# [ncl-talk] Problem with divergence calculation

Mateus da Silva Teixeira mateusstex at gmail.com
Wed Jul 10 13:03:20 MDT 2019

```Hi Dennis,

Thank you for your answer, but this didn't make difference in the
calculations. As I could read in documentation, there is no warning about
latitude order.

Trying more comparisons, I've calculated the wind gradients with
*grad_latlon_cfd* function to get *du_dx* and *dv_dy* and the results are
the same, as shown below:

*For latitude -90*
(0) du_dx manual      du_dx grad funct
(0) -32.9238     -32.9175
(1) -32.9238     -32.9175
(2) -28.8081     -28.8026
(3) -28.8081     -28.8026

(0) dv_dy manual       dv_dy grad funct
(0) 5.39676e-06     5.39574e-06
(1) 5.39676e-06     5.39574e-06
(2) 5.39676e-06     5.39574e-06
(3) 5.39676e-06     5.39574e-06

*For latitude -87.5*
(0) du_dx manual      du_dx grad funct
(0) 2.88688e-05     2.88633e-05
(1) 2.88688e-05     2.88633e-05
(2) 2.47451e-05     2.47403e-05
(3) 2.88688e-05     2.88633e-05

(0) dv_dy manual       dv_dy grad funct
(0) 2.69839e-06     2.69787e-06
(1) 2.51851e-06     2.51803e-06
(2) 2.33858e-06     2.33813e-06
(3) 2.33861e-06     2.33816e-06

And below the divergence, but along with the calculation using gradients

*For latitude -90*
(0) div manual      div function      div grad funct
(0) -0.24189     5.72546e-06     -0.235588
(1) -0.960165     5.72546e-06     -0.953863
(2) 2.43722     5.72546e-06     2.44274
(3) 1.71895     5.72546e-06     1.72446

*For latitude -87.5*
(0) div manual      div function      div grad funct
(0) 4.24092e-06     4.24011e-06     4.23487e-06
(1) 4.78015e-06     4.77923e-06     4.77414e-06
(2) 1.19561e-06     1.19538e-06     1.19042e-06
(3) 6.0385e-06     6.03735e-06     6.03253e-06

The data used for these calculations has its latitude ordered
south-to-north. I think that I'm missing something, but I can't figure it
out.

Best regards,

Mateus

Em qua, 10 de jul de 2019 às 13:23, Dennis Shea <shea at ucar.edu> escreveu:

> NCEP reanalyses are ordered North-to-South. The function requires
> South-to-North. Assuming (time,lev,Lat,Lon)
>
>  V = V(:,:,::-1,:)
>    printVarSummary(V)
>
> Look at the lat coordinate.
>
> Sent from my iPhone
>
> On Jul 10, 2019, at 8:33 AM, Mateus da Silva Teixeira via ncl-talk <
> ncl-talk at ucar.edu> wrote:
>
> Hi,
>
> I'm trying to reproduce with *center_finite_difference* function the
> computation of wind divergence, to compare with *uv2dv_cfd* function.
> However, I'm getting some strange values for divergence.
>
> For *Dv/Dy*, I'm using:
>
> dv_dy = center_finite_diff_n( v850, lat*g2r, False, 0, 0 )/rTerra
>
> For Du/Dx, I'm using:
>
>
>
>
>
>
> *dlon = (lon(2)-lon(1))*g2rdu_dx = new( (/dimsizes(u850)/), typeof( u850
> ), u850 at _FillValue )term3 = new( (/dimsizes(v850)/), typeof(v850),
> v850 at _FillValue )do i = 0, dimsizes(lat)-1      dx = rTerra * cos(
> g2r*lat(i) ) * dlon      du_dx(i,:) = center_finite_diff( u850(i,:), dx,
> True, 0 )*
>
> *      term3(i,:) = ( v850(i,:)/rTerra ) * tan( lat(i)*g2r )  end do*
>
> with *rTerra* being the mean radius of the Earth, and finally, for
> divergence (using the same equation calculated by *uv2dv_cfd*):
>
> *div = du_dx + dv_dy - term3*
>
> With *uv2dv_cfd*, I'm using:
>
> *divV = uv2dv_cfd( u850, v850, lat, lon, 3 )*
>
> Below, a comparison between the results for latitude 90, for both
> calculations:
>
> (0) div manual      div function
> (0) -0.435886     8.54325e-07
> (1) 0.282385     8.54325e-07
> (2) 0.641552     8.54325e-07
> (3) 0.640924     8.54325e-07
> (4) -3.11505     8.54325e-07
> ...
> (138) 0.0877819     8.54325e-07
> (139) 0.806053     8.54325e-07
> (140) -2.59076     8.54325e-07
> (141) -1.87243     8.54325e-07
> (142) 2.96093     8.54325e-07
> (143) -0.795052     8.54325e-07
>
> And below, the comparison for latitude 87.5, for both calculations:
>
> (0) div manual      div function
> (0) 2.54982e-06     2.54933e-06
> (1) 3.44865e-06     3.44799e-06
> (2) 4.34874e-06     4.34791e-06
> (3) 1.30406e-06     1.30381e-06
> (4) 2.92225e-06     2.9217e-06
> ...
> (138) 2.74009e-06     2.73957e-06
> (139) 1.3016e-06     1.30136e-06
> (140) 3.98753e-06     3.98678e-06
> (141) 7.39285e-06     7.39144e-06
> (142) 2.72861e-06     2.72809e-06
> (143) 2.54953e-06     2.54905e-06
>
> I've noted this problem only in the poles and seems to be related with
> *cos* function in the computation of gradient of zonal wind over
> longitude, since it doesn't give zero (or a very small value) for
> *cos(90)* or *cos(-90).*
>
> I'm using NCEP Reanalysis 1 data and NCL 6.4.0.
>
> Am I doing something wrong in these calculations?
>
> Thanks,
>
> Mateus
>
>
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