Parameterized Mesoscale Forcing Mechanisms for Initiating Numerically-Simulated Isolated Multicellular Convection

by

ADRIAN M. LOFTUS1

School of MeteorologyUniversity of Oklahoma

Norman, Oklahoma

DANIEL B. WEBERCenter for Analysis and Prediction of Storms

University of OklahomaNorman, Oklahoma

CHARLES A. DOSWELL IIICooperative Institute for Mesoscale Meteorological Studies

University of OklahomaNorman, Oklahoma

A manuscript submitted as an article to

Monthly Weather Review

December 2006

___________________Corresponding Author Address: Dr. Daniel B. Weber, Center for Analysis and Prediction of

Storms, University of Oklahoma, 120 David L. Boren Blvd., Suite 2500, Norman, OK 73019.

E-mail: dweber@ou.edu

1 Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, CO

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ABSTRACT

Two methods designed to parameterize mesoscale processes in a three-dimensional

numerical cloud model via boundary layer momentum and heat flux are presented and compared

to the commonly used technique of an initial perturbation placed within the model initial

condition. The flux techniques use a continuously reinforced convergent low-level wind or

thermal field to produce upward vertical motion on the order of 10s of cm s-1, by which deep

moist convection can be initiated. The sensitivity of the convective response to the strength and

size of the forcing is tested in numerical simulations using a conditionally unstable environment

with weak unidirectional shear.

Precipitation-free simulations using the momentum and heat flux techniques are

compared to comparable simulations performed using the traditional “initiating bubble” method.

The three methods tested produced an initial convective response, but only the momentum and

heat flux methods were able to produce sustained deep convection. Cell regeneration

frequencies varied from 8 to over 20 minutes, depending on the forcing magnitude, location with

respect to the surface, and geometric shape. The momentum flux forcing scheme produced the

most consistent series of convective cells during the 90 minute simulations.

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1 Introduction

Cloud modelers simulating moist deep convection must choose how they initiate

convection in a numerical model. Those wishing to study real data cases can attempt to

reproduce the atmospheric conditions, including active convection, via data assimilation such as

3D-VAR or other objective analysis methods (Xue et. al, 2003; Liu and Xue 2006) utilizing all

available observations including Doppler radar data. Studying convection in an idealized

framework requires the use of other methods to initiate convection. Several such methods have

been proposed for idealized numerical studies that include heat and momentum sources or cold

pools at the surface, and correspond to processes on horizontal scales from the mesoscale to the

synoptic scale. The interaction among various atmospheric scales with regard to initiating and

sustaining deep moist convection is an intriguing and complex issue. Environments generally

favorable for long-lived deep moist convection typically are provided in midlatitudes by

synoptic-scale systems, and some mechanism, such as thermals produced by surface heating or

ascent in association with surface boundaries, is usually required to lift moist air from near the

surface to its Level of Free Convection (hereafter, LFC). This ascent typically occurs on the

mesoscale (Weisman and Klemp 1984; Doswell 1987) and some numerical simulations of deep

moist convection have shown that variations in the structure and evolution of this ascent can lead

to significant differences in the resulting convection (Crook and Moncrieff 1988 [hereafter

CM88]; McPherson and Droegemeier 1991; Xin and Reuter 1996).

A common approach is to specify an initial buoyant perturbation (referred to here as an

“initiating bubble” or “IB”) in an otherwise horizontally homogeneous environment within a

numerical cloud model to generate the ascent needed to initiate deep moist convection (e.g.,

Steiner 1973; Schlesinger 1975; Klemp and Wilhelmson 1978; Weisman and Klemp 1982,

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among others). Although this approach is simple and provides useful results, it is unphysical and

requires additional forcing to sustain deep moist convection, usually via the development and

interaction of the cold pool with the environment. Other studies incorporated a cold pool as an

initial condition located at or near the surface that, combined with a favorable wind shear profile,

were able to produce sustained deep convection. A largely undocumented problem of which we

are aware with regard to IBs is that when a stable layer resulting in convective inhibition (CIN)

is present near the surface (a common feature of storm proximity soundings), cloud models using

the IB method often do not produce sustained deep convection. Instead, the initial storm

produced by the IB simply dissipates and no new simulated storms develop. Such results

generally remain undocumented because the simulation was considered to be unsuccessful.

This study will compare the IB method with two more physically realistic parameterized

approaches to providing ascent (Hill 1977; Tripoli and Cotton 1980; Schlesinger 1982; CM88;

Carpenter et al. 1998), that are fully non-linear three-dimensional representations of momentum

and heat flux. These can remain constant or vary in time, space, and intensity. The ultimate goal

of our project is to use the new initiating methods to study isolated multicellular convection,

specifically updraft and cell regeneration features including the updraft regeneration rate, within

a continuously forced mesoscale environment, without the complications associated with

precipitation physics and cold pool dynamics.

Section 2 provides an overview of the existing methods used to force deep moist

convection in numerical cloud models and introduces the new continuous mesoscale forcing

schemes. Section 3 describes the implementation of the forcing schemes, the numerical model,

select key parameters used in this study, and characterizes the impacts of the new schemes on the

model initial condition. Section 4 presents the simulations performed using the three CI

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mechanisms with idealized environmental conditions, as well as a discussion of the results of

these simulations. Section 5 presents the conclusions attained from this study and proposes some

future applications of the surface momentum flux and constant heat flux methods.

