Scientific Principles of Climate Science?

The scientific method is the basis of modern society with the basic requirement that a scientific theory as an expression of the scientific method, must allow making observable predictions.

The theory stating that the Earth rests on the backs of four invisible turtles the presence of which cannot be observed, is not a scientific theory. Controling an airplane by throwing dice is not a scientific approach and will not work, because the outcome a dice throw is not predictable.

The requirement of prediction connects to the mathematical concept of wellposedness formulated by the French mathematician Jean Leray in the 1930s: A mathematical model with certain output from certain input data, is said to be wellposed if small changes in input data result in small changes in output. The model is said to be illposed  if small changes in input can result in large changes in output.

The rationale is that output from an illposed model in general carries no relevant information, since small changes in input, which cannot be controlled,  can give widely different outputs making prediction impossible.  An illposed mathematical model therefore does not represent a scientific theory.

In principle, climate science can be viewed as a mathematical model of the thermodynamics of the Earth-atmosphere system, in the form of the Navier-Stokes equations. It was this model that led Leray to his study of wellposedness, motivated by the fact that the Navier-Stokes equations in general have turbulent solutions with pointwise values being very sensitive to small perturbations, thus being pointwise illposed. But meanvalues show to be insensitive and thus the Navier-Stokes equations show to be wellposed in an appropriate meanvalue sense, as developed in Computational Turbulent Incompressible Flow.

Climate science based on the NS equations may thus be capable of making predictions, although the computational technology required to model the whole Earth-atmosphere, lies far into the future.

Climate science is obsessed by a task of finding evidence of catastrophic anthropogenic global warming CAGW from CO2 emissions, which means finding a large effect of global warming of 3 C from the small change of an increase of the concentration of atmospheric CO2 from the present 390 ppm to 600 ppm. CAGW is thus based on an illposed model and as such cannot be viewed to have scientific support.  To be able to predict the effect of a change of 0.02% CO2, a very high precision climate model must be used, and such a model is not foreseeable.