Re: [ferret_users] integration from surface pressure level at each grid point

[Ryo Furue <furue@xxxxxxxxxx>]

Pratik,

On Mon, May 18, 2020 at 10:16 AM Pratik Kad <pratikkad17@xxxxxxxxx> wrote:

Hi Ryo

Thanks for the kind response. I tried with masking, But it does not consist when we are defining surface level. Please have a look. 

yes? list/l=1/x=83/y=28  pres, h, xyz
             Z (hPa): 0 to 1013

Column  1: PRES is Z[GZ=H]
Column  2: H is Height (m)
Column  3: XYZ is IF H GT 0 THEN H

              PRES     H      XYZ

10     /  1:    10.  29854.  29854.

30     /  2:    30.  22620.  22620.

50     /  3:    50.  19412.  19412.

70     /  4:    70.  17367.  17367.

100    /  5:   100.  15271.  15271.

150    /  6:   150.  12855.  12855.

175    /  7:   175.  11897.  11897.

200    /  8:   200.  11043.  11043.

225    /  9:   225.  10277.  10277.

250    / 10:   250.   9592.   9592.

300    / 11:   300.   8351.   8351.

350    / 12:   350.   7276.   7276.

400    / 13:   400.   6325.   6325.

450    / 14:   450.   5468.   5468.

500    / 15:   500.   4674.   4674.

550    / 16:   550.   3937.   3937.

600    / 17:   600.   3261.   3261.

650    / 18:   650.   2623.   2623.

700    / 19:   700.   2023.   2023.

750    / 20:   750.   1456.   1456.

775    / 21:   775.   1185.   1185.

800    / 22:   800.    922.    922.

825    / 23:   825.    666.    666.

850    / 24:   850.    416.    416.

875    / 25:   875.    171.    171.

900    / 26:   900.    -70.    ....

925    / 27:   925.   -311.    ....

950    / 28:   950.   -551.    ....

975    / 29:   975.   -791.    ....

1000   / 30:  1000.  -1031.    .... 

yes? list/x=83/y=28 h[z=875:10@din],xyz[z=1000:10@din]
             LONGITUDE: 83E
             LATITUDE: 28N

Column  1: H[Z=10:875@DIN] is Height (m)
Column  2: XYZ[Z=10:1000@DIN] is IF H GT 0 THEN H

                H     XYZ
I / *:     6189721.  6191862.

These two operations show different values. (Difference is -2141)

I guess the difference comes from the width of each gridbox.  It's hard to explain this without visual aid, but basically integration is

Δp_1  v_1  + Δp_2  v_2  + Δp_3 v_3 + . . . 

where "v" is the variable you want to integrate.  Think about what happens at the edges of your integration.  If you start your integration from z = 875 as above, you are using only half of Δp for that grid point.  Therefore, the masking method will give more or less closer values to the "correct" value of integration.   (To get even a better value, we would need to find out the exact pressure value at the surface, and to do so we would need to interpolate pressure and height, which would need a more sophisticated coding, which I guess can be accomplished by zaxreplace, but I'm not sure.)

Ryo