Impact of Mid-Pacific Ocean Thermocline on the Prediction of Australian Rainfall

Impact of mid-Pacific Ocean thermocline on the prediction

of Australian rainfall

Jose Eric Ruiz*, Ian Cordery, Ashish Sharma

School of Civil and Environmental Engineering, University of New South Wales, Anzac Parade, Kensington, NSW 2052, Australia

Received 3 May 2004; revised 3 May 2005; accepted 17 May 2005

Abstract

The predictability of Australian rainfall using ocean heat content information is examined. The thermocline, represented by

the second unrotated principal component of the 20 8C isotherm depth in the Pacific Ocean, is coupled with the Nino3 index to

form the predictive model. The relevance of the subsurface oceanic information is evaluated by comparing results with two

alternative approaches, both based on the use of sea surface temperatures. All approaches are applied to predict rainfall

available on a 1!18 latitude–longitude grid covering Australia. Results are grouped according to dominant climatic regimes,

and evaluated using leave-one-out cross-validation. The skill of each approach is measured using the linear error in probability

space (LEPS) score. For a given climatic region, an improvement in skill due to an additional predictor is indicated by a positive

shift in the empirical cumulative distribution function (CDF) of the LEPS scores of the constituent grids and by the number of

grids that have a statistically significant hindcasting skill. Results show that the addition of thermocline information results in a

significant increase in skill of hindcasts for all seasons and in several regions. The thermocline’s influence is particularly strong

during austral autumn when predictability of rain in the western and northern regions of Australia increased even up to a lag of

18 months. This is an encouraging result considering that prediction in autumn normally experiences a drop in skill due to the

spring predictability barrier. By possessing high persistence during the first half of the year, the ocean heat content is able to

defy the damping effect of the spring barrier. This study has demonstrated the potential of the thermocline as a direct predictor

of Australian rainfall especially at long lead times.

q 2005 Elsevier B.V. All rights reserved.

Keywords: Thermocline; Ocean heat content; Australian rainfall; LEPS; Forecasting; Crossvalidation

1. Introduction

The El Nino-Southern Oscillation (ENSO) is a

major source of interannual variability in the

amount and spatial distribution of rainfall in

0022-1694/$ - see front matter q 2005 Elsevier B.V. All rights reserved.

doi:10.1016/j.jhydrol.2005.05.012

* Corresponding author. Fax: C61 2 9385 6139.

E-mail address: [email protected] (J.E. Ruiz).

Australia (Frederiksen et al., 1999; Chiew and

McMahon, 2003). As with any forecasting exercise,

the benefits of being prepared for the potentially

damaging effects of extreme ENSO events are in

direct proportion to the lag of the forecast.

However, a major impediment to skillful long-term

weather forecasting is the boreal spring predict-

ability barrier, which results in limited predictive

skill for long forecast lags. The spring barrier, which

Journal of Hydrology 317 (2006) 104–122

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J.E. Ruiz et al. / Journal of Hydrology 317 (2006) 104–122 105

is common to many ENSO prediction schemes (e.g.

Zebiak and Cane, 1987; Latif and Graham, 1992), is

characterised by a reduction in skill of forecasts

during March–May. ENSO indices, such as SOI and

Nino3, experience a significant drop in autocorrela-

tion during late boreal winter and spring. The causes

and nature of the spring barrier remain unclear

although several theories have been put forward

(e.g. Ropelewski et al., 1992; Xue et al., 1994, and

Samelson and Tziperman, 2001). McBride and

Nicholls (1983), and Chiew et al. (1998) have

reported minimal skill of rainfall predictions in

Australia during austral summer and autumn.

Research efforts to overcome the damping effect

of the spring barrier in the prediction of Australian

rainfall are ongoing. Drosdowsky and Chambers

(2001) attempted the use of large-scale patterns of

sea surface temperature (SST) anomalies in the

Pacific Ocean as alternative predictors of southern

summer and autumn Australian rainfall. Compared

with SOI-based predictions, however, only a

marginal increase in skill was achieved.

The memory required for long-term forecasting of

rainfall arises from ocean dynamics. The ocean,

being the slower component of the ocean–atmos-

phere coupling, moderates seasonal and interannual

fluctuations of atmospheric variables through its

ability to transport heat from one location to another

over long time scales. Already, evidence from recent

studies has demonstrated improvement in the skill of

ENSO predictions when observed upper ocean

temperature data are assimilated into dynamical (Ji

and Leetmaa, 1997, and Rosati et al., 1997) and

statistical models (Xue et al., 2000, and Clarke and

Van Gorder, 2003). The relationship between ocean

heat content and El Nino events was first documented

by Zebiak and Cane (1987), and Zebiak (1989). They

describe a buildup of equatorial heat content prior to

a warm event and a rapid decrease in heat content

during the event itself. After a warm event,

replenishment in heat content happens until the

initiation of the next warm event. The delayed

oscillator theory proposed by Suarez and Schopf

(1988), and Battisti and Hirst (1989) also suggest that

the interplay between the subsurface oceanic Rossby

and Kelvin waves propagating and reflecting back

and forth between the eastern and western boundaries

cause interannual variability in the subsurface

structure of the Pacific Ocean.

This study explores the possibility of extending

the use of ocean heat content as a predictor of

rainfall. For regions in Australia where there is close

association between ENSO and rainfall, this method

could lead into rainfall predictions that are skillful at

long lags. In particular, the study aims to identify the

regions in Australia and the seasons and lags that

show improvement in the skill of rainfall predictions

when ocean heat information is added. We followed

an EOF approach to sort out the various principal

components of ocean heat content that represent the

various stages of development of an ENSO event.

While sea level height can be a good proxy of ocean

heat content, we decided to use the thermocline for

two reasons. Firstly, the dataset of the 20 8C isotherm

that represents the thermocline is readily available in

near real time from the Australian Bureau of

Meteorology Research Centre (BMRC). This advan-

tage will come in handy later for operational rainfall

prediction. Secondly, as will be discussed in the next

section, the thermocline is strongly associated with

SST anomalies in the eastern Pacific, which are good

indicators of an ENSO event. The thermocline has

already been the subject of scrutiny by several

studies with regards to its characteristics and its role

in ENSO dynamics. Monthly rainfall data available

on a 1!18 latitude–longitude grid covering most of

Australia was used to evaluate the utility of the

proposed approach.

