Surface Radiation Calculations

Basic system thermodynamics revisited (click image to view full size)

A colleague of mine emailed me an article (pdf link) containing the above figure. The author Ashworth (2008) contends among many things that the radiation energy balance shown in the figure above is wrong, and that it violates 1st and 2nd law of thermodynamics. I am writing this post to show that Ashworth is completely off base on that point and is not even close to interpreting the above figure correctly. I am not able to decipher any 2nd law implications from the figure though.
I don't have clear arguments or time right now for the all graphs of CO2/warming shown subjectively. It could go either way.

But first, imo, the author does not even know how to define a system for performing energy balances. Because of this he does not know how to add the necessary terms to achieve a 1st law energy balance. Clearly, if you look at the total energy balance, the incoming and outgoing solar radiation fluxes at the outer boundary of the atmosphere add up fine (342 coming in and 107+235 going out at the atmosphere level, from space).

This author is forgetting the fact that the earth is round and receives radiation at different times throughout the day and radiates it back. Consequently it is possible to radiate 390 (+ 78+24 also shown in the image) because earth is also getting back radiation of 324 apart from the 168.
Further if you do a surface balance that also adds up fine. See image of my excel calculation below.

The original paper from which they obtain the Fig 8 is here (pdf) where towards the end the authors clearly put forward the errors etc in the model and still clearly show that an energy balance has been achieved. Further the Ashworth "paper" is written like an opinion piece and (gasp) and shows lack of simple mathematical concepts.

But the bigger issue with anthropogenic CO2 related global warming is not the average daily solar fluxes, it is the release of the chemical energy trapped for millions of years in carbon bonds. The resulting CO2 release into the atmosphere is what is being considered as a precursor to global climate changes.

I should add at this point, my personal view on the subject of global warming and climate change is still not firmed up. I am merely an advocate for efficient use of resources, irrespective of whether they are carbon based or not. But what really bothers me sometimes is people pointing fingers at others, but making similar mistakes themselves.

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Redwoods vs solar panels

A CNN article on the conflicts between growing more trees and getting lesser sunlight for solar panels was interesting. Some bare facts:

1. Mark Vargas, who owns solar panels (an investment of 70,000 (2001 USD)) contends that his neighbour, Treanor's redwood trees are blocking sunlight for his solar panels
2. After 6 years, a judge cites CA's obscure sunlight availability law to rule in favor of Mark Vargas.
3. As alternate energy sources become more mainstream, many experts predict that conflicts similar to this case, will happen.

In response to Treanor's claims that the redwoods help capture CO2, Vargas "counters it would take two or three acres of trees to reduce carbon dioxide emissions as much as the solar panels that cover his roof and backyard trellis."
Legal issues aside, this case represents an interesting conflict. For starters, if we assume that the solar PV panels indeed help prevent more CO2 emissions than the redwoods (which turns out to be valid, see the appendix for back-of-the-envelope calculations), the question for environmental economists would be which option would generate the least negative externalites ? In other words, if we could put a price/ton on every pollutant (including CO2) evolved, which option would result in a lower price? Can the amount of services provided by redwoods be quantified in monetary terms?

Appendix
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Analysis of net CO2 emissions prevented by using solar PV and amount of CO2 fixed by redwood trees over the course of a year:
The data on photosynthetic CO2 fixation in coastal redwoods was taken from this paper (Osborne and Beerling, 2003). The authors of the above study used 3 year old trees to measure photosynthetic rates in a controlled atmosphere. Only results for coastal redwoods at pCO2 (partial pressure of CO2)=40 Pa (pascal) (corresponding to 395 ppm CO2 in the atmosphere) will be used in this analysis.
The PVWatts website was used to estimate costs and energy production from a single solar PV panel. San Francisco was chosen as the location (due to its proximity to Sunnyvale). The DOE web page puts the amount of CO2 emitted/unit of energy produced for coal power plants at 2.12 lb/kWh.
In Fig.7 (Osborne and Beerling, 2003) show the average rates of photosynthetic fixation (milli moles of CO2/plant/day) for different species. The area under the curve (in Fig.7 of the paper) for coastal redwoods gives the total CO2 photosynthetic fixation over the entire year. It comes to ~1650 mmol CO2/plant/year. This amount is however, for 3 year old plants. Let us assume that the amount of CO2 fixed increases linearly with the leaf growth and the plant age. If we consider a 12 year old tree, ~3350 mmol CO2/year are fixed by a single redwood tree. This amounts to 0.15 kg CO2/tree/year.

In comparison, Vargus installed 70,000 $ worth of solar PV panels. I assumed the average 2001 costs of solar PV panels to be 0.2$/kWh (current costs from the PVWatts website are 0.125 $/kWh). Per a 4 kW panel, the energy produced/year (from the PVWatts wevsite) would be ~5800 kWh. This represents an investment of ~1150 $/4kW panel. Since Vargus invested ~70,000$, he probably has 60 solar PV panels installed.
In a year, the AC electricity produced from all the panels (from the PVWatts website) would be 464000 kWh.If we assume that only 70% of the panels are operational at any given time, the figure becomes a little lower, ~330,000 kWh/year. I took electricity from thermal power plants as the basis for comparing CO2 emissions. Using the value of 2.12 lb CO2/kWh generated (and not accounting for transmission and distribution costs), I calculate that emissions of ~312 T of CO2/year will be avoided with the 60 solar PV panels.

Comparing the above two values (CO2 fixed/plant/year and CO2 avoided/year), we can clearly see that there is orders of magnitude difference between these two quantities. 60 solar PV panels prevents more CO2 emissions than ~1000 redwood trees. However, this is not the end of the story.

Solar PV panels are produced in a energy-intensive process which leads to CO2 emissions. For a complete CO2 emissions analysis, the emissions for solar PV manufacturing also need to be taken into account. However, this will not change the results here by very much as there is clearly differences in orders of magnitude between solar PV panel and a redwood tree.

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New Carbon Capture Pilot Plant in Wisconsin

ALSTOM, The Electric Power Research Institute (EPRI) and We Energies just announced a CO2 capture demonstration power plant in Wisconsin using a chilled ammonia process to remove the CO2 from the flue gas. The plant aims to capture about 90% of the CO2 emitted by the power plant. The size of the power plant is ~1210 MW (electric) [actually 2 x 617 MW]. According to this presentation on the web, ALSTOM clearly is seeking to take the lead on making conventional pc fired plants ready for a carbon constrained environment by retrofitting the plant.

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