1932; Bjerknes, 1966; Rasmusson and Carpenter, 1982). The ENSO impact on precipitation isnear-global in scale (Ropelewski and Halpert, 1987, 1989; Kiladis and Diaz, 1989). Other quasi-indepen-dent patterns of SSTAs have been found to be of considerable importance for a number of regions.Examples include the role of the Atlantic and Indian Oceans in Sahelian rainfall (Folland et al., 1991), thetropical Atlantic SST in northeast Brazil rainfall (Ward and Folland, 1991) and the Indian Ocean inAustralian winter rainfall (Nicholls, 1989).

To exploit the SST control on the atmosphere for seasonal forecasts, the SSTs themselves must bepredicted, either implicitly or explicitly. The approach in this paper is to construct statistical models, usingthe SSTs observed in the months before the East Africa short rains to predict the seasonal rainfall total.The models therefore rely implicitly on a form of SST persistence. Similar models, sometimes usingadditional predictor variables to SST, have been used widely for tropical prediction (see the review paperof Hastenrath, 1995) and also for extratropical prediction (Barnston, 1994). Longer-lead forecasts willbenefit from the explicit prediction of SSTs using coupled ocean–atmosphere models (Cane et al., 1986;Barnett et al., 1993; Ji et al., 1994) or statistical models (Graham et al., 1987; Barnston and Ropelewski,1992). For example, some success in using interannual forecasts of ENSO to predict crop yields inZimbabwe has been found (Cane et al., 1994). A further approach to seasonal forecasting is to force aGCM with the persisted or predicted SSTA field (Ward et al., 1993; Brancovic et al., 1994; Ji et al., 1994;Graham, 1994; and see the review paper of Palmer and Anderson, 1994). For some time yet, andespecially in the tropics, the human forecaster will likely give best guidance by blending statistical rainfallpredictions of the type made in this paper, with predictions from various GCMs.

1.2. East Africa seasonal climate

The aim is to develop a prediction scheme for the large-scale rainfall anomaly across the East Africaregion bounded by latitudes 5°N–15°S and longitudes 30°E–41.25°E (Figure 1(a)). The main economicalresource and other societal activities of the region depend on the seasonal rainfall. Extreme anomalies inthe seasonal rainfall total are associated with many socio-economic miseries including massive loss ofproperty and life. The seasonal patterns of rainfall in East Africa follow the seasonal patterns of theInter-tropical Convergence Zone (ITCZ) which lags the seasonal migration of the overhead sun. Mostparts of the equatorial East African region have two main rainfall seasons: March–May (long rainsperiod) and October–December (OND) (short rains period). The former rains are more abundant but thelatter tend to be the more variable. The OND period used in this study is representative of the short rainsfor most of the large scale study region. Of the area-average September–December rainfall total,September contributes on average about 10%, while October and November contribute greater than 70%.The early season September rains over the study region do not correlate significantly with the OND rains.Some parts of the western highlands also receive rainfall during the months of July and August associatedwith the maximum northerly/easterly shift of the meridional/zonal components of the ITCZ, thusinducing an influx of moist westerlies from the Atlantic Ocean and the moist Congo/Zaire basin. Also,some areas near the large water bodies like Lake Victoria receive substantial rainfall throughout the yeardue to the influence of land–lake breezes.

© 1998 Royal Meteorological Society Int. J. Climatol. 18: 975–997 (1998)

EAST AFRICA SHORT RAINS 977

Figure 1. (a) Location map of East Africa. (b) October–December grid-box rainfall point-correlation map 1949–1988. The baserainfall series is the grid-box centred at 1.25°N, 35.625°E. Correlations are ×10. Shaded boxes are statistically significant at the 5%

level. (c) Standardised short rains (October–December) anomaly time series for East Africa 1945–1992



The interannual variability of the East African seasonal rains results from a complex interactionbetween SST forcing, large-scale atmospheric patterns and synoptic-scale weather disturbances, includingmonsoon and trade winds especially in the Indian Ocean, the African jet streams, sub-tropical anticy-clones, tropical cyclones, easterly/westerly wave perturbations and extratropical weather systems (Krish-namurti, 1961; Fremming, 1970; Krishnamurti et al., 1973; Cadet and Diehl, 1984; Ogallo, 1988; Okeyo,1989; Ogallo et al., 1989; Mukabana and Pielke, 1991). The extent to which SSTAs influence the seasonalrainfall totals in East Africa has been widely studied (Cadet and Beltrando, 1987; Nicholson andEntekhabi, 1987; Farmer, 1988; Ogallo et al., 1989; Beltrando, 1990; Nyenzi, 1990; Hastenrath et al.,1993; Beltrando and Camberlin, 1993; Rowell et al., 1994). The short rains period showed substantiallystronger relationships with SSTAs and the SOI. Hence the potential development of a seasonal forecastfor the short rains period is the scope of this paper.

We investigate the extent to which the global/regional pre-rainfall season SSTAs alone may allow theEast Africa short rains to be predicted. The SSTAs influence the local marine boundary layer (tempera-ture, moisture content) and especially in tropical latitudes, these changes influence local atmosphericcirculation and moisture convergence (Lindzen and Nigam, 1987; Neelin and Held, 1987). Theseanomalies can then influence atmospheric circulation and rainfall anomalies over remote continentalregions.