Section 2 discusses the relationship between the

thermocline and SSTs in the equatorial Pacific and its

potential for ENSO prediction. Details on the rainfall

and subsurface ocean temperature data considered in

the analysis are given in Section 3. Section 4

discusses the two leading principal components of

the thermocline and SST anomalies in the tropical

Pacific Ocean and their usage in an ENSO

forecasting scheme. Section 5 presents the three

regression-based prediction techniques whose hind-

casting skills are compared in the study. The different

climate regions of Australia and the linear error in

probability space (LEPS) score method of measuring

hindcast skill are discussed in Section 6. Sections 7

and 8 present the results and conclusions of the

study, respectively.

J.E. Ruiz et al. / Journal of Hydrology 317 (2006) 104–122106

2. Connection between thermocline and equatorial

Pacific SSTs

The thermocline is the depth at which the

temperature gradient (rate of decrease of temperature

with increase of depth) is a maximum (Pickard and

Emery, 1990). At its mean state, the thermocline is

characterized by an overall eastward shoaling in

response to the prevailing westward wind stress of the

trades (Wang et al., 2000). But on annual and

interannual timescales, the Pacific thermocline exhi-

bits varying but distinctive features due to the

different physical processes involved (Chang and

Philander, 1994). For instance, during an El Nino, an

east–west redistribution of warm surface waters along

the equatorial region occurs so that the thermocline

deepens in the eastern tropical Pacific while it shoals

in the west. Zebiak and Cane (1987) attribute this

east–west variability to the thermocline’s ability to

remember the changes in the surface winds and

provide a delayed feedback, which may be critical in

turning the coupled ocean–atmosphere system around

from a warm to a cold state or vice versa. Galanti et al.

(2002) also found that the thermocline in the east

equatorial Pacific controls the SST response to

subsurface temperature anomalies. These studies

suggest that depth variations of the thermocline

could be an important factor in determining the

strength of the coupled ocean–atmosphere instability

that produces ENSO.

The time delay between instances of deepening or

shallowing of the thermocline in the western-central

Pacific and the intensification of SST anomalies in the

east permits the use of thermocline variations for

prediction purposes. Harrison and Vecchi (2001);

McPhaden and Yu (1999) observed that thermocline

shallowing, which often begins in the central basin of

the Pacific months before the SST anomaly has

reached its maximum value, often sets the stage for

the return of normal or cooler than normal SST in the

east. Meinen and McPhaden (2000) also found strong

lagged correlations between the warm water volume

(WWV) changes in the western Pacific and Nino3. In

the context of the recharge–discharge oscillator, Jin

(1997) describes how the thermocline or the WWV

that it represents affects the timing of El Nino and La

Nina events by controlling the temperature of the

waters upwelled in the equatorial Pacific. Jin (1997)

showed that positive and negative peaks of WWV

anomalies produce the transition from El Nino to La

Nina and back with the recharge being associated with

El Nino and the discharge with the La Nina phase of

the cycle.

Such a cyclic behaviour implies a priori predict-

ability that suits any statistical prediction scheme

(Kim and North, 1999). Already, the works of Xue

et al. (2000), and Clarke and Van Gorder (2003) have

shown that significant improvements in the skill of

ENSO predictions are possible when ocean heat

content is included in statistical models. By integrat-

ing thermocline information in a statistical ENSO

prediction scheme, Ruiz et al. (2005) also found that

Nino3 hindcasts were more skilful especially at long

lags due mainly to their ability to defy the damping

effect of the spring barrier. Fig. 1 illustrates the

superiority in terms of skill correlation (i.e. corre-

lation between the predicted and observed values) of

Nino3 hindcasts produced using ocean heat content

over other hindcasts produced using persistence and

SST. Note the enhanced performance of the Nino3

plus thermocline based approach even at lags as long

as 15 months. Note also the inability of the SST based

approaches to issue meaningful predictions beyond

the spring barrier. The complete analysis that led to

the results in Fig. 1 is described in Ruiz et al. (2005).

What this also suggests is that for regions in Australia

where rainfall is closely linked to ENSO, the use of

ocean heat content is likely to result in long-lead

rainfall forecasts. This is the focus of the study

reported in the rest of the paper.

3. Data

The National Climate Centre of the Australian

Bureau of Meteorology (BOM) provides monthly

gridded rainfall at a 1!18 latitude–longitude. Jones

and Weymouth (1997) analyzed all the available

quality-controlled rainfall data and converted to a

0.258 grid using a successive correction scheme. A

1980–2002 subset of the rainfall dataset that has a

coarser 1!18 latitude–longitude spatial resolution is

used in this study. The data was aggregated to a

3-monthly scale for the purpose of this study. The four

seasons analyzed are summer (December, January and

February), autumn (March, April and May), winter

Fig. 1. Crossvalidated skill correlation between predicted and observed Nino3 anomalies during the months of January, April, July and October

for the 1982–2002 period. Projections using Nino3 as predictor (thin black line), Nino3 and SST as predictors (thick grey line), and Nino3 and

thermocline (thick black line) as predictors are made during the month shown with lead times varying from 1 to 23 months.


(June, July and August) and spring (September,

October and November).

Data for the depth to the 20 8C isotherm, which

represents the thermocline, are provided by BMRC

and are readily available in real time for operational

forecasting purposes. Extracted for the 40 8N–30 8S,

30 8E–60 8W region, the monthly BMRC data has a

1!28 latitude–longitude grid resolution and is created

using an optimal interpolation technique that com-

bines hydrographic measurements with moored

temperature measurements from the tropical atmos-

phere and ocean (TAO) observation program (Smith,

1995).

The Nino3 index, taken as the SST anomaly

averaged over the eastern-central part of the equator-

ial Pacific Ocean, is often used as reference for the

strength of the ENSO episodes. It is now widely

known that warming in this region strongly influences

the global atmosphere. The Nino3 index used in this

study is obtained from the website of NOAA’s

Climate Prediction Centre (http://www.cpc.ncep.

noaa.gov/data/indices). It is taken as the departure

from the 1971–2000 mean of the SST averaged over

the area bounded by 5 8S–5 8N, 90–150 8W. Seasonal

values of the Nino3 index are obtained by simple

averaging of the monthly values.

