Gabriel Oxenstierna
All life on Earth (somehow) originates from the Sun’s heat.
But how much of the solar irradiation reaches us Earthlings?
The question is highly relevant, as the amount of reflected sunlight displays a remarkable decreasing trend over time. As will be shown, this trend alone explains most of the warming we’ve had in recent decades.
The Earth’s reflectivity is measured by albedo (a latin word meaning ‘whiteness’). Albedo measures the proportion of solar irradiation that is reflected back to space, either by the ground or in the atmosphere. If albedo is 100 percent, all light is reflected, and 0 percent means no light is reflected. Albedo is very different for different materials: pure snow can be as high as >90%, dirty snow can be as low as 20%. Water has albedo <10% (depending on the angle of reflection, see figure 1).[1] Clouds vary greatly and are between 30% and 80% depending on the type of cloud. The Earth’s albedo averages 28%.
Figure 1. What reflects more sunlight, clouds, snow, ice, or water?
If we start from the top, we have a pretty much constant solar irradiance. As soon as the radiation enters the atmosphere, photons begin to be reflected by ozone in the stratosphere, by clouds, water vapor and aerosol microparticles. Of the remaining solar irradiation that reaches the Earth’s surface, an additional part will be reflected away. The amount that is reflected varies greatly and depends on numerous factors such as the geographical location, ground conditions (land/sea/rural/urban), which season we’re in, temperature, altitude, and not least the weather at the location.
On a global scale, all that local randomness evens out, and we have a stable irradiation on a monthly basis. Figure 2 shows how much net solar irradiation that flows in, as a global average, per square meter: it is solar irradiation at the top of the atmosphere, about 340 W/m2, minus reflected shortwave irradiation of about 98 W/m2. Net approximately 242 W/m2.
Figure 2. Net solar irradiation that reaches Earth, watts/m2, calculated as incoming solar radiation minus reflected shortwave radiation. Seasonally adjusted monthly averages for each of the hemispheres. Thick lines are Loess smooths, March 2000 – September 2023. Data: Ceres Ebaf4.
There is a significant positive trend during the period 2000–2023. The increasing amount of solar irradiation reaching Earth is due to a trendwise decrease in reflected shortwave irradiation by 1.5 W/m2. On the other hand, solar irradiation decreased by approximately 0.2 W/m2 during the same period due to the solar cycle becoming less active.
We have thus had an increase in net solar radiation over the period of approximately 1.3 W/m2 according to the Ceres data. The long-term positive trend in shortwave radiation has been confirmed to exist since 1983 (with other satellite data).[2] That there is an established trend for 40 years makes it climatologically significant.
Figure 3. The trend of increase in shortwave radiation from 1983-2001. Copy of figure 1 in [2].
Albedo change explains the increase in net solar irradiation
Albedo is highly variable in time and space. Nevertheless, there is a great deal of stability on a global scale. In Figure 4, the development is shown separately for the Northern Hemisphere (NH) and the Southern Hemisphere (SH). They are very close to each other; the difference is stable and mostly less than 0.5 percentage points. SH has the slightly lower level, which is explained by the fact that it is dominated by sea (with ~80 percent of the surface area, compared to the NH’s ~60 percent). If we’re looking only at the nature of the Earth’s surface, the difference would be significantly higher due to the land/sea ratio – but the reflection from the clouds acts to even out the hemispherical differences.
Figure 4. Albedo for the period March 2000 – September 2023, calculated as reflected shortwave radiation measured at the TOA relative to incoming solar radiation. Seasonally adjusted monthly averages. Thick lines are Loess smooths. Data: Ceres Ebaf.