2 Convection Initiation Methods in Numerical Cloud Models

Cloud model simulations have been used extensively to understand the key processes that

govern the developments and lifecycles of various types of deep convection. Real convective

storms develop in association with diverse mesoscale processes capable of initiating deep moist

convection including: sea breeze fronts, outflow boundaries, drylines, surface heating variations,

flow over mountains, and fronts. Ascent associated with these features plays an important role in

the development and maintenance of many convective events (Doswell 1987). In addition,

continuous mesoscale forcing has been shown (Schlesinger 1982, Chen and Orville 1980) to

interact with the resulting convection, altering the time to initiation, the intensity, and the

duration of the convective storms. We present a brief review of the available forcing schemes

and present our proposed methods that will be used in a forthcoming numerical modeling study.

2.1 Thermally Induced Forcing

2.1.1 Initiating Bubble

Most numerical cloud model studies do not incorporate synoptic or mesoscale scale

forcing as convection initiation mechanisms, but rather rely on IB’s or cold pools to initiate deep

convection in the simulation. The IB method for convection initiation (hereafter, CI) involves

the insertion of a positively buoyant perturbation into the horizontally homogeneous base state

environment (Klemp and Wilhelmson 1978; Carpenter et al. 1998). The IB size is usually

several kilometers in horizontal extent, and has a vertical depth of order 1 km. The buoyancy

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perturbation typically has a Gaussian distribution within the IB volume and a peak magnitude on

the order of a few degrees Kelvin. Model sensitivity studies by Weisman and Klemp (1982,

1984) using the Klemp-Wilhelson model revealed that varying the magnitude of the temperature

perturbation and size of the IB appeared to affect the initial storm growth, but they concluded

that subsequent convective development was not very dependent on the IB conditions.

McPherson and Droegemeier (1991), on the other hand, found substantial differences in storm

structure and intensity for not only the initial storm but also for subsequent storms developing

well after the initial convection, resulting only from variations in the shape and magnitude of the

initial perturbation. In addition to the shape and magnitude, the height of the IB can have a

significant impact on the evolution of the resultant convection. This issue was addressed by

Brooks (1992), who reported that by increasing the height of the IB, and thereby placing a larger

portion of the IB volume above the LFC, an increase in the longevity of simulated deep moist

convection was observed. IB’s are simple and easy to implement into numerical models and,

given sufficient instability, can produce deep moist convection within 15 minutes of the

simulation start time. The instability must be sufficiently large to allow a cold pool to develop,

so precipitation physics plays in important role in the regeneration process. The release of a

large (order 10 km wide) buoyant bubble into a quiescent environment is physically unrealistic

from a mesoscale forcing perspective, since it is not clear that such IB’s actually exist, and the

release is a transient event not known to occur in nature. The problem with developing sustained

convection using the IB method when the initial sounding has low-level CIN has led to the use of

simulations with horizontally inhomogeneous environments (e.g., Muñoz and Wilhemson 1993),

where the IB is placed in an environment with no CIN and after sustained convection develops, it

then moves into an area that includes CIN.

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2.1.2 Constant Heat Flux

A more realistic approach to inducing thermal buoyancy into a numerical simulation is

achieved by specifying a constant heat source. This method is based on the idea that insolation-

produced diabatic heating within the planetary boundary layer (PBL) leads to thermals capable

of initiating deep moist convection. The diurnal variation of solar heating occurs on a time scale

much longer than the convective time scale, so it can be treated effectively as constant.

Two-dimensional simulations performed by Hill (1974, 1977) demonstrated the

occurrence of convection initiation within approximately two hours of the application of a

continuous surface heat flux. The regeneration of updrafts (i.e., multicellular convective cloud

structures) was produced in his simulations. The length of time required for deep moist

convection to develop in these experiments was related to the heat flux magnitude and the

stability of the initial ambient environment. In a three-dimensional study conducted by Balaji

and Clark (1988), the incorporation of a constant surface heat flux with random perturbations led

to the development of thermally driven circulations within the PBL, out of which multicellular

deep moist convection was initiated. The spatial and temporal scales on which the resulting

convection developed were determined to be independent of the heat flux forcing. Carpenter et

al. (1998) explored numerically simulated cumulus congestus clouds in three dimensions

initiated by way of a non-uniform surface heat flux. They superimposed a Gaussian surface heat

flux field in the center of the domain on a mean surface heat flux. Deep convective cloud

development, attained after roughly two hours of simulation time, produced oscillations in

maximum vertical velocity and cloud water content with a period of approximately 30 minutes.

Although this was not a simulation of deep cumulonimbus convection, the pulsating nature of the

cloud in response to the continuous forcing is suggestive of sustained multicellular storms.

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2.1.3 Constant Thermal (CT) Forcing

Our first proposed method that constitutes part of the parameterized multicell

thunderstorm study consists of a potential temperature perturbation θ′ prescribed by

−+

−+

−′=′222

2max cos

rad

c

rad

c

rad

c

zzz

yyy

xxx

θθ , (1)

where xc, yc, and zc, define the centroid of the bubble, xrad, yrad, and zrad are the radii of the bubble

in the x, y, and z directions, respectively, and maxθ ′ is the maximum magnitude of the perturbation.

The model θ′ field is initialized using Eq. (1) for both the IB and CT methods, but unlike the IB

method in which the buoyant bubble is prescribed only at the beginning of the simulation, the

constant thermal bubble approach continuously reinforces the bubble perturbation throughout the

simulation. This serves to provide a constant source of buoyancy to initiate deep convection,

analogous to that observed over a heat island on a sunny day. The time required to initiate

convection is considerably less than that required by the approach of Carpenter et. al (1998), an

important issue to consider when running hundreds of numerical simulations. Note that the CT

approach described above can also be characterized as a constant heat flux method, but pre-

specification of the flux is not possible, since the heat flux must be diagnosed during the

simulation from the potential temperature perturbation and resultant vertical velocity located

above the CT region.