The SST dataset was extracted from the 1854–

2002 Extended Reconstructed Sea Surface Tempera-

tures (ERSST) provided by NOAA’s National

Climate Data Centre (NCDC) (ftp://ftp.ncdc.noaa.

gov/pub/data/ersst). The ERSST dataset is available

over a monthly 2!28 latitude–longitude gridded field.

4. Principal modes of variability of the equatorial

Pacific thermocline and SSTs

4.1. Empirical orthogonal function (EOF) analysis

The two dominant unrotated EOF modes of the

isotherm depth anomalies in the Pacific Ocean explain

23 and 14% of the variance, respectively. While the

first EOF mode (EOF1) represents a west–east mode

of variability, the second EOF mode (EOF2) shows a

north–south dipole mode that could be taken as a

tilting about an axis near 5 8N. Alory and Delcroix

(2002) observed this mode to account in large part for

the buildup and depletion of warm water in the

equatorial Pacific. While the first EOF has high

concurrent correlations with Nino3 (rZK0.9), the

second EOF mode (shown in Fig. 2(a)) is only weakly

correlated with Nino3 (rZ0.2). However, lagged

http://www.cpc.ncep.noaa.gov/data/indices

http://www.cpc.ncep.noaa.gov/data/indices

http://ftp://ftp.ncdc.noaa.gov/pub/data/ersst

http://ftp://ftp.ncdc.noaa.gov/pub/data/ersst

Fig. 2. Spatial structures and monthly amplitudes of the second principal component or EOF of the (a) thermocline depth anomalies (varianceZ14%) and (b) SST anomalies (varianceZ14%) in the Pacific region for the 1980–2002 period.



correlations between the second EOF mode and Nino3

are significant reaching a maximum of 0.6 when

EOF2 leads Nino3 by 8 months. Judging from their

correlations with Nino3, it appears that the EOF2

mode depicts a developing ENSO episode while

EOF1 describes a peaking ENSO event. As a result,

our proposed approach uses the isotherm depth EOF2

in conjunction with Nino3 as the basis for predicting

rainfall in Australia.

The two leading modes of the SST anomalies in the

Pacific region for the period 1980–2002 were also

determined. Based on the spatial distribution of the

EOF loadings and from concurrent correlations with

Nino3 (rZK0.9), the first EOF mode, which accounts

for 36% of the variance, is said to contain the main

ENSO signal. On the other hand, the second SST EOF

mode, which represents 14% of the variance, is only

weakly correlated with Nino3 (rZ0.03). Figure 2(b)

shows the spatial structure of the second mode that is

characteristically dominated by negative loadings

except for a patch in the northern Pacific where

positive loadings occur. Lagged correlation analysis

indicates that the peak correlation (rZ0.44) occurs

with EOF1 lagging EOF2 by 13 months. These results

suggest that like its ‘subsurface’ counterpart, EOF2 is

also a precursor mode to EOF1 and hence signifies the

growth of an ENSO event. The second EOF of the

SST patterns in the Pacific Ocean is used in

conjunction with Nino3 as an alternative strategy for

predicting Australian rainfall.

To ensure that the regression prediction schemes

do not overestimate the skill of Nino3 hindcasts,

monthly amplitudes of the principal components are

derived using crossvalidation. The crossvalidation

procedure for deriving the SST and thermocline

principal components time series required the removal

of the year in consideration as well as the years prior

and after this year—a total of 36 months of data. From

the remaining data, the anomaly field is obtained. This

was repeated for all months, with the exception of the

months at the starting and ending years, to arrive with

a set of crossvalidated anomaly fields. EOF analysis is

applied on this anomaly set to derive the time series of

the principal component. As expected, the resulting

principal components derived from both the non-

crossvalidated and crossvalidated EOF analyses were

in close correspondence. For the thermocline field, the

EOF1 and EOF2 series from both analyses had

a correlation of 0.996 and 0.984, respectively. For

the SST field, correlations of 0.997 and 0.979 were

obtained between the non-crossvalidated and cross-

validated series of EOF1 and EOF2, respectively.

4.2. Persistence of the thermocline and SST anomalies

To determine the seasons when the thermocline

would be potentially useful as a predictor of

Australian rainfall, the persistence characteristics of

the second principal component of the thermocline

were evaluated. Results reveal the thermocline EOF2

starting September–December has the least persist-

ence (correlations falling below 0.7 after only 1–2

months). When starting in January–May, it tends to

have the greatest persistence (correlationsO0.7 for

lags of 7–9 months). These results suggest that

thermocline anomalies occurring near the end of the

calendar year will not persist beyond the following

summer while anomalies present in late summer and

autumn will persist for the next 2–3 seasons. Another

implication is that since a strong lag association exists

between ENSO and thermocline, then for regions in

Australia where there is close correlation between

ENSO and rainfall, improvements in skill are

expected for rainfall predictions in autumn and winter.

The second EOF of SST anomalies showed

significant persistence during the first six months of

the year during which autocorrelation greater than 0.7

were obtained for lags of 4–6 months. Conversely,

persistence starting at the latter part of the year usually

becomes insignificant (i.e. correlation!0.7) after

only 3 months. This implies that the SST patterns

used in this study as an additional predictor of

Australian rainfall is more likely to contribute to an

improvement in prediction skill for forecasts made

during the first half than in the second half of the year.

As a matter of interest, Nino3 tends to have the

greatest persistence when started from June–Septem-

ber for lags of 5–8 months and the lowest persistence

when started in January–May when correlations drop

after only 1–2 months.

