ERSST came in earlier in the afternoon but there has been no GHCNm since May 30 !

~

Vibe-coded a ERSST-ERA5-loti predictor today (using the predicted ERA5 adjusted from the super ensemble + and last 3 days of super ensemble for the ERA5 portion of subboxes) with Gemini's help (taking care to mask subboxes when necessary for ERSST,ERA5,GISTEMP data)...

The new method (dubbed ERSST-ERA5-loti) weighted together using the 3 ERA5->GISTEMP predictors yields 1.0918 C (weighting heavily (by inverse MSE) the ERSST predictor to the other aggregate of the other 3 methods (also weighted by inverse MSE, which would yield 1.1132 C by themselves) by nearly 3 to 1). Notably, the delta analog method is far higher than the rest at 1.13 but this new method has its prediction at 1.08 C!

The ERSST-ERA5-loti predictor uses several features in a Bayesian Ridge model for each month: the global, land and ocean anomalies from ERA5 in a 1991-2020 baseline (masking the appropriate subboxes by using the last best guess from the previous year of which subboxes to mask), and similarly calculates the ERSST ocean anomaly (also masking subboxes), a simple time trend feature, and additionally uses (somewhat dated) gistemp land/ocean/global subbox data from the original 1951-2020 baseline (from last October) as the train; a final correction is done using ARIMA on the residuals with LOTI data from the last month to provide a correction for the last year (which has had high positive residuals) and to estimate the std dev.

~

ERSST-ERA5-loti Prediction: 1.0918

Std dev: 0.0470

Point estimate (old, delta method, analog method, ERSST-ERA5-loti method) adjusted by prediction error mean: 1.1149, 1.1318 1.1049 1.0840

Point estimate (mix) adjusted by prediction error mean: 1.0918

Probs (mix) with super ens var

Std. dev.: 0.0470

Bin Probability (%)

<1.095 52.7

1.095-1.145 34.4

1.145-1.195 11.5

1.195-1.245 1.4

1.245-1.295 0.1

>1.295 0.0

The delta analog value and the ERSST-ERA5-loti predictor will continue to shift for the next 3 days until all the ERA5 data comes in.

ERA5 (last 3 days from super ensemble)

~

Some of the intermediate product data from the pipeline of the new predictor (the ocean anomaly is cooler than last month after masking) (columns are not great labeled -- first 3 columns after the date are the older gistemp run (1951-1980), and the anomaly_* columns are from the ERA5 subboxes masked (1991-2020)

mixed_anom_global mixed_anom_land mixed_anom_ocean anomaly_global anomaly_land anomaly_ocean num_masked_subboxes ersst_ocean_anom_1991_2020

