Practical likelihood functions are very flat-topped, so the idea that a maximum likelihood function (MLE) can be confined to a point is a theoretical mirage. See Chapter 3 of S. Konishi, G. Kitagawa, Information Criteria and Statistical Modeling, Springer, 2008. Even if you want to set aside Bayesian considerations, whose priors tend to sharpen the posteriors, the best you can do is expected likelihoods, because likelihoods in practice, just like p-values, are random variables. Accordingly, the MLE is a neighborhood, because a point has probability mass zero.
Besides, … the question of multimodality [wasn’t addressed]. Actual Expected Climate Sensitivity is a combination of the densities over oceans and land, each of which have different distributions and modes. (See https://goo.gl/pB7H24 which is from http://dx.doi.org/10.1126/science.1203513) Accordingly, their combination is (at least) bimodal. Ocean ECS has 4 modes. Land ECS has 2 modes, one slightly higher than the other, the higher being at +3.4°C and the second at about +3°C. Worse, the variance of land ECS is over twice than of oceans.
Finally, what you should be looking at is the ECS2x over land, not combined. Even if granted to want to go with the location of the highest mode, that’s +3.4°C.
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