## Common strategies and common sense in carbon dioxide reduction

CO2 reduction strategies comparison

Common strategies and common sense in carbon dioxide reduction

Please note, this is a work in progress. I will continue to update as I get time!

# 1. Introduction

## 1.1 Motivation

Have you ever been to a restaurant that didn’t put the prices on its menu?

There are many things we can do to help the environment, and help stop global warming. Here’s something that’s more difficult: to decide what the best ways are, what the most cost-effective ways are, instead of going in blind. Lacking good data, there’s that uneasy feeling, as if we just sat down to order at a restaurant that chose not to list the prices.

I couldn’t find a reasonable cost-benefit analysis of many of the actions we could take. So I’m going to try to do the calculations myself.

The main metric will be dollars spent per tonne of CO2 saved; I will also calculate the dollar cost for the average person (in a first-world country) to reduce their CO2 consumption down to the annual CO2 budget, if we were to use that strategy alone.

There will be other actions that we can take that do not fit into this analytical framework of dollars/tCO2, but we can still try to quantify how much CO2 they save, to help us decide whether the actions are worth taking or not.

This is not intended to be a discussion of cutting edge research. Instead, the point is to focus on actions that can be taken by most of us.

## 1.2 Disclaimer

Here are my credentials for this task: I don’t have any.

Don’t take my word for anything. I’ll try to show my calculations, so if there are any mistakes it should be easy to point them out. All corrections and suggestions gratefully accepted.

## 1.3 The ideas I looked at

Here’s a list of some of the possible actions that were considered.

1. Hybrid cars
2. Electric cars
3. Buying a smaller car
4. Heat-sink (“geothermal”) AC/heating
5. Tankless water heaters
6. Rooftop solar panels
7. Green electricity from the power grid
8. Saving forests or planting trees
9. Carbon offsets
10. Carbon capture
11. Biofuels
12. LED bulbs
13. House insulation
14. Energy efficient appliances
15. A vegetarian diet
16. Local food
17. Cycling instead of driving
18. Flying less often

# 2. Summary

## (In case you have dinner cooking on the stove and don’t want to read too much further.)

This table summarizes the results, so you don’t have to read the details below if you don’t want to. For each strategy, it provides the following information:

1. cost, using two different metrics: (a) dollars per tonne of CO2, and (b) the amount it would cost to go from the average US person to bring their CO2 consumption down to a sustainable carbon budget
2. cost or savings using other measures, for strategies that don’t fit the $/tCO2 metric 3. additional benefits and drawbacks that can’t be quantified easily S. No.StrategySavingsOther benefits and drawbacks 1Hybrid cars: in this case, hybrid Civic vs. regular Civic$100/tCO2, 3 months carbon budget / $100 Hybrid batteries use rare-earth metals, have environmental consequences 2Toyota Highlander, hybrid vs regular$800/tCO2, 12 days carbon budget / $100 Hybrid batteries use rare-earth metals, have environmental consequences # 3. Some useful numerical values ParameterValueReferencesComments CO2 budget per personApproximately 3 tonnes per personlinkIn most plans, the carbon budget starts higher and gradually drops. 3 tonnes per person is a very rough approximation of the midpoint of this process. This is the combined emissions from personal spending on housing, travel, food, products and services. CO2 produced per capita, per yearApproximately 16 tonnes per person, per year (USA) linkFor comparison, approx 5 tonnes per person per year (China), 1 tonne per person per year (India) Effect of carbon taxesA tax of$25/tCO2 would add 21 cents per gallon to the price of gasoline, 1.2 cents per kW-hour for electricity from non-renewable sources.linkPlease note that carbon taxes have severe flaws as way of remediating damage due to global warming. See chapter 4 of this article, or also this discussion: link
CO2 emission per unit of electricity4.5 × 10-4 tonnes/kW-hour linkThis calculation does not include line losses, or other gases such as methane. These are not significant at the level of accuracy that we will be working with.
CO2 per liter of gasoline burned2.2 × 10-3 tonnes CO2 per literlink8.9 × 10-3 tonnes CO2 per gallon
CO2 to carbon conversion3.7 tonnes of CO2 = 1 tonne of CRatio of the atomic weight of CO2 to the atomic weight of CSome sources give the carbon budget, while others give the CO2 budget. This is useful in converting between them. We will use CO2 for all calculations.
CO2 per kilometer of air travel0.2 kg CO2 per mile (!)link

# 4. Why should we care?

Obviously, this section is more personal and less quantitative. And it’s not the purpose of this article to get into details of the enormous effects of global warming on people and the environment. There’s already plenty of research about that, for example here and here and here and here and here.

