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A Statistical Downscaling Model for Southern Austr alia Winter Rainfall
YUN LI
CSIRO Mathematical and Information Sciences, CSIRO Climate Adaptation Flagship, Wembley, Western Australia, Australia
IAN SMITH
CSIRO Marine and Atmospheric Research, CSIRO Water for a Healthy Country Flagship, Aspendale, Victoria, Australia
(Manuscript received 24 July 2007, in final form 29 July 2008)
ABSTRACT
A technique for obtaining downscaled rainfal l projections from climate model simulations is described.
This technique makes use of the close assoc iation between mean sea level pressure (M SLP) patterns and
rainfall over southern Australia during winter. Principal compo nents of seasonal mean MSLP anomalies
are linked to observed rainfall anomalies at regional, gridpoint, and point scales. A maximum of four
components is sufficient to capture a relatively large fraction of the observed variance in rainfall at most
locations. These are used to interpret the MSLP patterns from a single climate model, which has been used
to simulate both present-day and future climate. The resulting downscaled values provide 1) a closer
repres entation of the observed present-day rainfall than the raw climate model values and 2) alternative
estimates of fut ure changes to rainfall that arise owing to changes in mean MSLP. While decreases are
simulated for later this century (under a single emiss ions scenario), the downsc aled values, in p ercent age
terms, tend to be less.
1. Introduction
There is already evidence that the global pattern of
annual streamflow trends is partly due to the effects of
anthropogenic climate change, mainly because of a
poleward expansion of the subtropical dry zone (Lu
et al. 2007). However, uncertainties in projected rainfall
changes for later this century plague estimates of im-
pacts on future runoff and water storages (Milly et al.
2008). In particular, there are several difficulties asso-
ciated with interpreting changes in variables simulated
at a resolution of 100–200 km in terms of changes to be
expected at smaller catchment scales. This affects the
ability to simulate, for example, expected changes in
surface runoff and streamflows into water catchments.
There is an increasing demand for more reliable esti -
mates of these changes by water resource managers
who need to make long-term decisions about future
infrastructure demands (e.g., new reservoirs, pipelines,
drainage, etc.). Southwest Western Australia has al-
ready been severely affected by a downturn in rainfall
and even more serious reductions in runoff (Bates et al.
2008), and there is a growing concern that this pattern of
reduced rainfall may be extending to the eastern states.
Southern Australia (the region southward of 308S)
receives the bulk of its annual rainfall during the winter
half of the year (i.e., May–October). Rainfall during the
austral winter months from June to August (JJA) is
largely controlled by large-scale atmospheric circulation
patterns, as opposed to convectively dominated sys-
tems that dominate regions to the north and in summer
(Smith et al. 2008). The winter patterns include incur-
sions of cold air outbreaks from higher latitudes asso-
ciated with depressions originating in the Indian Ocean
or Southern Ocean. On the other hand, the persistence
of anticyclones is associated with relatively dry condi-
tions. Variability of rainfall is strongly linked to the
relative strength and location of these patterns which
affect wind strength and direction (Sturman and Tapper
1996). A number of studies (e.g., Smith et al. 2000) have
documented the strong inverse relationship between
mean sea level pressure (MSLP) and southwest Western
Australia (SWWA) regional winter rainfall on monthly
Corresponding author address: Dr. Yun Li, CSIRO Mathemat-
ical and Information Sciences, Wembley, Western Australia 6913,
Australia.
E-mail: yun.li@csiro.au
1142 JOURNAL OF CLIMATE VOLUME 22
DOI: 10.1175/2008JCLI2160.1
Ó 2009 American Meteorological Society
and seasonal time scales. Allan and Haylock (1993)
suggested that southern Australian winter rainfall is mod-
ulated by a long-term MSLP signal with a pronounced
trend in recent decades. This large-scale pressure pat-
tern is referred to as the southern annular mode (SAM)
and influences rainfall across southern parts of the con-
tinent in some seasons (Meneghini et al. 2006; Hendon
et al. 2007). Li et al. (2005) modeled winter extreme
rainfall over SWWA and its associated changes with the
SAM. They showed that the upward trend of the SAM
is consistent with the decrease in extreme winter rainfall
observed over SWWA that has been apparent since the
mid-1960s.
Climate models sometimes have difficulty in realisti-
cally simulating rainfall at regional and smaller scales
(Hewitson and Crane 2006), which can affect the con-
fidence that can be placed in their attempts to simulate
future changes. This arises because of a number of fac-
tors, including the fact that different models use different
parameterization schemes for various physical processes
and that the results not only reflect the effects of forced
changes but also internal variability resulting from the
chaotic nature of the system (Ra
¨
isa
¨
nen 2007). In par-
ticular, ensemble rainfall projections for Australia are
characterized by relatively large uncertainties (Whetton
et al. 2005). For example, results from increased CO
2
experiments (Cai and Watterson 2002; Hope 2006)
show that SWWA becomes drier as midlatitude MSLP
increases. Although these results are useful, it also needs
to be borne in mind that the degree of drying suggested
by these GCM results is accompanied by considerable
uncertainty—particularly as the simulated amounts for
present-day conditions tend to underestimate the ob-
served amounts. For example, of seven climate models
analyzed by Hope (2006), the percentage errors asso-
ciated with estimates for present-day (1961–2000) mean
June and July rainfall for SWWA range from 280% to
0%. These same models yield percentage changes for
later this century (2081–2100) that range from 23% to
225%, the average reduction being 213%.
