[gradsusr] hdivg function

Mon Nov 15 16:32:13 EST 2010

Instead of doing strange differentials inside the divergence calculation, I
just calculate each component separately beforehand if it is at all
complicated.  Thus I use:

dx = Re*cos(lat(3.14159/180))*cdiff(lon,x)*(3.14159/180)
dy = Re*cdiff(lat,y)*(3.14159/180)

Then, divergence = cdiff(u,x)/dx + cdiff(v,y)/dy

Jeff Duda

On Mon, Nov 15, 2010 at 12:53 PM, Eric Altshuler <ela at cola.iges.org> wrote:

> This issue also came up about a month ago. For those of us who aren't C
> programmers and would have difficulty determining the formulas from the
> source code, I will say there are several incorrect formulas for hdivg(u,v)
> in this thread, and one correct formula (in Yaqiang Wang's most recent
> message). To make the correct answer perfectly clear, here it is again:
>
> dx = cdiff(lon,x)*3.1416/180
> dy = cdiff(lat,y)*3.1416/180
>
> du = cdiff(u,x)
> dv = cdiff(v*cos(lat*3.1416/180),y)
>
> div = (du/dx+dv/dy)/(6.37e6*cos(lat*3.1416/180))
>
> 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: "Arlindo da Silva" <dasilva at alum.mit.edu>
> To: "GrADS Users Forum" <gradsusr at gradsusr.org>
> Sent: Monday, November 15, 2010 10:55:55 AM
> Subject: Re: [gradsusr] hdivg function
>
>
> All,
>
>
> The most authoritative documentation on the hdivg function can be found
> here:
>
>
>
> http://opengrads.cvs.sourceforge.net/viewvc/opengrads/cola/grads2/src/gafunc.c?revision=1.1.1.9&view=markup
>
>
> That is, the source code :-). The hdivg() implementation can be found on
> line 2716. This file has the implementation of most grads functions.
>
>
> BTW, the link above is the web interface to the opengrads CVS repository.
> We keep in this particular directory the original releases from COLA, before
> any opengrads patches are applied:
>
>
> http://opengrads.cvs.sourceforge.net/viewvc/opengrads/cola/grads2/src/
>
>
> There is a pulldown menu called "Sticky Tag" that you can use to select a
> particular grads version.
>
>
> Arlindo
>
>
>
>
>
>
>
> On Mon, Nov 15, 2010 at 12:44 AM, Yaqiang Wang < yaqiang.wang at gmail.com >
> wrote:
>
>
> The correct one should be:
>
> define du = cdiff(u,x)
>
> define dx = cdiff(lon,x)*3.1416/180
> define dv = cdiff(v*cos(lat*3.1416/180),y)
>
> define dy = cdiff(lat,y)*3.1416/180
> display (du/dx+dv/dy)/(6.37e6*cos(lat*3.1416/180))
>
> Yaqiang
>
>
> Chinese Academy of Meteorological Sciences
> yaqiang.wang at gmail.com
>
>
>
>
> On Mon, Nov 15, 2010 at 12:47 PM, Yaqiang Wang < yaqiang.wang at gmail.com >
> wrote:
> > Thanks for Jeff's reply! But it seems that in GrADS the hdivg function
> > was calculated as following. Please mention the last sentence.
> >
> > define dv = cdiff(v,x)
> > define dx = cdiff(lon,x)*3.1416/180
> > define du = cdiff(u*cos(lat*3.1416/180),y)
> > define dy = cdiff(lat,y)*3.1416/180
> > display (du/dy+dv/dx)/(6.37e6*cos(lat*3.1416/180))
> >
> > Yaqiang
> >
> > Chinese Academy of Meteorological Sciences
> > yaqiang.wang at gmail.com
> >
> > On Mon, Nov 15, 2010 at 11:56 AM, Jeffrey Duda < jdduda at iastate.edu >
> wrote:
> >> Yaqiang,
> >> You are exactly correct.
> >>
> >> Jeff Duda
> >>
> >> On Sun, Nov 14, 2010 at 9:22 PM, Yaqiang Wang < yaqiang.wang at gmail.com>
> >> wrote:
> >>>
> >>> The GrADS documentation said that the cdiff function may be used to
> >>> duplicate the calculation done by the hcurl function:
> >>>
> >>> define dv = cdiff(v,x)
> >>> define dx = cdiff(lon,x)*3.1416/180
> >>> define du = cdiff(u*cos(lat*3.1416/180),y)
> >>> define dy = cdiff(lat,y)*3.1416/180
> >>> display (dv/dx-du/dy)/(6.37e6*cos(lat*3.1416/180))
> >>>
> >>> But there is no description of hdivg function. I guess hdivg function
> >>> could be duplicated using cdiff function as following. Please anybody
> >>> tell me if it is correct or not. Thanks!
> >>>
> >>> define dv = cdiff(v,x)
> >>> define dx = cdiff(lon,x)*3.1416/180
> >>> define du = cdiff(u*cos(lat*3.1416/180),y)
> >>> define dy = cdiff(lat,y)*3.1416/180
> >>> display (du/dx+dv/dy)/(6.37e6*cos(lat*3.1416/180))
> >>>
> >>> Yaqiang Wang
> >>>
> >>> Chinese Academy of Meteorological Sciences
> >>> yaqiang.wang at gmail.com
> >>> _______________________________________________
> >>> gradsusr mailing list
> >>> gradsusr at gradsusr.org
> >>> http://gradsusr.org/mailman/listinfo/gradsusr
> >>
> >>
> >>
> >> --
> >> Jeff Duda
> >> Iowa State University
> >> Meteorology Graduate Student
> >> 3134 Agronomy Hall
> >> www.meteor.iastate.edu/~jdduda<http://www.meteor.iastate.edu/%7Ejdduda>
> >>
> >> _______________________________________________
> >> gradsusr mailing list
> >> gradsusr at gradsusr.org
> >> http://gradsusr.org/mailman/listinfo/gradsusr
> >>
> >>
> >
> _______________________________________________
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>
>
>
> --
> Arlindo da Silva
> dasilva at alum.mit.edu
>
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-- 
Jeff Duda
Iowa State University
Meteorology Graduate Student
3134 Agronomy Hall
www.meteor.iastate.edu/~jdduda
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