[ferret_users] Details on using @AVE function correctly

[guimond@xxxxxxxxxxxxx]

Hi Jaison,
 Thank you for your response.  This is a very nice review of the @AVE 
functions and something I think should be added to the documentation.  
It is not obvious how the grid box weights are computed from what is 
given and one could easily trust the values when in fact they would be 
wrong.  I will post this response to the group.   So, basically using 
the calendar format (i.e. var[t=02-JAN-2001:05-JAN-2001@AVE]) of @AVE 
will ALWAYS underestimate the mean because of the 0.50 weight on each 
end.  I think another way to get at the correct method would be to:

let new_var = var[t=02-JAN-2001:05-JAN-2001]

let new_var_mean = new_var[t=@AVE]

This computes the mean over all the grid cells in range by removing the 
values from the rest of the data.


Any idea why @AVE was created like this?


Thanks again,

Steve


Quoting Jaison Kurian <jaison@caos.iisc.ernet.in>:

> Hi Steve,
>           I faced a simular confusion earlier...that time Ansley
> clarified my doubts.
>
>  Basically over "co-ordinate axes" ie. X/Y/Z/T, @AVE is weigthed
> by grid box lenth, based on the specified region. But over "abstract
> axes or indices" ie. I/J/K/L it is not. Let us see one example.
>
>    define axis/t=01-JAN-2001:06-JAN-2001:1/units=days/t0=31-DEC-2000 time
>    let var = SIN(t[gt=time])
>    set list/precision=10
>
>    ! first 3-methods to find ave
>
>    list var[l=2:5@AVE]
>    list var[t=02-JAN-2001:05-JAN-2001@SUM]/var[t=02-JAN-2001:05-JAN-2001@NGD]
>    list var[t="01-JAN-2001:12":"05-JAN-2001:12"@AVE]
>
>    ! fourth method to find ave
>
>    list var[t=02-JAN-2001:05-JAN-2001@AVE]
>
> The first 3 list commands will give the same answer, the sum of variable
> values from 2nd to 5th devided by number of points, ie. 4. But the last one
> will give a different anwer. Let me explain in detail.
>
> The first time point is "01-JAN-2001:00:00"
>   its bounds are  "31-DEC-2000:12:00" and "01-JAN-2001:12:00"
> The second time point is "02-JAN-2001:00:00"
>   its bounds are "01-JAN-2001:12:00" and "02-JAN-2001:12:00"
>
> Hence when you are specifying as the starting T for an average
> operation as "02-JAN-2001",only half of the grid box comes after
> this time (ie. from "02-JAN-2001:00:00" to "02-JAN-2001:12:00")
> hence this value gets only 0.5 weightage..similar is the case
> with the value on "05-JAN-2001". So, the average
>
>    var[t=02-JAN-2001:05-JAN-2001@AVE]
>
> will be computed as
>
>    (var[t=02-JAN-2001]*0.5+var[t=03-JAN-2001]*1+var[t=04-JAN-2001]*1+
>         var[t=05-JAN-2001]*0.5)/3
>
> This problem is overcome by specifying exact grid boundaries in method
> 3 above. In method 2 a combination of @SUM and @NGD has been used. Since
> @SUM is a non-weighted calculation, this will give the answer without
> any problems like method 4 above.
>
> Back to your question
> ---------------------
> So what should a proper method for simple mean ? Any of first 3 methods
> from above example. Then you may ask, how to make it easier with the
> time specified on calendar format : here is the trick
>
> let l1 = L[gt=var,t=02-JAN-2001]
> let l2 = L[gt=var,t=05-JAN-2001]
> list var[l=`l1`:`l2`@AVE]
>
> Hope this helps,
>
> Regards,
>
> Jaison
>
> On Mon, 16 Oct 2006 guimond@coaps.fsu.edu wrote:
>
> > Hi Jaison,
> >   I decided to e-mail you separatley about this question and then I
> > will post the responses to the group.  I have computed some means and I
> > am questioning how ferret goes about them.  Specifically, I have
> > computed the time mean of a var between two endpoints, call them t1 and
> > t2:
> >
> > let mean1 = var[t=`t1`:`t2`@AVE]
> >
> > According to the FERRET users guide, this will be the mean over the
> > "exact" region or from gridpoint to gridpoint, correct?  Now if I do
> > something like this:
> >
> > let mean2 = var[l=10:15@AVE], using time steps instead of time values.
> >
> > I will get a different answer because this method averages from
> > gridcell to gridcell and not gridpoint to gridpoint, correct?
> >
> > I am confused on what is the more accurate depiction of the mean here.
> > I want to average from one single time point, t1, to another time
> > point, t2.  This is why I used the formula for mean1.  Is this correct
> > for simple means?
> >
> > Thanks for your help,
> > Steve Guimond
> >
> > ----------------------------------------------------------------


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