A Simple Model Projecting Following Winter-Spring Climate from Summer ENSO

A Simple Model Projecting Following
Winter-Spring Climate from Summer ENSO
Indices – Applications to the 2010 Vancouver
Winter Olympics and Paralympics
Ruping Mo
Pacific Storm Prediction Centre
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 2009-001
Pacific Storm Prediction Centre
September 2009
Abstract
A weak-to-moderate El Niño event is developing over the equatorial Pacific
Ocean, where monthly mean sea surface temperature (SST) anomalies were from +0.5°C
to +1.5°C in July and August 2009. This study focuses on using correlations between
antecedent El Niño/Southern Oscillation (ENSO) indices and the climatic variables in the
following February and March, these being the time of the 2010 Vancouver Olympic and
Paralymic Winter Games respectively, to construct a predictive model with known skill.
In particular, the most significant cross correlations are between the temperatures of
Vancouver in February and the NINO3 index in the preceding July. The temperatures in
Vancouver in the spring season from March to May are also strongly correlated with
various ENSO indices. Regression models based on these ENSO signals achieve
meaningful scores for temperature predictions in February, March, and May. Predictions
with the July 2009 El Niño condition suggests the monthly mean temperature of Metro
Vancouver will be about 1°C above normal in February 2010 and near normal in March
2010. Less snowfall in Metro Vancouver is expected in February 2010 due to these
warmer conditions.
1
1.
Introduction
El Niño-Southern Oscillation (ENSO) is a manifestation of strong coupling 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 abovenormal SSTs developing in the equatorial Pacific. Its opposite is referred to as La Niña.
ENSO has been linked to climate anomalies around the globe (see Diaz and Markgraf
2000). This study focuses on the ENSO impacts on the weather conditions in Vancouver
of British Columbia (BC), where the next Olympic and Paralympic Winter Games will be
held in February and March 2010, respectively.
Various ENSO indicators have suggested that a weak El Niño is currently forming
over the equatorial Pacific, and a majority of dynamical model forecasts indicate that this
event will reach at least moderate strength over the next few months and last through the
winter of 2009-10 (NOAA 2009; WMO 2009). 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; Fleming
and Whitfield 2009). Here we present an analysis of the correlations between some
ENSO indices and the monthly mean temperature, precipitation and snowfall of Metro
Vancouver in the following winter and spring. The goal is to identify the ENSO signals
that can be used to develop reliable and applicable long-lead climate outlooks for the
upcoming Vancouver 2010 Winter Olympics.
2
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 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. This study
focuses on the period from January 1979 to present. The main reasons for choosing the
post-1978 period are to take advantage of better and more reliable data quality and to
avoid the complexity induced by a major regime shift in the Pacific in the late 1970s
(e.g., Gutzler et al. 2002; Ashok et al. 2007). Some recent studies (Sthal et al. 2006;
Fleming and Whitfield 2009; C. Doyle, personal communication) have indicated that both
of the ENSO and Pacific Decadal Oscillation (PDO) signals can be detected in the
precipitation and temperature records of weather stations in BC. The expected PDO
modulation of ENSO impacts on the conditions of Vancouver is not explicitly explored in
this analysis; it will be addressed in another study using longer data records (Mo et al.
2009).
Commonly used ENSO indices from various sources are employed in this study.
The Southern Oscillation Index (SOI), defined as the difference between the standardized
sea level pressure (SLP) observed at Tahiti of French Polynesia and that at Darwin of
Australia (see Fig. 1), is obtained from the Climate Prediction Center of USA
3
(http://www.cpc.ncep.noaa.gov/data/indices/). A possible drawback of this index is that it
is based on the pressure at two points only and therefore could easily be affected by local
weather disturbances. Generally speaking, large Negative SOI values are associated with
El Niño, and large positive values are with La Niña.
The multivariate ENSO index (MEI), based on a combination of six observed
variables (SLP, zonal and meridional surface winds, SSTs, air temperatures, and
cloudiness) over the tropical Pacific, is considered to be more representative of the
coupled ocean-atmosphere phenomenon of ENSO (Wolter and Timlin 1993, 1998). This
index can be obtained from the National Oceanic and Atmospheric Administration
(NOAA) of USA (http://www.cdc.noaa.gov/data/correlation/mei.data). Large negative
MEI values represent La Niña, and large positive values represent El Niño. In other
words, the MEI is negatively correlated with the SOI.