However, I would like to point out is that pure economic analyses of the costs of global warming are inadequate; and that levying carbon taxes as a way of solving the problem can also be inadequate. A lot of the analyses of the effects of global warming actually understate the moral imperative to combat it, especially by residents of first-world nations.

1. There are huge non-economic affects of global warming, such as habitat loss and species extinction.
2. Global warming is not just shunting money from poorer regions to wealthier ones. It’s shunting money from the victims of global warming to the agents of global warming.
3. Related to the previous point, the financial estimates of the harm done are not commensurate with the actual devastation. For example, take someone who gets two meals a day: if they are deprived of one of these meals, this gets counted as just a dollar or two of harm, but the actual damage would be considerable.
4. The people who are harmed do not have the choice whether or not to accept the change to their lives. For example, they may be forced to move from a land where they have lived for many generations, or abandon the only livelihood they know how to make; this is a fundamental uprooting that most of them would prefer not to do, whether or not they are compensated for it.
5. Borders are not open. Climate change may lead to some areas being less habitable and other areas more, with a smaller net effect. However, people who are badly affected do not have the choice to move to other places, even if they wanted to.
6. The money collected by carbon taxes is not distributed to the people who are most harmed by the affects of global warming. In particular, the tax money goes to the government where the economic activity happens, but the harmful effects are felt worldwide, and predominantly in regions with lower economic activity. So even with a carbon tax, there is a net effect of shunting money from poorer regions to wealthier ones.
7. The numbers actually used as carbon taxes in practice are influenced heavily by political factors separate from the actual social cost of the carbon. In particular, it cannot be set more than can be accepted by the politicans and populace.
8. The carbon tax is considered by many politicians to have repercussions on the economy, and is set lower than the expected social cost of carbon in order to take these repercussions into account.
9. Once the changes from global warming have been effected, they can last a very long time, accumulating damage. Therefore, actual prevention is much more valuable than remediation.
10. The estimates of the cost of global warming that carbon taxes are based on, are calculated by discounting future costs. That is, something that would harm a future generation $100, is given a cost of, say,$50, as it is assumed that we do not care as much about affects in the future. The moral hazards of this should be obvious.

# 5. Calculations for individual cases

## 5.1 Hybrid cars and other fuel-efficient cars:

### 5.1.1 Honda Civic vs. Honda Civic Hybrid

Assume that the fuel efficiency of a hybrid car (such as a Toyota Prius or a Honda Civic hybrid) is 50 miles/gallon $\approx$ 20 km/liter of gasoline, and that a gasoline-driven Honda Civic gets 35 miles/gallon, which is about 14 km/liter.

There are a couple of different ways of calculating this. We’ll do it both ways to see if they agree with each other as a sanity check. The first is by using “true cost of ownership” from Kelly Blue Book (kbb.com) or Edmunds (edmunds.com) to determine the costs, while the second is by simply using the upfront costs. The first method aims to be more accurate, while at the same time has more assumptions built into it.

#### 5.1.1.1 Calculation using “true cost of ownership”

We will do the calculations for a distance driven of 75,000 miles, which is 120,000 km. (The reason for choosing this particular number is that Edmunds calculates the total cost of ownership over this distance.)

Over this distance, the car will use approximately $120,000 km/(20 km/liter) = 6,000 liters$ of gasoline. This translates into $6 \times 10^3 \times 2.2 \times 10^{-3}$ tonnes of CO2 over the lifetime of the vehicle, or 13.2 tonnes of CO2.

For a conventional car, the number of tonnes of CO2 over the calculation period of the car would be $(120,000 km \div 14 km/liter) \times 2.2 \times 10^{-3} tCO_2/liter$ = 19 tonnes of CO2.

Therefore, the savings of gasoline over 120,000 km are 6 tonnes of CO2.

To find the dollar cost for that savings in gasoline, we will use the Edmunds total cost of ownership. For that distance (5 years at 15,000 miles per year), the total cost of ownership for the Honda Civic is $32,000, while that for a Honda Civic Hybrid is$33,300.

