For the first time since 1913, an entire calendar month has gone by without the observance of even one sunspot. See here.
Is this important?
It could matter to climate change, both theoretically and empirically. There is growing understanding that sunspots affect cloud formation on earth, and clouds are a big factor in climate modes -- indeed a factor that is not well understood. Better understanding of what determines cloud type and cover will help forecast climate. On the empirical side, "tests" of global warming at the aggregate temperature level essentially take the actual temperature record and adjust it for things like changes in solar radiation, volcanoes, atmospheric particulants, etc. What is left is presumed to be the effect of greenhouse gases. Summarizing very briefly, the "unexplained" temperature deviation from this process does match up reasonably well with the predictions of climate models (that is, the temperature is somewhat higher than it should be, after adjustment for non-GHG effects).
But note that, like so many things, this is a test of a joint hypothesis: that the adjustments are correct, and that the climate models are correct. If the adjustments are wrong, then what appears to be a correct climate model is actually wrong. Since solar activity (sunspots) has been high since 1940, and since that is theoretically and empirically related to warming, could it be that the adjustment to the temperature record for this effect has been too small? That would leave more of the observed warming to be explained by the models.
At any rate, if we are at a real low period for sunspots, and if that continues, we could be in for some cooling.
Showing posts with label climate change. Show all posts
Showing posts with label climate change. Show all posts
Sunday, September 07, 2008
Friday, October 19, 2007
The Stern Review on the Economics of Climate Change: Blistering Peer Reviews
In the latest issue of the Journal of Economic Literature, two papers deliver devastating reviews on the Stern Review on the Economics of Climate Change. The reviews are by serious, mainstream economists: William Nordhaus of Yale and Martin Weitzman of Harvard. These are not individuals and articles that can or should be ignored. Of course, they will be ignored by the mainstream media – while at the same time Al Gore’s receipt of the Nobel Prize carries the media day.
The Journal of Economic Literature is the sister publication to the American Economic Review and is put out by the American Economic Association, the leading professional society for economists. Abstracts of the papers, and instructions on how to buy them, are available here.
I have always said that my objections to the prescriptions of the most vocal climate change advocates are on three levels: one, the climate models depend too much on positive feedbacks that are not understood; two, the models have not really been tested, but instead are calibrated to the historical data; and three, even if one accepts the models, one then has to move into the economics of optimal policy, and there the best analysis suggests relatively modest reductions in carbon emissions for the near term. I like to ask environmentalists to summarize their prescriptions with the appropriate tax per barrel of oil: tell me what you think the price of oil should be increased by, in order to recognize the impact of carbon.
But back to the reviews of the Stern Review. So the Stern Review made big headlines when it came out, as it was commissioned by the UK government and was ostensibly a serious analysis of the economics of climate change. Both Nordhaus and Weitzman deliver fatal blows, although they try to temper it a bit. Here is a quote from Nordhaus:
“The central methodology by which science, including economics, operates is peer review and reproducibility. By contrast, the (Stern) Review was published without an appraisal of methods and assumptions by independent outside experts. Nor can its results be easily reproduced…(this) does mean that fatal flaws in evidence and reasoning, which might have been caught in the early stages under normal ground rules, may emerge after the report has been published.”
Weitzman says,
“However, in my opinion, Stern deserves a measure of discredit for giving readers an authoritative-looking impression that seemingly objective best-available-practice professional economic analysis robustly supports its conclusions, instead of more openly disclosing the full extent to which the Review’s radical policy recommendations depend upon controversial extreme assumptions and unconventional discount rates that most mainstream economists would consider much too low.”
Now in the spirit of full disclosure, I recommend everyone look at the papers for themselves. Nordhaus and Weitzman go out of their way to point out the positive aspects of the Stern Review. But the overwhelming conclusion, especially from Nordhaus, is that the extreme policy prescriptions of the Stern Review are way overblown.
To summarize the contrast: The Stern Review calls for a carbon tax of $350 per ton of carbon in 2015. Nordhaus’ model, which has been peer-reviewed many times, calculates the optimal carbon tax in 2015 to be ONE-TENTH of that, or only $35 per ton carbon. I find it useful to put these quantities in terms of something we understand more readily: $350 per ton carbon converts to $1 per gallon of gasoline, while $35 per ton carbon converts to 10 cents per gallon of gasoline. We are talking big differences here.
So what is wrong with the Stern Review’s economics? It is real simple – they use an extremely low interest rate, close to zero. Everything follows from this, and in my opinion, the assumption is crazy.
