How to calculate A, B hybrid pressure coefficients for CAM?

[h_parish@uci_edu]

Hi folks, I need to create a new high resolution vertical gird for CAM. As you know, CAM takes in model levels with their hybrid pressure coefficients:"hyai" and "hybi" for interface levels, and"hyam" and "hybm" for the mid levels.Here I will refer to these as A and B coefficients for simplicity.  The level pressure (p) and the A,B coefficietns are related by p(k) = A(k)*p0 + B(k)*ps in which p0 and ps are given ref and surf pressures and k is the level index. Now, the question is for given values of p, for instance known p(k) where k varies from 1 to 150, what is the mathematically "deterministic" way to compute A(i) and B(i) coeffiecients?I know one can start with a standard L30 grid and add levels in between every two levels by averaging the p(k) levels and their associated A(k),B(k) coefficents but I regard this as a second alternative. After all, the coefficients of the original L30 grid are computed based on a rule. I am eager to know that rule. Mcuh appreciate your comments.Cheers,Hossein   

 

[hannay]

Answer from Dave Williamson:

There is no standard method to generate CAM vertical grids. The method used in the past, developed by B. A. Boville, is described with examples in Appendix B of Williamson, D.L., J.G. Olson and B.A. Boville, 1998: A comparison of semi-Lagrangian and Eulerian tropical climate simulations, Monthly Weather Review, 126, 1001-1012. Application of the method requires some iteration between generating levels and running the model in order to obtain a reasonable level at which the tropopause forms. With modest resolutions the model had a tendency for the tropopause to form at a higher level than desired, resulting in an apparent strong cold bias compared against observations. Care is also needed with the first model level above the surface because of the surface exchange parameterization. With the vertical finite difference approximations used in the Eulerian spectral transform and earlier spectral element versions of the model the level thicknesses need to vary smoothly. Dividing layers of an existing grid into equal thickness sub-layers is not a good idea. It can lead to vertical noise as illustrated in Fig. 7. While the noise is not noticeable in the temperature field because of the strong vertical temperature gradient, it is there. Similar noise is probably less of a problem, if at all, with the vertical Lagrangian coordinate used in more recent versions of CAM, but I don't know if anyone has checked for it.

 

[h_parish@uci_edu]

Dear Cecile and Dave,Thanks very much for the info!Would you please elaborate a bit more on "care is needed with the first model level above the surface because of the surface parameterizaiton"? Any reference with details on this?Best, Hossein.