Models Methods Software

Dan Hughes

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.

Response to comments #178, and #205 on RealClimate.

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.


September 12, 2008 - Posted by | Uncategorized |


  1. Don’t dream Dan .
    Thay can’t give you what they don’t have .
    I am pretty sure that there is not a comprehensive functionnal description of the model expressed in form of continuous equations .
    Besides this thing moves with the time , it would have to be updated , reviewed , printed , published . Too much work .

    There are probably bits and pieces especially for the parts that change very often and that are thought delicate . But no summary .

    The proof of this hypothesis is easy – if such a complete and updated booklet existed then it would be indeed easy to say : mass conservation – chapter 3 , pages 25-31 , equations 27 through 34 .
    But as it is not said , the booklet doesn’t exist .


    Comment by Tom Vonk | September 18, 2008 | Reply

  2. Tom, for the models and codes that I have worked on, the booklet(s) you suggest does in fact exist. And I can do exactly what your example illustrates. I can point to Volume, Chapter, Section, and Equation Number for every equation used in every part of the complete model. I can additionally point to the same information for the as-coded discrete approximations for all equations. And I can point to the lines of code that contain the latter equations.

    It’s SOP for all engineering and science models and codes that has potential important consequences. Lots more information is given in this post. Independent Verification cannot be carried out in the absence of detailed documentation.

    Equally important, the extensive documentation provides for vastly improved completeness and correctness relative to both long-term and short-term maintenance and for incorporation of improvements into the models and codes. All these large complex codes have life-times measured in many decades. Documentation is crucial for maintaining the codes over time scales this long.

    Comment by Dan Hughes | September 19, 2008 | Reply

  3. The following comment has been posted at GISS/NASA RealClimate blog in response to the questions that are the subject of the thread here.

    “Dan Hughes,
    See “An introduction to three dimensional climate modeling”. The answer you’re looking for is in equation 3.31 (page 56) and repeated for emphasis as equation 3.53 (page 62). As you state/guess option (2) is used. The text describes reasonably carefully how this is constructed. There’s then a discussion of how this is transformed into a sigma co-ordinate (generally given a SIG monkier in modelE) on pages 63 through 68. I’d recommend NCAR CCM as being more readable and better documented, however it’s not too difficult to pick you way through the modelE stuff.

    If you’re interested in conditions describing where vertical hydrostatic balance is valid and invalid, this text refers me to J.R. Holton, “An Introduction to Dynamic Meteorology”, which it describes as having a discussion on this issue (which I’ve not read).”

    The equation systems in Chapter 3 of that book do not form a closed system of equations ready for solution. The boundary and initial conditions, for example, are not given. More importantly, the number of equations and number of unknowns are not the same. See Equs.(3.19 – 3.21) and (3.22 – 3.24), which contain the ‘frictional forces’ on the right-hand side, and these are not specified. The latter equations already include simplifications applied to the more general form of the former.

    Additionally, the specific equations system, Equs. (3.29 – 3.31) cited in the above comment are simplified approximations to the complete equations. And they are the steady-state form of the general equations, for one example. I doubt that present-day GCMs are based on steady state equations of motion for the atmosphere.

    Finally, the issue is not what equation systems have appeared in any number of books and papers. The issue is what equations are actually used in any given GCM. All GCMs need to be documented in detail. Referral to another model/code is a strawman to direct attention from the specific issues of any one model / code. If any results from any GCM are used in any reports and papers that specific model / code needs to be documented.

    The IPCC GISS/NASA ensemble-average approach is said to account for the sensitivity of the calculated numbers to specification of initial conditions. That statement is a mischaracterization of the true situation so long as all the models have different equation systems, numerical solution methods, and application procedures.

    Comment by Dan Hughes | September 19, 2008 | Reply

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