Various approaches to overcoming the uncertainties
accompanying future climate change projections are
being developed, including the assessment of the per-
formance of individual models as a guide to the reliability
of their predicted changes (Maxino et al. 2008; Perkins
et al. 2007; Suppiah et al. 2007; Whetton et al. 2007;
Perkins and Pitman 2008; Smith and Chandler 2008,
manuscript submitted to Climatic Change). Downscaling
is another method that can potentially assist in the as-
sessment of climate models. A simple test for a model is
that it not only provide an accurate estimate for present-
day regional rainfall, but that it should also simulate the
observed relationship between regional rainfall and
other key variables (e.g., MSLP). If these criteria can be
satisfied, then it is arguable that any simulated changes
in rainfall are more likely to be reliable than otherwise.
Downscaling cannot only provide an indication of any
such relationships, it can also potentially provide al-
ternative estimates for rainfall changes if the model-
simulated changes in the key variables are believed to
be more reliable than the rainfall estimates themselves
(e.g., Benestad 2001).
There are two main approaches to downscaling: dy-
namical (Christensen et al. 1998; Murphy 1999; Schmidli
et al. 2006) and statistical (Zorita and von Storch 1997,
1999; von Storch et al. 2000). The former involves
nesting regional models with relatively high horizontal
resolution with a coarser-resolution global climate model.
The latter approach is based on historical (empirical)
studies of the relationship between the l arge-scale cli-
mate anomalies and local climate fluctuations. There
are numerous ways t o develop statistical downscaling
models (Zorita and von Storch 1997; Fowler et al. 2007),
but it is important to note that a statistical downscaling
approach to climate change results implicitly assumes
that any derived historical relationships also hold for the
future (Wilby 1997).
A number of studies have involved statistical down-
scaling as a tool in seasonal rainfall predictions for
Australia (Hughes et al. 1999; Charles et al. 2004).
Hughes et al. (1999) developed a nonhomogeneous
hidden Markov model (NHMM) for SWWA using three
atmospheric predictors: the mean large-scale value for
MSLP, the north–south MSLP gradient, and east–west
gradient in geopotential height at 850 hPa. They found
that the model could provide credible reproductions of
at-site precipitation and their spatial association and
dry- and wet-spell length statistics for a range of site
locations. In a subsequent study, Charles et al. (2004)
also identified dewpoint temperature depression at 850
hPa (RH850) as an important factor and demonstrated
some predictability of rainfall occurrence probabilities
but less so with actual rainfall amounts. Another tech-
nique, referred to as analog-based downscaling, has been
used in an attribution study of the rainfall decline over
SWWA (Timbal et al. 2006) and in interpreting climate
change results for Australia (Timbal and McAvaney
2001; Timbal 2004; Timbal and Jones 2008). Hope et al.
(2006) used a self-organizing map (SOM) to identify
the typical synoptic patterns that govern daily rain-
fall events over SWWA and showed how a ch ange
in the frequency of rainfall-bearing events could ex-
plain the observed decline in winter rainfall since the
mid-1970s.
Rather than referring to just north–south or east–west
gradients of MSLP independently for each region or
1MARCH 2009 L I A N D S M I T H 1143
point of interest (as is typically done in the models de-
scribed above), or dealing with daily synoptic patterns, we
are more interested in the seasonal time scale and diag-
nosing a limited number of large-scale MSLP patterns
that may be relevant to rainfall over a range of regions
across southern Australia. This is done by deriving em-
pirical orthogonal functions (EOFs) and their associated
principal components (PCs) of observed MSLP fields
over the wider Australian region. These are then linked to
observed winter rainfall totals (from various regions) via
multiple linear regression, referred to as principal com-
ponent regression (Draper and Smith 1981; Jolliffe 2002).
The resultant predictor equations (or statistical models)
can then be applied to any subsequent MSLP field (either
observed or predicted) to provide an estimate for rainfall.
This can be particularly convenient where climate models
provide simulations for present-day and future MSLP
fields. An example of such an application is presented
using the results from a single model, the Commonwealth
Scientific and Industrial Research Organisation Mark
version 3.5 (CSIRO Mk3.5), set of results from an A2
emissions scenario climate change experiment and the
implications for model assessment discussed.
2. Data
Mean sea level pressure data were extracted from
the National Centers for Environmental Prediction–
National Center for Atmospheric Research (NCEP–
NCAR) reanalysis globally archived d ataset with a
horizontal resolution of 2.5 832.58 (additional infor-
mation is available online at http://www.cdc.noaa.gov/
index.html; Kalnay et al. 1996). The data analyzed here
comprise the gridded JJA average values for each year
covering the region 608S–08,908E–1808 (Fig. 1).
The rainfall data analyzed here were provided by
the National Climate Centre (NCC) of the Bureau of
Meteorology (BoM) and consist of gridded data on a
0.25830.258 grid. These are described by Lo et al.
(2007), who indicate their confidence in the validity of
the data after 1948. In addition, four target regions were
selected: 1) southwest Western Autralia—the region
southwest of the line joining 308S, 1158E and 358S,
1208E; 2) the south Australian region (SA)—the box
area bounded by 328–368S, 1358–1408E; 3) the Victorian
region (VIC)—the box area bounded by 378–398S, 1438–
1478E; and 4) the Tasmanian region (TAS)—the box
FIG. 1. Study area used for analyzing MSLP data and the four regional-scale study areas: 1)
SWWA (southwest of the line joining 308S, 1158E and 358S, 1208E); 2) SA (the box area
bounded by 328–368S, 1358–1408E); 3) VIC (the box area bounded by 378–398S, 1438–1478E);
4) TAS (the box area bounded by 418–438S, 1458–1488E).
