×

zbMATH — the first resource for mathematics

Stochastic and mesoscopic models for tropical convection. (English) Zbl 0998.86001
Summary: A new way to parametrize certain aspects of tropical convection through stochastic and mesoscopic models is developed here. The technical idea is to adapt tools from statistical physics and materials science to model important unresolved features of tropical convection. This new strategy consists of modeling the unresolved effects of convective inhibition in a coarse mesh mesoscopic parametrization through a “heat bath” model involving a stochastic spin flip model with very natural interaction rules for convective inhibition combined with a suitable external potential defined by the coarse mesh values. In turn, the values of the order parameter from this heat bath alter the vertical mass flux in regions of deep convection. Both stochastic and systematic deterministic mesoscopic parametrizations are developed here. The deterministic mesoscopic models derived in this fashion exhibit new phenomena such as multiple radiative equilibria in suitable parameter regimes. The simplest first numerical experiments reported here with the mesoscopic deterministic parametrization qualitatively reproduce several key features of the observational record regarding convectively coupled tropical waves. The systematic stochastic modeling strategy proposed here could also be very useful for capturing other features of tropical convection such as those involving cloud radiation feedbacks.

MSC:
86A10 Meteorology and atmospheric physics
82B99 Equilibrium statistical mechanics
PDF BibTeX XML Cite
Full Text: DOI Link
References:
[1] J METEOROL SOC JPN 66 pp 823– (1988)
[2] J GEOPHYS RES D 99 pp 8073– (1994) · doi:10.1029/94JD00045
[3] J ATMOS SCI 56 pp 374– (1999) · doi:10.1175/1520-0469(1999)056<0374:CCEWAO>2.0.CO;2
[4] J STAT PHYS 63 pp 933– (1991) · doi:10.1007/BF01029992
[5] Journal of Physical Chemistry 100 pp 19098– (1996)
[6] Katsoulakis, Physical Review Letters 84 (7) pp 1511– (2000) · doi:10.1103/PhysRevLett.84.1511
[7] J STAT PHYS 87 pp 37– (1997) · Zbl 0937.82037 · doi:10.1007/BF02181479
[8] J STAT PHYS 87 pp 63– (1997) · Zbl 0937.82034 · doi:10.1007/BF02181480
[9] J COMP PHYS 173 pp 361– (2001)
[10] J ATMOS SCI 57 pp 1515– (2000) · doi:10.1175/1520-0469(2000)057<1515:CISSTE>2.0.CO;2
[11] J ATMOS SCI 58 pp 896– (2001) · doi:10.1175/1520-0469(2001)058<0896:WAIFMT>2.0.CO;2
[12] J ATMOS SCI 58 pp 1567– (2001) · doi:10.1175/1520-0469(2001)058<1567:MFSIAC>2.0.CO;2
[13] Q J R METEOROL SOC 127 pp 445– (2001) · doi:10.1002/qj.49712757211
[14] J ATMOS SCI 57 pp 613– (2000) · doi:10.1175/1520-0469(2000)057<0613:LSDFAW>2.0.CO;2
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.