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In Numerical Forecasts of Mesoscale Convective Systems Meteorol. Atmos. Phys. 49, 93-106 (1992) Meteorology and Atmospheric Physics ~ Springer-Verlag 1992 Printed in Austria 551.515.4 The Pennsylvania State University, University Park, U.S.A. The Role of the Convective "Trigger Function" in Numerical Forecasts of Mesoscale Convective Systems J. S. Kain and J. M. Fritsch With 7 Figures Received November 18, 1991 Revised April 27, 1992 Summary sary to know the location and configuration of active convective cells that comprised mesoscale Three-dimensional numerical model simulations of a meso- convective systems. Consequently, convective scale convective system are performed to evaluate the sensitivity of the simulations to differences in the convective parameterization techniques typically relied on trigger function. The Penn State/NCAR mesoscale model empirically-based relationships between observed with the Kain-Fritsch convective parameterization scheme larger-scale processes and convective activity to is used as the modeling system for the study. All simulations predict when and where convection should occur. are performed on the June 10-11, 1985 squall line from the For example, some parameterizations were designed OK PRE-STORM field experiment. Individual simulations differ only in their specification of the trigger function within to initiate convection when a threshold value of the Kain-Fritsch scheme. Comparison of results from 12 hour mass or moisture convergence was exceeded at a simulations indicates that the position, timing, and intensity grid point where the atmosphere was conditionally of convective activity and mesoscale features vary substantially unstable (e.g., Kuo, 1974). Others operated under as a function of the trigger function formulation. The results the assumption of a state of "quasi-equilibrium" suggest that the convective trigger function is an integral between convective scale and larger scale proces- part of the overall convective parameterization problem, and that great care must be exercised is designing realistic trigger ses so that they initiated convection when the function formulations, especially as model resolutions ap- model atmosphere tended to deviate too far from proach the scale of individual convective clouds. some assumed or calculated equilibrium state (e.g., Arakawa and Schubert, 1974 [AS]). More recent models have much finer resolution 1. Introduction (e.g., AX ~ 25 km) and explicitly simulate many Convective parameterization is an important and of the mesoscale features that can play a major well known problem that has confronted .the role in determining when and where convection numerical modeling community for many years. will occur. Conceptually then, they are capable of Early convective parameterization theories and resolving much more accurately the locations of procedures were designed for synoptic and global convective activity. However, because parameters scale models in which the grid elements were so such as grid-scale convergence and destabilization large (e.g., AX ~ 500 kin) that they encompassed rate are governed by different dynamical con- entire mesoscale convective systems. For such straints on these scales, and because there is a coarse resolution, it was impossible and unneces- dearth of supporting observational evidence on 94 J.s. Kain and J. M. Fritsch these scales, it is not clear that larger scale relation- The complete set of criteria used to determine ships between resolvable scale dynamical processes when and where deep convection occurs in a and convective activity are sufficient predictors of numerical model is collectively termed the con- deep convection at these grid resolutions. For this vective "trigger function". The purpose of this reason, when parameterization closures based on paper is explore the sensitivity of numerical larger scale dynamical tendencies are used in simulations of the structure and evolution of a mesoscale models, additional criteria are often particular mesoscale convective system to the imposed in evaluating the potential for convective specific formulation of the convective trigger initiation. function. In the following section, the numerical These criteria are usually designed to reflect modeling system used in the sensitivity experi- some measure of the accessibility of potential ments is briefly described and the different trigger buoyant energy, or the probability of parcels function formulations are presented. Section 3 reaching their level of free convection (LFC) in a describes the results of the numerical experiments, conditionally unstable atmosphere. These ad- and section 4 discusses the implications of the ditional constraints are appropriate because the results in the general context of the cumulus param- onset of deep convection in a given vertical eterization problem. column is often strongly modulated by the strength of a capping stable layer beneath the LFC. For 2. Methodology example, the Anthes-Kuo scheme (Anthes, 1977), Different trigger function formulations are investi- as used in the Penn State/NCAR mesoscale model, gated by varying the convective initiation