## Communications in Mathematical Sciences

- Commun. Math. Sci.
- Volume 8, Number 1 (2010), 187-216.

### A stochastic multicloud model for tropical convection

Boualem Khouider, Joseph Biello, and Andrew J. Majda

#### Abstract

A stochastic model for representing the missing variability in global climate models due to unresolved features of organized tropical convection is presented here. We use a Markov chain lattice model to represent small scale convective elements which interact with each other and with the large scale environmental variables through convective available potential energy (CAPE) and middle troposphere dryness. Each lattice site is either occupied by a cloud of a certain type (congestus, deep or stratiform) or it is a clear sky site. The lattice sites are assumed to be independent from each other so that a coarse-grained stochastic birth-death system, which can be evolved with a very low computational overhead, is obtained for the cloud area fractions alone. The stochastic multicloud model is then coupled to a simple tropical climate model consisting of a system of ODEs, mimicking the dynamics over a single GCM grid box. Physical intuition and observations are employed here to constrain the design of the models. Numerical simulations showcasing some of the dynamical features of the coupled model are presented below.

#### Article information

**Source**

Commun. Math. Sci. Volume 8, Number 1 (2010), 187-216.

**Dates**

First available in Project Euclid: 23 February 2010

**Permanent link to this document**

http://projecteuclid.org/euclid.cms/1266935019

**Mathematical Reviews number (MathSciNet)**

MR2655906

**Zentralblatt MATH identifier**

05713687

**Subjects**

Primary: 65C05: Monte Carlo methods 65C20: Models, numerical methods [See also 68U20] 65C40: Computational Markov chains 65L05: Initial value problems 86A10: Meteorology and atmospheric physics [See also 76Bxx, 76E20, 76N15, 76Q05, 76Rxx, 76U05] 76M35: Stochastic analysis 76R99: None of the above, but in this section

**Keywords**

Stochastic modeling Markov chains tropical convection clouds convective parametrization climate modeling CAPE moisture

#### Citation

Khouider, Boualem; Biello, Joseph; Majda, Andrew J. A stochastic multicloud model for tropical convection. Commun. Math. Sci. 8 (2010), no. 1, 187--216. http://projecteuclid.org/euclid.cms/1266935019.