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  • View in gallery

    Sounding used to initialize the model.

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    Hovmoeller diagrams of total rainfall rate (shaded according to the color bar; mm h−1) from the 1-km control simulation.

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    Average vertical cross section of potential temperature change [shaded according to color bar; K (20 min)−1], buoyancy (contoured every 0.05 m s−2 from −0.3 to 0.15), and circulation vectors using U and 10W (m s−1).

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    Hovmoeller diagrams of the vertical velocity at 4-km altitude (contoured positive solid and negative dashed at ±0.03 and ±0.3 m s−1, respectively) and instantaneous diabatic heating rate (K h−1) shaded according to the color bar for the 1-km control simulation. Only every tenth grid point has been analyzed for comparison with the 10-km grid. The star at location (1.0, 0) marks the first occurrence of a MAUL.

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    Hovmoeller diagrams of convective rainfall rate (shaded according to the color bar; mm h−1) and grid-resolved rainfall (contoured at intervals of 0.5, 5, and 20 mm h−1): (a) KF1, (b) KF4, (c) LF1, and (d) LF4. The x axis is the position (km) relative to initiation of the CPS.

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    Hovmoeller diagrams of the vertical velocity at 4-km altitude (contoured positive solid and negative dashed at ±0.04 and ±0.15 m s−1, respectively) and diabatic heating (shaded according to the color bar; K h−1) for (a) KF1, (b) KF4, (c) LF1, and (d) LF4 scheme. The x axis is the position (km) relative to initiation of the CPS. The stars indicate the position of the first, deep MAUL in the 3–5-km layer.

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    Example sounding depicting a MAUL from the KF4 simulation. The MAUL is located from 850 to 600 hPa.

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    The 1-min CDT mean cross sections for (a) KF scheme and (b) LF scheme. Shown are the total temperature adjustment (shaded according to the color bar; K), along with the scaled (vertical velocity multiplied by 10) vector flow field (m s−1) in the plane of the model, vertical velocity (solid contours at 0.05, 0.5, and 1 m s−1 with 0.2 dashed), and cloud outline (darkened contour of 10−4 kg kg−1). The cloud outline is obtained from the sum of all microphysical species mixing ratios (cloud, rain, ice, snow, and graupel). The x axis is the position (km) relative to the gust front.

  • View in gallery

    The 1-min CDT mean cross sections for (a) KF scheme and (b) LF scheme. Shown are the rain (shaded from 0.1 to 3.1 by 1 g kg−1 s−1) and ice (contoured from 0.1 to 5.1 by 5 × 10−3 kg kg−1 s−1) hydrometeor tendencies, along with the negative buoyancy (dashed with values of −0.3, −0.2, −0.15, −0.1, −0.05, and −0.001 m s−2; buoyancy not contoured above 8.7 km) and cloud outline (darkened contour of 10−4 kg kg−1). The average precipitation rate (mm h−1) for the convective (solid) and grid-resolved (dashed) is inset at the top of the cross section. The x axis is the position (km) relative to the gust front.

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    Same as Fig. 8, but for the 4-min CDT.

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    Same as Fig. 9, but for the 4-min CDT.

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    Hovmoeller diagrams of hourly convective precipitation rate (shaded according to the color bar; mm h−1) and nonconvective precipitation rate (contoured at 0.5, 5, and 20 mm h−1) for experiments (a) KF4S, (b) KF4R, and (c) KF4L.The x axis is the position (km) relative to initiation of the CPS.

  • View in gallery

    Same as Fig. 12, but for experiments (a) LF4S, (b) LF4R, and (c) LF4L.

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    Specified temperature adjustment profiles A, B, C, used for strong adjustments found in the KF4 and LF4 simulations. The same adjustment profiles were used for both KF and LF simulations.

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    Hovmoeller diagrams of convective precipitation rate (shaded according to the color bar; mm h−1) and nonconvective precipitation rate (contoured at 0.5, 5, and 20 mm h−1) for experiments (a) KF4A, (b) KF4B, and (c) KF4C. The x axis is the position (km) relative to initiation of the CPS.

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    Same as Fig. 15, but for experiments (a) LF4A, (b) LF4B, and (c) LF4C.

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Idealized Mesoscale Convective System Structure and Propagation Using Convective Parameterization

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  • 1 Department of Agronomy, Iowa State University, Ames, Iowa
  • | 2 NOAA/Earth Systems Research Laboratory, Boulder, and Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado
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Abstract

The development and propagation of mesoscale convective systems (MCSs) was examined within the Weather Research and Forecasting (WRF) model using the Kain–Fritsch (KF) cumulus parameterization scheme and a modified version of this scheme. Mechanisms that led to propagation in the parameterized MCS are evaluated and compared between the versions of the KF scheme. Sensitivity to the convective time step is identified and explored for its role in scheme behavior. The sensitivity of parameterized convection propagation to microphysical feedback and to the shape and magnitude of the convective heating profile is also explored.

Each version of the KF scheme has a favored calling frequency that alters the scheme’s initiation frequency despite using the same convective trigger function. The authors propose that this behavior results in part from interaction with computational damping in WRF. A propagating convective system develops in simulations with both versions, but the typical flow structures are distorted (elevated ascending rear inflow as opposed to a descending rear inflow jet as is typically observed). The shape and magnitude of the heating profile is found to alter the propagation speed appreciably, even more so than the microphysical feedback. Microphysical feedback has a secondary role in producing realistic flow features via the resolvable-scale model microphysics. Deficiencies associated with the schemes are discussed and improvements are proposed.

Corresponding author address: James Correia Jr., Iowa State University, 3010 Agronomy Hall, Ames, IA 50010. Email: jimmyc@iastate.edu

Abstract

The development and propagation of mesoscale convective systems (MCSs) was examined within the Weather Research and Forecasting (WRF) model using the Kain–Fritsch (KF) cumulus parameterization scheme and a modified version of this scheme. Mechanisms that led to propagation in the parameterized MCS are evaluated and compared between the versions of the KF scheme. Sensitivity to the convective time step is identified and explored for its role in scheme behavior. The sensitivity of parameterized convection propagation to microphysical feedback and to the shape and magnitude of the convective heating profile is also explored.

Each version of the KF scheme has a favored calling frequency that alters the scheme’s initiation frequency despite using the same convective trigger function. The authors propose that this behavior results in part from interaction with computational damping in WRF. A propagating convective system develops in simulations with both versions, but the typical flow structures are distorted (elevated ascending rear inflow as opposed to a descending rear inflow jet as is typically observed). The shape and magnitude of the heating profile is found to alter the propagation speed appreciably, even more so than the microphysical feedback. Microphysical feedback has a secondary role in producing realistic flow features via the resolvable-scale model microphysics. Deficiencies associated with the schemes are discussed and improvements are proposed.

