  In recent years extensive studies on the Earth's climate system have been
carried out by means of advanced complex network statistics. The great majority
of these studies, however, have been focusing on investigating correlation
structures within single climatic fields directly on or parallel to the Earth's
surface. Here, we develop a novel approach of node weighted coupled network
measures to study correlations between ocean and atmosphere in the Northern
Hemisphere extratropics and construct 18 coupled climate networks, each
consisting of two subnetworks. In all cases, one subnetwork represents monthly
sea-surface temperature (SST) anomalies, while the other is based on the
monthly geopotential height (HGT) of isobaric surfaces at different pressure
levels covering the troposphere as well as the lower stratosphere. The weighted
cross-degree density proves to be consistent with the leading coupled pattern
obtained from maximum covariance analysis. Network measures of higher order
allow for a further analysis of the correlation structure between the two
fields and consistently indicate that in the Northern Hemisphere extratropics
the ocean is correlated with the atmosphere in a hierarchical fashion such that
large areas of the ocean surface correlate with multiple statistically
dissimilar regions in the atmosphere. Ultimately we show that, this observed
hierarchy is linked to large-scale atmospheric variability patterns, such as
the Pacific North American pattern, forcing the ocean on monthly time scales.