Four indices based on area-averaged SSTs over the NINO regions – NINO1+2,
NINO3, NINO3.4, and NINO4 (see Fig. 1) – are computed from the NOAA Extended
Reconstructed
SST
datasets
(ERSST
V3b,
available
from
NOAA
at
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.
4
Figure 1: Map of various ENSO index regions. The solid-boundary boxes represent the
NINO regions: 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, i.e., the dot-filled area); and NINO4 (5°S–5°N,
160°E–150°W). The dashed-boundary boxes represent the El Niño Modoki regions
(Ashok et al. 2007; Weng et al. 2007): the central region (Box C: 165°E–140°W, 10°S–
10°N); the eastern region (Box E: 110°W–70°W, 15°S–5°N), and the western region
(Box W: 125°E–145°E, 10°S–20°N).
Trenberth and Stepaniak (2001) have suggested that the zonal SST contrast
between the eastern and central Pacific should be considered to capture the different
evolution of ENSO events. They proposed using the Trans-Niño Index (TNI), which is
given by the difference in normalized anomalies of SST between NINO1+2 and NINO4
regions, to represent the east-west SST gradient along the equatorial Pacific. This
relatively new index may also be useful for predictive purposes (Trenberth and Stepaniak
2001; Kennedy et al. 2009). More recently, Ashok et al. (2007) introduced the El Niño
Modok Index (EMI) to describe the so-called El Niño Modoki (pseudo-El Niño) events
that are characterized by distinct warm SST anomalies in the central Pacific and weaker
cold anomalies in the west and east of the basin. EMI is defined as
EMI  SSTA C  0.5SSTA E  0.5SSTA W
5
(1)
where the brackets represent the area-averaged SST anomalies over each of the three
regions specified in Fig. 1. In this study, the TNI and EMI are also derived from the
ERSST V3b data.
The correlations between the above-mentioned ENSO indices are given in
Table 1. As expected, some of these indices are highly correlated with each other,
implying strong information redundancy in the data set. Among the highest correlations
are 0.92 between NINO3.4 and NINO3, 0.91 between NINO3.4 and MEI and between
NINO3 and MEI, and -0.89 between EMI and TNI. On the other hand, the correlations
between TNI and MEI and between EMI and NINO3 are very low. Ashok et al. (2007)
pointed out that the NINO3 index and EMI have very high correlations with the two
leading principal components, respectively, of the tropical Pacific SST anomalies, and
they likely represent two major orthogonal modes of the ocean-atmosphere coupled
system in the tropical Pacific.
Table 1: Correlation coefficients between various ENSO indices. The time series of the
indices are of 368 months from January 1979 to August 2009. For a two-tailed Student’s t
test with maximum effective sample size, the correlation coefficients required for the
95% and 99% confidence levels are 0.103 and 0.135, respectively.
SOI
MEI
NINO1+2 NINO3
NINO3.4 NINO4
TNI
SOI
1.00
MEI
-0.74
1.00
NINO1+2 -0.48
0.79
1.00
NINO3
-0.63
0.91
0.85
1.00
NINO3.4
-0.72
0.91
0.67
0.92
1.00
NINO4
-0.66
0.75
0.41
0.69
0.88
1.00
TNI
0.17
0.04
0.54
0.15
-0.20
-0.55
1.00
EMI
-0.41
0.24
-0.28
0.08
0.42
0.69
-0.89
6
EMI
1.00
The standardized ENSO indices of the last 12 months are shown in Fig. 2. The
corresponding SST anomalies are given in Fig. 3. It appears that a weak La Niña, or La
Niña Modoki, was present until March 2009, and a canonical El Niño event has been
developing since May 2009. The SST anomalies along the eastern equatorial Pacific
ranged from +0.5°C to +1.5°C in July and August 2009.
Figure 2: Eight ENSO indices of recent months. The data are standardized with respect to
the 1979–2008 climatology. Note that –SOI and –TNI are plotted to facilitate their
comparisons with other indices.