The essence of carbon policy is that we incur costs today for benefits many years into the future. Changing our energy usage patterns will be costly for us today, and the benefits of lower temperatures come 50, 100 or even 200 years in the future. Any time you are considering investing today for benefits in the future, you have to consider the interest rate. Investments to stabilize climate should yield returns – a rate of interest – in the ballpark that other investments yield. If we can invest in human capital, for instance, and earn 10% per year, why should we invest in climate stabilization if it yields a zero rate of return?
Nordhaus has some great examples to illustrate the unreasonableness of using a zero discount rate for climate policy: “Suppose that scientists discover a wrinkle in the climate system that will cause damages equal to .1 percent of net consumption starting in (year) 2200 and continuing at that rate forever after. How large a one-time investment would be justified today to remove the wrinkle that starts only after two centuries? Using the methodology of the (Stern) Review, the answer is that we should pay up to 56 percent of one year’s world consumption today…In other words, it is worth a one-time consumption hit of approximately $30,000 billion today to fix a tiny problem that begins in 2200…the Review would justify reducing per capital consumption for one year today from $10,000 to $4,400 to prevent a reduction of consumption from $130,000 to $129,870 starting two centuries hence and continuing at that rate forever after.”
Another point in this criticism is the essential inter-generational fairness issue. Per capita income worldwide has been growing at around 1.3% over many decades – and this is the number that the Stern Review uses. At that growth rate, per capital world consumption will grow from today’s $10, 000 to about $130,000 in two centuries. Which generation is the relatively poor generation? Are we so sure that we are impoverishing our children and our children’s children? What about all the new technologies, institutions such as democracy and market economies, physical infrastructure, and knowledge that we are bequeathing them? Do we not think that people 200 years from now will enjoy more leisure, better health, better technology, and generally be better able to pursue life, liberty, and happiness?
Read the articles, they are really convincing. For most of the media, of course, that will be too difficult. Much easier to report on Al Gore winning an Academy Award – oops, I meant a Nobel Prize.
The Journal of Economic Literature is the sister publication to the American Economic Review and is put out by the American Economic Association, the leading professional society for economists. Abstracts of the papers, and instructions on how to buy them, are available here.
I have always said that my objections to the prescriptions of the most vocal climate change advocates are on three levels: one, the climate models depend too much on positive feedbacks that are not understood; two, the models have not really been tested, but instead are calibrated to the historical data; and three, even if one accepts the models, one then has to move into the economics of optimal policy, and there the best analysis suggests relatively modest reductions in carbon emissions for the near term. I like to ask environmentalists to summarize their prescriptions with the appropriate tax per barrel of oil: tell me what you think the price of oil should be increased by, in order to recognize the impact of carbon.
But back to the reviews of the Stern Review. So the Stern Review made big headlines when it came out, as it was commissioned by the UK government and was ostensibly a serious analysis of the economics of climate change. Both Nordhaus and Weitzman deliver fatal blows, although they try to temper it a bit. Here is a quote from Nordhaus:
“The central methodology by which science, including economics, operates is peer review and reproducibility. By contrast, the (Stern) Review was published without an appraisal of methods and assumptions by independent outside experts. Nor can its results be easily reproduced…(this) does mean that fatal flaws in evidence and reasoning, which might have been caught in the early stages under normal ground rules, may emerge after the report has been published.”
Weitzman says,
“However, in my opinion, Stern deserves a measure of discredit for giving readers an authoritative-looking impression that seemingly objective best-available-practice professional economic analysis robustly supports its conclusions, instead of more openly disclosing the full extent to which the Review’s radical policy recommendations depend upon controversial extreme assumptions and unconventional discount rates that most mainstream economists would consider much too low.”
Now in the spirit of full disclosure, I recommend everyone look at the papers for themselves. Nordhaus and Weitzman go out of their way to point out the positive aspects of the Stern Review. But the overwhelming conclusion, especially from Nordhaus, is that the extreme policy prescriptions of the Stern Review are way overblown.
To summarize the contrast: The Stern Review calls for a carbon tax of $350 per ton of carbon in 2015. Nordhaus’ model, which has been peer-reviewed many times, calculates the optimal carbon tax in 2015 to be ONE-TENTH of that, or only $35 per ton carbon. I find it useful to put these quantities in terms of something we understand more readily: $350 per ton carbon converts to $1 per gallon of gasoline, while $35 per ton carbon converts to 10 cents per gallon of gasoline. We are talking big differences here.
So what is wrong with the Stern Review’s economics? It is real simple – they use an extremely low interest rate, close to zero. Everything follows from this, and in my opinion, the assumption is crazy.
