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.
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).
In response to comments, I’ve added the following paragraph
The Sun’s position in the sky changes constantly, so a snapshot momentary conventional global albedo is useless. At least the “CERES albedo” has a constant frame of reference, it may not be the exact albedo as measured from space, but it can be compared from month to month because the incoming and outgoing radiation are (at least theoretically) always from the same reference angle. The only changes (ignoring orbital drift and other sources of instrument error) are the albedo components on the surface (clouds, ice, etc.). At least the “CERES Sun” is not constantly moving.
A neat way of estimating Earth’s albedo is from Earthshine observed on the Moon. Recent paper here
Very true.
Wow, Stokes is right about something.
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?
https://isometric.com/writing-articles/why-albedo-matters-for-reforestation-projects
“causing the leaves of the trees to become so hot that you can burn yourself on the leaves”
Where does this happen ??
“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 !
You say that “The leaves of the trees become hotter than a black sheet of metal standing in the sun.”
Not true at all. For example, in flat-plate solar collectors, absorber plates reach 150°C. That will burn you.
On the other hand, In field situations with strong sun and low humidity, measured leaf temperatures are commonly 2–5 °C warmer than air.
Under rare conditions of extreme heat and high radiation, they may reach 45°-50°C, but beyond that they wilt and die. That won’t burn you.
w.
If the leaves don’t become significantly warmer, where does the solar radiation that isn’t reflected and doesn’t become thermal energy go?
Does the chemical process of photosynthesis use solar radiation without creating significant thermal energy?
If the leaves use solar radiation without creating significant thermal energy, the assumptions for the Earth’s energy imbalance aren’t correct.
The Earth’s energy imbalance is based on the assumption that all solar radiation that isn’t reflected becomes thermal energy.
https://www.life.illinois.edu/govindjee/paper/gov.html
The absorbed light energy is transformed into chemical potential energy within the glucose molecule, making the process energy-consuming rather than energy-releasing.
Victor, you say:
“If the leaves don’t become significantly warmer, where does the solar radiation that isn’t reflected and doesn’t become thermal energy go?
Does the chemical process of photosynthesis use solar radiation without creating significant thermal energy?
If the leaves use solar radiation without creating significant thermal energy, the assumptions for the Earth’s energy imbalance aren’t correct.”
Good question. The leaves turn the solar energy into chemical and mechanical energy, using it to create and power the plant itself.
Of course, when the plant dies, this chemical energy is released as heat as the plant decays.
So there is no effect on the earth’s energy imbalance.
w.
I have heard that fossil oil comes from dead trees, plants and algae.
Is it the chemical energy in the plants that turns into oil and sinks into the ground to form fossil oil?
“Is it the chemical energy in the plants that turns into oil and sinks into the ground to form fossil oil?”
It’s not just oil. Decaying plants provide food for all kinds of insects, microfauna, and bacteria. The energy changes from energy in the plant to energy in those “things” that do much of the decaying work. It’s a reason why soil can improve fertility over time. That stored energy doesn’t all get radiated away, a lot of it remains in the biosphere over time. It’s one reason why looking for a “radiative in/out” balance is a phantom, especially over short periods of time (even centuries let alone decades). If all energy in was radiated out the earth would never have become anything other than a sterile ball.
That energy balance happens over years and even centuries. It’s one of those biosphere cycles that have a LONG cycle time. The effect on energy balance simply can’t be recognized by trying to find a radiative in/out balance over a day, weeks, months, years, and even decades, e.g. 30 year “climate” intervals.
In fact, much of that “decay” doesn’t generate thermal impacts as far as radiation is concerned. Much of the “decay” is just translating the energy stored in the plant into food energy for insects, microfauna, and bacteria. I.e. it remains “stored” energy, not radiative flux. It’s why soil gets “better” over long periods of time instead of becoming sterile.
Something that you are overlooking is that the leaves transpire (as water vapor) the water that transports nutrients up to the leaves. It is well known that growing vegetation cools the air, and also cools the individual leaves.
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.
The scales are all labelled (W/m^2). Albedo is a ratio so has no units.
Oops, my bad. I got into too much of a hurry this morning when I programmed this.
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.
OK Rick, I fixed the units problem in the figure, nothing else changed.
This is the sort of detail that climate botherers will latch into to condemn your entire analysis. I know how easy it is to forget to adjust units in Panoply or whatever you are using for the images.