7
Figure 3: Sea surface temperature anomalies (°C) in the Pacific Ocean in recent months.
SSTs are obtained from the NOAA ERSST V3b data sets. Their anomalies are calculated
with respect to the 1979–2008 climatology.
8
3.
Correlation analysis
The cross correlations of the ENSO indices of each month with the monthly mean
temperature of Vancouver (T YVR ) of the same month and the following 12 months were
computed from data of 29 years (either 1979–2007 or 1980–2008). Values of the
correlation coefficient required for the 95% and 99% confidence levels for a two-tailed
Student’s t test are 0.37 and 0.47, respectively. As shown in Fig. 4a for the NINO3 index,
only a few correlations associated with the T YVR in those months from February to June
are statistically significant at the 95% confidence level. The maximum correlation
coefficient is 0.67, occurring when the NINO3 index in July leads the T YVR in February
in the following year. With this maximum correlation, about 45% of variance in
T YVR (Feb) is explained by an ENSO index available seven months earlier. Note that all
those correlations between the T YVR (Feb) and the NINO3 index in those months from
June to February are verified to be statistically significant at the 99% confidence level. In
contrast, all correlations of the NINO3 index with the T YVR in those months from July to
January are not significant at the 95% confidence level.
Lag correlations of T YVR (Feb) with the other three NINO indices and the MEI
(not shown) are similar to, but somewhat weaker than, those with the NINO3 index. For
example, the corresponding maximum correlations are 0.54 with NINO4(Jun) and
NINO4(Oct), 0.58 with NINO3.4(Jul), 0.56
withNINO1+2(Sept), and 0.61 with
MEI(Aug), respectively. As shown in Fig. 4b, the maximum correlation of –SOI with
T YVR (Feb) is 0.61 in September.
9
Figure 4: Lag correlations of ENSO indices of each month with the monthly mean
temperatures of Vancouver (T YVR ) of the same month and the following 12 months. The
labels of the horizontal axis represent the months for ENSO index. They are separated
into 12 groups by the vertical dashed lines. The months for T YVR are color coded, with
black for January, red February, yellow March, blue April, green May, and gray the rest
of months. The first bar and the last bar of each group share the same color and represent
the correlation coefficients with lead time τ = 0 and τ = 12, respectively. The horizontal
blue and red dashed lines mark the correlation coefficients required for the 95% and 99%
confidence levels, respectively, for a two-tailed Student’s t test.
As the mean temperature in March is concerned, Fig. 4a shows that its correlation
with the NINO3 index in previous December is the highest (0.53). Its correlation with
10
NINO3(Jul) reaches a local maximum of 0.49, which is also significant at the 99%
confidence level. In fact, all of its correlations with the NINO3 index in those months
from June to March are significant at the 95% confidence level. Its correlations with the
NINO1+2 index (not shown) are slightly stronger, with a maximum of 0.58 in December.
Fig. 4b shows a maximum correlation of 0.50 between –SOI(Jun) and T YVR (Mar), with a
lead time of nine months.
Significant, long-lead positive correlations between the T YVR in May and the EMI
in some previous months are shown in Fig. 4c. The maximum value is 0.61, achieved by
the EMI in May and June of previous year. The correlations between the TNI and the
T YVR are not shown; most of them are similar to those in Fig. 4c, except for an opposite
sign. It turns out that the correlations of EMI with T YVR in February and March are not
statistically significant; some significant values shown in the previous version of this
manuscript was due to a code error in the computing program.
The correlations between the ENSO signals and the monthly total precipitation
amounts of Vancouver (P YVR ) are shown in Fig. 5. While ENSO may have some
significant impacts on the P YVR in July, September, and October, those significant
correlations with T YVR shown in Fig. 4 have no correspondence with P YVR in Fig. 5. In
particular, there is no strong evidence to support the claim that El Niño events will lead to
drier winters in Vancouver. An El Niño Modoki signal in July or August may suggest
somewhat drier conditions in February of the following year, as indicated in Fig. 5c. Note
that the EMI had a weak negative value in July and had become even weaker in August
of this year (Fig. 2). Therefore, as far as the total precipitation amount is concerned, the
11
El Niño currently developing over the tropical Pacific is not expected to be much
different from normal in the coming winter.