1144 JOURNAL OF CLIMATE VOLUME 22
area bounded by 418–438S, 1458–1488E (Fig. 1). For each
region, the average winter (June–August) rainfall totals
over the 58-yr period from 1948 to 2005 were generated
(from the BoM Web site http://www.bom.gov.au/cgi-
bin/silo/cli_var/area_timeseries.pl). The driest region is
SA (111 mm) followed by VIC (249 mm), SWWA
(300 mm), and then TAS (373 mm). Finally, rainfall
data were extracted for sites corresponding to the lo-
cations of the capital cities within each region: Perth
Airport ( 31.928 38S, 115.97398E), Adelaide Airport
(34.95248S, 138.52048E), Melbourne Regional Office
(37.80758S, 144.978E), and Hobart Airport (42.8389 8S,
147.49928E).
The model data used to demonstrate the application
of the downscaling methodology were generated as part
of CSIRO’s participation in the World Climate Re-
search Programme (WCRP) Coupled Model Inter-
comparison Project phase 3 (CMIP3) (see http://www-
pcmdi.llnl.gov/ipcc/about_ipcc.php). The model used is
a version of the CSIRO Mk3 model (Gordon et al.
2002), referred to as Mk3.5 (Hirst 2007; Smith 2007),
and the climate change experiment is based on the A2
emissions scenario. Rotstayn et al. (2008, manuscript
submitted to Int. J. Climatol.) have assessed the Mk3.5
model in terms of its ability to simulate El Nin
˜
o–
Southern Oscillation (ENSO) teleconnection patterns
over Australia and found that it performs as well as, if
not better than, other international models.
3. Principal component analysis of MSLP
Let X(t) 5 [X
1
(t), X
2
(t), ..., X
p
(t)] be an n 3 p data
matrix, X
i
(t):i 5 1, ..., p; t 5 1, ..., n
fg
is a vector
containing n (yearly) values of the ith centered predic-
tor (MSLP anomalies related to the average over n
years at the ith grid point), and p is the number of
predictors (i.e., p 5 925 grid points over covering the
region 608S–08,908E–1808 in our study). The PC com-
ponent is obtained by
Z
m
(t) 5 å
p
k51
e
km
X
k
(t), m 5 1, ..., M; t 5 1, ..., n,
(1)
where e
km
are the elements (loadings) of the mth ei-
genvector of the covariance matrix
S 5
1
n 1
X
T
X.
The number M of components retained in the analysis is
based on a Scree test (Wilks 1995). Further details can
be found in Jolliffe (2002) and Wilks (1995).
The analysis of the MSLP data yields eight modes that
explain 95% of the total variance. The spatial patterns
are shown in Fig. 2, while the associated time series are
shown in Fig. 3. The trend correlation coefficient and
the correlations with the JJA Southern Oscillation index
(SOI) and the SAM index (Mo and White 1985; Karoly
1990; Gong and Wang 1999; Thompson and Wallace
2000) for each of the modes are shown in Table 1.
The first mode (Fig. 2a) represents an almost zonal
north–south gradient pattern but has a center over the
New Zealand region extending back over Australia,
contrasting with anomalies farther south. It explains the
majority (38%) of the variance in MSLP, and its time
series (Fig. 3a) exhibits a very significant increase (trend
correlation r 510.73) over the period from 1948
to 2005. It is also strongly linked to both the SOI
(r 5 0.44) and the SAM index (r 510.77), which
has also increased in strength over time. Note that the
link between these indices remains after the data are
detrended. The second mode (Fig. 2b) explains about
FIG. 2. (a)–(h) The first eight leading principal component pat-
terns of winter MSLP over the study area. Variance explained is
indicated in parentheses.
1M
ARCH 2009 L I A N D S M I T H 1145
28% variance and represents contrasting MSLP anom-
alies between the tropics and the Southern Ocean re-
gion directly to the south of Australia where it could be
expected to be associated with anomalous westerly
winds. Its time series (Fig. 3b) also exhibits a significant
increase (r 510.31) over time. After detrending, it can
be seen to be significantly linked to both the SOI
(r 510.36) and the SAM (r 5 0.41). The link to the
SOI corresponds to the fact that this mode explains
some of the MSLP variability over northern Australia.
It is similar to the pattern noted by Allan and Haylock
(1993, Fig. 7a) that is associated with relatively wet
winters in SWWA.
The third mode (Fig. 2c) explains about 13% of
the total variance and represents an east–west pattern
over the Southern Ocean. This pattern could be ex-
pected to be associated with anomalous southeasterly
winds over SWWA and anomalous southerly winds
over Tasmania. The fourth mode (Fig. 2d) explains 8%
of the total variance and is associated with negative
MSLP anomalies over the entire continent. It is linked
to interannual variations in the SAM (r 510.29).
Mode 6 (Fig. 2f) explains only 3% of the total variance
and is associated with positive MSLP anomalies cen-
tered on southeastern Australia. However, it is strongly
associated with the detrended SOI (r 5 0.54). The
remaining modes (5, 7, and 8) explain smaller-scale
features of MSLP variability and do not exhibit any
significant links to either ENSO or the SAM. Only the
first two modes exhibit significant long-term trends over
time.
The links between each of these modes and Austra-
lian winter rainfall is illustrated in Fig. 4, which shows
the correlations between individual gridpoint rainfall
FIG. 3. (a)–(h) The standardized time series (Z
1
–Z
8
) of the leading eight MSLP modes.