The other suggestion I have made above is to do the analysis across latitudes rather than the entire global grid. That shows the shift in convection and how advection is adjusting to that shift.
Seasonal differences may also be revealing. I think that it was seasonal changes across latitudes that led me to conclude the loss of ice was not very significant in the changing albedo. It is mostly cloud changes.
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.
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.
“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.
True. I wouldn’t state it exactly that way, but it is the main point of my post drilled down to its core.
Nicholas, whatever you did there appears to be nonsense….your integral of normal SW is pooched…but if integrating from -Pi/2 to +Pi/2 from pole to pole and and sunrise to sunset and then dividing by 2 for nightime is too difficult…all you have to know is that if the radius of Earth is R….then the Earths silhouette has and area of PiR^2 …while it’s radiating surface is 4xPiR^2. You should explain why you think that is incorrect…the radiation passing through the atmosphere between Rsurface and RTOA and exiting to space without being absorbed or reflecting off the shiny sea at low incidence angle….only results in couple of percent discrepancy…at least I’m assuming that’s what you mean…but “Shroedder physics” seems to have a number of intricacies……
Andy,
What type of sensor is used to measure sw radiation and how is calibrated? I am quite skeptical that it can measure sw radiation to
+/- 0.001 of a watt.
About 50% of incoming sunlight is IR light. What happens to this light?
Good question. the CERES satellites (Terra, Aqua, and Suomi) estimate outgoing SW (0.3-5 micrometers) using angular distribution models (ADMs). The values are not directly measured, but the models used are reasonably accurate and fairly well constrained. I’m going from memory here, but I think they are accurate to +- 2 W/m2 or so. However, that number is smaller than reality because there are more factors involved, the total uncertainty in outgoing (reflected) radiation is probably larger than 2 and may be as high as 6. It depends on how much is considered.
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,
w.
===
Here’s my question:
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.
===
Perplexity and all ai engines that I have used make lots of mistakes Willis. They are very useful, particularly as programming assistants, but they are not authorities. Calling them “artificial intelligence” is an exaggeration. They are not “intelligent,” they are what I call “natural language search engines.” They also make lots of mistakes.
Don’t take them seriously in this sort of problem, take them into account, but do your own thinking. It is clear to me that the simple mean that you and perplexity prefer, is very flawed. My reasoning is in the post.
Thanks, Andy. Explain to us the difference between the first and second equations in my post, and tell us why the second one is preferable.
Here is the logic again:
You claim to have put forward your reasoning in your post, but all I can find is this:
But that doesn’t explain away the problem shown by the equations.
Finally, you say:
True … but so do humans. You are making what I call the “argumentum ad machinam” by its similarity to “argumentum ad hominem” a known logical fallacy. You can’t show something is wrong by simply saying it’s AI, just like you can’t say “Willis is wrong because he doesn’t have a PhD.”
In both cases, the source of the claims is IRRELEVANT. All that matters is, are the claims true.
I can find no error in the AI logic … your turn.
w.
Next, a comment. You say:
Per CERES, the directly calculated global albedo is 0.291. If we assume that the error in both the average solar and the average reflected shortwave is ±3 W/m2, this gives the albedo as
0.2907 ± 0.0092
This doesn’t get us anywhere near the incorrect calculation of 31.3%
The problem with the way you are calculating it is simple—you’re not calculating global albedo.
Here’s a toy example. Suppose we have two equal area gridcells. One is in the tropics, receiving 300W/m2, and reflecting 120 W/m2. Albedo is 0.40. The other is in the temperate zone, receiving 150 W/m2 and reflecting 30 W/m2. Albedo again is 0.20.
Per your method, the albedo is the average albedo of the two, 0.30.
But in fact, they are receiving 450 W/m2 and reflecting 150 W/ms, so the true albedo of the two is 140/450 = 0.33 W/m2.
Now, please note that I’m NOT saying that your method is useless. It has value. For example, we’d expect that when the albedo goes down, more solar radiation would be absorbed, and the temperature would go up. And for the land, this is true.
But over much of the tropical Pacific, the opposite is true.
This is a most curious and unexpected fact, and it’s only revealed by using gridcell by gridcell albedo.
But that does NOT mean that we can calculate the global albedo as the average of the individual albedos. As discussed above, that gives the wrong answer.
Best to you, Andy, and thanks for all of your great posts.
w
The spherical ToA average everyone uses raises an interesting question.
What’s the albedo for the dark side of the spherical average?
