Long-term forecasting of extreme temperatures remains a challenge for meteorology: existing models are either limited to short lead times or require assumptions about probability distributions that are hard to estimate from rare events. This work stands apart from its archive neighbors, which predominantly feature El Niño forecasts, weather noise, and machine learning on GPUs. In contrast, it does not build a global model but seeks local analog rules that link distant locations with a time lag.
The authors compiled 78 data series: daily mean temperatures at 66 locations, visibility, wind, dew point, sea-level pressure, Southern Oscillation indices, and sea surface temperature. Each series is split into a training set (1973–2010) and a validation set (2011–2013). For each pair of locations, they compute the sum of deviations from the climatic norm over intervals from 1 to 365 days and with lead times from 14 to 365 days. A forecast rule is selected if such a sum preceded an extreme in the training set at least four times (with intervals exceeding 30 days). An extreme is defined as a deviation of more than two standard deviations from the mean for that date.
For positive extremes in Washington, three rules were found that predicted 18.2% of actual extremes (50% of all triggers). For negative extremes in Skopje, five rules yielded 11.1% exact hits. In all cases, the sign of the predicted deviation matched the actual one. The probability of obtaining such results by chance is less than 4.94% for Washington and 4.23% for Skopje, which is significant at the 95% level. Example: the heat on April 16, 2012 in Washington was predicted 60 days ahead using temperatures in Bucharest and Kyiv.
The work shows that rare extremes can be predicted without fitting distributions, relying solely on recurring patterns in data. This distinguishes it from archive neighbors that use either physical models or machine learning with big data. Here, the key contribution lies in the very principle of non-anticipativity: the forecast is built only on information available at the time of prediction, without 'peeking' into the future.
The method can be scaled to a global network of stations and extended to additional variables, including precipitation and pressure. Testing on synthetic data is possible, though the authors doubt that models will reproduce the nonlinear dynamics of extremes. Combining with ensemble approaches for uncertainty estimation is promising.
The method is applicable in energy for planning peak loads, in agriculture for protecting crops from frost or heat, and in healthcare for warning of heat waves.
Test the method on a larger number of stations and for precipitation; investigate which pairs of locations yield the most reliable rules.
For meteorology, the open question remains about the physical mechanisms of teleconnections underlying the found rules. Also unclear is how stable these rules are under climate change, when climatic norms shift.
The heat in Washington on April 16, 2012 was predicted from temperatures in Bucharest and Kyiv 60 days before the event, even though these cities are more than 7000 km apart.