A scaling relation for warm-phase orographic precipitation: a Lagrangian analysis for 2D mountains

作者：Miltenberger Annette K^*; Seifert Axel; Joos Hanna; Wernli Heini

来源：Quarterly Journal of the Royal Meteorological Society, 2015, 141(691): 2185-2198.

DOI：10.1002/qj.2514

• orographic precipitation
• precipitation efficiency
• Damkohler number
• microphysical time-scale
• advective time-scale
• trajectories

The precipitation produced by orographic clouds is the result of the interaction between nonlinear dynamical and microphysical processes. Focusing on warm-phase stable clouds, we propose that the precipitation efficiency is essentially controlled by the bulk Damkohler number of the system, i.e. the ratio of the characteristic advective to the microphysical time-scale of the cloud. These time-scales are investigated thoroughly for single air parcels along temporally highly resolved trajectories from quasi-two-dimensional numerical simulations with vertical Froude numbers between 0.38 and 2.31. Based on these results, analytical formulations for the Damkohler number of single parcels and for a bulk Damkohler number for the entire cloud are developed, which depend only on the far upstream flow properties and the cloud droplet number density. Relating the bulk Damkohler numbers to the precipitation efficiencies from the numerical simulations results in a unique scaling relation between the two non-dimensional numbers: no precipitation is observed for very small Damkohler numbers, while for large Damkohler numbers the precipitation efficiency asymptotically approaches a maximum value of about 0.8. For intermediate Damkohler numbers, the precipitation efficiency depends strongly on the microphysical properties of the clouds.

• 出版日期2015-7