2.2 Momentum Forcing

Forced mesoscale ascent pre-conditions the atmosphere for deep moist convection by

weakening any existing low-level CIN (Chen and Orville 1980) and deepening the moist layer

(see also Beebe 1958). As a result, saturation first occurs over an area comparable to the

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horizontal extent of the convergence field, owing to an increase in the vertical transport of

ambient moisture above the region of convergence (CM 88; Xin and Reuter 1996). Deep

convection then ensues under the appropriate conditions. The mesoscale and larger processes

can be approximated via several ways and are described and contrasted with our selection at the

end of this section.

2.2.1 Coupled Convergent and Divergent Forcing

Xin and Reuter (1996), in their investigation of the dependence of convective rainfall on

mesoscale convergence, used an axisymmetric two-dimensional numerical cloud model that

included a horizontally uniform convergence field at low levels along with a constant divergence

field aloft. The horizontally uniform ascent generated by this approach was successful in

initiating convection without the aid of an IB. The sensitivity of the model solution to the depth

and magnitude of the convergence region was also examined and, as in the studies previously

cited, the authors reported that increasing the forced ascent produced stronger deep moist

convection. Another study that demonstrated convective initiation purely by forced mesoscale

ascent associated with a near surface momentum flux was performed by Crook (1987). In this

two-dimensional numerical cloud simulation, the convective scale response to large-scale

convergent forcing by a surface cold front was investigated. The study showed that cold front-

induced circulation not only initiated storms, but affected the scale of resultant convection as

well. One of the difficulties with using a simulated cold front, as later described in CM88, was

that the ascent along the front exhibited some spatial and temporal variations as the front

interacted with the convection. Although Crook’s method is physically realistic, it is

problematic because ascent along a cold front is not an easily-controlled external variable.

Therefore, CM88 developed a method for initiating convection in their two-dimensional

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numerical cloud model via an imposed constant-amplitude, mesoscale internal gravity wave and

resultant momentum flux. The perturbation fields for this linear gravity wave were assimilated

to initialize a non-linear numerical cloud model. Numerical simulations using this method were

carried out using a conditionally unstable profile similar to that used by Rotunno et al. (1988).

Sustained multicellular convection developed above the region of maximum convergence, and

the convective cells were advected downstream by the background flow. Experiments were

conducted in which precipitation was first included and then excluded from the model, and the

effects of evaporative cooling were examined to determine whether or not subsequent convection

was caused as a result of forcing associated with the development of a cold pool. The authors

concluded that the dependence of the convective system on the development of a cold pool to

maintain the system was not of vital importance in the presence of large scale convergence,

although cold pool-associated forcing did act to strengthen the convection overall.

2.2.2 Hybrid Methods: Combined Thermal and Mechanical Forcing

Two-dimensional simulations incorporating constant ascent were carried out by Chang

and Orville (1973) and Chen and Orville (1980), who superimposed regions of time-invariant

low level convergence and upper level divergence onto ambient airflow. Through mass

conservation, the convergence-divergence coupling led to forced steady ascent in the model. In

addition, small random positive perturbations in temperature and water vapor mixing ratio were

added in order to initiate clouds, which later developed into deep convective clouds through

interaction with the model-generated upward vertical motion. Schlesinger (1982) performed

three-dimensional cloud simulations that included horizontally constant mesoscale vertical

motion via a method similar to that of Chen and Orville (1980) in a study of the dynamics of

severe storms in relation to mesoscale lift, boundary layer shear, and precipitation. In addition, a

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non-rotating weak buoyant updraft was used to initialize the updraft region. In these simulations,

the inclusion of parameterized large-scale ascent produced more vigorous and sustained deep

moist convection that developed over a shorter period of time than simulations without such.

Tripoli and Cotton (1980) parameterized mesoscale ascent by assuming an initial

horizontally homogeneous mean vertical velocity profile and adjusting the horizontal wind

components using a finite difference form of the anelastic mass continuity equation. Their

model underwent an initial dynamical adjustment period that allowed the pressure gradients to

adjust in order to maintain the altered vertical velocity profile, resulting in a stable, though not

necessarily steady, initial ascent. However, in order to initiate cloud development and

subsequent convection, a “bubble” of saturated air was also inserted into the domain. Varying

the magnitude of the surface convergence over the model domain had a marked affect on the

resulting simulated convection. They contended that, neglecting wind shear and precipitation

considerations, the intensity of cumulonimbus convection can be strongly correlated to the

supply of moist static energy to the storm via mesoscale surface convergence.

The conclusions of the previous investigations utilizing various momentum flux

approaches in convective cloud simulations are consistent with one another in that the inclusion

of mesoscale ascent typically enhances the strength and duration of convective activity. Also

evident in these studies is that persistent ascent acts to destabilize the initial environment and

thereby hastens the development of deep moist convection. However, the imposed momentum

forcing in these studies was not the primary CI mechanism, all of which used IB’s or a variant to

initiate convection.

2.2.3 Surface Based Convergence (SBC)

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For this study we have selected a simple low-level convergence wind field that is

prescribed via the velocity perturbation fields, through the use of the incompressible mass

continuity equation (Eqn 2), where mu′ and mv′ are the magnitudes of the zonal and meridional

mesoscale perturbation velocities, respectively, w′ is the magnitude of the forced (mesoscale)

vertical velocity and D is the divergence .

Dzw

yv

xu mm =

∂′∂

−=∂

′∂+

∂′∂

. (2)

The forcing layer velocity perturbations are derived by specifying the velocity potential,

denotedφm (x, y,z) , and assuming a Gaussian shape in the horizontal and a linear profile with

height. The velocity potential is:

−−

−−=

22

expexp)(),,(y

c

x

cm

yyxxzAfzyx

λλφ (3)

where xc and yc are the horizontal coordinates of the center of the ascent region, λx and λy are

”shape control parameters” of the divergence field in the x and y directions, respectively. A is a

constant that determines the maximum forcing magnitude, and )(zf is a linear function defined

as,

deepsfc

sfc

zzzz

zf−

−−= 1)( , (4)

where zsfc is the physical surface height and zdeep is the depth of the forcing region. The shape

control parameters are used to prescribe the horizontal width and ellipticity of the forcing region.

