Re: [ferret_users] unexpected difference depending on order of integration and annual cycle

Hi Billy,

It's probably due to your time-dependent mask. First try filling narrow longitude gaps with:

yes? let var_fill = IF max(var[x=@cia],var[x=@cib]) LE 2 THEN var[x=@fln]

Then omit years with particularly bad coverage:

yes? let var_crop = var_fill[t=1-jan-1995:1-jan-2016]

Then make your mask stationary in time, by masking out any longitudes that are EVER missing:

yes? let var_static = IF var_crop[t=@nbd] EQ 0 THEN var_crop

Then try your test again on VAR_STATIC.

Andrew

On Wed, Mar 22, 2017 at 4:39 PM, Martin Schmidt <martin.schmidt@xxxxxxxxxxxxxxxxx> wrote:

Hi William,

I do not have the complete explanation. But:

shade var

reveals missing values with time dependent distribution. Replacing "var" by "missing(var,0)" gives results independent off the order of operations.

The @mod transformation should imply some division by @ngd. What @ngd is depends on the order of operations. So far, things may by not fully linear any more?

Best,

Martin

On 03/22/2017 07:32 PM, William Kessler wrote:

Hi Ferreters -

I have a confusing difference in result depending on the order of operations. These should all be linear operations, so the order of doing them should not affect the result. I'm confused. 

The differences are smallish but could be significant. This is, by the way, the Ekman transport across 7.5S, and the differences are a few Sv.

In one case, I first find the annual cycle, then integrate the result in x. In the other, I first integrate in x, then find the annual cycle of the result. These should be identical, but aren't (attached gif plot). I don't know which is correct.

Why not? 

The attached cdf file (357Kb) has 5 variables:

VAR      original time series       
VAR_CL   annual cycle of original   
VAR_INT  x-integral of original     
VAR_INTCL  annual cycle of x-integral 
VAR_CLINT   x-integral of annual cycle 

These variables were defined by the following commands:

yes? let/tit="original time series" var=eky[y=7.5s,x=148e:82w]
yes? let/tit="annual cycle of original" var_cl=var[gt=month_irreg@mod]
yes? let/tit="x-integral of original" var_int=var[x=@din]
yes? let/tit="annual cycle of x-integral" var_intcl=var_int[gt=month_irreg@mod]
yes? let/tit="x-integral of annual cycle" var_clint=var_cl[x=@din]
yes? save/outtype=float/file=check_order_of_operations.cdf var,var_cl,var_int,var_intcl,var_clint

yes? plot/line/sym=27 var_intcl,var_clint

This is Ferret v6.94 (Mac)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
William S. Kessler
NOAA / Pacific Marine Environmental Laboratory
7600 Sand Point Way NE
Seattle WA 98115 USA

william.s.kessler@xxxxxxxx
Tel: +1 206-526-6221
Fax: +1 206-526-6744