Projecting Winter-Spring Climate from Antecedent ENSO and PDO Signals –

Applications to the 2010 Vancouver Winter Olympics and Paralympics

Ruping Mo1, Chris Doyle2, and Paul H. Whitfield2

1Pacific Storm Prediction Centre, Environment Canada, Vancouver, BC, Canada

2Meteorological Service of Canada, Environment Canada, Vancouver, BC, Canada

Corresponding author’s address: Ruping Mo Pacific Storm Prediction Centre, Environment Canada 201-401 Burrard Street Vancouver, BC V6C 3S5 Canada E-mail: ruping.mo@ec.gc.ca

Technical Report 2009-002 Pacific Storm Prediction Centre

December 2009

Abstract

A weak-to-moderate El Niño event is developing over the equatorial Pacific

Ocean. Meanwhile, the Pacific Decadal Oscillation (PDO) is flip-flopping between

positive and negative phases in the last few months. This study focuses on using

correlations of the antecedent El Niño/Southern Oscillation (ENSO) and PDO signals

with the climatic variables of Vancouver in the following February and March, these

being the time of the 2010 Vancouver Olympic and Paralymic Games respectively, to

construct a predictive model with known skill. It is shown that significant early ENSO

signals can indeed be detected in the Vancouver temperature records in February and

March, with the maximum correlation coefficients occurring when the ENSO signals in

June or July lead Vancouver temperatures in February for seven to eight months. These

long-lead ENSO signals are modified by the PDO signals to some extent.

Regression models based on the significant ENSO/PDO signals achieve

meaningful scores for temperature predictions. Given the current El Niño and PDO

conditions, the regression models suggest that the monthly mean temperature in Metro

Vancouver will be about 0.6 to 1.1°C above normal in February 2010 and about to

0.6°C around normal in March 2010. In Metro Vancouver, the projecting precipitation

amounts in February 2010 are in the range of 60–80 mm, with respect to the

climatological mean and median of 113 mm and 107 mm, respectively. The projecting

snowfall amounts in the same month are in the range of 0.0–1.3 cm, with respect to the

climatological mean and median of 7.9 cm and 1.8 cm, respectively.

3.0

1

1. Introduction

El Niño-Southern Oscillation (ENSO) is a coupled mode between the ocean and

atmosphere, characterized by significant sea surface temperature (SST) anomalies in the

central and eastern equatorial Pacific and a see-saw pattern of reversing sea-level

pressure between the eastern and western tropical Pacific (see Philander 1990; Trenberth

1997). El Niño represents the warm phase of the ENSO cycle with above-normal SSTs

developing in the equatorial Pacific. The opposite mode is referred to as La Niña. They

typically happen at irregular intervals of 2–7 years and last 9 to 24 months. ENSO is

considered as the strongest signal of interannual variability in the earth climate system,

and has been linked to climate anomalies around the globe (e.g., Diaz and Markgraf

2000).

There is also ENSO-like climate variability on a decadal to interdecadal timescale

in the North Pacific basin, which is commonly referred to as the Pacific Decadal

Oscillation (PDO; Mantua et al. 1997; Zhang et al. 1997; Chao et al. 2000; Biondi et al.

2001; Mantua and Hare 2002; Whitfield et al. 2009). While the origin of the PDO is not

clear, some studies have suggested that it results from the midlatitude–tropical ocean–

atmosphere interactions, and has a strong connection with the decadal variability of

ENSO (Gu and Philander 1997; Gershunov and Barnett 1998; Jin et al. 2001; Galanti and

Tziperman 2003; Wang et al. 2003; Vimont 2005; Dawe and Thompson 2007). PDO

variations have considerable influence on climate-sensitive natural resources in the

Pacific and over parts of North America (Whitfield et al. 2009).

This study, having been updated on a monthly basis since August 2009, focuses

on the ENSO and PDO impacts on the weather conditions in Vancouver of British

2

Columbia (BC), where the next Olympic and Paralympic Winter Games will be held in

February and March 2010, respectively. Previous studies have suggested that El Niño

events are usually associated with warmer and less snowfall winter conditions in southern

BC (Shabbar and Khandekar 1996; Shabbar et al. 1997; Taylor 1998). Some recent

studies (Kiffney et al. 2002; Stahl et al. 2006; Gobena and Gan 2006; Yu et al. 2007;

Fleming and Whitfield 2009) revealed that the ENSO impacts on the winter climate in

BC are modulated by the PDO in a manner that is either additive or reductive, depending

on their status. It is reasonable to expect that the greatest impacts from ENSO and PDO

would occur when they have matching signals (in phase) and high amplitudes, and high

amplitude effects would be reduced or mitigated when the signals are out of phase. Since

July 2009, various ENSO indicators have suggested a weak-to-moderate El Niño forming

over the equatorial Pacific, and various dynamical models suggested that this event will

either strengthen further or remain at the moderate strength during the next few months

(NOAA 2009; WMO 2009). Meanwhile, a negative PDO phase that started in September

2007 might have flipped to a positive phase since September 2009. Here we present an

analysis of the correlations of the ENSO and PDO signals with the monthly mean

temperature, precipitation and snowfall in Metro Vancouver in the following winter and

spring, based on records since 1939. Counting on the delayed atmospheric response to the

oceanic anomalies (e.g., Mo et al. 1998; Kumar and Hoerling 2003), our goal is to

develop an understanding of the skill with which early signals that can be used to develop

reliable and applicable climate outlooks on the order of several months, particularly for

the upcoming Vancouver 2010 Winter Olympics.

3

Section 2 describes the data used in this study and gives an update to the current

SST anomalies in the Pacific Ocean. Correlation analysis is performed in Section 3 to

identify the ENSO and PDO impacts on the climate in Metro Vancouver. Section 4

develops the regression models based on the significant correlations identified in

Section 3. The final section summarizes the major results.

2. Datasets and the current El Niño conditions

Monthly mean temperature (the average of daily maximum and minimum temperatures),

monthly total precipitation and snowfall amounts observed at the Vancouver International

Airport (YVR) are used to represent the conditions in Metro Vancouver. At YVR, the

daily weather observations began on 1 January 1937. To avoid some missing data in the

first two years, this study focuses on the period from January 1939 to present.

In correlation and regression analysis, it is usually required that the data be

normally distributed (e.g., Fisher 1925; Seber and Lee 2003). Since total precipitation and

snowfall amounts are known to be abnormally distributed, a transformation to the

Standardized Precipitation Index (SPI) is first applied to these data so that the

transformed values are more close to a normal distribution. The SPI was developed by

McKee et al. (1993) and is essentially a standardizing transform of the probability of the

observed precipitation (also see Guttman 1999). The correspondences between normally

distributed SPI values and precipitation categories are given in Table 1.