From (4), the magnitude of mφ is greatest at the surface, decreasing linearly to zero at the top of

the forcing region. Finally, the components of the horizontal perturbation flow are given in

terms of the velocity potential by

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∂φm

∂x= ′ u m = −

2A x − xc( )λx

2 e−

x−xc

λx

2

e−

y−yc

λy

2

f (z) , (5)

and

∂φm

∂y= ′ v m = −

2A y − yc( )λy

2 e−

x−xc

λx

2

e−

y−ycλy

2

f (z) . (6)

Divergence is simply the horizontal Laplacian of mφ , and the maximum magnitude

for the divergence maxD occurs at ),,( sfccc zyx , so the constant A is related to the

divergence maximum according to:

1

22max 11

2

−

+

−=

yx

DAλλ

. (7)

The vertical velocity, pressure, temperature, and moisture fields are allowed to adjust at all

points in the model domain. The perturbation u, v are specified according to (5) and (6) within

the region of convergence. There is no specification of a matching divergence field as described

with the previous methods. Therefore, the wind fields at points outside of the convergence

region are allowed to adjust with fewer restrictions. This allows for a model-developed

divergence field aloft that is a combination of the response of the atmosphere to the forced low-

level convergence and the anvil outflow associated with the convection. The SBC approach

represents a source of momentum and thus this method could be identified as a momentum flux

method, as proposed by CM88. The difference between the CM88 study and our method is we

cannot pre-specify the momentum flux magnitude since we do not have a fully compressible

analytical solution for the vertical velocity. As is the case for the CT method, we can diagnose

the vertical flux of horizontal momentum from the predicted solution.

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3 Model Description and Initialization

The three-dimensional non-hydrostatic numerical cloud model ARPI, developed at the

Center for Analysis and Prediction of Storms (CAPS), is used in the present study to perform the

simulations of deep moist convection in the presence of mesoscale forcing. This fully

compressible model is based largely on the Advanced Regional Prediction System (ARPS)

model developed by CAPS at the University of Oklahoma (see Xue et al. 2000) and was

originally designed to test the various types of boundary conditions available in ARPS. It has

since been optimized for speed of execution, to use it as a numerical cloud model for sensitivity

studies. The code is extensively documented (see Weber, 1997 for details) and the initialization

of the horizontally homogeneous base state variables follows that of the ARPS model. The

model includes a simple coordinate transformation, following Durran and Klemp (1983),

vertically-implicit and explicit vertical velocity and pressure solution techniques, and a linearized

upper radiation condition between vertical velocity and non-dimensional pressure. In addition,

the non-dimensional Exner function π is used in this model instead of pressure, unlike ARPS.

Moisture components are governed by the Kessler (1969) warm rain microphysics as

implemented by Durran and Klemp (1983), and sub-grid turbulence is parameterized using a 1.5

order closure scheme following the model of Sullivan et al. (1994).

3.1 IB and CT Forcing

For simulations utilizing an IB to initiate convection in the model, an initial distribution

of perturbation potential temperature is calculated according to Eq. (1) for points contained

within the ‘bubble region. The initial θ ′ values located outside of the perturbed region are set to

zero and allowed to adjust. The model equations are then integrated forward in time without

further external forcing of the perturbation fields. Simulations using the CT method to initiate

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vertical motion follow this same initialization procedure, except that the initial θ ′ values are

applied every large time step in the initial perturbed region, thereby providing continuous forcing

for ascent. All other model variables are allowed to adjust to the forcing.

3.2 Surface Based Convergence

Inclusion of the mesoscale perturbation velocities mu′ and mv′ at t = 0 imposes an

unbalanced state in the model and a response by the pressure, potential temperature and vertical

velocity as the time integration progresses. The total horizontal (u and v) components are a

combination of a non-divergent base state horizontal wind components ( u and v ) and the

computed values of mu′ and mv′ . The mu′ and mv′ are reset at the end of each small time step to

ensure continuous forcing within the forcing region. To limit the interaction of the imposed

perturbation convergent flow field on the lateral boundaries, the magnitudes of mu′ and mv′ at the

lateral boundaries are set to zero. The maximum values of λx and λy depend on the horizontal

domain size and are determined by setting 1sm0 −≈′≈′ mm vu in Eqs. (5 - 6) on the boundaries,

and then solving for xλ and yλ .

4 Mesoscale Forcing Comparison

Simulations were conducted to demonstrate differences between the IB, CT, and SBC

mesoscale forcing methods on the development of deep moist convection. The model domain

size used in this study was 48 x 48 x 20 km in the x, y, and z, directions, respectively. The grid

spacing is 400 by 200 m in the horizontal and vertical directions, respectively. Our justification

for 400 x 200 m grid spacing is not based on having obtained a “converged” solution, but rather

is a resolution that is capable of reproducing the general characteristics of moist deep convection,

such as the time of the onset of convection, overall cloud shape and development, and general

cell regeneration, all of which are well-represented in the 400 x 200 m grid spacing simulations.

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A formal resolution study is underway that will be reported on in a forthcoming paper that details

the impacts of model resolution on several cases involving the CT and SBC methods. The model

equations are integrated from t = 0 to 150 minutes to allow the deep moist convection to evolve

through several convective cycles, defined as distinct cloud regions with bubble-like appearance

moving through a less intense, in terms of vertical velocity and buoyancy, region of sustained

updraft.

