Download - Vertical transport of passive tracers by midlatitude thunderstorms: A 3-D modeling study

ELSEVIER Atmospheric Research 33 (1994) 259-281

A ' F X I O S t ~ H E R I ( ' H.ESEAf~.( 'H

Vertical transport of passive tracers by midlatitude thunderstorms: A 3-D modeling study

R e i n e r R. Alhe i t , T h o m a s H a u f

DLR, Institute of Atmospheric Physics, Oberpfaffenhofen, 82234 Weflling. German),

(Received December 23, 1992; revised and accepted June 15, 1993 )

Abstract

Measurements and theoretical investigations show that deep convective processes are important means for vertical trace gas transport. In this study vertical transport of inert tracers for two selected midlatitude thunderstorms is quantified by numerical 3-D simulations with the DLR cloud model MESOSCOP. One thunderstorm of weak to moderate type (CCOPE, July 19, 1981) and one vigorous cell of a multi-convective system (NDTP, June 28, 1989) were chosen. Emphasis is put on the vertical mixing due to dynamical effects, e.g. venting of the boundary layer, the net transport into the anvil and the downward mixing from the upper into the middle and lower troposphere. The simulations show that venting of the boundary layer by thunderstorms may reduce the grade of pollution near the surface by 50%. Significant amounts of trace constituents may be transported from the ground to the upper troposphere in half an hour or less. Observed steep increases in tracer concentrations between the cloud-free environment and the anvil mass of a single thunderstorm are also found in the model results. Mixing is described in terms of a transport matrix for the 19 July 1981 case. The matrix coefficients are determined from this thunderstorm simulation. In a previous paper similar 2-D simulations were performed for the same case. Transport matrices of the 2-D and 3-D simulations are intercompared. As a result, the general conclusions between 2-D and 3-D agree. In 2-D, however, vertical mass fluxes are less pronounced and weaken the asymmetry of the vertical transport. The transport matrix concept is suggested for thunderstorm related vertical mixing in a large scale model.

1. Introduction

Convect ive clouds are impor t an t for the vertical t ransport , p roduc t ion and de- s truct ion o f numerous trace species, which was emphas ized by several studies on t ropospher ic chemis t ry (e.g. Lelieveld and Crutzen, 1990, 1991 ). Venting of the

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260 R.R. Alheit, T. Hauf / Atmospheric Research 33 (I 994) 259-281

boundary layer by convection decreases the concentration of surface released pollutants and thus improves the air quality near the ground. Pollutants are transported upwards to the free troposphere very efficiently, allowing for long range transport. Another aspect of convectional transport is the possibility of fast vertical transport of ozone precursors (NOx, CO, hydrocarbons) which may con- tribute to photochemical 03 production in the free troposphere (Chatfield and Crutzen, 1984; Pickering et al., 1990).

Generally, trace gases with potential impact on the ozone budget or other greenhouse gases increase their influence with height, since reduced temperatures and lower concentrations of OH radicals enhance the life time of pollutants at high altitudes (Kleinman and Daum, 1991 ). In that respect, therefore, deep convection has a great importance, as it may reach even into the stratosphere. The intrusion of tropospheric air into the stratosphere affects the concentrations of trace gases such as 03, H20 and NOx, which is of particular interest in climate research (Wang et al., 1992). There is also a significant downward transport of trace gases by convection, either by vertical currents themselves, or by the scavenging of sedimentating hydrometeors, affecting air quality near the surface (AI- heit and Hauf, 1992).

Numerous studies dealing with principal mechanisms and quantitative aspects of upward and downward transport of trace gases by convective clouds have been performed during the last pentad. Observational studies were carried out, e.g., by Dickerson et al. (1987), Garstang et al. ( 1988, 1990), Pickering et al. (1989), Doddridge et al. (1991), Kleinman and Daum (1991) and Boe et al. (1992). Theoretical estimates were made, e.g., by Costen et al. ( 1988 ), Cho et al. ( 1989 ), Garstang et al. (1989), Moncrieff (1989), Jacob and Prather (1990), Langner et al. (1990), Pickering et al. (1990, 1991, 1992a, b, c), Scala et al. (1990), Penner et al. ( 1991 ), Yang et al. ( 1991 ), Alheit and Hauf ( 1992 ) and Ehhalt et al. (1992). Due to this intense work the knowledge about the vertical transport of trace species by shallow convection has increased, but less is known for deep convective processes. The general representation of deep convection in any large scale model is unsatisfactory and has to be improved (Emanuel, 1991; Lelieveld and Crutzen, 1991 ). Further, the contribution of deep convection to global trace gas transports needs quantification (Feichter and Crutzen, 1990).

