Application of a Markov Chain Monte Carlo Algorithm to Orographic Precipitation Analysis
Samantha Tushaus1, Derek J. Posselt1, Mario Marcello Miglietta2, Richard Rotunno3, and Luca delle Monache3
1University of Michigan, Ann Arbor, Michigan 2ISAC-CNR, Padua/Lecce, Italy 3NCAR, Boulder, Colorado
Moist neutral flow over a ridge is a relatively common orographic precipitation-producing scenario. However, there have only been a few modeling studies of such flows over a ridge in recent years. Numerical modeling of orographic precipitation associated with moist neutral flow using the Weather Research and Forecasting (WRF) model was previously undertaken by Miglietta and Rotunno (2005, 2006). Miglietta and Rotunno (2009, 2010) also examined flow over a ridge in a conditionally unstable atmosphere, this time using an explicitly cloud-resolving model (CM1; Bryan and Fritsch 2002). It was found that the distribution and intensity of orographic rainfall was highly sensitive to the details of the upwind sounding, as well as the slope and size of orography. Markov chain Monte Carlo (MCMC) algorithms constitute a class of algorithms that have been used to explore parameter sensitivities in remote sensing retrievals and model parameterizations (Posselt et al. 2008; Posselt and Vukicevic 2012; Posselt and Mace 2013); however, use of MCMC to explore interactions in the physical system is an original concept. Introducing an MCMC-based sensitivity analysis, in conjunction with the CM1, provides insight on the various combinations of upwind atmospheric parameters and mountain characteristics that lead to precipitation in specific regions. Such parameters include wind speed, Brunt-Väisälä frequency, surface temperature, and relative humidity, as well as mountain height and half-width.
Three combinations of mountain height, half-width, and wind speed were identified from data in Miglietta and Rotunno (2009) as cases resulting in upslope, top of mountain, and downslope precipitation. For those cases, the MCMC-CM1 combination was run to discover sets of parameters that produce orographic precipitation at a specific location on the mountain (e.g. the upwind slope). These experiments include a single integration or run of the CM1; a map of the probability density function of two parameters; and a robust MCMC sample of multiple parameters. Results obtained from the MCMC experiments expand our understanding of the interactions between upwind sounding characteristics and mountain orography that result in orographic precipitation.
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