Re: [ferret_users] Inaccurate area weights calculation

Dear Andrew,

FERRET v6.2
Linux(g77) 2.4.21-32 - 05/19/09

>From your message I infer that this version of Ferret should use
weighting w2 or something similar. I have attached two files to test
this for my specific grid. The (shorted) output is:

\$ ferret -script test.jnl
Column  1: YBOXLO is YBOXLO (axis LAT_T)
Column  2: YBOXHI is YBOXHI (axis LAT_T)
YBOXLO  YBOXHI
76.5S /  1: -90.00 -70.81
66.4S /  2: -70.81 -62.73
59.4S /  3: -62.73 -56.44
53.7S /  4: -56.44 -51.06
48.6S /  5: -51.06 -46.24
[...]
1.6S  / 18:  -3.18   0.00
[...]

Column  1: EX#1 is W1/W1[J=@SUM]
Column  2: EX#2 is W2/W2[J=@SUM]
EX#1    EX#2
76.5S /  1:  0.03826  0.02778
66.4S /  2:  0.02750  0.02778
59.4S /  3:  0.02725  0.02778
53.7S /  4:  0.02718  0.02778
48.6S /  5:  0.02716  0.02778
[...]
1.6S  / 18:  0.02712  0.02778

VARIABLE : CELL1[X=@DIN,Y=@DIN]/TOTAL_AREA
0.03811
VARIABLE : CELL2[X=@DIN,Y=@DIN]/TOTAL_AREA
0.02750
VARIABLE : CELL3[X=@DIN,Y=@DIN]/TOTAL_AREA
0.02725
VARIABLE : CELL4[X=@DIN,Y=@DIN]/TOTAL_AREA
0.02719
VARIABLE : CELL5[X=@DIN,Y=@DIN]/TOTAL_AREA
0.02716
VARIABLE : CELL18[X=@DIN,Y=@DIN]/TOTAL_AREA
0.02713

I think this shows that Ferret is using something similar to weighting
w1 (although not exactly the same) instead of the correct weighting w2.
Or am I missing something?