Corresponding author address: James Correia Jr., Iowa State University, 3010 Agronomy Hall, Ames, IA 50010. Email: jimmyc@iastate.edu

1. Introduction

Coarse grid spacing weather and climate simulations require the use of convective parameterization schemes (CPS) since these models cannot explicitly resolve cloud processes. Improving these models requires clarification of how and why convective parameterizations fail. Molinari and Dudek (1992) ask that more studies document why cumulus parameterization schemes (CPSs) succeed and fail. Cohen (2002) explored CPSs in an idealized sea-breeze experiment with the fifth-generation Pennsylvania State University–National Center for Atmospheric Research (PSU–NCAR) Mesoscale Model (MM5). Although only one sounding was used and the resolution was coarse (40-km grid spacing), he showed which schemes performed well and why certain schemes performed poorly. However, a description of why the Kain–Fritsch (KF; Kain and Fritsch 1990) scheme performed well was not undertaken, as that scheme was used as the metric to which all others were compared and contrasted. Zhang et al. (2003) performed regional climate simulations showing how improved representations of model physics improve the daily skill of these models. As global climate models approach the grid spacing of current mesoscale models (10–20-km grid length), the representation of mesoscale features using cumulus parameterization may become important to assessments of global climate change. Thus, improving existing, well-tested CPSs contributes both to short- and medium-range weather forecasting and to regional and global climate modeling.

How can the strengths and weaknesses of any CPS be detected? Liu et al. (2001) examined two-dimensional (2D) simulations with a fine grid length (1 km) compared to coarse grid length (15 km) simulations using the KF scheme. The scheme was modified to more accurately represent tropical convection (trigger function, cloud radius, and depth of the source layer were altered). They concluded that the KF CPS could simulate larger-scale aspects of convection but that shallow convection (cloud tops of 0.5–6 kilometers) could not be predicted, and that the scheme overpredicted overshooting cloud tops. Among the deficiencies found, the cloud mass flux was uniform with height and did not contain the variability found in the cloud-resolving model.

Davis et al. (2003) showed that propagating convection failed to occur in an idealized version of the Weather Research and Forecasting (WRF) model using the KF CPS with 12-km grid spacing. Furthermore, propagating convection was absent or weak in time-mean real-data forecasts with the WRF model based on precipitation climatologies compared to observations. They speculated that cold pools produced by CPSs were insufficiently cold to permit propagation. However, Anderson et al. (2007) have shown that a modified version of the KF scheme can produce propagating, nocturnal mesoscale convective systems (MCSs). Many authors (Zhang and Fritsch 1986, 1988; Zhang et al. 1994; Kain and Fritsch 1998) have shown that successful simulations of MCSs can be achieved with a CPS. Primarily, these simulations have used a grid spacing of 25 km as part of a nested configuration. It should also be pointed out that most of the simulated MCSs (Zhang and Fritsch 1986, 1988; Zhang et al. 1994; Zhang et al. 1989; Bélair and Mailhot 2001; Bélair and Zhang 1997; Stensrud and Fritsch 1994) were associated with a translating synoptic-scale 700–500-hPa trough.

What conditions may allow CPSs to produce propagating convection? Bukovsky et al. (2006) found particular convective adjustment profiles which yielded propagating convection using the Betts–Miller–Janjić (Janjić 1994) scheme. The scheme generated a deep layer of cooling that invoked a gravity wave response such that the scheme produced propagating convection. Indeed some observations of deep convection (of the MCS type) confirm that deep-layer cooling occurs within MCSs (Bryan 2005). Fovell (2002) and Fovell et al. (2006) also noted that a gravity wave response triggered by diabatic heating in a high-resolution squall line simulation was partially responsible for the maintenance and propagation of the squall line. Cram et al. (1992) noted that the propagation of a prefrontal squall line was related to convective scheme tendencies that generated a gravity wave. The parameterized heating profile also contained a deep layer of cooling. Such heating profiles have been identified primarily in trailing stratiform regions of MCSs (Houze 1989).

Anderson et al. (2007) used a modified version of the KF CPS to examine the 1993 floods over the midwestern United States. They found that the modified KF scheme produced a stronger grid-scale response to the parameterized convection and resulted in more coherent propagating precipitation systems as evidenced by Hovmoeller diagrams. Anderson (2004) showed that modified KF’s diurnal cycle of precipitation and total precipitation agreed better with observations than the unmodified KF. Anderson (2004) noted that pronounced pressure perturbations within surface outflow appeared stronger when embedded within higher grid-scale precipitation rate areas. He speculated that the stronger pressure perturbations were due to intense low-level cooling directly associated with grid-scale precipitation development cause by microphysical feedback from the CPS. This signal was not as strong in the unmodified KF simulations.

We hypothesize that the KF class of CPSs is capable of developing propagating convection due to parameterized downdrafts and outflow. This paper examines which scheme components affect the propagation speed and organization of parameterized convection. As Kain et al. (2003) showed, the magnitude of convective available potential energy (CAPE) determines the nature of the adjustment and thus rainfall. It is the rainfall that helps determine the downdraft parcel paths and the magnitude of the low-level cooling. Thus, examining the adjustment profiles from these simulations should help in understanding why and how convection propagates in the model.

Given the success of Liu et al. (2001) in using a 2D model, we explore the behavior of the CPSs in a set of idealized 2D squall line simulations. The 2D framework eliminates the possibility that propagation is caused by a synoptic-scale trough, which is appropriate because our goal is to document “self propagating” parameterized convection as opposed to convection propagating in step with an upper-level wave or front. The experiments are designed to explore how modifying the temperature and moisture adjustments affect the structure and propagation of the parameterized MCS. The paper is organized in the following manner: section 2 contains the model and experimental design, section 3 explores the control simulations while section 4 discusses the sensitivity simulations, and conclusions are discussed in section 5.

2. Model and experiment design

a. Numerical model

The WRF model (version 2.1.1) is a nonhydrostatic mesoscale model that uses Runge–Kutta third-order time integration, fifth-order horizontal advection, and third-order vertical advection on an Arakawa C grid (Skamarock et al. 2005) with a terrain-following mass-based vertical coordinate (in this paper there is no terrain). The domain size is 2000 km in the horizontal with a grid spacing of 10 km and 51 vertical levels (model top extends to 20 km). The model was run with a time step of 3 s and integrated for 12 h with output every 20 min. The microphysical scheme is the six-class scheme from Hong et al. (2004), while the planetary boundary layer scheme is from Hong et al. (2006) with a simplified surface-layer parameterization. The model uses diffusion in physical space, and a Rayleigh damping layer in the uppermost 5 km. As noted previously, to simplify the analysis we use a 2D idealized squall line case. The WRF model is unique in that even in the 2D setting, the dynamical core is cast in 3D but the V wind components and accelerations are zero.

