21 ms·

Here is the statistical analysis from the paper: The method of Roe et al. is summarized as follows. Let 1L be the change in glacier length over the past 130 ye

by acover 10y ago

Here is the statistical analysis from the paper: The method of Roe et al. is summarized as follows. Let 1L be the change in glacier length over the past 130 years (∼1.9 km), and let σL be the standard deviation of glacier length due to stochastic fluctuations in mass balance, b, from natural, interannual climate variability. The signal-to-noise ratio is defined by sL =1L/σL . Likewise, sb =1b/σb . Ref. 12 demonstrates that the two are related via sL =γ sb , where γ is an amplification factor that depends only on the duration of the trend and the glacier response time, τ . The probability density function (PDF) for sb is generated by combining the signal-to-noise ratios of the observed melt-season temperature and annual-mean precipitation trends, normalized by the summer (bs) and winter (bw ) mass-balance variability (Supplementary Fig. 1a,b,c), respectively. We take σbw = 0.3 myr−1 and σbs =0.5 myr−1 , based on the observed mass-balance variability at Gulkana Glacier and the analysis of the global datasets of glacier mass balance33. The glacier response time is given by τ =−H/bt , where H is a characteristic glacier thickness, and bt is the (negative) net mass balance at the terminus. We set H=590 m, based on the scaling relationship for glacier geometry suggested by Haeberli and Hoelzle34 and measured cross-sections35; and we set bt =−7 myr−1 , estimated by extrapolating the vertical mass-balance profiles calculated by Flowers et al.8 , thus giving a central estimate for τ of ∼80 years. A PDF is estimated assuming τ follows a gamma distribution incorporating a broad uncertainty of στ =τ /4 (Supplementary Fig. 1d). The PDFs for γ and sb are combined to give a PDF for σL from the relation σL =γ 1L| obssb . This, in turn, is used to evaluate the null hypothesis that 1L| obs occurred due to natural variability. Supplementary Fig. 1e shows our estimate that there is only a 0.5% chance that the observed retreat of Kaskawulsh Glacier happened in the absence of a climate trend.

Almaviva 10y ago
The 0.5% quote is fine. It's turning it into a 99.5% that is not fine. It's essentially like saying that a pair of dice that rolled a 12 has a 97% chance of being loaded, because there's only a 1 in 36 chance of rolling that high.
- archgoon 10y ago
  Let's think about this. Let's assume that when a river gets redirected, a scientist goes and investigates it (which seems reasonable), and is asked what is the chance that it happened by natural causes, or is due to global warming. Based on the analysis that @acover shared with us, we can see that out of a thousand such dispatches, 995 will be due to global warming and 5 will be due to natural variability. So it seems correct for that scientist to conclude "It's 99.5% due to global warming.". In fact, saying that it's .5% due to natural variability is equivalent. You are probably thinking of the jelly bean situation, where a test is performed to detect something within a sample population. The test has a failure rate, and the population has a base rate of occurrence. In this case (thanks @acover), they are directly calculating the base rate. Now, you could also ask "How many times in a year will a scientist be dispatched and be wrong", which is a again a different question (and is closer to the scenario you described).
  - acover 10y ago
    I am out of my depths but I do not think you are correct. The paper appears to create a model for a single glacier's retreat. Selects the parameters of this model by analyzing all glaciers. Then determines the retreat of this glacier is unlikely under this model. The issue is that there is a sampling bias. This glacier is not like most glaciers [I assume]. It was not randomly sampled from all glaciers. It was selected because of a river diversion due to glacial retreat. What did they do to compensate for this sampling bias? I don't see it.
  - drt1245 10y ago
    >Let's assume that when a river gets redirected, a scientist goes and investigates it This is a faulty assumption and is what leads to the wrong conclusion. The probability of 0.5% is for a randomly selected river. That is, if you went and examined 200 randomly selected rivers, 1 of them (on average) would be redirected due to natural variability. That does not imply that the remaining 199 were redirected due to global warming. It does not even imply that the remaining 199 were redirected at all! What is needed is the percentage of rivers that have undergone this redirection. Here's a simplified example: If it's ~0.5%, you conclude it's just natural variation. If it's >0.5%, you conclude that something (possibly global warming) is increasing the number of rivers that are being redirected. If it's <0.5%, you conclude that something is decreasing the number of rivers that are being redirected.

by acover 10y ago

Almaviva 10y ago

The 0.5% quote is fine. It's turning it into a 99.5% that is not fine. It's essentially like saying that a pair of dice that rolled a 12 has a 97% chance of being loaded, because there's only a 1 in 36 chance of rolling that high.

archgoon 10y ago
Let's think about this. Let's assume that when a river gets redirected, a scientist goes and investigates it (which seems reasonable), and is asked what is the chance that it happened by natural causes, or is due to global warming. Based on the analysis that @acover shared with us, we can see that out of a thousand such dispatches, 995 will be due to global warming and 5 will be due to natural variability. So it seems correct for that scientist to conclude "It's 99.5% due to global warming.". In fact, saying that it's .5% due to natural variability is equivalent. You are probably thinking of the jelly bean situation, where a test is performed to detect something within a sample population. The test has a failure rate, and the population has a base rate of occurrence. In this case (thanks @acover), they are directly calculating the base rate. Now, you could also ask "How many times in a year will a scientist be dispatched and be wrong", which is a again a different question (and is closer to the scenario you described).
- acover 10y ago
  I am out of my depths but I do not think you are correct. The paper appears to create a model for a single glacier's retreat. Selects the parameters of this model by analyzing all glaciers. Then determines the retreat of this glacier is unlikely under this model. The issue is that there is a sampling bias. This glacier is not like most glaciers [I assume]. It was not randomly sampled from all glaciers. It was selected because of a river diversion due to glacial retreat. What did they do to compensate for this sampling bias? I don't see it.
- drt1245 10y ago
  >Let's assume that when a river gets redirected, a scientist goes and investigates it This is a faulty assumption and is what leads to the wrong conclusion. The probability of 0.5% is for a randomly selected river. That is, if you went and examined 200 randomly selected rivers, 1 of them (on average) would be redirected due to natural variability. That does not imply that the remaining 199 were redirected due to global warming. It does not even imply that the remaining 199 were redirected at all! What is needed is the percentage of rivers that have undergone this redirection. Here's a simplified example: If it's ~0.5%, you conclude it's just natural variation. If it's >0.5%, you conclude that something (possibly global warming) is increasing the number of rivers that are being redirected. If it's <0.5%, you conclude that something is decreasing the number of rivers that are being redirected.