Two Hebrew folk meteorological proverbs tested: rainfall on Rosh Chodesh and Shabbat Mevarechim as predictors of monthly precipitation (Israel, 1950-2024)

Forecasters are evaluated by backtesting, which replays resolved questions and grades the probability the system would have assigned before the outcome was known. For LLMs, two channels leak the answer into this test. A model that retrieves can surface reports written after the event, turning forecasting into a lookup, and each new model is trained on data closer to the event, so a question that lay in the future for last year's models sits inside this year's training data. Either way, the test grades recall while claiming to grade foresight. We introduce Hindcast, which closes both leaks by grading a model as if it stood at a chosen past date $t_0$, before the outcome existed in either channel. Hindcast replays resolved Polymarket prediction markets against a frozen snapshot of public Reddit, lets the model read only posts written before $t_0$, and scores each forecast against both what happened and the market's own price at $t_0$, itself a human forecast made from the same past information. Because the cutoff is set per market and the snapshot never changes, the evaluation re-runs on new markets as models improve, without going stale. Once the leak is closed, retrieval still helps most models, but only where Reddit discussed the event beforehand. Where the archive carried only speculation, retrieval hurts.

Recent advances in machine learning have produced probabilistic weather forecasting models comparable to state-of-the-art numerical weather predictors. But no model consistently dominates spatio-temporally, and relative performance is highly context-dependent. This motivates adaptive methods for combining multiple forecasts to obtain improvements and robustness. While combined forecasts have been proposed in the literature, these are achieved either through supervised learning or through prediction with expert advice methods. We introduce AdaWeather, an adaptive framework that combines many probabilistic forecasts using both machine learning as well as mixture of experts to arrive at a unified improved probabilistic forecast. While traditional expert methods develop the regret bounds with respect to the best single expert in hindsight, we extend the algorithm and analysis to show our method has logarithmic regret compared to the best static mixture of experts in hindsight. Empirically, we focus on forecasting temperature, and observe improvements over existing methods.

European summer warming reflects interactions among background change, persistent ocean--land--circulation states, and same-season variability. We develop an empirical reduced-dynamics framework that decomposes regional summer indicators into inherited slow-state memory, its predictable component, and contemporaneous innovation. Projection-operator theory motivates the decomposition, implemented with finite causal filters, ridge-regularised prediction, and logistic risk models. Using ERA5-derived summer indicators for 28 IPCC AR6 European sub-regions over 1950--2024, with validation on 2006--2024, we find that Mediterranean-state memory improves mean summer-temperature prediction relative to trend-only and ARX baselines. The gain over ARX is modest, while moving-average, exponentially weighted, and tempered filters contain similar annual information, indicating that the data identify useful slow-state memory more robustly than a unique kernel shape. Predictable-state reconstruction is ridge-sensitive and therefore treated diagnostically rather than as a forecasting model. The strongest result concerns warm-tail risk. In parsimonious logistic models, high accumulated Mediterranean memory raises predicted upper-tail event probability by about 8--11 percentage points for annual maximum summer temperature, warm-day frequency, and warm-spell duration at 1-, 3-, and 5-year horizons. Regional bootstrap intervals remain positive for all targets and horizons. Circular-shift placebos yield one-sided probabilities of approximately 0.05--0.14 and do not survive strict family-wise correction across nine tests, so the evidence is moderate rather than decisive. Overall, annual projected memory is not a universal short-horizon predictor, but a physically interpretable inherited risk-loading variable identifying years and regions predisposed to warm-tail outcomes.