The PDO index, defined as the leading principal component (PC) of North Pacific

monthly SST variability (Mantua et al. 1997), is available from the Joint Institute for the

Study of the Atmosphere and Ocean (http://jisao.washington.edu/pdo/). A remarkable

4

characteristic of this index is its tendency for multiyear and multidecadal persistence,

with a few instances of abrupt sign changes. The associated pattern consists of SST

anomalies of one sign in the central-west Pacific between approximately 35° and 45°N,

ringed by anomalies of the opposite sign (Mantua et al. 1997; Zhang et al. 1997); the

positive phase of PDO is associated with positive PDO index with negative SST

anomalies in the central-west Pacific.

Table 1. The correspondences between normally distributed SPI values and precipitation categories.

SPI values Precipitation categories

2.00 and higher Extremely wet

1.50 to 1.99 Very wet

1.00 to 1.49 Moderately wet

–0.99 to 0.99 Near normal

–1.00 to –1.49 Moderately dry

–1.50 to –1.99 Severely dry

–2.00 and lower Extremely dry

Four NINO indices based on area-averaged SSTs over the tropical Pacific –

NINO1+2 (10°S–0°, 90°W–80°W), NINO3 (5°S–5°N, 150°W–90°W), NINO3.4 (5°S–

5°N, 170°W–120°W), and NINO4 (5°S–5°N, 160°E–150°W) – can be used as the ENSO

indicators (Trenberth 1997). In this study, these indices are computed from the NOAA

Extended Reconstructed SST datasets (ERSST V3b, available from NOAA at

5

http://www.cdc.noaa.gov/data/gridded/data.noaa.ersst.html; see Smith et al. 2008). Each

of these NINO indices captures different ENSO properties, and may be more useful than

the others if the concern is the ENSO impact on the climate in a particular region. The

canonical ENSO, characterized by anomalous SSTs extending from the coast of Peru to

the eastern and central equatorial Pacific (Rasmusson and Carpenter 1982; Philander

1990), is well represented by the NINO3 or NINO3.4 index. For these NINO indices,

large negative values represent La Niña, and large positive values represent El Niño.

Alternatively, the ENSO signals are also extracted from applying PC analysis on

SSTs over the tropical Pacific (20°S–20°N, 120°E–70°W). The PC analysis is performed

for each individual month over the 70-year period of 1938–2007. Beyond this period, the

PC time series are computed by projecting observed SSTs onto the PC eigenvectors. The

correlations of the first ENSO PC (PC1) of each month with the Pacific SSTs are shown

in Fig. 1. It is evident that this leading mode, which explains about 40%–65% of the SST

variance over the tropical Pacific, contains most of the ENSO signals and part of the PDO

signals. Its correlations with the NINO and PDO indices are given in Table 2. We see

that the correlations with all NINO indices are very high. In particular, the NINO3 index

is well represented by the PC1, with a near perfect correlation (0.99) in December. In

Fig. 1, it appears that the ENSO signals over the tropical Pacific extend into the

extratropics along the west coast of North America from October to the following April,

implying delayed warmer (cooler) conditions in the Vancouver area during El Niño

(La Niña) winters.

6

FIGURE 1: Correlation coefficients of the first principal component (PC1) of SSTs over the tropical Pacific (20°S–20°N, 120°E–70°W) with SSTs over the Pacific Basin (40°S–70°N, 120°E–65°W). The proportion of variance explained by PC1 is given at the upper-left corner of each map. Analysis is performed over the 70-year period of 1939–2008. The location of Vancouver is indicated by a black dot.

7

Table 2. Correlations of the first principal component of SSTs over the tropical Pacific with PDO and NINO indices in the 70-year period of 1939–2008.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec PDO 0.46 0.56 0.60 0.60 0.54 0.47 0.54 0.55 0.60 0.53 0.47 0.44

NINO1+2 0.77 0.67 0.68 0.83 0.92 0.91 0.90 0.90 0.85 0.90 0.90 0.89NINO3 0.98 0.96 0.91 0.94 0.97 0.97 0.96 0.98 0.97 0.98 0.98 0.99

NINO3.4 0.98 0.97 0.95 0.91 0.91 0.88 0.87 0.91 0.95 0.96 0.97 0.98NINO4 0.92 0.90 0.88 0.72 0.71 0.70 0.70 0.76 0.86 0.91 0.90 0.89

The NINO and PDO indices of the last 12 months are shown in Fig. 2. The

corresponding SST anomalies are given in Fig. 3. It appears that that a weak La Niña was

present until March 2009 and an El Niño event has been developing since May 2009.

This event strengthened to the moderate strength from October to November, with the

maximum SST anomalies along the central and eastern equatorial Pacific exceeding

+2.0°C. The PDO index had been in a negative phase until July 2009. It then flipped to

positive values from August to October, and flipped back to a negative value ( ) in

November.

40.0

FIGURE 2: The PDO and NINO indices of recent months. The NINO indices are standardized with respect to the 1939–2008 base period.

8

FIGURE 3: Sea surface temperature anomalies (°C) in the Pacific Ocean in recent months. The anomalies are computed with respect to the 1939–2008 base period. The location of Vancouver is indicated by a black dot.

9

3. Correlation analysis

In this study, the cross correlations of the ENSO and PDO signals of each month with

temperature/precipitation/snowfall data of Vancouver of the same month and the

following 12 months were computed over a 70-year period (either 1938–2007 or 1939–

2008). The statistical significance of correlation is determined by the Monte Carlo

simulations outlined in Appendix A.

Figure 4 shows the cross correlations of PDO, NINO3, and ENSO PC1–PC4 with

the monthly mean temperature of Vancouver (TYVR). Note that those small correlation

coefficients whose absolute values are statistically indistinguishable from zero at the 95%

confidence level are set to be zero. As the PDO impact is concerned (Fig. 4a), the main

feature is that the simultaneous correlations in those months from January to May are

very high, with the maximum value of 0.70 occurring in March. These simultaneous

correlations, however, have little value for operational forecast because of the zero lead

time associated with them. There are some long-lead, significant PDO signals for TYVR in

March. For instance, the correlation between PDO(Jul) and TYVR(Mar) is 0.41, with a

PDO lead time of eight months.