Albedo is the measure of the diffuse reflection of sunlight off a surface. Since there is no incoming sunlight on the dark side…it doesn’t matter what you think the dark side albedo is….
In a sense we are talking past each other. You are talking about planetary albedo as if the Earth were a point. If we do that, consider the Earth as an infinitesimally small point, then you are correct, the albedo is (with the data we have) ~29% and described by one mean input and one mean output. But that is seriously misleading and not very helpful scientifically.
My point is that the Earth is not a point and we don’t measure the input or the reflected out very accurately. Plus, albedo does not change across the surface in a consistent way. In the middle of figure 1, compare the upper two maps to the bottom one, you can easily see the difference. Consider the trend maps on the right-hand side and what the trend map of your model scenario (globally constant albedo) would look like.
I don’t put a trend map for your scenario in figure 1 because it is pointless, it is blank.
Bottom line, we don’t know what the albedo is precisely, we can only estimate it. We don’t know the incoming or outgoing SW, nor do we know the incoming or outgoing total radiation, we can only estimate them.
That said, what is important here? We need to consider the trends by region and look at the changes by region. With the measurement accuracy we have today, all we can say is that albedo is roughly 30%, perhaps +- 2%. Your simplistic estimate (assuming a point source) is 29%, it is within the uncertainty, but almost certainly wrong, because we know the Earth is not a point. My estimate is 31.3%, again almost certainly wrong since the data is not very good, but at least I’m explicitly considering the complexity of the problem, and I can map the regional albedo.
We can’t tell who is closer to the truth with the data we have, all we can be sure of is that we are both wrong. That said, I still like my estimate better, just my opinion.
That is exactly what measurement uncertainty is all about. Especially expanded uncertainty used for a 95% confidence. Inside that interval I don’t know, you don’t know, no one knows where the true value actually is. The fact that it can change in time makes the interval even wider.
When I grew up an uncertainty of 2% of full scale was considered excellent. Over the years, it really hasn’t changed much, especially when measuring properties that have variation.
Specifically regarding this quote:
I think you mean shortwave, not longwave. Your error calculation is incorrect. +-3 w/m2 is too small. You need to consider all potential errors and the fact that the total solar output includes both SW and LW and we have no idea how much LW is reflected. Ignoring that, the extended discussion in Loeb, 2009 shows the total potential error is much larger, perhaps +-5 to +-8 W/m2 or even higher. This is why a model is used to constrain the variables. This is not statistical uncertainty, but the uncertainty in actual measurements by different instruments, different instruments show a difference in TOA SW of up to 8.6 W/m2! Differences over 5 W/m2 are common.
If we assume +-6, then the true potential range is from 0.28 to 0.313, but given the unknowns, the total range is larger than that. Your estimate is within the range of uncertainty, debating whether your estimate or mine is more accurate is not really worth the time, we cannot know, and that is the take-away.
As for this: “you’re not calculating global albedo.” This is true, I’m not. I’m trying to compute the area-weighted global mean albedo, which is a different number. I’m not sure the “global albedo,” in the sense that the Earth is a single point, is a meaningful number. It’s kind of like ECS, an interesting number, but from the standpoint of climate is it meaningful? Probably not.
I should have read this post by you before commenting on the one before. You have a great handle on total uncertainty. Keep it up and don’t forget that expanded uncertainty has a place. Using it, you may get values Dr. Pat Frank has found!
You are correct that I meant shortwave, thanks for the heads-up
Fixed.
Next, you are NOT calculating the “area-weighted global mean albedo”. That is what I have calculated. Read my comment again. You are calculating a highly distorted value. As my comment says:
This equals α_global [area-weighted global mean albedo] only if (S_i) [gridcell solar] is constant across all gridcells (or uncorrelated with (α_i) [gridcell albedo] 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-weighted average of (α_i) overweights regions with low (S_i) relative to their contribution to the global energy budget.
In other words, your method is overweighting the poles and underweighting the tropics, giving you a meaningless figure.
Best regards,
w.
Your single-point global albedo is simply a snapshot albedo and computed as if the planet was frozen in time and place. It isn’t. I think my method can be described as the “area-weighted global mean albedo.” That is exactly what it is, and it is independent of the solar position, it describes Earth’s albedo characteristics quite well. That said, it is not Earth’s global albedo, and your calculation is not either, since as the Earth continues in its orbit and rotation, your albedo calculation necessarily changes minute-to-minute and at all time scales.