The essence of carbon policy is that we incur costs today for benefits many years into the future. Changing our energy usage patterns will be costly for us today, and the benefits of lower temperatures come 50, 100 or even 200 years in the future. Any time you are considering investing today for benefits in the future, you have to consider the interest rate. Investments to stabilize climate should yield returns – a rate of interest – in the ballpark that other investments yield. If we can invest in human capital, for instance, and earn 10% per year, why should we invest in climate stabilization if it yields a zero rate of return?
Nordhaus has some great examples to illustrate the unreasonableness of using a zero discount rate for climate policy: “Suppose that scientists discover a wrinkle in the climate system that will cause damages equal to .1 percent of net consumption starting in (year) 2200 and continuing at that rate forever after. How large a one-time investment would be justified today to remove the wrinkle that starts only after two centuries? Using the methodology of the (Stern) Review, the answer is that we should pay up to 56 percent of one year’s world consumption today…In other words, it is worth a one-time consumption hit of approximately $30,000 billion today to fix a tiny problem that begins in 2200…the Review would justify reducing per capital consumption for one year today from $10,000 to $4,400 to prevent a reduction of consumption from $130,000 to $129,870 starting two centuries hence and continuing at that rate forever after.”
Another point in this criticism is the essential inter-generational fairness issue. Per capita income worldwide has been growing at around 1.3% over many decades – and this is the number that the Stern Review uses. At that growth rate, per capital world consumption will grow from today’s $10, 000 to about $130,000 in two centuries. Which generation is the relatively poor generation? Are we so sure that we are impoverishing our children and our children’s children? What about all the new technologies, institutions such as democracy and market economies, physical infrastructure, and knowledge that we are bequeathing them? Do we not think that people 200 years from now will enjoy more leisure, better health, better technology, and generally be better able to pursue life, liberty, and happiness?
Read the articles, they are really convincing. For most of the media, of course, that will be too difficult. Much easier to report on Al Gore winning an Academy Award – oops, I meant a Nobel Prize.
Sunday, April 15, 2007
Updating Beliefs on Climate Change: Extreme Weather Events
With all the cold weather of late, I have been thinking of how we should update our beliefs about changes in climate parameters as extreme weather events occur. This analysis applies, of course, to the warm weather events we had in early winter, and the earlier cold snaps back in September around here. My son is also studying conditional probability in high school right now, so this is good for him as well.
There are at least two “takeaways” from this little excursion. The first is that, as we should have suspected, extreme weather events should indeed lead to some updating of our beliefs about climate change, but not a lot. More important, and my second takeaway, is that this excursion is a great way to see some of the basic ideas of Bayesian statistics.
So I am considering how my beliefs about the probability of climate change taking place change when I observe a (local) extreme cold weather event. Intuitively, a cold event should make us wonder if climate change – which should result in warmer temperatures – is actually occurring. But also intuitively, we should be really surprised if we learn too much from one single weather event.
Our starting point is Baye’s Rule:
Pr(climate change| event) =
{Pr(event | climate change) * Pr(climate change)} / Pr(event)
In words: The “posterior” probability of climate change conditional upon observing a weather event equals: The “prior” probability of climate change, Pr(climate change), times the probability of the event happening conditional upon climate change occurring, all divided by the unconditional probability of the weather event occurring.
If you multiply both sides by Pr(event), you see that both sides of the above equation give the probability of both climate change and the weather event occurring. The equality obviously holds therefore.
We normally use the term “posterior probability” for the left hand side of Baye’s Rule. The Rule tells us how our posterior probability is different from our “prior” probability after observing an event.
It is neat to see how Baye’s rule plays out in our climate context.
Let’s suppose that we have “diffuse” prior beliefs on climate change, that is, that Pr(climate change) from the right hand side of the equation equals ½. The question is how that prior belief changes after we observe an extreme weather event.
To do the analysis, we need to know Pr(event | climate change). Again in words, this is the probability of the weather event conditional upon climate change having happened. This is a key calculation. I take “climate change having happened” to mean that the distribution of daily temperatures in my local location having shifted to the right. Specifically, I assume that climate change has increased the average daily temperature by one degree. Let me also define my extreme weather event as a new record low temperature for the day April 16 in Hanover, NH. What is the probability of this event, conditional upon climate change having occurred? Well, it turns out that the long term average daily temperature for April 16 in Hanover is 33 degrees. And the standard deviation, I will assume, is about 7.5 degrees. The record low for this date is 15 degrees, having occurred in 1940.
