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INTERNATIONAL JOURNAL OF CLIMATOLOGY
Int. J. Climatol. 19: 1319–1336 (1999)
NUMERICAL FORECASTING OF MONTHLY CLIMATE IN
SOUTHERN AFRICA
WARREN TENNANT*
Climatology Research Group, Uni6ersity of the Witwatersrand, PO Wits 2050, South Africa
Recei6ed 7 April 1998
Re6ised 2 No6ember 1998
Accepted 11 No6ember 1998
ABSTRACT
The South African Weather Bureau began issuing monthly forecasts of rainfall and temperature for seven regions in
South Africa in 1995. With the availability of reanalysis datasets, historical forecasts may be done to assess the utility
of numerical monthly forecasts. Monthly hindcasts with observed sea surface temperature data were run every four
weeks from 1979 to 1995 using the T30 18-layer Center for Ocean – Land – Atmosphere Studies (COLA) general
circulation model. Verification results show that bias-correction of model output and ensemble averaging improves
forecast skill substantially. Monthly average sea level pressure and 500 hPa height forecasts are better than using
persistence for all areas globally. Model surface temperature and outgoing long-wave radiation anomalies have a
negligible bias but model rainfall anomalies suffer from geographically dependent biases. Variations in monthly
forecast skill was found not to correspond to ENSO events and a priori prediction of skill using ensemble spread was
not successful. In southern Africa, monthly forecasts that complement seasonal forecasts hold great potential to
benefit economic activities in the region. Copyright © 1999 Royal Meteorological Society.
KEY WORDS: southern
Africa; hindcast; skill; GCM; persistence; cluster analysis; ensemble; lagged average forecasting; bias;
ENSO; SOI
1. INTRODUCTION
It was John von Neumann who first suggested three distinct categories of atmospheric motion affecting
the time scale of numerical weather prediction (Pfeffer, 1960). The first includes atmospheric motion that
is determined mainly by initial conditions where forecasts are done by extrapolating tendencies over short
times. The second category includes the opposite extreme of motion, which is largely independent of
initial conditions. Forecasts of such states are done by using observed characteristics of low-frequency
variability. Motions occurring between these two extremes make up a third category, where initial
conditions become less important, but still relevant, and low-frequency modes increase in importance. The
degree of complexity in each category is largely responsible for the amount of progress made in
forecasting at each time scale. Seasonal predictions continue to have less skill than short-range predictions, despite improvements to seasonal prediction schemes that have occurred over the last decade.
Current capabilities in seasonal prediction are summarized by Barnston et al. (1994). Purely statistical
methods include canonical correlation analysis (CCA) (Graham et al., 1987a,b; Barnston and Ropelewski,
1992), principal oscillation patterns (POPS) (Xu and von Storch, 1990; Penland and Magorian, 1993) and
optimal climate normals (OCN) (Wilks, 1996).
To date, monthly forecasts using statistical and numerical methods have achieved only limited skill.
However, forecasts on this time scale can have an immense benefit to a large scope of end users. Further,
it is suggested that monthly forecasts should accompany seasonal forecast products because benefits
obtained from the application of seasonal forecasts without following specifications of medium-term
information are limited (Lyakhov, 1994).
* Correspondence to: South Africian
E-mail: tennant@cirrus.sawb.gov.za
Weather
Bureau,
CCC 0899–8418/99/121319 – 18$17.50
Copyright © 1999 Royal Meteorological Society
Private
Bag
X097,
Pretoria
0001,
South
Africa.
1320
W. TENNANT
General circulation models have been under investigation as a possible tool for extended-range
forecasting for some time. The Atmospheric Model Inter-comparison Project (AMIP) (Gates, 1992)
recently explored the utility of dynamical extended-range prediction. This international effort was to
determine the systematic climate errors of various atmospheric models by simulating the climate of the
decade 1979–1988 using the same set of sea surface temperature and sea ice boundary conditions. Results
were directed at obtaining a comprehensive evaluation of atmospheric models at the time and to provide
useful information for further model development. Results from an analysis of the ability of 15 GCMs to
simulate the tropical intra-seasonal oscillation show that a wide range of model skills exist, with no single
model being capable of capturing successfully the full extent of the oscillation (WCRP, 1995b). Further
support for models is found in the World Climate Research Programme (WCRP) Climate Variability and
Predictability Programme (CLIVAR). This has been launched to address questions of climate variability
and the predictability of global climate on time scales of a month to a century (WCRP, 1995a). One of
the major elements of the programme, CLIVAR-GOALS, is to determine the variability and predictability
of the Global Ocean – Atmosphere – Land System (GOALS) on seasonal to inter-decadal time scales.
Modelling is important to CLIVAR and a numerical experimentation group has been formed to
co-ordinate a modelling study to assess the predictability of seasonal mean circulation and rainfall one
season in advance.
On monthly time scales, dynamical extended-range forecasting is widely accepted as the method most
likely to ultimately provide the best forecasts. However, such forecasts must improve upon cheaper
empirical methods and some reference procedure, such as using persistence, to be used operationally.
Ensemble methods in dynamical extended-range forecasting have shown considerable possibilities of
improving monthly predictions of climate (Hoffman and Kalnay, 1983; Toth and Kalnay, 1993).
Despite monthly forecasting not receiving the same amount of attention as seasonal prediction, mainly
because of the complexity of prediction algorithms on this time scale, which have to take initial and
boundary conditions into account, some experimentation has been done. Shukla (1981) demonstrated that
the evolution of long-waves remain sufficiently predictable up to 1 month so that the combination of less
predictable shorter waves and long-waves remain predictable. Based on this finding, monthly forecasting
activities have been practised at several weather centres for some time. The UK Meteorological Office
produces deterministic and probabilistic forecasts from 30-day ensembles operationally every 2 weeks.
Specification equations relate the numerical output to surface climate anomalies (Richardson and
Harrison, 1994). The Japan Meteorological Agency runs weekly operational 30-day forecasts using their
T63L30 global model and a 10-member lagged average forecast ensemble (Kobayashi, personal
communication).