I’m not worried by the overweighting at the poles, that isn’t the point or purpose of my calculation. I suppose that could be changed, by computing the change in the sun’s location, and the changing solar angle for every position on Earth, but I don’t feel a strong need to do that. I just want to see how the “area-weighted global mean albedo” changes with time. The number is certainly not meaningless; it is quite useful.
Neither of our methods calculate the true albedo, the data is not that good.
Regarding the error analysis, your numbers are way too large. You are using Loeb 2009 rather than Loeb 2018, viz:
Clouds and the Earth’s Radiant Energy System (CERES) Energy Balanced and Filled (EBAF) Top‑of‑Atmosphere (TOA) Edition‑4.0 Data Product (Loeb et al. 2018, J. Climate) https://www.cen.uni-hamburg.de/en/icdc/data/atmosphere/docs-atmo/loebetal-jcli-2018.pdf
Methodology to create a new total solar irradiance record: Making a composite out of multiple data records (Dudok de Wit et al. 2017, GRL) https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1002/2016GL071866
Using 1 W/m2 as the error of the reflected SW and 0.5 W/m2 as the 1σ errors gives us a 95% confidence interval on the albedo of 0.285 – 0.297.
HOWEVER, this is a separate question from the incorrect method you are using to calculate what you are calling the “area-weighted global mean albedo”
w.
1σ is not error and it is not uncertainty. It is the standard deviation of a selected set of measurements and assumes normality and lack of systematic error. Neither applies here. I stick with my error estimate, the large variability in estimates from different devices remains and cannot be fixed by using a calculated standard deviation.
As for TSI estimates, they are corrected to 1AU, they are measured in space and are not very helpful in this exercise, which is dominated by changes on Earth’s surface and in Earth’s atmosphere. It is those changes affecting albedo that I am trying to describe. Besides TSI at Earth’s TOA and surface changes throughout the year and by the hour, see the attached illustration from my first post on this topic. Screw TSI at 1AU, it is a measure of the sun’s output and is only one factor in insolation. It is a quantity that is a starting point at the TOA along the equator, but a very minor player on Earth’s surface, where insolation daily goes from zero to about 970 W/m2 depending upon the time of day and latitude.
It is what happens on Earth that drives the climate, not a snapshot albedo or TSI measured in space. This is the point of my posts.
1 sigma or 2 sigma?
To summarize the albedo debate from my perspective.
The difference between our albedo estimates comes down to definition and purpose.
Your “point‑source” albedo is correct for the specific instant and geometry at which the Earth–Sun system is viewed from far away. But that value is not climatically meaningful because the solar zenith angle changes continuously—minute‑to‑minute, season‑to‑season, and over orbital cycles.
To study climate, what matters is global mean albedo, computed over the full CERES grid, weighted by area and integrated over time. This quantity tells us how much of the incoming solar energy the Earth system reflects on average, and how that reflection changes spatially and temporally.
A single‑instant whole‑Earth albedo seen from deep space might be ~29%, depending on the viewing geometry and time of year. But the global mean albedo, averaged properly over the full illuminated hemisphere and over time, is closer to 31% in CERES EBAF.
So the disagreement isn’t about arithmetic—it’s about what albedo means in a climate context. Point‑source albedo describes a momentary optical property. Global mean albedo better describes the Earth’s energy balance over long periods of time. It is the albedo measure that is important climatically.
Andy, I think you have a good handle on everything. I would only make one observation. A global mean albedo probably has little to do with climate at different points. It is the same problem with GMST. A single number can’t fully describe the variation over the globe. Consequently, one can not objectively use a single number anywhere on earth. Please think about including a standard deviation of the measured values so one can decipher what may occur at different locations over the globe.
I have pointed out mathematically exactly how your “global mean albedo” method underweights the tropics and overweights the poles. I still don’t understand why you see this as a good thing or a correct method.
Perhaps you can explain why overweighting one area of the planet and underweighting another is a valuable method.
“Global mean albedo” has a clear meaning in climate. It’s total outgoing shortwave divided by total incoming shortwave—total sunlight reflected by the earth, divided by total sunlight hitting the earth.
Here’s Merriam-Webster on the question:
Here’s the IPCC glossary definition:
You are NOT measuring that! You are giving us a distorted number with the tropics underweighted and the poles overweighted.