However, ENSO does have a significant effect on the snowfall amounts of
Vancouver
(S YVR )
in
February
Fig. 6. The maximum negative
12
and
March,
as
shown
in
Figure 5: Same as Figure 4, except for the monthly total precipitation amounts of
Vancouver (P YVR ).
Figure 6: Lag correlations of the NINO3, NINO4, and TNI with the monthly snowfall
amounts of Vancouver (S YVR ); see Fig. 4 for further details.
correlations of the NINO3 with February S YVR are consistent with those significant
positive correlations with February T YVR in Fig. 4a. In other words, for Metro Vancouver
El Niño events will lead to warmer conditions in February, and less snowfall to the sea
13
level because of the warmer conditions. Note that the S YVR in February is better
correlated with the NINO4 index than with the NINO3 index. The most significant
correlation in Fig. 6a is -0.46, occurring when the July NINO3 index leads the S YVR in
February in the following year. The best correlation in Fig. 6b is -0.57 between the
NINO4 in June and the S YVR in February. Incidentally, the maximum correlation between
the NINO4 and the T YVR is 0.54, occurring when the June NINO4 leads the T YVR in
February (figures not shown). This is less than the maximum correlation of 0.67 achieved
by the NINO3 in July (see Fig. 4a).
Although the NINO3 index has some strong positive correlations with the T YVR in
March (Fig. 4a), its negative correlations with the S YVR in March are not statistically
significant (Fig. 6a). Instead, Fig. 6c indicates that S YVR in March is significantly
correlated with the TNI in previous months from September to January.
4.
Regression models and predictions
Results from the correlation analysis in the previous section indicate the possibility of
ENSO-based long-lead prediction for Metro Vancouver in February and through the
spring season. In this section, some linear regression models are developed and applied to
produce temperature and snowfall outlooks for the 2010 Vancouver Winter Olympics.
Let Y (t ) be the variable to be predicted (e.g., T YVR or S YVR ) – the predictand. The
first step is to determine a least squares estimate of Y (t ) based on observations of M
predictors x1 , x 2 ,  , x M ,
YM (t )  a 0  a1 x1 (t   1 )  a 2 x 2 (t   2 )    a M x M (t   M ),
14
(2)
where Y M represents the least squares estimate of Y, the regression parameters
a 0 , a1 , , a M can be determined by the method of least squares, and the τ values represent
lead times.
In this study, skilful predictors are selected from the eight ENSO indices with
3    12 months, using a cross-validation procedure combined with a goodness-of-fit
test with the partial F statistic. The procedure begins with computing simple linear
regressions between each of the available M predictors and the predictand. The predictor
whose performance is the best among all candidate predictors, and is significantly better
than the trivial forecast based on climatological mean of the predictand, is chosen as the
first predictor. The model performance is measured by the mean square error (MSE) skill
score, MSESS, defined as (see Murphy, 1988),
MSESS = 1 – MSE(prediction) / MSE(climatology).
(3)
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   to  1 , 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
( N  1 ) 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
MSE(prediction).
MSE(climatology) is simply the variance of the predictand. The predictor with highest
15
positive MSESS will be chosen as the first variable to enter the regression model,
provided that it also passes the significance test of the partial F statistic (see Kleinbaum et
al. 1988 for an explanation of the F statistic).
After selecting the first predictor, trial multiple regression equations are
constructed using the first selected variable in combination with each of the remaining
M–1 predictors, and the second predictor is chosen as the one that does the best to
increase the MSESS and passes the significance test of the partial F statistic. This
selection procedure is repeated until no further skillful predictors can be found.
Table 2 lists a few models built from the above-mentioned procedure. Their skills
are measured by the MSESS. Their forecasts for 2010, together with the climatological
means, are given in the last column. For the T YVR in February, NINO3 in July of the
previous year is the obvious choice as the first predictor given the significant correlation
shown in Fig. 4a. The SOI in September is chosen by the model as its second predictor.