1146 JOURNAL OF CLIMATE VOLUME 22
time series and each mode, while Table 2 summarizes
the links with regional rainfall. First, all but modes 5 and
8 are significantly linked to one or more of the regional
rainfall time series. Of these, mode 7 is probably in-
consequential since it is only weakly linked to SWWA
(r 510.27), which is much more strongly linked to the
higher modes 1–4. Mode 6 has a negative impact on SA
rainfall (r 5 0.26) and reflects the fact that this mode
corresponds to positive MSLP anomalies and suppressed
rainfall over the entire continent (Figs. 2f and 4f), re-
flecting the influence of ENSO. However, SA rainfall is
more strongly linked to higher modes 1, 2, and 4. To
check the robust relationship between the rainfall and
MSLP modes, we use a bootstrap technique to assess
the correlations between the eight leading PCs and JJA
rainfall. This is done by resampling, 1000 times, each PC
series and the JJA rainfall with replacement, and then
determining if the resulting correlation is significant
(i.e., if the MSLP mode score series has strong link to
rainfall in a specific region then the 95% resampled
correlations should be significant greater than zero at
the 0.05 level). Figure 5 shows regions (marked in red)
where 95% of the 1000 resampled series resulted in
correlations significant at the 0.05 level. It is evident that
modes 1–4 still yield significant correlation patterns
(Figs. 5a–d). Mode 6, however, when resampled, appears
TABLE 1. Links between the leading eight JJA MSLP modes, the
SOI, and the SAM index (1948–2005). The numbers within pa-
rentheses in the fourth and fifth columns represent correlations
between detrended time series. Values significant at p , 0.05 are in
bold.
Time
series
Variance
(%)
Trend
correlation r SOI r SAM
Z
1
37.5 10.73 20.44 (20.36) 0.77 (0.53)
Z
2
27.9 10.31 0.24 (0.36) 20.08 (20.41)
Z
3
12.5 10.01 20.14 (20.15) 0.12 (0.25)
Z
4
8.2 10.15 0.04 (0.08) 0.29 (0.29)
Z
5
3.7 20.03 0.21 (0.21) 0.01 (0.21)
Z
6
2.6 20.12 20.49 (20.54) 20.38 (20.38)
Z
7
1.5 10.11 20.13 (20.10) 0.10 (0.01)
Z
8
1.3 10.15 20.12 (20.08) 0.05 (20.05)
SOI 20.25 1.00 20.17 (20.003)
SAM 10.70 1.00
FIG. 4. (a)–(h) Correlation patterns between JJA rainfall and the leading eight time MSLP modes.
1M
ARCH 2009 L I A N D S M I T H 1147
to only yield significant correlations over the eastern
half of the continent, outside of the regions of interest
here. This suggests that the pattern evident in Fig. 4f
represents an overestimate of the importance of this
mode over most of the continent. Likewise, none of the
remaining modes (5, 7, and 8) yield any significant
correlations, again highlighting the importance of re-
sampling when looking for robust links.
In summary, it appears that the most valuable links
between MSLP and regional rainfall are contained in
modes 1–4. Of these, mode 4 has a negative impact on
SWWA rainfall since it appears to be associated with
positive MSLP anomalies in this region (Fig. 2d). On the
other hand, it has a positive impact on SA rainfall (Fig.
4d), consistent with enhanced southwesterly winds over
this region. A similar relationship is seen with mode 3
(Fig. 2c) where it suppresses rainfall in SWWA owing
to positive MSLP anomalies but enhances rainfall in
southwest TAS (Fig. 4c) owing to enhanced southerly/
southwesterly winds there.
As expected, the leading modes of MSLP variability
have the strongest links to regional winter rainfall. We
TABLE 2. Correlations between regional rainfall totals and various indices (1948–2005). Values significant at the 0.05 level are in bold.
Region SOI SAM Z
1
Z
2
Z
3
Z
4
Z
5
Z
6
Z
7
Z
8
SWWA Raw 0.34 20.37 20.40 0.37 20.34 20.28 0.25 20.17 0.24 0.11
Detrended 0.30 20.32 20.37 0.47 20.35 20.26 0.25 20.2 0.27 0.15
SA Raw 0.36 20.03 20.25 0.47 0.16 0.44 0.08 20.28 0.19 20.03
Detrended 0.41 20.13 20.51 0.45 0.16 0.43 0.08 20.26 0.17 20.05
VIC Raw 0.43 20.19 20.36 0.59 0.20 0.18 0.15 20.18 0.02 0.11
Detrended 0.44 20.21 20.52 0.63 0.20 0.18 0.15 20.19 0.02 0.12
TAS Raw 0.31 20.12 20.15 0.69 0.31 0.06 0.21 0.07 20.17 0.12
Detrended 0.36 20.2 20.33 0.70 0.31 0.04 0.22 0.08 20.19 0.11
FIG. 5. (a)–(h) Bootstrap assessment of significant correlations between the eight leading PC score series and JJA
rainfall. This is done by resampling, 1000 times, each PC series and the JJA rainfall with replacement, and then
determining if the resulting correlation is significant. The regions with 95% of the 1000 resampled correlations
significant at the 0.05 level are marked in red.
1148 JOURNAL OF CLIMATE VOLUME 22
note that modes 1 and 2 (detrended) are oppositely
correlated with both the SOI and the SAM (Table 1).
While both modes correspond to positive MSLP anom-
alies over northern Australia, they correspond to con-
trasting anomalies over southern Australia (Figs. 2a
and 2b). As a consequence, mode 1 (mode 2) reflects
increases (decreases) in MSLP and suppressed (en-
hanced) rainfall over much of southern Australia (Figs.
4a and 4b).