4.3. Statistical ENSO forecasting

Ruiz et al. (2005) investigated the close association

between the thermocline and the eastern Pacific

SSTs by using the second principal component of


the thermocline field as an additional predictor to

Nino3 in a regression-based prediction scheme. As

exemplified in Fig. 1; Ruiz et al. (2005) found that

hindcasts produced by the scheme that included the

thermocline were more skillful than hindcasts

produced by the other two schemes that used

persistence and SST patterns for all months and for

most lags. In contrast, predictions based only on

Nino3’s persistence were generally the least skillful

often having negative skill correlation for lags beyond

six months. Although the addition of the second EOF

of the SST field improved the skill of persistence-

based predictions, the skill improvement was often

insignificant at longer lags and the skill correlation

was generally less than the thermocline-based

hindcasts. Short-term hindcasts produced by the

three schemes starting in July–December were

equally skilled. This was expected since during

these months the autocorrelation of Nino3, a common

predictor of these three schemes, is high. Between

January and June, when the persistence of the

thermocline EOF2 is high, short-term hindcasts

based on the thermocline were generally the most

skillful.

The thermocline-based scheme was found to have

the ability to produce forecasts that defy the spring

predictability barrier such that for hindcasts starting in

summer and autumn statistically significant skill

correlations were possible up to a lead of 18 months

into the future. While the other two schemes often

experienced a sudden decline and prolonged ‘dips’ in

their forecast skill during autumn and winter, the

thermocline-based scheme only suffered from slight

skill reductions and generally maintained a steady and

slow decline of its skill as the lag increased. SST-

based forecasts in autumn and winter also fared better

than persistence but were hardly skillful. Statistically

significant forecasts usually occurred in months when

persistence also had about the same skill. Hence, the

contribution from the second EOF mode of the SST

field in predicting SST anomalies was negligible.

The implication of the above results on rainfall

forecasting is that for regions in Australia where there

is a close association between ENSO and rainfall

variability, there is a strong possibility that the

addition of thermocline information could increase

the skill of rainfall forecasts. This is especially likely

during autumn when forecasts produced using

the usual ENSO indices generally suffer from the

spring barrier effect.

5. Proposed alternatives for prediction

of Australian rainfall

Linear regression is used in this study in

constructing the three prediction schemes whose

hindcasting skills are compared. The first uses

Nino3 as a single predictor while the second and

third models use Nino3 in combination with SST and

thermocline, respectively. We call these models

NINO, NINOCSST and NINOCSUB. The combi-

nation of predictors is possible since Nino3 is only

weakly correlated with the second principal com-

ponents of the SST and thermocline. Reference

hindcasts are produced using the NINO scheme and

any skill improvement contributed by either SST or

thermocline is determined from hindcasts using

NINOCSST and NINOCSUB, which henceforth

can be referred to as ‘composite models’. Hindcasts

are made for all seasons and lags are varied from 1 to

6 seasons.

It is fully recognized that the use of SST and

thermocline as single predictors or as combination in a

model could possibly produce hindcasts that are more

skillful than those produced by the three models

proposed here. But since the purpose of the study is to

indicate any skill enhancement contributed by either

SST or thermocline into a Nino3-based prediction

scheme, then limiting the hindcast analysis only to the

proposed composite models is warranted. It is also

probable that the relationship between rainfall and the

preceding anomaly patterns of SST or thermocline

could be nonlinear. Again, since the study aims to

evaluate only the potential of ocean heat content

information for long-term prediction of rainfall in

Australia, the issue on the form of dependence has not

been considered in detail.

A leave-one-out crossvalidation procedure is used

to produce the hindcasts. Crossvalidation techniques

estimate the skill of a forecast model from a series of

independent hindcasts over all the available data. For

a data sample of size N, the leave-one-out cross-

validation method involves training the model using

the NK1 years of data and then forecasting the value

for the year that was left out. This is repeated NK1


times until independent hindcasts are produced for all

N years. This crossvalidation method offers a better

alternative to the traditional method of sampling the

data into training and validation datasets. It gives a

more robust estimate of the true hindcast skill of the

model since it produces N hindcasts.

With NINOCSST and NINOCSUB, hindcasts are

produced using predictors from the same season.

Having a different lag for each predictor is also

feasible but is beyond the scope of this study. With 23

years of thermocline data and a maximum lag of 6

seasons, hindcasts were generated for 22 years,

inclusive of the 1981–2002 period. Seasonal hindcasts

are initially generated for each 18 grid across Australia

but the comparison between models is based on the

population distribution of skill scores for all grids

included in a specific region.

6. Evaluation of results

6.1. Climate regions in Australia

Australia has two distinctive rainfall patterns—the

summer rains and the winter rains. In summer, the

northern and eastern coastal regions experience heavy

rains. Monsoon produces summer rains along the

northern coast while the easterly trade winds bring

rains to the eastern coast (Ellyard, 1994). The

southern and western regions generally get the least

amount of summer rain. Winter rains are most

plentiful in regions exposed to the westerly winds.

These include the southwestern coast of western

Australia, the south Australian and Victorian coasts,

the region west of the dividing range and northwest

Tasmania.

Although hindcasting is performed on each grid,

the influence of the SST and thermocline patterns on

Australian rainfall is evaluated on a regional basis.

Here, Australia is subdivided into climate regions

patterned after BOM’s regional classification map that

was derived using the Koppen classification scheme.

The Koppen scheme classifies the climate of each

region based on temperature and rainfall, as indicated

by the native vegetation. In consideration of the

possible influence of the adjacent Indian Ocean, we

subdivided the climate regions further into western

and eastern subgroups using the 130 8E longitude as

the line of separation. The eight climate regions

considered in the hindcasting experiments are grass-

west, grass-east, subtropical-west, subtropical-east,

temperate-west, temperate-east, tropical-west, and

tropical-east. Sizes of these regions vary from

55,000 km2 for subtropical-west to 1.5!106 km2 for

grass-east. In total, these regions include 456 1!18

grids that cover around 66% of Australia’s land area.

The central desert region is excluded in the analysis

for obvious reasons. Fig. 3 shows how the Australian

continent is subdivided in this study.

The influence of ENSO on the interannual

variability of Australian rainfall is evident from

the bar plots included in Fig. 3. Except for the

temperate-east region, each grid or region tends to

have a lower (higher) mean annual rainfall (MAR)

during an El Nino (La Nina) year than during a

neutral year. An El Nino year has a mean SOI of

less than K5 while a La Nina year has a mean SOI

value greater than C5.

