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Re: diagonal section and integration handling difficulties



Hi Robert,
I'll start a discussion; others who do similar calculations might be able
to add more detail.  You can get data along any curve, such as a diagonal,
with the SAMPLEXY function. In the Users Guide under "SAMPLEXY,
function definition", there is an example which defines a straight line and
samples a field along it.  The result of sampling an X-Y-Z field along a curve
is an X-by- Z result, where X is now an index, the count of points along
the curve or diagonal line.

There is a discussion of what Ferret does with 2-dimensional integrals
on latitude-longitude grids, in Chapter 3, the section called "General
information about transformations." 

It doesn't sound like you are doing a 2-dimensional integral, but,  "If
@DIN is applied simultaneously to both the X and Y axes (in units of
degrees of longitude and latitude, respectively) the calculation will be
carried out on a per-unit-area basis (as a true double integral) instead
of a per-unit-length basis, sequentially."  Also,
when the axis units are
longitude and latitude, Ferret applies a latitude correction for integrals
and averages. This  may be why you are seeing unexpected results for
your integrations..  The reference for this discussion in the Users Guide
is under "COSINE(latituude)" in the index. Here is a relevant paragraph:

"When calculating integrals and derivatives (@IIN, @DIN, @DDC,
@DDF, and @DDB) Ferret attempts to use standardized units for the
grid coordinates. If the underlying axis is in a known unit of length Ferret
converts grid box lengths to meters. If the underlying axis is in a known
unit of time Ferret converts grid box lengths to seconds. If the underlying
axis is degrees of longitude a factor of COSINE (latitude) is applied to
the grid box lengths in meters. "

Ansley Manke

Robert Landsberger wrote:
Dear Ferreters,

actually working with a oceanmodel calculating stream intensitys it occured to us to check the produced data by integrating the stream components u (longitude direction) and v
(latitude direction) along any diagonal line in the datafield.

First question concerning is:
Is there a standard way of gaining the requested output? Or has there been any programfile published yet to help us in this task?

And second:
During our calculation we come to a situation similar to the one in the append lines.
We take the vertical section out of the original data file and reduce the data to a 2 dimensional field (as you may see the depth ist integrated already)
So all we need do to is to integrate the x-axis and we compute the directed stream of water. The question is why do we gain correct output for the integration with an existing y-axis and the wrong output for the integration along the x-axis for the integration without y-axis? For this is what occurs if we do not do a clear zonal or meridional section.

Any help is welcome

Robert Landsberger (ZMAW Hamburg/Germany)


Problem scratch:
name     title                                                   I         J         K         L
TEST1    V[Y=77,Z=@DIN]                   1:252     1:1       ...       1:12
      (Z=0:4868)
TEST2    V[Y=77@AVE,Z=@DIN]       1:252      ...        ...       1:12
      (Z=0:4868)
TESU1    TEST1[X=@DIN]/(1E6)             ...       1:1       ...       1:12
      (X=46W(-46):17E, Z=0:4868)
TESU2    TEST2[X=@DIN]/(1E6)             ...        ...        ...       1:12
      (X=46W(-46):17E, Z=0:4868)

yes? list/l=1 tesu1
            VARIABLE : TEST1[X=@DIN]/(1E6)
                       X=46W(-46):17E, Z=0:4868
            FILENAME : keks.cdf
            LATITUDE : 77N
            TIME     : 01-JUL-1992 14:54
        -1.205
yes? list/l=1 tesu2
            VARIABLE : TEST2[X=@DIN]/(1E6)
                       X=46W(-46):17E, Z=0:4868
            FILENAME : keks.cdf
            TIME     : 01-JUL-1992 14:54
        -5.348

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