Many centres did trial experiments on 30-day forecasts during the 1980s. The Japan Meteorological
Agency ran eight lagged average forecast ensemble winter cases. Evaluations show that the ensemble
mean was more skilful than the control or climate forecast, but skill during the last 10 days of the month
forecast was marginal (Yamada et al., 1991). The National Centers for Environmental Prediction (NCEP)
performed a number of 30-day dynamical forecasts at 24-h intervals from December 1986 to March 1987
(Tracton et al., 1989). These forecasts were generally better than persistence, however, most of the skill
was found in the first 10 days of the integration. The forecast skill was enhanced by employing time
averaging, lagged average forecasting, correction of systematic errors and empirical orthogonal function
filtering. At present, the only dynamical extended-range forecasts within the 1-month time scale done at
the centre are the use of the method of breeding growing modes (BGM) to generate ensembles for 2-week
forecasts (Toth and Kalnay, 1993). The Chinese National Meteorological Centre used their T42L10 model
for operational monthly forecasting and research into the monthly forecasting problem (Zheng et al.,
1993). The European Centre for Medium-range Weather Forecasts produced a set of 30-day integrations
with the operational ECMWF model from 1985 to 1988. They found modest skill that became marginal
beyond day 20 and that model resolution has a large effect on the model climate drift (Palmer et al.,
1990). At Météo-France, a global T42 version of the French numerical prediction model has been used to
produce monthly mean forecasts of the northern hemisphere winter months from 1983 to 1990. They
found the presence of skill even beyond day 30 but concluded that statistical post-processing is necessary
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
NUMERICAL FORECASTING OF MONTHLY CLIMATE
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to produce useful forecasts (Deque and Royer, 1992). The Canadian Weather Service has also experimented with dynamical extended-range forecasting (Ritchie et al., 1994).
In southern Africa, rainfall variability has an important impact on agriculture, housing and water
supply to rural communities, industries and tourism. The drought associated with the 1982–1983 El
Niño–southern oscillation (ENSO) event caused estimated damages close to US$1 billion (Moura et
al., 1992; Moura, 1994). With an increasing population and the associated demand for fresh water,
the development of objective and reliable methods for long-range rainfall predictions is becoming
increasingly important. In view of the need for monthly forecasts, particularly in southern Africa,
the South African Weather Bureau began issuing monthly forecasts of categorized rainfall and temperature for seven homogeneous rainfall regions within South Africa in 1995. The recent availability
of reanalysis datasets now allows a large number of dynamical extended-range historical forecasts to
be produced and verified. This database can then be used to determine the utility of monthly forecasts in South Africa and the surrounding region. Such information is vital to end-users of forecast
information who make decisions based on the forecasts (WUBSO, 1996). In this paper, historical
monthly forecasts from 1979 to 1995 were generated using observed sea surface temperatures (SST)
and are considered hindcasts because some of the information used as input to the model simulation
was only available after the actual forecast period (Barnston et al., 1994). Nevertheless, this
should not impact on the conclusions drawn from this study. The paper examines the historical
performance of GCM monthly forecasts over southern Africa to learn more about available skill of
this much needed product.
2. DATA AND METHODOLOGY
2.1. Generation of hindcasts
The Center for Ocean – Land – Atmosphere Studies COLA T30L18 GCM was used to create a
long series of monthly hindcasts. A description of the model can be found in Kirtman et al. (1997).
Prognostic variables in the COLA model are represented by spherical harmonics of legendre polynomials with triangular truncation at wave number 30, corresponding to a horizontal grid of 96× 48
points giving a resolution of about 400 km. Moisture is represented in the vertical on all 18 unevenly spaced s-co-ordinate levels. Physical processes simulated by the model are deep and shallow
convection, large-scale precipitation, radiation, surface physics, vertical diffusion and gravity wave
drag. A simple biosphere model is also included over land to enable the model to be used for
climatological studies. Data processed in this part of the model are deep soil temperature, ground
temperature, canopy temperature, soil moisture, liquid water storage, latest computed precipitation,
roughness, maximum mixing length and sea ice temperature.
Initial conditions for the GCM hindcasts were derived from the National Centers for Environmental Prediction (NCEP) global reanalyses data (Kalnay et al., 1996). Selected daily analyses, at
6-h intervals, from 1 January 1979 to 31 December 1995 form initial conditions for 221 hindcast
cases. Each case is separated by 4 weeks and the lagged average forecasting technique is used to
generate nine ensemble members, lagged by 6 h, for each case. In total, 1989 hindcasts have been
done. The reanalysis data were then used to evaluate GCM hindcasts of sea level pressure and 500
hPa heights.
Boundary condition data in the GCM include an optimum interpolation sea surface temperature
dataset (Reynolds, 1988; Reynolds and Marsico, 1993). For current operational forecasts the initial
observed sea surface temperature anomalies are persisted for the duration of the forecast. To date,
this has been the best way of forecasting sea surface temperatures up to 1 month, for example
Latif et al. (1993) (Figure 1). Remaining lower boundary data used by the GCM, 6iz. sea ice, snow
depth, soil moisture and vegetation type, are climatological fields created for the specific model
resolution.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
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W. TENNANT
Figure 1. Anomaly correlation coefficients of the El Niño– southern oscillation predictions with a coupled general circulation model
(CGCM) and principal oscillation pattern technique as a function of forecast lag and compared with results of the persistence
forecast (after Latif et al., 1993)
2.2. Post-processing of model output
Nearly every field output by a GCM has some sort of inherent bias. This is because the GCM does not
simulate the real atmosphere perfectly, but rather drifts towards its own model climate (Chen, 1989).
Furthermore, this drift is dependent on model resolution and increases in low resolution models (Palmer
et al., 1990). If the bias varies little with time, then it can be removed from a model forecast. Two ways
of doing this are tested. The first is by finding the linear relationship between the forecast and observed
anomalies through least squares regression grid point by grid point (Livezey and Schemm, 1988) (Figure
2(a)). Model forecasts are bias-corrected at each grid point so that the least squares regression fit produces
a line passing through the origin of the scatter plot with a gradient of unity (Figure 2(b)). However, this
Figure 2. Scatter plot of forecast against observed anomalies of sea level pressure (hPa) at the model grid box centred at 30°S, 25°E
over the period 1979 –1995 for (a) uncorrected GCM forecasts and (b) bias-corrected GCM forecasts. The dashed line is the best
fit using linear regression
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
NUMERICAL FORECASTING OF MONTHLY CLIMATE
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Figure 3. Time series of monthly dependent bias of sea level pressure (hPa) determined from cross-validation at the model grid box
centred at 30°S, 25°E
bias-correction method contaminates the forecast anomaly magnitudes and anomaly correlation coefficients do not improve satisfactorily. The second bias correction method tested finds a grid point bias for
each month by comparing GCM monthly climate and observed climate (Figure 3). Here, for example, the
bias of sea level pressure forecasts for a grid point in the interior of South Africa has an annually
repeating monthly pattern with maximums in June and December and minimums during March and
October. Forecast skill improvements were found to be better using this method and consequently all
bias-correction discussed in this paper was done this way. When calculating the model bias in a particular
year forecasts for that year were withheld to make the process more realistic. Bias-correction of model
forecasts for the tropics (20°N to 20°S) was found to be best done without a monthly dependency because
the monthly pattern, unlike over South Africa, is ill-defined in those latitudes.
