In the assessment of weather predictions, I routinely access the excellent website RAP Real-Time Weather Data. There is one product on this site that is quite informative with respect to tropospheric temperature anomalies on multi-decadal time scale, and it is their “500 mb Z-Anomaly” plots on their GFS model plots.
An example of one of the plots for a 120 hour forecast is given below.
A Northern Hemisphere perspective of these anomalies can be viewed at the Climate Prediction Center of NOAA (see). The contour interval for the 500 mb height anomalies is 120 m. The anomalies are departures from the 1979-95 daily base period means. Above average heights correspond to a warmer than average lower troposphere, while below average heights correspond to a cooler than average troposphere.
What is quite informative about these plots, if you follow them day by day over the year, is that the regions of above and below average 500 mb heights (which is what is displayed in these figures) has not shown evidence of any preference for more above average regions, as would be expected if the troposphere were significantly warming.
Snapshots as given below, of course, represent “just weather”, but if we examine this data over time, we should be seeing a movement since 1979 towards more regions of above average heights, if the troposphere is warming. The relatively small warming that has been reported (e.g. see), is swamped by the much larger regional variations in warming and cooling.