valid_date

2023-12-01 1.377519 2.043990 0.969033 0.849618 1.220008 0.619150 163 0.533718

2024-01-01 1.253380 1.719702 0.972136 0.700568 0.771375 0.657418 130 0.565262

2024-02-01 1.437205 2.234928 0.960542 0.813673 1.098417 0.642008 85 0.558540

2024-03-01 1.384441 2.148096 0.927454 0.731198 1.037960 0.546445 80 0.511427

2024-04-01 1.303471 1.900322 0.944800 0.666791 0.838704 0.562586 109 0.499449

2024-05-01 1.145133 1.524313 0.915568 0.655910 0.779686 0.580254 142 0.460152

2024-06-01 1.207819 1.703052 0.906297 0.668019 0.904912 0.521780 156 0.438015

2024-07-01 1.207098 1.700158 0.905937 0.651600 0.907535 0.492104 160 0.439888

2024-08-01 1.293515 1.960004 0.885098 0.707287 1.056088 0.488799 151 0.363787

2024-09-01 1.243570 1.817291 0.888836 0.726884 1.069012 0.511739 162 0.420883

2024-10-01 1.355217 2.115524 0.885117 0.800141 1.252806 0.515580 163 0.408489

2024-11-01 1.305689 2.029494 0.857784 0.726761 1.130253 0.473320 172 0.402416

2024-12-01 1.272353 2.005487 0.821029 0.752327 1.197735 0.475273 164 0.385637

2025-01-01 1.359179 2.215773 0.839048 0.774653 1.288923 0.461358 131 0.435265

2025-02-01 1.246236 1.947519 0.825068 0.606542 0.878641 0.442555 86 0.425203

2025-03-01 1.351475 2.225937 0.826939 0.653001 1.016076 0.434406 81 0.413631

2025-04-01 1.217876 1.903120 0.803854 0.601577 0.949547 0.390656 109 0.362246

2025-05-01 1.070632 1.502682 0.807548 0.532251 0.698247 0.430789 142 0.354269

2025-06-01 1.046238 1.461059 0.792045 0.467265 0.558011 0.411227 155 0.325548

2025-07-01 1.016958 1.312678 0.834920 0.436208 0.484352 0.406206 160 0.371042

2025-08-01 1.160056 1.681400 0.844275 0.470637 0.578061 0.403280 161 0.359056

2025-09-01 1.248739 1.967811 0.820923 0.651539 1.057294 0.396816 159 0.330069

2025-10-01 NaN NaN NaN 0.680923 1.185889 0.364496 145 0.202053

2025-11-01 NaN NaN NaN 0.643339 1.129358 0.339036 154 0.179403

2025-12-01 NaN NaN NaN 0.475717 0.733124 0.316046 148 0.221281

2026-01-01 NaN NaN NaN 0.490230 0.630107 0.405185 116 0.294682

2026-02-01 NaN NaN NaN 0.519300 0.675555 0.425098 85 0.413599

2026-03-01 NaN NaN NaN 0.537497 0.749775 0.409650 80 0.458403

2026-04-01 NaN NaN NaN 0.521255 0.530265 0.515803 202 0.455820

2026-05-01 NaN NaN NaN 0.546661 0.530906 0.556270 129 0.428528

ghcnm.v4.0.1.20260603:

109.153

Ooof. Looks like I will lose mana this time.

Looks very unlikely it won't go up significantly from here:

The Antarctica box is currently being infilled far too cool by a single station (Bellingshausen in the South Shetland Islands):

Elev. (m): 14.0, Station: AYM00089050, Name: BELLINGSHAUSEN_AWS

LAT/LON: -62.18/ -58.88, Value: -5.65, Anomaly: -2.43, Last30yrs -> mean: -2.95, min: -6.80, max: -0.45, std: 1.43

The Brazil box is also being poorly infilled so that will warm substantially too.

Given the release on the 10th (Wednesday), I think the data we have on the 8th (Monday) is what we will likely have... These are the stations from LAST month on that day:

Notably I've excluded the left most Antarctica box that ERA5 is cooler because I think its fairly well sampled at the moment from the single station I expect there to move it.

There are some other choices like whether some of the Nordic stations will bring it down in the Arctic slightly and same for Mexico (which we haven't gotten good coverage), whether we will get Rwanda/Uganda this month (haven't gotten it previously) which would warm it, but roughly there doesn't seem to be too much variability from the the base case.

Which again is half of the change expected from the boxes I expect more data (and not representative), which from the above comes to ~= +0.0439 / 2 ~= +0.022 C

Given we are at 1.0915 C, this puts my best guess at the moment at 1.1135 C.

This is based on the data expected to be available on June 8 (which would be labeled ghcnm.v4.0.1.20260607). This was nearly identical my prediction before yesterday's work that included ERSSTv5... (the three ERA5->GISTEMP models).

I'm very confident now it will end up in this bin, maybe <5% we end up in either bin on either side (the warm one being slightly more likely) -- I've kept a sizable position (that doesn't reflect my epistemic probabilities) in them in case there is a large revision upwards/downwards to existing stations....

June 2026 market

@ChristopherRandles June market? (same bins sounds good at the moment to me).

Notable temperature rise over first 14 days of May in medium range super ensemble forecast, as the rise (using a lin. reg.) for the first 14 days of May would be ranked 6th out of 87 years if the current forecast validates (a 0.64 C difference from May 14 to May 1).

ranking of May 1-14:

1968: 0.05661318681318699

2002: 0.054540659340659346

2003: 0.0510989010989007

2012: 0.04960439560439526

1980: 0.047881318681318605

2026: 0.04756657045929035

1960: 0.04687032967032967

A week later, at this point the first week of May looks like it has validated and the second week forecast has gone even higher, with the slope over these two weeks ranking it 3rd out of 87 years (a 0.72 C difference from May 14 to May 1)...

1968: 0.05661318681318699

2002: 0.054540659340659346

2026: 0.05112604117877309

2003: 0.0510989010989007

2012: 0.04960439560439526

1980: 0.047881318681318605

After looking at the CFS weekly that appears to show a much less anomalous end of the month then the middle (especially Antarctica)..

It spurred me to then spend sometime looking at the long range GEFS from a couple days ago to see if it has a different opinion then the climatology or what appears that CFS might be showing (from just visually).