4. Principal component regression models
for rainfall
We use principal component regression (PCR) (e.g.,
Draper and Smith 1981; Jolliffe 2002) to arrive at a
predictive model for rainfall [ Y(t)] as follows:
Y(t) 5
å
M
m51
a
m
Z
m
(t) 1 e
t
, (2)
where e
t
is the residual variability not described by the
(M
5 8) MSLP modes that we have identified. For this
analysis, we could retain all eight modes but it is ap-
parent that not all the modes are necessary depending
on the region (see section 3). The method for develop-
ing or ‘‘calibrating’’ a predictive model is to use data
from a ‘‘training’’ period comprising the 43 years, 1948–
90, and to verify using data for the 15 years, 1991–2005.
The aim is to develop a robust model that provides a
downscaled prediction for rainfall given a predicted
large-scale MSLP field. Note that the rainfall data can
comprise regional-scale averages, gridpoint values, or
specific station values.
To decide how many modes are necessary to help
describe any particular rainfall time series, we use cross-
validation (Stone 1974). That is, using data from the
training period, we monitor the additional variance
explained by progressively adding in each of the modes.
We find that, in most cases, the first four (Z
1
to Z
4
)
modes are sufficient to help explain the variance. In the
FIG. 6. (a)–(d) The relative contribution in mm (thick lines) of each of the first four MSLP modes to
regional winter rainfall totals. The boxes (thin horizontal lines) represent the 50% (95%) confidence
intervals.
1M
ARCH 2009 L I A N D S M I T H 1149
case of Tasmania, only three of the modes add any
significant information.
Figure 6 provides an illustration of the relative con-
tribution (in mm) of each of the four components to the
regional winter rainfall totals in terms of the regression
coefficients associated with each of the first four stan-
dardized MSLP modes. The 95% confidence levels are
estimated using 1000 bootstrap replications as described
in the appendix. The total percentage variance explained
for each region is SWWA: 52%, SA: 55%, VIC: 61%,
and TAS: 56%. It is evident that Z
1
represents a negative
influence on rainfall for all four regions, whereas Z
2
represents a positive influence, particularly for TAS.
This is consistent with Figs. 4a and 4b and the fact that
the SAM has increased over recent decades (Cai et al.
2005; Li et al. 2005; Meneghini et al. 2006). As expected,
Z
3
and Z
4
have a negative influence on SWWA, but
positive influences on the eastern regions.
To quantify the uncertainty associated with any pre-
dictions with the model, we apply a bootstrap sampling
approach proposed by Stine (1985, see appendix A).
The estimates of the 95% confidence intervals of pre-
dicted rainfall for 1000 bootstrapping samples with re-
placement using independent testing MSLP data over
1991–2005. The uncertainty of the model is then indi-
cated by the spread of bootstrapping prediction inter-
vals for a given input MSLP field, shown as dashed curves
in Figs. 7 and 8.
5. Results
Figure 7 compares the predicted and observed rainfall
for all four regions, while Fig. 8 compares the results for
individual capital city stations within each of the regions
(Perth, Adelaide, Melbourne, and Hobart). In all cases,
a separate model was derived using the observed data
FIG. 7. (a)–(d) Predicted (red dash curve) vs observed JJA rainfall amounts (black solid curve) for
each of the four regions. The results for 1948–90 correspond to the training period, while the results for
1991–2005 correspond to the verification period. The blue dash curves are upper and lower bands of
the 95% confidence interval for the verified predictions.
1150 JOURNAL OF CLIMATE VOLUME 22
over the training period 1948–90. The predicted values
after 1990 therefore indicate the true skill of this ap-
proach. The uncertainty in terms of bootstrapping 95%
confidence intervals associated with the verified pre-
dictions after 1990 are also indicated in Figs. 7 and 8 by
the dashed curves.
Table 3 summarizes this skill by showing the associ-
ated correlation coefficients and the ratio of rms errors
(RMSE) to the climatology of JJA rainfall.
In general, the performance of the models evident in
the training period is maintained during the subsequent
verification period. All models perform reasonably well
at the regional scales since the percentage variance
explained in each case is relatively high (about 50% in
both periods) and the correlation between predicted
and observed values are all highly significant at the 0.01
level. In the case of the results for the four capital city
sites, it can be seen that the downscaling performance is
generally less, which is to be expected if local (unpre-
dictable) factors are contributing to the observed rainfall
amounts in each gauge. These factors are less relevant at
the larger regional scales since they tend to cancel out in
the averaging process.
To detect where this downscaling technique is most
useful, we have also used high-resolution (0.25830.258)
gridded rainfall data within each of the four selected
regions. Figure 9 indicates how the performance of the
models varies across the grid points within each region
by showing the correlation between observed and
predicted rainfall over the verification period 1991–
2005. In SWWA (Fig. 9a) the skill increases from the
south where it is moderate (r ’10.5) to high (r ’10.9)
in the north. In SA (Fig. 9b) the reverse holds true
where the skill is highest along the coastal regions but is
poor (r ’10.3) in the far north. Over VIC (Fig. 9c), the
skill is highly variable, being lowest (r ’10.5) in the
northwest and southeast of the box. Finally, the skill
over TAS (Fig. 9d) is highest over the northwest and
FIG. 8. (a)–(d) As in Fig. 6 but for the four station sites.
1M
ARCH 2009 L I A N D S M I T H 1151
central regions and lowest toward the east and south,
where Hobart is located.
6. Application to climate change simulations
We apply the downscaling models to MSLP data de-
rived from climate model (GCM) simulations for both
the present-day and future climate. The climate model
(CSIRO Mk3.5) has been used in an experiment in
which greenhouse gases are prescribed to increase ac-
cording to the A2 emissions scenario (Solomon et al.