A skilful seasonal rainfall prediction would significantly contribute to the socio-economic activities ofthe East African region. Rainfall anomalies impact on the agricultural sector and disruption to this andother weather related activities could be minimised if seasonal rainfall anomalies were skilfully predictedbefore the season. This would help in the decision-making and policy formulation necessary to planningstrategies for sustainable development.

2. DATA

2.1. Rainfall data

The grid-box rainfall database developed by Hulme (1994) is used. Its construction was based on aThiessen polygon approach and the version used here has a grid with resolution of 2.5° latitude×3.75°longitude. This is a suitable resolution for empirical analysis given the density of stations and the spatialcorrelation of the data. The handling of missing data is described by Hulme (1994). One important featurethat keeps the dataset useful for the type of study here is that a station must have at least 83% of monthswith data to qualify, and then the small number of missing months are interpolated by the meanpercentage anomaly in surrounding stations. If there are no stations nearby with data, then a grid-boxtotal is set to missing. The distribution of stations included in the gridding analysis is given by Hulme(1992), his Figure 2(a)). Many grid-boxes in equatorial central Africa are missing after the mid-1970s dueto lack of station reports.

The region of study (Figure 1(a)) can be sub-divided into smaller rainfall regions (Ogallo, 1989).However, there is also strong spatial coherence of rainfall anomalies across the whole region (Figure 1(b))and it is this large-scale signal that has the highest likelihood of being connected to large-scaleatmospheric variations associated with SSTs. The region in Figure 1(a) was defined based on acompromise between a forecast unit of practical application and a forecast unit with generally coherentrainfall anomalies related to similar SST patterns (this latter aspect is shown in section 3). The regionsouth of 15°S has a tendency for OND rainfall anomalies of sign opposite to those in East Africa (Figure1(b)).

To measure the area-average rainfall anomaly over East Africa in each OND season, a meanstandardised anomaly index for each year j (xj) is calculated using the grid-boxes included in the region:

xj=1Nj

%Nj

i=1

Rij−R( i

si

(1)



where R represents rainfall in mm, R( i is the mean rainfall at grid-box i over a chosen base period (here1941–1970, chosen for its good data coverage), si is the standard deviation of rainfall totals at grid-boxi over the base period and Nj is the number of grid-boxes available in the year j. Over the period1945–1988, the number of grid-boxes available is very stable, with never more than four out of the 24boxes missing. Note that the standardised index is in effect interpolating missing grid-boxes by thestandardised average anomaly of all available grid-boxes. The standardised anomaly is used to give equalweight to each available grid-box, regardless of standard deviation, avoiding over-emphasis on the wettestregions which tend to have larger standard deviations. This is very useful for empirical analysis, since theaim is usually to calculate an index that is representative of the relative variations in rainfall averaged overthe region from year to year. The East African rainfall index calculated using Equation (1) (Figure 1(c))shows substantial interannual variability. In contrast to many indices over tropical Africa (Nicholson,1986) the series does not contain persistence from one year to the next (lag 1 serial correlation= −0.21).This simplifies statistical analysis, since it is reasonable to assume full degrees of freedom in all correlationanalyses.

2.2. Sea-surface temperatures

The UK Meteorological Office Historical sea-surface temperature dataset version 4 (MOHSST4,Bottomley et al., 1990) covering the period 1901–1995 is used. The dataset contains a quality controlledand bucket-corrected (Folland and Parker, 1995) analysis of monthly SSTAs relative to a 1951–1980climatology that was originally constructed at the 5-day 1° latitude×1° longitude resolution so that eachindividual SST observation is referred to a very accurate climatology. The SST anomalies are herecombined into 10° latitude×10° longitude grid-boxes extending over the world’s ocean (Ward andFolland, 1991). The improved data coverage and reduced noise of a 10°×10° dataset outweighs the lossof spatial resolution for this application. Ward and Folland (1991) give information on the data coverageand show spatial point correlation maps, including ones for the Equatorial Indian and Pacific Oceans.The high correlations for adjacent boxes, and smooth decay with distance, can be used to infer that thedata are sufficiently accurate to study interannual variability.

2.3. Marine atmosphere

Some analyses of the relationship between SST patterns and the marine atmosphere are offered tostrengthen the argument that the SST patterns have a very large scale impact on tropical circulation. This

Figure 2. Correlation (in tenths) between 10° latitude×10° longitude sea-surface temperature anomalies for July–September andstandardised East Africa short rains index, 1949–1988. Shaded boxes are statistically significant at the 5% level



strengthens the claim that the SST influence extends to the East African continental region. The analysesuse the near-surface divergence dataset developed in Ward and Hoskins (1996). The divergence isestimated using wind data from the comprehensive ocean atmosphere dataset (Woodruff et al., 1987),combining the data into seasonal mean vector wind anomalies on the 10°×10° scale and removing trendsthat were not supported by trends in pressure gradients. The case study in Ward and Hoskins (1996)demonstrated that the data are sufficiently accurate to detect large-scale relationships between SST andnear-surface divergence over the open ocean.

3. RELATIONSHIP BETWEEN THE EAST AFRICA SHORT RAINS AND SEA-SURFACETEMPERATURES

The study focuses on the period of most reliable SST and rainfall data, which was judged to be a periodspanning the mid-1940s to the late 1980s. Specifically, diagnostic work in section 3 uses the 1949–1988period (consistent with the available marine surface atmosphere data from Ward and Hoskins (1996)),while the seasonal hindcast experiments based solely on SST use 1945–1988.

