A visual assessment of Figures 1 and 2b) from the paper suggests that there exists a systematic relationship between the meridional velocity and MSE patterns and the structure of the meridional heat transport. In order to test this hypothesis robustly, we analyse the role played by the v and H anomalies in driving the extreme events.
We begin by relating specific sign combinations of the two anomalies to the poleward and equatorward transport regions seen in Figure 1. In order to do this, the signs of v’ and
H’
for every time-step and at each point of the cross-sectional composite are recorded. Each grid point is then assigned a colour corresponding to the most frequent sign combination. The frequency of this combination must by definition exceed 25%, but clearly varies between grid points. The dominant sign combinations and their frequencies of occurrence for NH DJFs are illustrated in Figure S1.
The central transport core is dominated by poleward advection of warm, moist air.
However, this only accounts for around 62% of the events. The remaining portion is found to be driven by equatorward advection of cold air. The two equatorward transport features are found to be driven by different sign combinations. The one to the east of the extreme event core corresponds to equatorward advection of warm air; the upper-level one to poleward advection of cold air. In these regions, however, the dominant sign combinations account for less than 40% of the events, and no firm conclusion can be drawn at a hemispheric level. These results highlight the significant variability of the v’
and
H’
signals even where the composite transport presents a robust pattern, as discussed in Section 3.2 in the paper.
The sign combination map described above indicates that, at least in some portions of the extreme event composites, there is a measure of synchronisation between the v’ and H’ anomalies. In order to have a more robust insight into how this relates to the

rich transport structure highlighted in Figure 1, we compute composite covariance maps. These are again pressure-longitude composites of all extreme events for a given hemisphere/season combination. We define composite covariance at each individual grid box of the zonal cross-section as:
cov( v’
, H
’) = v’H’ – v’ H’
,
(2) where the overbars denote taking an average of the variable over all extreme events.
Note that this quantity relates meridional velocity anomalies to MSE ones across all extremes, and should not be confused with temporal covariance. When large values of one anomaly correspond to large values of the other one, and the same holds for the smaller values ( i.e.
the two anomalies tend to show a synchronized behavior), the composite covariance is positive. In the opposite case, when large values of one anomaly mainly correspond to small values of the other one, the composite covariance is negative. The sign of the composite covariance therefore provides information on the linear relationship between the two anomalies. The magnitude of the composite covariance is related to the strength of this relationship.
The extreme event composite covariance maps are very similar for all four season/hemisphere combinations. As an example, Figure S2 shows the map for NH
DJFs. The diagonal striping marks regions of equatorward heat transport, identical to those in Figure 1. Note that the figure displays unitless values, normalized relative to the covariance maximum. Comparing this to Figure 1, it can be seen that positive composite covariance corresponds to poleward transport, while negative composite covariance (albeit much smaller than the positive one) generally matches the equatorward transport.

The composite covariance is therefore highest (most positive) where the poleward transport peaks, and vice-versa for the equatorward transport. This indicates that extreme transport events are at least partly phase-driven. The above results are in agreement with those of a spectral analysis of the transport extremes (Messori and
Czaja, 2014). Note that, since composite covariance is not necessarily related to the sign of each variable, these findings are not obvious a priori . Indeed, it is very easy to construct an artificial dataset where poleward transport is generated by v’ and H’ arrays displaying negative composite covariance.