Therefore, the cost per tonne of CO2 is (33,300 – 32,000)/6 = $200/tonne of CO2. #### 5.1.1.2 Calculation using direct costs Assume that the life of the car is 150,000 mi or 250,000 km. Number of tonnes of CO2 over this lifetime for a regular car: $250,000 \times 2.2 \times 10^{-3} \div 14$ = 40 tCO2. For a hybrid, by the same calculations, this number is 27.5 tCO2. So the difference is approximately 12 tCO2. From Edmunds.com, we estimate the extra cost of a hybrid at$5,000. We will assume that the price of gas is $3/gallon. Over the full lifetime of 150,000 miles, the gasoline car will use 150,000/35 = 4300 gallons of gasoline. The hybrid will use 150,000/50 =3000 gallons. The savings in gas will recoup 1300 * 3 =$3900 dollars of the difference in cost. The savings in CO2 emissions will be $1300 \times 8.9 \times 10^{-3} \approx 12 tonnes$.

By this calculation, the efficiency of buying a hybrid is $(5000-3900) \div 12 \approx$100/tCO2$. These calculations are very sensitive to the difference in price; if it were$6000 rather than $5000 the answer would be approximately$200/tCO2.

### 5.1.2 Toyota Highlander vs Toyota Highlander Hybrid

This cost per tonne is very sensitive to the gas mileage of the cars. It makes sense to repeat this calculation for a “typical” SUV. We choose the Toyota Highlander.

mileagetotal cost of ownership (120,000 km)tonnes of CO2 (120,000 km)
Toyota Highlander 18/24 mpg $41,903 33 tonnes CO2 Toyota Highlander Hybrid 28 mpg$49,878 23 tonnes CO2

This gives a cost per tonne of CO2 of (50,000-42,000)/(33-23) = $800/tCO2. Note that if we use Kelley instead of Edmunds, it is$600/tCO2.

### 5.1.3 Drawbacks other than CO2 emissions

There are significant drawbacks to hybrid and electrical cars that are not reflected here: batteries can be pretty messy and energy intensive to manufacture. By most analyses, this extra cost to manufacture is not large compared to the savings from the added energy efficiency ([4], [5]).

## 5.2 Electric cars

For electric cars, there are two important cases to consider: the electrity can come from fossil fuels, or it can come from renewable (carbon-neutral) sources.

The carbon cost of an electric car comes from two parts: the cost to manufacture, and the carbon cost of the electricity. For hybrid and gasoline cars, the second cost dominates, but for electric cars both have to be taken into consideration ([4], [5]). Note that if the manufacturer derives its electricity from renewable sources, that part also vanishes, but we assume that this is not the case.

### 5.2.1 Charging from fossil fuel sources

The ratings for US electric cars are given in MPGe, or miles per gasoline equivalent: the distance travelled for a charge of electricity equivalent to the energy of one gallon of gasoline. This amount of energy is 33.7 kW-hours.

Remember that carbon cost of electricity is $6.9 \times 10^{-4}$ tonnes of CO2 per kW-hour.

We will choose the Nissan Leaf as a representative for electric cars. For this vehicle, the fuel economy is 114 MPGe, or 30 kW-hours/100 mi.

For this vehicle, the Edmunds True Cost to Own for the standard 5 year/15,000 miles per year situation is $23,000. This takes into account a tax credit of$7,500. The Kelley Blue Book estimate of the total cost of ownership is $35,835, which is$28,000 if you consider the tax credit. We will choose a value of $25,000. It’s tough to decide what exactly to compare this to. We’ll choose a Honda Civic as the closest equivalent. As mentioned above, the Edmunds True Cost to Own is$32,000, and it emits 19 tonnes of CO2 over the calculation period.

For the Nissan Leaf, the amount of CO2 emissions to travel 75,000 miles is $75,000 miles * 0.3 kW-hours/mile * 6.9 * 10^{-4} tCO_2/kw-hour$. This is 15.75 tonnes of CO2.

So the Nissan Leaf gets 114 miles per energy equivalent of a gallon of gasoline, while the Honda Civic Hybrid gets 45 miles per gallon of gasoline, yet the Nissan Leaf creates approximately the same CO2 emissions per mile. This was certainly a surprise. Presumably this has to do with the inefficiencies of burning fossils fuels and converting to electricity — or the numbers used from the EPA, for CO2 emitted per gallon of gasoline and per kW-hour of electricity, may be inaccurate. Also note that this disagrees with the numbers from the reference [5], but I don’t know how they obtain their numbers.