3.1. Rainfall correlation with global 10°×10° sea-surface temperatures

The cross-correlations for 1949–1988 between July–September (JAS) SSTAs in each available 10°×10° area and the standardised East Africa OND rainfall series is shown in Figure 2. The statisticalsignificance of each correlation was assessed using a standard t-test and the shaded area shows values thatare significant at the 5% level.

Significant correlations are found for 15.6% of the boxes analysed in the tropical Pacific and IndianOceans. This is encouraging, because these regions can be expected in principle to provide the strongestsource of SST forcing. Positive correlations are found in the central tropical Pacific (highly statisticallysignificant) and equatorial western Indian Ocean (on the boundary of 5% significance). Straddling thesetwo regions, significant negative correlations are found in the equatorial western Pacific and sub-tropicalsouth-western Pacific, under the South Pacific Convergence Zone (SPCZ). This arrangement of correla-tions mirrors the boreal summer SST anomaly pattern that Meehl (1994) proposes to be an importantpart of an air–sea coupled process that operates on the biennial timescale. In this regard, it is interestingthat the OND East Africa rainfall series does indeed have a modest negative lag 1 serial correlation(r= −0.21).

There is a weak positive relationship between southeastern Atlantic SSTAs and the East African shortrains. Though generally not statistically significant, a modest influence of the southeastern Atlantic onEast Africa is physically plausible by influencing the strength and moisture content of the air mass thatflows into Equatorial Africa from the Atlantic.

Figure 3(a–d) shows maps of the correlation between OND rainfall across tropical Africa and fourselected SST grid-boxes. The aim is to assess the spatial pattern of rainfall anomalies associated with themost important SST regions for East Africa, following the guidance of Figure 2. A central Pacific box waschosen at the northeastern edge of the Nino4 region (Figure 3(a)). This SST series has many significantpositive correlations extending from 15°S northwards through East Africa and into Somalia and Ethiopia.Statistically significant negative correlations are found in Figure 3(a) south of 15°S, deriving mainly fromthe months of November and December (monthly analyses not shown), suggesting some predictability forNovember–December rainfall in this region also. This pattern of relationships is consistent withRopelewski and Halpert (1987, 1989) and Kiladis and Diaz (1989), with the rainfall anomaly south of15°S persisting and intensifying through the Southern Hemisphere summer months. The map ofcorrelations with the western Pacific/eastern Indian Ocean grid-box (Figure 3(b)) is almost the perfectmirror image of the map with the central Pacific (Figure 3(a)). The maps with western Indian Ocean SST(Figure 3(c)) and southeastern Atlantic SST (Figure 3(d)) have generally fewer significant correlations, butboth contain a suggestion of opposite correlations between East Africa and Central/Western Africa2.5°–12.5°N.



The above results develop the earlier, mainly simultaneous SST–rainfall studies (Ogallo et al., 1989;Hastenrath et al., 1993; Beltrando and Camberlin, 1993; Rowell et al., 1994; among others). These newresults describe promising relationships with the SSTs leading the rainfall.

Figure 3. Correlation (in tenths) over 1949–1988 between rainfall anomalies for October–December and the 10° latitude×10°longitude July–September sea-surface temperature anomaly time series for the box centred at (a) 5°N, 155°W; (b) 5°S, 105°E; (c)5°S, 45°E; and (d) 25°S, 15°E. Shaded boxes are statistically significant at the 5% level. The base SST grid-boxes were selected to

represent the main correlation centres in Figure 2



Figure 3 (Continued)

3.2. Association of SST eigen6ectors with the marine atmosphere and African rainfall

To derive a few time series that can express much of the large-scale variability in the SSTA data,empirical orthogonal functions (EOFs) (e.g. see Jolliffe, 1986) were calculated. The EOFs used here werecalculated by Folland et al. (1991) using the covariance matrix of all seasons global SST for the period1901–1980. For inclusion in the analysis, a 10° latitude×10° longitude grid-box was required to have atleast 60% of seasons with data. Remaining missing data were interpolated temporally. It is noted thatonce the EOF patterns have been derived, time coefficients (i.e. the time series) of the patterns can be



calculated using any given set of SSTA fields (e.g. JAS). The time coefficients for rotated patterns (seebelow) are here calculated following Jolliffe (1995) who projects observed data anomaly fields onto therotated loading patterns. Thus the time series directly measure the strength (amplitude) of the rotatedloading pattern.

The first three global all seasons unrotated SST EOFs (not shown) did not show significant predictivecorrelations with the East Africa standardised rainfall anomaly. Folland et al. (1991) observed that globalEOF2 represents a quasi-worldwide pattern of SSTAs associated with El Nino warming events in thetropical Pacific. The JAS time coefficients of EOF2 correlate strongly with the JAS Tahiti minus DarwinSOI (r= −0.77). It is therefore surprising that this EOF shows no significant correlation with the EastAfrican rainfall index, given previous studies (Nicholson and Entekhabi, 1986; Ropelewski and Halpert,1987; Farmer, 1988; Ropelewski and Halpert, 1989). SST EOF2 does have some significant positivecorrelations with rainfall over the western areas and the north coast of the region (Figure 4(a)) butstronger predictive relationships are found with other SST EOFs.