6.2. Grids with MAR greater than 600 mm

The climate regions defined in the previous section

cover large areas such that within the regions there

could be grids where the annual rainfall is insignif-

icant for forecasting purposes. By taking only grids

whose MAR is greater than 600 mm, we were able to

limit our second analysis only to regions where

forecasting has more practical value. For brevity’s

sake, these grids will henceforth be called GM600s.

Of the 697 1!18 latitude–longitude grids that make

up Australia, only 174 grids qualify as GM600s. This

is about 25% of Australia covering an area of about

2!106 km2. The bulk of these GM600s are situated in

the northern and eastern coastal regions of the

continent where summer rainfall is abundant and

where ENSO’s influence is strong. The GM600s in

western Australia has an aggregated land area of only

44,000 km2. A different set of climate regions is

derived for the GM600s, with their identification

based on the state to which they belong. These

GM600s are grouped as follows: Queensland-north

(QLD-N), Queensland-south (QLD-S), New South

Wales (NSW), Victoria (VIC), Tasmania (TAS),

Northern Territory (NT), West Australia-north (WA-

N), and West Australia-south (WA-S).

Fig. 3. Influence of ENSO on annual rainfall for the eight climate regions in Australia for the period 1980–2002. The regional classification is

adopted from the modified Koppen classification system of the Australian Bureau of Meteorology (BOM). The central desert region is not

included in the analysis. The bar plots show the mean annual rainfall (MAR) per grid during an El Nino year (EN), a neutral year (NE) and a La

Nina year (LN).



6.3. Linear error in probability space (LEPS) score

Ward and Folland (1991); Potts et al. (1996)

introduced the idea of evaluating the skill of a forecast

in terms of a LEPS score. What LEPS aims to provide,

is a scoring system that measures the error in a

forecast that is taken as the distance between the

position of the forecast and the corresponding

observation in units of their respective cumulative

probability distributions. Potts et al. (1996) define

LEPS score S as

S Z 3ð1 K jPf KPvjCP2f KPf CP2

v KPvÞK1

(1)

where Pf and Pv are the cumulative distribution

functions (CDF) (or nonexceedance probabilities) of

the hindcast and the verifying observation, respect-

ively. LEPS scores are normalized in such a manner

that climatological or random forecasts are rated zero

and perfect forecasts at the extremes of the

distribution score higher than perfect forecasts in the

middle of the distribution. The scores are also scaled

so that their magnitude decreases uniformly with

increasing separation between the forecast and

verifying observation. The maximum value of S is 2

which occurs when PfZPvZ0 or PfZPvZ1 and the

minimum LEPS score is K1 which occurs when PfZ0 and PvZ1 or PfZ1 and PvZ1. Eq. (1) is an

improvement of earlier versions of the LEPS score

that suffered from ‘bend back’ which occurs when

maximally incorrect forecasts can be slightly less

negative than those for less erroneous forecasts. Potts

et al. (1996) gives a detailed discussion on the

derivation of Eq. (1) and the principles of normal-

ization and scaling of the LEPS score.

When an ensemble of forecasts is to be assessed, it

is often desirable to have a measure of overall skill

over the range from 100 to K100%. In this study, the

skill-score version of LEPS is preferred since we are

trying to compare how each regression model

produces hindcasts for the twenty-one years of

crossvalidation. To obtain a skill range for each grid

from 100 to K100%, the average skill (SK) for the 21

years is defined for continuous forecasts as

SK Z

P100S

PSm

(2)

where the summation is over all pairs of forecasts and

observations. The definition of Sm depends on whether

the corresponding S is positive or negative. If S is

positive, Sm is the maximum possible score given the

observation, that is, the score assuming the forecast

was correct, because 100% skill is logically the result

of forecasting the same category or value as is

subsequently observed. If S is negative, Sm is the

worst possible score given the observation. Sm is

calculated from Eq. (1) for positive values of S by

setting PvZPf. When S is negative for a given Pv, the

largest negative score is found from the value of Pf

that is farthest away from Pv in the cumulative

probability distribution. This will be the value of S

corresponding to PfZ1 or PfZ0.

6.4. Stepwise algorithm for LEPS score calculation

A stepwise algorithm for calculating LEPS SK

score for each grid can now be formulated. The

algorithm, which is applicable for all three-prediction

schemes, consists of the following steps:

1. Derive the regression equation using all rain and

predictor(s) data except the year to be hindcasted.

2. Produce a hindcast of the year missed out using

the derived regression equation.

3. Repeat steps 1 and 2 to generate the hindcasts of

the remaining years.

4. Calculate the non-exceedance probabilities of a

hindcast and its corresponding observed value by

taking separate distributions for hindcasts and

observations. Denote these probabilities as Pf and

Pv, respectively.

5. Substitute Pf and Pv into Eq. (1) to get the LEPS

score S of the hindcast.

6. If S is positive, calculate Sm as the maximum

possible S score from Eq. (1) with PfZPv.

7. If S is negative, calculate Sm as the worst possible

S score given the observation. If PvS0.5 then

Sm is calculated from Eq. (1) using PfZ0.

Otherwise, if Pv!0.5 then Sm is calculated

using PfZ1.

8. Repeat steps 4–6 for all years.

9. Get the sum of all S and Sm values separately.

10. Substitute the totals of the S and Sm values into

Eq. (2) to calculate the overall skill score SK of

the ensemble hindcasts.


6.5. Skill correlation

In addition to the LEPS SK score, hindcasts

produced by the three prediction schemes are also

verified using skill correlation, which describes the

strength of linear relationship between forecasts and

corresponding observations. If there was an exact

linear relationship between forecasts and obser-

vations, which implies a perfect forecast skill,

the correlation would be at its maximum possible

value of 1. On the other hand, if there were no linear

relationship the correlation would be zero. As in real

forecasting, the correlation is usually an intermediate

value between 0 and 1 but nevertheless should give an

indication, within a linear framework, on the quality

and relative accuracy of the hindcasts in the sample.

The skill correlation, which is computed over the

1981–2002 period, is used in this study only to

validate the results of the LEPS scoring scheme.

