There has been quite a lot of buzz in the last day or so about Energy Secretary Steven Chu claiming that making the roofs of buildings white (and brightening paved surfaces such as roads and parking lots) would “offset” a large part of the warming effect of humanity’s carbon dioxide emissions. The basis for this idea – which is not new — is that brighter surfaces reflect more of the sunlight reaching the Earth’s surface back to outer space. I found a presentation of the study he is basing his comments on by Hashem Akbari of Lawrence Berkeley National Lab here. A less technical summary of those results fit for public consumption is here.

I found some of the Akbari presentation calculations to be needlessly complicated, maybe because he was computing how much of humanity’s CO2 emissions in terms of billions of tons of CO2, or in millions of cars, could be offset. I dislike such numbers since they give no indication of what those mean relative to the whole atmosphere or their warming effect. Such big numbers lead people to buy hybrid cars while thinking they are helping to save the planet. As I have pointed out before, it takes 5 years of CO2 emissions by humanity in order to add just 1 molecule of CO2 to each 100,000 molecules of atmosphere. This obviously gives a very different impression than “billions of tons of CO2”.

So, we need to dispense with numbers that mislead people about what is really of interest: *What fraction of the impact of more CO2 on the climate system can be alleviated through certain actions?*

So, I thought I would make some calculations of my own to determine just what fraction of the ‘extra CO2 warming effect’ can be canceled out with the cooling effect of brighter roofs and pavement, on a global basis. Here are the pertinent numbers, along with some parenthetical comments.

**The Goal: Offset the Radiative Forcing from More CO2 in the Atmosphere**

Doubling of the CO2 content of the atmosphere has been estimated to cause 3.8 Watts per sq. meter of radiative forcing of the climate system, a value which will presumably be reached sometime late in this century. The current CO2 content of the atmosphere is about 40% higher than that estimated in pre-industrial times. Note this does NOT say anything about how much temperature change the radiative forcing would cause; that is a function of climate sensitivity – feedbacks – which I believe has been greatly overestimated anyway. For if climate sensitivity is low, then the extra CO2 in the atmosphere will have little impact on global temperatures, as will any of our ‘geoengineering’ attempts to offset it.

But let’s use that number as a basis for our goal: *How much of the extra 3.8 Watts per sq. meter of radiative forcing by late in this century (or about 40% of that number today) can be offset by brightening these manmade surfaces?*

This calculation is somewhat simpler than what Akbari presented, but assumes the intermediate calculations he made are basically correct. I will be multiplying together the following five numbers to estimate the Watts per sq. meter of radiative cooling (more sunlight reflected to outer space) that we might be able to achieve. Again, these numbers are the same or consistent with the numbers Akbari uses.

(1) The radiative forcing from a change in the Earth’s albedo (reflectivity): Akbari uses 1.27 Watts per sq. meter for a 0.01 change in albedo, which is the same as 127 Watts per sq. meter per unit change (1.0) in albedo. I think this might actually be an underestimate, but I will use the same value he uses.

(2) The fraction of global land area covered by urban areas: Akbari claims 1% (0.01) of land is now urbanized, a statistic I have seen elsewhere. I think this is an overestimate, but I will use it anyway.

(3) The fraction of the Earth covered by land: I’ll assume 30% (0.3).

(4) The fraction of urban areas that are modifiable: Akbari assumes 60% (25% roofs + 35% pavement). I think this number is high because Akbari is implicitly assuming the sun is always directly overhead during the daytime, whereas throughout the day the sides of buildings are illuminated by the sun more, and the roofs (and shadowed pavement) illuminated less, but I will use 60% (0.6) anyway.

(5) The assumed increase in albedo of the modified (brightened) surfaces: Akbari assumes an albedo increase of 0.4 for roofs and 0.15 for pavement, which when combined with his assumed urban coverage of 25% roofs and 35% pavement, results in a weighted average albedo increase of about 0.25.

When you multiply these 5 numbers together (127 x 0.01 x 0.3 x 0.6 x 0.25), you get about 0.06 Watts per sq. meter increase in reflected sunlight off the Earth from modifying 60% of all urban surfaces in the world. Comparing this to our goal — offsetting 3.8 Watts per sq. meter for a doubling of CO2 — we find you have only offset 1.6% of the carbon dioxide emissions.

Or, if today we could magically transform all of these surfaces instantly, we will have offset (1.6/0.4=) only 4% of the radiative forcing that has been accumulated from the last 100+ years of carbon dioxide emissions.

Of course, getting the whole world to ‘permanently’ recoat 60% of the surface area of their urban areas would be no small task, even to achieve such a small offset (1.6% by late in this century, or 4% today) of the warming effect of more CO2 in the atmosphere.

But this discussion does not address the positive energy savings from white roofs reducing the cooling load on buildings, something Akbari mentions as another benefit. From poking around on the internet I find that for single-story buildings, about 20% of the cooling load comes from the roof — not all of which is recoverable from a brighter roof. Energy savings would diminish for multi-story buildings, such as those in urban (as opposed to suburban) areas. [This source of energy savings can be estimated more easily. From other sources I find that about 5% of U.S. energy use is for air conditioning. If we could reduce that by, say, ten percent through brighter roofs, then 0.5% (one half of one percent) of our energy demand could be alleviated.]

And as I mentioned at the outset, if climate sensitivity is low, then the warming effect of more CO2 (as well as the cooling effect of any geoengineering ‘fixes’ to the problem) will have little effect on global temperatures, anyway.

The lesson here is that when put it in context of the *total* CO2 ‘problem’ — rather than just throwing big numbers around — the brightening of roofs and paved surfaces would offset only a tiny fraction of our CO2 emissions. The remaining question is just how much of this ambitious goal could be achieved, and at what cost.