The purpose of this article is to improve the understanding of vertical trace gas transport by midlatitude thunderstorms and to quantify it. Updrafts and downdrafts related to a thunderstorm are particularily responsible for effective vertical tracer transports, rather than the cloud itself. The precise description of downdrafts and updrafts as a base for an effective parametrization of convection, however, requires knowledge of detailed cloud processes as deduced from, e.g., numerical cloud models (Emanuel, 1991 ). This study is based on 3-D numerical cloud model simulations coupled with a layered tracer scheme similar to Lafore and Moncrieff ( 1989 ) and Scala et al. (1990). Horizontally averaged tracer concentrations before and after a thunderstorm are compared and related analyti- cally by a transport matrix. The matrix elements are determined from this comparison. Thus the net effect of a thunderstorm is studied rather than a selected

R.R. Albeit, T. Hauf / Atmospheric Research 33 (1994) 259-281 261

set of trajectories, which hardly cover the complete mixing characteristics. A parameterization scheme for the vertical tracer redistribution in global circulation models or global atmospheric chemistry model is suggested.

Two cases were investigated. The first is a single cell of the vigorous mesoscale convective system of 28 June 1989, which was investigated during the North Da- kota Thunderstorm Project (NDTP). The second case is a small isolated thunderstorm that occured on 19 July 1981 in the Cooperative Convective Precipita- tion Experiment (CCOPE). For the latter case the transport matrix was calculated. We suggest that the matrix elements are of special interest because they facilitate parameterization of vertical trace gas transports in large scale models. Alheit and Hauf ( 1992 ) performed a 2-D simulation of the same case. It is a further objec- tive of this study to compare the respective 2-D and 3-D transport matrices.

The paper is organized as follows. In the next section a brief model description is presented. Then the development of the two thunderstorms and the related vertical trace gas transport are discussed. The transport matrix for the CCOPE case is determined and compared with that of the 2-D simulation. Applications of the matrix to hypothetical initial tracer distributions are presented. Summary and conclusions are given in the last section.

2. The 3-D cloud model

The 3-D cloud model MESOSCOP (Mesoscale Flow and Cloud Model Ober- pfaffenhofen), was used for the numerical simulations. It is described in Schu- mann et al. (1987). In the past, it has been successfully used for a number of deep convective cloud simulations, e.g. by HCiller ( 1988 ). Budget equations were added to simulate the transport of inert tracers. The budget equations make use of the positive definite advection scheme according to Smolarkiewicz (1984). Microphysics is based on a bulk formulation, i.e. the cloud particles (cloud drops, rain drops, cloud ice particles, snow, graupel and hail) are represented solely by their volume concentrations. Saturation with respect to water is assumed to be the upper threshold of water vapor concentration. The microphysical interac- tions between the different types of cloud particles are described in terms of mass transfer rates according to Lin et al. (1983), H/Sller (1986) and Haul (1993). The spatial redistribution of inert tracers is only affected by dynamical processes. Gas scavenging by cloud particles is neglected in the model.

As a result of numerical simulations, the vertical redistribution of trace species due to dynamical effects can be described in terms of a transport matrix, similar to the transilient matrix of Stull (1988), Ebert et al. (1989) and Raymond and Stull (1990). This approach assumes that a single thunderstorm changes an initial tracer profile Ti to a modified tracer profile Tm, where both profiles represent horizontal averages. This modification can be discribed by a matrix C, the transport matrix:

T m = C ' T ~ . (1)

262 R.R. Alheit, T. Hauf / Atmospheric Research 33 (1994) 259-281

Eq. ( 1 ) reads for the elements of the vectors (Tm}, {Ti} and the matrix {C}:

{Tm}k = ~ {C}kl{Ti}I, (2) l=1

where n is the number of respective layers. { Ti}t denotes the initial partial trace gas density at level l, { Tm}k denotes the resulting partial trace gas density at level k, and {C}k~ represents the average percentage of a tracer from source layer l ar- riving at destination layer k.

If {Ti} is zero, except for one layer l, Eq. (2) can be simplified:

{Tm}k =Ckl{Ti}l. (3)

Initialising with respective tracer profiles, the coefficients Ck~={C}kt of the transport matrix can be determined. To do this, the spatial redistribution of the tracer has to be simulated and the concentrations have to be averaged horizontally in all levels. The calculation of the transport matrix, therefore, requires either n repeated simulations with varying nonzero source layer l, or n budget equations for each respective source layer.

