From Watts Up With That?

Richard Willoughby

Summary

This article examines Earth’s orbital precession and its influence on the solar radiation reaching Earth.  It then considers how the seasonal changes in solar EMR are contributing to observed changes in Earth’s climate.

A simple matrix of Earth’s climate zones and annual seasons is introduced to provide a coherent basis for comparing changes from year-to-year and the annual anomalies to the average of the years 1980 to 2010.

Introduction

Earth’s orbit around the barycentre of the solar system and the Sun’s movement relative to the barycentre causes a continually evolving geometric relationship between Earth and Sun.  The geometry of the relationship can be reduced to two variables at any point in time – the distance between their respective centres and the declination of Earth’s equatorial plane to the rays from the sun.  These two variables can be used to calculate the solar electro-magnetic radiation (EMR) reaching the top of Earth’s atmosphere (ToA) and its zenith angle at any latitude on Earth. 

NASA JPL provides daily declination and distance data through the Horizons portal.  Charts 1 and 2 show the values as determined for the two variables for every day of 1850.  Chart 2 also includes the daily ToA EMR based on a solar constant of 1361W/m².

In 1850, Earth reached one Astronomic Unit (AU) distance from the Sun on day 91, which was 11 days later than the March equinox on day 80.  The maximum distance between Earth and Sun in 1850 was 1.01676AU on day 184; 12 days after the June solstice.  Taking a solar constant of 1361W/m², the minimum zenith solar EMR was 1306.5W/m².  The distance again reached 1AU on day 275; 9 days after the September equinox.  The minimum distance of 0.98323AU occurred on the last day of the year, which was 9 days later than the December solstice.  The peak solar EMR at zenith in 1850 was 1407.8W/m² or 101.3W/m^2 above the minimum. 

Changes in Declination & Distance from 1850 to 2040

There has never been and never will be two days in Earth’s existence with identical Earth-Sun declination and distance.  Charts 3 and 4 indicate how these variables have, and will, change from 1850 to 2040 as daily anomalies with respect to 1850.  Each of the charts has 69,761 individual points so only the trends and significant variation are evident.

The anomalous distance is diverging due to the orbital eccentricity reducing; distance at perihelion is increasing while distance at aphelion is reducing.  Both the distance and declination anomalies exhibit a step change around 1900.  The declination anomaly exhibits its maximum in 1904 of 0.419 degrees then declines to 1992 before increasing again.

The significance of these changes in Earth’s geometric relationship to the Sun can be best appreciated by considering the spatial and temporal variation of solar EMR reaching Earth’s atmosphere for specified time and latitude.  Chart 5 looks at the most significant difference for the 190 years examined here.  It compares the difference in daily average intensity for both 60N and 60S through 2037 relative to 1912. 

The peak difference at 60N of 7.245W/m² occurs on day 91.  The difference at minimum for 60N is 7.235W/m² occurring on day 241; 150 days after the maximum difference.  The minimum and maximum differences for 60S occur on day 66 at 7.31W/m² down and day 285 at 7.155W/m² up with a separation of 219 days between the minimum and maximum difference.

Seasonal and Zonal Differences

Chart 5 above highlights the significant variation in solar intensity that orbital changes can have spatially over a relatively short time frame of 125 years.  However there is some symmetry about these changes such that the accumulated EMR available in both hemispheres each year is almost identical.  Taking 2037 as an example, the March equinox will occur 187 days before the September equinox.  Correspondingly, the southern hemisphere will be exposed to the same total solar radiation in just 178 days.  Hence the solar intensity in the SH has to be considerably higher on average given the shorter period of exposure. 

Looking at the thermal response to solar EMR at selected locations gives insight into zonal and seasonal response.  The examples are taken from the BoM Climate Data as it provides easily accessible daily temperature readings for a large number of sites.  The first example is a coastal location, Low Head, in northern Tasmania at 41S.  Chart 6 is a plot of maximum daily temperature and ToA solar EMR at 40S for 2023.

This is a temperate location that shows highly correlated thermal response to ToA solar EMR when the EMR is lagged by 39 days indicative of moderate thermal lag. 

Charts 7 and 8 indicate the thermal response for tropical coastal locations in Queensland.

In both tropical locations, the correlation is worse than the temperate zone with both responses exhibiting departure above 425W/m² when the location goes into monsoon with its attendant temperature regulation around 30C.  The response delay for Brisbane is only 22 days compared with 38 days for Hamilton Island due to the Island being surrounded by water, which has a slower response to solar EMR.  Hamilton Island also cools quite rapidly once the lagged EMR falls below the monsoon threshold.

