Final Report for:

EXPLICIT SIMULATION AND PARAMETERIZATION OF MESOSCALE CONVECTIVE SYSTEMS

U.S. Department of Energy Atmospheric Radiation Measurement Program

Grant #: DEFG03-94ER61749

William R. Cotton, Principal Investigator

Colorado State University Dept. of Atmospheric Science Fort Collins, CO 80523-1371

Period of Activity: November 1, 1993 - April 30, 1997

Date: August 12, 1997

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, make any warranty, express or implied, or assumes any legal iiabdi- ty or responsibility for the accuracy, completeness, or usefulness of any information, appa- ratus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessar- ily state or reflect those of the United States Government or any agency thereof.

Contents 1 Introduction 1

1.1 Parameterization of heating, moistening, and momentum transports by MCSs 2 1.2 Activation and de-activation of the MCS scheme . . . . . . . . . . . . . . . . 5 1.3 Testing and evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Adaptive-grid Single-column model for parameterization of middle and high clouds (cirrus) generated by active MCSs and cumulonimbi outflow 16

3 FuturePlans

4 References

5 Publications Supported

6 Theses supported

I 1

19

19

23

25

1 Introduction

This research has focused on the development of a parameterization scheme for mesoscale

convective systems (MCSs), to be used in numerical weather prediction models with grid

spacing too coarse to explicitly simulate such systems. This is an extension to cumulus

parameterization schemes, which have long been used to account for the unresolved effects

of convection in numerical models. Although MCSs generally require an extended sequence

of numerous deep convective cells in order to develop into their characteristic sizes and to

persist for their typical durations, their effects on the large-scale environment are significantly

different than that due to the collective effects of numerous ordinary deep convective cells.

These differences are largely due to a large stratiform cloud that develops fairly early in the

MCS life-cycle, where mesoscale circulations and dynamics interact with the environment in

ways that call for a distinct MCS parameterization. Comparing an MCS and a collection

of deep convection that ingests the same amount of boundary layer air and moisture over

an extended several-hour period, the MCS will generally generate more stratiform rainfall,

produce longer-lasting and optically thicker cirrus, and result in different vertical distributions

of large-scale tendencies due to latent heating and moistening, momentum transfers, and

radiational heating (Houze, 1977; Cotton et al. 1995; Gallus and Johnson, 1991; Alexander

and Cotton, 1997; Machado and Rossow 1993).

In spite of the distinct nature of MCSs relative to ordinary convective clouds, current

general circulation models (GCMs) do not contain convective parameterization schemes that

specifically account for contributions from MCSs. Most GCMs have upright, deep convective

parameterization schemes such as Arakawa and Schubert’s (1974) but do not consider con-

tributions by the more slantwise ascending and descending branches of the stratiform anvil

clouds of MCSs. Since our research (Cotton et al., 1995; Alexander and Cotton, 1997) in-

dicates that the slantwise branches can vertically transport a great deal of lower troposphere

moisture into the upper troposphere independent of the deep convective clouds, the absence

1

of such a parameterization can lead to a substantially drier and less radiatively-active upper

troposphere than occurs in reality.

1.1 Parameterization of heating, moistening, and momentum transports by MCSs

We have developed an MCS parameterization scheme that is suitable for use in GCMs. The

MCS parameterization scheme is designed such that it is compatible with the view that GCMs

are widely variable in terms of their horizontal resolution. The GCMs with finer resolution

may explicitly resolve some of the slow manifold or balanced responses to MCS heating and

momentum transports. The GCMs with coarser resolution, on the other hand, will require

parameterization of all the impacts of MCSs. The parameterization scheme must, therefore,

be modular in structure with components retained or removed, depending upon the GCM

resolution.

Our strategy was to perform fully three-dimensional cloud-resolving simulations of both

the deep convective, and more slantwise, stratiform components of MCSs in middle and

tropical latitudes. From analysis of these ‘synthetic’ or simulated data, a parameterization

scheme has been fabricated and calibrated. The reason we have selected observed cases rather

than idealized simulations is that it allows us to evaluate the credibility of those simulations

before we undertake the major effort of analyzing them and using the model-output data to

guide us in the development of the parameterization scheme.

The simulations are initialized from the objective analysis of observed large-scale data

on a relatively coarse grid (say, grid spacing of 50 km or more). Following initialization,

the model is integrated forward for 6 to 10 hours or more, and the results are compared

with observed data. If the results appear credible, then successively finer grids, each nested

within its larger host grid, are spawned until grid spacing of 1 to 2 km is obtained. For these

organized systems, this grid spacing is adequate to resolve explicitly both the deep convective

drafts and the mesoscale flow branches. It is the fine grid, which we call the cloud-resolving

grid, that is used to perform analysis for formulating the MCS parameterization scheme.

