[ncl-talk] Inconsistency in dimension averaging using dim_avg_n

[Dave Allured - NOAA Affiliate]

Tabish, the differing results may be caused by missing values in your
array, resulting in unequal weighting of the remaining values in 2-step
averaging.  This is basic math, not a particular NCL behavior.  Offhand I
would say that the single step method is the only correct method here.

No, dim_avg_n never performs a weighted average, whether or not coordinate
arrays are included.  As the documentation says, missing values are
properly excluded from each individual averaging calculation.

Perhaps someone else can comment on the best way to perform a spatial
weighted average.


On Wed, Aug 21, 2024 at 7:31 AM Tabish Ansari via ncl-talk <
ncl-talk at mailman.ucar.edu> wrote:

> Hello,
>
> I've got a 3D variable called "monthlypm25NCP". It has 12 timesteps and 41
> lat x 41 lon values.
>
> Here's the variable summary:
> Variable: monthlypm25NCP
> Type: float
> Total Size: 80688 bytes
>             20172 values
> Number of Dimensions: 3
> Dimensions and sizes:   [12] x [41] x [41]
> Coordinates:
> Number Of Attributes: 1
>   _FillValue :  9.96921e+36
>
> Since this is a derived variable from another 3-hourly variable, the
> coordinate arrays are not retained. (I could have copied them over but I
> didn't in this instance.)
>
> Now, I want to average this 3D variable over the lat-lon grid to reduce it
> to a 1D variable containing only 12 values (one for each month).
>
> I tried using the dim_avg_n in two different ways to achieve this:
>
> *1. In 2-steps: *
> monthlypm25NCPsum1= dim_avg_n(monthlypm25NCP, 2)
> monthlypm25NCPsum = dim_avg_n(monthlypm25NCPsum1, 1)
> print(monthlypm25NCPsum+"")
>
> Result:
> (0)     167.83
> (1)     150.403
> (2)     124.87
> (3)     102.86
> (4)     90.6969
> (5)     80.4786
> (6)     75.9811
> (7)     71.1969
> (8)     93.9213
> (9)     117.72
> (10)    136.6
> (11)    139.528
>
> *2. In a single step:*
> monthlypm25NCPsum = dim_avg_n(monthlypm25NCP, (/1,2/))
> print(monthlypm25NCPsum+"")
>
> Result:
> (0)     155.3
> (1)     140.645
> (2)     116.423
> (3)     96.4202
> (4)     84.4638
> (5)     76.3392
> (6)     72.5972
> (7)     67.5716
> (8)     88.2773
> (9)     110.789
> (10)    129.426
> (11)    131.247
>
> I was expecting the results to be identical but strangely they're not, as
> you can see above.
>
> Can you please explain what's causing the difference here?
>
> Is it possible that in the second case, the dim_avg_n function is
> recognizing the lat-lon grid and using a weighted averaging based on actual
> grid area? But how can it recognize that when I have not included the
> coordinate arrays?
>
> Ultimately, I do want to perform a weighted averaging over the lat-lon
> grid and have obtained a separate matrix that contains gridcell area (I
> used the cdo tool to obtain it). Should I do a sparse matrix multiplication
> with the gridcell area before performing the grid averaging in NCL or does
> the dim_avg_n function take care of the grid area itself?
>
> Thanks
> Tabish
>
> --------------------------------------------------------------------------------------
> Dr Tabish Ansari
> Research Associate
> Air Quality Modelling Group
> Research Institute for Sustainability (RIFS) - Helmholtz Centre Potsdam
> Potsdam, Germany
>
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