A binomial stochastic framework for efficiently modeling discrete statistics of convective populations

Abstract

Convective cloud populations in Earth's atmosphere cover a broad range of spatial scales. Their occurrence acts on planetary scales, by persistently covering substantial areas of the globe. On the other end, individual clouds have dimensions from a few meters up to tens of kilometers. The spatial structure of cumulus populations acts on the intermediate (meso)scales and can take many forms, including random-like distributions (Nair et al., 1998) but also more organized patterns including cold pool structures and convergence lines (Bony et al., 2020;Zuidema et al., 2012).Understanding the spatial structure of cumulus populations is important for various reasons. Global weather and climate models require parameterizations to represent the impact of subgrid-scale processes on the

Empirical values and assumptions in the convection schemes of numerical models

“…Later, Tan et al (2018) extended the EDMF approach by using prognostic plumes and adding downdrafts, among other changes. Neggers (2015) reformulated the EDMF approach in terms of discretized size densities with a limited number n of bins. This new version, referred as to ED(MF) n , was studied in an SCM.…”

“…The first scheme using multiple plumes is that of Arakawa and Schubert (1974). Different schemes have been proposed based on multiple plumes for deep (e.g., Donner, 1993;Donner et al, 2001;Nober and Graf, 2005;Wagner and Graf, 2010) and shallow convection (e.g., Neggers et al, 2002;Sušelj et al, 2012;Neggers, 2015). Due to the lack of observations on cloud entrainment, Neggers et al (2002) used LES results to formulate an expression for the lateral entrainment rate as a function of the vertical velocity of each parcel, while Sušelj et al (2012) described moist updraft characteristic through a PDF.…”

“…Other parameterizations, such as those of Graf (2010), Nober andGraf (2005), and Neggers and Siebesma (2013), make use of active population dynamics such as those in the Lotka-Volterra equations (Lotka, 1910(Lotka, , 1920Volterra, 1926), wherein two species interact with a predator-prey behavior. Neggers (2015) also introduced population dynamics in a new EDMF called the ED(MF) n . The author used bin macrophysics, wherein plumes are described in terms of discrete size densities formed by a limited number n of bins.…”

“…Understanding spatial organization of convection is not only important for developing stochastic and scale-aware parameterizations but also due to its impact in the radiativeconvective equilibrium (Neggers and Griewank, 2021) . Few studies have proposed parameterizations to represent convective organization in GCMs (e.g., Donner, 1993;Donner et al, 2001;Mapes and Neale, 2011;Donner et al, 2011;Khouider and Moncrieff, 2015;Moncrieff et al, 2017).…”

“…Mesoscale organization is represented by explicit convectively driven circulations using a CSRM and transient cumulus by the BMJ convective parameterization (Betts, 1986;Betts and Miller, 1986;Janjić, 1994). PDF-based or spectral schemes based on a discretized distribution (e.g., Neggers et al, 2003;Wagner and Graf, 2010;Park, 2014a, b;Neggers, 2015) include size information into the system, which allows representing impacts of spatial organization (Neggers et al, 2019;van Laar, 2019). More recently, Neggers and Griewank (2021) developed a binomial stochastic framework referred to as the Binomial Objects on Microgrids (BiOMi) model, which proved to capture convective memory and simple forms of spatial organization, among other important convective behaviors, at a cheap computational cost.…”