The most important feature in Fig. 4 is the existence of some strong long-lead

ENSO signals for the TYVR in February and March. As shown in Fig. 4b for the NINO3

index, the maximum correlation coefficient is 0.56, occurring when the NINO3 index in

June leads TYVR in February for eight months. The correlation of NINO3 in June with

TYVR in March is 0.50, with a lead time of nine months. Note that all the correlations of

TYVR in February and March with NINO3 in previous months back to March of the

previous year are statistically significant at the 95% confidence level. The correlations of

10

TYVR in January with NINO3 in previous months back to May of the previous year are

also statistically significant, but the coefficient values are noticeably lower than those

associated with TYVR in February and March. The correlations of the NINO4, NINO3.4,

and NINO1+2 with TYVR are not shown, as they are not significantly different from their

NINO3 counterparts shown in Fig. 4b. The correlations of PC1 with TYVR shown in

Fig. 4c are also similar to those in Fig. 4b, except that the best signal for TYVR in

February is PC1 in July (instead of June) of the previous year. Fig. 4e suggests that there

could be some early signals for TYVR in February associated with the third PC (PC3) in

March and April of the previous year. The question is if these early signals are

independent of the signals from the PC1 in July.

Figures 5 and 6 show the correlations of SSTs with TYVR in February and March,

respectively. Both of them indicate an early oceanic signature with positive correlations

near the Aleutian Islands and along the equatorial Pacific, and negative correlations in

between, as well as a simultaneous PDO signal. For TYVR in February, a center of

positive correlations over the western equatorial Pacific in March of the previous year can

be considered as an early ENSO signal (Fig. 5a). This signal strengthens and appears to

propagate eastwards as equatorial Kelvin waves in the following months, forming another

maximum center over the NINO3 region in June (Fig. 5d). It also appears that the

equatorial Kelvin waves split upon reaching the eastern boundary of the Pacific, with a

portion as reflected equatorial Rossby-gravity waves propagating westwards and another

portion as deflected coastal Kelvin waves propagating polewards. The two off-equator

positive correlation centers in Fig. 5f and Fig. 5g resemble a Rossby-gravity wave

structure. The coastally trapped Kelvin waves cannot be directly resolved from the 2°

11

latitude x 2° longitude SST data. However, the coastal Kelvin waves can generate

extratropical Rossby waves, which act to widen the along-shore SST anomalies. The

correlation pattern over the Northeast Pacific in Fig. 5ℓ resembles an extratropical

Rossby wave structure. The ENSO signals for TYVR in March are more complicated, as

shown in Fig. 6. In addition to the positive correlations along the equatorial pacific, there

is a strong, persistent subtropical signal over the South Pacific; this signal is much weaker

in Fig. 5.

The correlations of the monthly SPI of Vancouver precipitation (PYVR) and

snowfall (SYVR) with selected ENSO/PDO signals are shown in Figures 7 and 8,

respectively. For PYVR in February, the best signal is NINO4 in August of the previous

year (Fig. 7b). This negative correlation suggests that an El Niño event will lead to

slightly drier conditions in February. The corresponding signal from PC1 in August (not

shown) is not significant at the 95% confidence level. Instead, the signal for PYVR in

February from PC3 in September (Fig. 7c) is equivalent to the signal from NINO4 in

August. The associations of PYVR in March with the ENSO signals are generally weak,

with no correlation coefficients being statistically significant at the 95% confidence level.

As far as the total precipitation amount is concerned, therefore, the El Niño currently

developing over the tropical Pacific is not expected to be much different from normal in

March 2010. It appears that the PDO impacts on PYVR in both February and March

(Fig. 7a) are also statistically insignificant.

Fig. 8a shows that the simultaneous negative correlations of the PDO with SYVR

in those months from December to March are very high. This is consistent with the

corresponding significant positive correlations with the TYVR shown in Fig. 4a. As

12

FIGURE 4: Correlations of the ENSO/PDO signals of each month with the mean temperatures of Vancouver (TYVR) of the same month and the following 12 months. Small correlation coefficients that are statistically indistinguishable from zero at the 95% confidence level from the Monte Carlo simulations (see Appendix A) are set to be zero. The labels of the horizontal axis represent the months for ENSO/PDO signals. They are separated into 12 groups by the vertical dashed lines. The months for TYVR are color coded, with green for January, red February, yellow March, and gray the rest of months. The horizontal blue dashed lines correspond to the correlation coefficients required for the 95% confidence level from a two-tailed Student’s t test.

13

FIGURE 4 (continued).

14

FIGURE 5: Correlations of SSTs with TYVR in February. The analysis is performed over a 70-year period (1939–2008 for TYVR, and either 1938–2007 or 1939–2008 for SSTs). The location of Vancouver is indicated by a black dot.

15

FIGURE 6: Same as Fig. 5, except for TYVR in March.

16

FIGURE 7: Same as Figure 4, except for SPI of the total precipitation amounts in Vancouver (PYVR).

17

FIGURE 8: Same as Fig. 4, except for SPI of the snowfall amounts in Vancouver (SYVR).

mentioned earlier, however, these significant simultaneous correlations have little values

in operational forecasting. In this regard, the significant negative correlations of SYVR in

February with the antecedent ENSO signals (Fig. 8b,c) are much more useful to the

forecasters. These negative correlations are consistent with the corresponding positive

(negative) correlations with temperature (precipitation) shown in Fig. 4 (Fig. 7). For SYVR

18

in March, its correlations with ENSO signals are generally weak, with no coefficient

being statistically significant at the 95% confidence level. Instead, Fig. 8a indicates that it

is significantly correlated with the PDO index in some previous months.

4. Regression models and predictions

Results from the correlation analysis in the previous section indicate the possibility of

ENSO/PDO-based long-lead prediction for Metro Vancouver in February and March. In

this section, some linear regression models are developed and applied to produce

temperature and snowfall outlooks for these two months in 2010.

Let be the variable to be predicted (e.g., T)(ty

xx , , 21

YVR) – the predictand. The first

step is to determine a least squares estimate of based on observations of p

predictors ,

)(ty

px ,

(1) ),(ˆ)(ˆ)(ˆˆ)(ˆ 2221110 ppp txtxtxty

where represents the least squares estimate of y, are the regression

parameters, and the τ values represent lead times.

y p ˆ ,,ˆ ,ˆ10

In this study, skillful predictors are selected from the PDO index and either the

four NINO indices or the first four leading PCs of SSTs over the tropical Pacific, with

MAXMIN . A screening procedure based on the Monte Carlo simulations is used to

select the predictors (see Appendix B for further details). In this study, we let the

maximum lead time 12MAX months. The minimum lead time, MIN , depends on the

data availability. If forecast was issued in September 2009, for example, one could let

19

6MIN so that predictors available up to August 2009 could be used to predict TYVR in

February 2010. The model performances are measured by the 2R statistic and the mean-

square-error skill score, MSESS (see Appendix B).