Note that this is not just a problem with albedo. It appears whenever you have a gridded value involving a fraction. You can’t just average the fractions to get the mean value. You have to average the underlying numerators and average the underlying denominators (area weighted if necessary) and then divide one by the other to get the true average.
Perhaps an example will make this clearer.
Imagine a flat plate with two equal areas. One area receives 300 W/m2 of shortwave radiation and reflects 100. The other receives 30 W/m2 and reflects 20.
The plate as a whole is receiving 330 W/m2, and it is reflecting 120. Clearly, the average albedo is 120 / 330 = .363. Total out divided by total in.
However, the albedo of one area is 1/3 (.333) and the albedo of the other area is 2/3 (.666). Averaging these two gives an incorrect answer of 0.5 for the average albedo. That would imply that half the radiation striking the plate is reflected, which is clearly not true. The area with the smaller incident radiation (on the earth, the poles) is overweighted, and the area with larger radiation (on the earth, the tropics) is underweighted.
Best to you, and as ever, thanks for your always interesting posts.
w.
WRT:
First, I understand what you are saying, I just do not think it matters. Your description of albedo (total incoming divided by total reflected) is correct, but it is not constant and changes minute to minute, season-by-season, and so on. We know it is roughly 30%, but it cannot be measured or calculated because as soon as you do it changes.
What I am doing with my calculation is ignore all that, it doesn’t matter with regard to a rotating planet with an elliptical orbit and a sun with a relatively constant output. What matters from the standpoint of climate is the changing atmosphere and surface and how that influences albedo. That is what I’m trying to compute when I calculate the area-weighted cell-by-cell CERES albedo mean. I called it “CERES albedo” intentionally. It is not the true (and abstract) albedo you refer to. The true albedo is not a climatically significant number, it is an abstract approximation, which is why I compared it to ECS. With proper satellite data you could measure it, but what good is it? As soon as you measured it, it would change, and the changes are not related to climate necessarily. I don’t know how to explain it better than that.
I acknowledge what you are saying is true, I just don’t think it matters. I suppose I could figure out a way to get closer to the abstract concept with geometry, but I don’t need to. I’ll just try and remember to always say “CERES albedo”, which only changes as Earth’s surface changes, since it is straight up and down at every point, this is the issue you don’t like, but it is actually an advantage that I am trying to capitalize on. That is the number we need, the true albedo of a point Earth (the albedo you refer to) is of little value.
Like I said you are correct, I just don’t think it matters, my purpose is different. I want to map the Earth features (for example clouds and ice) that affect albedo and how they change. Measuring albedo the way you want to, tells me nothing, it’s just a valueless number that responds mostly to Earth’s orbit and tilt, you’d never be able to extract anything useful about climate from it on short time periods, even if you could measure it accurately.
Thanks, Andy. You say:
Huh? The exact same thing is true regarding your method of calculating the albedo. In both cases, what is being measured is constantly changing, which is why we use averages.
The problem is that your average systematically overweights the poles and underweights the tropics in a constantly changing manner. You still haven’t explained how such an inaccurate measure is of any use at all.
w.
The whole point of my method it that it allows me to examine the elements of a changing albedo. Your method gives us a more accurate instantaneous estimate of global albedo, but what can you use it for? What are the elements of the changes?
The Sun’s position in the sky changes constantly, so a snapshot momentary global albedo is useless. At least the “CERES albedo” has a constant frame of reference, it may not be the exact albedo, but it can be compared from month to month because the incoming and outgoing are (at least theoretically) always from the same reference angle.
The only changes (ignoring orbital drift and other sources of instrument error) are the albedo components on the surface, clouds, ice, etc. At least the “CERES Sun” is not constantly moving.
My working hypothesis on climate, is that on the century time frame, it is oscillating surface thermal energy storage that drives climate changes. We can see some clues to this in the ocean oscillations (ENSO, AMO, etc.). My idea is that another important climate change aspect might be changing albedo, but the classic total out/in albedo is not much help, it is lacking the details we can get from CERES.
The CERES albedo may not be a true albedo, but you can see the components in a consistent way from year to year with it. That is the value. The classic albedo changes constantly, but you cannot see the elements of the change it is just two numbers being divided.
Thanks, Andy.
It seems there is some confusion. You say:
“The whole point of my method it that it allows me to examine the elements of a changing albedo. Your method gives us a more accurate instantaneous estimate of global albedo, but what can you use it for? What are the elements of the changes?”