Correlation, as a measure of skill, has the tendency to

either overrepresent or underestimate the accuracy of

hindcasts and the reasons for these limitations are

discussed by Barnston (1992).

6.6. Confidence measure for the LEPS SK score

and skill correlation

A confidence measure to verify whether a chosen

predictor is a significant predictor of Australian

rainfall is defined as the upper limit (95% percentile)

of the skill score for the case of no dependence

between predictor and predictand variables. By

randomly rearranging observed rainfall values of a

sample grid, each simulation results in a new sample

where the predictor is independent of the predictand.

Using this independent sample, hindcasts are pro-

duced by crossvalidation for each year. From the set

of hindcasts, the skill score is computed. Statistically

significant threshold values (5% significance level)

were estimated as the 95% CDF of the score of five

hundred randomised samples. This procedure is

repeated for eight grids that are taken from the

different climate regions. For the one-predictor

scheme, averaging resulted in a threshold value of 7

and 0.2 for the LEPS SK score and skill correlation,

respectively. As with any statistical model, the

hindcast skill can be increased by increasing the

number of predictors. Hence, the threshold of

acceptance for the NINOCSST and NINOCSUB

schemes should also increase. From the distribution of

the scores, we estimate the upper 5th percentile as 10

for the LEPS SK score and 0.3 for the skill correlation.

6.7. Comparing the hindcast performance

of prediction schemes

For a particular grid, an increase in the SK score or

skill correlation signifies higher predictive skill of the

composite model than the NINO model. The predictive

skill of a prediction scheme could be assessed either on

a per-grid or regional basis. Rather than considering

the results of the 456 grids individually, the overall

skill of a model in hindcasting rain over a climate

region is assessed instead. By resorting to the

evaluation of collective skill, the comparison between

the NINO model and the composite models is

simplified. Of course, a more thorough and accurate

comparison of predictive performance between

models can only be achieved by looking at each grid.

However, this is uncalled for since what this study

hopes to achieve is only to demonstrate the potential of

SST and thermocline patterns in adding skill to

hindcasts of Australian rainfall on a larger scale.

For a given region, the selection of the best regression

model is facilitated by the use of the empirical CDF of

the SK scores. The CDF is calculated as the

nonexceedance probability of the SK score in the

sample. By plotting the CDF of the regression models

together, any shift in the curve is easily detected. A shift

to the right (left) means an enhancement (reduction) in

the overall skill of the gridded hindcasts. To illustrate

this point, a sample plot of two CDF curves is shown in

Fig. 4. Based on the positioning of the curves, it is

obvious that Model 2 has higher forecasting skill than

Model 1. The superiority of Model 2 is also supported by

the fact that about 75% of its skill scores are greater than

the 95% significance criterion for LEPS SK score.

Model 1 could be taken as the reference model, which

for this study is the NINO model and Model 2 could be

either of the NINOCSST and NINOCSUB models. A

visual check can adequately verify any skill improve-

ment if the CDF of the NINOCSST or NINOCSUB

models appear ‘shifted’ to the right of the CDF curve of

the NINO model.

In addition to the positioning of the CDF curve,

any influence of the SST and thermocline patterns on

Fig. 4. Comparison of hindcasting skill between models is facilitated by the positioning of the empirical CDF curves of their LEPS SK scores

relative to each other and on the percentage of scores that are statistically significant. For two-predictor models, the 5% significance criterion is

an LEPS SK score of 10. In the above illustration, Model 2 is superior compared to Model 1 in both respects.


the rainfall of a particular climate region can only be

justified if the SK scores of the constituent grids also

satisfy the following requirements:

(1) At least 50% of the SK scores of the composite

model must be greater than the corresponding SK

scores of the NINO model.

(2) At least 30% of the SK scores of the composite

model must be statistically significant.

(3) A Wilcoxon signed-rank test should reveal a

significant difference between the means of the

SK scores of the composite model and the NINO

model.

7. Results

7.1. Rainfall hindcasts for the climate regions

Using the three prediction schemes, crossvalidated

hindcasts of gridded seasonal rainfall are produced for

the 1981–2002 period with lags varied from 1 to 6

seasons (3–18 months). Composite models NINOCSST and NINOCSUB use the same starting month for

their two component predictors. Based on the

hindcasts and their corresponding observations, the

LEPS SK score and skill correlation are calculated. In

general, the results of both SK and skill correlation

agree closely with each other. Hence, only results

from the LEPS scoring scheme are discussed

hereunder.

Grids whose SK scores exceed the 5% significance

level are identified and plotted similar to what is

shown in Fig. 5. The plotted maps could display a

patchy or noisy spatial structure due to the large noise

variance in seasonal rainfall data at the gridded scale.

Nonetheless, clusters of significant grids are usually

the norm rather than the exception. Any improvement

contributed by the SST and thermocline patterns is

manifested in an increase in the number of grids that

have significant skill. The use of maps becomes less

effective, however, when the ‘composite’ maps

Fig. 5. Sample season-lag combinations that compare hindcasting skill of NINO, NINOCSST and NINOCSUB models. Grids where the LEPS

SK score is statistically significant (5% significance level) are shown in black. Otherwise, they are shown in gray. The desert region is shown in

white. Hindcasts were produced for the 1981–2002 period.


Fig. 6. Comparison plots of empirical cumulative distribution function (CDF) curves of the crossvalidated LEPS SK scores of hindcasts

produced using the three prediction schemes for selected climate regions and season-lag combinations.


appear similar to the NINO map in terms of spatial

coverage. Considering that grids could take any SK

score higher than the 10 (the 5% significance

criterion), the maps provide no direct comparison

between the skill of NINO model and the composite

models on a regional level. The task becomes even

more complicated for large regions where a signifi-

cant number of grids are involved.

By limiting its scope on a regional scale, the

method of CDF plots provides a better way of

differentiating the predictive skill between models.

Each panel of Fig. 6, for instance, shows the CDF

plots of the three prediction schemes for a climate

region that was shown in Fig. 5 to contain significant

grids. Unlike Fig. 5, however, Fig. 6 presents a more

accurate and obvious depiction of the disparity

between the skill of the NINO model and the

composite models. Supplementary to this initial

assessment is the Wilcoxon signed-rank test, which

determines whether the two distributions have similar

means. The number of statistically significant grids is

also determined to ensure that the requirements

specified in Section 6.7 are satisfied.