Folland et al. (1991) performed a VARIMAX rotation (Richman, 1986) on EOFs 4–13, since theseunrotated patterns were clearly of more regional scale. The JAS and OND values of the rotated EOFtime-coefficients were correlated with the OND rainfall index (Table I). The highest relationship occurswith the rotated global eigenvector 5 (REOF5) time-coefficients in JAS. It is interesting that REOF5 islargely independent of the SOI (r= −0.13) despite strong weights in the Pacific and Indian Oceans. Theweights in REOF5 (Figure 5(a)) are positive across the central and eastern tropical Pacific and stronglypositive in the northwestern Pacific. This combination yields a strong relative minimum in the westerntopical Pacific, while there is a smaller relative maximum in the western Equatorial Indian Ocean. Mostlikely it is this arrangement of gradients that leads the EOF to have such a strong association with ONDnear-surface divergence over the western Pacific and Indian Ocean (Figure 6(a)) and the rainfall overtropical Africa (Figure 4(b)). REOF5 correlates most strongly with rainfall over East Africa, but there arealso significant negative correlations in southeastern Africa and positive correlations in southwesternAfrica. REOF5 is perhaps the least known pattern out of the three REOFs that are used in the forecastsystem (see below). It will need to be monitored carefully to check that it is recurring in the climate systemand maintaining its relation with East African rainfall. At the very least, it is interesting that such alarge-scale signal in the African rainfall and near-surface marine divergence can be extracted using anindex (REOF5) that is independent of the SOI, it suggests that at least some of the East African rainfallvariance that is independent of the SOI is not attributable to local scale chaotic features.

REOF4 (Figure 5(b)) measures a further aspect of tropical Pacific SST variability, strongly related toENSO (correlation with SOI= −0.71). It has a statistically significant simultaneous correlation with theOND East African index. The JAS correlation is smaller, but it is found that the coefficients immediatelybefore the rainy season in September correlate at near the 5% significance level with many East Africangrid-boxes (Figure 4(c)). Like REOF5, REOF4 specifies a strong near-surface divergence anomaly overthe tropical Pacific and Indian Ocean (Figure 6(b)). However, the near-surface divergence pattern isdifferent from that related to REOF5, and this is probably why the two are explaining independentportions of East African rainfall variance (see regression analysis in the next section). The REOF4correlation map (Figure 6(b)) also displays a train of alternate positive and negative divergencecorrelations extending toward the northeastern Atlantic and European region, suggesting the influencedomain of REOF4 may extend to Northern mid-latitudes.

The final useful predictor is found to be REOF2 (Figure 5(c)) which has large positive weights over theSouth Atlantic accompanied by weaker negative weights in the tropical North Atlantic and a weaknorth–south dipole in the western Indian Ocean. REOF2 in JAS is independent of the SOI (r=0.00). TheEast African rainfall correlations with REOF2 in Table I are weak. However, the September coefficientsof REOF2 correlate well with OND tropical Atlantic and westen Indian ocean near-surface divergence(Figure 6(c)), suggesting potential to influence continental rainfall. The modified marine atmosphere likelyleads to some physically real modest correlations between REOF2 and grid-box rainfall totals over EastAfrica (Figure 4(d)). It is noted in Figure 4(d) that REOF2 has good predictive potential for West Africain OND, and this REOF2 has in fact already been used since 1986 for experimental realtime predictionof JAS Sahelian rainfall (Ward et al., 1993).



The above results provide good evidence for a relationship between pre-rainfall season SSTs and theOND large-scale circulation over the tropical oceans. Overall, 50.0% of the tropical near-surfacedivergence boxes analysed in Figure 6 have significant correlations with one of the three SST EOFpredictors. With atmospheric circulation modified so strongly over the tropical oceans, and the westernIndian Ocean in particular, the correlations of the SST EOF predictors with East African rainfall are veryplausible. The next section exploits these results to develop empirical seasonal forecast models for the EastAfrican seasonal OND rainfall anomaly.

Figure 4. As in Figure 3, but for (a) July–September values of SST unrotated EOF2; (b) July–September values of SST rotatedEOF5; (c) September values of SST rotated EOF4; and (d) September values of SST rotated EOF2



Figure 4 (Continued)

4. EMPIRICAL TECHNIQUES OF FORECASTING THE EAST AFRICA SHORT RAINSSEASON

Statistical seasonal forecast models are built by relating the pre-season values of the SST EOFs to theobserved rainfall anomaly. Following the methods in Ward and Folland (1991), the two statistical forecasttechniques are:

(i) Multiple linear regression (MLR)(ii) Linear discriminant analysis (LDA)



Table I. Correlations between the East Africa standardised October–December rainfallindex and the October–December or July–September global SST rotated eigenvector

time coefficients (1949–1988)

Eigenvector no. 1 2 3 4 5

October–December SST 0.12 0.22 −0.32* 0.32* 0.42**July–September SST −0.12 0.15 −0.14 0.21 0.61**

* Statistically significant at the 5% level.** Statistically significant at the 1% level.

4.1. Multiple linear regression (MLR)

The forecast standardised rainfall anomaly R, is given in the model by:

R=b0+b1X1+b2X2+ · · · +bpXp+o (2)

where Xi is the value of the ith predictor, bi the model regression parameters for predictor i, p the numberof predictors in the model and o the unmodelled variance in the rainfall series (o assumed to be distributednormally). The bi values are estimated from the ‘training period’ data.

