An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and
on numerical solutions of a planetary geostrophic basin model.
Dan Hughes blog
on numerical solutions of Lorenz equations is a good read.
The principle of the first method lies
on the numerical solution of Newton's equations of motion to propagate the system, whereas the second stochastically generates states of a system according to a predetermined statistical mechanical probability distribution.
Not exact matches
When the geometry of such a system is specified, the simulator allows the user to vary primary and secondary scattering foil material and thickness and to see results in approximately 100 milliseconds, about 10 million times faster than Monte Carlo simulations, which are simulations and computational algorithms that rely
on random sampling to obtain results for extremely complex problems that have only
numerical solutions.
The report indicates that the child really kicked butt
on the estimating
solutions to problems and
numerical estimation strategies, but fell short in classification and logical reasoning.
It is very clear that changes to certain aspects of the mathematical models,
numerical solution methods, and application procedures are in fact based
on «the match to observations».
Ultimately the numbers calculated by the GCMs are the outcome of
numerical solution methods applied to algebraic approximations to the continuous equations
on discrete temporal and spatial grids.
There are also broadly similar ways of thinking in, e.g.,
numerical integration, and in the
solution of differential equations
on progressively finer grids.)
The people who utter the D word do not care about what the objects of their ires actually think: because the issue is not one's opinion
on the GHG properties of CO2, and not even what the temperature record says, or what the equations may indicate, or how good the
numerical solutions we call Models are.
article by Heinz and me (reference available
on request), once the minimal scale (smallest scale feature of vorticity) is properly resolved by a
numerical model, the correct Navier - Stokes dissipation form (second order derivatives) can be used and produces the correct spatial spectrum, i.e. the
numerical solutions converge.
The success of
numerical weather prediction at predicting say the 500 hpa height field
on the time scale of the lifetime of a baroclinic wave (nominally 4 - 7 days) is a testimony to the credibility of these
solutions
But the mathematical analysis of the frequencies, the demonstrations of the problems with the continuum systems using convergent
numerical solutions on the Exponential thread, and the dynamical core manuscript itself should make the issues very clear.