Ensemble forecasts cover a subset of the probability space of outcomes based on the given initial and
boundary conditions of the atmosphere. This information must be used to maximise the skill of resulting
forecasts. Techniques to do this include averaging and forming clusters of ensemble members.
2.3. E6aluation of hindcasts
An important distinction must be made between forecast accuracy or similarity and forecast skill.
Accuracy is defined as the average degree of correspondence between forecasts and observations (Murphy,
1988a). It is possible to select a field from historical observations that will closely match a verifying
observed field because the atmosphere does repeat itself to a certain degree. Therefore, if one were to
forecast by randomly selecting historical fields, some accurate forecasts may be made occasionally. Such
a method has no scientific skill (Anderson and van den Dool, 1994). Skill is defined as the accuracy of
generated forecasts relative to the accuracy of other forecasts produced by some reference procedure, such
as using persistence (Murphy, 1988a). It is thus important to determine the skill of a forecast and not
merely its accuracy.
Many evaluation methods are found in the literature. These are designed to evaluate various aspects of
modelling and forecasting. They range from basic measures of error to complex skill scores. Gridded
forecast fields output by models are compared with verifying analysis fields. The most popular measures
of skill are the root-mean-square error (RMSE), the anomaly correlation coefficient (ACC) and average
error (Brier and Allen, 1951; Murphy and Epstein, 1989). Anomalies throughout this paper are calculated
by subtracting the relevant GCM or observed month-dependent climatological values. The World
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
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W. TENNANT
Meteorological Organisation (WMO) requires all numerical weather prediction centres to publish these
statistics of their models annually (WMO, 1992). In this paper, the above measures of model skill will
be used to evaluate sea level pressure and 500 hPa height prognostic fields of the GCM for the sector
around southern Africa and compare them with other parts of the globe.
RMSEs can be divided into two parts, the systematic and non-systematic. The systematic RMSEs
represent the error that is similar at all points in the gridded field, while the non-systematic part
contains the remaining random errors (Hoskins and Pearce, 1983). Accurate models have low systematic RMSEs. RMSEs are not a perfect tool and weaknesses include favouring model forecasts that
underestimate variability (Brier and Allen, 1951). Notwithstanding, an advantage of this measure of
skill is that it retains the unit of the forecast variable. The root-mean-square skill score (RMSSS)
(Stanski et al., 1989) may be used to measure improvements in model skill when some change is
made. For example, the amount of skill the GCM forecasts demonstrate relative to persistence forecasting may be quantified this way. This score will also be used to compare model skill over different
parts of the globe.
Anomaly correlation coefficients measure the similarity of the spatial patterns between the forecast
and observed fields (Murphy, 1988a). Long-term forecasting is mainly concerned with the departure of
a particular variable from the climatological mean. Anomaly correlation coefficients are ideal for
evaluating the ability of a model to forecast these changes. On their own, anomaly correlation
coefficients fail to detect gross model biases and sometimes high values can be misleading (Watterson,
1996), such as when a perfect correlation is found between two fields that differ by a constant factor
throughout.
Bias-correction of GCM output can be done in two ways. The nearest to real time forecasting when
calculating model biases is retroactive real time forecasting (Barnston et al., 1994). Here, model
simulations from the first 10 years of the simulation period are used to calculate the model bias that
is subtracted from forecasts for year 11. A new bias, calculated using forecasts from year 1 to year 11,
is removed from forecasts for year 12 and so on to year 17. The other method used when calculating
model biases is cross-validation (Michaelsen, 1987). Data from all years of the experiment, except the
current year, is used to calculate the bias that is removed from forecasts in that year. With cross-validation, forecast data that would only be available after the current year is used, a true hindcast
scenario. This is done to include the largest possible set of forecasts for model verification.
Model forecasts of sea level pressure and 500 hPa heights are evaluated in a window centred over
southern Africa from 30°W to 60°E and 20°S to 60°S. In addition, for comparison, the same prognostic fields are evaluated over the entire globe, the northern hemisphere north of 20°N, the southern
hemisphere south of 20°S and the tropics from 20°N to 20°S. Diagnostic variables of surface temperature and rainfall are evaluated over South Africa against observed data from 77 temperature stations
and 510 rainfall stations that are interpolated to model output grid boxes using spatial weighting
based on station proximity to other stations (Figure 4). Outgoing long-wave radiation fields are
evaluated over Africa and the Indian and the South Atlantic Oceans for the period June 1974 to July
1992. RMSE and bias are determined for each model grid box and anomalies are determined with
respect to the model climate.
3. RESULTS
Two important steps exist when formulating a forecast. The first is an objective method to provide
forecast guidance and the second extracting useful information from this guidance. Evaluation results
of the COLA T30 GCM output and the impact of bias-correction on forecast skill are shown and this
is followed by the value of ensemble forecasting. GCM diagnostic fields are mostly parameterised and
are occasionally unreliable. Results are shown where such fields may be useful in the southern Africa
region. It is of further interest to compare model skill during strong and weak boundary forcing
events and to compare skill in southern Africa with elsewhere.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
NUMERICAL FORECASTING OF MONTHLY CLIMATE
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Figure 4. Map showing COLA T30L18 model grid boxes with the location of (a) rainfall and (b) temperature stations used for
model diagnostic output evaluation
3.1. GCM prognostic output
Bias-corrected model forecasts of sea level pressure and 500 hPa heights have RMSEs substantially
lower than those when using persistence (Figure 5). The same is found with the anomaly correlation
coefficient scores (Figure 6). These scores clearly show that 30-day GCM forecasts have skill over
southern Africa. Model ensemble average forecasts have large errors before bias-correction showing the
large effect model drift has on verification scores.