To ensure mass conservation with respect to air for each level k, and tracer conservation for each tracer l, the constraints

~ Ckl = 1,k~ 1,...,n (4) /=1

and

~ Ckl = 1 ,l~ 1 ,...,n ( 5 ) k=l

have to be fulfilled. It can be shown that this requires the formulation ofEqs. ( 1 ) to ( 5 ) in terms of partial densities, rather than mixing ratios.

It is well known that single thunderstorms have a well defined dynamical time scale, especially with respect to vertical motions. The simulations show that for simulation times longer than this time scale of about one hour, the tracer profiles Tm are approximately constant with time. For thunderstorms, therefore, the transport matrix is only weakly time dependent, in contrast to turbulence transports (Stull, 1988). The sensitivity of the transport matrix to boundary conditions and domain size was not investigated in this study. It should be noted that the matrix values depend on the horizontal extensions of the model domain.

If the transport matrix once has been determined, the effect of this thunderstorm, or of those with the same transport matrix, on any tracer distribution can be easily determined by Eq. ( 1 ).

3. Case studies

3.1 .28June 1989

During the North Dakota Thunderstorm Project from 12 June through 22 July 1989, various aspects of northern High Plains thunderstorms were investigated.

R.R. Alheit, T. Hauf / Atmospheric Research 33 (1994) 259-281 263

One of the mature-storm objectives was to study the transport of natural trace gases, such as 03, CO, by thunderstorms (Boe et al., 1992). Well documented observations exist for 28 June which are suitable for model simulations of strong convective activity and vertical tracer transport (Boe and Johnson, 1990).

On 28 June 1989 a large longliving mesoscale convective system (MCS) cov- ered wide areas of North Dakota (ND). A surface synoptic analysis for 27 June, 12 UTC shows a warm frontal boundary layer over eastern Montana and South Dakota (Fig. 1 ). During the afternoon of 28 June the MCS developed explosively over the western regions of ND, moving into central ND. At that time, isolated thunderstorms had developed in south central ND. In the late afternoon the east- ward moving MCS became more like a squall line.

Observations showed that cells within the MCS had radar reflectivities up to 60-65 dBz. Strong updrafts with vertical wind velocities of 20-30 ms-1 were evident from aircraft penetrations (Orville et al., 1990). On 28 June there was severe hail production by the thunderstorms with hailstones of 7.6 cm diameter.

Fig. 2 shows the 29 June 00 UTC sounding obtained at Bismarck, ND, with which the model was initialized. The model domain was 40 km X 40 km in the horizontal and 16 km in the vertical. The grid size was 1.0 k m x 1.0 k m x 0 . 4 km. The numerical time step was 5 s. Top and bottom boundaries of the model were closed, while for the lateral directions periodic boundary conditionswere chosen. To initiate convection, a heat source was centered in the XY-plain near the surface. The maximum heating rate in terms of increased entropy was 0.06 Jkg- K-~ s-1. It decreases exponentially towards the lateral boundaries and was switched off after 30 min of model time. The simulation was stopped after a model time of one hour when the simulated thunderstorm had reached the decaying stage and most of the liquid and solid cloud particle mass had vanished. With this setup of the numerical experiment a simulation of one cell of the MCS is intended.

- ~ , lO16

\1012 \ / \ ]12

I( \ \ 1 '

Fig. 1. Surface weather chart of 27 June 1989 12 UTC with temperatures in °C (dashed), pressure in hPa (solid), winds in ms-~ and air mass borders.


100

150

200

250

300

400

50O

700

850

1000

-40

\ \ \ \ y / ' 1 \ \ \ \ \ / \ / I \ \,,, \',,, \'.,,'., / " , - " _ _ / \ / x \ J ,1

.,. \ \ . f \ \ / / \ . / . . / " \ / / I

\ \ \ /

z-

-30 -20 -10 0 10 20 30

h__.

40

Fig. 2. Sounding obtained on 29 June 1989 00 UTC at Bismarck, ND. Pressure levels are in hPa, temperatures (right) and dew point temperatures (left) are in °C and winds are in knots.

Fig. 3 shows vertical cross sections from the simulated cell for various cloud parameters after 30 min of model time when the cloud was in the mature stage. From that figure one can see that cloud base was at about 2.4 km and that the overshooting dome reached a height of about 12.5 km. The anvil was forming between 10 and 12 km above ground level (AGL). Overshooting was a common observation on this day in North Dakota.

