Climate Modeling (Meteo 523): Project One

Meteo 523, Spring 2001

Climate Modeling Project One

Representation of the Atmosphere Through Parameterizations

Update on Project 1, 15 March 2001:

Here is a summary of the aspects of the problem I asked you to consider for Part 3 of Project 1 "Extending and improving climate model parameterization".
Scope of the paper

First, assume unlimited financial resources and let your scientific imagination go wild, thinking of all of the important improvements that could be made to your parameterization;

Now you find that your funding has been reduced: what are the most important components of your "wish list" that must be achieved? What are the ways in which you can make your code as computationally efficient as possible to make it interesting to a wide range of the climate community?

At what resolutions would you expect the fundamental assumptions inherent in your parameterization to break down? These should at least be identified.

If you have recommended the use of lookup tables, over what range of model parameters are they valid? For example, are the assumptions underlying the calculations relevant only for a limited range of model grid spacings? temperatures? wind speeds? land/ocean?
Practical considerations

Include essential figures in the written form of your paper.

I plan to use these papers as the basis of discussion for parameterization, so if you have a strong opinion on something relevant to parameterizations generally, or your topic specifically, feel free to add a separate section in this last Project 1 paper focussing on that issue.

What is Parameterization and Why Do We Need It?

    The governing equations of the atmosphere include source terms which are not inherently predictable nor can they be well observed. One example is the four-dimensional distribution of diabatic heating: while the progression of the seasonal and diurnal variation of the incident solar radiation at the top of the
atmosphere is known, the effects of clouds and water vapor (as well as other gases) throughout the atmosphere confound diagnosis of both short and long
wave radiation profiles around the globe. Hence, the diabatic heating source term in the thermodynamic equation is an unknown, and we have a system of
six equations and at least seven unknowns. This is a poorly posed mathematical problem and cannot be solved uniquely unless one of the unknowns can
be expressed in terms of the remaining unknowns. This is known as parameterization.
    Thus, we need parameterizations to close a system of equations in which the number of dependent variables (the unknowns u,v,w,T,q,p,Q,P,E) exceed
the number of equations in the system [3 momentum, continuity, thermodynamic, moisture]. If multiple phases of water are included, further equations must
be introduced to restore the equality between the numbers of equations and unknowns.
    Based on this discussion, we see that a parameterization is a mathematical construct designed to summarize the workings of one component of the
atmosphere in terms of variables which are already being predicted. Hence, a parameterization might solve for the distribution of an individual field or
variable, an atmospheric structure or the net effects of an individual weather phenomenon. Examples of these are diabatic heating (as in our example above),
the structure of the planetary boundary layer and the effects of convective clouds respectively.

This Project

The importance of parameterizations is explored by focusing on their role in numerical models, the underlying assumptions in their implementation and their representation of physical processes. There are three components to this project:

Description of a physical model: Numerical models are built on conceptual models of how the atmosphere works. Hence, in order to successfully simulate something, we must have evaluated the importance of potential forcings. In this component of the project, I expect you to come up with (i) an annotated diagram or one page written description of how some process in the atmosphere works; and (ii) to present this in a 5-10 minute oral presentation.
Documentation of a physical parameterization: Here you will compare your physical model to a numerical realization based on work by experts in the field. You will give a 15 minute presentation to the class on the essentials of a single parameterization presently in use. Presentations for this will be given in class on Tuesday 13 March (immediately after Spring break).
Extension of that physical parameterization: You are now in control of an infinite budget and can make a quantum leap in parameterization results. Describe (in up to 5 pages - you may have additional room for figures) how you would advance the science. This paper is due on Thursday, 22 March 2001. We will use these papers as the basis of class discussion on priorities for model development.

Project Milestones

Overview talks for part of Project 1 were presented in class on Thursday 25 January 2001: Each class member reviewed the mechanisms involved in one atmospheric process. Topics covered were:

Jason Cole	Longwave radiation interactions	Mlawer et al. (1997)
Ken Pelman	The sea breeze (boundary layers)	Zinn and Kowalski (1995)
James Simpas	Aqueous phase chemistry	Sander (1999)
Xuguang Wang	Convective clouds	Zhang and McFarlane (1995)

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Last Updated: 15 March 2001