2

Before we could perform these simulations, a convective parameterization scheme had to

be devised which can be applied on coarse grids with a range of mesh sizes down to the host

grid of the cloud-resolving grid. The scheme reported by Weissbluth and Cotton (1993) was

developed using the methodology of performing cloud-resolving simulations of steady, intense

convective storms such as exist in most MCSs. This scheme, which we call a level 2 . 5 ~

scheme, predicts on vertical velocity variance, instead of turbulence kinetic energy as in a

standard Mellor and Yamada (1974) turbulence closure scheme. This scheme has performed

adequately in a tropical MCS simulation (Alexander and Cotton, 1994), as well as a mid-

latitude squall line (Hertenstein et al., 1994) and a mid-latitude mesoscale convective complex

(MCC) (Olsson and Cotton, 1997a,b; Alexander and Cotton, 1997). Originally we planned to

use it as the basis of the convective engine which would be interfaced with the mesoscale flow

branch parameterization scheme. However, subsequent testing of the scheme revealed that it

did poorly in representing the less intense, non-steady modes of convective clouds. It also

represents only one convective cell within a grid volume, which is an undesirable property

for use in GCMs. We therefore elected to interface our MCS parameterization scheme to the

Arakawa and Schubert (1974) scheme, which represents a full spectrum of cloud types, and

which was extended by Randall and Pan (1993) to include predicted vertically-integrated

cloud kinetic energy. Rafkin (1996) has further extended the Randall and Pan (1993) scheme

to allow use in a broad range of grid sizes from GCMs to fine-resolution mesoscale models.

The MCS scheme that we have devised is derived from cloud resolving simulations with

the Regional Atmospheric Modeling System (RAMS) of a tropical MCS observed during the

1987 Australian monsoon season (EMEXS), and one of a midlatitude MCC observed during

a 1985 field experiment in the central plains of the U.S. (PRESTORM 23-24 June 1985). In

each case, the finest grid of RAMS covers an area on the order of tens of thousands square

kilometers (- 18,000 km2 for EMEX9, - 17,300 km2 for PRESTORM). Large scale data are assimilated in the coarse grid of RAMS and then the model is run forward with two

grids for several hours using the Weissbluth and Cotton (1993) cumulus parameterization

scheme. Then each simulation is run for several hours using all grids and no convective

3

parameterization (over 6 hours for EMEXS, 3.5 hours for PRESTORM 23-24 June). In

both cases, the model simulates organized convection and an adjacent stratiform region

which closely resemble the observed system. The analysis of these data then focuses on

conditional sampling of the stratiform region of each system. The conditional sampling of the

fine grid data of each MCS simulation attempts to identify mesoscale updrafts and mesoscale

downdrafts within the stratiform region of each system. Once these mesoscale updraft and

downdrafts are identified, analyses of heat and moisture sources and vertical transports

(discussed further below) in these conditionally-sampled mesoscale updrafts and downdrafts

are used to determine the shapes of vertical profiles of various physical processes as well as

relationships between various components of an MCS’s water budget.

The thermodynamic part of the MCS parameterization that we have developed is ana-

logous to the formulation of Donner (1993)) with improvements of a more sophisticated

convective driver (the Arakawa-Schubert convective scheme with convective downdrafts) and

inclusion of the vertical distribution of various physical processes obtained through condi-

tional sampling of the two cloud-resolving MCS simulations. The Wu and Yanai (1994)

convective momentum parameterization has also been included as a separate component of

the parameterization scheme. The mesoscale parameterization is tied to a version of the

Arakawa-Schubert convective parameterization scheme which is modified to employ a pro-

gnostic closure, as described by Randall and Pan (1993). The parameterized cumulus con-

vection provides condensed water, ice, and water vapor to the anvil cloud, where the distinct

processes associated with mesoscale circulations are parameterized.

The mesoscale thermodynamic parameterization depends on knowing the vertically-integrated

values and the vertical distributions of the following quantities: (1) deposition and condens-

ation in mesoscale updrafts, (2) freezing in mesoscale updrafts, ( 3 ) sublimation in mesoscale

updrafts, (4) sublimation and evaporation in mesoscale downdrafts, ( 5 ) melting in meso-

scale downdrafts, and (6) mesoscale eddy fluxes of entropy and water vapor. The relative

magnitudes of these quantities are constrained by assumptions made about the relationships

4

between various quantities in an MCS’s water budget deduced from the cloud-resolving sim-

ulations.

The scheme is then tested by comparing the heating and drying tendencies produced by

feeding it mean soundings from the simulations with tendencies diagnosed from the condi-

tional sampling of the simulations. Further details of the scheme and its evaluation can be

found in Alexander (1995) and Alexander and .Cotton (1997).

1.2 Activation and de-activation of the MCS scheme

The most critical issue for implementing such an MCS parameterization scheme is when and

where to activate it and shut it down. Jiang et al. (1996) formulated a means of activating and

deactivating the MCS scheme, depending on the intensity and longevity of the parameterized

convection. They partitioned the total unresolved kinetic energy into contributions from

the deep convection (CKE) and the mesoscale circulation branches (MKE) . An example of diagnosed CKE and MKE evolution based on conditional sampling of the PRESTORM

explicit simulation is shown in Fig. 1. It shows rapid development of CKE due to strong

convection early in the simulation, followed by the lagged development of MKE existing

in the mesoscale flow branches. The MKE curve is an underestimate of the actual MKE

maximum and longevity, because the explicit domain covered only a portion of the active

MCS that was observed and modeled in the larger host grid.

