Re: [ferret_users] how to extract 2D subgrid variance?

[Lev Tarasov <lev@xxxxxx>]

> let h2 = h^2
> let h2_ave = h2[gx= . . . @AVE, gy= . . . @AVE]
> let h_ave= h[ . . . average  . . .]
> let h_var = h2_ave - h_ave*h_ave

Brilliant, it works. Thanks Ryo.

lev

Lev Tarasov -   Dept of Physics and Physical Oceanography,
		Memorial University of Newfoundland.
                email: lev@xxxxxx
                http://www.physics.mun.ca/~lev/
		Tel (709)-864-2675
		Fax (709)-864-8739

On Mon, 19 Aug 2019, Ryo Furue wrote:

> Date: Sun, 18 Aug 2019 13:26:43
> From: Ryo Furue <furue@xxxxxxxxxx>
> To: Lev Tarasov <lev@xxxxxx>
> Cc: users Group Ferret <ferret_users@xxxxxxxx>
> Subject: Re: [ferret_users] how to extract 2D subgrid variance?
>
> Dear Lev,
>
> On Sat, Aug 17, 2019 at 2:30 AM Lev Tarasov <lev@xxxxxx> wrote:
>
>               At times I need to extract the subgrid variance of a bed
>       topography, and I've been using:
>       let hbvar=HBG[gx=XLONGRF5@var,gy=YLATGRF25@var]
>       ! HBG is from a higher resolution data set
>
>       but have just noted (from some explicit checking and then rechecking the
>       ferret docs):
>
>       Note: This transformation is suitable for regridding only in a single
>       axis. [ . . . ]
>       So how can I regrid/extract the 2D subgrid variance?
>
>
> This idea hasn't been tested, but I think you can calculate the correct 2D variance using @AVE, which does a 2D averaging (See the Ferret User Guide):
>
> let h2 = h^2
> let h2_ave = h2[gx= . . . @AVE, gy= . . . @AVE]
> let h_ave= h[ . . . average  . . .]
> let h_var = h2_ave - h_ave*h_ave
>
> Note that ave( [a - ave(a)]^2 ) = ave(a^2) - [ave(a)]^2 .
>
> Cheers,
> Ryo