Tree-ring-anchored analog reconstruction of daily climate distributions from instrumental data with Bayesian distributional regression: Application to the European Alps

Daily to seasonal weather information remains rare in Quaternary science, because proxy archives typically resolve only seasonal or annual means. Yet climate is felt at daily timescales, through frost, snowfall, wind and precipitation. Here a framework of Bayesian Additive Models for Location, Scale and Shape is presented that anchors a modern day-of-year marginal climatology to a proxy-reconstructed seasonal mean, two millennia into the past. Tree-ring proxies constrain the seasonal mean temperature anomaly; instrumental station records supply the daily distributional structure, conditioned on that anomaly. Modeling location, scale and shape jointly yields arbitrary percentiles with posterior uncertainty, for temperature and for snowline altitude, wind chill, snow depth, precipitation and wind. A central distinction is maintained between proxy-anchored daily climatologies and modern conditional climatologies for variables the summer proxy does not constrain. Applied to 15 BCE–16 CE, when a Roman military camp occupied Septimer Pass (Switzerland), the reconstruction gives summers averaging 4–7°C, daily minimum temperatures above freezing only from mid-June to mid-September, snow depth at the analog site peaking near 1.5m in April, and, under the stronger of the two wind records, felt temperatures below 0°C throughout the year. Together these describe an environment in which the camp could have been occupied for a few months at most. Cross-validation bounds what the framework delivers. Against an unconditional climatology the skill is high for temperature and the quantities derived from it. Against a stricter day-of-year baseline it is indistinguishable from zero, so what the proxy delivers at daily resolution is the level, and the distributional structure is inherited. That limit is structural rather than a shortcoming of implementation: attainable skill is the product of the between-year share of daily variance and the proxy’s squared correlation with it. Both are measurable from instrumental data, so together they decide in advance whether a comparable reconstruction is worth attempting elsewhere in the Quaternary.