Two prognostic equations are developed for vertically-integrated CKE and MKE, respect-

ively. The CKE equation is given by

C K E dt W K E

sac 1 -- - MBA - - - dCKE

where A is the cloud work function defined in Arakawa and Schubert, MB is cloud base

mass flux, TCKE is the CKE dissipation time, and Sac denotes the auto-conversion of CKE

to MKE. The MKE equation is given by

dMKE - M K E - SaC+Gg - GL - Gs - Gp - -

TMKE dt

5

PRE-STORM 243Uff85 - CKE, - - - MKE I _ _ _ . ,...........................-.......... .....*...............-.-~--....~-~.~~~ ..-.-. .

Figure 1: Evolution of CKE and MKE in an explicitly simulated mid-latitude MCS.

where

is thermal buoyancy production rate,

is loading buoyancy production rate,

is shear production rate,

6

---

is pressure gradient force, and TMKE is the dissipation time of MKE.

The CKE is primarily generated by convective updrafts and downdrafts, and once gen-

erated, CKE dissipates at a specified rate [O(lh)]. CKE is a prognostic quantity used in the

Randall and Pan (1993) scheme, and an extension of that scheme to a broad range of grid

spacings in the host model has recently been developed by Rafkin (1996). The MKE equation

has two fundamental sources. Some of the CKE generated by the deepest convective clouds

is converted to MKE. If sufficient convection is maintained to generate a certain threshold

in MKE, then the MCS scheme is activated. Once activated, the second source accounts

for further MKE generation due to mesoscale heating and water loading, pressure gradient

forces, and shear production within the mesoscale circulation branches of MCSs. The sink of

MKE is defined as a simple dissipation term with a dissipation that is slower than ordinary

deep convection [O(5h)].

The threshold value of MKE used to activate the MCS scheme is determined from the

cloud work function (similar to CAPE), as Lord (1982) pointed out that the cloud work

function is a generalized measure of moist convective instability. The cloud base mass flux

MB is related to CKE by C K E = a - M B ~ as first proposed by Arakawa and Xu (1990). The

parameter a depends on the cloud fractional area, the depth of the clouds, and the fraction

of the total kinetic energy that comes from the vertical component of the velocity, and is set

to a constant for now. Considering a steady state, the CKE equation becomes

d r n A = TCKE

(7)

Given a CKE value of 4000Jm-2, (Y = 5 x lo8 m4kg-l, and TCKE = 600s, the cloud

work function has a value of A = 2357 Jkg-l. Convection persisting for a few hours in

an environment with CAPE exceeding 2000 Jkg-' is likely to organize and develop into an

MCS. Therefore we have tested vaIues of this order, such that when MKE exceeds 3000 or

7

c

4000 Jm-2 the MCS heating, moistening, and momentum parameterization is activated. If

MKE recedes below the given threshold value, the MCS scheme will be turned off. Once the

MCS scheme is activated, additional MKE sources will further modify the MKE evolution.

An example of parameterized CKE and MKE evolution, based on a single-column model

application of the scheme for a TOGA COARE case is shown in Fig. 2. It shows that CKE

1

1

1

n cy

E : W

W Y ZE

Y 0

2

TOGA. COARE DEC26, 1992

. . . . . . . . . . .

2000 - 1000 -

0000-

9000 - . . . . .

CKE

. . '".;

. . .

. . . . . . . . . . . . . . . .

6000 . . . . . . : . . . . . . . . . . . . .

8000 - 7000 -

5000

4000

3000

2000

I000

0

\ . . . . . . ,; \ . . . . . . . . . . . . . *., :. . . . . . . . -7 . . . . I ' a:- . . . '* : -..*

. \ . . . . . \ :

-1000 ! ooz 032 062 09z 122 152 182 212 26DEC

&ADS: COLA/lGES 1997

Figure 2: Evolution of parameterized CKE and MKE in a single-column model, based on a tropical MCS case. The lower MKE curve is due to the autoconversion and dissipation terms in (2), while the curve MKEMOD includes the additional terms after activation of the MCS scheme.

reaches a maximum in 6 h and then decreases as environmental CAPE is consumed. The lower

MKE curve is due to the auto-conversion and dissipation terms in (2)- Its lagged development

and dissipation reflect the typical time-dependence of the mesoscale flow branches relative

8

to the generating convection in MCSs, as seen in our explicit simulations (Fig. 1) and as

generalized by Zipser (1982). Above the activation threshold of MKE, the additional source

terms in (2) begin producing self-reinforcing contributions to the MCS lifecycle. The upper

MKE curve includes additional sources due to thermal buoyancy and water loading buoyancy.

The two orders of magnitude smaller values of CKE and MKE in Fig. 2 than in Fig. 1 are

due to the assumption in the Arakawa-Schubert scheme that convection occupies a small

fractional area in a GCM grid column, whereas the simulated MCS in Fig. 1 essentially filled

the entire fine grid.

We are also considering normalizing the magnitudes of the MCS heating, moistening, and

momentum transport rates to the magnitude of MKE above the threshold values, to account

for the greater role by the stratiform region in larger MCSs. A major issue we have faced is

whether there is a universal threshold value of MKE for defining an MCS. Our basic research

on MCSs suggests that there probably is not and that the threshold value will at the very

least vary with latitude. This is because we associate the development of the mesoscale flow

branches of an MCS to the degree of balance of the system (Cotton et al., 1989; Hertenstein et

al., 1994; Olsson and Cotton, 1997a,b). The more balanced is the MCS, the more systematic

are the mesoscale ascending and descending flow branches and their associated heating and

moistening rates.

