EMULATE Report
D11: Surface Temperature Anomalies and SLP Cluster
Association
Pascal Yiou, Nicolas Fauchereau
Laboratoire des Sciences du Climat et de l’Environnement, UMR CEA-CNRS-UVSQ, Gifsur-Yvette, France
Introduction
The goal of this deliverable is to determine patterns of co-variations between pressure and
temperature patterns over the last 150 years. Since we are dealing with non-Gaussian and
qualitative variables (the cluster attribution is a qualitative discrete variable), we opted here
for a statistical methodology that is not based on the conventional linear correlation. This
brings a more accurate picture of the cluster/temperature association than a correlation
between seasonal averages of cluster frequencies and temperatures because it accounts for the
information contained in the daily data.
Datasets
We used the seasonal clusters of sea-level pressure (SLP) from the EMSLP data set obtained
by Andreas Philipp, and the daily mean temperature (TG) of the ECA dataset.
We considered three-month seasons (MAM, JJA, SON, DJF) for SLP clusters and surface
temperature. Daily temperature anomalies were estimated from an estimate of the daily
seasonal cycle from 1961 to 1990. The association between SLP clusters and temperature was
hence done on temperature anomalies, to avoid seasonal drifts during MAM and SON.
The number of regimes varies from one season to another, as obtained by A. Philipp
(Deliverables D5 & D6) as shown in Table 1.
Season months
Number of clusters
MAM
11
JJA
6
SON
8
DJF
9
Table 1: Number of clusters for each season obtained by A. Philipp with a simulated
annealing method on the EMSLP dataset.
In the ECA data set, we kept the station records that start before 1900 and that have less than
20% of missing or questionable data. Thus we kept 76 stations out of 288.
Methodology
Correlations
For each regime (and each season), we computed the correlations (Pearson and Spearman)
between the regime frequencies and the anomalies mean temperature TG. We focus on the
Spearman correlation (or rank correlation), which is more appropriate here since the regime
frequencies are discrete variables and a priori do not follow a Gaussian distribution. The main
caveat of the correlation plots is that some SLP clusters are very rare during the 20 th century,
which leads to very few different values of cluster frequencies. Thus, the correlation results
with “rare” clusters should be taken with caution.
Regime-Temperature association
For each station and each season, we determined the 0, 20, 40, 60, 80 and 100th quantiles of
temperature anomalies. Therefore we can define five categories of temperature anomalies:
“very cold”, “colder than normal”, “median”, “warmer than normal”, “very warm”. Those
five categories have the same probability of occurrence, namely 20%. The temperatures
associated with the quantiles are, of course, variable from one station to another, but the
quantile occupation is a more robust diagnostic.
For each season, each station and each quantile of temperature, we determined the number of
days spent in each SLP cluster. Thus, for each season and each station, we obtain a
contingency table connecting the frequency of clusters with the temperature anomalies. For
example, the Paris Montsouris station in JJA yields the following contingency table (Table 2).
Very cold
Cold
Median
Warm
Very warm
Cluster 1
548
667
693
606
539
Cluster 2
471
515
569
748
908
Cluster 3
618
439
356
285
272
Cluster 4
246
228
208
154
89
Cluster 5
33
58
85
105
103
Cluster 6
6
5
7
4
2
Table 2: Number of days spent in each cluster of SLP and each quantile category of TG
anomalies in Paris (Montsouris) in the Summer (JJA). The numbers in bold indicate the
maximum for each row and indicates the optimal temperature range for each cluster.
In the end, we determine the most probable quantile of temperature for each cluster. This
operation makes the association between clusters and temperature anomalies regardless of the
relative frequency of each cluster. This approach generalizes the one of Yiou and Nogaj
(Geophys. Res. Lett., 2004) who mainly focused on extreme quantiles (above the 90 th and
below the 10th quantiles).
Results
The correlations show some spatial coherence, although they are generally very small and
barely significant for MAM, JJA and SON seasons (Figure 1 to Figure 4). As expected, the
significance levels increase during the winter. Winter (DJF) regimes 1 and 5 have the highest
correlations with temperatures. Those correspond to regimes of the positive phase of the
NAO, and an Atlantic ridge and a Siberian high.
For all seasons, we observe an interesting spatial coherence of the cluster/TG association,
with north-south and east-west gradients (Figure 5 to Figure 8). This association seems to be
enhanced for “very cold” or “very warm” anomalies, which is surprising because all quantile
categories are equiprobable. The spatial patterns are rather similar to those identified by
correlation, but they have more contrast, especially over stations where correlations are weak
or not significant. The association analysis emphasizes that short-lived events (i.e. a few days)
of cold or warm temperatures may have little impact on the seasonal mean. For instance,
cluster No. 6 in JJA favours “on average” colder temperatures, but it has a rather low
frequency, and 7 times out of 24 (i.e. a relative majority), temperature will be in the median
quantile in Paris.
Figure 1: Spearman (rank) correlation coefficient between regime frequency and
temperature for the Winter (DJF) season.
Figure 2: Spearman (rank) correlation coefficients between regime frequency and
temperature for the Spring (MAM) season. The colour codes indicate the correlations
for each station.
Figure 3: Spearman (rank) correlation coefficients between regime frequency and
temperature for the Summer (JJA) season.
Figure 4: Spearman (rank) correlation coefficient between regime frequency and
temperature for the Autumn (SON) season.
Figure 5: Association between SLP clusters and TG anomalies in the winter (DJF).
Figure 6: Association between SLP clusters and TG anomalies in the spring (MAM).
Figure 7: Association between SLP clusters and TG anomalies in the summer (JJA).
Figure 8: Association between SLP clusters and TG anomalies in the autumn (SON).