The background environment (Fig. 1) is horizontally homogeneous and contains a weakly

stable layer at the top of a neutrally-stratified boundary layer, with weak unidirectional shear

from 850 to 300 hPa. The PBL is approximately 800 m deep and is not well-mixed with respect

to moisture. The level of free convection for a surface parcel is at a height of 710 m, just below

the stable layer, resulting in a maximum calculated value of convective available potential

energy (CAPE) of approximately 2900 J kg-1.

The computational mixing coefficients used for the simulations damp the smallest

wavelength magnitudes every time large time step to approximately 80% of their original value.

Model solutions for each experiment are examined via the distribution of cloud water mixing

ratios (qc) and time series depictions of the domain-wide maximum vertical velocities (wmax),

which were associated with the most intense convective updrafts within the main updraft region.

Visual inspection of cloud mixing ratio fields were found to be very useful in identifying discrete

cells within the updraft and matched well with other indicators of discrete cell development and

movement such as vorticity generation, buoyancy, and resultant deformation. Tests were done

using the SBC forcing to determine the length of time in which the solution is unaffected by the

lateral boundaries. Compared with runs using 4 and 16 times larger horizontal domains, the

solutions with the 48 x 48 km horizontal domain are almost identical for the first 75 minutes

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from the start of the simulation (30 minutes from the onset of convection). For the next 30

minutes, the simulations exhibit very similar solutions in terms of phase and magnitude of

maximum vertical velocity and liquid water content for the individual convective cells. After

105 minutes (60 minutes after onset of deep convection), the maximum domain-wide vertical

velocity contains noticeable differences between the tests, and we will not discuss the 48 x 48

km domain solutions after that time.

4.1 Initiating Bubble (IB) and Constant Thermal (CT) Experiments

The first results we present involve the IB and CT approaches to generating moist deep

convection. In these experiments, the vertical radius (zrad) is varied (Tables 1 and 2), and the

potential temperature perturbation is specified to be either ellipsoidal or half-ellipsoidal in shape.

The value of maxθ ′ is located at zc = 0 m (the surface) for the half-ellipsoid forcing, and at a height

zc = zrad for a full ellipsoid perturbation, where zc denotes the height of the perturbation center.

All cases are conducted using big time step of 5 seconds with the exception of IBHLF5, for

which the large time step was reduced to 2.5 seconds to accommodate a stronger vertical

velocity.

The effects of using half and whole ellipsoidal perturbation region to initiate deep moist

convection are examined using time series plots of wmax (Fig. 2). Greater peak values of wmax are

observed with the convection initiated via IB or CT methods using the full ellipsoid region than

that initiated using half ellipsoid shapes (Fig. 2). This result is similar to that observed by

Brooks (1992) in which bubbles located at greater heights developed into more intense

convection than bubbles located at lower heights, although he also varied the magnitude of

maxθ ′ of the IB's in conjunction with the vertical location of the bubble.

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For the CT case, the wmax values for the full ellipsoid regions (Figs. 2c, d) shows deep

moist convection is initiated in all 5 cases. Initial peak updraft speeds of approximately 25 m s-1

are observed for regions having vertical radii of 600 to 1000 m. Greater initial peak updraft

speeds of approximately 35 m s-1 and 40 m s-1 are evident as zrad of the source region increases to

1200 and 1400 m, respectively.

Figures 2a, b also show that the IB convection takes longer to develop when initiated

with a whole ellipsoid versus a half ellipsoid. For the IB whole bubble cases (Fig. 2a),

increasing the vertical radius of the perturbed region appears to increase the amount of time

required for initiation of deep moist convection. The vertical extent of the IB does not appear to

have much of an effect on the resulting values of wmax, as similar peak magnitudes are attained in

nearly all of the IB cases (Fig. 2a,b),, contrary to the results of the CT tests (Fig. 2c, d). Results

from McPherson and Droegemeier (1991) and Brooks (1992) suggest that, for equal magnitudes

of maxθ ′ , initial convective intensity may be much more sensitive to the width rather than the depth

of the IB. In all IB experiments, deep moist convection is not sustained beyond the initial

convective development as expected, owing to (1) the absence of precipitation and the

development of a cold pool in the simulations, and (2) the presence of a stable layer near the

surface. Concerning point #2, of course, without precipitation and the associated cold pool

forcing, no further development is possible in our simulation. But even if precipitation is turned

on in the simulation, the presence of CIN near the surface might still be enough to inhibit

convection after the initial storm created by the IB (as discussed in section 1). As shown in Figs.

2c and d, sustained deep moist convection due to CT forcing does not develop for forcing

regions with the smallest vertical diameters, HEATHLF1 and HEATHLF2, in which peak wmax

values of only about 3 m s-1 are observed. As the vertical extent of the perturbation increases,

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the time required for the initial deep moist convection to develop decreases. Unlike the results

for the IB cases, this result seems to be independent of the vertical location of maxθ ′ . In both the

full and half ellipsoid CT cases, regeneration is evident with a regeneration rate, defined as the

elapsed time between two subsequent peaks in wmax, of 8-10 minutes for the cases with the

higher placement of the center compared to the lower center placed tests. For the half ellipsoid

CT cases, the wmax response is weaker and the regeneration rates are longer (approximately 15

minutes than the full ellipsoid scenario). It is unclear why the CT cases with small forcing area

produced strong initial convective responses but failed to sustain strong convection. Mixing

associated with the initial convective circulations near the source region may have reduced the

potential instability.

4.2 SBC Experiments

The indicated ranges for the SBC forcing parameters shown in Table 3 should not be

considered definitive. Rather, they have been chosen to determine general trends in the

convective responses as the geometry and strength of the forcing is altered in this limited study.