In the simulation the major precipitation type reaching the ground was rain. It was formed mainly via the riming of single ice crystals, formation of graupel, further growth by riming and the melting of these graupel particles. Hail also reached the ground in the simulation. The microphysical characteristics of the

Fig. 3(a) . Vertical cross sections of wind fields after 30 min of model time in the XZ-plane at Y= 38 km (left panel ) and in the YZ-plane at X = 20 km (right panel ) for simulated NDTP case. The plates show the calculated vertical wind fields (bottom), the wind vector fields projected into the corresponding planes (middle) and the stream lines calculated from the wind vector fields (top). The maximum contoured updraft and downdraft velocities and line increments in the bottom plates are on the left 18, - 16 and 2, on the right 26, - 16 and 2 ms -~, respectively. (b) Vertical cross sections of various cloud microphysical parameters after 30 min of model time in the XZ-plane at Y= 38 km (left panel) for simulated NDTP case. The left panel shows from the bottom to the top the mixing ratios of hail, cloud water and water vapor. The plates on the right panel show from the bottom to the top the mixing ratios of rain water, graupel and ice crystals. The maximum contoured concentrations and line increments in the plates are for hail 3.20 and 0.20, for cloud water 1.53 and 0.09, for water vapor 11.20 and 0.70, for rain water 6.80 and 0.40, for graupel 7.60 and 0.40 and for ice crystals 0.144 and 0.009 gkg- ~, respectively.

R.R. Alheit, 7". H a u f l Atmospheric Research 33 (1994) 259-281 265

(a) 16.0 : ~ . : ~ ~ , ~ , .

0 . 0 ~ 0

,..V~\, C ,, , ~ i ~ ~

20 40 disDance (kin)

6,0[

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0.0 ~- 0 20 40

disLance (kin)

~t [iiiiiiiiiiiii iii:::: :: ::::::::::: : ~ ~" ii:::::::::::!:i!!!i!!!iiiii!!ii!i ~ ~ .11111211' : : . . . . . . . . . . . . . . . . . .

:~ . . . . . . . . . ,, / ,llt_ ~ . . . . -

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: : : : : : : : : : : : : : : ! i l ~!:::i i i i i i i ! !! i i i i ,,;: . . . . . . . . . . . . . . . . . . . . . . . . . . . : ; , , , ~ z " - , , . : : .... : : : : : : : : : : : : : : : : : : : : : : : : : : : --

' " ] l ' ' l l l # / ; , , / l l . . . . . . . . . . . ~ , . . . . . . . . . . . . . . . . . . . . . . . : . / l / l / I l l .x

,,,,, ~ ................ : : ........................... ~ , ~ "~

!:::::::i:::t !!i::::?:!??????ii ...................................... . . . . . . . . . . . . . . . . . . . . , / / l l / t i , , , , , r . ~ \ : ~ , - : ~ : : : : . . . . . . . . . , ................................ ,

20 41 0 70 , distance (kin) disLance (kin) 160 16.0

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0.0 0.0 0 20 40 0 20 40 distance (kin) distance (kin)

266

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distance (kin)

CLOUD WATER

8.0

R.R. Alheit, T. Hauf / Atmospheric Research 33 (1994) 259-281

tm

20 40 dis[anee (kill)

HAIL

80

20 distance (kin)

40 0

Fig. 3. Continued.

[ ICE CRYSTALS

20 40 distance (kin)

i

: I 8o4

0 20 40 d i s L a n c e ( k i n )

RAIN

~0

80

0 20 40 distance (kin)

R.R. Alheit, T. Hauf /Atmospheric Research 33 (1994) 259-281 267

modeled cloud, especially the formation of hail, were qualitatively in good agreement with the field observations.

Since we are interested in vertical trace gas transport, we investigated the spatial redistribution of conservative tracers with two distinct initial tracer profiles. Fig. 4 shows cross sections of tracer distributions resulting from an initial profile which represents a ground based pollution layer of 3 km depth. It is evident that pollutants from near the surface were transported into the upper troposphere in less than half an hour, reaching the anvil region only weakly diluted.

From tropospheric ozone measurements a vertical ozone profile was con- structed which served as a further initial profile (Fig. 5 ). Aircraft measurements indicated ozone concentrations in the lower and middle troposphere of about 35- 50 ppb, and 140-160 ppb in the anvil region outside the cloud. Inside the cloud at 5.5 km AGL concentrations of about 50 ppb (Boe et al., 1992 ) are found while in the anvil 80-115 ppb were measured (Fig. 6). Thus horizontal differences in ozone concentration of about 50-60 ppb were observed between outside and inside the anvil.

Vertical and horizontal cross sections through the model domain (Fig. 7 ) show that low tracer concentrations reach from the boundary layer up to the anvil region near the updraft core (see Fig. 3). Observed ozone variability in the anvil region is well resolved by the model. The range of simulated ozone concentrations at anvil level is 70-130 ppb and close to the observed range of 80-160 ppb. Beside possible chemical reactions the differences in the ranges may be solely due to uncertainties in the initial distribution.