GCMs in general underestimate variability but this is geographically dependent (Kaas, 1993). The
COLA model’s inter-monthly variability is studied by comparing plots of forecast and observed standard
Figure 5. Average RMSEs of 30-day forecasts from 1989 to 1995 for the area 30°W – 60°E and 20° – 60°S. Biases are determined
using retroactive real-time forecasting beginning in 1979
Copyright © 1999 Royal Meteorological Society
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W. TENNANT
Figure 6. Average anomaly correlation coefficients of 30-day forecasts from 1989 to 1995 for the area 30°W – 60°E and 20° – 60°S.
Biases are determined using retroactive real-time forecasting
deviation (Figure 7). The model captures all of the 500 hPa height variability north of 35°S except in the
central Atlantic Ocean and most of the sea level pressure variability in the same area especially over South
Africa. Further south, the model underestimates variability somewhat. Tropical disturbances play an
important role in the summer rainfall of southern Africa (Tyson, 1986). It is in these latitudes, and over
South Africa, where the COLA model is estimating atmospheric variability best suggesting the potential
for accurate summer rainfall forecasts.
3.2. Effect of ensemble a6eraging and clustering
The ensemble average has a higher correlation (0.37) than each individual ensemble member (ranging
from 0.25 to 0.35) (Figure 8). This result has been written up by many others, inter alia, Leith (1974) and
Brankovic et al. (1990). Lagged average forecasting necessitates the use of weights when calculating the
ensemble average (Murphy, 1990). Weights for the forecasts ranging from 30 to 32 days are determined
from an exponential curve with a half-life of 10 days and a coefficient of unity. This assumes that an
analysis is perfect and GCM daily forecasts reach an anomaly correlation coefficient of 0.6 at about 10
days. A similar damper was used to simulate diminishing model skill in the prediction of monthly 700 hPa
heights over North America (Harnack et al., 1986). This way of averaging produces anomaly correlation
coefficients of 0.39 that are higher than the numerical ensemble average of 0.37 (Figure 8). Correlations
in Figure 6 are an average for the latter 7 years and in Figure 8 are an average over the entire 17 years
of the experiment and consequently differ.
Usually ensemble member forecasts are not spread evenly over a domain of possible outcomes. Instead,
two or three clusters usually become evident within an ensemble of nine members. Cluster analysis
techniques (Everitt, 1974; Krzanowski, 1990) may be used to identify these. In this experiment, the group
average method was used to cluster 500 hPa fields, which have higher skill scores than the sea level
pressure fields. Systematically choosing clusters according to the number of ensemble members in the
cluster produces average anomaly correlation coefficients from 0.28 for the smallest of three clusters to
0.36 for the largest of two clusters (Figure 8). If clusters are chosen optimally, it is possible to achieve a
high level of skill. Using hindsight to select the cluster with the highest anomaly correlation coefficient at
Copyright © 1999 Royal Meteorological Society
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Figure 7. Standard deviation patterns of observed and bias-corrected forecasts of 500 hPa heights and sea level pressure fields for
the period 1979–1995. Biases are determined using cross-validation
each forecast period pushed the anomaly correlation coefficient up to 0.54 for southern Africa (Figure 8).
The mean-square-spread (Barker, 1991), which measures the agreement between individual forecasts in a
cluster, has been used in forecasts up to 2 weeks ahead to indicate, a priori, the confidence in a particular
forecast cluster. However, for monthly average forecasts studied here the mean-square-spread among
ensemble members in the cluster proved not to be a good objective method in finding the best cluster
(Figure 8). For now, ensemble averaging remains the best way to enhance dynamical extended-range
forecast skill, but cluster analysis has great potential for enhancing the skill further.
Figure 8. Comparison of the average anomaly correlation coefficients of 30-day, bias-corrected 500 hPa height forecasts from 1979
to 1995 over the area 30°W–60°E and 20°–60°S. Best (solid) and poorest (hatched) ensemble member, numerical ensemble average,
weighted ensemble average, best (solid) and poorest (hatched) cluster, best case-by-case cluster and case-by-case cluster with the
minimum mean-square-spread. Monthly biases removed are determined by cross-validation
Copyright © 1999 Royal Meteorological Society
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W. TENNANT
Figure 9. Observed and forecast January sea level pressure anomalies during the 1983 El Niño and 1989 La Niña events
3.3. Temporal 6ariation of skill
Seasonal GCM forecasts are strongly dependent on boundary forcing and skill is greatest during El
Niño and La Niña events when there is a strong boundary signal (Barnett et al., 1994). However, monthly
forecasts are still very much dependent on initial conditions. Two case studies of the January observed
and forecast sea level pressure illustrate the point (Figure 9). During the 1983 El Niño event, the model
simulates the area of negative anomalies in the South Pacific Convergence Zone and in the Southern
Ocean very well but underestimates the intensity by about half the magnitude. Model responses to the
additional boundary forcing compare well with observations over the northern hemisphere. For the La
Niña case in 1989, the model again does well in the northern hemisphere. The observed atmospheric
response to the La Niña is weak and the model responds at the same magnitude. It also gets the correct
sign in the anomaly in the South Pacific Convergence Zone and south of South Africa. In these cases the
model responds more realistically during the La Niña event.
However, case studies may be misleading as comparing southern Africa and global time series of GCM
skill scores with the southern oscillation index (SOI) reveals (Figure 10). There is no significant correlation
between the 5-month running means of global GCM skill or GCM skill over southern Africa and the SOI
(Table I). Although there is only one La Niña event, correlations in Table I are calculated from 13
independent forecasts throughout the cycle of the event. However, the relatively strong correlation
between global skill and the SOI of −0.78 remains insignificant for this number of forecasts.