Its correlation with T YVR (Feb) is -0.61 (Fig. 4b). The third and last pick of SOI(Jun)
comes as a complete surprise. The correlation of SOI(Jun) with T YVR (Feb) is only -0.11,
which is not significantly different from zero. However, the addition of this predictor
greatly improves the model performance.
Figure 7 shows the cross-validation and prediction of T YVR (Feb) with NINO3(Jul)
as the only predictor in the regression equation. Obviously, this simple empirical model is
unable to keep up with every El Niño/La Niña episode. For example, the warm condition
associated with the 1986-87 El Niño and the moderate cold condition with the 2008-09
La Niña are not predicted. The extreme cold conditions in 1989 and 1990 are noticeably
under-forecast. The moderate cold conditions forecast for 2000 and 2008 are false alarms,
16
although a strong La Niña was developing in 1999-2000. The warm condition in 1991
and cool conditions in 1993 and 1994 are not forecast. But they are not ENSO-related,
anyway. Otherwise this simple model performs reasonably well for forecasting warm
conditions associated with the El Niño episodes of 1982-83, 1991-92, and 1997-98, and
the cool conditions associated with the La Niña episodes of 1981-82, 1984-85, 1985-86,
and 2000-01. With respect to the current El Niño event, the model predicts a moderate
warm condition (1°C above normal) for February 2010. Note that in this model the
regression on the NINO3 index is linear. However the blue dots in the scatter plot
(Fig. 7b) do not stay exactly on a straight line. The slight scatter is caused by the leaveone-out cross-validation, which generates N slightly different linear regression equations
to produce N predictions. It is also shown in Fig. 7b that the median is somewhat higher
than the mean of the observed T YVR (Feb), suggesting a left-skewed distribution of the
data. The skew is nevertheless slight and acceptable. The goodness-of-fit, or lack of
goodness-of-fit, of the model is shown in Fig. 7c.
The improvements from including the second (SOI in September) and third (SOI
in June) predictors into the regression model for T YVR (Feb) are shown in Fig. 8. The
2
cross-validation squared multiple correlation ( RCV
) increases from 0.35 to 0.41, and the
MSESS increases from 0.39 to 0.44, after the second predictor is added. With all three
2
and MSESS further increase to 0.56 and 059,
predictors in the equation, RCV
respectively. Comparing Fig. 8a with Fig. 7a shows that the 3-predictor model gives
much better forecasts for the cold condition with the 1988-89 La Niña and the warm
condition with the 1986-87 El Niño. Prediction of the temperature in February 2010 from
this 3-prediction can be given in early October when the SOI in September is available.
17
The best regression model for T YVR (Mar) is shown in Fig. 9. This model takes
SOI(Nov) and SOI(Jun) in the previous year as its first and second predictors. It is much
less skillful than the model for T YVR (Feb). Since SOI(Nov) of this year has not yet
available, the second best model, which takes SOI(Jun) and NINO4(May) as its first and
second predictors, is used to make the prediction of the monthly mean temperature for
March 2010 (Fig. 10). The predicted mean temperature is 6.9°C, which is very close to
the climatological mean of 6.8°C in March. An update of this forecast will be given when
SOI(Nov) of this year is available.
Table 2: ENSO-based long-lead regression models and their predictions for 2010. Model
marked by "†" represents the second best choice, which may be less skillful but has
2
are the squared multiple correlation of the simulation and
longer lead time. R 2 and RCV
cross-validation, respectively. MSESS is the mean square error skill score defined by
Eq. (2). F p is the partial F statistic (see Kleinbaum et al. 1988). F p * indicates that the
contribution of the corresponding predictor to the prediction skill, given others already in
the model, significantly contributes to the prediction skill at the 90% confidence level;
F p ** indicates the contribution being significant at the 95% confidence level.
