Effects of cumulus parameterizations on predictions of summer flood in the Central United States

Abstract

This study comprehensively evaluates the effects of twelve cumulus parameterization (CUP) schemes on simulations of 1993 and 2008 Central US summer floods using the regional climate-weather research and forecasting model. The CUP schemes have distinct skills in predicting the summer mean pattern, daily rainfall frequency and precipitation diurnal cycle. Most CUP schemes largely underestimate the magnitude of Central US floods, but three schemes including the ensemble cumulus parameterization (ECP), the Grell-3 ensemble cumulus parameterization (G3) and Zhang-McFarlane-Liang cumulus parameterization (ZML) show clear advantages over others in reproducing both floods location and amount. In particular, the ECP scheme with the moisture convergence closure over land and cloud-base vertical velocity closure over oceans not only reduces the wet biases in the G3 and ZML schemes along the US coastal oceans, but also accurately reproduces the Central US daily precipitation variation and frequency distribution. The Grell (GR) scheme shows superiority in reproducing the Central US nocturnal rainfall maxima, but others generally fail. This advantage of GR scheme is primarily due to its closure assumption in which the convection is determined by the tendency of large-scale instability. Future study will attempt to incorporate the large-scale tendency assumption as a trigger function in the ECP scheme to improve its prediction of Central US rainfall diurnal cycle.

Appendices

Appendix 1

1.1 Cumulus parameterizations

All deep and shallow cumulus schemes in CWRF are mass-flux based parameterizations, in which different closure assumptions are used to determine the cloud base mass flux by linking the existence and intensity of convection to large-scale processes. According to closure assumptions, all schemes are divided into three major groups and their associated features are briefly summarized below.

1.1.1 Multiple closure schemes

The GD, G3, and ECP schemes are all ensemble mass-flux type schemes with multiple closure assumptions and variants of parameters in the static control including updraft and downdraft entrainment and detrainment and precipitation efficiency. The GD scheme was first introduced by Grell and Dévényi (2002) in which the dynamic control closures are based on convective available potential energy or cloud work function, low-level vertical velocity, or integrated vertical advection of moisture. The G3 scheme is developed on the basis of the GD scheme, but excludes the quasi-equilibrium assumption from closure ensemble members. The ECP scheme is modified from the G3 scheme but with numerous improvements by primarily adding relative weights for different dynamic closures and including regional dependence between the land and ocean. The ECP scheme includes five major closures to determine the cloud base mass flux. The AS closure (Arakawa and Schubert 1974) assumes an instantaneous equilibrium between the large scale forcing and the convection by relaxing the cloud work function toward a climatological value. The W closure (Brown 1979; Frank and Cohen 1987) assumes that net cloud base mass flux is determined by environmental mass flux averaged from the surrounding nine points at lower tropospheric levels such as cloud base or updraft originating level. The MC closure (Krishnamurti et al. 1983) is the widely-used moisture convergence assumption in which convection develops to balance the column integrated moisture convergence. The KF closure is based on Kain and Fritsch (1993) assumption in which the convection acts to reduce the CAPE towards zero over a specific time scale (around 40 min in the ECP scheme). The TD closure is also based on the quasi-equilibrium assumption but determines the convection by the increase rate of large-scale instability (Grell 1993). In the current ECP scheme, the moisture convergence and averaged cloud-base vertical velocity closure is separately implemented over land and oceans.

1.1.2 Total instability adjustment schemes

Three CUPs (ZML, NKF, TDK) are based on the total instability adjustment closure assumption in which the convection acts to reduce the CAPE towards zero over a specific time scale. The ZML is the parameterization of Zhang and McFarlane (1995) with modifications to facilitate its application in high resolution models for deep convection (Liang et al. 2012). The moist convection occurs only when the local atmosphere is conditionally unstable in the lower troposphere. The updraft ensemble is only comprised of those plumes which can penetrate through this convective layer and these updrafts are assumed to have same initial upward mass fluxes from the sub-cloud layer to simplify the formulations.

The NKF scheme (Kain 2004) is a modified version of Kain and Fritsch (1993). It utilizes a one-dimensional cloud model with explicitly representation of effects of moist updrafts and downdrafts, the entrainment, detrainment and simple microphysics involved. This scheme triggers the convection when the net column convective instability is present and the parcel temperature is higher than the environmental value. To induce stronger convection in the presence of the large-scale upward motion, a perturbation to the parcel temperature which is proportional to the grid-scale vertical motion at the lifting condensation level is incorporated as an additional trigger function. The TDK scheme is originally designed by Tiedtke (1989) and revised by Nordeng (1995). It is a bulk mass flux model based on the CAPE removal closure. The convection is activated when the moisture convergence is greater than a limit of boundary layer turbulent moisture flux. This scheme considers three types of convection: (1) deep convection that occurs under disturbed, conditionally unstable conditions in the presence of lower tropospheric large-scale moisture convergence; (2) shallow convection that occurs in a suppressed environment and is mainly driven by the turbulent surface moisture flux; (3) mid-level convection that occurs mainly in conditional unstable condition, but with the cloud base above the PBL.