Table 3 lists some regression models built for the February YVR temperatures.

Their forecasts for 2010, together with the climatological means, are given in the last

column. When the four NINO indices and the PDO index are taken as potential

predictors, the NINO3 index in June is the obvious choice as the first predictor for

predicting TYVR in February, given the significant correlation shown in Fig. 4b. It is the

only predictor chosen for the model with 3MIN . This model provides an eight-month

lead time for operational forecast. Its cross-validations and prediction for February 2010

are shown in Fig. 9. We see that in the past 71 years (1939–2009), the model performs

poorly for 18 years (i.e., 1939, 1948–49, 1956–58, 1961, 1963, 1969, 1975, 1977, 1987,

1989–91, 1993–94, and 2004). In particular, the warm conditions associated with the

1957–1958 and 1986–87 El Niño events, and the cold conditions with the 1948–49 and

1988–89 La Niña events are noticeably under-forecast. The predicted warm condition

associated with the 1993–94 El Niño event is a false alarm. The warm conditions in 1963

and 1991, and the cool conditions in 1993 and 1994, are also poorly forecast. But they are

not ENSO-related, anyway. On the other hand, this model performs reasonably well for

forecasting warm conditions associated with the El Niño episodes of 1969–70, 1982–84,

1987–88, and 1997–98, and the cool conditions associated with the La Niña episodes of

1949–51, 1954–56, 1970–72, 1984–86, and 2000–01. With respect to the current El Niño

event, this model predicts a moderate warm condition (~0.9°C above normal) for

February 2010. Note that in this model the regression on the NINO3 index is

20

linear. However the blue dots in the scatter plot (Fig. 9b) do not stay exactly on a straight

line. The slight scatter is caused by the leave-one-out cross-validation, which generates n

slightly different linear regression equations to produce the n predictions. Fig. 9c shows

the goodness-of-fit, or lack of goodness-of-fit, of the model. It indicates that the extreme

cold conditions, as compared to the extreme warm conditions, are well under-forecast.

When the first four ENSO PCs are used to replace the four NINO indices as

potential predictors, the regression model for TYVR(Feb) selects PC1(Jul) of the previous

year as its first predictor. In addition, PC2(Apr), PC2(May), and PC2(Feb) of the

previous year are selected as the second, third, and fourth predictor, respectively. This

multiple regression model appears to be more skillful than the above-mentioned simple

Table 3: Regression models for the February Vancouver temperatures, TYVR(Feb), and their predictions ± 95%PCI for February 2010. The definitions of PCI (prediction confidence intervals), 2R , and MSESS, together with the screening procedure for selecting the best predictors are given in Appendix B. The predictions for February 2010 (the last column) are based on currently available predictors with the assumption that the strengths of ENSO/PDO signals in November 2009 would persist through February 2010; predictions based on this persistence assumption are marked by "†". Predictand / MIN Predictors MSESS/2R Prediction (climate)

TYVR(Feb) / 3MIN 1st: NINO3(Jun) τ = 8 0.31 / 0.29 4.25.5 °C (4.6°C)

TYVR(Feb) / 3MIN 1st: PC1(Jul) τ = 7

2nd : PC2(Apr) τ = 10

3rd: PC2(May) τ = 9

4th: PC2(Feb) 12

0.31 / 0.29

0.35 / 0.32

0.42 / 0.37

0.48 / 0.42

4.26.5 °C (4.6°C)

4.26.5 °C (4.6°C)

2.23.5 °C (4.6°C)

2.27.5 °C (4.6°C)

TYVR(Feb) / 0MIN 1st: NINO3(Jun) τ = 8

2nd : PDO(Feb) τ = 0

3rd: PDO(Dec) τ = 2

0.31 / 0.29

0.37 / 0.33

0.45 / 0.39

4.25.5 °C (4.6°C)

3.21.5 °C† (4.6°C)

2.22.5 °C† (4.6°C)

21

FIGURE 9: Cross-validations of the mean temperatures TYVR in February from a simple regression model with the NINO3 index in June of the previous year as the only predictor. (a) Observations (red dots) versus predictions (blue boxes with whiskers); the band at the middle of the box is the prediction value, the ends of the box represent one standard deviation of the prediction error, and the ends of the whiskers represent two standard deviation that corresponds to the 95% confidence interval (see Appendix B). (b) The scatter plot of the predicted (blue dots) and observed (red dots) values; the horizontal black line marks the mean of the observations. (c) Another plot of observed versus predicted values.

22

regression model (Table 3). Its performance is plotted in Fig. 10. It is shown that warm

bias over the extreme conditions in the simple regression (Fig. 9c) has been corrected to

some extent (Fig. 10c). Fig. 10b shows that a simple regression model with PC1(Jul) as

the only predictor is as skillful as the model with NINO3(Jun) as the predictor (Fig. 9b).

The skill improvement of the PC-based model comes from adding PC2(Apr), PC2(May),

and PC2(Feb) as additional predictors. It is interesting to note that, as shown in Fig. 4d,

TYVR(Feb) does not appear to be significantly correlated with either PC2(Apr),

PC2(May), or PC2(Feb). In fact, its correlations with PC3(Apr) and PC3(May) are much

more significant (Fig. 4e). In multiple regressions, however, the contributions from

additional predictors are related to their partial correlations, rather than their overall

correlations, with the predictand. With respect to the current El Niño event, this model

also predicts a slightly warmer condition (~1.1°C above normal) for February 2010.

Even with 0MIN , the regression equation for TYVR(Feb) still picks

NINO3(Jun) or PC1(Jul) as its first predictor. In addition, the PDO in February of the

sa year ( 0me ) and December of the previous year ( 2 ) are selected as the second

and third predictor (Table 3). This model, however, is practically useless for future

prediction, unless the future PDO as its predictor can itself be correctly predicted from

other statistical or dynamical models. Based on the assumption that the PDO index in

November 2009 ( ) will persist through February 2010, its prediction of T40.0 YVR for

February 2010 is 5.2°C (Table 3), or 0.3°C cooler than the prediction from the simple

model with NINO3(Jun) as the only predictor. If we assume that the PDO index would

increase to 0.75 (1.00) in December 2009 and to 1.00 (1.50) in February, the predicted

TYVR in February 2010 would be 5.6°C (5.7°C).

23

FIGURE 10: Cross-validations of the mean temperatures TYVR in February from a multiple regression model with ENSO PC1(Jul), PC2(Apr), PC2(May), and PC2(Feb) of the previous year as predictors (see Table 3 and Fig. 9 for further explanations). The result from a simple regression model with PC1(Jul) as the only predictor is shown in (b).