It should be noted that ozone was treated here as an inert gas without any

i 6 . 0

8.0

[6 .0 - -

2~

8 .0

0 . 0 ~ - - 0 ZO 4O

d i s L a n c e (km) 0

d i s t a n c e (kin)

Fig. 4. Vertical cross sections of calculated tracer mixing ratios after 30 min of model time in the XZ- plane at Y=38 km (left) and in the YZ-plane at X = 2 0 km (right) for simulated NDTP case. The tracer was initially homogeneously distributed in the lowest 3 km of the domain with a value of 1. The maximum contoured concentrations and line increments in the plates are 0.96 and 0.06 on the left, 1.02 and 0.06 on the fight, respectively.

268 R.R. Alheit, T. Hauf /Atmospheric Research 33 (1994) 259-281

T 6

15 14 13 12 11 10

E ~9 .c

8 .E f,

6-

5

4 -

3

2

1

0 0

~ A

/

l A observed data /

5O loo 15o 2o0

ozone concentration in ppb

Fig. 5. Measured ozone values and derived vertical profile used for model initialisation (NDTP case ).

T v 8

o 0

200

100

outside anvil inside anvil

i i I 10

time in min

I I J

20 30

Fig. 6. Measured ozone concentrations on 28 June 1989 as function of time during the ascent of the research aircraft and subsequent penetration of an anvil. After 6 min the aircraft had climbed to a height of 8.8 km, after 20 min to a height of 10.9 km and after 23 rain to a top height of I 1.3 kin. After 23 min the aircraft stayed at heights between 11.2 and l 1.3 km. Penetration of the anvil was indicated by a measured steep increase in ice crystal concentration between approximately 22 and 23 min (not shown here ). (R. Dickerson, pers. commun., 1992 ).


io.o i ......................

o o :- . . . . . . . ~ ~ ' ~ . . . . . . . . . . . . . . . 0 20 40

distance (km)

1 6 . 0 . . . . . . . . . . . . . . . . . . . . . ' . . . . . . . . . . . . . .

80-

l 'L, / / I -

/ 380 J t

0 20 4 0 dis tance (kiT-)

Fig. 7. Vertical cross sections of calculated ozone mixing ratios after 30 rain of model time in the XZ- plane at Y= 38 km (left) and in the YZ-plane at X = 2 0 km (right) for the simulated NDTP case. Lowest values as initially assumed at heights of about 3 km are transported upward to heights of about 8 to 10 km. The maximum and minimum contoured concentrations and line increments in the plates are 147, 35 and 7 ppb, respectively.

chemical reactions or uptake in hydrometeors. Our results suggest that low ozone concentrations observed in the anvils of thunderstorms may be caused by dynamical redistribution effects only. Ozone destruction due to incloud chemical processes, as hypothesized by Lelieveld and Crutzen ( 1991 ), is not necessary to explain low anvil ozone concentrations in this case. However, both processes, advection of low ozone concentrations and chemical destruction of ozone, may operate simultaneously.

3.2. 19July 1981

The Cooperative Convective Precipitation Experiment was a field research program to account for the enhanced needs of comprehensive datasets on convective clouds. It was conducted in southeastern Montana, USA, from 18 May through 7 August 1981. Two of the major objectives were studies of convective clouds in their early stage of development and research on mature cumulonimbi of varying size and intensity (Fankhauser et al., 1983). The welldocumented CCOPE case of 19 July 1981 covers the complete life cycle of a thunderstorm in the area of Miles City, Montana, USA.

On 19 July 1981 the meteorological situation in the northern states of the US was characterized by surface high pressure reaching from the west to the east coast. A shallow midtropospheric trough over the north-western US/Canadian boundary area induced a slight surface pressure minimum over the northern-central US. However, surface pressure gradients stayed small and wind shear was also weak. The conditions supported cumulus convection. A number of small isolated shortlived thunderstorms were registered in this region on that day.

2 7 0 R.R. Alheit, T. Hauf /Atmospheric Research 33 (1994) 259-281

Observations of the studied cloud started at 16: 05 MDT, when the cloud still was a small cumululus embedded in a cumulus field. The cloud development then was characterized by a period of explosive growth between 16: 20 and 16: 30 MDT. The dissipational stage of the cloud began at 16:40 MDT. At 16:55 MDT the major activity of the thunderstorm had finished and only some weak precipitation was left under a widespread resting anvil.