Rather than comparing absolute values, I compare the day-over-day changes between the final adjusted temps from the super ensemble (after adjusting for its long term biases), and the GEFS long range (from wednesday -- a couple days ago):

>>> (final_deltas - gefs_long_deltas).iloc[-9:]

valid_date

2026-05-23 0.016614

2026-05-24 -0.001179

2026-05-25 -0.003278

2026-05-26 -0.016506

2026-05-27 -0.005293

2026-05-28 -0.006945

2026-05-29 -0.013297

2026-05-30 -0.012357

2026-05-31 -0.009789

Technically for the 23rd we only have GEPS/GEFS (no EPS so I included it as reference; 24th onwards is the usual adjusted Prophet extrapolation after all adjustments).

Integrating the deltas requires a bit of code but then it comes out that GEFS long range is about +0.0239 C on average over what I already had for the last 8 days. This is actually a small contribution, that amounts to a suggestion of about +0.006 C for the month.

Given how much worse GEFS long range is compared to climatology usually, I'm going to still assume the climatology is a better judge at the long range, given that it doesn't amount to anything wildly different and the trend is roughly consistent (although a bit less steep than GEFS long range) (not anything too concerning to discount the Prophet extrapolation).

~

Comparing the mean subboxes from April 2026 and April 2024 from the latest gistemp run..

Using the mean of these subboxes (equally weighted), the ocean was only a tiny bit cooler in 2026 (-0.007), but the land anomaly was significantly cooler in 2026 than 2024 (-0.335 C). This makes it the best analog...

~

The first two weeks of May 2024's rise (slope of 0.02489) is roughly half of what 2026 is forecast to be, although there is a plateau and a slight drop in the forecast for 2026 for the 3rd week.

As I've had some poor performance mainly with the old, basic ERA5->GISTEMP model I developed a couple years ago (the p-value for the monthly model of May for instance is 0.09 given the 1940 offset start year, but using an offset of 1950 reveals a p-value of 0.54, resulting in needing to use the yearly model; so I need to to revisit this to come up less brittle scorer / revise the whole model).

For now I compare the ERA5 data directly from May: 2026 is forecast about 0.004C warmer than 2024 in terms of t2m (gistemp has 2024 as 1.1591 for reference). The old GISTEMP->ERA5 monthly model for May 2026 (offset 1940+) would put it unadjusted at 1.19 and the yearly model (1950+) at 1.21. Given the below I'm more tempted to investigate whether recent analogs are better...

Comparing ERA

>>> final_may['2t_adj']

valid_date_month

1940-05-01 14.745484

1941-05-01 14.654323

1942-05-01 14.653065

1943-05-01 14.632097

1944-05-01 14.663581

...

2023-05-01 15.656968

2024-05-01 15.913581

2025-05-01 15.792226

2026-05-01 15.918095

Comparing April as well:

>>> final_april['2t_adj']

valid_date_month

1940-04-01 13.756900

1941-04-01 13.554867

1942-04-01 13.558367

1943-04-01 13.589467

1944-04-01 13.731333

...

2023-04-01 14.682133

2024-04-01 15.031800

2025-04-01 14.962900

2026-04-01 14.885267

For the above, April ERA5 (2026-2024): 14.885 - 15.032 = -0.147

While for GISTEMP April it was (likely): 1.1773 - 1.31358 = -0.136

-0.136 - -0.147 ~= 0.011 C

This isn't bad.. (using 2024 as an analog for 2025, the value is even smaller at ~ -0.003)

What is it for May then for ERA5 (2026 - 2024) after all adjustments for 2026?

15.918095 - 15.913581 ~= 0.005

GISTEMP for May 2024 was ~ 1.159

Suggesting a May 2026 of 1.159 + 0.005 = 1.164 C

This is below what I get (without adjusting for own past forecast errors) with the old GISTEMP->ERA5 model of 1.189 C (and a yearly model using a 1950+ offset of 1.214 C).

Given the other recent delta analog models I've been using has performed better recently I'm leaning towards this other, ad-hoc calculation using 2024 as an analog for another week until the medium range ensemble covers the end of the forecast, or until I do some actual statistical tests to see which works better.

Here is the partial anomaly for May thus far (it will warm up since its missing the last 7 days and its normalized to the month's value, so it will be an underestimate mostly )

The dip in the middle of the month has gotten deeper.