2007). Mean winter (JJA) MSLP fields were calculated
for both present-day conditions (1971–2000) and for
later this century (2071–2100). Figure 10 compares the
observed (NCEP) long-term average JJA MSLP with
those simulated by the GCM for present-day and future
conditions. The pattern correlation between the ob-
served and the GCM-simulated long-term average JJA
MSLP is 0.969 for the present day and 0.967 for the
future. The MSLP values simulated for the future are
higher than present over most of the continent, with the
largest increases found just to the south. Decreases are a
feature of the differences toward the very high latitudes.
To downscale the GCM-generated values for MSLP
to regional JJA rainfall, we calibrated PCR model using
the observed rainfall and NCEP data from 1948 to 2005
based on the first four MSLP modes. The predictive
model linking rainfall (Y) to MSLP (via X) can be
written as Eq. (A2) in the appendix, which enables us to
generate downscaled rainfall estimates using GCM-
generated values for MSLP.
The relationship between observed, simulated, and
downscaled rainfall totals is summarized in Fig. 11. The
mean downscaled value is shown for each region ac-
companied by the 95% confidence intervals (thin hori-
zontal lines in Fig. 11). These confidence intervals re-
flect the uncertainty associated with the downscaling
model as estimated by the bootstrap procedure in the
appendix. In the SWWA case, the downscaled value
represents a significant underestimate, in the case of SA
and VIC they represent slight overestimates, while, in
the case of TAS, the downscaled value is a significant
overestimate. In all cases, the raw GCM values repre-
sent underestimates. Table 4 summarizes the results for
the four regions and indicates that, in the case of SWWA,
the GCM underestimate is 260%. [This is comparable
to the average underestimate (256%) from seven GCMs
analyzed by Hope 2006.] In all cases, the downscaled
values are higher than the GCM values but the per-
centage errors are much less: SWWA (232% cf.
260%), SA (114% cf. 220%), and VIC (113% cf.
251%). In the case of TAS, the downscaled error of
120% is similar in magnitude to the GCM error (217%)
although different in sign. On average, the GCM un-
derestimates winter rainfall totals by 237% whereas the
downscaled values represent an average overestimate of
only 14%. Note that the average of the absolute error in
the downscaled values is 20%, much less than the 37%
associated with the GCM values.
The GCM results for later this century all indicate
decreases compared to the present-day values. The
largest decrease (236%) is simulated for SA and
the smallest (27%) for TAS. In the case of SWWA, the
simulated decrease of 217% is comparable to the av-
erage (218%) from the seven GCMs analyzed by Hope
(2006). The downscaled values also indicate decreases,
the largest being 223% for SA and the smallest being
25% for SWWA. In the case of TAS, the downscaled
value (212%) is slightly larger than the GCM estimate
(27%). The average decrease according to the GCM
values is 222%, much higher than the average down-
scaled estimate of 213%. Moreover, according to the
Wilcoxon–Mann–Whitney rank sum test (Iman 1994),
the mean values for present and future downscaled
rainfall are significantly different (with p value ’ 0), and
the difference and the percentage difference (%diff) be-
tween the present and future periods are also significantly
different from zero (with p- value ’ 0). The associated
95% confidence intervals are given in brackets in the final
two columns of Table 4. Note that the Wilcoxon–Mann–
Whitney rank sum test (Iman 1994) is used because the
distribution of the downscaled rainfall series is un-
known. By taking into account the uncertainty of the
downscaled rainfall, it is evident that winter rainfall
over all southern Australian regions displays a highly
significant decrease with the smallest change evident
over SWWA (2
5%). These decreases are consistent
with the increases in simulated MSLP.
TABLE 3. Performance of the downscaling models at reproduc-
ing regional- and station-scale rainfall over the training period
(1948–90) and the verification period (1991–2005). Here r is the
correlation between the predictions and observations, r(%) is the
ratio of RMSE (mm) to the climatology of JJA rainfall.
Training period
(1948–90)
Verification period
(1991–2005)
r r (%) r r (%)
Regions
SWWA 0.72 12 0.69 13
SA 0.74 22 0.61 22
VIC 0.78 15 0.64 19
TAS 0.75 16 0.80 12
Stations
Perth 0.69 15 0.68 13
Adelaide 0.66 24 0.66 20
Melbourne 0.36 25 0.54 26
Hobart 0.51 31 0.55 25
1152 JOURNAL OF CLIMATE VOLUME 22
7. Discussion
We have analyzed winter (JJA) average MSLP data
for the Australian region (608S–08,908E–1808) and
found that the four leading modes can be used to ex-
plain a large fraction of the variability in winter rainfall
over much (but not all) of southern Australia. PCR
models have been developed that allow downscaled
estimates of rainfall to be made given predicted MSLP
fields. Rainfall predictions can be made at either re-
gional, grid square, and point scales. The results indicate
that robust models can be derived with relatively high
predictive capability, particularly at large regional scales,
but this performance is not uniform within regions. For
example, the variability of rainfall at capital city sites
Melbourne (within VIC) and Hobart (within TAS) ap-
pear to be less strongly linked to the large-scale MSLP
patterns than Perth (within SWWA) or Adelaide (within
SA). Even so, MSLP explains about 30% of the total
variance in the worst case and up to ;45% in the best
case.
GCM estimates for winter rainfall totals represent
relatively large underestimates (on average, 237%).