Cloud base height was observed to be about 3 km AGL and maximum observed cloud top height was 10.5 km according to Dye et al. ( 1986 ) and 13 km according to Heymsfield and Miller (1988). Observed maximum radar reflectivities were about 55 dBz and vertical velocities from aircraft were 10-15 ms -1 (Helsdon and Farley, 1987 ). The thunderstorm produced some small hail up to 8 to 9 mm diameter. Precipitation resulted from melting graupel and small hail. Numerous studies exist for this case, focussing on various aspects of cloud research, e.g. performed by Knight (1982), Dye et al. (1986), Helsdon and Farley (1987), Schu- mann et al. (1987), Fankhauser (1988), Heymsfield and Miller (1988), Hrller ( 1988 ), Geresdi (1990), Knight (1990), Murakami (1990), Musil et al. ( 1991 ) and Alheit and Hauf ( 1992 ).

Due to the extensive information which is available from literature for this case, we here limit the description of the model results to vertical tracer transport aspects. Microphysical and dynamical characteristics of 3-D model simulations with MESOSCOP for the 19 July cloud have already been presented by Schu-

16-

15 ~

14-

13

12

11

10

._c 8

~ 7

6

5

4

3

2

1

0 ,0 .2 .4 .6 .8 1.0

partial t racer densi ty in m -3

Fig. 8. Initial vertical profile of tracer mixing ratio used for model initialisation (CCOPE case).

R.R. Alheit, T. Hauf / Atmospheric Research 33 (1994) 259-281

15 min

12

% % ~ ~"

271

30 min

12

E ~

t6t

45 min 60 min

Fig. 9. Time evolution of calculated spatial tracer distribution after 15, 30, 45 and 60 min of model time for the CCOPE case and an initial tracer profile according to Fig. 8. The outlined surfaces enclose regions of tracer concentrations equal or higher than 20% of the initial tracer surface concentration.

mann et al. (1987) and H611er (1988). There, and also in the present paper, the sounding of Miles City, Montana, on 19 July 1981, 14.40 MDT was used for the model initialization. It can be found in literature, e.g. from Helsdon and Farley (1987). Here, the model domain had extensions of 30 k m × 3 0 km in the horizontal and 16 km in the vertical. Horizontal and vertical grid spacing were 0.75 km and 0.4 km, respectively. The numerical time step was 10 s. Boundary conditions were the same as for the NDTP case. Convection was stimulated by a 25 min heating in the XY-plane near the surface by increased entropy (max. 0.1 Jkg-1 K-1 s-~). As for the NDTP case, the simulation was stopped after one hour of model time.

Fig. 8 shows the initially assumed tracer profile for a polluted boundary layer.


In Fig. 9 a time series of the evolution of the spatial tracer distribution due to thunderstorm activity is plotted. The outlined surfaces enclose volumes with 20% or more of the initial maximum tracer concentration. It can be seen that after approx. 30 min of model time the tracer had been transported from its source to the upper troposphere into the anvil region. The tracer is found after 45 min of model time in a small anvil-like outflow with tracer concentrations of about 20%. The extension was less than the ice anvil (not shown here), indicating low anvil influx of the tracer and mixing with environmental nonpolluted air. This finding is in good agreement with results of Heymsfield and Miller (1988 ). They calculated the anvil mass flux and the anvil mass flux/cloud base influx ratio for several CCOPE clouds and found for the 19 July cloud very low values for both mass flux and ratio as compared to the other CCOPE cases.

From Fig. 9 it also can be seen that venting of the boundary layer by thunderstorm activity may lead to a significant decrease of tracer concentrations in wide regions of the boundary layer. Especially penetrating downdrafts from the middle troposphere on the downstream side of the thunderstorm during the decaying stage decrease the tracer concentrations at the surface to values below 20% of the initial concentrations. This result agrees well with results of 2-D simulations of the same cloud which were carried out by Alheit and Hauf ( 1992 ), using, however, a different cloud model.

The 3-D simulations confirm the hypothesis that thunderstorms may increase surface air quality significantly. For the assumed tracer profile and the 19 July cloud this overall increase was more than 50%, locally even more than 80%. The calculations also show that inert anthropogenic tracers may be transported up to the tropopause in half an hour or less by midlatitude thunderstorms, even by small isolated cells. The simulation results, however, suggest that trace gases reaching the upper troposphere and flowing into the anvil of this weak storm are heavily diluted as compared to source concentrations. Adiabatic lifting of lower tropospheric air masses in the cores of small thunderstorms, therefore, cannot be generalized. This has to be taken into account whenever deep convection and related vertical transports are parameterized in large scale models.

