Canadian Contretemps

Guest Post by Willis Eschenbach

Driving home today, I heard about a new report from one of those Canadian “we work for the Government but we’re actually really truly independent, honest we are” kind of organizations. It’s called “PAYING THE PRICE: THE ECONOMIC IMPACTS OF CLIMATE CHANGE FOR CANADA.” It is chock full of the usual nonsense about how, in a country plagued by cold Arctic winds and suffering from a short growing season, a couple degrees of warming will be a multi-billion dollar national tragedy. It featured the usual huge numbers, warming will cost multiple tens of billions of dollars per year. (Curiously, there is no mention of any billions in supposed costs from the 20th century warming.)

I got to wondering about how they estimated these huge costs. I mean, were they based on scientific studies, or from actuarial data, or were they estimated from past damages, or were they just extracting the numbers from their fundamental orifices?

The answer, I found out, is “none of the above”. Once again, it’s models all the way down. In this case, it’s a whiz-bang model called Page09. Here’s their diagram of how it all works, from page 37 of the cited report.

Figure 1. Description from the climate report of the model used to estimate the damages from warming temperatures.

Damage functions? I like the sound of that, I never heard of a “damage function”, but then I was born yesterday. So I set out to understand the Page09 damage functions.

In my research I find this:

Within the PAGE09 Model, damage from climate change is modelled firstly as combination of specified damage functions for sea level rise, economic effects and non-economic effects.

In this reference they give the general form of the damage function. I have spread out the right side of the equation to show the two different parts.

Climate change economic and non-economic impacts before adaptation are captured as a proportion of GDP by the climate change damage function. As do all the other main IAMs with the exception of MERGE, damage is defined as a non-linear function (Bosello and Roson, 2007). Welfare impacts (WI) are expressed as a polynomial function of the difference between regional and tolerable temperature levels (RTT) as follows:

WI(t, d, r) = [RTT(t, d, r) / 2,5 ^POW ]        *         W(d, 0) *[WF(r)/100] * GDP(t, r)

where t corresponds to time, d identifies the damage type (economic, non-economic, sea level rise) and r the region; 2.5 are the °C corresponding to the tolerable increase in temperature due to global warming; POW is the power of the polynomial impact function; W(d, 0) is the impact in the focus region (i.e. EU) at 2.5 °C and WF(r) is the regional weight applied to EU impact to calculate the impact in other world regions. SOURCE

Let me give a stab at translating that into English. First, the left hand side in brackets says take the amount by which the region is warmer than the tolerable range RTT(t,d,r) . Divide that by 2.5, and take that to some power POW. That gives you the damage impact index.

Second, the right hand side just adjusts the damage index calculated on the left hand side, to convert the impact into a dollar value. The important thing to note is that for a given damage type and region, the right hand side is a constant, that is to say it does not vary with T. All the work is done by the left-hand side.

Another reference gives the exact same equation for the damage function, with different symbols:

1.3.2 Model adjustments

At the core of the damage function in PAGE09 is the Equation (5).14

d = alpha * (TACT/TCAL) ^ beta

where d is the damage, alpha is the damage at the calibration temperature, TCAL is the calibration temperature rise, and TACT is the actual temperature rise, beta is the damage exponent.

The calibration temperature is on average 3°C. Therefore, if the actual temperature rise is 3 °C, on average, the damage equals alpha. The damage exponent, beta, becomes more important as temperatures rise above TCAL. In the standard model, beta is entered as triangle (1.5, 2, 3). Therefore, on average, the exponent is 2.167 (slightly above a quadratic), meaning that at twice the calibration temperature (on average, TACT equals 6°C), the damage will be 4.5 times alpha. SOURCE

The damage function graphs out as shown in Figure 2, for various values of the power coefficient POW (also called “beta”) and RTT(t, d, r) (also called “TACT”).

Figure 2. The form of the damage function for the triangular number POW = {1.5, 2, 3}. Note that for a 5° rise the maximum curve (POW = 3) forecasts eight times the damage.

