Jo Nova has a post today about an investigation of climate modeling mathematics by her husband David Evans. Evans believes he has uncovered a significant and perhaps major flaw in the mathematics at the core of the climate models.
The climate models, it turns out, have 95% certainty but are based on partial derivatives of dependent variables with 0% certitude, and that’s a No No. Let me explain: effectively climate models model a hypothetical world where all things freeze in a constant state while one factor doubles. But in the real world, many variables are changing simultaneously and the rules are different.
Partial differentials of dependent variables is a wildcard — it may produce an OK estimate sometimes, but other times it produces nonsense, and ominously, there is effectively no way to test. If the climate models predicted the climate, we’d know they got away with it. They didn’t, but we can’t say if they failed because of a partial derivative. It could have been something else. We just know it’s bad practice.
The partial derivatives of dependent variables are strictly hypothetical and not empirically verifiable – like the proverbial angels on a pinhead. In climate, you cannot vary just one variable, hold everything else constant, and measure the change in the other variable of interest. Employing partial derivatives in climate therefore incurs unknown approximations – so it is unreliable.
One might argue that the partial derivatives are good approximations, maybe all we’ve got and better than nothing. But this is an unknowable assertion because the partial derivatives are with respect to dependent variables. One might argue that certain climate variables are almost independent, in which case partial derivatives with respect to those variables are only slightly unreliable — and you’d be on more solid ground. But you wouldn’t really know how solid, so any model relying on these partial derivatives would have to be tested against reality — and if the model turned out not to work too well, it may be because the partial derivatives have the wrong values, or it might be because they are conceptually inappropriate, or it could be for some other reason entirely, and you wouldn’t know because said partial derivatives are not empirically verifiable.
It sounds to me as if that estimate is quite a wild card in this case, and perhaps it is this factor that creates such broadly different outcomes in climate models, as seen below:
Evans had previously done some work in this area that held some great promise, but in my opinion he released that work prematurely, and it was heavily refuted.
This looks like a much more concrete issue that will be hard to justify and/or explain away.
UPDATE: (9/29/15) Jo Nova adds this via email, with the request it be included here.
People are quoting us in comments with things we didn’t say, and getting caught by tangential things. It will make the discussion on WUWT more productive.
1. David didn’t say this was a “major error”. To summarize:
The partial derivatives used by the basic model do not,
mathematically, exist, and they are not empirically verifiable —
so they are a poor basis for a model. We use this clue in
later posts of this series to construct a better basic model.
2. This is part 4 of a long series. People need to read the
background to fully understand it. Some inferences are leading
to a pointless discussion. eg: of course partial differentials
can and do work in lots of models. In part 1, David pointed
out that most successful physical models get tested and either
dumped or improved in a short time frame. Climate models,
though, can remain wrong for decades. In parts 2 and 3 David
explains precisely what the basic climate model is.
3. David’s work last year was not refuted. We published one
correction, showing that the notch was suggestive of a delay,
but not mandatory as first thought. The delay (which is what
matters) is still supported by other independent studies of
empirical evidence which we cited. As this series will show,
the big findings from the last round stand up even stronger
than before. Publishing it then was very useful as we got some
useful feedback. The notch is real, it still suggests a delay
of one half a solar cycle, and that fits the data better than
any other explanation. We’ll be going through all that in more
4. The main point is the disconnect between science and “PR”:
their use of partial derivatives on dependent variables may be
partly right or wholly wrong — yet the IPCC says they are 95%