4. The transport matrix

4.1. Determination of C

For the 19 July 1981 cloud we determined the transport matrix C by numerical 3-D simulations. With 40 vertical grid points the matrix consists of 40 × 40 elements. An element {C}kz, k> l, above the diagonal indicates an upward transport from the/ th to the kth level, while elements below the diagonal denote a downward transport. For a better visualizing of the matrix their elements are plotted as isolines. The topography of the plot then indicates levels of high or low net vertical transport effects. A detailed description of this technique can be found in Ebert et al. (1989).


Generally, as long as the active phase of the cloud is lasting, i.e. updrafts and downdrafts with high vertical wind speeds are present, the matrix changes in time. With decaying cloud dynamics vertical redistributions become negligible and the matrix remains nearly constant. This last stage of development was reached after approx. 45 min of model simulation time.

Fig. 10 shows the time evolution of the calculated transport matrix C for the 19 July 1981. From the very beginning the matrix is asymmetric. During the first 30 rain with high updraft velocities, the plotted curves become deformed significantly above the diagonal. Simultaneously, below the diagonal the isoline distances become larger. Upward transport is confined to the updraft core and reaches greater heights, while subsidence of environmental air covers a broader area but has lower transport distances.

4o I 0 35 t = 35~ t = 30min /

! 6 30 30

5

5 10 15 20 25 30 35 40 0 15 20 )5 30 35 40 tracer (sourceqevel] tracer (sourceTeve]]

/ ~ . / 1 - u ~ / / . / / / / ] f Z

30 30

i

1 10

5

1 r i i

5 I'Q 1'5 20 2'5 3'0 3'5 40 5 0 15 20 25 30 35 40 tracer (source-level] ~:racer (source-level]

Fig. 10. Time evolution of the transport matrix during the model simulation of the CCOPE case. For details see text.

274 R.R. Alheit, T. Hauf /Atmospheric Research 33 (1994) 259-281

From 30 min through 45 min downdrafts with related downward transport of tracer substance from the middle troposphere to the surface occured. This is re- fleeted in the corresponding matrix where up to 30 min the isolines below the diagonal are almost parallel, but then are deformed significantly. Isolines reaching the abscissa indicate transport from higher levels to the surface.

Between 45 rain and 60 min the model cloud decays and the transport matrix remains almost unchanged. Note that the matrix is still asymmetric. Net upward transport from the surface up to the tropopause is stronger and far reaching than downward transport. This result agrees well with the general theory for convective motions (Langner et al., 1990). Obviously an eddy diffusion parametreri- zation cannot account for that asymmetry (Langner et al., 1990).

How can the transport matrix be used? Assuming that the vertical trace gas profile { Ti} is given, either observed or calculated, the multiplication of { C} with { Ti} according to Eq. (2) yields the modified tracer profile { Tm}. It describes the net mixing effect of the thunderstorm, for which C was determined previously, on the given profile {Ti}. A repeated multiplication describes the effect of two subsequent thunderstorms and a multiple multiplication simulates the cumula- tive, modifying effect of a series of thunderstorms. In the following, we want to present a few examples for the application of the matrix on distinct initial tracer profiles.

4.2. Examples

Fig. 11 shows the assumed initial profile Ti representing for a polluted lower troposphere and the modified tracer profile Tm. Significant tracer amounts have been transported up into the anvil region. The local maximum between 9 km and 10 km indicates that the transport from the lower troposphere up to the anvil level is quantitatively of greater importance than the transport into the transient region two kilometers below the anvil. Isolated thunderstorms do not redistribute anthropogenic trace species vertically homogeneously throughout the troposphere. This is an important aspect for numerical climate modeling.

In the next example a thin pollution layer is initially assumed at a height of about 4.5 km (Fig. 12, curve T~). The modified profile Tm shows that from the lower parts of the middle troposphere trace gases may be transported up to the tropopause as well as down to the surface by one and the same thunderstorm. Similar to the first example, more tracer substance is transported into the anvil region than into the levels beneath. A great portion of the tracer is transported to the surface. This is an effect of the strong downdraft originating in the middle troposphere and reaching the ground during the decaying stage of the cloud.

Similarily as above, a thin layer is initially positioned at a height of approx. 8 km (Fig. 13). The tracer is now redistributed almost equally by upward and downward transport but does not reach the ground. A second application of C shows that after preconditioning due to a first thunderstorm tracer substance may reach the ground. In other words: the first thunderstorm redistributes the tracer

R.R. Albeit, T. Hauf /Atmospheric Research 33 (1994) 259-281 275

¢ -

c -

11

10

9

8

5

i . . . . . . 1E-4 1E-3 1E-2 1E-1 lEO

tracer concentration

Fig. 11. Application of calculated transport matrix C( t = 60 min ) on a hypothetical initial tracer profile T,. Curve Tm represents the modified profile. The local maximum of Tm at heights of about 10 km is a result of anvil outflow. The anvil covers larger areas than the main updraft core.