3.4. Diagnostic model output
Model forecast surface temperature and rainfall are evaluated for the grid boxes centred at 33.75°S
18.75°E (winter rainfall region) and 30°S 30°E (summer rainfall region). RMSEs and biases of the model
climate, actual forecast values and anomalies are considered. Model forecast anomalies are determined
with respect to the model climate while observed anomalies are determined with respect to the observed
Copyright © 1999 Royal Meteorological Society
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NUMERICAL FORECASTING OF MONTHLY CLIMATE
Figure 10. Time series of 5-month running means of the SOI, GCM skill over southern Africa and global GCM skill
climate. Forecast surface temperature anomalies have a negligible bias and lower RMSE than actual
forecast values which have a positive bias (Figure 11(a)). This bias is greater in the summer rainfall area.
The model monthly surface temperature climate has a positive bias in both the summer and winter rainfall
areas.
Table I. Correlation between the 5-month running mean of the SOI and GCM skill (anomaly correlation coefficient)
for the globe and southern Africa over the period 1979–1995
El Niño years
La Niñà years
Other years
All years
Correlation with skill over
southern Africa
Correlation with
global skill
Number of
years
Number of
forecasts
−0.02
−0.4
0.08
0.18
−0.03
−0.78
−0.13
0.16
5
1
11
17
61
13
143
217
Copyright © 1999 Royal Meteorological Society
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Figure 11. Average RMSEs and biases of the COLA T30L18 GCM climate, forecasts and forecast anomalies of (a) surface
temperature, (b) rainfall and (c) outgoing long-wave radiation for two model boxes in the summer and winter rainfall areas of South
Africa for the period 1979 – 1995
Copyright © 1999 Royal Meteorological Society
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Model forecast rainfall has a skew, rather than a normal, distribution and biases are a function of the
magnitude of the forecast amounts. Bias correction was attempted by multiplying the forecast rainfall
anomaly by the ratio of the standard deviation of the model climate and observed rainfall. In this way
forecast rainfall amounts are reduced in areas where the model overestimates rainfall variability and
increased in areas where rainfall variability is underestimated. The bias was reduced (Figure 11(b)) but not
as effectively as with the surface temperature forecasts. The model climate rainfall has a negative bias in
the winter rainfall area and a positive bias in the summer rainfall area. The positive monthly bias of 147
mm at 30°S 30°E is more than the wettest month’s average in that area. RMSEs for rainfall anomaly
forecasts in the winter rainfall region are increased when bias correction is applied. This is not necessarily
a deterioration in the forecast because underestimating rainfall amounts will result in low RMSEs.
Seasonal model climate maps of outgoing long-wave radiation (OLR) biases over the Indian and South
Atlantic Oceans show negative values over most of the Indian Ocean and positive values over Indonesia
and equatorial west Africa peaking in spring (Figure 12). This suggests that the model is overestimating
convection (negative OLR bias) over the Indian Ocean and not simulating enough of it over much of the
land in tropical Africa. Over South Africa, negative biases are found over the summer rainfall areas in the
east and positive biases in the winter rainfall areas in the west (Figure 11(c)).
3.5. Global skill
The RMSSS is used to compare the local skill of the COLA T30L18 GCM over southern Africa with
that in other areas. This score quantifies the improvement in model forecasts over persistence forecasts.
It is clear that on average the GCM performs substantially better than using persistence in all regions
(Figure 13). Sea level pressure forecasts for southern Africa have a higher level of skill than their northern
hemisphere and global counterparts. However, 500 hPa height forecasts are most skilful in the northern
hemisphere. Results for monthly northern hemisphere 500 hPa height forecasts compare well with those
Figure 12. Seasonal maps of COLA T30L18 outgoing long-wave radiation model climate biases
Copyright © 1999 Royal Meteorological Society
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Figure 13. RMSSS over various regions showing the decrease in RMSEs of monthly GCM forecasts (dark shading) over using
persistence (light shading) for the period 1979 – 1995
obtained by the Japan Meteorological Agency, which have an average anomaly correlation coefficient of
0.46 while running in forecast mode since March 1996 (Kobayashi, personal communication). In the
tropics, the GCM is able to improve notably on the already low RMSEs when using persistence. The
RMSSS is dependent on how poor persistence may perform. Note that the best RMSSSs correspond to
areas where persistence results in high RMSEs.
4. DISCUSSION
Numerous studies have shown the benefits of ensemble methods in increasing monthly forecast skill
(Leith, 1974; Brankovic et al., 1990; Yamada et al., 1991). Results presented in this paper show how the
ensemble mean outperforms each of the ensemble members. Palmer (1993) recognised the utility of
ensemble forecasting as a measure of the importance of initial conditions on the skill of a dynamical
extended-range forecast. A case-by-case plot of ensemble member skill of the COLA GCM 30-day
forecasts shows a large spread in the anomaly correlation coefficients (Figure 14). In each case the same
boundary forcing is used proving that the variations in forecast skill are caused by differences in initial
conditions. Ensemble averaging acts to reduce random forecast errors caused by uncertainties in these
initial conditions (Murphy, 1988b). Time averaging also has benefits to forecast skill by filtering higher
frequency scales of motion to leave the more predictable, low-frequency waves (Shukla, 1981). However,
high-frequency waves have an effect on the low-frequency modes and if not parameterised correctly,
model drift increases degrading the forecast. Stewart (1994) investigated methods of improving a
low-resolution model by analysing the contribution of unresolved scales using a higher resolution model
and simulating these in a combined deterministic and stochastic parameterisation scheme. Notwithstanding, forecast skill does improve with higher resolution GCMs that have sophisticated subgrid scale physics
(Sirutis and Miyakoda, 1992), although there is evidence that it is beneficial to form a forecast ensemble
from GCMs with different horizontal resolutions (Deque, personal communication). Higher 1-month
forecast skill may consequently be achieved by using high-resolution GCMs and employing ensemble
methods and output filtering.
Bias-correction of GCM output is considered a further vital step in enhancing forecast skill (Miyakoda
et al., 1986; Livezey and Schemm, 1988; Tracton et al., 1989; Murphy, 1990). In this study, uncorrected
model forecasts, which sometimes have larger errors than persistence forecasts, become skilful by a
substantial margin once the bias is removed. The COLA model has a particular seasonality in its bias,
which is easily identified and removed at each grid point. The adjustment of model anomaly forecasts so
that a linear regression fit passes through the origin of a scatter plot of observed and forecast anomalies
with a gradient of unity caused an unrealistic increase in the forecast anomaly variability (Figure 2). It
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
1333
NUMERICAL FORECASTING OF MONTHLY CLIMATE
Figure 14. Case-by-case scatter plot of ensemble member forecast skill. The area between highest and lowest skill at each case is
shaded
seems that, at least for COLA GCM monthly forecasts, there is no linear relationship between bias and
anomaly magnitude.
