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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: [email protected]
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.
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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
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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
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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.
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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.
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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.
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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.
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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
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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°
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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
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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.
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FIGURE 4 (continued).
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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.
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FIGURE 6: Same as Fig. 5, except for TYVR in March.
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FIGURE 7: Same as Figure 4, except for SPI of the total precipitation amounts in Vancouver (PYVR).
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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
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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
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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
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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)
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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.
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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).
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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
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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
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