The Earth’s Orbit and Seasonal Radiative Balance

I wanted to better understand why global temperature was highest when Earth was farthest from the sun, so this post is not about climate change.  Instead, it explores the annual timing of the Earth’s natural warming and cooling cycle-driven by the elliptical orbit of the Earth around the Sun. The analysis focuses on deviations from the running average of radiative fluxes and global surface temperature, isolating orbital effects on Earth’s energy balance. For each type of measurement, I used Principal Component Analysis (PCA) to obtain the dominant seasonal variation, applying PCA to multiyear data after subtracting the one-year running average.

NASA’s CERES satellite system provided continuous measurements of incoming and outgoing radiation from March 2000 to July 2024. (Hopefully this effort will continue or be renewed by other systems when satellites reach end of life.)  The measurements include incoming solar flux and the Earth’s reflected short wave and emitted long wave radiation, reported for both “all sky” and “clear sky” conditions. This analysis uses “all sky” data only.

Solar radiation received by Earth varies with its distance from the Sun, following the inverse square law. The Earth’s orbit is elliptical, with an eccentricity of 0.01672, making it nearly circular. While small, this eccentricity causes seasonal changes in solar flux. Calculating the Earth-Sun distance over time requires accounting for the eccentricity, the earth’s orbital period (365.256363 days) and the variable orbital speed (faster near perihelion, slower near aphelion). Finally, Moon’s orbit around the Earth causes a wobble in Earth’s orbit around the Sun so that the day of perihelion varies from year to year. The effect of eccentricity on angle is shown below.

Because the earth’s eccentricity is so small, the ellipse angle is always within 1° of the angle calculated assuming a circular orbit. Although the correction is small, I kept it.

The influence of the moon’s orbit on the day of the perihelion is not as easily predicted. The Moon not only causes the Earth’s axis of rotation to wobble slowly (26,000 years per cycle), it also slightly oscillates the Earth’s distance from the sun. The effect of this oscillation on day of perihelion since 2000 is shown below. Of less importance here is that, because of axis precession, the time of perihelion advances by one day every 58 years.

On average right now perihelion occurs around January 4 with aphelion approximately 183 says later, around July 6.

Below is the Earth-Sun distance versus time of year assuming an orbit eccentricity of 0.01672 and perihelion on Jan. 4. The unit of distance is the astronomical unit, au, which is the average distance between Earth and Sun.

Seasonal Incoming Solar Radiation

 Here is the NASA CERES measurement for incoming solar radiation over the past 25 years.

Below is what PCA (Principal Component Analysis) shows for the annual variation of incoming solar radiation (circles).  Also plotted is the annual variation of inverse square of orbital distance (blue line).

The CERES data shows a seasonal variation in incoming solar flux that closely follows that predicted based on orbital distance. The maximum and minimum dates agree with January 4 and July 6. The “neutral times,” when incoming radiation equals the average, are March 2 and September 4. Between Sept. 4 and Mar. 2, the earth receives more than the average. The rest of the time it receives less.   

Net Radiative Flux

Global temperature is determined by net flux: the difference between incoming radiation and the outgoing reflected plus emitted radiation. If net flux were zero then the earth’s global temperature would remain unchanged. As seen below, the one year running average (blue) of net flux has been increasing, but net flux mostly oscillates around zero.

Here is how net flux deviates from average (circles and red line) compared with the annual variation of inverse orbital distance squared (blue line).

The seasonal variation of the net flux is 23% less than the seasonal variation of incoming solar. The neutral points are shifted to Apr 17 and Aug 31.

Cumulative Heat

Global temperature does not react instantly to net radiative flux. Instead, cumulative heat, the integral of net flux over time, determines warming or cooling. Here is the cumulative heat and its one year running average (blue).

It has been increasing since 2000 at an accelerating rate (with seasonal oscillations).

Below is its seasonal oscillation (circles and red line) compared with net flux (blue line).

The dates of maximum and minimum retained heat correspond to the neutral points of net flux, near April 17 and August 31. How do these dates, April 17 and August 31, compare with dates of maximum and minimum global or world temperature?  Not good.

Global Surface Temperature

Climate Reanalyzer publishes ERA5 daily surface temperature estimates for 6 geographical areas, namely for the world, northern hemisphere, southern hemisphere, tropics (latitudes 23.5°S-23.5°N, about 26% of the earth’s surface), Artic (66.5-90°N, about 13% of the earth’s surface), and Antarctic (66.5-90°S, also about 13% of the earth’s surface). The estimates go back to 1940. Below is the seasonal variation of surface temperature for the northern hemisphere, the southern hemisphere, and the world.

The seasonal variation (root mean square) of the northern hemisphere is 2.4 times larger than that of the southern hemisphere. Note that the seasonal difference between the north and south hemispheres is mostly due to the tilt of the earth’s axis of rotation. The highest temperature for the northern temperature occurs about June 29. This makes sense since the summer solstice is June 21.

The world surface temperature is the average of the northern and southern hemispheres, so its seasonal variation is less than that of either northern or southern hemispheres, but, because of the elliptical orbit, it is not zero. The dates for maximum and minimum world or global temperature are Jun 25 and Jan 10. So why does that not track with the dates of maximum and minimum cumulative heat, April 17 and August 31? Is the heat concentrated differently than the temperature? The answer can be yes due to differing heat capacitances of Earth’s regions. So where is the heat concentrated in April?

Below is the seasonal variation of surface temperature for antarctica, the artic, and the tropics.

The seasonal variations for the Arctic and Antarctic regions (rms of 10.7 and 7.3 °C) are greater than for that of the tropical region (rms of 0.36°C), but neither show a peaking of temperature near April 17. The tropics, however, does peak at April 23, which is close to the April 17 date. This supports the idea that tropical regions are first to absorb and retain the heat, which then distributes globally.

 Linear Combination

Cumulative heat should be a linear combination of temperature changes across regions, weighted by heat capacities. Here is a linear fit using the seasonal temperature variations in tropics, northern hemisphere, and southern hemisphere. Note that the area of tropics (latitudes 23.5°S-23.5°N) includes 13% of each hemisphere, so the areas of the three, namely tropics, northern hemisphere, and southern hemisphere, but are not independent.  

Summary

This post analyses natural seasonal changes in Earth’s radiative energy balance due to its elliptical orbit using satellite and surface temperature data.

• Incoming solar radiation peaks near perihelion (Jan 4) and dips near aphelion (July 6).
• Cumulative heat from the net radiative flux reaches max near April 17 and min near August 31.
• Globally averaged surface temperature, however, lags due to regional differences in heat capacity-with the tropics playing a key role in early heat retention. The max and min dates are June 25 and January 10.

The Earth’s elliptical orbit, though close to circular, creates significant and measurable seasonal oscillations in energy balance and surface temperature.