4.2.1 Sensitivity to Divergence Magnitude

As the forcing magnitude ( maxD ) is increased (top panel Fig. 3), the time required for

deep moist convection to become established decreases and the maximum updraft velocity

increases. This result agrees qualitatively with Xin and Reuter (1996), who found that an earlier

onset of surface rainfall (and, therefore, an earlier onset of deep moist convection) was

associated with an increase in the magnitude of low-level convergence. Thus, the intensity of the

deep moist convection is related to the magnitude of Dmax for simulations in which the volume of

the forcing region remains constant. This sensitivity is also consistent with results found by

Tripoli and Cotton (1980). For the tests conducted in the current study, once deep moist

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convection develops, recurrent convective cells develop in all of the simulations presented in

Fig. 3, except for CONVMAG1. Also observed is a decrease in the period of convective updraft

regeneration as the forcing magnitude increases. As the forcing magnitude increases from |-5.0 x

10-4 s-1| to |-5.0 x 10-3 s-1|, the regeneration period decreases from approximately 20 minutes to 10

minutes. Animations of the cloud water mixing ratios for these cases visually confirm this

decrease in cell regeneration period with increasing values of Dmax.

4.2.2 Sensitivity to Forcing Layer Depth

Convective initiation is observed to occur at similar times (Fig. 3, middle panel) for cases

CONVDEEP3, CONVDEEP4, and CONVDEEP5, in which the forcing layer depths range from

1000 to 1400 m with a constant divergence magnitude |-1.0 x 10-3 s-1|. As the forcing layer depth

is decreased below 1000 m (CONVDEEP2 and CONVDEEP1), however, convective initiation is

delayed until later in the simulation, as found by Xin and Reuter (1996). However, the

numerical model and the forcing characteristics applied in the current work are quite different

from those of the aforementioned study. In the current study, the deeper forcing layers extend

above the PBL top, such that air parcels within the stable layer are incorporated into the forced

ascent region by the convergent flow. Incorporation of this stably-stratified air with that from

the PBL by the forced ascent decreases the local stability of the stable layer more rapidly than

would occur by turbulent mixing from below the stable layer alone. The regeneration rate

decreases slightly, during the 65 and 105 minute interval, as the forcing layer depth increases

(Fig. 3, middle panel).

4.2.3 Sensitivity to Horizontal Forcing Region Size

Deep moist convection is observed for all but the smallest horizontal forcing area case

(Fig. 3, bottom panel, CONVWIDE1), in which peak magnitudes of wmax attain values of only 5

20

20

m s-1 by 90 minutes. As the width of the forcing area increases, convective intensity increases

and the cell regeneration rate decreases. These results suggest that convection is sensitive to the

horizontal width of the convergence region for a specified forcing magnitude and layer depth.

This is consistent with results from CM88, who demonstrated that the air within the forcing

region experienced a larger total vertical displacement for wider convergence zones than for

narrower forcing regions, causing parcels to undergo longer periods of forced ascent and

eventually leading to more vigorous convective updrafts.

The time required for initiation to occur does not appear to be affected by the width of the

convergence region. We have already shown that timing of convection initiation is strongly

related to the magnitude of the forcing magnitude for both the CT and convergent forcing cases.

The maximum magnitude of the forced ascent is largely independent of λx and λy, because

although the horizontal area over which air is forced to rise varies, the maximum magnitude of

this forced ascent is equal in all cases. It seems logical, therefore, that convection initiation

occurs at similar times. Convective updrafts continue to redevelop throughout the simulations

(Fig. 3, bottom panel), but not as evidently as in the other sensitivity tests. In addition, wider

forcing regions result in a decrease in the average regeneration period of the convective updrafts.

4.3 Convection Initiation Method Intercomparison

Three experiments using similar initial spatial perturbation dimensions of 10 x 10 x 1.2

km in the horizontal and vertical directions, respectively, were conducted. The maximum

potential temperature perturbation ( maxθ ′ ) in the IB and CT cases is located at the surface, as is

the maximum magnitude in the SBC case. The perturbations vanish at a height of 1.2 km in each

case. Vertical cross sections of the qc fields (Fig. 4) depict the early and later stages of

convective development for the three cases. Results are presented at different times in the SBC

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21

case because the initial convection produced via a convergent flow field takes longer to develop.

Differences exist in the structure of the convective clouds produced by the different initiation

mechanisms, especially in the later phases of development (Figs. 4d, e, and f). The elapsed

simulation time between the early and later phases of convection for each case is 21 minutes.

However, the evolution and structure of the deep moist convection in each simulation is

remarkably dissimilar within this timeframe.

In the IB case (Fig. 4d), the deep moist convection is in its dissipating stage and only the

upper portion of the original cloud remains, as expected. The CT simulation (Fig. 4e) shows the

deep moist convection in a mature stage, consisting of several updrafts in close proximity to one

another such that they appear merged into a single updraft or plume. The distribution of qc in the

SBC simulation (Fig. 4f) is associated with three separate convective entities, suggesting that the

deep moist convection is occurring in several discrete stages or bubbles. In general, deep moist

convection generated in the HEATHLF4 case attains the greatest peak magnitude of wmax among

the three simulations at 29 m s-1 (Fig. 5), and the peak wmax value is slightly larger in

CONVDEEP3 than in IBHLF4 (26 m s-1 versus 23 m s-1). Therefore, the intensity and character

of the deep moist convection is evidently quite sensitive to the CI mechanism. The deep moist

convection in IBHLF4 only exhibits one convective cycle between approximately 15 and 50

minutes simulation time. The HEATHLF4 case only produced one significant convective cycle,

as measured by wmax , during this time as well. However, the period of the cycle in this CT

simulation appears to last longer than in the IB case, as shown by the slower rate of decrease in

the wmax magnitudes between 35 and 65 minutes (Fig. 5) and a continuous cloudy updraft evident

from just above the forcing to the anvil (Fig. 4e). Several separate peaks in wmax are displayed in

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22

CONVDEEP3 between 60 and 90 minutes, corresponding to the multiple discrete and separate

updrafts in Fig. 4f.