Another use of ensemble forecasting is to use the ensemble spread to predict, a priori, the confidence
in a forecast (Murphy, 1990; Barker, 1991). However, the ensemble spread of 30-day average forecasts
verified in this study do not correlate well with forecast skill (Table II). This may be a result of a relatively
small ensemble size because the correlation of the ensemble mean-square-spread with forecast error has
been found to increase with larger ensembles (Barker, 1991). It may also be that the relationship between
forecast error and ensemble spread is dependent on case-to-case predictability. Model variability between
cases is known to exceed variability due to model uncertainties (Sirutis and Miyakoda, 1992). To test the
impact of predictability on the ensemble spread and forecast error relationship the forecast cases were
sorted into bins according to the skill of the ensemble average (Table II). Good forecast cases, where the
anomaly correlation coefficient exceeds 0.6, account for more than a third of the cases but correlations
show that ensemble spread increases slightly with forecast skill, contrary to expectations. As the skill of
the forecasts decrease the correlation improves, especially for sea level pressure forecasts. However, the
higher correlations are found only with a small portion of the cases when the model has no skill.
Difficulties encountered with using cluster analysis methods to improve forecast skill above that of the
ensemble mean in this study may also be a result of the lack of a clear link between forecast skill and
ensemble spread. However, the potential remains for clustering to exclude unskilful ensemble members
from the average and enhance forecast skill.
Table II. Correlation of ensemble spread and ensemble average skill for GCM 30-day forecasts divided into bins
based on forecast anomaly correlation coefficients (ACC). Numbers in brackets are actual number of cases
Bin (ACCs)
1.0 to −1.0
1.0 to 0.6
0.6 to 0.2
0.2 to −0.2
−0.2 to −0.6
−0.6 to −1.0
500 hPa
Heights
% of cases
−0.07
100 (221)
−0.07
34 (76)
0.11
44 (98)
−0.07
17 (37)
−0.12
4 (9)
−0.17
1 (1)
—
Sea level
Pressure
% of cases
−0.02
100 (221)
−0.02
38 (85)
0.03
43 (96)
−0.01
14 (29)
−0.28
4 (9)
−0.44
1 (2)
−1.00
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
1334
W. TENNANT
Boundary forcing does play a role in 30-day GCM forecast skill. Using observed SSTs produces better
forecasts than using climatological SSTs (Mo and Kalnay, 1991). However, the effect on the skill in the
midlatitudes is lower than in the tropics. It was found, both locally and globally, that the skill of monthly
forecasts in this study is not well correlated to the strength of the anomalies in the boundary forcing,
further supporting the notion that monthly forecast performance is more sensitive to initial conditions
(Sirutis and Miyakoda, 1992). Sometimes skill is found during predictable, stable climate regimes but the
change between regimes, which does not require any external forcing, is often unpredictable and can result
in poor skill (Reinhold, 1987; Palmer and Anderson, 1993). Blocking and stable climate regimes are very
rare in the southern Africa region and cannot account for much of the skill that is found in the area
(Hoskins and Pearce, 1983). This suggests that the COLA GCM captures a number of the dynamical
processes in the atmosphere that govern the time evolution of the system very well.
Biases of model diagnostic forecasts of anomaly outgoing long-wave radiation and surface temperature
are negligible providing more useful information than direct forecasts of these parameters that may have
a large systematic error. Such parameters may be used in a downscaling method to produce local scale
forecasts of rainfall and surface temperature (Kim et al., 1984). In South Africa, outgoing long-wave
radiation anomalies have been shown to be useful in detecting dry and wet spells (Jury and Levey, 1993).
However, GCM rainfall forecasts for South Africa should be used with caution and only after careful
bias-correction. Other findings show that GCM’s as a whole simulate large scale features well but suffer
in the area of parameterised variables, such as rainfall, where global average precipitation values are
usually acceptable but locally may vary by a factor of 2 (Gates, 1985).
5. SUMMARY AND CONCLUSION
Monthly forecasts for southern Africa are a reality with the use of a low resolution GCM that produces
an ensemble of nine members. Historical simulations over a 17-year period, that are bias corrected using
known model drift, produce ensemble average forecasts with higher verification scores than from using
persistence. This shows that on average monthly forecasts are skilful. Over southern Africa this skill is on
a par with other regions of the world. Since each model forecast parameter may hold unique benefits for
the overall product, the best final forecast may be obtained from a combination of various model forecast
parameters, including 500 hPa heights, sea level pressure, outgoing long-wave radiation, surface temperature and rainfall.
Monthly forecasting is highly dependent on initial conditions and to a large extent on boundary
conditions making it the most complex of all forecasting time scales. This relatively new branch of
forecasting driven by the ever increasing demand for monthly forecasts, particularly as a complement to
seasonal forecasts, has prompted meteorological centres to begin focusing their efforts on improving the
skill of monthly forecasts. The results presented here demonstrate that GCMs are able to produce skilful
monthly forecasts of various aspects of the atmosphere system globally and, in particular, for the southern
Africa region. Generally, findings in this paper agree with the current understanding of the effects of
boundary forcing, ensemble methods, bias-correction of model output and predictability of different
scales of motion. Discrepancies in findings include the use of the ensemble spread for a priori skill
prediction. Possible reasons for this have been discussed. With the advancement in computing capabilities
and a further refining of post-processing techniques more skilful forecasts are becoming increasingly
realisable.
REFERENCES
Anderson, J.L. and van den Dool, H.M. 1994. ‘Skill and return of skill in dynamic extended-range forecasts’, Month. Weather Re6.,
122, 507 – 516.
Barker, T.W. 1991. ‘The relationship between spread and forecast error in extended-range forecasts’, J. Clim., 4, 733 – 742.
Barnett, T.P., Bengtsson, L., Arpe, K., Flugel, M., Graham, N., Latif, M., Ritchie, J., Roeckner, E., Schlese, U., Schulzweida, U.
and Tyree, M. 1994. ‘Forecasting global ENSO-related climate anomalies’, Tellus, 46A, 381 – 397.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
NUMERICAL FORECASTING OF MONTHLY CLIMATE
1335
Barnston, A.G. and Ropelewski, C.F. 1992. ‘Prediction of ENSO episodes using canonical correlation analysis’, J. Clim., 5,
1316 – 1345.
