The authors have provided a revised version of their manuscript. My review has concentrated mainly on the responses to questions. Even though the authors made a case that the climatological results they obtain are robust, there are still some contentious aspects on the experiment design and I will attempt here to make my case more explicitly.
The authors rebutted my comment on the 'a-physical' character of their experiment design as follows:
1. there are no combinations of these parameters which can be excluded for the early Eocene period
2. This approach does not make the assumption that the only effect of eccentricity on the Earth's climate is through its effect on the amplitude of the precession cycle
They argument one is a useful condition to avoid wasting computing time, but not sufficient to guarantee a good design. Condition 2. is perhaps true but in fact comes at the price of wrong assumptions.
I agree that my condemnation of the design as 'a-physical' was not the most explicit, so I will rephrase my argument differently.
Latin Hypercube and related techniques (maxi-min, etc.) are mathematically justified by the hypothesis that distances in the input space (here $e$, $\varpi$, $\varepsilon$) translate _a priori_ into distances in the output space. Of course this is never a posteriori quite true (hence the interest of actually doing the experiment), but this hypothesis is the prior assumption which precisely justifies the interest of maximising distances in the input space (this is, _a priori_, the best way to make experiments maximally informative). See textbooks on this (e.g. Santner, Williams and Notz).
A LHS with maximisation of Euclidian distances in the $\{e,\varpi,$varepsilon\}$ space, as done here, therefore implies two wrong assumptions: there is a non-zero distance between two experiments with different $\varpi$ but zero eccentricity (while the insolation input is rigorously the same), and there is a twice greater distance between $\varpi$=359 degrees and $\varpi$=0 degrees, than between, say $\varpi$=100 degrees and $\varpi$=280 degrees. Both are wrong, not because of assumptions on model response, but because $\varpi$ is (1) an angle which (2) loses meaning at $e=0$.
On the other hand, as Devleeschouwer or Araya-Melo have shown, an $\{e\sin\varpi$,$e\cos\varpi\}$ input space does not prevent at all to detect effects of eccentricity. However, because of the geometry of insolation, we can never expect the same climate in two experiments with both high eccentricity but two opposite phases of $\varpi$. Net effects of eccentricity tend to come as the result of a non-symmetrical (non-linear) effects of positive and negative climatic precession anomalies (a form of rectification), or possibly more subtle effects in the tropics which could also be detected with a $\{e\sin\varpi$,$e\cos\varpi\}$ experiment design.
Of course I do not want to block a nice paper for that reason alone, but I cannot accept the line of defense that LHS sampling a $\{e,\varpi\}$ space is a good option, out of the fear of spreading bad practice. |