Short Term Global Warming (in the wild)

Let me start by saying I’m not an expert on global warming. I’m absolutely sure the earth is getting warmer (think melting ice caps) and very sure that it is caused by humans (green house gases). But who knows. Remember, if someone yells their dissenting opinion loud enough, it becomes fact, right?

Anyway, I’ve read some articles about how global warming has “stopped” in the last ten years. For instance, this article: “Climatologists Baffled by Global Warming Time-Out” states: “At present, however, the warming is taking a break,” confirms meteorologist Mojib Latif of the Leibniz Institute of Marine Sciences in the northern German city of Kiel. Latif, one of Germany’s best-known climatologists, says that the temperature curve has reached a plateau. “There can be no argument about that,” he says. “We have to face that fact.”

It goes on to say: “Even though the temperature standstill probably has no effect on the long-term warming trend, it does raise doubts about the predictive value of climate models, and it is also a political issue. For months, climate change skeptics have been gloating over the findings on their Internet forums. This has prompted many a climatologist to treat the temperature data in public with a sense of shame, thereby damaging their own credibility.”

This sounds like he is claiming that the warming has stopped. I disagree with this. You can have a system that is, on the average increasing over the long term, while still observing very flat or even declining trends when we know the overall system is increasing. That doesn’t mean that the system isn’t increasing, it just means we’ve seen one realization of the random system that hasn’t increased entirely by chance.

Here is a simulation experiment. (All these numbers are made up, but they prove the point):
Consider at year 1 the average temperature is 75 degrees. Call this x[1]. Then at year two we observe a realization from a normal random variable whose mean is 1.005*75 with standard deviation 1. Call this x[2]. x[3], the temperature in the the third year, will than be an observation from a normal random variable with mean 1.005*x[2] and standard deviation 1.

Over the long run this is an increasing sequence, but let’s look at what happens in the relatively short term. I simulated 10,000 of these such chains for 100 “years” each.

After 5 years 20.4% of these sequences we below the starting temperature of 75 degrees. After 10 years, 12.8% were below 75 degrees. Think about that. We have a known increasing sequence and after 10 years, 12.8% of them ended below where they started. Global warming is like this. We can see small periods of decline, in fact we EXPECT to see small periods of decline, within this increasing sequence.

What happens when we look at this sequence after 50 years? 0.006% are below the starting temperature of 75 degrees. After 100 years, 0 are below 75 degrees.

So to say that global warming is “taking a break” based on ten years of evidence seems like bad science to me. And this is certainly not evidence invalidating the long term usefulness of climate change models.

Cheers.

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Posted on November 24, 2009, in Uncategorized. Bookmark the permalink. 4 Comments.

  1. This is a nice piece. What did you use to run your simulations? I am guessing R, can you add to your post your r file?

    • ## Number of “years”
      n<-100
      ## Number of simulations
      jn<-1000
      ## standard deviation
      sigma<-1
      beta<-1.005
      x<-vector(mode="numeric",length=n)
      y5<-vector(mode="numeric",length=jn)
      y50<-vector(mode="numeric",length=jn)
      y10<-vector(mode="numeric",length=jn)
      y100<-vector(mode="numeric",length=jn)
      x[1]<-75
      for (i in 2:n)
      {
      x[i]<-rnorm(1,beta*x[i-1],sigma)
      }
      plot(x,type="l",ylim=c(65,150))

      for (j in 1:jn)
      {
      x[1]<-75
      for (i in 2:n)
      {
      x[i]<-rnorm(1,beta*x[i-1],sigma)
      }
      lines(x,type="l")
      y10[j]<-x[10]-x[1]
      y100[j]<-x[100]-x[1]
      y5[j]<-x[5]-x[1]
      y50[j]<-x[50]-x[1]
      }
      sum(y5<0)/jn
      sum(y10<0)/jn
      sum(y50<0)/jn
      sum(y100<0)/jn

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