This shows that in all cases used in, damage rises faster than temperature.

There are some odd parts of using this form of a damage function.

First, the one that rises the fastest with increasing warming (POW = 3, green line) starts out the slowest. What would be the physical reason for that?

Second, it assumes that human beings don’t learn. Sure, if there is one year of warmer weather, some farmers will lose money from planting the wrong thing, or at the wrong time. But if the warmer weather continues, the farmers will plant earlier and rejoice that the growing season is longer.

There is also another problem with this kind of analysis. In addition to assuming that farmers are stupid and that damage goes up geometrically as temperatures rise, there is no provision for the benefits of the warming. They pay lip service to the idea of benefits in the report, but I see no serious understanding of the difference between the costs and the benefits of warming for Canada. One difference is that the costs are often short-term (adjustment costs), while the benefits of the warmer climate are often longer lasting.

Again, farming is a good example. The costs to farming of a warming are short-lived. For a few years the farmers would plant something that might not be optimum for the new, warmer climate. But after that, the longer growing season is a benefit forever … how can they not include things like that?

Around the latitude of Canada, the change in average temperature as one goes north is on the order of 2.5° (where damage = 1) for every couple hundred miles. So if you took a Canadian farm and moved it two hundred miles south, do you seriously think that the farmers would suffer huge problems?

The same thing is true of the forests. They claim there will be huge damage to the forests from a few degrees temperature rise … but for many forests in Canada, the same forest exists two hundred miles to the south of a given point … and two hundred miles to the north of that point. That’s a change of FIVE DEGREES, OMG, THE SOUTHERN TREES MUST BE BURNING UP, THEY ARE FIVE DEGREES WARMER THAN THE NORTHERN TREES, COULD BE EIGHT TIMES THE DAMAGE …

I fear I can’t appropriately express my contempt for this kind of grade-school level of thinking about damage impact. If that’s the best a bunch of “damage analysts” can come up with, I’d fire them on the spot.

Always learning, I find out that this family of models are called “IAMS”, for Impact Assessment Models. The most trenchant comment I have found about them comes from the first source cited above, which says (emphasis mine):

An interesting challenge to the methodology of IAMs comes from a series of papers from Weitzman (2009a, 2009b, 2009c). In these papers, he puts forward a number of critiques of the current cost-benefit analysis of climate change, especially the approach embodied in IAMs.

Weitzman’s observations go even further with the elaboration of what is referred to as the ‘dismal theorem’. The idea is basically that under certain conditions, the expected loss from high-consequence, low-probability events can be infinite. In such a situation, standard cost-benefit analysis is therefore no longer an appropriate tool. Weitzman argues that, given the extent of our current understanding, these conditions apply to climate change.

Taking this idea to its limit would suggest that IAMs have little relevance for policy, as the response ought always to be to choose policies that do everything possible to avoid an infinite loss, even if there is only a small probability of such an outcome.

This “dismal theorem” is an extremely important conclusion, and is applicable to a host of the modeling exercises involved with thermal doomsday scenarios.

So Canadians, when they throw this high-cost, low-value modeling exercise in your face, you can just say “Sorry, go hawk your model results somewhere else. IAMS have little relevance for policy”.

Finally, as a businessman, I’ve done a host of cost-benefit studies. I have no problem with a proper historically based cost-benefit analysis of some possible future occurrence or action. However, the “PAYING THE PRICE …” report is nothing of the sort.

My condolences to my northern neighbors, who have their own Kyoto crosses to bear …

w.

PS — The climate models say that the maximum effect of the putative warming will be seen in the extra-tropical winter nights. Is this a problem? I mean, I don’t hear a lot of Canadians saying “Dang, it’s getting way too warm after midnight in February” …

PPS — my favorite argument is that the problem is not the absolute temperature change, it is the speed of the temperature change that is claimed will cause the problems. Yeah, at the much-hyped theoretical future rate of 0.03 degrees of warming per year, watch out when you step on board. If you’re not ready for it, the G forces from suddenly taking on that magnitude of high-speed warming can cause whiplash …