If we assume that daily temperatures are normally distributed, then the probability of breaking that 15 degree record given the historical mean of 33 degrees is .008198. With climate change, the average shifts up to 34 degrees and the probability of breaking the record goes down: to .005649.
We now have everything that we need to complete Baye’s rule. The denominator of the equation is a little tricky; it is the unconditional probability of the new low temperature record. To find this, we use this equation:
Pr(event) = Pr(event | climate change) * Pr (climate change)
+ Pr(event |no climate change) * Pr(no climate change)
This is just adding up the different ways that we could observe the extreme weather event: there are two ways, either through climate change or not through climate change.
We have all of these probabilities mentioned in the above discussion. If we calculate it out, we get Pr(event) = (.005649*.5) + (.008198*.5) = .0069235.
Now take the first term of Baye’s Rule and divide by the denominator; this is called the likelihood ratio. In our case, this ratio is .005649/.0069235 = .8159168.
Our posterior belief about climate change after observing the extreme cold event is about 82% of our prior belief before we observed the extreme event.
This is more than I would have expected going into this exercise. What determines how much our prior beliefs are affected?
First, note that the stronger our prior beliefs, the less we would change our priors after observing the cold event: The denominator of Baye’s Rule is a weighted average of the probability of the cold event under two different scenarios, climate change or no climate change. The weight on climate change increases as our prior belief on climate change increases, and this makes the weighted average move closer to the probability of the extreme event conditional on climate change.
As the denominator moves closer to the probability of the extreme event conditional on climate change, the likelihood ratio moves closer to one, and our prior belief is affected very little by the extreme cold event. Intuition: With strong prior beliefs on climate change, a cold event does little to affect them. With weak prior beliefs on climate change, a cold event makes us even more skeptical. Wonder why people are affected differently by events? Bayes would not be surprised!
The other thing that affects our much our prior beliefs change is the term
Pr(event | climate change) relative to Pr(event | no climate change). This gets to the heart of how informative the cold event is. Think about it: If climate change really doesn’t do anything to the probability of cold events happening, then these two probabilities would be equal, and the likelihood ratio in Baye’s Rule would equal one. (Why might climate change not affect the probability of extreme cold events? Well, if climate change did nto affect the distribution of daily temperatures very much, that would work.) And in that case, our posterior probability equals our prior probability. Makes sense, no?
On the other hand, what would make the extreme cold event very informative? This would happen if Pr(event | climate change) relative to Pr(event | no climate change) was large. This would be the case if climate change made extreme cold events very unlikely, so that the ratio of these two terms would be very small. Then the likelihood ratio would be small, and our posterior probability of climate change would be small relative to our prior probability.
Well, in conclusion, this got a little more complicated than I thought, but I learned a bit from it.
One lingering concern I have is over a “data mining” sort of issue. Let me put it this way: Seeing a record cold event in SOME locality in the country is much less informative than seeing a record cold event in one particular locality such as Hanover. Somewhere in the country is going to see a record cold event pretty often; one locality will see one only rarely. The above analysis does not apply to the event of just seeing a record cold event SOMEWHERE (well, it does apply, but the probabilities need serious adjusting -- especially the probabilities of observing extreme weather events).
All of this was stimulated because I wanted to spend the night at my camp. When I got there, this late Nor’Easter had blown out the electricity and the downdraft in my woodstove was so extreme I couldn’t get a fire started. Real pain. I was tempted to stay and cook my dinner on the Coleman stove, but came back home instead. Nasty weather.
There are at least two “takeaways” from this little excursion. The first is that, as we should have suspected, extreme weather events should indeed lead to some updating of our beliefs about climate change, but not a lot. More important, and my second takeaway, is that this excursion is a great way to see some of the basic ideas of Bayesian statistics.
So I am considering how my beliefs about the probability of climate change taking place change when I observe a (local) extreme cold weather event. Intuitively, a cold event should make us wonder if climate change – which should result in warmer temperatures – is actually occurring. But also intuitively, we should be really surprised if we learn too much from one single weather event.
Our starting point is Baye’s Rule:
Pr(climate change| event) =
{Pr(event | climate change) * Pr(climate change)} / Pr(event)
In words: The “posterior” probability of climate change conditional upon observing a weather event equals: The “prior” probability of climate change, Pr(climate change), times the probability of the event happening conditional upon climate change occurring, all divided by the unconditional probability of the weather event occurring.
If you multiply both sides by Pr(event), you see that both sides of the above equation give the probability of both climate change and the weather event occurring. The equality obviously holds therefore.
