Discussion of RealClimate Comments: Part 0
The persons in charge of the GISS/NASA RealClimate Web site have made it clear that continued discussions of this issue are not welcomed over there. So I’ve moved over here.
Patrick, I have books and I have papers; several books and many many papers. To know what makes up a specific model we need the continuous equations for that model. The same goes for the discrete approximations, numerical solution methods, and the actual coding.
Not even addressing the parameterizations of sub-grid processes, it is highly unlikely that any of the codes utilize the basic fundamental equations of fluid motions; let’s call them the Navier-Stokes equations. For one thing, the very difficult problem of turbulence must be addressed. For another, the spatial resolution used in the calculations cannot begin to resolve the gradients of driving potentials for mass, momentum, and energy exchanges both within the solution domain and at its boundaries. For a third, the extremely difficult issues associated with multi-phase flows must be addressed. The list goes on and on.
Thus all the codes utilize model equations developed from the basic equations by adopting Idealizations, appropriate assumptions, and associated approximations. SImply pointing to a book written about the Navier-Stokes equations as a source of information for what is used in a specific model and code is not a correct specification of the answer.
Let’s take as an example the momentum balance model for the vertical (radial) direction for the atmosphere. The number of possible formulations for this single equation is somewhat large. Consider the following possibilities:
(1) no equation at all
(2) an equation expressing the hydro-static balance between the pressure gradient and the gravitational force
(3) a form in which only a few terms have been dropped from the fundamental formulation
(4) the complete un-modified form of the fundamental statement of the momentum balance
(5) various modifications applied to the above (as applicable) to include different approaches to modeling of turbulence.
And this list is only a zeroth-order cut and I’m sure many others can be listed.
Why are the actual continuous equations so important, beyond providing an indication of what phenomena and processes can and cannot be described. The system of PDEs plus ODEs contains critical information relative to the characteristics of the model equations, well-posed or ill-posed, boundary condition specifications ( where, how many, and what), propagation of information within the solution domain and at the boundaries, and the proper approach for solving the discrete approximations to the continuous equations. Ad hoc specification of boundary conditions based solely on the discrete approximations is a well-known source of difficulties in numerical solution mehtods, for one example. The correct representation of discrete approximation for integrals of div and curl in non-orthogonal coordinate systems, for another. Some model equation systems for the basic hydrodynamics of atmospheric fluid flows are known to not be well-posed, as another. There are many other critical aspects that are set by the system of continuous equations.
I and several others have attempted to find in the published literature a summary of the actual final form of the continuous equations used in, for example, the GISS/NASA ModelE model and code. None of us have been successful. We have been directed to the papers cited on the ModelE Web pages. The information is not in those papers. Recently, Gavin Schmidt directed me to a paper from 1983. The vertical-direction momentum balance model in that paper is the hydro-static version listed as (2) above.
So, somewhere between papers published in 1983 and those on the ModelE Web pages published in 2006 there might be a specific statement of the equation for the vertical momentum balance model that is actually used in the GISS/NASA ModelE code. We have been told several times that it’s there, yet we can’t be directed to the specific paper, page number, and equation.
Several people have attempted to find that specific statement and none have been successful. I hope you will accept a challenge and start a search for that equation.