To find the physical location of the elements of the changes, I look at either the gridcell by gridcell trends, or the gridcell trends in the surface albedo, or the gridcell trends in the cloud albedo.
However, what you can’t do is just take an average of those gridcell by gridcell changes and use it as the global mean cloud or surface or total albedo. That method overweights the poles and underweights the tropics.
Finally, you seem to think I’m talking about a “snapshot momentary conventional global albedo”. I’m not. I’m talking about this:
This is an accurate time series of global albedo, unlike your incorrect time series, viz:
You claim that there is an “albedo peak” around 2007, but that’s just an artifact of your incorrect calculation method. No such peak exists.
w.
You don’t explain your graph, but I’m guessing you computed the graph as the area weighted global mean toa_sw_all/solar_mon.
OK, fine, so what? You still have to go back to cell-by-cell to examine the changes, which is my whole point. That necessity doesn’t go away. Why do you think my peak is in error, I know of no such error.
Your calculation is completely different from mine (guessing since you don’t explain it) I don’t see how the two can be compared. I only used complete years and used calendar year averages (to avoid problems with seasonal changes). Looking at your plot you used all the data and 2000 is incomplete, so that is not a good idea. I doubt your plot is valid for that reason alone.
Further accurate is not really possible with this data. The data has large uncertainty as Loeb makes very clear, and the difference between the 2001 and 2025 values is too small, relative to the error. This is not really debatable and global means will not do the job anyway, which is why I want to do the whole analysis cell-by-cell. You can continue with global means if you want, it just will not get you anywhere in my opinion.
You need to provide much more explanation to be convincing.
I added a clarifying paragraph at the end of the post. Hope it helps, at least it shows what I was intending to do.
8 different models from 8 different global climate “experts.”
7 of them net cooling, 1 net warming.
1 says the 7 are wrong.
8 values for albedo, 34.2% & 117 W/m^2 to 27.5% & 94 W/m^2
Difference of opinion = 6.7% & 23 W/m^2.
Not the point of Andy’s work, but it should be important to remember that reflectance, i.e. albedo, from surface materials does vary with wavelength, especially between visible and infrared. Using a single value for all wavelengths is a simplification. Buried inside MODTRAN are tables of spectral reflectance for quite a few common materials, like beach sand.
And especially for vegetation that has strong absorption in red and blue, and strong reflectance in green (for most plants). And in the Winter the deciduous trees pretty much turn grey. Thus, the ‘albedo’ has seasonal variations as well.
How do you tell which photons have been reflected versus those emitted?
No SW sources on Earth- must be reflected. LW sources on Earth, so you will have reflection and emission.
No natural sources, however there are man made sources and they are readily seen at night from space. Of course few will be operational during daytime but not zero, probably irrelevant but perhaps not.
I’m ore worried about the Libido than the albedo, yuk yuk yuk.
Becomes less of a problem once you become old. That’s why old people talk about the weather.
“ Libido”
What’s that ???
As a famous old Greek once said about getting older “It’s like being unshackled from a lunatic”.
The mind is still willing…. but… 🙁
“plus we do not know how much solar longwave radiation (LW) is reflected”
I know nothing about solar longwave. I know about solar near infrared shortwave, I doubt that gets reflected as easily as visible shortwave.
There is no degree of difficulty when it comes to emission or reflection at any wavelength.
Actually, photosynthetic plants have much larger reflectance in NIR than most geological materials. It is one of the characteristics of plants that allow accurate thematic classification of multispectral imagery, commonly using what is called the “normalized-difference vegetation index” (NDVI).
“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”
We’ve already established that you have no idea what the word “radiation” means, Andy. For example, can you tell us what the phrase “radiant energy” means? If not, perhaps you should just sit down. Physics isn’t your field, and it shows.
You are quite confused. CERES uses flux because that is what can be measured. They measure power per unit area. When I write “average solar radiation arriving at the top of the atmosphere,” that is exactly the way NASA uses the word “radiation.” You might be confusing flux with energy and that is the cause of your confusion. Just as conduction and convection are not energy, radiation is not energy. Radiation is a mechanism for energy transport, radiant energy is the energy carried by EM radiation. Radiative flux is the rate of energy transport.
Exactly!
He has been told this repeatedly. He is a troll hoping to create an argument that goes round and round with ad honinems as the main purpose.
You have given the correct answer! Don’t feed the troll.
Thanks, people get weird ideas about energy and power.
“people get weird ideas about energy and power.”