The above approach is very similar to a canonical correlation analysis (CCA) using EOF predictors andpredictands (Barnett and Preisendorfer, 1987; Graham et al., 1987; Barnston, 1994). The area averagestandardised rainfall index (Figure 1(c)) is almost identical (correlation=0.99) to the time series of thefirst EOF of East African OND rainfall, calculated using the 24 East African grid-boxes. The first rainfallEOF explains a large fraction (55.5%) of the total rainfall variance. Our approach neglects lower orderpatterns of rainfall variability, but these are not likely to be so strongly influenced by SST, given the sizeof East Africa (Figure 1(a–b)). In the CCA approach, all SST EOFs (up to a user selected cut-off) areused in the prediction specification. In our approach, a sub-set of rotated SST EOFs have been used,selected on the basis of their statistically significant contribution to the MLR model, and reinforced bytheir association with large-scale marine atmospheric variability.

4.2. Linear discriminant analysis (LDA)

In the application here, the statistical technique linear discriminant analysis uses the observed SST EOFcoefficients to predict the probability of a set of pre-defined rainfall categories. Five discrete rainfallcategories (‘quints’) are defined (very dry, dry, average, wet, very wet), each of which is equally likely tooccur over a long period. The driest 20% of seasons define quint 1, the next driest 20% define quint 2, etc.

LDA uses the Bayes probability theorem to estimate the posterior (forecast) probability of all fivequints, given the predictor values (Afifi and Azen, 1979). For one predictor, X, the forecast probabilityof Qi is:

P(Qi/x)=qi fi(x)

% qj fj(x)(3)

Summation is taken over all five quints and qi, the posterior probability of category i is, in this case,always 0.2. The factor fi(x) is the probability of observing the predictor value x prior to a quint i rainfallseason, and is estimated from the probability density function of x calculated over the training period(there are five density functions, one for each quint).

When more than one predictor is needed, the multivariate distributions of predictors are used (assumedto be multivariate normal). Given p normally distributed predictor variables, the log of the multivariateprobability density function of X for quint i can be expressed as:

ln(fi(X))=ai1x1+ai2x2+ · · · +aipxp+Gi, Gi= −12 m i

TS−1mi (4)



Figure 5. Empirical orthogonal function (EOF) covariance analysis of 1901–1980 all seasons 10° latitude×10° longitude SSTanomalies (from Folland et al., 1991). The patterns are derived through a VARIMAX rotation of unrotated EOFs 4–13. (a) RotatedEOF5; (b) rotated EOF4; and (c) rotated EOF2. The original 10° latitude×10° longitude grid-box values of the EOFs have been

isoplethed. The units are the EOF weights multiplied by 100 and the isopleth interval is 1



Figure 6. Correlation (in tenths) over 1949–1988 between 10° latitude×10° longitude near-surface divergence anomalies forOctober–December and (a) July–September values of SST rotated EOF5; (b) September values of SST rotated EOF4; (c) September

values of SST rotated EOF2



where X is a vector of observed predictor variables x1, x2, . . ., xp, S the covariance matrix of the predictorvariables in the training period, and mi is a vector containing the mean value of each predictor variablein those years when quint i is observed.

The multivariate LDA prediction equation is achieved by substituting Equation (4) into Equation (3):

P(Qi/X)=exp(di)

% exp(dj)(5)

where di, the discriminant score for category i, is

di=ai1x1+ai2x2+ · · · +aipxp+Gi+ ln(qi) (6)

The results from section 3 and from the MLR technique above are used to guide the choice of predictorEOFs used in the LDA model.

Ward and Folland (1991) described a range of scores that give varying weight to different attributes ofthe forecast. Skill scores are often scaled so that a ‘reference forecast strategy’ (RFS) scores 0% and a setof ‘perfect forecasts’ score 100%. Here, the forecasts by LDA are assessed using a ‘Hit’ skill score (SH)that uses chance as RFS (see Livezey et al., 1990; Livezey, 1995):

SH=�H−C

T−Cn

×100 (7)

where H is the number of hits (correct forecasts), C the chance number of hits, and T the total numberof forecasts.

5. RESULTS FOR MLR AND LDA HINDCASTS OF THE EAST AFRICA SHORT RAINS

The EOF predictors identified in section 3 are applied to the empirical model techniques described insection 4 to assess the predictability of East African short rains for the 1945–1988 period. Forecasts thatare made for years in the historical record to assess the skill of a model are termed hindcasts, to emphasisethat they were not made and issued in real time.

5.1. Multiple linear regression models

Fitting the model over the whole 1945–1988 period, the prediction equation is

R=0.00+0.57(REOF5)+0.30(REOF2)+0.24(REOF4) (8)

For this demonstration, each series was standardised to have a mean of zero and a standard deviation of1, so that the model coefficients give an indication of the relative contribution of each predictor. Atwo-tailed t-test of statistical significance for each regression coefficient shows that REOF5 is significantat much better than 1%, REOF2 at about 1% (p=0.012) and REOF4 at better than 5%. The multiplecorrelation fit for the model is 0.69.

Regional ocean SSTA eigenvectors were also tried as predictors (not shown) but found to havesomewhat lower skill than the global SSTA eigenvectors. The SOI can however replace REOF4 with littleeffect on the model. For example, for the 1945–1988 period, the model becomes

R=0.00+0.54(REOF5)+0.25(REOF2)−0.28(SOI) (9)

REOF5 remains significant at much better than 1%, while REOF2 (p=0.034) and the SOI (p=0.020) areboth significant at 5%. This result supports Farmer (1988) who identified some predictability on theKenya coast from the SOI. The multiple correlation is almost identical to before (r=0.70). The main aimof this paper is to focus on predictability from SST, so the SOI is not included in the more detailedanalyses below. However, in an operational forecasting environment, it seems sensible to consult modelsthat include the SOI in addition to models built solely using SST.



