Theor. Appl. Climatol. 88, 169–177 (2007)
DOI 10.1007/s00704-006-0251-7
Printed in The Netherlands
1 Department of Environmental Studies, University of Zululand, KwaDlangezwa, South Africa
2 Department of Meteorology, University of Pretoria, Pretoria, South Africa
3 Department of Environmental and Geographical Science, University of Cape Town, Rondebosch, South Africa
4 Department of Geography, University of W€urzburg, Germany
Evaluating spatial scales of climate variability
in sub-Saharan Africa
M. Jury1, H. Rautenbach2, M. Tadross3, and A. Philipp4
With 8 Figures
Received October 12, 2005; revised February 6, 2006; accepted April 23, 2006
Published online August 28, 2006 # Springer-Verlag 2006
Summary
Spatial scales of variability in seasonal rainfall over Africa
are investigated by means of statistical and numerical tech-
niques. In the statistical analysis spatial structure is studied
using gridded 0.5! resolution monthly data in the period
1948–1998. The de-seasonalized time series are subjected
to successive principal component (PC) analysis, allowing
the number of modes to vary from 10 to 24, producing cells
of varying dimension. Then the original rainfall data within
each cell are cross-correlated (internal), then averaged and
compared with the adjacent cells (external) for each PC
solution. By considering the ratio of internal to external cor-
relation, the spatial scales of rainfall variability are evaluated
and an optimum solution is found whose cell dimensions are
approximately 106 km2. The aspect of scale is further studied
for southern Africa by consideration of numerical model
ensemble simulations over the period 1985–1999 forced with
observed sea surface temperatures (SSTs). The hindcast pro-
ducts are compared with observed January to March (JFM)
rainfall, based on a station-satellite merged analysis of pre-
cipitation (CMAP) data at 2.5! resolution. Validations for dif-
ferent sized areas indicate that cumulative standardized errors
are greatest at the scale of a single grid cell (104 km2) and
decrease 20–30% by averaging over successively larger
areas (106 km2).
1. Introduction
To initiate statistical models or validate numerical
models, meteorological data observed at specific
sites are often aggregated into clusters. If the
spatial dimensions of aggregation are small, lo-
calised temporal fluctuations can induce a poor
signal to noise ratio (Kumar et al., 1996). Noisy
‘target’ data will contribute to instability in sta-
tistical models that are inherently limited by as-
sumptions of historical replication (Barnston et al.,
1994; Carson, 1998). Numerical models are often
swamped by extra-tropical internal variability and
random variations in ocean-atmosphere coupling
(Landman and Mason, 1999; Goddard et al.,
2001; Rautenbach, 2003), yet certain climatic sig-
nals exhibit a degree of persistence or rhythm de-
pendent on tropical anomalous heating that shifts
with zonal planetary waves.
Rainfall, as a major element of climate, is het-
erogeneous and exhibits a skew probability dis-
tribution. It is thus a difficult target variable that
requires special consideration. In evaluating sea-
sonal rainfall forecasts for NE Brazil Gong et al.
(2003) found that certain spatial scales were more
reliable due to the uptake of multiple, remote
climatic influences. Southern Africa, the focus of
this paper, has summer rainfall that is character-
ized by high variability and significant associa-
tions with the El Ni~no – Southern Oscillation
(ENSO) and its patterns of tropical sea surface

temperature (SST) and zonal overturning cir-
culations (Jury et al., 1994; Enfield and Mayer,
1997; Rocha and Simmonds, 1997; Enfield et al.,
1999; Jury et al., 1999; Reason and Mulenga,
1999; Reason et al., 2000; Jury et al., 2002). It
exerts significant socio-economic impacts, mainly
through agricultural production and availability
of water resources in the dry sub-tropics. The
annual cycle over the interior of southern Africa
is of large amplitude; very little rain falls from
May through August. The steep topography
of the eastern escarpment, sub-tropical easterly
flow, and contrasting warm Indian and cool
Atlantic oceans, ensure sharp gradients in rain-
fall. From the southwestern desert to the north-
eastern highlands, rainfall increases from 300 to
1200mmyr"1. The synoptic pulsing by westerly
mid-latitude troughs yields a 15–30 day rhythm
(Levey and Jury, 1996), whilst interannual fluc-
tuations are aligned with regional ENSO signals
(Jury et al., 1994; Mason and Jury, 1997; Rocha
and Simmonds, 1997; Reason andMulenga, 1999;
Reason et al., 2000; Rautenbach and Smith, 2001;
Jury et al., 2002) and a 2–5 year rhythm induced
by ocean Rossby waves (Jury and Huang, 2004).
Year to year swings of summer rainfall>50% are
common and relate to the alternation of dry wes-
terly and moist easterly flows.
Certain studies have considered climate var-
iability using ensembles of simulations from
atmospheric general circulation models (aGCM)
forced with observed SSTs (Kumar et al., 1996;
Rautenbach, 2003), seeking to distinguish the
chaotic component of climate (that is sensitive
to initial conditions) from the predictive com-
ponent that may be forced by SST or modulated
by surface conditions (vegetation, topography and
soil moisture). Such forecasts are based on pre-
dictions of tropical SST as representative of the
low-frequency component of the climate system
that is coherent several months in advance. To
provide an index of model skill at 3-month lead-
time, the ensemble simulated seasonal rainfall
and the observed values may be compared. A low
correlation would suggest either a climate domi-
nated by random internal variability (weak signal
to noise ratio) or a poorly optimized forecast.
With an understanding of relationships between
terrestrial climate and regional ocean-atmosphere
coupling, models may be developed to reduce
risks (Mason and Tyson, 2000; Jury, 2002). With
physical laws and sub-grid scale parameterisa-
tions, predictive numerical models are being ap-
plied to provide users and resource managers
with guidance that can reduce vulnerability. Yet
the optimum level of aggregation for model out-
puts is not well known and may vary from place
to place. Forecasts applied at local (user) level
without aggregation, could be expected to be
unreliable.
The purpose of this study is to evaluate spatial
scales of climate variability over sub-Saharan
Africa to find a suitable level of aggregation. In
the first part we consider how best to regionalise
rainfall data, in the second part we consider
numerical and statistical model outputs over the
period 1985–1999. Cumulative errors are assessed
at successively larger spatial scales over southern
Africa.
2. Data and methods
2.1 Historical regionalisation
Gridded monthly total rainfall data for continen-
tal Africa south of 15! N were obtained from
the Climate Research Unit (University of East
Anglia) at 0.5! degree resolution for the period
1948–1998. The data is derived from 2307 sta-
tion observations using an optimum interpolation
technique (New et al., 2000). Although the inter-
polation technique is robust in areas with sparse
and irregularly spaced data, the gridded fields
should be treated with caution across central
Africa. Hutchinson (1995) provides a theoretical
description of its application to surface climate
variables such as precipitation.
To understand the origins of inter-annual cli-
mate fluctuations it is necessary to identify areas
of coherent response. In this regard, many meth-
ods can be used to cluster time varying fields,
among which is principal components (PC) anal-
ysis. Here we apply PC analysis through the co-
variance matrix technique to reduce the original
de-seasonalized rainfall data into sub-sets ranked
in order of importance. Varimax rotation is ap-
plied to simplify and isolate the structure of the
eigenvectors and facilitate interpretation. Climatic
indices may thus be extracted according to the
spatial loading patterns of the highest ranking
PCs (Mpeta, 2002). The PCA technique forces
the time scores of adjacent cells to be orthogonal,
170 M. Jury et al.