I thought it would be an interesting exercise to look at the annual change in global mean surface temperature (GMST) in the atmosphere at 2 meters above ground level versus the annual change in solar radiation incoming (SRI) at the top of the atmosphere (TOA).

The earth’s orbit is slightly elliptical. Eccentricity is a measure of the departure of an ellipse from a true circle. The earth’s eccentricity varies over long time scales and is estimated to have ranged from a low of 0.000055 to a high of 0.0679, with a geometric mean of 0.0019. The present eccentricity is 0.017 and decreasing very slowly. That doesn’t seem like much, but the earth’s distance from the sun currently increases by 3.4% over the course of a year from the minimum distance in early January to the maximum distance in early July. That variation in distance causes about a 6.8% increase in TOA SRI relative to the minimum amount at the greatest distance in early July in order to reach the maximum amount at closest distance in early January, assuming a constant output of radiation from the sun.

The US National Aeronautical and Space Administration (NASA) Clouds and the Earth’s Radiant Energy System (CERES) measurements from satellites include TOA SRI. I downloaded monthly CERES TOA SRI for the period from March 2000 through July 2018. I also have compiled monthly estimates of GMST from the Climate Forecast System Reanalysis (CFSR) output of initial conditions four times per day, with monthly data prior to 2010 provided by the University of Maine Climate Change Institute (UM CCI) and data from 2010 through 2018 calculated from the Climate Data Assimilation System (CDAS) output of 2-meter surface air temperature.

A time series graph comparing TOA SRI with GMST is provided in Figure 1 below (click to enlarge). It shows the annual cycle of GMST with a peak in July and minimum in January, whereas the TOA SRI peaks in July with a minimum in January – the complete opposite. At first, this seems counter-intuitive since increased incoming solar radiation should cause increased temperature and yet the data show the opposite. My guess is that there is a time lag mediated primarily by the oceans and possibly also affected by the much greater percentage of land in the northern hemisphere, but I have not read up on the subject. This graph also includes centered running 12-month averages (Run 12) for both TOA SRI and GMST.

Figure 2 below compares the CERES TOA SRI with the CFSR Northern Hemisphere (NH) mean surface temperature. The phase of the annual cycle in temperature is similar to that of the global temperature cycle and is nearly opposite the phase of the TOA SRI cycle. Notice that the amplitude of the annual temperature cycle is much larger than the global cycle.

Figure 3 below compares the CERES TOA SRI with the CFSR Southern Hemisphere (SH) mean surface temperature. The phase of the annual cycle in temperature is very close to the phase of the TOA SRI cycle, but advanced forward by about a month. Notice that the annual temperature cycle is larger than the global cycle, but not near as large as the NH cycle.

Figure 4 below compares the CERES TOA SRI with the CFSR tropics (30N-30S) mean surface temperature, which covers the 50% of the global surface that receives most of the incoming solar energy.

The not quite linear cyclical nature of the relationship between SRI and GMST is illustrated by the scatter plot in Figure 5 below.

By lagging the GMST by 6 months, the relationship to TOA SRI looks more meaningful, as seen in Figure 6 below.

I calculated and compiled annual statistics for each year. During the study period, the 2001-2017 TOA SRI average of the 17 annual averages was 340.023 watts per meter squared (watts/m^{2}) with a standard deviation of only 0.087 watts/m^{2}. The monthly averages ranged from 329.113 to 351.516 watts/m^{2}. The annual range in monthly TOA SRI averaged 21.998 watts/m^{2} with a standard deviation of only 0.106 watts/m^{2}. The highest annual range was 21.838 and lowest 22.261 watts/m^{2}. The average percentage of the annual range relative to the lowest month each year was 6.682%. Note that I did not bother to weight the annual averages based on number of days per month because I do not expect a significant difference.

Similarly, the 2001-2017 average of the 17 annual averages of GMST was 287.810 Kelvin (K) with a standard deviation of 0.133 K and a range in monthly averages from 285.505 K to 289.864 K. The lowest annual average was 287.735 K in 2008 and the highest was 288.051 K in 2016. The annual range in monthly GMST averaged 3.775 K with a standard deviation of 0.166 K and varied from 3.511 K to 4.128 K.

For 2001-2017, the CFSR monthly surface temperature data shows an average annual range of 12.589 K for the northern hemisphere and an average annual range of 5.227 K for the southern hemisphere. The southern hemisphere cycle is only one month delayed from the TOA SRI cycle. Both of the hemispheric cyclical temperature swings are larger than the global swing and include both seasonal earth tilt plus eccentricity effects. The global swing should be the net remainder resulting from the eccentricity induced TOA SRI effect.

**Initial Thoughts
**

So, if we assume that the annual range in TOA SRI is the primary driver for the annual range in GMST, then we can calculate that GMST rises (or falls) by 3.775/21.998 = 0.172 K per 1 watt/m^{2} of TOA SRI change. The implication is that if a doubling of CO_{2} causes a radiative forcing of 3.7 watts/m^{2}, the corresponding rise in GMST would be 3.7 x 0.172 = 0.635 K and this would include any feedbacks that normally occur in the earth system over an annual cycle. The main difference is that the ramp up in solar input from orbital eccentricity occurs over only a 6 month period each year, whereas the doubling of CO_{2} might take on the order of a century. However, both are responses to changes to the earth’s radiation balance. So far, I have not been able to think of any compelling reasons why the difference in time scales would make much difference in the resulting effect on GMST. Possibly the short period cycling of the solar input may not allow enough time to reach full impact on GMST in either direction, leading to a quasi-steady state oscillating result?

I’m afraid this assessment may be too simplistic or that I may have overlooked some important influences. Thus, I’m not at all certain this approach is a valid method for estimating the effect on GMST from a doubling of CO_{2}. I will be interested hear what readers have to say and I would be especially interested in learning how well the global climate models handle this annual cycling of both TOA SRI and GMST.

**After Further Review**

I’m now seeing that the annual cycle in global temperature is dominated by the seasonal cycle related to the earth’s axial tilt. I thought it might still be possible to estimate the effects of eccentricity on the seasonal cycle in each hemisphere, and from that result, estimate the net effect on the global temperature cycle from eccentricity. However, I found that backing out a rough estimate of the effect of eccentricity actually increased the global annual temperature range, because it increases the NH annual temperature range more than it decreases the SH annual temperature range. Consequently it does not appear possible to determine the effect of eccentricity on global temperature without using a climate model to test the effect of varying degrees of eccentricity. Like many things I’m learning about climate … it is very complex.

**References**

Eccentricity discussion:

https://en.wikipedia.org/wiki/Milankovitch_cycles

CERES project description:

https://en.wikipedia.org/wiki/Clouds_and_the_Earth’s_Radiant_Energy_System

CERES data download:

https://ceres.larc.nasa.gov/order_data.php

UM CCI Reanalyzer:

https://climatereanalyzer.org/

CDAS monthly average downloads:

https://nomads.ncdc.noaa.gov/modeldata/cfsv2_analysis_monthlymeans_pgb/

Climate sensitivity discussion:

https://en.wikipedia.org/wiki/Climate_sensitivity

Earth’s energy budget discussion:

https://en.wikipedia.org/wiki/Earth%27s_radiation_balance