The experiments use a range of convective time steps (i.e., time between calls to the subroutine, denoted CDT) with each convection scheme tested. Preliminary tests were performed with CDT varying from 1 to 9 min. Simulations were compared and found to exhibit similarities with a discontinuity at 4 min. The 5–9-min simulations were of little interest since they were very similar to the 4-min simulations. As a result, only the 1- and 4-min simulations were examined.

The advective time scale in the KF CPS is defined as
i1520-0493-136-7-2422-e1
where V500 is the wind speed (m s−1) at 500 hPa, Vlcl is the wind speed at the lifting condensation level (lcl) and dx is the grid spacing (m). The convective time scale tcon is obtained by applying a constraint for tadv with a range of 1800 to 3600 s:
i1520-0493-136-7-2422-e2
If the product of the mean wind [the denominator in Eq. (1)] and convective time scale exceeds the grid length, then tendencies are applied only for the amount of time the convection will be in the grid box.
Two variations of the KF CPS are used: the original KF [not the later so-called KFeta scheme of Kain (2004)] and the Anderson et al. (2007) version (hereafter LF). The LF scheme departs from the original KF in that updraft detrainment of heat, moisture, and condensate begins above the level of minimum saturated equivalent potential temperature, whereas the KF scheme begins detraining above the level of equilibrium temperature. This change effectively spreads the upper-level heating over a deeper layer. The schemes have the same trigger function and so satisfy, to some degree, the requirement proposed by Cohen (2002) that convection should trigger similarly in all model runs. The trigger function is based on a temporal average of grid-resolved vertical motion. This vertical velocity is interpolated to zlcl, the height of the source-layer mixture’s LCL, to obtain wlcl. A resistance is then calculated as a function of zlcl:
i1520-0493-136-7-2422-e3
where cr = 10−5 s−1. The resistance is subtracted from wlcl and the resulting value is used to calculate the temperature perturbation at the LCL:
i1520-0493-136-7-2422-e4
where α = 0.4 km−1/3 s1/3. Here DTlcl is added to the temperature of the lifted parcel at the LCL to determine the CAPE (undiluted updraft parcel path). The convective system was forced to initiate in a consistent manner by setting DTlcl to 0.5 K at one grid point at the initial time. The resulting scheme activation then began a cascade of effects which further triggered the scheme to activate.

b. Experiment design

Sensitivity experiments consisted of (i) altering the CPS microphysics to produce less convective precipitation, (ii) modifying the downdraft temperature effects in the lowest levels, (iii) changing the convective time step, and (iv) testing three idealized profiles to determine the sensitivity to the magnitude and shape of the heating. The experiments are described and abbreviated in Table 1.

To examine convective propagation, we isolate the major scheme components and how they alter the resulting propagating convection (Table 1). The two basic elements that, as we will show later, affect propagation are (i) temperature and moisture tendencies and (ii) microphysical tendencies. The temperature and moisture tendencies satisfy the schemes’ closure by removing 90% of the CAPE via a combination of updrafts, downdrafts and compensating subsidence. The closure process is sensitive to the environmental sounding as it determines the magnitude of CAPE. The microphysical tendencies respond to the magnitude of CAPE as well but depend on tunable parameters that control how much of the convective rainfall is partitioned into water species.

The KFmR simulations (where m corresponds to CDT in minutes) vary the partitioning between rainfall and grid-scale microphysical feedback in order to test what role the microphysical or temperature tendencies play in convective propagation. The partitioning is altered to increase microphysical tendencies thus reducing convective rainfall. The KFmS simulation simply sets all microphysical tendencies in the column to zero. The KFmL simulation sets low-level negative temperature tendencies to zero, thus preventing any low-level cooling or cold pool. The only process that could contribute to cold pool formation is explicitly resolved precipitation reaching the ground.

Simulations KFmA, KFmB, and KFmC use varying magnitudes of heating and cooling to examine how a deeper cold pool influences propagation. The KFmA simulations use a heating profile similar to that found by Bukovsky et al. (2006) where the low-level cooling depth extends to 4 km and the maximum heating is applied at 6 km. The magnitude of the maximum heating is set at 3 K while maximum cooling is set at −3 K. KFmB halves these heating and cooling rates. KFmC is similar to KFmA except the heating maximum is 1.5 K. KFmC tests the response to the upper-level heating magnitude. These simulations ignore the schemes’ closure criteria but because of the deeper low-level cooling, and commensurate reduction in CAPE, do not continually activate as in the control simulations.

3. Control simulations

The thermodynamic sounding (Fig. 1) has previously been used to study 2D squall lines (Rotunno et al. 1988; Pandya and Durran 1996; Bryan et al. 2006). The wind shear is confined to the lowest 2.5 km where the wind speed at the lowest model level is −10 m s−1 and decreases linearly to zero at 2.5 km. This sounding has been found to produce a trailing stratiform MCS in many models (Bryan et al. 2006), and thus we expect to see a similar response in our simulations.

The simulations presented here all produce propagating organized convection, which we refer to as MCSs. This is not in agreement with Davis et al. (2003) who found that parameterized convection was weak and failed to organize and propagate, using the same two-dimensional WRF model, albeit with 12-km grid spacing, a slightly different sounding [same shear, less CAPE, and more convective inhibition (CIN)], and a cold pool initiation method. The cold pool initiation method was used in this study and also yielded propagating convection. The goal is not to test convective initiation sensitivity to the sounding but rather to examine the mechanisms of propagating convection in these simulations.

a. The 1-km reference simulation

We used the same sounding (Fig. 1) to initialize the WRF model with 1-km grid spacing as a reference for the CPS simulations. The 1-km model used the 1.5-order turbulence kinetic energy scheme, no cumulus parameterization, and a Rayleigh damping scheme starting at 15 000 m with 51 vertical levels. Since the model physics are distinctly different between the 1- and 10-km versions, only a general comparison will be made. The simulated MCS began propagating 2 h into the simulation and the speed remained nearly constant over the following 10 h (Fig. 2).

A cross section was constructed by averaging three hours of output relative to the gust front position (defined as the location of the −1-K perturbation potential temperature at the lowest model level). The buoyancy, B,
i1520-0493-136-7-2422-e5
where θ′ is the perturbation potential temperature, θ is the potential temperature, and q represents the water vapor and hydrometeor species. Buoyancy is used to examine the properties of the cold pool in the simulations. Bulk characteristics of the simulated MCS included a descending rear inflow jet, front-to-rear flow or jump updraft, and an overturning updraft (Fig. 3). The cold pool depth, defined by the height where the buoyancy is zero, was 4 km and marked the transition between rear inflow, and front-to-rear flow above. Significant negative potential temperature changes occurred across the gust front and cold pool top with weak positive changes within deep updrafts along the gust front. Deep gravity wave motions were seen in animations of the vertical velocity and wave trapping occurred along the underside of the anvil in the region of minimal positive buoyancy ahead of the gust front. Convective cells developed within 50 km of the gust front, implying that “n = 2” gravity waves (vertical velocity maxima in the low levels and vertical velocity minima in the midlevels) were partly responsible for convective initiation close to the gust front. Note that the convective cells that develop ahead of the gust front do not produce significant precipitation amounts.