These may be caused by a number of factors including
poor physical representation of precipitation processes,
the absence of significant topography due to the coarse
horizontal resolution, or that the model underestimates
the moisture content of the atmosphere because of
problems elsewhere. Whatever the causes, the results
indicate some caution should be attached to the climate
change results for winter rainfall when such large dif-
ferences exist. However, the downscaled values provide
much more realistic estimates for present-day rainfall,
the average error being only 14% (average absolute
error being 20%).
The downscaled estimates for future changes to rain-
fall suggest a relatively small decrease of 29 mm for
SWWA compared to the GCM value of 221 mm. This
FIG. 9. The correlation between predicted and observed JJA rainfall over the verification
period 1991 to 2005 at grid points within each region: (a) SWWA, (b) SA, (c) VIC, and (d) TAS.
1M
ARCH 2009 L I A N D S M I T H 1153
translates to a percentage change of 25% compared to
the GCM value of 217%. In the case of SA, the abso-
lute decreases in rainfall are very similar (232 and 229
mm) but the percentage differences are different (236%
and 223%). In the case of VIC (233 and 245 mm) the
downscaled changes are much larger, but the GCM se-
verely underestimates present-day rainfall so that the
downscaled percentage change (216%) is, in fact, much
less than the GCM value (227%). Finally, the down-
scaled changes for TAS (254 mm) are much larger in
magnitude than the GCM changes (223) but the per-
centage changes are not so different (212% compared
to 27%).
We further show that the climate change signals, in
terms of the downscaled rainfall over these regions, are
highly significant (with p values ’ 0) based on the
Wilcoxon–Mann–Whitney rank sum test (Iman 1994).
The average of the downscaled percentage changes is
213%, which is much less than that of the GCM (222%).
The question here is which set of values is likely to be
more accurate. A commonsense assumption is that that
the better the model representation of present-day con-
ditions, the more reliable an y subseq uent p redicted
changes. Whetton et al. (2007) demonstrate that, at least
in the world of climate mode results, this is appropriate
for rainfall at midlatitude regions. Importantly, they
showed that the degree of matching of current patterns
of MSLP was highly relevant to reliability of predicted
changes in the future. On this basis, downscaled values
are more likely to represent the changes in precipitation
that may arise owing to increased CO
2
concentrations in
the atmosphere than the raw model values themselves.
In this one specific case, the decreases simulated by
the GCM for later this century may be overestimates.
In applying this technique to GCM results, it will be
important to assess how well each GCM simulates both
the present-day mean MSLP patterns and also MSLP
variability. In this particular case, the GCM is know to
FIG. 10. Long-term average winter MSLP (hPa): (a) from NCEP data in 1970–2000; (b) simulated by
the CSIRO Mk3.5 for the present period 1970–2000; (c) simulated by the CSIRO Mk3.5 for the future
period 2071–2100. (d) MSLP difference between the future and present periods.
1154 JOURNAL OF CLIMATE VOLUME 22
perform well at simulating observed rainfall–ENSO
teleconnection patterns over Australia (Rotstayn et al.
2008, manuscript submitted to Int. J. Climatol.), but we
have not performed a detailed MSLP assessment. This
needs to be borne in mind when considering this single
result since a proper projection of rainfall changes will
need to be supplemented by similar analyses of other
GCM results.
It should be noted that the downscaling method in
this paper can only represent the changes in rainfall
linked to changes in the atmospheric circulation as we
only used one predictor field (MSLP) in the downscal-
ing model. Changes in rainfall in the future may be
brought about by changes in other factors not consid-
ered in the downscaling methods, for example, changes
in atmospheric humidity. To some extent, some changes
in humidity may be accounted for by the changes in the
MSLP patterns insofar as they can affect the direction of
the prevailing winds. They will not, however, be able to
account for large-scale changes in humidity associated
with global warming, but this effect is difficult to in-
corporate using present-day observations (Charles et al.
1999).
Like all other statistical downscaling methods, the
assumption of stationarity may be questionable (e.g.,
Huth 1997; Slonosky et al. 2001; Fowler and Kilsby
2002). The degree of nonstationarity in projected climate
change was assessed by Hewitson and Crane (2006) who
suggested that circulation dynamics may be robust to
nonstationarities.
Finally, in addition to the assumptions of linearity and
stationarity, downscaling results are constrained by the
quality of the predictors (e.g., MSLP) simulated by the
GCMs. In this case, a greater consensus about the ex-
pected changes to the MSLP patterns may lead to an
improved consensus of the expected changes to rainfall
by downscaling techniques. Further work will investi-
gate the application of these techniques to an ensemble
of GCM results.
Acknowledgments. We thank two anonymous ref-
erees whose comments greatly improved the paper. We
FIG. 11. Present (1971–2000) and future (2071–2100) JJA rainfall totals (thick lines) for (a) SWWA,
(b) SA, (c) VIC, and (d) TAS. The symbol ‘‘o’’ represents the observed value; the ‘‘1’’ and ‘‘x’’
symbols represent the GCM-simulated values for the present and future periods, respectively. The
boxes (thin horizontal lines) represent the 50% (95%) confidence intervals.
1M
ARCH 2009 L I A N D S M I T H 1155
thank Mark Collier for providing the CSIRO Mk3.5
data. This work was supported by a Western Australian
state government Indian Ocean Climate Initiative, the
CSIRO Climate Adaptation Flagship project and the
CSIRO Water for a Healthy Country Flagship project,
and the Australian Department of Climate Change
via the Australian–China Climate Change Partnership
Program.
