And so begins the list of errors. 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.

To see an example of how partial differentials can produce quixotic contradictions in a normal and simple situation, see what happens when they are used with the Ideal Gas Law in this PDF from MIT.

Partial derivatives are useful when there are only a few, independent variables. But in the climate paradox, there are a lot of variables and most of them are dependent. Partial derivatives might work, or they might blow up. For them to make sense we’d need to live in a world which can be held in a constant steady state while one factor does a step change. It’s a situation that probably hasn’t happened in the last 4.5 billion years.

The field of climate science draws on maths, but rarely draws on the leading mathematical minds. This first error of the three illustrates how people who may be well trained in geography or oceanography (or divinity) can miss points that professional mathematicians and modelers would not.

The big problem here is that a model built on the misuse of a basic maths technique that cannot be tested, should not ever, as in never, be described as 95% certain. Resting a theory on unverifiable and hypothetical quantities is asking for trouble. Hey but it’s only the future of the planet that’s at stake. If it were something more important, climate scientists would have brought in some serious maths guys.

This error is fairly easy to describe; the harder, bigger errors are coming soon, as we try to roll out the points as fast as we can. — Jo

________________________________________________

# 4. Error 1: Partial Derivatives

#### Dr David Evans, 26 September 2015, Project home, Intro, Previous , Next, Nomenclature.

There are three significant errors with the conventional basic climate model (which was described in the basic climate model core part 1,and basic climate model in full part II). In this post we discuss the first error, the misapplication of the mathematical technique of partial derivatives, because it is the easiest of the three to describe.

By the way, noting that there are problems with the conventional model is hardly new even in establishment circles, but apparently itemizing them is a little unusual. For example, Sherwood et. al said in 2015 ^{[1]}: *“While the forcing–feedback paradigm has always been recognized as imperfect, such discrepancies have previously been attributed to variations in “efficacy” (Hansen et al. 1984), which did not clarify their nature.”*

### Overview

The basic model relies heavily on partial derivatives. A partial derivative is the ratio of the changes in two variables, *when everything apart from those two variables is held constant.* When applied to the climate, this means everything about the climate must be held constant while we imagine how much one variable would change if the other was altered.

For example, how does changing the surface temperature affect how much heat is radiated to space (the outgoing longwave radiation, or OLR), if everything else — including humidity, clouds, gases, lapse rates, the tropopause, and absorbed sunlight — stays the same? (This particular partial derivative is the Planck sensitivity, central to the conventional model.)

## Recent Comments