Barnston, A.G., van den Dool, H.M., Zebiak, S.E., Barnett, T.P., Ji, M., Rodenhuis, D.R., Cane, M.A., Leetmaa, A., Graham,
N.E., Ropelewski, C.R., Kousky, V.E., O’Lenic, E.A. and Livezey, R.E. 1994. ‘Long-lead seasonal forecasts — Where do we
stand?’, Bull. Am. Meteorol. Soc., 75, 2097–2114.
Brankovic, C., Palmer, T.N., Molteni, F., Tibaldi, S. and Cubasch, U. 1990. ‘Extended range predictions with the ECMWF models:
time lagged ensemble forecasting’, Q. J. R Meteorol. Soc., 116, 867 – 912.
Brier, G.W. and Allen, R.A. 1951. ‘Forecast verification’, in T.F. Malone, (ed), Compendium of Meteorology, American
Meteorological Society, pp. 843–851.
Chen, W.Y. 1989. ‘Estimate of dynamical predictability from NMC DERF experiments’, Month. Weather. Re6., 117, 1227 – 1236.
Deque, M. and Royer, J.F. 1992. ‘The skill of extended-range extra-tropical winter dynamical forecasts’, J. Clim., 5, 1346 – 1356.
Everitt, B. 1974. Cluster Analysis. Heinemann, London, 122 pp.
Gates, W.L. 1985. ‘The use of general circulation models in the analysis of the ecosystem impacts of climatic change’, Clim. Change,
7, 267 – 284.
Gates, W.L. 1992. ‘AMIP: the Atmospheric Model Intercomparison Project’, Bull. Am. Meteorol. Soc., 73, 1962 – 1970.
Graham, N.E., Michaelsen, J. and Barnett, T.P. 1987a. ‘An investigation of the El Niño – southern oscillation cycle with statistical
models. 1. Predictor field characteristics’, J. Geophys. Res., 92, 14251 – 14270.
Graham, N.E., Michaelsen, J. and Barnett, T.P., 1987b. ‘An investigation of the El Niño – southern oscillation cycle with statistical
models. 2. Model results’, J. Geophys. Res., 92, 14271– 14289.
Harnack, R., Kluepfel, C. and Livezey, R. 1986. ‘Prediction of monthly 700 mb heights using simulated medium-range numerical
forecasts’, Month. Weather Re6., 114, 1466–1480.
Hoffman, R.N. and Kalnay, E. 1983. ‘Lagged average forecasting, an alternative to Monte Carlo forecasting’, Tellus, 35A, 100 – 118.
Hoskins, B. and Pearce, R. 1983. Large-Scale Dynamical Processes in the Atmosphere. Academic Press, New York, 397 pp.
Jury, M.R. and Levey, K.M. 1993. ‘The climatology and characteristics of drought in the eastern Cape of South Africa’, Int. J.
Climatol., 13, 629 –641.
Kaas, E. 1993. ‘Greenhouse induced climate change in the Nordic countries as simulated with the Hamburg climate model. Part I:
Direct model output’, Scientific Report No. 93 – 2, Danish Meteorological Institute, Copenhagen, 20 pp.
Kalnay, E., Kanamitsu, M., Kistler, R., Collins, W., Deaven, D., Gandin, L., Iredell, M., Saha, S., White, G., Woollen, J., Zhu,
Y., Chelliah, M., Ebisuzaki, W., Higgins, W., Janowiak, J., Mo, K.C., Ropelewski, C., Wang, J., Leetma, A., Reynolds, R., Jenne,
R. and Dennis, J. 1996. ‘The NCEP/NCAR 40-year reanalysis project’, Bull. Am. Meteorol. Soc., 77, 437 – 471.
Kim, J.-W., Chang, J.-T., Baker, N.L., Wilks, D.S. and Gates, W.L. 1984. ‘The statistical problem of climate inversion:
determination of the relationship between local and large scale climate’, Month. Weather Re6., 112, 2069 – 2077.
Kirtman, B.P., Shukla, J., Huang, B., Zhu, Z. and Schneider, E.K. 1997. ‘Multiseasonal predictions with a coupled tropical
ocean – global atmosphere system’, Month. Weather Re6., 125, 789 – 808.
Krzanowski, W.J. 1990. Principles of Multi6ariate Analysis. Oxford University Press, Oxford, 563 pp.
Latif, M., Sterl, A., Maier-Reimer, E. and Junge, M.M. 1993. ‘Structure and predictability of the El Niño – southern oscillation
phenomenon in a coupled ocean–atmosphere general circulation model’, J. Clim., 6, 700 – 708.
Leith, C.E. 1974. ‘Theoretical skill of Monte Carlo forecasts’, Month. Weather Re6., 102, 409 – 418.
Livezey, R.E. and Schemm, J.K. 1988. ‘The relative utility of persistence and medium-range dynamical forecasts of monthly mean
700 mb heights’, Month. Weather Re6., 116, 266–268.
Lyakhov, A.A. 1994. ‘Analysis of economic benefits of short term, medium term and long term forecasts’, WMO Conference on
Economic Benefits of Meteorological and Hydrological Ser6ices, Geneva, Switzerland, 19 – 23 September 1994. [Available from
World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
Michaelsen, J. 1987. ‘Cross-validation in statistical climate forecast models’, J. Clim. Appl. Meteorol., 26, 1589 – 1600.
Miyakoda, K., Sirutis, J. and Ploshay, J. 1986. ‘One-month forecast experiments, without anomaly boundary forcings’, Month.
Weather Re6., 114, 2363–2401.
Mo, K.C. and Kalnay, E. 1991. ‘Impact of sea surface temperature anomalies on the skill of monthly forecasts’, Month. Weather
Re6., 119, 2771 – 2793.
Moura, A.D., Bengtsson, L., Buizer, J., Busalacchi, A., Cane, M.A., Lagos, P., Leetmaa, A., Matsuno, T., Mooney, K., Morel, P.,
Sarachik, E.S., Shukla, J., Sumi, A. and Patterson, M. 1992. International Research Institute for Climate Prediction: A Proposal.