APPENDIX
Bootstrapping Prediction Intervals
In general, a fitted PCR model (2) based on the least
squares fit to the n year training data (X(t), Y(t)):f
t 5 1, ..., ng is
^
Y(t) 5
å
M
m51
^a
m
Z
m
(t), (A1)
which can be rewritten as
^
Y(t) 5
å
M
m51
^a
m
å
p
k51
e
km
X
k
(t)
0
@
1
A
5 å
p
k51
^
b
k
X
k
(t), (A2)
where
^
b
k
5 å
M
m51
^a
m
e
km
. Now, assume we have N . n
year observed datasets. A calibrated or ‘‘trained’’ model
based on the dataset (X(t), Y(t)): t 5 1, ..., nfgcan be
tested for its robustness by using independent data
( X(t 1 h), Y(t 1 h)): h 5 1, ..., N n
fg
.
To quantify the uncertainty of downscaled rainfall
estimates using Eq. (A2) related to a ‘‘future’’ X
i
(t 1 h)
(i 5 1, ..., p; h 5 1, ..., N n), we need to establish
the cumulative distribution function G for the confi-
dence interval of the prediction error Y(t 1 h)
^
Y(t 1 h), where
^
Y(t 1 h) 5
å
p
k51
^
b
k
X
k
(t 1 h) by using
(A2). A 100(1 a)% predication interval for a future
rainfall Y(t 1 h) based on a ‘‘future’’ X
i
(t 1 h)
(i 5 1, ..., p; h 5 1, ..., N n) is given by
[
^
Y(t 1 h) 1 G
1
(a/2),
^
Y(t 1 h) 1 G
1
(1 a/2)].
(A3)
However, as the distribution F of the residual variability
e
t
in the PCR model (2) is unknown, we cannot obtain
the distribution G analytically. So we apply a bootstrap
sampling approach proposed by Stine (1985) to estimate
the distribution G. Briefly the adapted approach is as
follows.
First, the parameter estimate
^
b
k
are calculated using
the observed training data (X(t), Y(t)), t 5 1, ..., n
fg
.
These estimates are then used to calculated fitted values
^
Y(t) using Eq. (A2) and residuals e
t
5 Y(t)
^
Y(t). For
an independent testing data X(t 1 h), 1 # h #
f
N ng, predicted value
^
Y(t 1 h) 5
å
p
k 5 1
^
b
k
X
k
(t 1 h).
The error distribution F is estimated by the empirical
distribution of residuals, which we denote F
n
. This is
then used to construct B bootstrapped samples of the
form
TABLE 4. Regional JJA mean rainfall for both the present (1971–2000) and future (2071–2100). A comparison between observed,
GCM simulated, and downscaled GCM values. The 95% confidence levels for the downscaled (DS) amounts are based on 1000 bootstrap
samples with replacement and are shown in parentheses in columns 3 and 6. The confidence levels for the difference and the percentage
differences (between the future and present periods) are estimated based on the Wilcoxon–Mann–Whitney rank sum test and are shown
in parentheses in the final two columns.
Region
Present (1971–2000) Future (2071–2100)
Source Amount (mm)
Diff
with obs (mm) Diff (%) Amount (mm)
Diff with
(1971–2000) (mm) Diff (%)
SWWA Obs 300
GCM 121 2179 260 100 221 217
DS 205 (154, 261) 295 232 196 (142, 254) 29(212, 27) 25(24.99, 22.5)
SA Obs 111
GCM 88 223 220 56 232 236
DS 126 (94, 158) 115 14 97 (66, 130) 229 (230, 227) 223 (223.5, 221.5)
VIC Obs 249
GCM 122 2127 251 89 233 227
DS 282 (230, 337) 152 13 237 (182, 293) 245 (246, 241) 216 (215.9, 214)
TAS Obs 373
GCM 307 266 217 284 223 27
DS 448 (387, 508) 175 20 394 (335, 453) 2
54 (261, 253) 212 (213.5, 211.9)
Average GCM 237 222
DS 14 213
1156 JOURNAL OF CLIMATE VOLUME 22
(X(t), Y
(t)), t 5 1, ..., n
fg
,(X(t 1 h), Y
(t 1 h)),
with
^
Y
(t) 5
^
Y(t) 1 e
t
and Y
(t 1 h) 5
^
Y(t 1 h) 1 e
9
t
,
where e
t
and e
9
t
are independently sampled from F
n
;
that is, they are randomly sampled with replacement
from the set of residuals e
1
, ..., e
n
fg. The asterisk su-
perscript denotes a value constructed for a particular
bootstrap sample.
Each bootstrapped sample is used to calculated a
simulated estimate
^
b
k
, predicted value
^
Y
(t 1 h), and
predicted error e
9
t
5 Y
(t 1 h)
^
Y
(t 1 h). The em-
pirical distribution of e
9
t
, which we denote
~
G, is then an
estimate of the distribution of the bootstrap prediction
errors. It can be used as the distribution function G in
Eq. (A3). Therefore, a 100(1 a)% predication interval
for a future rainfall Y(t 1 h) can be estimated as
[
^
Y(t 1 h) 1
~
G
1
(a/2),
^
Y(t 1 h) 1
~
G
1
(1 a/2)]. (A4)
In our rainfall analysis, estimates of the 95% confidence
interval of predicted rainfall for 1000 bootstrapping
samples using independent testing MSLP data over
1991–2005 are shown as dashed blue curves in Figs. 6
and 7. Further, bootstrapping estimates of the uncer-
tainty (50% and 95% confidence intervals for 1000
bootstrap replications) of downscaled GCM-simulated
present and future MSLP to regional mean rainfall to-
tals based on the model calibrated using observed
rainfall and NCEP MSLP are shown in Fig. 11.
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