Coarsened Hovmoeller diagrams of vertical velocity at 3.9 km (Fig. 4) depict these gravity wave modes. The “n = 1” subsidence wave was generated because of the initiating method and traveled the fastest (31 m s−1), while the secondary n = 2 wave traveled much slower (15 m s−1). The other wave modes have speeds at or slightly above the propagation speed of the squall line and were mostly associated with the initiation of new convective cells. These latter waves were less coherent since they were directly modified by the development of the convective cells.

Relatively shallow moist absolutely unstable layers (MAULs; Bryan and Fritsch 2000) developed 20 min into the simulation across a multiple grid points (location of the star in Fig. 4 marks the first occurrence of a deep MAUL). The MAULs are not necessarily associated with large diabatic heating rates primarily because the diabatic heating was the instantaneous rate and some of the MAUL may have recently developed (i.e., diabatic heating rate was still small) or may have been in the process of stabilizing (i.e., instantaneous diabatic heating rate reduced as the column stabilized).

Some aspects of the 1-km simulation should be represented by the 10-km simulations. In particular the parameterized simulations should be able to replicate the front-to-rear flow branch, gravity wave response to heating (diabatic or parameterized tendencies), and the development of the leading anvil and outflow layer. Rear inflow is not expected, as this nonlinear characteristic is dependent upon the microphysics and convective heating in real MCSs (see Gallus and Johnson 1995).

b. Propagation

Carbone et al. (1990) describes transportive systems as those that move with the mean wind, unlike propagating systems, which move faster than the mean wind in a wavelike fashion. Given the idealized wind profile, the propagation speeds of the simulated MCSs (Table 2) are larger than the mean wind over a depth of 10 km. (The mean wind depends on the layer examined but was found to vary between −3 and +3 m s−1 with the 0–6- and 0–10-km layers having a mean wind of 1 m s−1 approximately 100–150 km ahead of the gust front). Thus, all simulations exhibit propagating convection.

Each scheme’s dependence on the propagation and evolution of the convective time step was examined using Hovmoeller diagrams for KFm and LFm (Fig. 5). The KF scheme is more sensitive to the convective time step than the LF scheme. The schemes may be affected by the convective time step through their dependence on the grid-scale vertical velocity. Such an influence probably arises because more time between convective calls allows computational diffusion to damp out short wavelength vertical velocity features, limiting the positive feedback between the cumulus tendencies and model dynamics.

A subjective analysis using Hovmoeller diagrams revealed that in both the LF and KF schemes, MCSs began propagating 3 h into the simulation. This coincided with the time when the number of active grid points reached 4 or greater (not shown). Since damping decreases as wavelength increases, it is speculated that this number of consecutively active grid points corresponds to a wavelength just large enough to survive the model damping and allow upscale growth.

c. Gravity waves

Most of the simulations had spurious convection ahead of the gust front. The persistent activation well in advance of the gust front was investigated by examining cross sections of vertical velocity. Hovmoeller diagrams of vertical velocity revealed the presence of gravity wave motions similar to those shown by Fovell (2002) and Fovell et al. (2006). The first gravity wave mode was a tropospheric deep subsidence wave (Fig. 6). The LF scheme generated stronger subsidence than KF, and each scheme’s response was stronger with a larger CDT. Overall, the time of gravity wave generation appeared to be linked to an increase in the number of active grid points (not shown). The model diabatic heating (Fig. 6) appeared to play a direct role in both MCS propagation and the generation of secondary wave modes (the so-called n = 2 mode described by Mapes 1993).

Examination of the vertical velocity and diabatic heating suggested that the wave activity emanated from areas where large diabatic heating–cooling occurred. Since the region of grid-scale diabatic heating was embedded within a region of active parameterized convection, the gravity waves remain obscured. Once the convective tendencies were applied, the vertical motion profile was determined mostly by the convective heating, so that the relatively small vertical motion due to the gravity waves was obscured. Power spectra analysis (not shown) indicated that the waves aliased into a number of scales and frequencies rendering an analysis of the characteristics of these waves fruitless. Although they are obscured, these waves have been inferred via the convective scheme activation ahead of the cold pool. However, the convective tendencies overwhelm these circulations.

In comparison to the 1-km control simulation, KF1 and LF1 are very similar in generating the primary n = 1 wave, whereas KF4 and LF4 are delayed in generating this wave. Neither the KF1 or KF4 simulations produced the second gravity wave marked by midlevel ascent. The LF1 and LF4 did produce this second gravity wave which caused the spurious convection in those simulations.

Kain and Fritsch (1998) showed that MAULs were present in their successful MCS simulations. Soundings at grid points with large diabatic heating rates contained relatively deep (100–500 hPa) MAULs (Fig. 7). The initial shallow (25–100 hPa) MAULs that formed did not correspond well to the gravity wave–induced vertical velocities in KF4 and LF4 (Table 3; the two simulations had a MAUL form by hour 2 and hour 1.3, respectively). KF1 did not produce MAULs of substantial depth until nearly 5 h into the simulation, while LF1 did produce shallow MAULs 1.33 h into the simulation. The shallow MAULs and gravity wave induced vertical velocities did not appear linked in the 1-min CDT simulations, but do appear linked in the 4-min CDT simulations.

The relatively deep MAULs (seen as stars in Fig. 6) appeared prior to and upstream of the gravity wave-induced vertical velocities in KF4, LF4, and to a lesser extent in LF1. The association between MAULs and the gravity waves is nearly absent in KF1. We speculate that the lack of large diabatic heating rates after MAUL onset suggests that though a MAUL formed, the instability was either quickly released or the instability was short lived. Thus the weaker gravity wave in KF1 compared to LF1 was probably due to the initiating convection rather than to physical process. Since MAULs were infrequent in KF1 (not shown), the n = 2 waves were shorter lived and weaker. In KF4 (LF4) the n = 1 gravity wave was delayed until 5 (3) hours into the simulation. The initial, shallow MAULs that formed in KF4–LF4 were not long lived and do not correspond to the suspected initiation region of the gravity waves. However, in both simulations, MAULs are associated with large diabatic heating rates at the same time that the number of activations of the CPS exceeds 3 grid points. Shortly thereafter, the n = 1 gravity wave propagates away. Only in LF4 does the n = 2 mode exert an influence on convective initiation, generating spurious convection well ahead of the gust front.

It was not possible to discern how the waves and the MAULs interacted with the convective tendencies, but the MAUL appeared to have a locally positive impact on the strength of the waves’ circulation as measured by the magnitude of the vertical velocity close to the MCS (5–7 grid points away from active convection). Over time, subsequently generated waves appear to move with the MCS as opposed to faster than the system. Since the waves coincide with propagation of the parameterized convection, we speculate that the MAULs are exerting an influence on propagation via the n = 2 wave. Tracing these waves back to the source is impossible given the obscuration of convectively generated gravity waves by the convective heating profile.