For 4MIN with NINO and PDO indices as potential predictors, the regression

model for predicting TYVR(Mar) selects NINO1+2(Nov), PDO(May), and PDO(Jun) of

the previous year as its first, second, and third predictor. Its skill scores and prediction of

24

TYVR(Mar) in 2010 are shown in Table 4. This model predicts a near-normal condition

(0.3°C below normal, to be precise). If the first four ENSO PCs are used to replace the

four NINO indices as the potential predictors, the corresponding model selects PC1(Nov)

and PC2(Oct) of the previous year as its predictors, and predicts 6.9°C for TYVR(Mar) in

2010, which is 0.6°C warmer than the climatological mean of 6.3°C. With 0MIN , the

selected predictors for TYVR(Mar) would be PDO(Mar) of the same year and

NINO4(Dec) of the previous year (Table 4). Despite the impressive skill scores

associated with it, this model is practically useless because some required predictor

values are not available in advance. Its prediction of TYVR(Mar) in 2010 would be 6.6°C

if the ENSO/PDO indices in November would persist through March 2010 (Table 4). The

predicted value would increase to 7.5°C (7.8°C) if the NINO4 index in November would

persist through December 2009 and the PDO index would increase to 1.00 (1.50) in

March 2010.

Table 4: Same as Table 3, except for TYVR(Mar). The predictions for March 2010 (the last column) are based on currently available predictors with the assumption that the strengths of ENSO/PDO signals in November 2009 would persist through March 2010; predictions based on this persistence assumption are marked by "†".

Predictand / MIN Predictors MSESS/2R Prediction (climate)

TYVR(Mar) / 4MIN 1st: NINO1+2(Nov) τ = 4

2nd : PDO(May) τ = 10

3rd: PDO(Jun) τ = 9

0.29 / 0.26

0.34 / 0.30

0.39 / 0.33

0

0

0

.26.6 °C (6.3°C)

.22.6 °C (6.3°C)

.20.6 °C (6.3°C)

TYVR(Mar) / 4MIN 1st: PC1(Nov) τ = 4

2nd: PC4(Oct) τ = 5

0.28 / 0.27

0.35 / 0.32

1.21.7 °C (6.3°C)

0.29.6 °C (6.3°C)

TYVR(Mar) / 0MIN 1st: PDO(Mar) τ = 0

2nd : NINO4(Dec) τ = 3

0.50 / 0.48

0.55 / 0.52

7.19.5 ° C† (6.3°C)

7.16.6 °C† (6.3°C)

25

As the SPI of monthly total precipitation amount is concerned, no skillful

predictor can be found for PYVR(Mar). For 0MIN with NINO and PDO indices as

potential predictors, the regression model for PYVR(Feb) picks up NINO4(Aug) as the

only predictor, and its predicted SPI value for February 2010 is –0.50, which is slightly

below normal and is categorized as a near normal condition (see Table 1, Table 5 and

Fig. 11). This predicted SPI value corresponds to 81 mm of precipitation, as compared to

the climatological mean of 113 mm or the median of 107 mm. The confidence on this

prediction is low, however, given the low skill scores associated with the model. A more

skillful model can be obtained when the four NINO indices are replaced by the first four

leading ENSO PCs as potential predictors (Table 5 and Fig. 12). This model selects

PC3(Sep), PC4(Aug), and PC1(May) of the previous year as its first, second, and third

predictor, and predicts an SPI value of –1.02 for February 2010, which is in the below-

normal category and corresponds to 61 mm of precipitation.

For the SPI of monthly total snowfall amount, the regression model for SYVR(Feb) with

NINO and PDO indices as potential predictors selects NINO3.4(Jun) as its only predictor

(Table 5 and Fig. 13). This model appears to be more skillful than the corresponding

model for PYVR(Feb). A model with even higher skill scores can be obtained when the

four NINO indices are replaced by the first four leading ENSO PCs (Fig. 14). However,

these skill scores should be interpreted in a cautious way because, as visually evident in

Fig. 13 and Fig. 14, the snowfall data are not well transformed to normality by the SPI

algorithm. The difficulty comes from the fact that these snowfall data are both

continuous and discrete; the discrete component corresponds the exact zero snowfall.

Over the 71-year period of 1939–2009, there were 27 years with zero snowfall amount at

26

YVR in February. Special treatment of these zero observations is usually required, and

the regression model could be possible using the established framework of generalized

linear models (e.g., Smyth 1996; Chandler and Wheater 2002; Dunn and White 2005);

pursuing these models is beyond the scope of this study. The predicted SPI values for

SYVR(Feb) in 2010 from our simple and multiple regression models (Fig. 13 and Fig. 14)

are −0.12 and –0.34, respectively. They correspond to snowfall amounts of 1.3 cm and

0.0 cm, respectively. The corresponding climatological mean and median are 7.9 cm and

1.8 cm, respectively. The minimum SPI of this dataset is –0.30, which corresponds to the

zero snowfall amount. The maximum snowfall amount is 60.8 cm with an SPI value of

2.43. As the snowfall at YVR in March is concerned, there are 38 years with exact zero

snowfall amount over the 71-year period of 1939–2009. For this kind of data, the

performance of linear regression model is seriously hindered.

Table 5: Same as Table 3, except for the SPI of total precipitation amounts (PYVR) and snowfall amounts (SYVR). The definition of SPI is given in Section 2. Predictand / MIN Predictors MSESS/2R Prediction ± 95%CI

PYVR(Feb) / 0MIN 1st: NINO4(Aug) τ = 6 0.13 / 0.10 93.150.0

PYVR(Feb) / 0MIN 1st: PC3(Sep) τ = 5

2nd : PC4(Aug) τ = 6

3rd: PC1(May) τ = 9

0.12 / 0.10

0.20 / 0.15

0.28 / 0.22

95.157.0

88.170.0

80.102.1

SYVR(Feb) / 0MIN 1st: NINO3.4(Jun) τ = 8 0.25 / 0.23 24.112.0

SYVR(Feb) / 0MIN 1st: PC1(July) τ = 7

2nd : PC2(Apr) τ = 10

3rd: PDO(Jun) τ = 8

0.23 / 0.21

0.28 / 0.24

0.34 / 0.28

26.117.0

22.118.0

19.134.0

27

FIGURE 11: Cross-validations of SPI of the total precipitation amounts PYVR in February from a simple regression model with the NINO4 index in August of the previous year as the only predictor (see Table 5 and Fig. 9 for further explanations).