5 Preliminary Conclusions and Future Work

Non-precipitating deep moist convection was simulated to compare three CI mechanisms

using the three-dimensional numerical cloud model ARPI. The present work expands the studies

of CM88 to three dimensions, is not limited to linear forcing, and examines differences in the

convective response to CI mechanisms for a limited set of environmental condition and forcing

geometry and strength. For a domain of 48 x 48 x 20 km in extent, simulated convection without

precipitation processes was unaffected by the boundaries for the first 75 minutes and minimally

affected until 105 minutes. Cloud water content and vertical motion distributions produced by

the different initiation methods revealed significant differences in the structure and evolution of

the convection, especially during the later stages of development.

5.1 Initiation

All methods tested produced deep convective responses. The time required for deep

moist convection to begin decreased as the depth of the CT region or forced convergence region

increased, contrary to the IB results. Likewise, increasing the magnitude or depth of the

convergence or CT region reduced the CI time for the SBC experiments, while more time was

required for initiation using the IB method. For the SBC method, increasing the size of the

convergent region did not affect the timing of CI.

5.2 Convective Intensity

The maximum vertical velocities for the different methods had peak values of 20 m/s or

greater is cases that developed convection. For the IB cases, the maximum updraft intensities

were unaffected by the forcing depth or center location, while the continuous forcing methods

23

23

displayed sensitivity to forcing layer depth, forcing distance from the surface, and in the SBC

method cases, forcing magnitude. The CT mechanism generated more intense convection when

the forcing center was located at a greater height and updraft intensity increased as the vertical

extent of the heat source region increased. The CT method generated sustained deep moist

convection that was, on average, more intense than what was observed in the similar IB cases.

Increasing the magnitudes of the maximum convergence and forcing width also led to intensity

increases in all of the cases examined.

5.3 Regeneration

As expected, all IB simulations demonstrated a lack of redevelopment of convection

without precipitation-induced cold pools. The CT method generated deep moist convection that

exhibited convective regeneration periods ranging between 10-20 minutes. Cell regeneration

was found to be a function of forcing location and vertical extent with deeper heated regions

removed from the surface reducing the time between new cells, as diagnosed by maximum

updraft velocity and liquid cloud water. Forced convergent simulations displayed convective

updraft regeneration periods between 8 and 25 minutes. The regeneration frequency was more

sensitive to the magnitude and depth of the convergence region than to its width with increases

of each acting to enhance the cell regeneration frequency. For the cases evaluated in this study,

the SBC method produced convection that exhibited the most consistent cell regeneration and

sustained convection. The Brunt-Väisälä frequency is approximately 2 minutes in the

convectively unstable region, considerably less than the cell regeneration rates observed in our

tests.

The SBC method developed and implemented in this study appears to be adequate to

represent mesoscale forcing in a numerical cloud model to initiate deep moist convection in a

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24

physically realistic fashion, even in the presence of low-level CIN. The simulations performed

in this study demonstrate the ability of the continuous forcing techniques to initiate and maintain

non-precipitating deep moist convection. Sensitivity experiments will be performed to make

certain that the pertinent characteristics of the solutions are not resolution-dependent.

Droegemeier et al. (1994) reported sensitivity of the maximum updraft speeds and vertical

vorticity to resolution in simulations of supercells, but that overall, the storm behavior was

similar using coarse (~1 km) and fine (250 m) resolutions. Bryan et al. (2003) demonstrated

differences in the convective overturning of updrafts as grid resolution is increased in

simulations of linear convection and suggests that grid spacing on the order of 100 m may be

necessary to attain a converged solution.

Differences in environmental factors with respect to the resulting convection type are not

considered in the present study. These aspects will be addressed in a non-dimensional parameter

range study (NDPRS) as part of a larger investigation of isolated multicellular convection. The

NDPRS will examine a system of combined parameters that describe the convective atmosphere

in terms of the initiating mechanism as well as the ambient profiles of temperature, moisture, and

winds.

Acknowledgments. This research has been supported by the National Science Foundation under

grant contract #ATM-0350539 and the University Of Oklahoma School of Meteorology. We

also have received support from the Pittsburgh Supercomputing Center, the National Center for

Supercomputing Applications, and the Oklahoma Supercomputing Center for Education and

Research. We also thank Alan Shapiro, Evgeni Fedorovich, and Lance Leslie for several helpful

suggestions regarding this work.

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25

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FIGURE CAPTIONS

Figure 1: Skew-T plot illustrating the background environment vertical profiles of temperature,

moisture and winds used in the simulations.

Figure 2: Time series of domain-wide wmax (m s-1) values for (a) full ellipsoid and (b) half

ellipsoid perturbation IB experiments and (c) full ellipsoid and (d) half ellipsoid shaped CT

experiments.

Figure 3: Time series of wmax for SBC forcing simulations in which the (top) forcing magnitude

divergence, (middle) forcing layer depth, and (bottom) the horizontal width, λx = λy, of the

forcing region are varied.

Figure 4: Cloud water content (g kg-1) for an IB case (a,d), a CT case (b,e) and a SBC case (c,f).

Simulation times for the top two rows of XZ cross-sections are at t = 30 and 51 minutes for left

and right columns, respectively, and in the bottom row are at t = 60 and 81 minutes for left and

right columns, respectively. Contour intervals are 1.0 g kg-1, and tick marks are 400 m in the

horizontal and 200 m in the vertical.