(As a check of this rather startling conclusion, note that one gallon of gasoline is equivalent to 33.7 kW-hours of electricity. So the amount of CO2 emissions per 1MW-hour of gasoline is 8.9 kg CO2/gallon * 1 gallon/33.7 kW-hours * 1000 kW-hours/1MW-hour * 1 tonne/1000 kg = 0.26 tonnes/MW-hour. But the value used for electricity is 0.69 tonnes/MW-hour. I do not have an explanation why electricity is so much more expensive other than inefficiencies of generation and conversion.)

Therefore, over a 75,000 mile ownership, the Nissan Leaf saves $7,000 and also saves approximately 3 tonnes of carbon dioxide. If the$7,500 tax credit is taken away, owning a Nissan Leaf has an efficiency of $500/3 =$166/tCO2. Again, this number is extremely sensitive to the estimate of the total cost of ownership, and also the cost of the car we’re comparing it with, so this number does not have a high degree of significance. It does, however, seem robust to say that the price of the car is competitive with comparable cars, and will save a few tonnes of CO2.

### 5.2.2 Charging from renewable sources

Of course, the electricity used for recharging the electric car batteries may be obtained from renewable sources. In this case, the only emissions are those used in producing the car and battery. The above reference provides a value of 8.8 tCO2 for this, which is approximately 3 tCO2 more than for a gasoline powered car.

However, note that the cost of electricity will then be slightly higher, thereby increasing the total cost of ownership.

Over 150,000 miles, the number of kW-hours used would be 150,000 miles * 0.3 kW-hours/mile = 45,000 kW. The average price of electricity per kilowatt-hour in the US is $.13/kW, rising to$.20/kW in New England (see [6]. If we choose to use electricity sourced from green sources, the extra cost is 2.4 cents per kilowatt-hour.

## 5.3 Heat Sink (“Geothermal”)

Make an estimate of the savings in terms of gas; find the amount of gas used without this; and electricity for air-conditioning. How much extra electricity gets used? We will need the lifetime of a system. Check the book, and the article mentioned in the email.

## 5.4 Solar panels

Costs of making it, including environmental costs, and water.

Lifetime of solar panels

Total energy output over lifetime

Cost per kilowatt-hour of the electricity.

co2 saved.

## 5.5 Green electricity from the grid

Cost per unit of electricity with and without.

co2 per unit of electricity.

## 5.6 Saving forests

Cost of buying a hectare of rain forest. Amount of carbon in the hectare of rain forest. What is the probability that, if you hadn’t bought it, it would have been cut down? Can we assume that the higher that probability is, the more valuable the land is, so choose a value along the upper part of the range? This does make some sense; using the value of the land as a proxy for the likelihood it will be used for other purposes. We could additionally use a value for this probability based on how fast the rain forest is disappearing.

Carbon in the hectare of rain forest, we may be able to assume that if the trees were cut down, there would be one meter of wood on the ground?

Need the carbon content of each kilo of organic material.

Mention very large benefits in terms of non-climate change environmental factors.

Look at TED talk about how this is one of the best methods.

There are also estimates of how much carbon each hectare of forest processes per year. This seems strange, because it doesn’t mention how much is released by bacteria or termites breaking down the dead wood. Maybe find out how accurate this estimate is. In case you want to look at this, then you can estimate the annual cost of a hectare of rainforest by doing a cost of house to rent conversion, and applying that to the cost of a hectare of forest.

## 5.7 Carbon credits

cost of carbon credits (also look for carbon offsets).

where do they come from? cap and trade?

are they any good?

Probably a complete fraud. But look at how they work, how much they cost per tonne of carbon.

## 5.8 Biofuels

I’m not sure what I meant. Wood burning? Corn ethanol? This is tough to quantify and may make sense to skip.

## 5.9 LED bulbs

Life of led bulb. Life of ordinary bulbs. Amount of energy used over life of led bulb. Energy used over life of ordinary bulbs. Difference in cost of bulbs, energy. Co2 expenditure.

## 5.10 House Insulation

Yay, we got some info on that. Also do your own calculations, starting from the average heating costs.

## An “original” proof of the Basel Sum

I recently got bored and decided to try to find a proof of the Basel Sum. In an unexpected departure from tradition, I actually found one. As a further surprise, it seems to be a lot simpler than any other proof I’ve seen: just a few steps, and each one pretty obvious.

A reminder: the Basel sum states that

And an important clarification: this proof is “original”, in the sense of I came up with it myself, yay, but most definitely not original in the sense of I was the first to come up with this proof. The Basel sum is exceedingly well traveled territory mathematically, and I would be surprised if I was in the first 1000 people to come up with this proof independently.