Charts 9 and 10 show the thermal response in the Antarctic region where freezing occurs.  The thermal responses in this region are not as well correlated with the lagged EMR as the temperate zone or tropics.

Macquarie Island is a small, remote location in the South Pacific at 55S influenced by the Southern Ocean.  Chart 9 plots the minimum temperature to highlight how the minimum levels off around 2C despite the solar EMR falling below 220W/m², which appears to be the threshold where freezing sets in.  Despite Macquarie Island being surrounded by ice-free ocean, it has snow down to water edge during winter.

Mawson Base is located on Antarctica at 68S where sea ice forms.  The best correlation occurs when EMR is lagged by 15 days so the response lag is more like an inland location rather than ocean edge.  Once the lagged EMR is below 220W/m², the temperature exhibits large swings indicative of low thermal inertia and varying advection from warmer regions.  Mawson becomes thermally isolated from the warmer ocean water that remains water above minus 1.7C but beneath sea ice.

Climate Zones &Annual Phases

From Earth’s perspective, the exposure to solar radiation can be classified into six latitudinal zones and four annual phases.  For the purpose of comparison here, the Zones are:

Northern Hemisphere: Arctic 60N to 90N, Temperate 30N to 60N, Tropical 0N to 30N

Southern Hemisphere: Antarctic 60S to 90S, Temperate 30S to 90S, Tropical 0S to 30S

The annual phases are taken from December Solstice to March Equinox to June Solstice to September Equinox to December Solstice.  The zones and phases can be visualised as a six by four matrix as shown in Matrix 1 for conditions in 1850.

The “Freezing” phase or season occurs predominantly in the Arctic and Antarctic zones.  Similarly, the “Monsoon” season is predominantly in the tropical zone of both hemispheres.  The “Days” are area averaged for the zone such that the maximum is the length of the season in days.  The threshold for freezing is taken at 220W/m² at each latitude and for monsoon 425W/m² at each latitude.  

Both the “Heating” and “Cooling” seasons are based on area average daily solar EMR across the entire hemisphere.

Advection is broadly taken as shifting heat across seasons and polewards.  The heat is in the form of both latent and sensible heat.  Accordingly, advection is related to precipitation and will influence snowfall in freezing zones.  The advection value is simply calculated as the difference between heating and cooling in respective hemisphere and is therefore no more than a qualitative indicator.  Advection between hemispheres is assumed negligible.

Orbital Driven Anomalies for Seasons and Zones

Chart 11 displays the variation in Monsoon and Freezing days from 1850 to 2040 as anomalies with respect to the average from 1980 to 2010.

Although there is variation of the order of 2% from year-to-year, there is no identifiable trend.

Chart 12 examines the anomalies wrt 1980-2010 average for heating, cooling and advection for both hemispheres.

All plots of Chart 12 exhibit identifiable trends with the NH trending upward and the SH trending downward.  There is also significant variation year-to-year.

Weather Prediction

The season and zone matrix has some alignment with significant weather events observed since 1850.  For example, an above average NH Monsoon (0.51days) is indicated in Matrix 2 for 1900.  The 1900 typhoon season was notable for deaths in Japan, Hong Kong, Vietnam and Taiwan.  In the same year, the monsoon failed in northern Australia, consistent with the low SH monsoon down (0.31days) but southern Australia experienced record rainfall in May with Yarra River flooding consistent with SH Advection being 0.67W/m² above average.

Looking back from 2025 to 1850, 2022 experienced the highest NH Heating season as shown in Matrix 3.  The NH Cooling season was also up on average.  By contrast, the SH Cooling was also up but the SH Heating season was down on the average.

2005 was also a year of relatively high NH Heating (0.43W/m²) and NH Advection (0.37W/m²) was also higher.  Combined, these would be expected to increase late season tropical storms.

Looking ahead, 2038 is a standout year for anomalous NH Heating with it being up by 0.55W/m² on the 1980 to 2010 average and 1.23W/m² up on 1852.  NH Advection is also anomalously high in 2038.

Climate Trends

There have been substantial orbital changes since 1850 but they are miniscule compared to what is to come.  By 2100, the anomalous NH Heating relative to 1850 is up 1.3W/m² and NH Advection is up 2.2W/m² as shown in Matrix 5.  Combined, these changes will result in higher early season snowfall over current experience.