5.2. Expected real-time skill for the MLR models

To assess the true skill of a forecast system, it is vital to minimise the risk of artificial skill that arisesbecause the system has information that would not be available in real-time application. Of course, thescientist already knows something about the climate of the historical period and this makes all attemptsto assess skill using past data difficult. The safest solution is to define a period for model development anda completely independent period for model testing. The most severe skill inflation results from over-fittingmodel predictors to the predictand (including offering excessive numbers of predictors in step-wiseprocedures) and then using that same model training period to test the model. We have avoided thisproblem by making hindcasts for (i) 1945–1966 and (ii) 1967–1988 using models created from trainingperiods 1967–1988 and 1945–1966, respectively. However, we have chosen to use the 1901–1980 SSTEOFs as predictors because these EOFs were derived after much experimentation on data coverage andthe number of EOFs to retain for rotation (Folland et al., 1991) such that their statistical properties andphysical interpretability are particularly satisfactory. It is therefore true that, for hindcasts prior to 1981,these 1901–1980 EOFs will give a slightly better representation of SST variability than would beachievable in real-time. This may lead to a small inflation of skill, though it is emphasised that there isno statistical fitting of the SST to the rainfall during our quasi-independent hindcast testing periods.

Figure 7(a) shows hindcasts for 1945–1966 made by the 1967–1988 model. In Figure 7(a) we also showhindcasts for 1967–1988 made by the 1967–1988 model, the particularly close fit of observed andhindcast during the model training period is evident and illustrates the problem of over-fitting modelpredictors to predictand, though in fact the problem is not especially severe in this instance. A similardiagram for the 1945–1966 model is shown in Figure 7(b). Table II shows verification statistics for thequasi-independent hindcasts.

Hindcasts for the 1967–1988 period have higher skill than those for the earlier period (Table II). Thecorrelations between hindcast and observed rainfall suggest that about 30–60% of the East Africa ONDrainfall variance may be predictable from the SST EOF coefficients observed prior to OND. Consistentwith the lower correlation skill in 1945–1966, the root mean square error (RMSE) and mean absoluteerror (ABS) is also higher. Neither period has a statistically significant bias in the mean value of thehindcasts.

Bias in the variance of the MLR hindcasts (Table II) can be reduced by using ‘inflated regression’ asshown by Ward and Folland (1991). This would be expected to increase RMSE, while rfv will not beaffected. The reduced variance of MLR hindcasts relative to observed leads to a lack of extreme hindcastsas shown in Figure 7. This is especially true for positive rainfall anomalies, which partly results from thepositive skewness (G1=1.443) in the rainfall series distribution. However, these problems can be adjustedfor by human seasonal forecasters and by using MLR in association with LDA; Ward and Folland (1991)discuss how non-normality of the rainfall series is not a serious problem for LDA.

5.3. Linear discriminant analysis

The LDA model was fitted over the 1945–1988 period using the same predictors as used in the MLRmodel. The results are summarised in a contingency table (Table III) showing the individual quint that ishindcast to have the highest posterior probability against the corresponding observed quint. The correctquint is specified in 20 out of the 44 years, and the ‘hit’ skill score is 31.8%. Wet extremes appear easierto forecast than dry extremes. The number of years was too short to make two independent periods fortesting. However, the successful division of training and testing periods for the MLR model suggests thatthe skill here should not be dramatically inflated.

Gilman (1986) noted that a ‘well-calibrated’ forecast system is one where there is a close match betweenthe forecast and observed frequencies of each category range. The total number of hindcast quints 1 and5 together (extremes), 2 and 4 together, and 3 only, are 19, 17, and eight, respectively. The correspondingobserved values are 18, 17, and nine which matches the hindcast frequencies almost perfectly, so thehindcasts are extremely well calibrated. In particular, LDA is hindcasting the extreme wet category andthe extreme dry category with realistic frequency. This good calibration for categorical prediction is not



always the case for LDA. Ward and Folland (1991) demonstrated that LDA can have a tendency to givehighest posterior probability to the extreme quints, even though the probabilities themselves arewell-calibrated.

5.4. Verification at a smaller spatial scale

The above results develop a strong argument for predictability in the large-scale area-averaged rainfall.For some applications, it will be necessary to have an indication of the skill at smaller spatial scales. Toget a preliminary indication of this, the 1945–1988 quasi-independent MLR hindcasts (taken from Figure7(a) and 7(b)) have been correlated with each individual grid-box rainfall series (Figure 8). The meancorrelation over the East African region is 0.46, compared to the area-averaged index correlation of 0.62.The skill is therefore lower, but does hold up fairly well at the smaller spatial scale, especially throughcentral and northern East Africa. There is a suggestion for lower skill in the south of the region, whichseems to be the start of a transition to opposite rainfall anomalies and SST connections, suggested by thenegative correlation of rainfall with the hindcasts south of 15°S. Consistent with the earlier SST–rainfall