Predictand
Predictors
T YVR (Feb)
1st: NINO3(Jul) τ = 7
nd
2
R 2 / RCV
/ MSESS / F p
0.44 / 0.35 / 0.39 / 21.56**
Prediction (climate)
5.8°C (4.8°C)
2 : SOI(Sept) τ = 5
0.51 / 0.41 / 0.44 / 4.02*
3rd: SOI(Jun) τ = 8
0.65 / 0.56 / 0.59 / 10.32**
1st: SOI(Nov) τ = 4
0.32 / 0.24 / 0.28 / 13.25**
2nd: SOI(Jun) τ = 9
0.43 / 0.33 / 0.36 / 5.15**
1st: SOI(Jun) τ = 9
0.27 / 0.19 / 0.23 / 10.16**
6.7°C (6.8°C)
2nd: NINO4(May) τ = 10
0.35 / 0.22 / 0.25 / 3.30*
6.9°C (6.8°C)
S YVR (Feb)
1st: NINO4(Jun) τ = 8
0.26 / 0.13 / 0.17 / 10.06**
2.4 cm (6.3 cm)
S YVR (Feb)
1st: NINO3(Jul) τ = 7
0.22 / 0.13 / 0.17 / 7.77**
1.2 cm (6.3 cm)
T YVR (Mar)
T YVR (Mar)†
S YVR (Mar)
st
1 : TNI(Oct) τ = 5
0.20 / 0.07 / 0.10 / 6.81**
2nd: EMI(Jun) τ = 9
0.32 / 0.17 / 0.20 / 5.02**
18
Figure 7: Cross-validations and prediction of the monthly mean Vancouver temperatures
(°C) in February from the regression model with the NINO3 index in July of the previous
year. (a) The hindcast anomalies from the leave-one-out cross-validation and the
corresponding observations up to 2009, with the last blue bar being the real prediction for
February 2010. (b) The scatter plot of the hindcast (blue dots) and observed (red dots)
temperatures; the horizontal green and black lines mark the median and climatological
mean of the observations, respectively. (c) A plot of observed versus predicted
temperatures.
19
Figure 8: Cross-validations of the monthly mean Vancouver temperatures (°C) in
February from the multiple regression models with two and three ENSO indices as
predictors, respectively. The green color represents the model with NINO3(Jul) and
SOI(Sept) as predictors, and the blue color represents the model with NINO3(Jul),
SOI(Sept) and SOI(Jun) as predictors.
20
Figure 9: Cross-validations of the monthly mean Vancouver temperatures (°C) in March
from the regression models with one and two ENSO indices as predictors, respectively.
The green color represents the model with SOI(Nov) as the solo predictor, and the blue
color represents the model with SOI(Nov) and SOI(Jun) as predictors.
21
Figure 10: Cross-validations and prediction of the monthly mean Vancouver temperatures
(°C) in March from the regression models with one and two ENSO indices as predictors,
respectively. The green color represents the model with SOI(Jun) as the solo predictor,
and the blue color represents the model with SOI(Jun) and NINO4(May) as predictors.
Two equally skillful (or equally unskillful) regression models for S YVR in
February are shown in Fig. 11 and Fig. 12, respectively. As shown in Fig. 6, the NINO4
in June achieves a better correlation with S YVR in February than the NINO3 in July does.
In Table 2, however, their regression prediction skills appear to be indifferent. The model
22
with the NINO4 index in June as the predictor (Fig. 11) produces fair to good snow
forecasts for 1981, 1983, 1986, 1989, 1992, 1996, 1998, 2001, 2003, and 2005–2007. The
heavy snow in 1985 (27.3 cm) and the extreme snowy condition in 1990 (45.4 cm) are
poorly under-forecast by this model, and the snow forecasts given to 1995 and 2000 are
obviously wrong. Its prediction of snowfall amount for February 2010 is 2.4 cm. The
model with NINO3 in July as the predictor (Fig. 12) achieves fair to good forecasts for
1983, 1984, 1986, 1989, and 1992. It also under-forecast the snowy conditions in 1985
and 1990. Its prediction of snowfall amount for February 2010 is 1.2 cm. Its over-forecast
of the negative anomaly in 1998 is interesting. This particular forecast of negative
anomaly corresponds to an unrealistic negative snowfall amount, as shown in the scatter
plot in bottom panel of Fig. 12. It serves as a reminder that linear regression may not be
an appropriate model for snowfall amount, whose distribution is far away from normal. In
fact, the apparent difference of the median from the climatological mean of the observed
snowfall amounts in the scatter plot indicates that the data distribution is right-skewed.