An important feature of this MCS parameterization is that it attempts to replicate effects

which are scale dependent on the size of the system, as reviewed in Cotton et al. (1995).

That is, given adequate large-scale forcing, large production rates of CKE lead to significant

production of MKE. This is consistent with the initial upscale evolution of strong convection

into an incipient organized MCS as described by McAnelly et al. (1997). In turn, MKE

drives the parameterized, self-reinforcing effects of the slantwise mesoscale flow branches.

For instance, the deep convergence and mesoscale ascent in mature MCSs produce a deeper

source layer of moisture and increases precipitation efficiency, compared to ordinary deep

convection (Cotton et al., 1995). In addition, the mesoscale ascent helps produce a larger

9

t

and longer-lasting cirrus canopy that is colder, more reflective and optically thicker than in

smaller, less organized deep convective systems (Machado and ROSSOW, 1993).

Better understanding of the behavior of CKE and MKE is apparently the key to guide us

to complete the MCS parameterization component. Data collected from the Southern Great

Plains ARM CART and from TOGA COARE were analyzed to identify a wide range of MCS

cases and ordinary deep convective cases to finalize the MCS scheme. We began our testing

with the data collected from TOGA COARE field experiment since it covers a concentrated

four month period and the data are more complete.

1.3 Testing and evaluation

A single-column model (SCM) was used to test the MCS trigger mechanism and the effect

of the MCS scheme on the large-scale temperature and moisture to the extent possible. The

single column model consists of the Randall and Pan (1993) cumulus parameterization scheme

coupled to our MCS parameterization scheme. The SCM was driven by observations of

soundings and run forward for a period of 12 to 48 hours. Local tendencies due to large-scale

vertical advection are also included, based on prescribed large-scale forcing that initially

equals the observed precursor conditions and then diminishes to zero over a several hour

period.

Cases were selected for testing based on their temporal minimum in IR temperature,

averaged over the Intensive Flux Array (IFA). Classes 1, 2 and 3 achieved average IR tem-

peratures colder than 230K, between 250K and 230K, and between 270K and 250K, respect-

ively; Fig. 3a shows the composite evolution of IFA-averaged IR temperature for the three

classes. Figure 3b,c shows a more detailed composite evolution for classes 1 and 3, respect-

ively, based on IRA-fractional areas colder than several IR thresholds. As can be seen, class

1 had larger, colder, and longer-lasting cloud tops, and consists of cases with strong MCSs.

Class 3 consisted of deep convection that was less organized, and class 2 was intermediate.

The composite Q1 and Q2 budgets of the three classes (Fig. 4), derived from observational

data, confirms the hierarchy of the classes in terms of their large-scale impacts. The strong

10

cc I

F

H

c 0 .-

-P U a L

LL

c 0 .- 4

U a L

LL

Composite Life-Cycles o f I F A - A v g T - I R 1 2101 I I I I I 1 I I I I I

250

270

290

1 . 0

0 . 8

0 . 6

0 . 4

0 . 2

0 . 0

1 . 0

0 . 8

0 . 6

0 . 4

0 . 2

0 . 0

0 24 48 72

T-IR A r e a < 2 7 3 , 2 5 0 , 2 3 0 , 2 1 0 , 1 9 0 K

0 24 48 Time ( h )

72

Figure 3: Composite IR lifecycles for convective systems in TOGA COARE. (a) IFA-averaged IR temperature for classes 1, 2 and 3. Each class consists of 9 cases, and the minimum for each case is aligned at hour 36 in the composite. (b) (c) Fractional area with IR temperatures colder than several thresholds, for classes 1 and 3, respectively.

11

.

36-h lifecycle of class 1 in terms of apparent heat source in shown in Fig. 4a, and Fig. 4b,c

shows the 36-h average of Q1 and Q2, respectively, for all three classes.

SCM testing of cases in these different classes revealed the importance of the MCS scheme

to producing parameterized heating and moistening profiles that were consistent with the Q 1

and Q2 budgets. Figure 5a shows the 24-h average heating in a class 1 case due to the

convective scheme, the MCS component and total heating. A significant MCS component

contributes to heating in the mid-upper troposphere that is comparable to the convective

maximum heating, and also contributes to significant low-mid tropospheric cooling. A class

2 case (Fig. 5b) shows a relatively minor contribution due to the MCS scheme, while in the

class 3 case (Fig. 5c) the MCS scheme never became activated. The MCS scheme contributed

to the total Q2 budget (not shown) in a similar manner according to class.

The parameterized surface precipitation from the SCM runs for different classes similarly

revealed that the class 1 cases were stronger, longer lasting and greater impacted by the

MCS scheme. Figure 6a shows the evolution of hourly rainfall rates for a class 1 case, and

shows a significant stratiform component due to the MCS scheme. A class 2 case (Fig. 6b)

shows that it produces less rainfall, with a smaller proportion due to the MCS scheme. Table

1 shows the 2 4 h total rainfall amounts due to the convective and MCS components of the

parameterization. The class 3 case, with little MCS organization, produces only about 25%

as much precipitation as the class 1 case, and no rainfall due to the MCS component. The

proportion of mesoscale rain in the class I case is comparable with observationally derived

estimates of stratiform rainfall in MCSs (Houze, 1977).