Figure 5: Time series of wmax (m s-1) for simulations using three different CI methods shown in

Fig. 4. Dashed, solid, and dotted lines represent the CT, SBC, and IB cases, respectively.

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Figure 1: Skew-T plot showing the background environment vertical profiles of temperature, moisture and winds used in the simulations.

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31

(a) (b)

0

5

10

15

20

25

30

0 15 30 45 60 75 90 105 120 135 150Time (min)

wm

ax (m

s-1

)

IBFUL1IBFUL2IBFUL3IBFUL4IBFUL5

0

5

10

15

20

25

0 15 30 45 60 75 90 105 120 135 150Time (min)

wm

ax (m

s-1

)

IBHLF1

IBHLF2

IBHLF3

IBHLF4

IBHLF5

(c) (d)

0

10

20

30

40

50

0 15 30 45 60 75 90 105 120 135 150

Time (min)

wm

ax(m

s-1

)

HEATFUL1HEATFUL2HEATFUL3HEATFUL4HEATFUL5

0

10

20

30

40

50

0 15 30 45 60 75 90 105 120 135 150

Time (min)

wm

ax(m

s-1

)HEATHLF1

HEATHLF2

HEATHLF3

HEATHLF4

HEATHLF5

Figure 2: Time series of domain-wide wmax (m s-1) values for (a) full ellipsoid and (b) half ellipsoid perturbation IB experiments and (c) full ellipsoid and (d) half ellipsoid shaped CT experiments.

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0

10

20

30

40

50

0 15 30 45 60 75 90 105 120 135 150

Time (min)

wm

ax(m

s-1)

CONVMAG1: -1e-4CONVMAG2: -5e-4CONVMAG3: -7.5e-4CONTROL: -1e-3CONVMAG4: -2.5e-3CONVMAG5: -5e-3

0

5

10

15

20

25

30

35

0 15 30 45 60 75 90 105 120 135 150Time (min)

wm

ax(m

s-1)

CONVDEEP1: 600m

CONVDEEP2: 800m

CONTROL: 1000m

CONVDEEP3: 1200m

CONVDEEP4: 1400m

05

10

1520253035

404550

0 15 30 45 60 75 90 105 120 135 150

Time (min)

wm

ax(m

s-1)

CONVWIDE1: 2500mCONTROL: 5000mCONVWIDE2: 7500mCONVWIDE3: 10000m

Figure 3: Time series of wmax for SBC forcing simulations in which the (top) forcing magnitude (divergence) is varied, (middle) forcing layer depth is varied, and (bottom) the horizontal width, λx = λy, of the forcing region is varied.

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(a) (d)

(b) (e)

(c) (f)

Figure 4: Cloud water content (g kg-1) for an IB case (a,d), a CT case (b,e) and a SBC case (c,f). Simulation times for the top two rows of XZ cross-sections are at t = 30 and 51 minutes for left and right columns, respectively, and in the bottom row are at t = 60 and 81 minutes for left and right columns, respectively. Contour intervals are 1.0 g kg-1, and tick marks are 400 m in the horizontal and 200 m in the vertical.

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0

5

10

15

20

25

30

35

0 15 30 45 60 75 90 105 120 135 150

Time (min)

wm

ax (m

s-1

)

HEATHLF4

CONVDEEP3

IBHLF4

Figure 5: Time series of wmax (m s-1) for simulations using three different CI methods shown in Fig. 4. Dashed, solid, and dotted lines represent the CT, SBC, and IB cases, respectively.

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Table 1. IB experiment designations and associated forcing parameter settings.

Full

Ellipsoidzrad (m) zc (m) xrad , yrad (m)

Half

Ellipsoidzrad (m) zc (m) xrad , yrad (m)

IBFUL1 300 300 5000 IBHLF1 600 0 5000

IBFUL2 400 400 5000 IBHLF2 800 0 5000

IBFUL3 500 500 5000 IBHLF3 1000 0 5000

IBFUL4 600 600 5000 IBHLF4 1200 0 5000

IBFUL5 700 700 5000 IBHLF5 1400 0 5000

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36

Table 2. CT experiment designations and associated forcing parameter settings.

Full Ellipsoid

Heat Sourcezrad (m) zc (m)

xrad , yrad

(m)

Half Ellipsoid

Heat Sourcezrad (m) zc (m)

xrad , yrad

(m)

HEATFUL1 300 300 5000 HEATHLF1 600 0 5000

HEATFUL2 400 400 5000 HEATHLF2 800 0 5000

HEATFUL3 500 500 5000 HEATHLF3 1000 0 5000

HEATFUL4 600 600 5000 HEATHLF4 1200 0 5000

HEATFUL5 700 700 5000 HEATHLF5 1400 0 5000

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Table 3. SBC experiment designation and associated forcing parameter settings.

Run Name Dmax (s-1) zdeep (m) λx , λy (m)

CONTROL -1.0x10-3 1000 5000

CONVMAG1 -1.0x10-4 1000 5000

CONVMAG2 -5.0x10-4 1000 5000

CONVMAG3 -7.5x10-4 1000 5000

CONVMAG4 -2.5x10-3 1000 5000

CONVMAG5 -5.0x10-3 1000 5000

CONVDEEP1 -1.0x10-3 600 5000

CONVDEEP2 -1.0x10-3 800 5000

CONVDEEP3 -1.0x10-3 1200 5000

CONVDEEP4 -1.0x10-3 1400 5000

CONVWIDE1 -1.0x10-3 1000 2500

CONVWIDE2 -1.0x10-3 1000 7500

CONVWIDE3 -1.0x10-3 1000 10000