system
Given the following post, respond as if you're commenting on Reddit:
human
What is the temporal scale of weather autocorrelation? To what extent is there such a thing as a "cold year" or a "warm year"?

I'm interested in to what extent temperatures in one part of the year predict temperatures in subsequent parts of the year (especially to what extent a warm spring predicts a warm summer). This should be important to several aspects of the life cycles of the insects I work with, but I can't find anything on it in the literature.

My takeaway from reading some popular science sources (e.g. weather services websites) is that a warm spring is no herald of a warm summer, and that temperatures often average out across the whole season. So perhaps there's no correlation on a two- or three-month scale, and no such thing as a "warm year" or a "cold year", other than by mere contingency.

But at the other extreme, temperature does have a certain degree of inertia - daily temperatures don't fluctuate within the entire range, but rather today's weather correlates to some extent with tomorrow's weather. Pressure systems take time to form and move around, right? So there must be some level of temporal resolution at which present temperatures correlate with future temperatures. Is it days, weeks, months?

I'd be super grateful for sources, if they're available. :)
gpt
The temporal correlation of 'weather' at mid-latitudes is 3-7 days and is predominantly set by the time-scale of meanders in the jet stream. The dynamic 'memory' of the atmosphere is 2-4 weeks which sets the maximum correlation time-scale for an 'atmosphere-only' planet to be about a month.  Any non-seasonal variability on longer time-scales than a month cannot be self-generated within the atmosphere and are dependent on coupled interactions with the ocean such as El Nino (and to lesser extent atmosphere-cryosphere interactions). The ocean's primary influence on weather is through the slowly evolving spatial distribution of sea-surface temperatures which sets the lower boundary-condition on the atmosphere. Predictions of ocean surface temperatures are improving but are still hampered by the small scales which need to be resolved (10s of km) and sparsity of ocean observations.