~

Spent some time today working on a couple things:

1) a new ERA5->GISTEMP program that selects from a variety of analog models, with the best selected for each month (with varying start cutoff years from which to choose the best performing model):

local_linear: 4 / 12 months

local_quadratic: 4 / 12 ""

delta_analog: 2 / 12 ""

huber_local: 2 / 12 ""

This provides a better center prediction than the old ERA5->GISTEMP model. I'm not sure if it's better than the other delta analog I came up with for post mid-month that uses gridded data -- I will have to check the variance when we get the data.

2) After this I reworked the variance estimation from the forecast prediction using the past recorded forecast errors I have collected (not using a hindcast method; so it's historical/empirical) to provide much more plausible variances (before it was far underconfident far out and I had to judge subjectively).

3) Combining these with the recent (hindcast) forecast errors from (1) I have a new pipeline (it seems sane and it passed several diagnostics):

Point estimate adjusted by prediction error mean (unadjusted by own past forecast errors): 1.1428

Point estimate adjusted by prediction error mean (adjusted by own past forecast errors): 1.1731

End of month type (no forecast error variance)

Std. dev.: 0.0363

Bin Probability (%)

<1.095 1.6

1.095-1.145 20.4

1.145-1.195 50.7

1.195-1.245 24.9

1.245-1.295 2.3

>1.295 0.0

With empirical forecast error variance:

(ERA5->GISTEMP model variance, forecast predictive variance): 0.0013, 0.0014

Total predictive variance: 0.0027

Total predictive std: 0.0520

Std. dev.: 0.0520

Bin Probability (%)

<1.095 6.7

1.095-1.145 22.8

1.145-1.195 36.8

1.195-1.245 25.3

1.245-1.295 7.4

>1.295 1.0

I've shifted my bets from now on to this new adjusted foreast for now.

New ECMWF upgrade (r50) rolled out today (although I think perhaps from the 06Z run than the 00Z run which I waited for), so there might be some larger jumps tomorrow when I update)..

Values for end of month continue to slightly drop...

My best estimate of what spatially the current outlook looks like for the month (the end of the month is still smoothed quite a bit spatially by the super ensemble, and it could change in a few days, but for the moment there doesn't appear there will be any obvious localized extreme anomalies for the month as a whole):

Now have 3 different estimate methods to combine (I.e. the old one I used last year, delta method useful for only latter half of month, and the more recent analogs method), adjusted by recent residuals yields the three center point predictions (with the analogs method having the best performance): 1.1314, 1.1699 1.1202

Weighting them I get a center point prediction of 1.1341 C currently.

As I currently have an oversized position in the 1.15-1.20 bin relative to the 1.10-1.15 bin, I haven't updated too strongly in those bins, but I'll try to remember from today to start putting a relatively large buy limit order for 1.10-1.15 at my probability estimate for it.

(For the moment I only think the lowest bin and the top two bins are about the right probability at the moment).

Placed a buy order for 1400 mana @ 40% for 1.10-1.15 in case anyone wants to sell some mana for immediate profit (my best probability estimate at the moment for that bin anyway).

Bots are driving me nuts as I have an even more asymmetric position now.

Not much changed since yesterday, with only a marginal nudge downwards, as I get a 1.1314 C center point prediction from weighting the three predictors as mentioned above (after all adjustments).

@parhizj I am the bots

My last predictor that was in the 1.15-1.20 bin finally dropped a bit with the latest update into the lower bin so now all three are in the 1.10-1.15 bin. This puts the point prediction after all adjustments at ~ 1.11C

I've added a new version of the old diagnostic plot of the below (which uses the uncalibrated (model spread + model disagreement) variance. The old one:

And will now switch to using one that makes use of the historical lead time information (i.e. debiasing by lead time, relative to the latest ERA5 preliminary copernicus ), it also uses now the historical variance (this isn't based off the last debiased error by lead time step), with block bootstrap over two week chunks (although it is basically identical in the medium range), and only used for when I have 100 samples at that lead time, otherwise it defaults to Prophet's estimate in the very long range-- i.e. you can see it switch in December

New one below (edit fixed, was not using debiased 2t mean on lead time):

This is despite ECMWF switching to a new model (it's only a rough estimate anyway since ideally I would calibrate the spread with reforecasts of each ensemble member but this is too much work at the moment; as such it is not the best representative of the spread since it covers the variance over many less analog months (and not just near the day of year which would be more appropriate). The variance in the long range prophet will probably be always be a bit off though (either too small or too large).