Exactly how or if the MAULs excite gravity waves in these simulations is unknown. One process that may contribute to the development of gravity waves may be perturbing the MAUL region via the convective tendencies, microphysical heating, or advection schemes similar to what Bryan (2005) found with a 1-km grid spacing model.

d. Spatial structure

What properties make the parameterized convection propagate? The spatial structures across convective time steps were compared to see what makes them different. The mean cross sections were constructed by averaging the vertical profiles relative to the gust front. Here the gust front is identified by the location of the −1 K potential temperature perturbation that coincides with active convection. From this reference point variables 200 km on either side of the gust front were extracted.

Pandya and Durran (1996) used 2D simulations at 1-km grid spacing with prescribed thermal forcing to simulate a squall line. They found that certain configurations (their Fig. 20) of “parameterized” heating and cooling favored a realistic, propagating squall line. When the configuration resembled a strictly vertical arrangement (as might be obtained from a CPS) the squall line contained an elevated rear inflow jet that was too strong, deep anvil outflow that was too low, and front-to-rear flow that was disrupted. The configuration that best resembled observations occurred when the low-level cooling lagged the deeper heating and both were tilted rearward. Thus horizontal gradients of thermal forcing were associated with a realistic depiction of a squall line. The following subsections will examine the gradients of heating in our simulations and draw a comparison to Pandya and Durran (1996). The 1-km simulation produced here is very similar to the vertical heating arrangement as seen in Pandya and Durran (1996).

Mean cross sections of the parameterized adjustment and the grid-scale response were examined to see if realistic flow features developed that could lead to propagation. Parker and Johnson (2004, hereafter PJ04) discuss the flow features that describe a realistic front-fed trailing stratiform (TS) MCS. The major flow branches include (i) a front-to-rear storm relative inflow that ascends and weakly overturns while some of this flow exits the convective region with some of its momentum; and (ii) a rear-to-front midlevel flow that is a response to a quasi-static pressure minimum driven by hydrometeor loading, melting, evaporation, and sublimation that then descends owing to the downward accelerations.

1) The 1-min CDT

The KF1 gust front (Fig. 8a) separated two areas of active convection. Convection directly ahead of the gust front or buoyancy gradient (Fig. 9a) was triggered by a gravity wave in advance of the simulated MCS (it appears weak in the figure because of the averaging performed to capture the mean structure of the simulation). The structure of the MCS resembled the conceptual model of PJ04, with a front-to-rear flow branch that overturned, but contains weak rear inflow. Composite mean vertical velocity was predominantly upward and maximized in the low levels near the leading edge of the gust front. Mean vertical velocity is weak in what may be described as the trailing stratiform region (note that the weak temperature adjustment toward the rear of the gust front resembles the shape of the stratiform rain region).

Parameterized heating in the MCS is represented by the total temperature adjustment computed by the scheme. Heating and cooling strengthen toward the gust front region. To the rear of the MCS heating weakens and is primarily elevated with only weak cooling below. Detrained cloud water tendencies are small (Fig. 9a) and nonconvective (i.e., grid resolved) rainfall is virtually nonexistent. The cloud field is less developed because the number of activated grid points is halved compared to the LF4 and KF4 simulations (Table 4). Convective rainfall rates are also small (<3 mm h−1) and the parameterized cooling yields a shallow cold pool. The large values of detrained ice are a product of the scheme design in that most hydrometeor mass is transported aloft and detrained in the anvil.

The LF1 simulation exhibited similar characteristics to KF1 but did not have the spurious convection immediately ahead of the gust front, though there was spurious convection further ahead of the gust front (Fig. 5). The front-to-rear flow branch overturned throughout the MCS and weak rear inflow was present (Fig. 8b). The mean vertical velocity at the gust front was stronger than in KF1 and resembled a jump updraft or front-to-rear inflow ascending the cold pool. The deeper cold pool was cooler, which allowed for a larger vertical velocity at and above the gust front. Note also that the upward vertical velocity extends across the stratiform rain region.

The parameterized heating in LF1 resembles the shape of a typical MCS vertical cross section on radar. Compared to KF1 there was more 2D structure to the heating gradients. The detrained cloud water was nearly an order of magnitude larger in LF1 despite a similar magnitude of detrained ice as KF1 (Fig. 9). The additional water led to significant nonconvective rainfall rates, which increased to the rear of the system. The jump in nonconvective rainfall rate was associated with downdrafts toward the rear of the system. The convective rainfall rate was largest at the gust front, and it tailed off to the rear of the MCS. This is consistent with what Zhang et al. (1994) proposed for parameterized MCSs, namely that there should be a transition between subgrid- and grid-resolved processes. When both processes are active (so-called double counting), the precipitation will be enhanced especially when hydrometeor tendencies contribute to the grid-resolved precipitation.

2) The 4-min CDT

The KF4 simulation had less spurious convection ahead of the gust front in comparison to KF1 (Fig. 10a versus Fig. 8a). The cold pool is deeper and cooler, and a jump updraft was present. Rear inflow was not visible in the composite. The mean vertical velocity maximized in the low levels at and above the gust front and remained upward in the stratiform rain region, albeit disorganized. The differences between KF4 and KF1 are much more pronounced than the differences between the KF4, LF1, and LF4 simulations. As stated previously, KF1 had substantially fewer active grid points and thus exhibited different behavior.

The structure of the parameterized heating in KF4 more closely resembles that in LF1 than in KF1 (Fig. 10a), but differences in the depth of the heating are apparent. Detrained cloud ice was substantially larger in KF4 than in LF1, but cloud water in KF4 was similar to LF1 (Fig. 11a). The microphysical tendencies were not linked vertically because of the small magnitudes of cloud water. This is reflected in the small and uniform nonconvective rainfall rates. We infer that both parameterized cooling and small nonconvective rainfall rates were responsible for the deeper and cooler cold pool in KF4 compared to LF1. The convective rainfall peaked at the gust front and decreased rearward.

The LF4 simulation was very similar to LF1 with the exception of spurious convection ahead of the MCS (Fig. 10b). The gravity wave activity had increased and was manifested as spurious activations both well ahead of and immediately near the gust front (Figs. 5, 10 and 11). Both LF simulations tended to generate strong gravity wave–induced upward motion, resulting in spurious activations through the vertical velocity dependence of the trigger function. The mean vertical velocity in LF4 was very similar to that in LF1 with the only substantive difference being the lack of strong downward motion well to the rear of the gust front. The main differences in microphysical tendencies were the reduction in cloud mixing ratio to the rear, the weaker convective rainfall rate maximum and the uniform nonconvective rainfall rates (Fig. 11).

