Observations indicate that the seasonal cycle imposes a regular change in surface temperature. The surface temperature variation, in turn, imposes a cycle in outgoing longwave radiance (OLR) as well as in absolute atmospheric humidity. This strong variation has some relevancy to predicted climate variations of a longer time frame.
The CFS Reanalysis data indicates the strong covariance of OLR with surface temperature:
These covariances are dominated by the Northern Hemisphere ( because of the large fraction of land mass in the Northern Hemisphere ) and in reality, the seasonal variation is part of the bipolar oscillation between Northern and the smaller Southern variation:
Never the less, the global average seasonal cycle ( which is quite large, around 4C ), provides an opportunity to examine variation in the greenhouse effect as we see in the chart of each months Emissive Temperature versus Surface Temperature:
The CFS data provides the Outgoing Longwave Radiance.
The OLR = sigma * Te^4 where Te is the emissive temperature.
So Te is the fourth root of OLR/sigma.
In the image above, we note:
1. The ‘unity line’ is that where Te = Ts. For a planet without a greenhouse gas atmosphere, points are on this line.
2. The slope of the observed line reflects the feedbacks of the system. A slope of one indicates no change in the greenhouse effect with temperature.
3. The difference between an observed point and the ‘unity line’ indicates the ‘greenhouse effect’. That is, the Greenhouse effect is the difference between the Emissive temperature and the Surface temperature.
4. A line is not necessarily the best representation of the points of seasonal variance, but for the range of observed values, it serves to make the points about feedback and greenhouse effect.
Since in the seasonal cycle, water vapour varies with temperature, the water vapour feedback should be reflected in the plot of emissive temperatures. In this plot, as surface temperatures increase, the difference between the unity line and surface temperatures also increases. This represents a positive feedback.
Of course, other things are changing through the course of the seasons. Dynamics move various features ( jet streams, ITCZ, ridges, etc. ) around. And there are seasonal changes with how much energy is stored and released within the oceans.
Never the less, the seasonal variation is a useful analogue for certain aspects of emissions to space resulting from temperature change.