Figure 7. Hindcast and observed East African OND standardised rainfall anomalies. The predictors are September values ofREOF2 and REOF4, and July–September values of REOF5, fitted to the rainfall using multiple linear regression. (a) Observed(solid line with crosses) and hindcast (dashed line with circles) using a model fitted over 1967–1988. Thus the hindcasts to the rightof the dashed vertical line are for the dependent model training period and the hindcasts to the left are independent of the period

for multiple regression fitting. (b) As for (a) but for a model fitted over 1945–1966



Table II. Skill of multiple linear regression hindcasts for the East Africa short rains(October–December rainfall index). The predictors (SST REOF2, REOF4, REOF5) use

SST information up to and including September

Training period Hindcast period rfv RMSE ABS Bias sf sv

1967–1988 1945–1966 0.56 0.68 0.48 0.22 0.52 0.791945–1966 1967–1988 0.78 0.37 0.31 0.01 0.43 0.591945–1980 1981–1994 0.60 0.50 0.37 0.16 0.57 0.53

rfv, the correlation between the hindcast and observed rainfall in the testing period; RMSE, the rootmean square error of hindcasts; ABS, mean absolute error of the hindcasts; Bias, mean bias of thehindcasts; sf, the standard deviation of the hindcast values; sv, the standard deviation of theobserved values.

Table III. Frequency of hindcast and observed rainfall ‘quint’ for October–December1945–1988 in East Africa

Observed quint

Q1 Q2 Q3 Q4 Q5

Hindcast quint Q1 3 0 4 2 0Q2 3 7 1 0 0Q3 1 1 3 3 0Q4 1 0 1 1 3Q5 1 1 0 2 6

correlation maps (Figures 3 and 4), Figure 8 suggests this forecast system also has positive skill to thenorth and northeast of East Africa, extending into Ethiopia and Somalia (Hutchinson, 1992; Beltrandoand Camberlin, 1993).

Figure 8. Verification of the OND quasi-independent East Africa hindcasts (Figure 7) at each individual grid-box. The map showsthe correlation (in tenths) between the hindcast time series for East Africa and each OND grid-box time-series 1945–1988. Shaded

boxes are statistically significant at the 5% level



Figure 9. Assessment of East Africa multiple linear regression hindcasts in years independent of the EOF analysis period. EastAfrica standardised rainfall anomaly (solid) and hindcast (dashed). Model predictors are the same as in Figure 7. Model is trained

on 1945–1980

One weakness here is that some boxes contain more than one station, which will tend to reduce noise,raise skill levels and complicate the geographical pattern of skill. Further work of this type is needed toenhance the utility of the forecasts. It may also be possible to raise the skill levels on the smaller spatialscale by training models to specific subregions of East Africa. However, this may be difficult to proveusing statistical models given the small sample of years with reliable data.

5.5. Hindcasts for 1981 to present

Section 5.2 presented MLR hindcasts using testing and training periods. One problem though, asdiscussed in section 5.2, is that the testing periods were not independent of the period used to calculatethe SST EOF base patterns (1901–1980). To make a completely independent test of the East Africaprediction scheme, a MLR model was constructed for the period 1945–1980, and hindcasts were made forthe period 1981–present. To verify the hindcasts for 1993–1994, the standardised series in Figure 1(c) wasupdated using grid-boxes available in the latest version of the rainfall dataset (M. Hulme, ClimaticResearch Unit, University of East Anglia, personal communication). The hindcasts (Figure 9) correlatewith the observed at 0.60 (statistically significant at the 5% level) so the independent hindcasts are so farperforming close to the mean hindcast skill found for 1945–1988 (r=0.62), though a few more post-1980hindcasts are still needed for full acceptance and confidence in the forecast system.

The skill of the independent hindcasts is very badly affected by the extreme wet prediction for 1994.However, a real-time experimental forecast using this regression model (M. Davey, Hadley Centre, UKMeteorological Office, personal communication) was viewed to have useful skill, verifying against thewettest year so far for the 1990s. Human interpretation, treating such an unprecedented forecast withcaution, but nonetheless anticipating above average rainfall, can add value in such situations. For 1995,the observed rains were close to normal (DMC, Nairobi, personal communication), so the hindcast(Figure 9) was correct in predicting drier conditions than the previous year.

5.6. Predictor stability for different lead-times and sub-periods

The utility of the forecast system described in previous sub-sections would be greatly enhanced ifforecasts could be made with longer lead-times. This is particularly true since September is also sometimesdeemed to be part of the short rains season. It is therefore disappointing that REOF4 (ENSO-related



predictor) and REOF2 (tropical Atlantic predictor), are not found to be significantly related to the ONDrainfall index until September. On the other hand, REOF5 is strongly related to the rainfall index as earlyas June (r=0.51). Further modelling and diagnostic work is recommended to better understand thephysical significance of REOF5.

Another important issue for predictability is the stability of the relationships over time. Figure 10 showsrunning 15-year correlations between the rainfall index and the three EOF predictors. The relationshipwith REOF5, after the earliest years, is remarkably stable. In contrast, REOF2 and REOF4 oscillate inimportance, with REOF4 being strong in the first half of the record and REOF2 strong in the second half.Further investigations are needed to explore whether these fluctuations are above the noise level, whetherphysical explanations for the fluctuations exist, and whether MLR model parameters can be updated ina way to optimally track the fluctuations in real-time.