The goodness-of-fit plots in Fig. 11 and Fig. 12 also show the obvious lack of goodnessof-fit of these linear models.
In regression analysis, and in statistical tests of significance in general, it is
usually required that the data be normally distributed (see Kleinbaum et al. 1988). Stidd
(1953) showed that although the distributions of original precipitation amounts are highly
right-skewed, the cube roots of precipitation amounts are often distributed normally (also
see Kandall 1960). If the cube-root transformation is applied to the snowfall data S, i.e.,
Z = S1/3, then a linear regression on Z
M
Z M (t )  a 0   a m x m (t   m )
m 1
23
(4)
is equivalent to a nonlinear regression on S ,
3
M


S M (t )  a 0   a m x m (t   m ) .
m 1


(5)
Figure 11: Same as Figure 7, except for the snowfall amounts in February (cm) based on
the NINO4 index in June. The prediction of the snowfall amount is 2.4 cm, as compared
to the climatology of 6.3 cm.
24
Figure 12: Same as Figure 7, except for the snowfall amounts in February (cm). The
prediction of the snowfall amount is 1.2 cm, as compared to the climatology of 6.3 cm.
One can apply a least-squares regression analysis on Eq. (4), and transform the
final solutions back to the original data. Figure 13 shows the results derived from the
cute-root regression model for S YVR (Feb) with NINO3(Jul) as the predictor. A
comparison with Fig. 12 indicates that the transformation leads to noticeable
improvement. In particular, no significant below-zero snowfall amounts are forecast in
Fig. 13. The cube-root climatological mean, defined in the caption of Fig. 13, is very
25
close to the climatological median, suggesting the distribution of the transformed data is
closer to the normal distribution.
Discussions of the regression model for S YVR will be added in the next update of
this manuscript when October data are available.
Figure 13: The cube-root regression model for S YVR (Feb), with NINO3(Jul) as the
predictor. Note that the anomalies in (a) is with respect to the cube-root climatology
 (S

3
YVR
)1 / 3 / N , which is 1.4 cm in this case (the golden line in the scatter plot), as
compared with the simple climatology
S
YVR
/ N , which is 6.3 cm (the black line in the
scatter plot). The prediction of snowfall amount for February 2010 is 0.2 cm.
26
5.
Summary and discussions
The ENSO impacts on the monthly mean weather conditions in Metro Vancouver have
been examined in a lag correlation perspective. We focus on two issues in this study: 1)
How, when, and to what extent are the weather conditions in Metro Vancouver
influenced by the ENSO events? 2) Is it possible to provide useful outlooks for Metro
Vancouver based on the long-lead ENSO signals? It is shown that the strong ENSO
signals are not detectable all year round in the Vancouver area. Surprisingly, the normal
conditions in Vancouver persist even through most parts of the winter (DecemberJanuary) 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 0.67, about 45% of the February temperature variance
during the period 1980–2008 can be explained by the NINO3 index in July of the
previous year. The significant change of temperatures in turn affects the February
snowfall in Vancouver. Strong and more complicated ENSO impacts are detected in
Vancouver temperatures through the spring season.
The long-lead ENSO signals identified in our correlation analysis are used to
develop statistical prediction models for Metro Vancouver. With the current El Niño
conditions in the tropical Pacific, these statistical models suggest that Vancouver monthly
mean temperature will be 1°C above normal in February 2010, and will be near normal in
March 2010. The total snowfall amounts in February will be in the range of 0–3 cm at sea
level. Given the standard atmospheric lapse rate of 6.5°C/km, the 1°C warmer condition
in February implies that the snow level would be 150 meters above normal. While these
long-lead projections could provide some valuable information to the 2010 Vancouver
27
Winter Olympics and Paralympics, one should keep in mind that they are just some
climate projections rather than deterministic predictions. In addition, these projections are
based on the ENSO impacts alone. Other climate systems, such as the PDO, 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, 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. Other 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.
Acknowledgments. The author would like to thank Trevor Smith, David Jones, Brad
Snyder, Ian Okabe, and Paul Joe for their encouragements and helpful discussions.
Constructive suggestions and comments on an earlier version by Paul Whitfield and Chris
Doyle helped to improve this manuscript.
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