[gradsusr] CDIFF Versus HDIVG?

[LeeJoice, Robert N]

Eric,

Thank you very much for the assistance.  You were correct in my error.  I
have corrected and verified for both divergence and vorticity.  I appreciate
the help and the very detailed explanation.

Thank you for your time,

Robert


On 10/19/10 6:58 PM, "Eric Altshuler" <ela at cola.iges.org> wrote:

> Hello Robert,

Your expressions for du and dv are incorrect for calculating
> divergence. I assume you copied the expressions from the grads documentation
> page for cdiff, where an example is presented for calculating vorticity.
> However, the expressions are different when calculating divergence. Use the
> following:

du = cdiff(ugrdprs,x)
dv = cdiff(vgrdprs*cos(lat*3.1416/180),y)

I
> based these expressions on the formula for divergence in spherical coordinates
> given in Holton's book, in the appendix on vector analysis (I have the 4th
> edition, but older editions should have the same appendix).

As an aside, I
> think it's possible to obtain more accurate approximations for divergence and
> vorticity than those given in the grads documentation, because the factor
> cos(lat) can be taken outside the derivative operator and differentiated
> analytically rather than using finite differencing. Using the product rule of
> differentiation and a bit of algebra, I have derived the following sequence of
> calculations for these quantities (my definitions of intermediate quantities
> are different, but the end result is the
> same):

pi=3.14159265359
dtr=pi/180
a=6.371e6
dx=a*cos(dtr*lat)*dtr*cdiff(lon,
> x)
dy=a*dtr*cdiff(lat,y)
div=cdiff(u,x)/dx+cdiff(v,y)/dy-v*tan(dtr*lat)/a
vor=
> cdiff(v,x)/dx-cdiff(u,y)/dy+u*tan(dtr*lat)/a
def1=cdiff(u,x)/dx-cdiff(v,y)/dy-
> v*tan(dtr*lat)/a
def2=cdiff(v,x)/dx+cdiff(u,y)/dy+u*tan(dtr*lat)/a

In these
> formulas, substitute your wind variable names for u and v. In addition to
> divergence and vorticity, there are also calculations of the components of
> deformation, def1 and def2, and total deformation is equal to mag(def1,def2).
> These formulas (in terms of continuous fields) can also be found in Bluestein
> (1992), "Synoptic-Dynamic Meteorology in Midlatitudes", Vol. I, p. 111.

Best
> regards,

Eric L. Altshuler
Assistant Research Scientist
Center for
> Ocean-Land-Atmosphere Studies
4041 Powder Mill Road, Suite 302
Calverton, MD
> 20705-3106
USA

E-mail: ela at cola.iges.org
Phone: (301) 902-1257
Fax: (301)
> 595-9793

----- Original Message -----
From: "Robert N LeeJoice"
> <rnleejoi at nps.edu>
To: gradsusr at gradsusr.org
Sent: Tuesday, October 19, 2010
> 3:27:26 PM
Subject: [gradsusr] CDIFF Versus HDIVG?


I was wondering if there
> is a difference in the differencing scheme between CDIFF and HDIVG. I ask
> because I did a modified example from the documentation, i.e., divergence vice
> vorticity. The documentation states that CDIFF uses centered differencing.
> HDIVG says the same. The images suggest something else unless I¹m missing
> something. 

CDIFF file 
if(var='DIV') 
'run bluewhitered.gs -2.0 .5 10'
> 
'define dv = cdiff(vgrdprs,x)' 
'define dx = cdiff(lon,x)*3.1416/180'
> 
'define du = cdiff(ugrdprs*cos(lat*3.1416/180),y)' 
'define dy =
> cdiff(lat,y)*3.1416/180' 
'display
> (du/dx+dv/dy)*1e5/(6.37e6*cos(lat*3.1416/180))' 
'run cbarn.gs 0.8 1 10.4 4.7'
> 
endif 

HDIVG file 
if(var='DIV') 
'run bluewhitered.gs -2.0 .5 10' 
'd
> 1e5*hdivg(ugrdprs,vgrdprs)' 
'run cbarn.gs 0.8 1 10.4 4.7' 
Endif 

Here are
> the images in order... 

Thank you for any comments, 

Robert LeeJoice 
PhD
> Candidate, Naval Postgraduate School
> 

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