28

FIGURE 12: Cross-validations of SPI of the total precipitation amounts (PYVR) in February from a multiple regression model with ENSO PC3(Sep), PC4(Aug), and PC1(May) of the previous year as predictors (see Table 5 and Fig. 9 for further explanations). The result from a simple regression model with PC3(Sep) as the only predictor is shown in (b).

29

FIGURE 13: Cross-validations of SPI of the snowfall amounts SYVR in February from a simple regression model with the NINO3.4 index in June of the previous year as the only predictor (see Table 5 and Fig. 9 for further explanations).

30

FIGURE 14: Cross-validations of SPI of the snowfall amounts SYVR in February from a multiple regression model with ENSO PC1(Jul), PC3(Oct), and PDO(Jun) of the previous year as predictors (see Table 5 and Fig. 9 for further explanations). The result from a simple regression model with PC1(Jul) as the only predictor is shown in (b).

31

5. Summary and discussions

The ENSO/PDO impacts on the monthly mean weather conditions in Metro Vancouver

have been examined in a lag correlation perspective. We focus on three issues in this

study: 1) How, when, and to what extent are the weather conditions in Metro Vancouver

influenced by the ENSO events? 2) How the ENSO impacts are modulated by the PDO?

3) Is it possible to provide useful outlooks for Metro Vancouver based on any long-lead

ENSO/PDO signals? It is shown that the strong ENSO signals are not detectable all year

round in Vancouver. Surprisingly, the normal conditions in Vancouver persist even

through most parts of the winter (December-January) when anomalous ENSO conditions

in the equatorial Pacific have usually peaked. The strongest response to the ENSO signals

is found in the February temperatures. With a correlation of 0.56, about 31% of their

variance during the period 1939–2008 can be explained by the NINO3 index in June of

the previous year. Long-lead, significant ENSO signals are also found for Vancouver

temperatures in March, and significant simultaneous correlations between PDO and

Vancouver temperatures are found in both February and March. It is shown that an El

Niño event may lead to slightly drier conditions in February. Taking into account of the

ENSO impact on temperature, Vancouverites can expect less snowfall near sea level in

February during an El Niño. However, the ENSO impacts on the Vancouver precipitation

and snowfall in March are not statistically significant.

The long-lead ENSO/PDO signals identified in our correlation analysis are used

to develop statistical predictions for Metro Vancouver. Given the current El Niño/PDO

conditions, these statistical models predict that the monthly mean temperature at YVR

would be about 0.6 to 1.1°C above normal in February 2010 and about to 0.6°C 3.0

32

around normal in March 2010. The latest observations indicate that the PDO index is flip-

flopping around zero. Therefore the real PDO impact remains uncertain. If the current

negative PDO index would flip back to some significant positive values in the next few

months, then its modification could result in warmer conditions in Vancouver with 1.1°C

and 1.4°C above normal possible in February and March 2010, respectively. Given the

standard atmospheric lapse rate of 6.5°C/km, the 0.6–1.1°C warmer conditions at sea

level in February 2010 imply that the freezing level would be 90–170 meters above

normal, and the 0.6–1.4°C warmer conditions in March 2010 would correspond to

freezing level being 90–220 meters above normal.

Before fitting statistical models to total precipitation and snowfall amounts, an

SPI algorithm is applied to these data for the purpose of transforming to normality. The

SPI transformation works reasonably well for the wet-season monthly total precipitation

amounts in Vancouver. Given the current El Niño/PDO conditions, the predicted total

precipitation at YVR in February 2010 would be in the range of 60–80 mm, with respect

to the climatological mean and median of 113 mm and 107 mm, respectively. Skillful

ENSO/PDO-based regression model is not available for the precipitation at YVR in

March. The predicted snowfall amounts in February 2010 at YVR would be in the range

of 0.0–1.3 cm, with respect to the climatological mean and median of 7.9 cm and 1.8 cm,

respectively. However, it is pointed out that, in the presence of many zero observations,

the snowfall amounts may not be transformed to normality by the SPI algorithm or any

other means. Such data should be treated cautiously. They could be better modeled using

established framework of generalized linear models (e.g., Smyth 1996; Chandler and

33

Wheater 2002; Dunn and White 2005) or other nonlinear regression methods (see Hsieh

2009).

Our statistical predictions for February and March 2010 are consistent with the

latest dynamical deterministic and probabilistic seasonal forecasts of Environment

Canada (http://www.weatheroffice.gc.ca/saisons/index_e.html), which was issued on 1

December 2009 and suggested warmer and drier conditions for the Canadian West Coast

in the period of January–March 2009. This is in noticeable contrast to the forecasts issued

on 1 November 2009 calling for cooler and drier conditions for the period of December

2009–February 2010.

Results from this study could provide some valuable information to the 2010

Vancouver Winter Olympics and Paralympics. One should keep in mind, however, that

these results are statistical climate projections rather than deterministic predictions. In

addition, they are based on the ENSO and PDO impacts only. Other climate systems,

such as the Arctic Oscillation and the Madden-Julian Oscillation, may also insert strong

influences on the weather conditions in Vancouver. While taking all these factors into

account might produce a better prediction, but that was beyond the scope of this study.

In addition to this empirical study, one should further consider the dynamical

implications of the long-delayed correlation relationships. Some evidence seems to

suggest that the equatorial/coastal oceanic Kelvin waves, through their interactions with

the oceanic Rossby waves, are capable of carrying the summer ENSO signals from the

tropical Pacific to the Canadian West Coast in the following winter. The existence and

robustness of such an oceanic channel remain to be confirmed through further theoretical

and modeling studies.

34

Acknowledgments. We thank Trevor Smith, David Jones, Brad Snyder, and Ian Okabe for

helpful discussions. The detailed explanations of the PDO index from Dr. Nathan Mantua

are greatly appreciated. Comments of Drs. Amir Shabbar and Alex Cannon on earlier

versions are highly appreciated. RM is also indebted to Andrew Fabro, Diana Hall, and

Sarah Perrin for bibliographic assistance. The figures in this study were made using

NCAR Command Language (http://www.ncl.ucar.edu/).

APPENDIX A:

Testing the Significance of Correlation Coefficients

a. Parametric approach – Student’s t statistic

Let the correlation coefficient, calculated from a population of paired scores X and

Y, be XY . When the coefficient is calculated from a sample set of n paired scores, it is

denoted as . It may be that the true correlation XYr XY is zero and that is not, simply

as a matter of random sampling variation. To check on this possibility, one can test the

null hypothesis that

XYr

0XY against the alternative that it is not. Based on the

assumptions that there is independence among the pairs of scores and that the population

of the pairs of scores has a normal bivariate distribution, Fisher (1925) showed that when

0XY , the value given by

(A1) 12 2XYXY rnrt

is distributed approximately as Student’s t statistic with 2n

1(100

degrees of freedom.