Before we start the proof, a reminder of the definition of the double factorial. For an even number , . Similarly, for an odd number , . And we can choose to define .

Step 1:

Let

Then,

Subtracting these two equations, we get

(1)

Step 2:

(2)

This is easy to prove by induction, using integration by parts.
Click here for the proof, if you really, really want it. But you probably don't.

Seriously, no feelings will be hurt if you skip this.

Define

Then,

Hope you feel it was worth it!

Step 3:
Start with the Taylor series for :

Note that this is absolutely convergent. Now simply substitute .

(3)

Step 4:
In equation (3), integrate from to .

Step 5:
So the RHS is what we looked at in equation (1). This means

so

(4)

Addendum: I did some more research. Euler himself did something very similar (here). The earliest version of this exact proof that I could find was by Boo Rim Choe in the American Mathematical Monthly in 1987 (Vol. 94, No. 7 (Aug. – Sep., 1987), pp. 662-663 ).

## Reunion

Written after my 25th college reunion.

## Reunion

You’re back in your hostel — in the lounge, of course, watching tv, of course (Chhaya Geet? A Test match?). You’re sitting on one of those wicker chairs — remember how the mosquitoes could creep up from behind and bite you in the butt? Shift your gaze a little to the right from the television, along the shelves. Do you see that locked little drawer? Keep your focus on that for a little while, please.

One year, we realized that that locked drawer was, well, locked. And that it had been locked ever since anyone could remember. We broke the lock, and out of the vault came: a tape recorder and radio boombox. All reunion long, this memory kept annoying me — itching like a mosquito bite on the butt. And it took a little while, a little scratching, to figure out why this memory was so persistent.

Who were these people who left it in there, locked it up, and walked away? What were they thinking? We don’t know anything, except that they did indeed do it and then vanished. This was their Stonehenge, their Easter Island.

What about the kids in the hostels today? What if we had done that, what would they be thinking when they saw the artefact? Actually, that’s an easy question to answer. They’d be saying, what the fuck is is a “tape recorder”, because I’ve spent the last three hours trying to get it to talk to the wifi.

We are the ghosts who walk their corridors. But it’s more than that. For too long, we’ve been ghosts to each other too. Not in touch; or even if we have, we’ve been nothing more than the tiny tug on an electron in a web server in Lithuania, sending a pulse to a monitor a thousand kilometres away. We’re more than that, we’re flesh and blood, perhaps flesh and blood and a little bit of alcohol for those few days. The reunion is our reminder of this.

But it’s more than just that, too. As we see it reflected in our friends’ eyes, it is a reminder to ourselves most of all of our own existence as full human beings. We forget that in our routine; and we don’t even know we forget it. We need our own reminders.

But what of the kids we met, today’s kids, who only knew us as their ghosts? What do they think of us now they’ve seen us in person? That’s another easy answer. The bastards think we’re old; and they’re right. Wallace Stevens said that death is the mother of beauty. Nothing would matter if not for the prospect of its loss. The reminder of our flesh and blood reality is our opportunity to look around with sharper eyes at the wonder around us.

## Ten of my favorite books

This was going around Facebook a while ago — what are your ten favorite books?

I’m going to restrict myself to fiction, and I’m going with the ones that affected me the most at the time I read them, rather than necessarily the best.

1) Satanic Verses, Salman Rushdie. Mindboggling to me at the time. Still wonderful. Bonus: Haroun and the Sea of Stories, by the same author, one of the best kid’s books around, both for kids and grownups.

## A manifesto for macro

I once applied (unsuccessfully) for a solo photo exhibition at a local art gallery.   They asked for a writeup to describe it; this writeup ended up being a manifesto for macro photography, why I enjoy it so much.

And here’s a link to the pdf: https://edgeofthecircle.net/macro_writeup.pdf

## Some thoughts on consciousness and evolution

Consciousness is a by-product of evolution.  If we try to understand what drove evolution to create consciousness, we understand the attribute itself much better.  Here are some of my notes in trying to weave together a perspective on evolution, and what light it sheds on consciousness.

Notes on Consciousness through evolution

## A motivation for cricket

Opinions on cricket are not hard to come by. That it’s a torturously complicated sport with rules about rules about rules, just for the pleasure of the ritual. Or it’s terribly boring, nothing ever happens and there’s nothing to watch. And the crowd consists of a bunch of old men who natter on about the iniquities of the estate taxes while waxing their moustaches.