In summary, our testing showed that the MCS scheme we developed is able to distinguish

the strong MCS activities from non-MCSs. Our objective has been to achieve parameterized

CKE and MKE evolution, along with their associated effects on the large-scale environment,

which mirror the observed degree and effects of deep convection and mesoscale flow branches

across the entire scale spectrum of convective systems. Our initial development of the MCS

parameterization has shown promise in meeting this objective.

12

Class 1 41 (K/day 1 100

250

400

550

700

850

1000 y-

I I I I I I I

0 24 48 72

(b) Class123 36h A v g 41 (C) Class123 36h A v g 42 100

250

400

E - 550 a

700

850

1000 5

1

Figure 4: (a) Composite evolution of Q1 profile for class 1. (b) 36-h average Q1 profile, centered at composite hour 36, for classes 1, 2 and 3. (c) Same as (b) except for Q2.

13

100 - 200 E 300 - 400 E 500 2 600 g 700

800 900

P

I - 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 The apparent heat Q1 (Wday) (class 1) (b)

1 0 0 - 1 I 1 1 1 1 I I I t I I I I I - - - - -

- 200 E 300 7 - 400 :

500 : - 2 600 : -

700 1 800 1 900-1 I I I I I I I I I I I I I I I I I I I -

- 5 - 4 - 3 - 2 - 1 O 1 2 3 4 5 6 7 8 9

P

- - - - - - - -

The apparent heat Q1 (Wday) (class 2) (4 1 00 - 200

E 300 - 400 500

2 600 700

2 800 900

P

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5 6 7 8 9 The apparent heat Q1 (Wday) (class 3)

Figure 5: 24-h average Q1 heating in a SCM for a class 1, 2 and 3 case (a, b and c, re- spectively). Convective (solid), MCS component (short dashed), and total heating (long dashed).

14

h

_c \ E E v

a,

a L c rd

O I

-P

.-

Strat, Total Rainrates, Class 1 0 . 8 ~ ~ ~ ~ I ~ I I ~ I I ~ I I ~ I ~ ~ ~ ~ ~ I ~

0 . 4 0*6i 0 . 2

0 . 0 0 3

i 6

7 9 1 2 Time ( h l

-c \ E E v

a,

rd L c

rd CK

4

.-

15 18 21

Strat, Total Rainrates, Class 2 0 . 8 l i ~ i i ~ i l ~ i l ~ l l ~ l l ~ i i ~ i l

1

0 3 6 9 12 I 5 Time ( h )

18 21 24

Figure 6: Hourly precipitation rates for a class 1 case (a) and a class 2 case (b) . Total heights of bars give total rain rate, while shorter bold bars give stratiform contribution due to the MCS scheme.

15

i

*- I

Table 1: SUMMARY of CUMULUS and MCS PRECIPITATION

CASES CUMULUS PRECIP MESOSCALE PRECIP

(10l2 kg) (10l2 kg)

1 class 1 I 2.38 (71.3%) 1 0.96 (28.7%) I class 2 I 1.48 (80.4%) 1 0.36 (19.6%)

class 3 0.83 (100%) 0.00 (00%)

2 Adaptive-grid Single-column model for parameterization of middle and high clouds (cirrus) generated by active MCSs and cumulonimbi outflow

Among the feedbacks of MCS to the general circulation is the increase of upper level moisture

that remains after the MCS has decayed or propagated out of the region. Therefore, to

parameterize the complete impact of MCS on the larger scales, the GCM must adequately

model upper level clouds. To obtain the vertical and temporal resolution necessary for cloud-

scale physics, an adaptive-grid single-column cloud model has been created to nest in time

and space in a localized area with limited frequency in a large-scale model. Nebuda (1996)

examined the feasibility of the approach by using the existing physics in RAMS at that time.

The three basic components of the nested 1D cloud model are microphysics, turbulence, and

radiation.

The structure of the nested cloud model includes the three components of microphysics,

radiation, and turbulence to capture the essential features of an upper-level cloud. The

microphysical component (Walk0 et al., 1995) of the nested model requires the host model

to provide the mass and concentration of liquid and ice water. The nested model uses

this information to predict the seven water categories of total water, water vapor, rain,

16

small ice (pristine ice), large ice (snow), and aggregates. Cloud water is computed as a

residual of the other water categories. By increasing the two hydrometeor species in the host

model to five in the nested model, a bimodal ice spectra of cloud ice is possible along with

improvements in the modeling of riming, collection, and variable fall speeds. A turbulence

model (Weissbluth and Cotton, 1993) which predicts the vertical velocity variance, (w’w’),

is applied to model the mixing created by the radiative destabilization. The broadband

radiation model (Chen and Cotton, 1983), which distinguishes liquid water from ice, can

create the maximum heating/cooling rates at the correct location due to the increased vertical

resolution of the nested model. Using these components, the adaptive, nested cloud model

provides microphysical information which can be used in the host radiation scheme as well

as improve budgets of heat and water.

