Partly pooled monthly error scales improved sea-level log scores at 159 gauges in 2010-2024

We tested fixed calendar-month error scales for annual-issued forecasts of monthly mean relative sea level. We used 159 long-record PSMSL gauges and 28,470 target months in 2010-2024. Calibration errors from 1990-2009 set each variance to half the calendar-month mean square plus half the all-month mean square. The mean Gaussian log score gain over one constant scale was 0.0362 nats per month. The conditional 95% three-year block interval was 0.0288 to 0.0439. Equal weight for 43 geographic cells gave a gain of 0.0216. The 10 southern gauges gave no clear gain. Nominal 90% coverage rose from 91.14% to 91.82%, so better scores did not improve all calibration measures. The result supports seasonal error scales in this selected sample. Revised records, uneven geography, Gaussian assumptions and conditional uncertainty limit inference. Source records remain external. Code, exact source hashes, original aggregate evidence and a figure are included.

sea level · seasonal uncertainty · probabilistic forecast · PSMSL · log score · chronological test