We normally use the term “posterior probability” for the left hand side of Baye’s Rule. The Rule tells us how our posterior probability is different from our “prior” probability after observing an event.
It is neat to see how Baye’s rule plays out in our climate context.
Let’s suppose that we have “diffuse” prior beliefs on climate change, that is, that Pr(climate change) from the right hand side of the equation equals ½. The question is how that prior belief changes after we observe an extreme weather event.
To do the analysis, we need to know Pr(event | climate change). Again in words, this is the probability of the weather event conditional upon climate change having happened. This is a key calculation. I take “climate change having happened” to mean that the distribution of daily temperatures in my local location having shifted to the right. Specifically, I assume that climate change has increased the average daily temperature by one degree. Let me also define my extreme weather event as a new record low temperature for the day April 16 in Hanover, NH. What is the probability of this event, conditional upon climate change having occurred? Well, it turns out that the long term average daily temperature for April 16 in Hanover is 33 degrees. And the standard deviation, I will assume, is about 7.5 degrees. The record low for this date is 15 degrees, having occurred in 1940.
If we assume that daily temperatures are normally distributed, then the probability of breaking that 15 degree record given the historical mean of 33 degrees is .008198. With climate change, the average shifts up to 34 degrees and the probability of breaking the record goes down: to .005649.
We now have everything that we need to complete Baye’s rule. The denominator of the equation is a little tricky; it is the unconditional probability of the new low temperature record. To find this, we use this equation:
Pr(event) = Pr(event | climate change) * Pr (climate change)
+ Pr(event |no climate change) * Pr(no climate change)
This is just adding up the different ways that we could observe the extreme weather event: there are two ways, either through climate change or not through climate change.
We have all of these probabilities mentioned in the above discussion. If we calculate it out, we get Pr(event) = (.005649*.5) + (.008198*.5) = .0069235.
Now take the first term of Baye’s Rule and divide by the denominator; this is called the likelihood ratio. In our case, this ratio is .005649/.0069235 = .8159168.
Our posterior belief about climate change after observing the extreme cold event is about 82% of our prior belief before we observed the extreme event.
This is more than I would have expected going into this exercise. What determines how much our prior beliefs are affected?
First, note that the stronger our prior beliefs, the less we would change our priors after observing the cold event: The denominator of Baye’s Rule is a weighted average of the probability of the cold event under two different scenarios, climate change or no climate change. The weight on climate change increases as our prior belief on climate change increases, and this makes the weighted average move closer to the probability of the extreme event conditional on climate change.
As the denominator moves closer to the probability of the extreme event conditional on climate change, the likelihood ratio moves closer to one, and our prior belief is affected very little by the extreme cold event. Intuition: With strong prior beliefs on climate change, a cold event does little to affect them. With weak prior beliefs on climate change, a cold event makes us even more skeptical. Wonder why people are affected differently by events? Bayes would not be surprised!
The other thing that affects our much our prior beliefs change is the term
Pr(event | climate change) relative to Pr(event | no climate change). This gets to the heart of how informative the cold event is. Think about it: If climate change really doesn’t do anything to the probability of cold events happening, then these two probabilities would be equal, and the likelihood ratio in Baye’s Rule would equal one. (Why might climate change not affect the probability of extreme cold events? Well, if climate change did nto affect the distribution of daily temperatures very much, that would work.) And in that case, our posterior probability equals our prior probability. Makes sense, no?
On the other hand, what would make the extreme cold event very informative? This would happen if Pr(event | climate change) relative to Pr(event | no climate change) was large. This would be the case if climate change made extreme cold events very unlikely, so that the ratio of these two terms would be very small. Then the likelihood ratio would be small, and our posterior probability of climate change would be small relative to our prior probability.
Well, in conclusion, this got a little more complicated than I thought, but I learned a bit from it.
One lingering concern I have is over a “data mining” sort of issue. Let me put it this way: Seeing a record cold event in SOME locality in the country is much less informative than seeing a record cold event in one particular locality such as Hanover. Somewhere in the country is going to see a record cold event pretty often; one locality will see one only rarely. The above analysis does not apply to the event of just seeing a record cold event SOMEWHERE (well, it does apply, but the probabilities need serious adjusting -- especially the probabilities of observing extreme weather events).
All of this was stimulated because I wanted to spend the night at my camp. When I got there, this late Nor’Easter had blown out the electricity and the downdraft in my woodstove was so extreme I couldn’t get a fire started. Real pain. I was tempted to stay and cook my dinner on the Coleman stove, but came back home instead. Nasty weather.
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