3) Discussion

The analysis thus far has shown that both 4-min CDT simulations adequately invoke a grid-scale response that helped develop the surface-based cold pool and mimicked the heating gradients depicted by Pandya and Durran (1996). There is a benefit to picking an appropriate convective time step, as this influenced scheme activation and thus the microphysical effects generated by the schemes. Recall that little nonconvective rainfall was generated in the KF simulations. Only the LF scheme, which had substantially larger hydrometeor feedback, produced significant nonconvective rainfall. The KF simulations tended to have lower nonconvective rainfall rates and warmer cold pools.

In comparison to the 1-km simulation, the four control simulations have a deep, albeit weak, cold pool. KF4 and LF4 have shallower cold pools due to larger grid-resolved rainfall rates. This can be seen as the 0.001 m s−2 buoyancy contour descends across an increase in the averaged grid-resolved precipitation rates (Fig. 11). All simulations exhibit deeper parameterized heating, reaching between 8 and 9 km, whereas the diabatic heating in the 1-km simulation approaches 8 km. The largest difference is that the cold pool is confined to the lowest levels in the parameterized simulations, with the cold pool depth topping out at 2 km. This is in stark contrast to the 1-km simulation where the cold pool depth is roughly 4 km.

The mechanism for propagation appears to be a positive feedback between convective tendencies and grid-scale vertical velocity. Gravity waves were continually generated in the convective region and propagate ahead of the MCS. As the low-level positive vertical velocity produced by the gravity wave circulation moved ahead, it preconditioned the low-level environment for convective initiation. When the wave amplified away from the convective region, vertical velocity increased and scheme activation occurred. There were occasions, however, when the downward circulation branch of the gravity wave inhibited convective initiation near the gust front.

The strength of the gravity wave was linked to the convective time step and vertical location of maximum heating. This can be seen as delayed onset of negative vertical velocity when comparing KF1 to KF4 (time step dependence) and KF4 to LF4 (location of maximum heating) in Fig. 6. Earlier it was proposed that the convective time step dependence was present because model diffusion damps the vertical velocity of poorly resolved developing waves. Further, the KF scheme had a greater sensitivity to the convective time step than the LF scheme because detrainment occurred lower in the LF scheme, compensating subsidence was spread over a deeper layer, and the resulting warming was lower than KF. Since the detrainment in KF was higher and confined to fewer layers, the subsidence and thus heating was enhanced near the level of equilibrium temperature. The vertical location of maximum heating in LF was positioned below the anvil cloud layer in a location where the waves grew rapidly.

The time of convective propagation coincided with two major developments: MAUL production and an increase in the number of adjacent, convectively active grid points. Computational damping in the model is strongly wavelength dependent, so having more grid points active produces larger (i.e., longer wavelength) vertical velocity structures that can better survive the model damping. The LF scheme, in which convection also begins propagating when four or more grid points become active, does not have the same CDT dependence. The interaction between the MAUL, number of activated grid points and convective tendencies appears to play a role in the n = 2 gravity wave mode.

4. Sensitivity tests

Each scheme produced propagating convection, but how sensitive is the structure and propagation to details of the scheme design? The goal is to understand which part of the scheme design (vertical location of heating maximum, magnitude of detrained water substance, or depth of low-level cooling) produces or inhibits propagation. The LF scheme has a lower level of maximum heating and more detrained water substance, but the propagation speeds were comparable to those obtained with the KF scheme despite improved representation of cloud structures. To address the impact of the hydrometeor feedback on propagation, a set of three tests was performed whereby the following changes were imposed in both the KF and LF schemes:

  1. Suppress (KF4S; LF4S) or enhance (KF4R; LF4R) the hydrometeor feedback.
  2. Suppress the low-level cooling artificially (KF4L; LF4L).
  3. Artificially adjust the heating profile to alter the position and magnitude of the heating aloft, or reduce the strength of the low-level cooling (KF4A, B, C; LF4A, B, C).

a. Microphysical feedback

In the KF4S and LF4S simulations all hydrometeor feedbacks were set to zero. The propagation speeds of both KF4S and LF4S were slower than in KF1, LF1, and KF4, while that for LF4S increased relative to LF4. KF4S (Fig. 12a) was characterized by a very slow propagation speed, and grid-resolved rainfall was absent. LF4S (Fig. 13 a) initially generated grid-resolved rainfall, but rainfall faded as the MCS evolved. The spatial structure of KF4S revealed very little cloud and virtually no structure in the vertical (not shown). LF4S exhibited the same negative impact (not shown). For both KF4S and LF4S nonconvective rainfall was absent while the convective rainfall rate was markedly peaked and narrow. From these results, it is clear that the grid-scale rainfall was dependent upon the hydrometeor feedback.

In KF4S and LF4S the gravity wave activity was similar to KF4 and LF4, respectively. Despite similar gravity wave structures, the MCS in LF4S propagated faster than in LF4, but it was not clear why. Perhaps other gravity wave modes emerged, but this was difficult to discern because of scheme activation in the suspected wave region. The heating profile created a deep ascent profile which, if enough grid points are active, can obscure the gravity waves.

The amount of condensate lost (δrc) by the updraft in a given layer, δz, is specified in the Kain–Fritsch parameterization as
i1520-0493-136-7-2422-e6
where rco is the condensate at the bottom of the layer, c1 is the rate constant, and w is the updraft vertical velocity. The constant, c1, was changed from 0.01 s−1 to 0.005 s−1 in the KF4R and LF4R simulations, which directly increased the hydrometeor feedback at the expense of the convective precipitation. The Hovmoeller diagram for KF4R (Fig. 12b) depicts a much reduced convective rainfall rate and an increase in the number of grid points activated ahead of the MCS. The additional activations ahead of the MCS are attributed to gravity waves that have sufficient low-level upward vertical velocity to overcome the resistance in the trigger function [the resistance never exceeds 0.032 m s−1; see Eq. (3)]. These gravity waves are present in LF4R (Fig. 13b); however, the convective heating profile is such that the rainfall areas do not propagate (activated grid points are stationary and do not spread downstream with the wave). Eventually the parameterized MCS merges with these gravity wave–initiated areas of convection.

The propagation speeds are only slightly faster in both KF4R and LF4R than in their respective control runs (KF4 and LF4), indicating that enhanced feedback does not contribute significantly to propagation speed. The cloud fields expand in both simulations despite the slight increase in rain and snow feedback and the reduced convective precipitation rate. With the additional hydrometeor feedback the dynamic structure of the MCS has changed little.

