seasonal cycle subtraction needs to be improved

[gaelforget]

Discontinuities through time are visible e.g. in Zonal Mean vs Time (anomalies) in this notebook.

Likely these reflect that the climatology for different months is shifted in time relative to a trend (by 11 months for Jan v Dec), such that the December average corresponds to a later period than the January average.

Possible solution would be to use (?) GLM.jl to estimate trend and seasonal cycle jointly, with proper accounting of time.

[gaelforget]

Hi @hdrake

ps. not sure what Ran's GitHub is

[hdrake]

@liu-ran

[gaelforget]

• I put an interactive example in this version of the ECCO Pluto notebook.
• It picks a zonal mean time series, and filters it using GLM.jl to fit a functional form (trend + optional seasonal terms). This is predicted in the notebook.
• It also applies the derivation of climatological means by averaging all Jan, then all Feb, etc. This is seasonal() in the notebook.
• You can change the variable, depth level, latitude index, number of terms in the fit, as illustrated in WIP (climatological mean and trend estimation) #139

[gaelforget]

This is what order 3 looks like.

[gaelforget]

See #140 , incl docstrings for fit_time_series, simple_monthly_climatology

ping @YuanyuanSong99

[liu-ran]

I recently compared the two approaches for constructing a climatology:

1. A high-order harmonic fit (GLM-based)
2. A detrending approach that removes the long-term mean tendency (as our paper did)

Using a daily SST time series from ECCOv4r4 as a test case, I examined how each method defines anomalies and how this affects the relationship between anomaly tendencies and tendencies of anomalies.

Generally, the fitted approach produces a smooth and continuous climatology, reducing discontinuities at the turn of the year and around leap days. However, the mismatch is redistributed across the entire time series, leading to small but persistent errors throughout the year.

The detrended approach preserves high accuracy within each calendar year and significantly reduces the yearly discontinuities at year boundaries. However, it does not resolve inconsistencies associated with leap days (February 29). (I don't know how to handle the issue of leap day.)

Overall, these results suggest that a perfectly consistent climatological seasonal cycle cannot be defined. Just because the seasonal cycle is not strictly periodic over an integer number of days.

( See my results: (https://pluto.land/n/j1kifjb7)
and the dataset and code: (https://github.com/liu-ran/julia_pluto_SST_climatology/) )