Results of the crossvalidated hindcasting exper-

iments for the climate regions using NINOCSST and

NINOCSUB models are summarised in Table 1. In

this table, season-lag combinations that show an

increase in skill with the addition of SST or

thermocline are shown as filled circles. For these

season-lag combinations, the CDF of the composite

model is positively different from the NINO CDF with

at least 30% of the component grids having skill

greater than the 5% significance level. In addition, at

least 50% of the grids in these regions should have SK

scores that increased in magnitude when the compo-

site model was used. It was observed that in general

such regions have the majority of their constituent

grids increase their skill score by at least 30%.

Table 1

Season-lag combinations that show significant improvement in skill of rainfall hindcasts with the addition of SST and thermocline

Model Projected season Lag (seasons) Grass Subtropical Temperate Tropical

West East West East West East West East

NINOCSST DJF 1 – – – – – – – –

2 – – – – C – – –

3 – – – – C – – –

4 – – – – C – – –

5 – – – – C – – –

6 – – – – – – – –

MAM 1 – – – – – – C –

2 C – C – – – C C

3 C – C – – – – –

4 C – C – – – – –

5 – – – – – – – –

6 C – – – – – C –

JJA 1 – – – – – – – –

2 – – – – – – – –

3 – – – – – – – –

4 – – – – – – – –

5 – – – – – – – –

6 – – – – – – – –

SON 1 – – – – – – C C

2 – – – – – – C C

3 – – – – – – C –

4 – – – – – – C C

5 – – – – – – C –

6 – – – – – – – –

NINOCSUB DJF 1 – – – – – – – –

2 – – – – – – – –

3 C – C – C – – –

4 C – C – C – – –

5 – – – – – – – –

6 – – – – – – – –

MAM 1 C – C – C – C C

2 C – C – C – C C

3 C – C – C – C C

4 C – C – – – C C

5 – – – – – C C C

6 – – – – – – C C

JJA 1 – C – C – – – –

2 – C – C – – – –

3 – – C C – – – –

4 C – C C – – – –

5 – – C – – – – –

6 – – C – – – – –

SON 1 C C – C – C C –

2 – – – C – C – C

3 – – – C – – – C

4 – – – – – – – –

5 – – – – – – – –

6 – – – – – – – C

The filled circle ‘C’ signifies that the addition of SST or thermocline resulted in a significant improvement in the skill of hindcasts for a particular

region. This improvement is assessed based on the following criteria: (1) there should be an obvious rightward shift of the empirical cumulative

distribution function (CDF) of the composite model from the CDF position of the NINO model; (2) at least 50% of the grids comprising the region must

have skill scores greater than the NINO skill; (3) at least 30% of the grids comprising the region must have skill scores greater than the 5% significance

level; and (4) the Wilcoxon signed-rank test should reveal that the skill scores of the NINO model and the composite model have different means.



The addition of SST has resulted in the general

improvement in skill in the western regions that

encompasses all seasons and lags. SST’s influence,

however, is most evident during autumn when all

except the temperate region experience a significant

shift in the distribution of the skill scores. Although

the predictability of summer rain is also enhanced for

the temperate-west region for lags of 2–5 seasons, this

improvement has minimal practical value since the

amount of summer rain in this region is insignificant.

With spring rainfall in the tropical west region,

NINOCSST outperformed NINO and NINOCSUB

by producing the most skillful hindcasts with at least

80% of the grids gaining an increase in skill of more

than 30%. Of the four eastern climate regions, the

tropical-east is the only region that showed improve-

ment in skill with the use of SST patterns. This applies

to autumn hindcasts given a lag of 2 seasons and to

spring hindcasts for lags of 1, 2 and 4 seasons.

Judging from the number of season-lag combi-

nations that have enhanced skill, the NINOCSUB

model has better predictive skill than NINOCSST.

While NINOCSST showed skill only for 3 seasons,

NINOCSUB produced skillful hindcasts in all

seasons with autumn and spring covering more

regions and lags. In five out of the eight climate

regions, NINOCSUB produced autumn hindcasts

that were more skillful than NINO for most of the

lags. Out of these five regions only the tropical-east is

located in the eastern half of Australia. Unlike

autumn, the influence of the thermocline on spring

rainfall is more predominant in eastern Australia

especially over the subtropical and tropical regions

where enhancement in hindcast skill is seen for three

different lags. The extent of the thermocline’s

influence on spring rain over the grass-east and

temperate-east regions is limited to 1 and 2 seasons,

respectively.

NINOCSUB had also enhanced the skill of winter

rainfall but only for the grass and subtropical regions.

More predictability is observed in the subtropical-

west for lags of 3–6 seasons while hindcasts for the

subtropical-east region, which includes most of

Queensland and northern part of New South Wales,

are skillful for lags of 1–4 seasons. The addition of

thermocline also resulted in the improvement in skill

of winter hindcasts up to a lag of 4 seasons in the grass

regions. Only the western sections of the grass,

subtropical and temperate regions have more than

30% of their constituent grids increase in skill when

NINOCSUB is used to hindcast summer rainfall for

lags of 3 and 4 seasons. For each of these three

regions, at least 60% of their grids increase in skill by

30% or more.

The thermocline’s persistence is strong during the

January–June period but becomes radically weak

during the remaining half of the year. On the other

hand, persistence of Nino3 is strong from July–

December but is weak during summer and winter.

Hence, it is likely that by combining Nino3 and

thermocline in one model, skillful hindcasts are

possible for a lag of a year or longer. The ability of

the NINOCSUB model to produce skillful hindcasts

up to 18 months lag is evidence of this theory.

Obtaining skillful hindcast of autumn rainfall is

encouraging considering that forecasts of Australian

rainfall are normally least skillful during this season

due to the spring predictability barrier.