~

June looks like to start off like May but a weak/ambiguous MJO signal in the second week of June at the moment so not much confidence we will see continue to see such a steep rise...

analog_method,delta method,old weights: 0.5611, 0.2324, 0.2065

Point estimate (old, delta method, analog method) adjusted by prediction error mean: 1.1073, 1.1385 1.0979

Point estimate (mix) adjusted by prediction error mean: 1.1093

Probs (mix) with super ens var

Std. dev.: 0.0460

Bin Probability (%)

<1.095 37.8

1.095-1.145 40.3

1.145-1.195 18.7

1.195-1.245 3.0

1.245-1.295 0.2

>1.295 0.0

I've modified the above chart to include the subseasonal ECM (ECM46) (odd days only, meaning its 2-3 days behind -- I'm only using the odd day forecasts for now so I don't have to interpolate on the reforecasts to calibrate the variance) for reference.

The variance is as best as I could calibrate it to the on-the-fly reforecasts (using tuned, spline EMOS) that are provided. It's is still a bit under dispersive though, spread-skill ratio (spread/error) mean is about 0.88 for days 16-38 -- after then the model sort of collapses as far as variance from day 40, at least as far as I can interpret it); this is only done with a handful (7) of samples though from the last month or so. the EC46 is ARIMA(1,0,0) adjusted but should be minimal given I'm only using after the medium range.

The shift to bring the dated EC46 forecast, referenced uses the mean of the delta from the two days of the super ensemble's medium range that overlaps with EC46. The shift is noted in the legend. Other than that the CI is as the latest changes for the super ensemble, and prophet.

The trend is mostly following Prophet, with a slight plataeu indicated after the medium range finishes.

Not much change for the probabilities for me for May over last 5 days as month comes to a close. (1.105 C)

Meanwhile on polymarket it has been > 70% for the last 4 days on the most likely bin.

As always I disagree with how confident people should be... but 🤷 .

I'm once again in a particularly asymmetric position this month still, only profiting if it doesn't end up in 1.10-1.15.

~

Looking back at beginning of May...

The (slope of the rise) first two weeks of May ended up ranking 7th (instead of 6th) as the super ensemble forecast showed at the end of April. I call that a hit for the medium range.

However a week after that the super ensemble did poorly, as forecasts with inits around May 7 did especially poorly for lead times 8 days out or more (similarly to what happened in April), and ended up exaggerating how warm May was going to be (red is model was too warm relative to obs.):

~

Now looking to June...

With this in mind, will we see something similar as far as errors in June? Maybe, but not as large as I would expect, as the slope of the trend for the second half of June naturally won't be as steep.

Notably, for the first 10 days though of June (as far as ECM medium range goes now) we have the slope ranked #2 !

1995: 0.04785494505494492

2026: 0.04652830402572993

1986: 0.04478681318681309

1988: 0.04318241758241797

1996: 0.042898901098900995

1947: 0.0426769230769232

2013: 0.042261538461538614

Afterwards, EC46 shows the trend though is now (slightly) below climatology in the latest run:

This makes it continue to look like there is a greater chance of a plateau/dip in trend after what the medium range shows presently, like what happened in May...

Analysis from superensemble for yesterday May 27 came in quite a bit colder then expected, which is unusual. I.e. here are the last 10 forecasts I did for it from older inits to today (last one is ~ tau=0h super ensemble analysis (except for geps which includes a couple tau=6h forecasts)):

[np.float64(16.115467685246234), np.float64(16.087889314238634), np.float64(16.097090013120667), np.float64(16.089386706331844), np.float64(16.059621980704456), np.float64(16.05610415912528), np.float64(16.019827199567374), np.float64(16.035886100615055), np.float64(16.064108874761605), np.float64(15.99339020147704)]

>>> np.mean(may27[:-1])

np.float64(16.069486892634572)

>>> np.mean(may27[-1])

np.float64(15.99339020147704)

About 0.07C cooler than predicted for the last 9 days, and even the day of !

We'll have to wait a day or two to see if this validates in the ERA5 preliminary data.

~

Edit (correction after looked at wrong product):

This only being a single day and a marginal change in the month temperatures alone (-0.002C), with the delta analog data also dropping (-0.004) it only pushed the lowest bin probabilities up marginally.

(spotted this when I do the usual toggling between the diagnostic charts for the last 2 days):

Edit (update):

Not sure what went wrong yesterday, but it looks like it was on my end, as only that the final adjusted value got messed up for that run somehow for that specific day (I have been adjusting a lot of the code and writing new code in different systems but its hard to see how it got affected).

Preliminary ERA5 came in for May 27, and it near was expected previously, 16.067.

(Run from today May 29):

Notable is the shift for EC46 today has dropped since yesterday by about -0.09C to +0.15C as it comes in better alignment with the end of the medium range super ensemble.