Therefore, the correlation coefficient value required for the )% confidence level

of significance to reject the null hypothesis of 0XY is given as

35

(A2) , )2( 2)2/1,2(

2)2/1,2( nnc tntr

where is the )2/1,2( nt )2/1( percentage point of the Student’s t distribution with

degrees of freedom. )2( n

In practice, there is often serial correlation in the observed data. The effect of

serial correlation on (A1) and (A2) was quantified by Chelton (1983) through the use of

the effective sample size (instead of the actual sample size n), which can be estimated

by

effn

(A3) , )()()()(

eff

L

L YXXYYYXX rrrr

nn

where )(r

(Lr

is the lag-τ auto- or cross-correlation coefficient, and L is large enough so

that the ’s become statistically indistinguishable from zero. Thiébaux and Zwiers

(1984) pointed out, however, that the estimates of are not unique, and the serial

correlation in data violates some assumptions underlying the use of the Student’s t

distribution.

)

effn

b. Nonparametric approach – the Monte Carlo technique

To avoid the controversy and complexity associated with the above-mentioned t

statistic, in this study we use a Monte Carlo technique to test the null hypothesis of

0XY . This method does not depend explicitly on the sample size, and does not

require knowledge of the data distribution. It can be, therefore, applied to variables whose

sample distributions are either unknown or known to be substantially different from

normality. To conduct a Monte Carlo test, we start with creating an artificial data batch of

36

X~

and Y , where X~

is a randomly shuffled version of X, and computing the

corresponding correlation coefficient. These two steps are then repeated times, where

( in this study), and the absolute values of the corresponding

correlation coefficients are sorted in ascending order. For our 1000 iterations, the null

hypothesis of

tn

nnt 1000tn

XY 0 is rejected at the 95% confidence level if XYr is greater than the

950th value of the sorted absolute correlation coefficients of the Monte Carlo simulations.

APPENDIX B:

Screening Regression Models

a. The prediction confidence intervals and 2R statistic of a linear regression model

Given a data set of n years, the regression model defined in

Section 4 can be written in a matrix form as

n

iipii xxy11 ,,,

(B1) )(ˆ ,ˆˆ 1 yXXXββXy

where

ˆ

ˆ

ˆ

ˆ ,

1

1

, 1

0

1

1111

pnpn

p

n xx

xx

y

y

βX y,

ˆ

ˆ1

ny

y

y

To calculate prediction confidence intervals (PCI) around a forecast value

from Eq. (B1) at a set of given predictor values of

0y

]1[ 001 pxx 0xx , we

assume that the prediction errors from Eq. (B1) follow a normal distribution. We can then

37

construct a t-statistic and obtain the )%1(100 PCI for from (e.g., Seber and Lee

2003),

0y

(B2) . )1/( n]ˆ)(1[)2/1,2(0 pt n βX)XXXx0

ˆ][1 (βyyx0

2

y

R A useful statistic to check is the value of a regression fit, defined as

(B3) , )()ˆ( 222 yyyyR ii

where the summations are over ni ,,1 , and n 1 iyy . 2R measures the

proportion of total variation of the predictand about its mean y explained by the

regression. In fact, R is the correlation between y and ˆ y , and is usually called the

multiple correlation coefficient.

b. Screening regression models based on Monte Carlo simulations

Our screening procedure for selecting the best predictors begins with computing

simple linear regressions between each of the available p predictors and the predictand.

The variable whose 2R is the highest among all candidate predictors will be chosen as

the first predictor to enter the regression model, provided that its 2R is also statistically

significant at the 95% confidence level. The significance level is determined from a large

number (again, in this study) of Monte Carlo simulations, which are carried

out using randomly shuffled versions of the predictor in question as bogus predictors; the

95% confidence level of significance is the 5% tail value of the simulations. After

selecting the first predictor, trial multiple regression equations are constructed using the

first selected variable in combination with each of the remaining p–1 predictors, and the

second predictor is chosen as the one that does the best to increase the

1000tn

2R and passes the

38

significance test of the Monte Carlo simulations. This selection procedure is repeated

until no further skillful predictors can be found. To prevent over-fitting the model, we

will choose no more than five predictors for any model in this study.

c. The mean-square-error skill score

In this study, the 2R statistic is used to judge the predictors during the screening

process. Its value, therefore, can be considered as a skill score of the regression model.

The prediction skill of the model can also be measured independently by the mean square

error (MSE) skill score, MSESS, defined as (see Murphy 1988),

MSESS = 1 – MSE(prediction) / MSE(climatology). (B4)

The last term in the above equation is the MSE of the forecast scaled by the MSE of the

climatological forecast. Note that MSESS has a range of 1 to , with positive values

representing skillful forecast (better than climatological forecast).

A scheme called “leave-one-out” cross-validation is adopted to calculate MSESS.

In this scheme, the model development set with n historical data records is successively

divided into n mutually exclusive dependent and independent sets in which each of the

independent set consists of one data record and the corresponding dependent set consists

of the remaining ( ) data records. A regression model is developed with each

dependent set and used to predict the corresponding independent (leave-out) set.

Repeating this procedure to obtain n predicted values, which are used to compute the

MSE of predictions. The MSE of climatology is simply the estimated variance of the

predictand.

1n

39

References

Biondi, F., A. Gershunov, and D. R. Cayan, 2001: North Pacific decadal climate

variability since 1661. J. Climate, 14, 5–10.

Chao, Y., M. Ghil, and J. C. McWilliams, 2000: Pacific interdecadal variability in this

century’s sea surface temperatures. Geophys. Res. Lett., 27, 2261–2264.

Chandler, R. E., and H. S. Wheater, 2002: Analysis of rainfall variability using

generalized linear models: A case study from the west Ireland. Water Resources

Res., 38, 1192–1202.

Chelton, D., 1983: Effects of sampling errors in statistical estimation. Deep-Sea Res., 30,

1083–1103.

Dawe, J. T., and L. Thompson, 2007: PDO-related heat and temperature budget changes

in a model of the North Pacific. J. Climate, 20, 2092–2108.

Diaz, H. F., and V. Markgraf (Editors), 2001: El Niño and the Southern Oscillation:

Multiscale Variability and Global and Regional Impacts. Cambridge University

Press, 512 pp.

Dunn, P. K., and N. White, 2005: Power-variance models for modeling rainfall. In:

Proceedings of the 20th International Workshop on Statistical Modelling. Sydney,

Australia, 149–156.