Compared with the previous sensitivity simulations, the respective gravity wave structures for the LF simulations occurred earlier, while for the KF simulations the gravity waves amplified enough to activate the scheme. The gravity waves play a crucial role in these spurious activations. It appeared that large, grid-resolved, microphysical heating in combination with the parameterized heating was sufficient to trigger these waves. The increased hydrometeor feedbacks caused both the KF4R and LF4R simulations to produce strong gravity waves.

b. Elimination of low-level cooling

Low-level cooling was eliminated in the KF4L and LF4L simulations (i.e., all negative low-level temperature tendencies in the scheme were set to zero) after the first hour of simulation time. While not physically realistic, this experiment allows us to examine whether propagation is directly linked to the maintenance and intensity of parameterized low-level cooling. The same procedure was used by Spencer and Stensrud (1998) to simulate flash flood events.

The propagation rate for these simulations is largely unchanged (Table 2; Figs. 12c and 13c) compared to their respective control runs. The only way to strengthen the cold pool in KF4L and LF4L is through microphysical processes on resolved scales. This did not occur, and as a result the MCSs propagated similarly to KF4 and LF4. The gravity wave response was similar between KF4L and LF4L, again underscoring the importance of the heating profile in generating the waves. It is difficult to discern the wave response in conjunction with the gust front, but, given the similar propagation speeds to the control simulations, the absence of parameterized low-level cooling had little effect. It appears that the gravity waves had more of an impact than the parameterized gust front despite the fact that the sounding was not ideal for gravity wave trapping and subsequent propagation. Thus we proceed to explore further the role of the temperature adjustment based on the recent work of Bukovsky et al. (2006).

c. Specified adjustment

Three additional simulations were performed for each version of the scheme to test how the temperature adjustment affects the propagation speed. A specified adjustment profile was used with a cosine function containing a minimum at the surface and a maximum near 6 km, linearly decreasing to zero between 6 km and cloud top (Table 5; Fig. 14). Simulations KF4A–LF4A increase the cooling rate and deepen the layer that is cooled while simulations KF4B–LF4B and KF4C–LF4C have a reduced cooling rate compared to KF4 and LF4. Simulations KF4B–LF4B and KF4C–LF4C also have a reduced heating rate aloft. Since these simulations are artificial in that only the temperature profile was adjusted (and all other scheme behavior was left untouched), they provide a basis for understanding the previous sensitivity to the height of the level of maximum heating and to the strength and depth of the cold pool.

Trier et al. (1996) examined the integrated low-level buoyancy,
i1520-0493-136-7-2422-e7
where z was 2 km deep and C2 is the square of the theoretical cold pool propagation speed, in close proximity to the gust front to estimate the theoretical cold pool propagation speed. The propagation speeds of the specified adjustment profile simulations were within 10% of the theoretical cold pool propagation speed (not shown). KF4A, B, C and LF4A, B, C (Figs. 15 and 16) produced propagation that was steady and linked directly to the initial propagating gravity waves.

The first two simulations (A and B) show that the shape of the heating pattern played a critical role in parameterized MCS propagation. Setting the cold pool depth to near 3 km produced propagation for all tested magnitudes of cooling. The heating maximum location replicated a gravity wave (e.g., Fovell 2002) in the KF scheme and enhanced a similar wave in the LF scheme. The magnitude of the heating maximum (B and C) played a crucial role in the development and strength of the upper-level outflow as depicted by the u wind field just below and near the top of the parameterized heating (not shown).

In contrast to KF4A, the unmodified KF scheme typically produced strong upper-level outflow, maximum heating at higher levels and moderate but shallow low-level cooling. The LF scheme was similar but with a lower level of maximum heating. The KF and LF cloud models are unable to produce the heating profile Bukovsky et al. (2006) found necessary for propagation with their CPS. This would require redesigning the cloud model to reduce the updraft heating, enhance the downdraft cooling or both.

5. Conclusions

We have investigated propagation of parameterized convection in the KF class of CPSs through two-dimensional idealized squall line simulations with a grid length of 10 km. These simulations examined the sensitivity to the convective time step, the effects of hydrometeor feedback, and the importance of the vertical heating–cooling profile.

Major findings include the following:

  1. The schemes’ temperature and moisture adjustment gradients were vertically oriented in the mean similar to what Pandya and Durran (1996) found for underdeveloped squall lines (those that did not replicate observed flow in trailing stratiform leading line MCSs). The schemes produced a heating–cooling dipole that was vertically aligned rather than tilted rearward as in well-developed squall lines.
  2. Hydrometeor feedback was important to developing grid-resolved circulations. Unfortunately, the hydrometeor tendencies, no matter how large, were not enough to correct for the vertical heating–cooling orientation. Suppressed hydrometeor feedbacks made little difference to the parameterized MCS propagation speed.
  3. The LF heating profile, with its lower level of maximum heating compared to the unmodified KF, produced a gravity wave response that resembled that found by Fovell (2002). The unmodified KF produced an elevated heating maximum which did not produce as strong a gravity wave as the modified KF. It is suggested that the relatively weak low-level response was damped by the model’s computational diffusion, thereby introducing a convective time step dependence as found in our results.
  4. Simulations with an artificially altered heating profile revealed that the magnitude of upper-level heating was important for the development of upper-level outflow.
  5. The depth of low-level cooling was more important to propagation than the magnitude of the low-level cooling. The convective heating produced atop the cold pool in the control simulations acted to retard the cold pool propagation. When the cold pool was deeper, the propagation speed increased to the theoretical cold pool propagation speed (Rotunno et al. 1988).

The trigger function was identical in all of the simulations. Thus it is clear that the cloud model (tendency feedback) is as important to the initiation of convection as the trigger function. This feedback contributed to the production of gravity waves, which in turn triggered convection ahead of the gust front. The gust front amplified the vertical motion already present and helped produce propagating convection. The stronger the gravity wave response, the more spurious convection was present. The LF scheme produced a similar gravity wave response to the 1-km simulation but suffered from increasing spurious convection well ahead of the gust front. Increasing the trigger function resistance to temper the spurious convection and prevent too many activations from occurring may be necessary.

The results suggest that two processes are of fundamental importance for propagation: depth of low-level cooling and the location of the heating maximum. Although hydrometeor feedbacks appear to be important, their absence did not prevent the MCS from forming. However, many studies (Zhang and Fritsch 1988; Zhang et al. 1989; Stensrud and Fritsch 1994; Spencer and Stensrud 1998) have shown that a large grid-resolved response in a saturated environment has been necessary to the successful simulation of MCSs using this CPS. Pandya and Durran (1996) have shown that the rearward tilted heating–cooling dipole is very important for squall lines, but a tilted pattern could not be duplicated with this nonevolving cloud model.

Future work should include modifying the cloud model to realistically produce propagation rates comparable to observations. This should not be done arbitrarily, but in a manner that mimics the observed behavior of deep convection. This may be possible by stabilizing the column in successive layers (top down as opposed to bottom up), thus creating a heating profile that, in the time average sense, slopes rearward with height. To achieve realistic thermal structures for MCSs, the CPS must be able to vary the maximum heating–cooling in both the horizontal and vertical. This type of modification should affect how the scheme evolves at a specified grid point and may allow the scheme to exhibit better temporal characteristics which in turn should mimic observed MCSs. Achieving a heating profile with spatial dependence similar to that used by Pandya and Durran (1996) should allow better representation of MCSs.

