Calculating Earth’s Albedo, Part 2

By Andy May

It came up in the comments on my last post, CERES Albedo. What is the best way to compute Earth’s albedo? The CERES data is supplied as a 1° x 1° latitude/longitude grid. It is widely accepted that Earth’s global mean albedo is around 30%. The question is then: What is the best way to estimate it using the CERES satellite data? There are two basic ways. One is to use the average solar radiation arriving at the top of the atmosphere (CERES EBAF variable “solar_mon”), which is about 340.2 W/m² and divide that into the total solar shortwave radiation (SW) leaving (reflected from) the Earth (toa_sw_all). Using these two numbers we get an albedo of about 29%.

The second way is to compute the albedo for each of the 64,800 one-degree latitude & longitude cells and then compute the area-weighted global mean of all the albedo calculations. When this is done, the albedo is 31.3%. Statistically this is the same as the 29% calculation because the errors in measuring solar_mon and toa_sw_all are large (> ±2 W/m²), plus we do not know how much solar longwave radiation (LW) is reflected, but the problem is worth examining. Figure 1 shows the elements. Click on it to enlarge it and show it in full resolution.

Figure 1. Three calculations of Earth’s albedo.

The spreadsheet on the left of figure 1 shows the area-weighted yearly means for the CERES outgoing SW and the incoming solar radiation. Dividing the first column by the second results in the last column, labeled “conventional gm albedo.” The basic calendar year cell-by-cell area-weighted albedo global average albedo is next and labeled “cbc albedo.” The next column (“cbc rm36 albedo”) is computed by taking a 36-month running mean (centered) of both toa_sw_all and solar_mon, then computing a month-by-month and cell-by-cell albedo, then extracting an area-weighted global mean albedo from that dataset for each year. In terms of yearly global mean albedo, it matches the year-by-year and cell-by-cell calculation closely.

The set of maps in the middle of figure 1 show that the two cell-by-cell albedo calculations are very similar for 2025. The simple “SW out/solar in” calculation is the same value for every cell and the important detail we see cell-by-cell is hidden in the global mean.

The right-hand maps and graph show the 25-year trends that result from the two ways of computing the cell-by-cell albedo means. The upper trend map shows areas of decreasing albedo in either light yellow or blue. Areas of increasing albedo are shown in orange to red. The year-by-year albedo changes in the upper trend map are plotted in red on the graph at the bottom right of figure 1.

The middle right trend map is the trend in albedo after taking a 36-month centered running average. Notice it is almost a mirror image of the upper year-by-year trend map. Taking the 36-month running mean has offset the very active albedo data and reversed its slope, as shown by the blue line in the lower right corner of figure 1.

Conclusions

Essential details of the global albedo distribution are lost when using global averages as is done in the conventional calculation. Taking a running average of either the components of the albedo calculation or the computed albedo causes a shift and a change in slope in the albedo trend.

The best way to compute global albedo is to do it cell-by-cell and then make an area-weighted global mean of the cell-by-cell albedo values. I prefer to use calendar yearly means to remove seasonality because running means distort the trends. This means the best estimate of albedo, using CERES data, is 31.3%. This is also the best way to determine the albedo trend (the red line in the graph).

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Nick Stokes

May 23, 2026 2:38 pm

A neat way of estimating Earth’s albedo is from Earthshine observed on the Moon. Recent paper here

Andy May

Author

Reply to Nick Stokes

May 23, 2026 3:29 pm

Very true.

Victor

May 23, 2026 2:56 pm

It is the trees that warm the earth.
Trees reflect less sunlight and make the earth darker.
Trees absorb sunlight and use it for photosynthesis, which is the most efficient process on earth, causing the leaves of the trees to become so hot that you can burn yourself on the leaves.
The leaves of the trees become hotter than a black sheet of metal standing in the sun.

The researchers came to this conclusion using satellite measurements of the trees’ light reflection.
Have the scientists gone out into the forest and measured the temperature of the leaves?

One feedback mechanism that has started to gain more attention is albedo change. Albedo describes how much incoming solar energy the Earth’s surface reflects back into space. Generally, lighter colored surfaces have a higher albedo and reflect more solar energy than darker surfaces. You may have experienced this phenomenon when wearing a dark colored t-shirt on a hot, sunny day.
For the climate, albedo is important because energy that is absorbed by the Earth’s surface gets converted into heat. So, when there is an increase in the amount of solar energy that is absorbed rather than reflected, it has a warming effect on the Earth’s climate.
When planting trees makes the land surface darker it means more solar energy will be absorbed, creating a warming effect. Depending on how much carbon the forest removes, this warming effect from the albedo change can outweigh some or even all of the climate benefit of the carbon removal from the project.
A recent study even found that albedo changes could wholly negate the cooling effect of up to 12% of afforestation, reforestation, and revegetation projects reviewed, making albedo a critical factor for buyers seeking high-quality carbon removal.

https://isometric.com/writing-articles/why-albedo-matters-for-reforestation-projects

Sweet Old Bob

Reply to Victor

May 23, 2026 3:03 pm

“causing the leaves of the trees to become so hot that you can burn yourself on the leaves”

Where does this happen ??

Sweet Old Bob

Reply to Victor

May 23, 2026 3:45 pm

“A recent study even found that albedo changes could wholly negate the cooling effect of up to 12% of afforestation, reforestation, and revegetation projects reviewed, making albedo a critical factor for buyers seeking high-quality carbon removal.”