criteria allows convection only when the negative area for within a single convective parameterization scheme. pseudo-adiabatic ascent (on a thermodynamic dia- Sensitivities are demonstrated through fully gram) becomes less than the positive area; the AS prognostic numerical simulations of a mesoscale scheme, as used by Grell (1991), does not allow convective system. convection until the lifting required for parcels to reach their level of free convection becomes less 2.1 Numerical Modeling System than some specified depth (Grell, personal com- munication). The numerical model used for this study is the In some schemes designed specifically for meso- Pennsylvania State University/National Center scale models (i.e., Kreitzberg and Perkey, 1976; for Atmospheric Research (PSU/NCAR) meso- Fritsch and Chappell, 1980 [FC]; Frank and scale model (Anthes and Warner, 1978; Anthes Cohen, 1985; Kain and Fritsch, 1990 [KF]), the et al., 1987). The model configuration and physical ability of rising parcels to reach their LFC is parameterizations are very similar to the setup estimated using parcel theory and the buoyancy used by Zhang et al. (1989), including equation. In order to overcome a layer of negative - A two-way interactive nested grid (Zhang et al., buoyancy below the LFC, air parcels must typi- 1986) with coarse grid resolution of 75 km and cally have some positive vertical velocity and/or fine grid resolution of 25 kin; hygrothermal perturbation. The magnitude of this - Explicit prediction of precipitation processes, perturbation can be either assigned a constant including predictive equations for cloud water, value to be used at all grid points (as in Kreitzberg cloud ice, rain water, and snow (Zhang, 1989; and Perkey as well as Frank and Cohen) or related Dudhia, 1989); in some way to resolvable-scale dynamical ten- - Anthes and H. L. Kuo (Anthes, 1977; Kuo 1974) dencies (as in FC and KF). Although there is some parameterization of deep convection on the evidence that perturbation values can be related coarse grid only; to mesoscale forcing (e.g., Chen and Orville, 1980), - A high resolution Blackadar (1979) planetary a firm quantitative link between the two has not boundary layer parameterization (Zhang and yet been established. Indeed, even numerical in- Anthes, 1982; Zhang and Fritsch, 1986). vestigations using cloud scale (i.e. AX ~ 1-2 kin) models typically rely on artificial imposition of The present model physics package differs most random hygrothermal perturbations to initiate significantly from that of Zhang et al. (1989) in its deep convection. implicit parameterization of moist convection. The Convective "Trigger Function" in Numerical Forecasts of Mesoscale ConvectiveSystems 95 120 W 80 2.2.1 Original Fritsch-Chappell Trigger (FCT) The trigger function used in the original FC scheme is based on observational and numerical modeling , i evidence that the size and strength of boundary 40N layer hygrotherms that act as the "roots" of incipient convective clouds are a function of the strength of larger-scale boundary layer conver- gence (Bean et al., 1972, 1975; Chen and Orville, 1980). Specifically, FC related sub-grid scale 3o N .- 30 N temperature perturbations (6T) to the model resolvable scale vertical velocity (Wo) at the lifting ] condensation level (LCL) such that 6Tocwo/3 , where 6 T and Wo have units of K and m s - 1, res- 120 ii0 W lO0 W 90 W pectively. The current application is performed in a manner similar to FC. Beginning with the model Fig. 1. Coarse-grid domain for numerical simulations.First inset is the fine-grid domain, second inset indicates the area layer closest to the ground, the thermodynamic over which the results are presented properties of adjacent layers overhead are mixed in a mass-weighted fashion until the combined depth of the mixture, @m, is at least 60 hPa (the actual depth is a function of the depth of the indi- vidual layers). The mixture is "lifted" to its LCL FC convective parameterization scheme, used where its temperature and pressure are calculated. only on the higher resolution grid by Zhang et al. If the sum of the mixture's LCL temperature plus has been replaced by the KF scheme. Although 6T is greater than the grid-scale temperature at the KF scheme relies on the same basic closure that level, the buoyancy equation is used to estimate assumptions as FC, it utilizes more sophisticated whether this perturbation is strong enough to representations of cloud-environment interactions allow the parcel to reach its LFC. If not, a similar and imposes rigorous constraints on mass, moi- mixture of layers beginning with the second-lowest sture, and energy conservation, among other more layer is checked in the same way, and so on, until subtle differences. a buoyant mixture is found or each layer in the The model uses a terrain-following sigma lowest 300 hPa has been tested. vertical coordinate with 19 vertical levels on both 2.2.2 Anthes-Kuo Type Trigger (AKT) coarse and fine grids. The horizontal dimensions of the grids are 49 x 41 for the coarse resolution This trigger function is nearly identical to that and 61 x 49 for the fine resolution.
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