Efficient std computation using DROP

[maqsoodrajput]

Aim: Implement $E[X^2]$

For efficient ssh_variability computation, the idea is to implement $\sigma = E[X^2] - (E[X])^2$, where $X$ is the monthly data frequency.

Specific to AQUA:

• Check the data frequency. Make sure that the results are consistent with hourly, daily or monthly frequency.
• Store the $X^2$ on monthly frequency, catalog entry and able to read via Reader.
• Unit for $X^2$ term.
• Tests
• Update the documentation

The full issue is in AQUA-diagnostics issue #164

[maqsoodrajput]

Hi @jhardenberg and @oloapinivad, would it be fine if I make some additions in Reader, Drop and Timstat modules for the sshvariability diagnostics?

[mnurisso]

Hi @jhardenberg and @oloapinivad, would it be fine if I make some additions in Reader, Drop and Timstat modules for the sshvariability diagnostics?

as you did as a new statisic it makes sense, we cam choose the name but the strcture looks good

[maqsoodrajput]

Discussion:

So the zos monthly variable in High resolution is 15GB for our historical 1990.

<xarray.Dataset> Size: 15GB
Dimensions:  (time: 300, values: 12582912)
Coordinates:
  * time     (time) datetime64[ns] 2kB 1990-01-01 1990-02-01 ... 2014-12-01
    lat      (values) float64 101MB dask.array<chunksize=(3000000,), meta=np.ndarray>
    lon      (values) float64 101MB dask.array<chunksize=(3000000,), meta=np.ndarray>
Dimensions without coordinates: values
Data variables:
    zos      (time, values) float32 15GB dask.array<chunksize=(10, 3000000), meta=np.ndarray>
Attributes: (12/17)
    Conventions:  CF-1.8
    activity:     baseline
    class:        d1
    date:         19900101
    experiment:   hist
    expver:       0001
    ...           ...
    paramId:      263000
    period:       1990
    realization:  1
    stream:       clmn
    type:         fc
    history:      \n2026-03-09 12:06:44 AQUA💧: Retrieved from IFS-NEMO_histor...

If we store $X^2$ it would be adding 15GB more only for monthly data...