1.1.3 Quasi-equilibrium closure-based schemes

The remaining eight schemes (BMJ, GR, MIT, GFDL, SAS, NSAS, CSU, and UW) are all established on the QE closure assumption but with alterations. The BMJ scheme is a moist adjustment parameterization developed by Betts (1986) and Betts and Miller (1986), and modified by Janjic (1994) for both deep and shallow convection. It assumes that the profiles of temperature and moisture in a column with sufficient resolved-scale vertical motion and instability are instantaneously relaxed toward to observed neutral structures. It does not explicitly represent the subgrid updrafts and downdrafts and the mesoscale microphysical processes.

The GR scheme is proposed by Grell (1993) as a simplified mass flux scheme that only consists of a single pair of updraft and downdraft without direct mixing between them. Convection in this scheme is determined by the rate of destabilization in which the change of instability due to convection balances the changes due to nonconvective effects. The convection is not activated until a lifting depth criterion is met.

The MIT scheme is the parameterization of Emanuel (1991) and Emanuel and Živković-Rothman (1999). The closure employs a subcloud-layer quasi-equilibrium hypothesis (Raymond 1995) which states that convective mass fluxes will adjust so that air within the subcloud layer remains neutrally buoyant with respect to upward displacements to just above the top of the subcloud layer. It utilizes the buoyance-sorting assumption of Raymond and Blyth (1986) which assumes that mixing in clouds is highly episodic, rather than continuous as in the entraining plume model. Convection occurs whenever the environment is unstable to a parcel in reversible adiabatic ascent from the surface.

The GFDL scheme is the parameterization developed by Donner (1993) as implemented by Donner et al. (2001). The convection is triggered when the large-scale CAPE generation rate is positive and the maximum convective inhibition cannot exceed 10 J Kg⁻¹. This scheme is unique in that it augments cloud base mass flux with convective-scale vertical velocities to include the microphysics of mesoscale anvils, leading to a consistent interaction between convection, microphysics and radiation.

The SAS scheme is a simplified version of Arakawa and Schubert (1974) scheme developed by Pan and Wu (1995). It determines the cloud base mass flux by relaxing the cloud work function to a critical value over a fixed timescale. To trigger the convection, this critical value must be exceeded and is assumed to be a function of the cloud base vertical motion. As such, the critical value is allowed to approach zero as the large-scale rising motion becomes strong. This scheme also defines the upper limit of convective inhibition using the lifting depth trigger in which the depth between the parcel originating level and level of free convection must be less than 150 hPa.

The NSAS scheme is based on the SAS scheme but with several modifications to trigger functions. For instance, the fixed value of lifting depth trigger (150 hPa) is changed to vary within the range of 120–180 hPa, in proportional to the cloud base grid-scale vertical velocity. This intends to produce more convection in large-scale convergence regions but less convection in subsidence areas (Han and Pan 2011).

The CSU scheme is the parameterization of Arakawa and Schubert (1974) but with a prognostic cumulus kinetic energy (CKE) closure (Pan and Randall 1998) and interactive liquid and ice cloud microphysics (Fowler and Randall 2002). This prognostic closure relaxes the quasi-equilibrium assumption by explicitly predicting the CKE for each cumulus subensemble. The cloud-base mass flux is determined by the CKE and a dimensional parameter (α) which is related to the adjustment time defined by original Quasi-equilibrium assumption. In current version of CSU scheme, a constant value of α (10⁸) is given for all cloud types.

The UW scheme is a bulk mass-flux based shallow cumulus parameterization of Bretherton and Park (2009) in which entrainment and detrainment is derived using a buoyancy-sorting algorithm. This scheme has a combined closure and trigger based on convective inhibition. It assumes that shallow convection can only form if the source air has sufficient vertical velocity to penetrate the weak inversion at the top of subcloud layer and reach its level of free convection. The cloud base mass flux is determined as to maintain dynamical equilibrium between the subcloud turbulent boundary layer and the base of cumulus cloud layer.

Appendix 2

2.1 Three microphysics schemes

The Goddard Cumulus Ensemble (GCE) model (Tao et al. 2003), the New Thompson (Thompson et al. 2008), and the Morrison et al. (2009) scheme are compared to examine the sensitivity of summer precipitation diurnal cycle predictions to large-scale microphysics. All three microphysics parameterizations are mixed-phased schemes, including six classes of water substances: water vapor, cloud water, rain, cloud ice, snow and graupel.

The GCE scheme is one-moment bulk microphysical schemes based on Lin et al. (1983) with several modifications. They include the prognostic equations for mixing ratios of cloud hydrometers, the options to choose either graupel (low density and high number concentration) or hail (high density and low number concentration), and the instantaneous adjustment for saturation computation to evaluate evaporation of rain and deposition or sublimation of snow/graupel/hail.

The New Thompson scheme is greatly improved compared to one-moment scheme by including a two-moment prognostic scheme for cloud ice. Differing from the GCE scheme, it assumes a generalized gamma distribution for all species instead of purely exponential distribution.

However, the Morrison scheme is a two-moment microphysical scheme. The prognostic variables are number concentrations and mixing ratios of six water species whose particle size distributions are represented as gamma distributions.