We have a continuing, and significant negative trend. This means that more solar irradiation enters and warms the Earth. That the albedo trend is negative is well established, and has been demonstrated with different methods: Ceres satellite data, and also by measuring the Earth’s back-radiation towards the Moon.[3][4][5]
What causes the albedo decrease? Several factors contribute: a decreasing cloud cover (both its extent and optical depth) has been shown to be the primary factor [3][4]; increasing vegetation (‘global greening’) is also a well-established secular trend of significant importance. Decreasing amounts of aerosols are of less importance. This can be imputed from the stable difference between NH and SH in figure 4, as aerosols have a local, short-term effect that mainly affects the NH.[6]
The climate is very sensitive to a reduced albedo. Scientists at NASA claim that a reduction in albedo of 1 percentage point produces a warming effect equal to a doubling of CO2 in the atmosphere.[7] Accordingly, the albedo decrease we have had in the last 24 years corresponds to almost 2.0 W/m². The increase in CO2 corresponds to only 0.7 W/m². See calculations below.
Conclusion: The ongoing, longterm reduction in albedo has produced more than twice as much warming effect in recent decades as the radiative forcing from CO2.
Calculations
1. Forcing from CO2
The IPCC states 3.9 W/m2 increased forcing from a doubling of CO2.[8] Mathematically, we search a factor that gives 3.9 from a doubling, expressed as a logarithm, ln(2/1). That factor is 5.63:
3.9 = x * ln(2/1) è x = 5.63
We can now insert start and end values for CO2 instead of the numbers ‘2’ and ‘1’. In March 2000 we had about 370 ppm and in September 2023 about 420 ppm. The theoretical forcing from CO2 for the period would then be:
5.63 *ln(420/370) = 0.71 W/m²
2. Forcing from albedo decrease
a. Using the data. Estimating the global albedo decrease from March 2000 to September 2023 with OLS yields a negative slope of -0.0019 percentage points (pp) per month, and the total decline for the period is 0.54 pp.
Assuming a linear relationship during the period, a reduced albedo of 0.54 pp gives an increased solar irradiation of:
0.0054 * 340 W/m2 = 1.84 W/m2
b. Using the NASA rule of thumb. Alternatively, calculated according to the NASA researchers’ claimed relationship of the warming effect of a 1 percent albedo reduction mentioned above, and using IPCC:s value for forcing from CO2 of 3.9 W/m2, the theoretical forcing of the global albedo reduction for the 24 years is: [7]
3.9 * 0.0054/0.01 = 2.1 W/m²
In both variants a. and b., the resulting figure is more than 2.5 as large as the forcing from CO2. The calculations have not taken into account the slightly decreasing solar radiation over time, but this affects the result only marginally.
References
[1] The albedo of water is calculated according to the Fresnel relationships, see e.g.:
https://en.wikipedia.org/wiki/Albedo#Water https://en.wikipedia.org/wiki/Fresnel_equations
[2] Do Satellites Detect Trends in Surface Solar Radiation?, Pinker and 2 co-authors, Science 2005, https://doi.org/10.1126/science.1103159 .
[3] The albedo of Earth, Stephens and 5 co-authors, 2015, https://doi:10.1002/2014RG000449
[4] The changing nature of Earth’s reflected sunlight, Stephens and 8 co-authors, 2022, https://doi.org/10.1098/rspa.2022.0053
[5] Earth’s Albedo 1998–2017 as Measured from Earthshine, Goode and 5 co-authors, 2021, https://doi.org/10.1029/2021GL094888
[6] Divergent global-scale temperature effects from identical aerosols emitted in different regions, Persad and Caldeira, Nature 2018, https://doi.org/10.1038/s41467-018-05838-6
[7] Changes in Earth’s Albedo Measured by Satellite, Wielicki and 5 co-authors, Science 2005, https://doi.org/10.1126/science.1106484
[8] IPCC 2021, AR6 WG1, chapter 7, p. 925
Technical note
In order to create the diagrams, I first downloaded data from Ceres (NetCDF4 format). The data were then preprocessed in the program CDO (Climate Data Operators) in Linux (in my case Ubuntu under Windows). All the time series data were calculated as surface-weighted monthly values in CDO. After that, the resulting data files were read into R/Rstudio where the figures were created with GGplot. All data and software are free to use/open source.
Gabriel Oxenstierna is a PhD at Stockholm University and one of the Clintel signatories.
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