The key to understanding Spencer’s choice of a 700 m mixed layer depth is in Figure 6. My best-fit values for alpha and beta at h = 700 m were 3.71 W/m^2/°C and 1.55 W/m^2, respectively. My technique was somewhat different from Spencer’s–for some reason he averaged together thousands of different curves that seemed to fit the data pretty well, and I assume he averaged the adjustable parameter values from these different model runs, as well. Therefore, he obtained similar, but not identical, values: alpha = 3.0 W/m^2/°C and beta = 1.17 W/m^2. Remember that for Spencer’s hypothesis to work, he needed to obtain an alpha value corresponding to negative (alpha > 3.3) or weakly positive feedback. The value alpha = 3.0 corresponds to positive feedback, but it is much weaker than the range Spencer gives for the IPCC models (alpha = 0.9-1.9). So why not choose a mixed layer depth of 800 or 1000 m, and obtain an even larger alpha value? Because the graph in Figure 3 dictates that Spencer also needed a beta value close to 1 W/m^2. And guess what? His ad hoc statistical method automatically gave him answers in the right range!
Did he purposefully manipulate his method to produce just the right values? I actually don’t think so. Roy’s computer program may have generated just the right values simply due to luck, combined with a marked misunderstanding of his model system and a flawed statistical method. When I generated the 24 model curves in Figure 5, which all fit the data equally well using widely different parameters, I collected the averages of all the best-fit parameters and got: alpha = 3.3 W/m^2/°C, beta = 1.38 W/m^2, h = 625 m, and ∆To = -0.66 °C. Wow, those are close to Roy’s preferred parameters, right? Well, the truth is that at first I ramped the ocean depth from 50 to 1000 m, and some of my average parameter values were too low. All I had to do to get what I wanted was change the upper bound to 1200 m. But that’s the point, isn’t it? I could get whatever I wanted by judiciously choosing the right boundary conditions… or by dumb luck.
This discussion brings up another intriguing question. What if we were to choose a realistic mixed-layer depth? What kind of alpha and beta values would we obtain then? In Figure 6, the values for h = 100-200 m are alpha = 0.53-1.06 and beta = 0.22-0.44. In other words, the feedback would have to be just as positive as, or more positive than, that assumed by the IPCC models. And as for beta, Ray Pierrehumbert pointed out that if it were as high as Roy Spencer wants it to be, it would produce fluctuations in the net radiation flux that are much larger than actually observed via satellite. He instead suggested a more reasonable value of 0.25 W/m^2 for beta. So what do you know? By assuming a reasonable mixed layer depth, you can obtain a beta value that is consistent with satellite observations, and an alpha value that indicates feedback that is at least as positive as the IPCC asserts. But then, they wouldn’t be consistent with Roy Spencer’s method for estimating beta shown in Figure 3, or with his hypothesis that climate feedbacks are more negative than the IPCC estimates.
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