Many thanks,
Marco

Andrew Wittenberg wrote:
> Dear Marco,
>
> What version of Ferret are you running?  The area weighting should be
> correct for Ferret versions 6.00 and later (i.e. computed as your w2).
> [Developers, refer to Trac ticket #1348, fixed April 2007.]
>
> Andrew
>
>
> On Mon, 17 Aug 2009, Marco Steinacher wrote:
>
>> Dear Ferret Users,
>>
>> I'm struggling with a problem related to the inaccurate calculation of
>> weights for area-weighted operations like @ave and @din in Ferret when
>> using a very coarse grid.
>>
>> The grid has 36x36 equal-area cells and it is regular spaced in
>> longitude (10deg). In the NetCDF file the coordinates of the center
>> (lat_t) and of the edges (lat_u using the 'edges' attribute) is given
>> (see below).
>>
>> When looking only at the grid cells at one longitude (eg. i=1) the
>> weight of each grid cell should be 1/36 = 0.028. However, the weights
>> calculated by Ferret differ largely. Obviously Ferret calculates the
>> weights as
>>
>>  w1 = (lat_u[j+1]-lat_u[j])*dlon*cos(lat_t[j])
>>
>>
>>  w2 = ( sin(lat_u[j+1]) - sin(lat_u[j]) )*dlon
>>
>> (Here, dlon is the spacing of the grid cells in longitude and, of
>> course, everything is converted to radians for the calculation). For j=1
>> we get the following (normalized) weights
>>
>>  w1 = 0.038
>>  w2 = 0.028.
>>
>> w2 is correct but the weight calculated by Ferret is more than 30%
>> higher!
>>
>> I'm wondering if anybody has experienced similar problems and if there
>> is any workaround to force Ferret to use the correct area-weights for
>> @ave etc. Any comments and suggestions on this issue are very welcome!
>>
>> Many thanks,
>> Marco
>>
>>
>> PS: I know that I can use var[x=@sum,y=@sum]/var[x=@ngd,y=@ngd] to get
>> the arithmetic average which is equal to the weighted average in this
>> specific case. Nevertheless, I would prefer to be able to use @ave, @din
>> etc. as well.
>>
>> --------------------------------------------------------
>>
>> double lat_t(lat_t) ;
>>                lat_t:long_name = "Latitude (T grid)" ;
>>                lat_t:units = "degrees_north" ;
>>                lat_t:minimum = -76.4637972626189 ;
>>                lat_t:maximum = 76.4637972626188 ;
>>                lat_t:edges = "lat_u" ;
>>
>> double lat_u(lat_u) ;
>>                lat_u:long_name = "Latitude (U grid)" ;
>>                lat_u:units = "degrees_north" ;
>>                lat_u:minimum = -90. ;
>>                lat_u:maximum = 89.9999991462264 ;
>>
>> lat_t = -76.4637972626189, -66.4435356908988, -59.4415682140651,
>>        -53.6639424853861, -48.5903778907291, -43.9829631303587,
>>        -39.7090165530684, -35.6853347126521, -31.8554308240259,
>>        -28.1786427405299, -24.6243183521641, -21.1684488458325,
>>        -17.7915905730076, -14.4775121859299, -11.2122714176497,
>>         -7.98355614555541, -4.78019184719916, -1.59175417658591,
>>          1.5917541765859,   4.78019184719916,  7.98355614555541,
>>         11.2122714176497,  14.4775121859299,  17.7915905730076,
>>         21.1684488458324,  24.6243183521641,  28.1786427405299,
>>         31.8554308240259,  35.6853347126521,  39.7090165530684,
>>         43.9829631303587,  48.5903778907291,  53.6639424853861,
>>         59.4415682140651,  66.4435356908988,  76.4637972626188 ;
>>
>> lat_u = -90,               -70.8118635462791, -62.7339555492672,
>>        -56.4426902380793, -51.0575587310186, -46.2382573073202,
>>        -41.8103148957786, -37.6698869643296, -33.7489885958886,
>>        -30,               -26.387799961243,  -22.8853804761586,
>>        -19.4712206344907, -16.1276202131608, -12.8395884069042,
>>         -9.5940682268606,  -6.37937020844281, -3.18473853672041,
>>         -3.18055468146e-15, 3.18473853672041,  6.3793702084428,
>>          9.59406822686046, 12.8395884069041,  16.1276202131608,
>>         19.4712206344907,  22.8853804761586,  26.387799961243,
>>         30,                33.7489885958886,  37.6698869643296,
>>         41.8103148957786,  46.2382573073202,  51.0575587310186,
>>         56.4426902380793,  62.7339555492672,  70.8118635462791,
>>         89.9999991462264 ;
>>
>> --
>> ***************************************
>> Marco Steinacher
>>
>> Climate and Environmental Physics
>> Physics Institute, University of Bern
>> Sidlerstrasse 5, CH-3012 Bern
>>
>> Phone ++41 (0)31 631 34 02
>> Fax   ++41 (0)31 631 87 42
>> steinacher@xxxxxxxxxxxxxxxx
>> http://www.climate.unibe.ch/
>> ***************************************
>>

--
***************************************
Marco Steinacher

Climate and Environmental Physics
Physics Institute, University of Bern
Sidlerstrasse 5, CH-3012 Bern

Phone ++41 (0)31 631 34 02
Fax   ++41 (0)31 631 87 42
steinacher@xxxxxxxxxxxxxxxx
http://www.climate.unibe.ch/
***************************************
use test.nc
define grid/like=test grd

! list edges
list yboxlo[g=grd],yboxhi[g=grd]

! calculate weights w1 and w2

! list normalized weights
list w1/w1[j=@sum],w2/w2[j=@sum]

! list weights calculated by Ferret at j=1,2,3,4,5,18
let all = if test gt 0 then 1
let total_area = all[x=@din,y=@din]
let cell1 = if test eq 1 then 1
let cell2 = if test eq 2 then 1
let cell3 = if test eq 3 then 1
let cell4 = if test eq 4 then 1
let cell5 = if test eq 5 then 1
let cell18 = if test eq 18 then 1
list cell1[x=@din,y=@din]/total_area
list cell2[x=@din,y=@din]/total_area
list cell3[x=@din,y=@din]/total_area
list cell4[x=@din,y=@din]/total_area
list cell5[x=@din,y=@din]/total_area
list cell18[x=@din,y=@din]/total_area

Attachment: test.nc
Description: Cdf file