Construction of a Two-Layer Orographic Rain Model and an Hourly Probability-of-Rain Product for Hawaiʻi Island

This technical note describes how an hourly probability-of-rain product for Hawaiʻi Island was built. Airflow comes from two reduced-gravity shallow-water layers beneath the trade inversion: a thin surface layer warmed by day and cooled at night, beneath the trade layer. Moisture is carried in each layer as a saturation deficit and cloud water; rain is advected, falls out and evaporates. The model is run for 60 real trade-wind days driven by the 02 HST Hilo sounding. The ensemble-mean rain rate is converted to point probabilities by logistic model output statistics (MOS), and gauge residuals are added back by regression-kriging. Verification used 20 hourly gauges (2010–2025) in leave-one-gauge-out, 15 km buffer and time-split holdouts. The product reaches a Brier skill of +0.063 to +0.080 against an island-wide diurnal curve, about two-thirds of the +0.112 attainable by a perfect point climatology. An extension classifies every day into eight rain regimes with a non-homogeneous hidden Markov model driven by the Hilo sounding, and gives each regime its own map. Change-of-support calculations bound how closely any area-averaging model can match point gauges. The accompanying archive contains the model code, the probability fields, the gauge frequencies and the regime calendar. Interactive map: https://lucky-manatee-c8f224.netlify.app