We construct and analyze climate networks based on daily satellite measurements of temperatures and geopotential heights. We show that these networks are stable during time and are similar over different altitudes. Each link in our network is stable with typical 15% variability. The entire hierarchy of links is about 80% consistent during time. We show that about half of this stability is due to the spatial 2D embedding of the network, and half is due to physical coupling mechanisms. The network stability of equatorial regions is found to be lower compared to the stability of a typical network in non-equatorial regions.
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