-

To determine the resolution necessary to model upper-level clouds, RAMS was used in

a 1D format to simulate several cirrus clouds at various altitudes with a range of vertical

resolution and timesteps. Simulations were also computed for both five and two hydro-

meteor species to determine the impact of microphysical complexity on the results. These

sensitivity tests revealed that the results were dependent on both the timestep and vertical

resolution. When the timestep was much longer than 180 seconds, the microphysical scheme

would over-predict the amount of nucleated ice in one timestep which would significantly

dictate the following behavior of the cloud ice. A large timestep such as those found typically

in large-scale models also failed to correctly simulate melting, evaporation, sublimation, and

sedimentation. Poor vertical resolution would not capture the smaller details of the cloud

species’ vertical profiles. A vertical spacing on the order of 100 m to 200 m was necessary to

capture the physical processes of collection and sedimentation. When the number of cloud

species is limited to the general categories of liquid and ice, the deepening and precipitation

trails created by the sedimentation of larger ice does not occur. As a result, the cloud will

exist in a shallower layer and have higher ice water mixing ratios. This fact will alter the

computed radiative heating rates changing the cloud feedback to the general circulation. The

sensitivity studies indicate that a nested cloud parameterization is necessary to obtain the

17

resolution and accuracy of the upper-level cloud feedback while maintaining the affordability

of the large-scale model.

As part of his M.S. thesis Chris Golaz has developed a stand-alone version of an adaptive-

grid single column model. The model uses different types of turbulence closure schemes.

They include two 1.5 order and one 2.5 order schemes. Lower order schemes include an

e - I closure based on Bechtold et al. (1992) and an e - E closure based on Langland and Liou (1996) and Dyunkerke and Driedonks (1987). Both use a prognostic equation for the

turbulent kinetic energy coupled either with a mixing length diagnosis scheme for e - I or an

additional prognostic equation for the turbulence kinetic energy dissipation rate 6 for e - e. The higher order closure is based on Galperin et al. (1988).

Several options are available for the computation of cloud water and fractional cloudiness.

The simplest is an all-or-nothing cloudiness scheme which diagnoses cloud water as a residual

between the total mixing ratio and the saturation mixing ratio. Alternatively, fractional

cloudiness can also be computed using an empirical scheme developed by Ek and Mahrt

(1991). Finally, the subgrid-scale condensation scheme from Sommeria and Deardorff (1977)

and Mellor (1977) has also been implemented. This scheme has the ability to simultaneously

predict fractional cloudiness and cloud water mixing ratio.

The single column model has been fully coupled with the microphysical parameterization

from RAMS (Walko et ai., 1995). This parameterization can include up to eight different

categories of water; it is a bulk microphysics scheme that predicts one moment, mixing ratio,

for each water category and uses a generalized gamma distribution as basis function for

the number concentration distribution. A two-stream radiation module (Harrington, 1997),

which interacts with the hydrometeor size distributions in the Walko et al. scheme has also

been implemented in the single-column model.

This version of the adaptive grid single-column model is transportable to any host model

including GCMs with appropriate interfacial codes.

18

3 Future Plans

If continuation funding is obtained, our plans are to:

0 Further refine and test the MCS initialization scheme using DOE ARM Great Plains

and Tropical Western Pacific CART site data.

0 Further develop and test the momentum parameterization scheme.

0 Test the SCM using ARM CART site data.

0 Implement the MCS parameterization in coarse grid spacing versions of RAMS and test

the scheme performance in a number of situations, including comparison with several

cloud-resolving simulations.

4 References

Alexander, G. David, 1995: The use of simulations of mesoscale convective systems to build

a convective parameterization scheme. Atmos. Sci. Paper #592, Colorado State Uni-

versity, Dept. of Atmospheric Science, Fort Collins, CO 232 pp.

Alexander, G. David, and W.R. Cotton, 1994: Explicit simulation of a tropical mesoscale

convective system. Preprints, Tenth Conference on Numerical Weather Prediction,

17-22 July, Portland, Oregon.

Alexander, G. David, and William R. Cotton, 1997: The use of cloud-resolving simulations

of mesoscale convective systems to build a convective parameterization scheme. Con-

ditionally accepted for publication- in the J. Atmos. Sci.

Arakawa, A. and W.H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the

large-scale environment. Part I. J. Atmos. Sci., 31, 674-701.

Arakawa, A and K.-M. Xu, 1990: The macroscopic behavior of simulated cumulus convection

and semiprognostic tests of the Arakawa-Schubert cumulus parameterization. Proc. of

19

the Indo-U.S. seminar on parameterization of sub-grid scale processes in dynamical

models of medium-range prediction and global climate. Pune, India.

Bechtold, P., C. Fravalo, and J.-P. Pinty, 1992: A model of marine boundary-layer cloudiness

for mesoscale applications. J. Atmos. Sci., 49, 1723-1744.

Chen, C. and W.R. Cotton, 1983: A one-dimensional simulation of the stratocumulus-capped

mixed layer. Boundary-Layer Meteorol., 25, 289-321.

