Based off of June 1, 00-06Z run:

Another plataeu mid month seems indicated by medium range superensemble and shape of trend for the extended range subseasonal model.

The subseasonal continues to remain higher, although the medium range has shifted downwards towards the end of its forecast in the two runs prior.

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For my future reference:

I spent the last few hours finally tuning the weighting for the statistical model I've been using for reference in the first 10 days for the last year (arimax, 1-harmonic) against the dynamic superensemble+Prophet now that I have a year of data.

For future reference (on the first of the month), the variance for the statistical is ~ 3 times the dynamic+super-ensemble

monthly_predictive_var, monthly_predictive_var_stat, monthly_predictive_var_weighted

(0.0044, 0.0127, 0.0075) respectively

Since I'm weighting by 1/MSE by lead time days (accounting for days left in prediction for month), the weights end up for

weight_for_statistical, weight_for_super_and_prophet

0.38, 0.62 respectively.

This was a bit surprising against my intuition how much weight is given to the super ensemble+Prophet early on in the month, which shows I have been underweighting it in the first 10 days in the past.

I've also perhaps been slightly underestimating the variance at this stage (nothing above 20% is indicated with this much variance at this stage in this weighted model; in the past I think I went up to 25%?, and also a bit too harshly bet down far away bins).

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Example chart from June 1 using the statistical (ARIMAX) model (not Prophet):

Toggling between the two, the super ensemble is clearly above the statistical one in the medium range, and only slightly above for the comparable Prophet portion beyond that.

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So other than the ad-hoc shift (which is large) by using the recent errors for each of the three ERA5->GISTEMP models, everything else is as objective as I can make it now.

For the moment I get a (after all adjustments) a point prediction of ~ 1.21 C for June:

Point estimate (mix) adjusted by prediction error mean: 1.2067

I've also changed my betting strategy based on these probabilities since last month or so to be more algorithmic in the calculation of bet sizes but its still not ideal.

Tiny dip and a rise is now clear at end of medium range. EC46 from couple days ago still about 0.14C below end of mid-range, but shifted to it continues to follow Prophet extende from medium range and close to the ARIMAX estimator from ERA5 also.

Since I've been weighting the statistical (1 harmonic) ARIMAX from the beginning of the ERA5 period in the data I use (unfortunately the code I have only adjusts the actual data for the month of interest) I now output the combined for the medium range and where it overlaps with prophet (the stat arimax doesn't go out as far (45 days) as Prophet, months into the future).

Anyway for the the medium range you can see the statistical model's effect on the result where it raises the temps in the middle of the medium range (where there is a dip below what you would expect) and lowering it at the end of the medium range (where there is a rise on tau=D+16, although some of that is from GEFS+GEPS biases where EPS is not available then).

I still am not using EC46 for after the medium range in terms of predictions (its just for reference).

You can also observe the widened (weighted) CI in the medium range as a result.

Superensemble from same runs today (through 06Z):

super ensemble + prophet extended from it (with EC46 as reference):

(super ensemble + prophet extended from it) weighted against statistical arimax (1 harm, from end of ERA5)

@parhizj yikes.

@ScottSupak If looking at EC46, don't look too much into the absolute numbers (since it is shift is ad-hoc) just the trend, which shows for the last 2-3 runs, with the mean case there will be roughly a plataeu on average going into July for the first week or so and then a trend upwards on average.

@parhizj looks like the tail risk is mostly on the upside, yeah?

@ScottSupak All of my models assume a normal distribution on point predictions (I only try to account for the variance of everything -- I don't even bother trying to correct the skew/kurtosis).

I think those betting the lowest bin down are just betting it won't be anomalously cooler than April, which is a fair bet all things considered given that preliminary (not well debiased yet by what little empirical data I gather) SST forecasts for daily (anomalized) versions of ONI/RONI based off of ERA5/EC46 data that I process are higher for June than April so that should be good reason to assume it will also carry over to the LOTI value.

Also CPC officially put out an El Nino advisory today: https://www.cpc.ncep.noaa.gov/products/analysis_monitoring/enso_advisory/ensodisc.shtml

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On other randomness in case it may help anyone... I wasted hours try to setup a pipeline to download the rest of the ERA5 data faster from other sources (Earth Data Hub) only to find out that the data is quantized (0.0156 K spacing) to an unacceptable level for my future purposes (cds being from the daily post-processed dataset which are about 2MB / day, and the EDH which are 0.8MB) ...

>>> cds_vals = cds["t2m"].values.squeeze()

>>> edh_vals = edh["t2m"].values.squeeze()

>>> # look at the least significant bits by checking how many unique values there are

>>> print("cds unique values:", np.unique(cds_vals).shape[0])

cds unique values: 529432

>>> print("edh unique values:", np.unique(edh_vals).shape[0])

edh unique values: 3779

>>> # and the spacing between sorted unique values

>>> cds_sorted = np.sort(np.unique(cds_vals))

>>> edh_sorted = np.sort(np.unique(edh_vals))

>>> print("cds min spacing:", np.diff(cds_sorted).min())

cds min spacing: 6.1035156e-05

>>> print("edh min spacing:", np.diff(edh_sorted).min())

edh min spacing: 0.015625

>>> print("cds median spacing:", np.median(np.diff(cds_sorted)))

cds median spacing: 9.1552734e-05

>>> print("edh median spacing:", np.median(np.diff(edh_sorted)))

edh median spacing: 0.015625

Climate Prediction Center: ENSO Diagnostic Discussion