1100 Wayne Avenue, Suite 1225, Silver Spring, MD 20910, USA. p. 51.
Moura, A.D. 1994. ‘Prospects for seasonal-to-interannual climate prediction and applications for sustainable development’, WMO
Bull., 43, 207 – 215. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
Murphy, A.H. 1988a. ‘Skill scores based on the mean square error and their relationships to the correlation coefficient’, Month.
Weather Re6., 116, 2417–2424.
Murphy, A.H. and Epstein, E.S. 1989. ‘Skill scores and correlation coefficients in model verification’, Month. Weather Re6., 117,
572 – 581.
Murphy, J.M. 1988b. ‘The impact of ensemble forecasts on predictability’, Q. J. R. Meteorol. Soc., 114, 463 – 493.
Murphy, J.M. 1990. ‘Assessment of the practical utility of extended range ensemble forecasts’, Q. J. R. Meteorol. Soc., 116, 89 – 125.
Palmer, T.N. 1993. ‘Extended-range atmospheric prediction and the Lorenz model’, Bull. Am. Meteorol. Soc., 74, 49 – 65.
Palmer, T.N. and Anderson, D.L.T. 1993. ‘Scientific assessment of the prospects for seasonal forecasting: a European perspective’,
Res. Dept. Tech. Rep. No. 70, ECMWF, Reading, UK.
Palmer, T.N., Brankovic, C., Molteni, F., Tibaldi, S., Ferranti, L., Hollingsworth, A., Cubasch, U. and Klinker, E. 1990. ‘The
European Centre for Medium-Range Weather Forecasts (ECMWF) program on extended-range prediction’, Bull. Am. Meteorol.
Soc., 71, 1317 – 1330.
Penland, C. and Magorian, T. 1993. ‘Prediction of Niño 3 sea surface temperatures using linear inverse-modelling’, J. Clim., 6,
1067 – 1076.
Pfeffer, R.L. 1960. Dynamics of Climate. Pergamon Press, Oxford, 137 pp.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
1336
W. TENNANT
Reinhold, B. 1987. ‘Weather regimes: the challenge in extended-range forecasting’, Science, 235, 437 – 441.
Reynolds, R.W. 1988. ‘A real-time global sea surface temperature analysis’, J. Clim., 1, 75 – 86.
Reynolds, R.W. and Marsico, D.C. 1993. ‘An improved real-time global sea surface temperature analysis’, J. Clim., 6, 114 – 119.
Ritchie, H., Lefaivre, L. and Dugas, B. 1994. ‘DERF experiments with the Canadian Global Spectral Forecast Model’, in 10th
International Conference on Numerical Weather Prediction, July 18 – 22, 1994, Portland, OR, American Meteorology Society,
Boston.
Richardson, D.S. and Harrison, M.S.J. 1994. ‘Ensemble forecasting at the UK Meteorological Office’, Tech. Report 82, Forecasting
Research Division, UK Meteorological Office, Bracknell, UK.
Shukla, J. 1981. ‘Dynamical predictability of monthly means’, J. Atmos. Sci., 38, 2547 – 2572.
Sirutis, J. and Miyakoda, K. 1992. ‘The impact of subgrid-scale physics on one month forecasts’, in Sikka, D.R. and Singh, S.S.
(eds), Physical Processes in Atmospheric Models, Wiley, New York, pp. 398 – 404.
Stanski, H.R., Wilson, L.J. and Burrows, W.R. 1989. ‘Survey of common verification methods in meteorology’, WWW Tech. Rep.
8, WMO/TD-No. 358. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
Stewart, D.A. 1994. ‘Predictability of low-frequency planetary waves in a simple low-resolution model’, Month. Weather Re6., 122,
405 – 423.
Toth, Z. and Kalnay, E. 1993. ‘Ensemble forecasting at NMC: the generation of perturbations’, Bull. Am. Meteorol. Soc., 116,
2522 – 2526.
Tracton, M.S., Mo, K., Chen, W., Kalnay, E., Kistler, R. and White, G. 1989. ‘Dynamical extended range forecasting (DERF) at
the National Meteorological Center’, Month. Weather Re6., 117, 1604 – 1635.
Tyson, P.D. 1986. Climatic Change and Variability in Southern Africa. Oxford University Press, Oxford, p. 102.
Watterson, I.G. 1996. ‘Non-dimensional measures of climate model performance’, Int. J. Climatol., 16, 379 – 391.
WCRP, 1995a. ‘Atmospheric model intercomparison project (AMIP): Intraseasonal oscillations in 15 atmospheric general circulation models (results from an AMIP diagnostic subproject)’, WMO/TD-No. 661, 32 pp. [Available from World Meteorological
Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
WCRP, 1995b. ‘CLIVAR: a study of climate variability and predictability’, WMO/TD-No. 690, 157 pp. [Available from World
Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
Wilks, D.S. 1996. ‘Statistical significance of long-range ‘optimal climate normal’ temperature and precipitation forecasts’, J. Clim.,
9, 827 – 839.
WMO, 1992. ‘Manual on the GLOBAL DATA-PROCESSING SYSTEM’, WMO/TD-No. 485. [Available from World Meteorological Organization, Case Postale 2300, CH-1211 Geneva 2, Switzerland.]
WUBSO, 1996. Workshop on the use and benefits of seasonal outlooks, Presented by the Long-term Prediction Division of the
Directorate Research and Training: South African Weather Bureau, Private Bag X097 Pretoria 0001, 46 pp.
Xu, J.-S. and von Storch, H. 1990. ‘Predicting the state of the southern oscillation using principal oscillation pattern analysis’, J.
Clim., 3, 1316 – 1329.
Yamada, S., Maeda, S., Kudo, T., Iwasaki, T. and Tsuyuki, T. 1991. ‘Dynamical one-month forecast experiments with the JMA
global prediction model’, J. Meteorol. Soc. Jpn., 69, 153 – 159.
Zheng, Q., Song, Q. and Jiang, P. 1993. ‘An improved T42L10 spectral model and its application to monthly operational forecast
in 1992’, Q. J. Appl. Meteorol., 4, 50–56.
Copyright © 1999 Royal Meteorological Society
Int. J. Climatol. 19: 1319 – 1336 (1999)
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