Cotton, W.R., Lin, M.-S., C.J. Tremback, and R.L. McAnelly, 1989: A composite model of

mesoscale convective complexes. Mon. Wea. Rev., 117, 765-783.

Cotton, William R., G. David Alexander, Rolf Hertenstein, Robert L. Walko, Ray L. McAnelly,

and Melville Nicholls, 1995: Cloud Venting. Earth Science Rev., 39, 169-206.

Donner, L.J., 1993: A cumulus parameterization including mass fluxes, vertical momentum

dynamics, and mesoscale effects. J. Atmos. Sci., 50, 889-906.

Dyunkerke, P. G., and A. G. M. Driedonks, 1987: A model for the turbulent structure of the

stratocumulus-topped atmospheric boundary layer. J. Atmos. Sci., 44, 43-64.

Ek, M., and L. Mahrt, 1991: A formulation for boundary-layer cloud cover. Ann. Geophys-

icae, 9, 716-724.

Gallus, W.A., Jr., and R.H. Johnson, 1991: Heat and moisture budgets of an intense mid-

latitude squall line. J. Atmos. Sci., 48, 122-146.

Galperin, B., L. H. Kahtha, S . Hassid, A. Rosati, 1988: A quasi-equilibrium turbulent energy

model for geophysical flows. J. Atmos. Sci., 45, 55-62.

Harrington, Jerry Youngblood, 1997: The effects of radiative and microphysical processes

on the simulation of warm and cold season Arctic stratus. Ph.D. dissertation, Col-

20

orado State University, Dept. of Atmospheric Science, Fort Collins, CO 80523, in

preparation.

Hertenstein, R.F., and W.R. Cotton, 1994: Simulation of a midlatitude squall line using

multiple interactive grid nesting. Preprints, Tenth Conference on Numerical Weather

Prediction, 17-22 July, Portland, Oregon.

Hertenstein, R.F., P.Q. Olsson, and W.R. Cotton, 1994: Evolution of potential vorticity

associated with two mesoscale convective systems. Preprints, Sixth Conference on

Mesoscale Processes, 17-22 July, Portland, Oregon.

Houze, R.A., Jr., 1977: Structure and dynamics of a tropical squall-line system. Mon. Wea.

Rev., 105, 1540-1567.

Jiang, H., R.L. McAnelly, W.R. Cotton, 1996: The trigger function to activate an MCS para-

meterization scheme in GCM. Proceedings, 7th Conference on Mesoscale Processes,

9-13 September 1996, Reading, UK, American Meteorological Society.

Langland, R. H., and C.-S. Liou, 1996: Implementation of an E - E parameterization of

vertical subgrid-scale mixing in a regional model. Mon. Wea. Rev., 124, 905-918.

Lord, S.J., 1982: Interaction of a cumulus cloud ensemble with the large-scale environment,

Part 111: Semi-prognostic test of the Arakawa-Schubert cumulus parameterization. J.

Atmos. Sci., 39, 88-103

Machado, L.A.T., and W.B. Rossow, 1993: Structural characteristics and radiative properties

of tropical cloud clusters. Mon. Wea. Rev., 121, 3234-3260.

McAnelly, R.L., J.E. Nachamin, W.R. Cotton, and M.E. Nicholls, 1997: Upscale evolution

of MCSs: Doppler radar analysis and analytical investigation. Mon. Wea. Rev., 125,

1083-1110.

21

Mellor, G. L., 1977: The gaussian cloud model relations. J. Atmos. Sei., 34, 356-358, 1483-

1484.

Mellor, G.L. and T. Yamada, 1974: A hierarchy of turbulence closure models for planetary

boundary layers. J. Atmos. Sci., 31, 1791-1806.

Nebuda, Sharon E., 1995: Development of an upper-level cloud parameterization for large

scale models. Atmospheric Science Paper No. 582, Colorado State University, Dept.

of Atmospheric Science, Fort Collins, CO 80523, 125 pp.

Olsson, P.Q., and W.R. Cotton, 1997a: Balanced and unbalanced circulations in a primitive

equation simulation of a midlatitutde MCC. Part I: The numerical simulation. J.

Atmos. Sci., 54, 457-478.

Olsson, P.Q., and W.R. Cotton, 1997b: Balanced and unbalanced circulations in a primitive

equation simulation of a midlatitutde MCC. Part 11: Balanced analysis. J. Atmos.

Sci., 54, 479-497.

Rafkin, Scot C.R., 1996: Development of a cumulus parameterization suitable for use in

mesoscale through gcm-scale models. Ph.D. dissertation, Colorado State University,

Dept. of Atmospheric Science, Fort Collins, CO 80523.

Randall, D.A., and D.-M. Pan., 1993: Implementation of the Arakawa-Schubert cumulus

parameterization with a prognostic closure. Meteorological Monograhps: The repres-

entation of cumulus convection in numerical models. K.A. Emanuel and D.J. Ray-

mond, eds., 137-144.

Sommeria, G., and J. W. Deardorff, 1977: Subgrid-scale condensation in models of nonpre-

cipitating clouds. J. Atmos. Sei., 34, 344-355.

22

Walko, R. L., W. R. Cotton, M. P. Meyers, J. Y. Harrington, 1995: New RAMS cloud

microphysics parameterization. Part I: the single-moment scheme. J. Atmos. Res.,

38, 29-62.