Physicists don’t. Engineers sure do, though… right, Andy the engineer?
Sit down, Jim. You have no business in this conversation after you told us that “semantics are irrelevant”. In other words, you are functionally illiterate, and plan to stay that way.
“Don’t feed the troll.”
Sit down, you lying ignorant twerp.
“ad honinems [sic]”
Oh, I forgot hypocritical. Sit down, you lying ignorant hypocritical illiterate twerp.
“You are quite confused.”
No, Andy. That is a lie.
“CERES uses flux because that is what can be measured.”
You have literally no idea what they are measuring. Nor, I would venture, do they.
“You might be confusing flux with energy”
No, Andy, I am not “confusing” anything. That is another lie.
“radiation is not energy”
Who told you that? Textbook reference, please. Even our resident genius Willis the fisherman told us that “radiation is energy”. Is he wrong?
“Radiation is a mechanism for energy transport, ”
You mean like a bus? Or a luminiferous aether? Where did you get that definition from? Please show me the textbook page. From this century, please.
“radiant energy is the energy carried by EM radiation”
No, Andy, energy does not need to be “carried” by EM radiation, the way you yourself can be “carried” by a bus. That idea is at least 100 years out of date. Please try to keep up.
Remember, “radiant” is an adjective. That means “radiant energy” is a type of energy. Nothing more, and nothing less. Who taught you your English? Or your physics?
Besides being an annoying troll, you are very ignorant of radiative physics. But just so other readers do not get confused, let me be as clear as possible:
Radiation is the electromagnetic mechanism by which energy is transported. It carries radiant energy (usually measured in Joules), and the rate at which that energy crosses an arbitrary surface is named radiative flux (measured as power density in W/m²). Radiation itself is not power (energy/second) or energy, but it produces measurable power densities.
That is about as clear as I can make it. Radiation is a physical process, like conduction or convection.
“Besides being an annoying troll”
Liar. Did your Engineering Ethics professor teach you to behave this way? Or was it your parents?
“you are very ignorant of radiative physics”
Another lie.
“Radiation is the electromagnetic mechanism”
It isn’t any such thing. EM radiation consists of electric and magnetic fields. Do you know what fields are, Andy?
“radiant energy (usually measured in Joules),”
This is, indeed, my entire physics lesson. And now you have successfully learned it. Congratulations! So, then, why did you say “radiation […] 340.2 W/m2”?
“radiative flux”
A hallucinated and unmeasurable fiction. Certainly not what CERES (or anyone else) has measured.
“Radiation itself is not power”
Fascinating. But you also said “radiation is power”. So, were you lying then, or are you lying now?
stevekj,
I frequent this site because, while I’m not a ‘physicist’, I do have enough technical training in ‘engineering’ to suspect that the radiative-centric model of energy transport through the troposphere that is being fed to us by climate scientists is not only phenomenological, but has also been hijacked to support the dismantling of modernism in favor of primitivism.
On that basis, and given that the physics of electromagnetic dynamics is highly complex, I’m always willing to listen to others in order to fill in gaps in my knowledge of to correct outright mistakes. But comments like ‘sit down’ or ‘from this century’ are not nearly as helpful as someone providing constructive commentary or even links to address these gaps in my knowledge of the subject.
Thanks for the feedback, Frank. You know, I have been trying to teach physics here politely for over a decade now. But it is very difficult to teach physics to engineers who have been brainwashed their entire lives, and were never taught to think clearly in the first place – which is, of course, why they went into engineering and not science. When they start lying to my face and calling me a troll, that’s when I tell them to “sit down”. Not before.
And when they bring up antique and very poorly worded quotes from Clausius or Planck about “heat rays” or “compensated heat”, that’s why I ask them to refer to modern physics. Those guys were certainly brilliant in their time, given what they had to work with, but the field has moved on quite a bit since the 1880s. As you know.
Now, Jim here, for example, didn’t like my definitions (from the textbook), which didn’t match his hallucinations for some reason. So, rather than learning physics, which is admittedly hard, he instead told us that “semantics are irrelevant”. Then, of course, he called me a troll. What would you call someone like that? Besides an illiterate lying twerp? He has no business in this conversation. Or any conversation, for that matter, because all conversations involve words, and words have meanings. Most of us learned that by about grade 2, if not 1. But not Jim!
I think you are doing very well, yourself, and there aren’t many gaps in your knowledge that I can see! Certainly not as many as there are in Andy’s or Jim’s.