Fisher, R. A., 1925: Statistical Methods for Research Workers. Oliver and Boyd, 239 pp.

Fleming, S.W., and P.H. Whitfield, 2009: Spatiotemporal mapping of ENSO and PDO

surface meteorological signals in British Columbia, Yukon, and Southeast Alaska.

Atmosphere –Ocean (accepted).

40

Galanti, E., and E. Tziperman, 2003: A midlatitude–ENSO teleconnection mechanism via

baroclinically unstable long Rossby waves. J. Phys. Oceanogr., 33, 1877–1888.

Gershunov, A., and T. P. Barnett, 1998: Interdecadal modulation of ENSO

teleconnections. Bull. Amer. Meteor. Soc., 79, 2715–2725.

Gobena, A. K., T. Y. Gan, 2006: Low-frequency variability in southwestern Canadian

stream flow: Links with large-scale climate anomalies. Int. J. Climatol., 26, 1843–

1869.

Gu, D., and S. G. H. Philander, 1997: Interdecadal climate fluctuations that depend on

exchanges between the tropics and extratropics. Science, 275, 805–807.

Guttman, N. B. 1999: Accepting the standardized precipitation index: A calculation

algorithm. J. Amer. Water Resources Assn., 35, 311–322.

Gutzler, D. S., D. M. Kann, and C. Thornbrugh, 2002: Modulation of ENSO-based long-

lead outlooks of southwestern U.S. winter Precipitation by the Pacific decadal

oscillation. Wea. Forecasting, 17, 1163–1172.

Hsieh, W. W., 2009: Machine Learning Methods in the Environmental Sciences.

Cambridge University Press, 349 pp.

Jin, F.-F., M. Kimoto, and X. C. Wang, 2001: A model of decadal ocean–atmosphere

interaction in the North Pacific basin. Geophys. Res. Lett., 28, 1531–1534.

Kiffney, P. M., J. P. Bull, and M. C. Feller, 2002: Climatic and hydrologic variability in a

coastal watershed of southwestern British Columbia. J. Am. Water Res. Assoc., 38,

1437–1451.

Kumar, A., and M. P. Hoerling, 2003: The nature and causes for the delayed atmospheric

response to El Niño. J. Climate, 16, 1391–1403.

41

Mantua, N. J., and S. R. Hare, 2002: The Pacific decadal oscillation. J. Oceanogr., 58,

35–44.

Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis, 1997: A Pacific

interdecadal climate oscillation with impacts on salmon production. Bull. Amer.

Meteor. Soc., 78, 1069–1079.

McKee, T. B., N. J. Doeskin, and J. Kleist, 1993: The relationship of drought frequency

and duration to time scales. Proc. 8th Conf. on Applied Climatology, American

Meteorological Society, 179–186.

Mo, R., J. Fyfe, and J. Derome, 1998: Phase-locked and asymmetric correlations of the

wintertime atmospheric patterns with the ENSO. Atmosphere –Ocean, 36, 213–239.

Murphy, A. H., 1988: Skill scores based on the mean square error and their relationships

to the correlation coefficient. Mon. Wea. Rev., 116, 2417–2424.

NOAA, 2009: ENSO Diagnostic Discussion Archive, available online at:

http://www.cpc.ncep.noaa.gov/products/expert_assessment/ENSO_DD_archive.shtml.

Philander, S. G., 1990: El Niño, La Niña and the Southern Oscillation. Academic Press,

293 pp.

Rasmusson, E. G., and T. H. Carpenter, 1982: Variations in tropical sea surface

temperature and surface wind fields associated with the Southern Oscillation/El

Niño. Mon. Wea. Rev., 110, 354–384.

Seber, G. A. F., and A. J. Lee, 2003: Linear Regression Analysis. Wiley–Interscience,

582 pp.

Shabbar, A., and M. Khandekar, 1996: The impact of El Niño-Southern Oscillation on

the temperature field over Canada. Atmosphere –Ocean, 34, 401–416.

42

Shabbar, A., B. Bonsai, and M. Khandekar, 1997: Canadian precipitation patterns

associated with the Southern Oscillation. J. Climate, 10, 1043–1059.

Smith, T. M., R. W. Reynolds, T. C. Peterson, and J. Lawrimore, 2008: Improvements to

NOAA’s historical merged land-ocean surface temperature analysis (1880-2006). J.

Climate, 21, 2283–2296.

Smyth, G. K., 1996: Regression analysis of quantity data with exact zeroes. In:

Proceedings of the Second Australia–Japan Workshop on Stochastic Models in

Engineering, Technology and Management. TMC, University of Queensland,

Brisbane, Australia, 572–580.

Stahl, K., R. D. Moore, and I. G. McKendry, 2006: The role of synoptic-scale circulation

in the linkage between large-scale ocean-atmosphere indices and winter surface

climate in British Columbia, Canada. Int. J. Climatol., 26, 541–560.

Taylor, B., 1998: Effect of El Niño/Southern Oscillation (ENSO) on British Columbia

and Yukon winter weather. Report 98-02, Aquatic and Atmos. Sci. Division,

Pacific and Yukon Region, Environment Canada, 10 pp.

Thiébaux, H., and F. Zwiers, 1984: The interpretation and estimation of effective sample size. J.

Clim. Appl. Meteor., 23, 800-811.

Trenberth, K. E., 1997: The Definition of El Niño. Bull. Amer. Meteor. Soc., 78, 2771–

2777.

Vimont, D. J., 2005: The contribution of the interannual ENSO cycle to the spatial

pattern of ENSO-like decadal variability. J. Climate, 18, 2080–2092.

Wang, X., F.-F. Jin, and Y. Wang, 2003: A tropical ocean recharge mechanism for

climate variability. Part II: A united theory for decadal and ENSO modes. J.

Climate, 16, 3599–3616.

43

44

Whitfield, P. H., R. D. Moore, S. W. Fleming, and A. Zawadzki, 2009: Pacific decadal

oscillation and the hydroclimatology of western Canada – Review and prospects.

Canadian Water Res. J. (accepted).

WMO, 2009: World Meteorological Organization El Niño/La Nina update; available

online at http://www.wmo.int/pages/prog/wcp/wcasp/enso_updates.html.

Yu, B., A. Shabbar, and F. W. Zwiers, 2007: The enhanced PNA-like climate response to

Pacific interdecadal and decadal variability. J. Climate, 20, 5285–5300.

Zhang, Y., J. M. Wallace, D. S. Battisti, 1997: ENSO-like interdecadal variability: 1900–

93. J. Climate, 10, 1004–1020.