7.2. Hindcasts for the above-600 rainfall regions

Results of the hindcasting experiments using the

three prediction schemes for all grid locations that

have a MAR greater than 600 mm (denoted GM600s)

are presented in Table 2. With the addition of SST

patterns, significant positive shifts in the CDF of

LEPS scores were obtained for summer rainfall in

GM600s in Queensland particularly in QLD-N where

NINOCSST produced skillful hindcasts for lags of 2,

4 and 5 seasons. The influence of SST patterns in the

Pacific shifts westward during the following autumn

when hindcasts for NT and WA-N are skillful at lags

of 1, 2 and 6 seasons. Best results for the NINOCSST

model are its hindcasts for spring rain in GM600s

located north of Australia where a large number of

grids remain significant for up to a lag of 5 seasons.

The GM600s in NSW, VIC and TAS showed no

improvement at all with the addition of SST patterns

as predictor in any season. As mentioned in the

preceding section, winter is the only season when the

use of SST showed no effect on hindcast skill of any

region.

The addition of thermocline as predictor resulted in

more skillful hindcasts in all seasons except summer.

The region that showed improvement in skill of winter

hindcasts is QLD-S. The thermocline’s considerable

Table 2

Seasons when increases in skill of rainfall hindcasts for regions with mean annual rainfall (MAR) O600 mm are possible with the addition of

SST and thermocline

Model Projected season Lag (seasons) State

WA-S WA-N NT QLD-N QLD-S NSW VIC TAS

NINO CSST DJF 1 – – – – – – – –

2 – – – C – – – –

3 – – – – – – – –

4 – – – C – – – –

5 – – – C – – – –

6 – – – – C – – –

MAM 1 – – C – – – – –

2 – C C – – – – –

3 – – – – – – – –

4 – – – – – – – –

5 – – – – – – – –

6 – – C – – – – –

JJA 1 – – – – – – – –

2 – – – – – – – –

3 – – – – – – – –

4 – – – – – – – –

5 – – – – – – – –

6 – – – – – – – –

SON 1 – C C C – – – –

2 – C C C – – – –

3 – C C C – – – –

4 – C C C – – – –

5 – – C – – – – –

6 – – – – – – – –

NINO CSUB DJF 1 – – – – – – – –

2 – – – – – – – –

3 – – – – – – – –

4 – – – – – – – –

5 – – – – – – – –

6 – – – – – – – –

MAM 1 – – C – – – – –

2 C – C – – – – –

3 C – C – – – – –

4 – – C C – – C –

5 – – C C – C C –

6 – – C C – C – –

JJA 1 – – – – C – – –

2 – – – – C – – –

3 – – – – C – – –

4 – – – – C – – –

5 – – – – – – – –

6 – – C C – – – –

SON 1 – – C – C C C –

2 – – C C C C – –

3 – – C C C C – –

4 – – – – – – – –

5 – – – – – – – –

6 – – – C – – –

The filled circle ‘C’ signifies that the addition of SST or thermocline resulted in a significant improvement in the skill of hindcasts for a particular region.

This improvement is assessed based on the following criteria: (1) there should be an obvious rightward shift of the empirical cumulative distribution

function (CDF) of the composite model from the CDF position of the NINO model; (2) at least 50% of the grids comprising the region must have skill

scores greater than the NINO skill; (3) at least 30% of the grids comprising the region must have skill scores greater than the 5% significance level; and (4)

the Wilcoxon signed-rank test should reveal that the skill scores of the NINO model and the composite model have different means.



influence on autumn rainfall is reflected in the number

of season-lag combinations that have significant

improvement in skill. For instance, the NT GM600s

showed increases in skill for all lags. There was also

improvement in the skill of spring hindcasts for up to a

lag of 3 seasons although this effect is limited only to

GM600s in northeastern region of Australia. Not all

regions though responded positively to the use of

thermocline data. GM600s located in Tasmania and

WA-N showed no improvement in their skill for any

season-lag combination.

In comparing the two additional predictors, it

appears that the thermocline has more influence than

SST on the GM600s in terms of the number of seasons

and lags that experience greater hindcast skill. They

also differ in the seasons when they exert the greatest

and the least influence. SST is most influential on

spring rainfall and least influential on winter rainfall.

The thermocline, on the other hand, has significant

influence on autumn and spring rainfall but has no

influence on summer rainfall.

8. Conclusion

The potential of subsurface ocean temperatures as

predictors of Australian rainfall is explored. Hindcasts

of seasonal rainfall for lags ranging from 1 to 6 seasons

are produced using the second unrotated principal

component of the thermocline depth anomalies in the

Pacific Ocean for the 1980–2002 period. The study

builds on the results of recent studies that demonstrate

an improvement in the skill of ENSO forecasts when

the subsurface component of the ocean is added as a

predictor. There is a potential for subsurface ocean

temperatures in predicting Australian rainfall particu-

larly in regions where ENSO is a major cause of

interannual climate variability.

Overall, the results point to the considerable

potential of the thermocline for long-term forecasting

of seasonal rainfall in Australia. The influence of

ocean’s heat content on Australia encompasses all 4

seasons, all climate regions and lags. Autumn stands

out as the season when the influence of the

thermocline is considerable in terms of the number

of regions and lags affected. The thermocline’s

influence is dominant in the northern and western

regions where significant increases in LEPS scores are

observed even up to lag of 6 seasons or 18 months.

Since the length of the subsurface data covers only

about 23 years, conclusions drawn from the results of

the analysis can only be used as an indication of the

potential of subsurface ocean temperatures as pre-

dictors of Australian rainfall. When longer records

become available in the future, checks on the

stationarity of thermocline data and the stability of

its relationship with rainfall will be possible.

Our previous work (Ruiz et al., 2005) demon-

strated the significant contribution of the ocean’s heat

content in enhancing the skill of Nino3 hindcasts.

What this study demonstrated is that the use of

thermocline for ENSO prediction can be extended

into using it directly to predict Australian rainfall. As

the results have shown, considerable potential exists

for the thermocline in this area and a separate study

that investigates its use in streamflow forecasting is

currently underway.

Acknowledgements

The authors would like to thank the Bureau of

Meteorology Research Centre (BMRC) for providing

the rainfall and subsurface ocean temperatures data

and the NSW Department of Commerce for partly

funding this research.

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Impact of Mid-Pacific Ocean Thermocline on the Prediction of Australian Rainfall

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