Your use of victimology is admirable but useless.
I am an electrical engineer. I studies in the 1970’s and learned all the calculus, differential equations and vector analysis necessary to use Maxwell’s equations and how EM waves carry energy.
Like it or not, your obtuse dance around the tree refutations are simply arguments based on taking a slightly different tack to try and refute someone’s text descriptions of EM radiation.
If you would show your math that describes what you think, we could resolve the issue. Not a text description, but actual equations. Planck used Maxwell’s equations in his Theory of Heat Radiation, perhaps you could start there and show your derivation of your theory.
“I am an electrical engineer.”
That’s your problem, not mine. But since you brought that up, what did your Engineering Ethics professor teach you about insulting your teachers? And what did your parents teach you about that, for that matter?
“EM waves”
What EM waves, Jim? Are they in the room with us right now?
“If you would show your math”
No, Jim, a lack of math isn’t your main issue.
I don’t know why you’re even still here, after you told us that “semantics are irrelevant”. Why are you typing all these words? None of them mean anything, do they? That’s what you told us.
“your theory.”
None of what I’m teaching is “my theory”, Jim, so you can shove that particularly arrogant lie where the sun don’t shine. No, it’s Willis’s, and of course it comes right from the physics textbook, which is naturally where he got it from. Here it is, in his words:
1) Radiation is [a form of] energy
2) Energy is the capacity to do work
3) [Mechanical] Work is what happens when a force is applied across a distance [or more generally, the expenditure of energy, accompanied by an increase in entropy]
4) Power is the rate of doing work
What, precisely, is the problem?
Copilot AI …
“There is no single-word name, but scientists describe it as:
‘Photosynthetic carbon fixation followed by geologic burial and thermal maturation of organic matter.’
In everyday language:
Sunlight → photosynthesis → buried organic matter → fossil fuels.”
Didn’t we cover this in high school?
Albedo is pretty simple. What percentage of the incident solar radiation is reflected back to space? I see no need for area-weighting, and no need to consider only shortwave. Energy in determines the amount of energy in the atmosphere, and with the lapse rate determines “Surface” actually at two meters, temps. What are you guys going on about?
I want to look into what changes albedo. CERES data is divided into shortwave and longwave. Only a small fraction of sunlight is longwave, between 0.01% and 0.1%, so by eliminating longwave from the calculation we can easily remove Earth’s surface emissions, which are also longwave.
Area-weighting is needed because the units are W/m2. As for the debate, Willis is concerned that global albedo, which you describe, total_out/total_in, is different from the albedo I am calculating, which is the total area-weighted mean cell-by-cell albedo, but I need to compute that to look at how surface changes affect albedo.
Thanks, Andy. I don’t understand this comment:
“As for the debate, Willis is concerned that global albedo, which you describe, total_out/total_in, is different from the albedo I am calculating, which is the total area-weighted mean cell-by-cell albedo, but I need to compute that to look at how surface changes affect albedo.”
How is your method (which overweights the poles and underweights the tropics) superior to mine when looking at how surface changes affect albedo?
w.
So you guys are going on and on about changes to either the 3rd or 4th decimal point of albedo? Albedo determines the amount of energy absorbed by the surface and atmosphere of the Earth. When it changes, due to cloud cover, ice coverage, land use changes, it may well be responsible to all this contretemps about the so-called Surface (actually at 2 meters) Temperature of the Earth.
CERES does what it does. I think I will quote Stokes, as The Earthshine off the Moon may be easier to analyze. The Earth’s surface, all the different materials, sand, rock, dirt, ice, grasslands and forests, ocean, contributes as you say a tiny fraction of Earthshine. Clouds and ice change every second. as Earthshine will reveal changes to albedo, in turn changes to input of Energy, in turn changes in the energy content of the Atmosphere, determining from the lapse rate temps at 2 meters accounting for the Wind and the latitude changes in insolation. Sure, what the f does CO2 have to do with it? One thing and one thing only, CO2 changes the altitude at which the Earth is freely able to radiate to Space, changing the temp at which the Earth freely radiates to Space, but, but, but, no one can calculate this. I tried, forget it.
Moon
Sorry, obviously the temp changes the energy radiated.
Moon
Sorry again, obviously more CO2 raises the altitude at which the Atmosphere is freely able to radiate to Space, lowering the temperature at which the Atmosphere radiates to space, lowering the Energy Transfer, but, but, but, no one can calculate this.
Moon