The work presented here highlights fundamental deficiencies with the KF class of CPSs. The KF schemes (and most other convective parameterizations) lack a temporal component in which the source layer rises with time along with the maximum of heating as found by Pandya and Durran (1996). An evolutionary component, such as that proposed by Moncrieff and Liu (2006), may be appropriate for this CPS. Some of these issues may be related to the trigger function, in that the resistance may be too weak to prevent further activation after some degree of stabilization has occurred. Further exploration of the interaction between the trigger function and cloud model is warranted given the strong gravity wave response in the presence of MAULs. It remains to be seen if the 2D results presented here are applicable in 3D real-data simulations depicting propagating parameterized convection.

Acknowledgments

We wish to thank the anonymous reviewers for their insight and constructive comments, which greatly improved the paper. Daryl Herzman is gratefully acknowledged for computer support. This research was supported by Iowa Agriculture and Home Economics Experiment Station project 3806, under Hatch Act and State of Iowa funds. The authors wish to acknowledge use of the Ferret program for analysis and graphics in this paper. Ferret is a product of NOAA’s Pacific Marine Environmental Laboratory. (Additional information is available at http://ferret.pmel.noaa.gov/Ferret/.)

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Fig. 1.
Fig. 1.

Sounding used to initialize the model.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 2.
Fig. 2.

Hovmoeller diagrams of total rainfall rate (shaded according to the color bar; mm h−1) from the 1-km control simulation.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 3.
Fig. 3.

Average vertical cross section of potential temperature change [shaded according to color bar; K (20 min)−1], buoyancy (contoured every 0.05 m s−2 from −0.3 to 0.15), and circulation vectors using U and 10W (m s−1).

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 4.
Fig. 4.

Hovmoeller diagrams of the vertical velocity at 4-km altitude (contoured positive solid and negative dashed at ±0.03 and ±0.3 m s−1, respectively) and instantaneous diabatic heating rate (K h−1) shaded according to the color bar for the 1-km control simulation. Only every tenth grid point has been analyzed for comparison with the 10-km grid. The star at location (1.0, 0) marks the first occurrence of a MAUL.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 5.
Fig. 5.

Hovmoeller diagrams of convective rainfall rate (shaded according to the color bar; mm h−1) and grid-resolved rainfall (contoured at intervals of 0.5, 5, and 20 mm h−1): (a) KF1, (b) KF4, (c) LF1, and (d) LF4. The x axis is the position (km) relative to initiation of the CPS.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 6.
Fig. 6.

Hovmoeller diagrams of the vertical velocity at 4-km altitude (contoured positive solid and negative dashed at ±0.04 and ±0.15 m s−1, respectively) and diabatic heating (shaded according to the color bar; K h−1) for (a) KF1, (b) KF4, (c) LF1, and (d) LF4 scheme. The x axis is the position (km) relative to initiation of the CPS. The stars indicate the position of the first, deep MAUL in the 3–5-km layer.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 7.
Fig. 7.

Example sounding depicting a MAUL from the KF4 simulation. The MAUL is located from 850 to 600 hPa.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 8.
Fig. 8.

The 1-min CDT mean cross sections for (a) KF scheme and (b) LF scheme. Shown are the total temperature adjustment (shaded according to the color bar; K), along with the scaled (vertical velocity multiplied by 10) vector flow field (m s−1) in the plane of the model, vertical velocity (solid contours at 0.05, 0.5, and 1 m s−1 with 0.2 dashed), and cloud outline (darkened contour of 10−4 kg kg−1). The cloud outline is obtained from the sum of all microphysical species mixing ratios (cloud, rain, ice, snow, and graupel). The x axis is the position (km) relative to the gust front.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 9.
Fig. 9.

The 1-min CDT mean cross sections for (a) KF scheme and (b) LF scheme. Shown are the rain (shaded from 0.1 to 3.1 by 1 g kg−1 s−1) and ice (contoured from 0.1 to 5.1 by 5 × 10−3 kg kg−1 s−1) hydrometeor tendencies, along with the negative buoyancy (dashed with values of −0.3, −0.2, −0.15, −0.1, −0.05, and −0.001 m s−2; buoyancy not contoured above 8.7 km) and cloud outline (darkened contour of 10−4 kg kg−1). The average precipitation rate (mm h−1) for the convective (solid) and grid-resolved (dashed) is inset at the top of the cross section. The x axis is the position (km) relative to the gust front.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 10.
Fig. 10.

Same as Fig. 8, but for the 4-min CDT.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 11.
Fig. 11.

Same as Fig. 9, but for the 4-min CDT.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 12.
Fig. 12.

Hovmoeller diagrams of hourly convective precipitation rate (shaded according to the color bar; mm h−1) and nonconvective precipitation rate (contoured at 0.5, 5, and 20 mm h−1) for experiments (a) KF4S, (b) KF4R, and (c) KF4L.The x axis is the position (km) relative to initiation of the CPS.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 13.
Fig. 13.

Same as Fig. 12, but for experiments (a) LF4S, (b) LF4R, and (c) LF4L.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 14.
Fig. 14.

Specified temperature adjustment profiles A, B, C, used for strong adjustments found in the KF4 and LF4 simulations. The same adjustment profiles were used for both KF and LF simulations.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 15.
Fig. 15.

Hovmoeller diagrams of convective precipitation rate (shaded according to the color bar; mm h−1) and nonconvective precipitation rate (contoured at 0.5, 5, and 20 mm h−1) for experiments (a) KF4A, (b) KF4B, and (c) KF4C. The x axis is the position (km) relative to initiation of the CPS.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Fig. 16.
Fig. 16.

Same as Fig. 15, but for experiments (a) LF4A, (b) LF4B, and (c) LF4C.

Citation: Monthly Weather Review 136, 7; 10.1175/2007MWR2229.1

Table 1.

The naming conventions used along with a description of the KF and LF experiments. LF abbreviations/descriptions are similar and thus not repeated. The letter “m” is replaced by the convective time step (m = 1 for 1 min; m = 4 for 4 min).

Table 1.
Table 2.

Propagation speed (m s−1) of the parameterized MCS for each CPS used. “M” stands for missing due to the simulation lacking a continuous −1 K isotherm.

Table 2.
Table 3.

The position (km relative to the initiation point), time (h), and depth (hPa) of the shallow, initial MAULs in the control experiments.

Table 3.
Table 4.

The number of grid points in which the convective scheme is activated for each control simulation over the entire 12-h period.

Table 4.
Table 5.

Experiment design for the specified adjustment simulations. LF abbreviations are similar and thus not repeated. The letter “m” is replaced by the convective time step (m = 1 for 1 min; m = 4 for 4 min).

Table 5.
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