Improving Representation of Tropical Cloud

1. Introduction

The simulation of clouds has been a major source of uncertainty in projections of future climate using general circulation models (GCMs) (Stephens, 2005; Li et al.,2009; Bony et al., 2015). One limitation of cloud simulation is the coarse spatial resolution of GCMs (tens of kilometers to 100-200 km), which leaves clouds smaller than grid size unresolved (Barker et al., 2003; Randall et al., 2003). Consequently, clouds in GCMs usually cover only part of a grid layer and the overlap of fractional clouds in the vertical layers has to be addressed artificially in radiation calculations by imposing overlap assumptions (Tompkins and Di Giuseppe, 2015; Zhang and Jing, 2016). For a given vertical distribution of cloud fractions, the assumption of cloud overlap determines the total cloud cover or total cloud fraction (Ctot), which has a considerable influence on solar and terrestrial radiative transfer (Wang et al., 2016).

The cloud overlap assumption most widely used in recent decades is the maximum random overlap (MRO) assumption (Morcrette and Fouquart, 1986; Tian and Curry, 1989), in which clouds within layers that are vertically continuous are assumed to have a maximum overlap, whereas those that are separated by cloud-free layers are considered to overlap randomly. Such treatment is insufficient to represent the realistic features of cloud overlap as observed by ground-based radar (Hogan and Illingworth, 2000; Mace and Benson-Troth, 2002) and depends largely on the vertical resolution of the host model (Bergman and Rasch, 2002).

In contrast with the simple, crude cloud overlap treatments such as the MRO assumption, Liang and Wang(1997) were among the first to explicitly depict the subgrid distribution of clouds of distinct physical types and to apply different treatments of vertical overlap for different types of clouds. This sophisticated, physically based treatment of cloud overlap (termed “mosaic”) has been demonstrated to improve cloud radiative forcing and radiative heating in both cloud-resolving model(CRM) domains (Liang and Wu, 2005; Wu and Liang,2005a, b) and climate simulations (Zhang F. et al., 2013).

Another ingenious approach is the analytical representation of cloud overlap proposed by Hogan and Illingworth (2000) and Mace and Benson-Troth (2002) based on radar observations. This method is called general overlap (GenO). In GenO, for two layers of clouds at heights of Zk and Zl with cloud fractions of Ck and Cl, respectively, Ctot is defined as

Lcf is the decorrelation length (in km) representing theEqs. (1) and (2), the extent of overlap degrades exponentially from maximum overlap to random overlap as the vertical separation of clouds increases. This relationship of decreasing overlap with increasing distance has been reported from both radar observations and simulations by CRMs (Oreopoulos and Khairoutdinov, 2003). The merits of GenO are two-fold: (1) it realistically depicts the distance-related feature of cloud overlap and (2) it is independent of the vertical resolution of the host model and thus more widely applicable among models with various vertical configurations.

In GenO, the extent of cloud overlap is determined by Lcf. For given fractional clouds in a vertical column, the use of larger values of Lcf results in smaller values of Ctot(prone to maximum overlap) and smaller values of Lcf result in larger values of Ctot (prone to random overlap).The parameter Lcf is highly variable both spatially and temporally because of variations in the shapes and formation processes of clouds. Therefore, when applying GenO, one challenge is to determine an optimum value of Lcf for each GCM grid point. Various attempts have been made to obtain detailed information about Lcf (e.g.,Di Giuseppe, 2005; Kato et al., 2010; Shonk et al., 2010;Oreopoulos et al., 2012; Peng et al., 2013; Zhang H. et al., 2013). It has been demonstrated that Lcf is related to the cloud type and atmospheric dynamics (Naud et al.,2008; Di Giuseppe and Tompkins, 2015; Li et al., 2015)and that it has a global median value of approximately 2 km (Barker, 2008). Simplified expressions have also been extracted to represent Lcf in GCMs, either as a function of latitude and/or season without interannual variations (Shonk et al., 2010, Oreopoulos et al., 2012; Jing et al., 2016) or as a function of cloud type, which is affected by the limited cloud classification schemes of the host models (Zhang et al., 2014). These approaches either lack a direct link between Lcf and the instant largescale meteorological conditions that foster the clouds or address the dynamic (e.g., wind shear) impact on cloud overlap over the globe without considering the very different circulation conditions in different regions.

The formation and evolution of clouds are essentially associated with large-scale circulation (Bony et al.,1997). Therefore one physically robust approach to describe Lcf is to establish a direct connection between Lcf and large-scale circulation conditions. CRMs, because of their ability to simulate cloud micro- and macro-physical structures as well as meteorological conditions in detail,have long been used as a tool to explore cloud physics and to obtain parameterizations applicable in GCMs(GEWEX Cloud System Science Team, 1993; Randall et al., 2003; Wu and Li, 2008). This study uses simulation results from a global CRM to explore the relationship between Lcf and atmospheric circulation. Unlike previous studies that attempted to explore such a relationship over the whole globe, we focus on the tropical region and vertical motion only, considering that there are large uncertainties in cloud radiative forcing due to vertical overlap treatment in the intertropical convective zone (ITCZ)(Barker and R?is?nen, 2005; Zhang and Jing, 2010;Lauer and Hamilton, 2013) and that the formation and maintenance of clouds in this particular region are closely related to vertical convection. We will attempt to establish a statistical, mathematical description of the Lcf-convection connection, which is a novel application in GCMs, and then evaluate its effectiveness in improving the GCM-scale cloud cover and radiation calculations.

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