Weissbluth, M.J., and W.R. Cotton, 1993: The representation of convection in mesoscale

models. Part I: Scheme fabrication and calibration. J. Atmos. Sei., 50, 3852-3872.

Wu, X., and M. Yanai, 1994: Effects of vertical wind shear on the cumulus transport of

momentum: Observations and parameterization. J. Atmos. Sei., 51, 1640-1660.

Zipser, E.J., 1982: Use of a conceptual model of the life-cycle of mesoscale convective sys-

tems to improve very-short-range forecasts. Nowcasting, K. Browning (Ed.), Academic

Press, New York, 191-204.

5 Publications Supported

Alexander, G. David and William R. Cotton, 1994: Explicit simulation of a tropical meso-

scale convective system. Proceedings, 4th Atmospheric Radiation Measurement Sci-

ence Team Meeting, Feb 28 - Mar. 3, 1994, Charleston, South Carolina.

Alexander, G. David, and W.R. Cotton, 1994: Explicit simulation of a tropical mesoscale

convective system. Preprints, Tenth Conference on Numerical Weather Prediction,

17-22 July, Portland, Oregon.

Cotton, William R., G. David Alexander, Rolf Hertenstein, Robert L. Walko, Ray L. McAnelly,

and Melville Nicholls, 1995: Cloud Venting. Earth Science Rev., 39, 169-206.

Cotton, W.R., D. Alexander, R. Hertenstein, and M. Weissbluth, 1994: Analysis techniques

using data from explicit simulations of mesoscale convective systems. Proc., 8th Conf.

on Atmospheric Radiation, 23-28 January 1994, Nashville, TN.

23

Cotton, W.R., H. Jiang, R.L. McAnelly, 1997: Sensitivity of TOGA COARE cloud systems

to different microphysical parameterization in RAMS. 22nd Conference on Hurricanes,

19-23 May, 1997. Ft. Collins, CO.

Cotton, W.R., H. Jiang, S.C.R. Rafkin, G.D. Alexander, R.L. McAnelly, 1996: Parameter-

ization of cumulus and MCSs in GCMs to mesoscale models. Proc., ECMWF/GCSS

Workshop on New Insights and Approaches to Convective Parameterization, 4-7 Novem-

ber, 1996, Reading, U.K.

Cotton, William R., Bjorn Stevens, David Duda, and Graeme Stephens, 1994: Develop-

ment of a CCN-albedo-stratocumulus parameterization scheme. Proceedings, 4th At-

mospheric Radiation Measurement Science Team Meeting, Feb. 28 - Mar. 3, 1994,

Charleston, South Carolina.

Cotton, William R., Bjorn Stevens, and Sharon Nebuda, 1995: A question of balance -

simulating microphysics and dynamics. Preprints, Conference on Cloud Physics, 15-

20 January, 1995, Dallas, Texas.

Hertenstein, R.F., and W.R. Cotton, 1994: Simulation of a midlatitude squall line using

multiple interactive grid nesting. Preprints, Tenth Conference on Numerical Weather

Prediction, 17-22 July, Portland, Oregon.

Hertenstein, R.F., P.Q. Olsson, and W.R. Cotton, 1994: Evolution of potential vorticity

associated with two mesoscale convective systems. Preprints, Sixth Conference on

Mesoscale Processes, 17-22 July, Portland, Oregon.

Jiang, H., W.R. Cotton, R.L. McAnelly, 1997: Testing a coupled cumulus-MCS parameter-

ization in different tropical convective environments. 22nd Conference on Hurricanes,

19-23 May, 1997. Ft. Collins, CO.

24

Jiang, H., R.L. McAnelly, W.R. Cotton, 1996: The trigger function to activate an MCS

parameterization scheme in GCM. Proceedings, 7th Conf. on Mesoscale Processes,

9-13 September 1996. Reading, U.K., AMs.

Meyers, M.P., D.A. Wesley, S.C.R. Rafkin, T.L. Jensen, J. Edwards, W.R. Cotton, 1996:

Mesoscale model applications in the forecast office. Part I: RAMS model configuration

for operations. Proc., 11th Conf. on Numerical Weather Prediction, 19-23 August,

1996, Norfolk, VA, AMs.

Stevens, Bjorn, William R. Cotton, and Graham Feingold, 1995: The microphysical char-

acteristics of convection in marine stratocumulus. Preprints, Conference on Cloud

Physics, 15-20 January, 1995, Dallas, Texas.

Weissbluth, M.J., and W.R. Cotton, 1993: The representation of convection in mesoscale

models. Part I: Scheme fabrication and calibration. J. Atmus. Sci., 50, 3852-3872.

6 Theses supported

Nebuda, Sharon E., 1995: Development of an upper-level cloud parameterization for large

scale models. Atmospheric Science Paper No. 582, Colorado State University, Dept.

of Atmospheric Science, Fort Collins, CO 80523, 125 pp.

Alexander, G. David, 1995: The use of simulations of mesoscale convective systems to build

a convective parameterization scheme. Atmos. Sci. Paper #592, Colorado State Uni-

versity, Dept. of Atmospheric Science, Fort Collins, CO 232 pp.

25