6. SUMMARY AND CONCLUSIONS

This study demonstrated the relationship between the pre-rainfall season SST anomaly patterns and theinterannual variability of the short rains (OND season) over East Africa. The relationship concept wasuse to make rainfall hindcasts by applying two different statistical techniques: multiple linear regression(MLR) and linear discriminant analysis (LDA). The MLR model was used to provide ‘best-estimate’hindcasts of the standardised rainfall anomaly whereas LDA predicted the posterior probability that therainfall will be in each of five categories or quints. The predictors for the models were rotated globaleigenvectors of SST (REOF5, REOF4 and REOF2). These predictors showed moderate to strongrelationships with rainfall in East Africa, as well as with rainfall further north and south and throughWest Africa. The predictors also showed a strong and widespread relationship with OND near-surfaceconvergence and divergence anomalies throughout the tropical Pacific, Indian and Atlantic Oceans, so aneffect on the large-scale continental rainfall of tropical Africa is very feasible. Some predictability fromREOF4 related to ENSO also appeared to extend to the mid-latitude northeast Atlantic, suggesting apromising avenue for further research.

Both the MLR and LDA techniques showed some encouraging positive skill for the East Africanregional rainfall anomaly. We have emphasised that the testing scheme employed for the MLR model mayhave inflated skill estimates a little for hindcasts prior to 1981, because the SST EOFs were derived using

Figure 10. Running 15-year correlation between the OND East Africa rainfall index and July–September values of rotated EOF5(solid line with circles), September values of REOF4 (dotted line with stars) and REOF2 (long dash line with triangles). The first

correlation is for 1949–1963 and the last is for 1974–1988



information in the whole 1901–1980 period. Hindcasts for 1981–1994 did achieve similar skill levels to thoseprior to 1981, but a few additional years are needed yet to properly assess the system in the periodindependent of the EOFs.

When applying the techniques operationally in the future, considerable interpretation and flexibility willbe required by the human forecaster. It is known that many of the statistical teleconnections throughoutthe climate system have fluctuated in strength through the period of reliable historical records, and thiswas shown to be the case for two of the three EOF predictors used. Indeed, the MLR skill is substantiallyhigher in the 1967–1988 period, than in 1945–1966. It will be necessary to update the model parametersand monitor the teleconnections, which may fluctuate due to natural climate variability or through climateresponse to, for example, increasing greenhouse gases. Forecast methods based on GCMs may be bettersuited to unusual SST patterns, since they are directly modelling the effect of the SSTs on the atmosphere.However, GCMs are vulnerable to model errors which can lead to a wrong specification of the SST impact;a small geographical shift of a remote teleconnection in a model can lead to a dramatic forecast failure.Thus, the optimum is felt to be a blend of forecasts made by modelling the SST impact using statisticalmodels and using comprehensive GCMs.

The results here and in other papers strongly suggest that SST variations can affect the OND seasonalrainfall total over East Africa. Persistence of SST allows strong prediction skill here only with zero lead-timeon the OND season. One of the EOF predictors does show some promise for longer lead-time predictions,but further diagnostic work is needed. It will also be interesting to explore if long-lead predictions of SSTcan add to the forecast system and bring a longer lead-time.

A key issue concerns the spatial scale of the seasonal rainfall anomalies. It was shown that the skill ofthe MLR model declines from about 40% explained variance (area average) to 25% explained variance (meanverification for each local 2.5° latitude×3.75° longitude grid-box), though the decline is not uniform acrossthe region, with skill lowest in the southernmost districts. This is important knowledge for applications.It is possible that the decline in skill in some parts of East Africa may partly be alleviated by forming smallerscale forecast regions. However, at least some of the decline in skill is due to an increasing fraction of internalatmospheric variability on the smaller spatial scale, for example due to extreme local storms or persistentlocal scale circulations. Spatial variations in the seasonal rainfall total associated with these phenomenaare most likely not predictable from SST, whose influence is in the large-scale. A further and related areafor future study concerns the extent to which skill degrades as the temporal period is reduced from a seasonto a month or shorter. There may also be variations in the level of skill depending on month. For exampleHastenrath et al. (1993) suggest a stronger SST influence on East African rainfall in October–Novemberthan in December, and this is born out when our hindcasts are verified for each month (not shown).

The results from this study suggest clear potential for predicting, at zero lead-time, between 30 to 60%of the interannual variance of OND area-averaged rainfall across East Africa. The region’s economy dependson rain-fed agriculture. Skilful rainfall forecasts, even given as the OND season is getting under way, willsurely make a valuable addition to the existing monitoring systems that report the quality of the seasonas it progresses.

ACKNOWLEDGEMENTS

Early work benefitted from discussion with Dr Graham Farmer and from research by Stuart Brooks (UKMeteorological Office). Much of this present study was done when the first author was at the Hadley Centrefor Climate Prediction and Research, Meteorological Office, UK, on a WMO VCP fellowship. We areparticularly indebted to the UK Meteorological Office for providing the computing facilities to enable theresearch to be carried out. Significant progress was also made at two workshops held during 1994 at theAfrican Centre of Meteorological Applications for Development (ACMAD), Niamey, Niger. Discussionswith participants are gratefully acknowledged. We are also grateful to Dr Mike Hulme (Climatic ResearchUnit, University of East Anglia) for kindly providing the gridded rainfall data (under support from UKDepartment of Environment, Transport and the Regions (DETR), Contract No. EPG 1/1/48) and to J.Ininda, D.P. Rowell and C.K. Folland for helpful discussion. Comments from the two referees alsosubstantially enhanced the paper.



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Documents

Towards the prediction of the East Africa short rains based on sea-surface temperature–atmosphere coupling