A data‐driven method for the stochastic parametrisation of subgrid‐scale tropical convective area fraction

Abstract

Observations of tropical convection from precipitation radar and the concurring large-scale atmospheric state at two locations (Darwin and Kwajalein) are used to establish effective stochastic models to parameterise subgrid-scale tropical convective activity. Two approaches are presented which rely on the assumption that tropical convection induces a stationary equilibrium distribution. In the first approach we parameterise convection variables such as convective area fraction as an instantaneous random realisation conditioned on the large-scale vertical velocities according to a probability density function estimated from the observations. In the second approach convection variables are generated in a Markov process conditioned on the large-scale vertical velocity, allowing for non-trivial temporal correlations. Despite the different prevalent atmospheric and oceanic regimes at the two locations, with Kwajalein being exposed to a purely oceanic weather regime and Darwin exhibiting land-sea interaction, we establish that the empirical measure for the convective variables conditioned on large-scale mid-level vertical velocities for the two locations are close. This allows us to train the stochastic models at one location and then generate time series of convective activity at the other location. The proposed stochastic subgrid-scale models adequately reproduce the statistics of the observed convective variables and we discuss how they may be used in future scale-independent mass-flux convection parameterisations.

Stochastic Convection Parameterization with Markov Chains in an Intermediate-Complexity GCM

“…The time series of M b in Figs. 2c and 2f compare well with time series produced by the same schemes using observed hvi values (Dorrestijn et al 2015;Gottwald et al 2016). In addition, the large range in different mass flux behavior displayed in Figs.…”

“…Therefore, in the present paper, we show results of the implementation of the stochastic multicloud model of Dorrestijn et al (2015), referred to as Dor15, and a scheme similar to the CMC scheme of Gottwald et al (2016), referred to as Gott15, in a GCM of intermediate complexity; the climate model Simplified Parameterizations, Primitive Equation Dynamics (SPEEDY) (Molteni 2003;Kucharski et al 2006Kucharski et al , 2013.…”

“…In a GCM grid column, the N CMCs yield area fractions s m for each cloud type 1 # m # 5, which are defined by Previous studies based on observational data (Dorrestijn et al 2015;Gottwald et al 2016) show that the expectation value of s 4 is an increasing function of hvi, with a maximum of around 0.03 for hvi ' 15 hPa h 21 .…”

“…In that respect this explorative study should be considered as a natural intermediate step from recent offline studies (Dorrestijn et al 2015;Gottwald et al 2016) toward an implementation into the state-of-the-art GCMs.…”

“…In Gottwald et al (2016), a similar data-driven stochastic scheme has been developed. Observational datasets from Darwin and Kwajalein were used to construct parameterizations of the convective area fraction s c , also conditioned on the large-scale vertical velocity.…”