In 2100, NH Cooling season has 1W/m2 lower average EMR than 1850 and both monsoon and freezing days are lower.  The only significant trend in the SH is the monsoon being up by 1.5days.

The NASA JPL data is available up to the year 9999.  By then, the solar EMR will be substantially reversed with respect to the hemispheres from what it was in 1850 per Matrix 6.

The increase in NH Advection tracks steadily upward from 1850 but NH Monsoon increases more rapidly after the year 5000.  If NH glaciation is not already under way by 5000 the snowfall will accelerate at a greater rate after that.

It is worth noting that in the present era, almost all land south of 60S is covered in thick ice.  In 2025, perihelion occurred on day 3 of the year when declination was -22.7 degrees compared with day 365 in 1850 when declination was at -23.45 degrees.  So only a 4 day/0.75 degree shift but it has already resulted in identifiable climate change.  In 9999, perihelion will occur on day 141 when the NH is facing the sun with declination at 20.2 degrees.  The storms across the North Atlantic and North Pacific during the NH Cooling phase will rival those presently observed in the Roaring 40s, Furious 50s and Screaming 60s in the SH. 

Discussion

In previous studies, the solar EMR was averaged over monthly intervals and declination was based on Earth’s orbital plane rather than actual declination of Earth’s equatorial plane to the line to the centre of the sun.  This high resolution study has produced some unexpected results such as the 14+W/m² seasonal difference in daily solar EMR across seasons as shown in Chart 5.  There was also a prior presumption that the SH monsoon would be steadily decreasing and the NH monsoon would be steadily increasing contrary to what this study demonstrated.  The eventual northward shift in monsoon is not apparent till year 5000.

Some effort was made to tease out the conditions that drive the temperature in the Nino34 region.  There was a weak positive correlation with NH Heating and NH Cooling and negative correlation with SH Heating and SH Cooling; all lagged one year.  But there was no combination of these variables found that improved the correlation over a single variable.  From previous observations, the variation in the solar constant has some correlation to the temperature in the Nino34 region.  Also the reconstructed variation in the solar constant over the past 200 years is of the same magnitude as the seasonal variation in ToA solar EMR caused by orbital variation.  Combining both variations is for future study.

Conclusions

The daily variation in Earth’s geometric relationship with the sun correlates well with observed temperature trends and also gives some indication of weather extremes from-year-to-year. 

The coming changes in Earth’s climate due to precession of the orbit will be far beyond human experience in recorded history.  The NH will experience season-to-season difference of 50W/m² at 60N with increased solar EMR during the NH Heating season and dramatically lower solar EMR during the NH Cooling season.  The season-to-season swing in the SH is even greater than the NH but to milder extremes than present as shown in Chart 11; less solar EMR during SH Heating but more during SH Cooling.

From an historical climate perspective, the seasonal solar EMR at the time confirms the medieval warm period per Matrix 7.

From 1000 to 1850, the solar EMR during the Heating season in both hemispheres declined but more dramatically in the SH.  The Cooling season in both hemispheres had higher solar EMR in 1850 but freezing days increased in the NH.  NH Monsoon was down significantly in 1850 but SH Monsoon was higher in 1850.  Advection declined in both hemispheres from 1000 to 1850.  It is worth noting here that the most dramatic period in changing solar EMR in recorded history occurred from 1500 to 1700.  The Heating season in both hemispheres were increasing to 1500 then there was a dramatic reversal to lower heating seasons (NH down 8W/m2, SH down 12.4W/m2) by 1700, which was little different to 1850.  The so-called Little Ice Age is well aligned with orbital changes.  

Finally, the total energy reaching either hemisphere does not change much from year-to-year, but the seasonal ToA solar power flux can change measurably from year-to-year.  The thermal response to high and low level solar EMR is muted by the phase change of liquid water and water vapour to ice.  Atmospheric ice over tropical oceans regulates the level of thermalised EMR above surface temperature of 30C and surface ice on oceans and lakes insulates the water below to reduce heat loss below 0C for freshwater and minus 1.7C for ocean water.

The Author

Richard Willoughby is a retired electrical engineer having worked in the Australian mining and mineral processing industry for 30 years with roles in large scale operations, corporate R&D and mine development.  A further ten years was spent in the global insurance industry as an engineering risk consultant where he developed an enduring interest in natural catastrophes and changing climate.