This is total BS !

RickWill

May 23, 2026 3:24 pm

Given that the driver of the changes is orbital precession, the response across latitudes will give as much or even more insight than the full grid.

There is more cloud in the low northern latitudes, where maximum daily average sunlight is increasing most and generally less at all other latitudes apart from the middle of Antarctica.

The reduction in permanent surface ice is not as significant with regard albedo as I expected. The reduction is as significant in the mid latitudes as the higher latitudes where annual snow hangs around.

RickWill

May 23, 2026 3:30 pm

The scales are all labelled (W/m^2). Albedo is a ratio so has no units.

Andy May

Author

Reply to RickWill

May 23, 2026 3:35 pm

Oops, my bad. I got into too much of a hurry this morning when I programmed this.

Nicholas Schroeder

Reply to RickWill

May 23, 2026 4:29 pm

Albedo is a percentage of ISR both in W/m^2.
A proper heat balance is conducted in BTU/eng h or kJ/metric h.

Rud Istvan

May 23, 2026 3:42 pm

So I was curious.
The CMIP6 global multimodal ensemble albedo is about 30% with a very tight distribution—probably a tuned cloud driven parameter result. ‘Safely tuned’. Easy result to Google.
But yet another reason most CMIP6 models run hot, as ‘tuned consensus’ is below the 31.3% Andy ‘correctly’ calculates here from CERES observations.

Per Google AI, a 1% increase in solar SW insolation forcing in CMIP6 would ‘rapidly’ increase GAST by a model dependent 1.5-3C. 31.3-30 is a 1.3% increase in modeled insolation.

Andy May

Author

Reply to Rud Istvan

May 23, 2026 4:13 pm

Excellent point. As this discussion and the CERES-EBAF model results show, we can’t even measure albedo to +-1%, yet a 1% change is huge in climate terms. Good to keep in mind.

Nicholas Schroeder

May 23, 2026 3:54 pm

“One is to use the average solar radiation arriving at the top of the atmosphere (CERES EBAF variable “solar_mon”), which is about 340.2 W/m2….”
340.2 is the ISR, 1,360 Wm^2/4 which is a ToA spherical model and inappropriate.
Attached is an appropriate model for averaging ISR.

Willis Eschenbach

Editor

May 23, 2026 4:21 pm

Let me start by repeating what I said in your previous post, viz:

Thanks, Andy. In general, taking averages of gridcell ratios as you are doing is less accurate than taking the average of the numerator and the denominator and then taking the ratio of the two.

I asked perplexity.ai to explain this. See below.

Best to you,

===
Here’s my question:

I have a gridded global dataset of average TOA reflected sunshine, and another of gridded sunshine.
Albedo is the ratio of the two, reflected/sunshine
Which is more accurate—
a) take the weighted mean of the reflected and the weighted mean of the sunshine, and divide the first by the second, or
b) divide the gridded reflection by the gridded sunshine, and take the weighted mean of the albedo of the individual gridcells
The first method gives ~ 0.29, and the second gives ~ 0.31

Here’s the answer:

===
Method (a) is the mathematically correct way to get the global mean albedo: compute the area‑weighted mean reflected flux and the area‑weighted mean incoming flux, then take their ratio.

Method (b) generally gives a biased result unless every gridcell has the same incoming sunshine.

Why (a) is the right global mean

Define for each gridcell (i):
· (R_i): time‑mean reflected shortwave at TOA (e.g. W/m²)

· (S_i): time‑mean incoming shortwave at TOA (same units)

· (A_i): area of the gridcell

Then by definition, the global‑mean planetary albedo is

This is exactly your option (a): area‑weighted mean (R) divided by area‑weighted mean (S).

Why (b) differs

Option (b) computes per‑cell albedo (α_i = R_i / S_i), then takes an area‑weighted mean of (i):

This equals α_global only if (S_i) is constant across all gridcells (or uncorrelated with (α_i) in a very particular way), which is not true for Earth because insolation varies strongly with latitude, season, and clouds. High‑latitude and cloudy regions tend to have different (S_i) and (α _i) than low‑latitude clear regions, so a simple area average of (α_i) overweights regions with low (S_i) relative to their contribution to the global energy budget.

A simple toy example:

· Cell 1 (tropics): (S_1 = 400), (α_1 = 0.25) → (R_1 = 100).

· Cell 2 (high lat): (S_2 = 200), (α_2 = 0.50) → (R_2 = 100).

· Equal areas.

Then

but the simple area mean albedo is

Option (b) overestimates the global mean because it gives the low‑insolation, high‑albedo region the same weight as the high‑insolation, low‑albedo region, even though it reflects less absolute power.
Interpreting your 0.29 vs 0.31

Your ~0.29 from method (a) is consistent with commonly cited estimates of Earth’s planetary albedo (~0.29–0.31, depending on period and dataset). The ~0.31 from method (b) is exactly the kind of upward bias you expect when you area‑average per‑cell albedos without weighting by incoming flux.

So:

· Use (a) for global mean planetary albedo relevant to energy balance.

· Use (b) only if you explicitly want the unweighted area‑mean of local albedos as a descriptive map statistic, not as an energy‑correct global albedo.
===