~= r -

15

14

13

12

11

9

8

7

6

5

4

3

2

1

0 1 E-4

/

f 1E-3 1E-2 1E'-I tracer concentration

1 EO

Fig. 12. As in Fig. 11, except for an initial profile Ti representing a thin midtropospheric layer.

2 7 6 R.R. Alheit, T. Hauf lAtmospheric Research 33 (1994) 259-281

c-

Y:

15[ - -

14

11 ?- I

9

8

/ / 6s -';;// 4

3 / /" .,I i" / /"

2 ,I" I

i i

0 . . . . . . 1E-4 1E-3 1E-2 1E'-1 lEO

tracer concentration

Fig. 13. As in Fig. 12, except for a thin upper tropospheric layer. Dashed and dashed-dotted lines represent modified profiles after one and two successive applications of the transport matrix C(t = 60 min), respectively. The resulting profiles are calculated via T~. = C- Tm and Tin- = C" T~..

E v

e-

l--

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

1E-4 1E-3 1E-2 1E-1 tracer concentration

" ' - . T~.~

I I ,

/ , / ' ~ / • /

/ /

lEO

Fig. 14. As in Fig. 13, except for a thin layer near the tropopause and for three successive applications of C.


into the middle troposphere, so that the next is able to transport the tracer to the ground.

The higher trace gases are released, the longer it takes for thunderstorms to move it to the ground. This is shown by the last example (Fig. 14), where even 4 subsequent applications of C do not indicate significant downward transport from the anvil level to the ground.

It should be noted that these findings hold for the 19 July 1981 thunderstorm only. Thus, generalizations should be done carefully.

4.3. Comparison with 2-D results

In a recent study, Alheit and Hauf ( 1992 ) determined the transport matrix C of the 19 July 1981 thunderstorm based on 2-D simulations with the Clark model. Besides the dimensionsionality there are other differences between the two models such as different vertical extension of the model domain, grid spacing, boundary conditions, cloud initiation methods and description of the microphysical processes. The vertical extension in the 2-D simulation was 15 km, while it was 16 km in the 3-D simulation. The horizontal and vertical grid space were 1 km and 0.5 km for the 2-D run and 0.75 km and 0.4 km for the 3-D run, respectively. The lateral boundaries in the 2-D model were open but corrected for tracer transport while in the 3-D model they were chosen periodic. The 2-D microphysical model is based on a highly sophisticated spectral description of the cloud particle size distributions, while in the 3-D model a bulk parameterization was used. To stim- ulate convection in the 2-D run, a surface sensible heat flux of 70% and a latent heat fraction of 5% of the incoming solar flux was assumed, while in the 3-D model a warm bubble was prescribed in the boundary layer in terms of increased entropy. Looking at the general features of the simulated 2-D and 3-D cloud, but without going into much detail, a good agreement with respect to the precipitation forming process, occurrence of precipitation, graupel production, occurrence of downdrafts, updraft speeds, cloud base height, cloud top height and life time of the cloud is found.

A comparison of C(2-D) with C(3-D) shows similar structures. The asymmetry with stronger upward than downward transport is evident in both simulations. The penetrating downdraft originated in both simulations in the middle troposphere. Lifting of tracer substance is more pronounced from the lowest source levels inside the boundary layer than from source levels directly above in both simulations. This can be seen from the wavy structure of the matrices in the upper left quarter of the matrices. The lowest diagonal values are found for both matrices in the lower left. This indicates a stronger mixing in the boundary layer than above and agrees well with general observations of mixing properties in the troposphere.

Looking for details, there are two significant differences between the two matrices. At first, 3-D transport is more effective than 2-D as isolines are more spread. In a 3-D model there is generally a greater chance for large eddies to occur some-


where in the XYZ-domain than in a XZ-domain of a 2-D model. Regions of slight lifting and subsidence also tend to occur preferably in 3-D rather than in 2-D models. Both effects associate with pronounced off-diagonal elements.

The second major difference in the matrices is the significant shifting of the isolines for lower source levels (lower values on the abscissa) towards higher destination levels (higher values on the ordinate ) for 3-D calculations as compared with 2-D. This indicates a quantitatively much more effective upward transport from the boundary layer into the anvil in 3-D than in 2-D. To explain the difference and to intercompare 2-D with 3-D modeling, the 2-D model is hypotheti- cally extended in the lateral direction by an amount equal to the main updraft diameter. Then, in 3-D mass fluxes at cloud base, in the main updraft and in the anvil are stronger than in 2-D. There might be other reasons for this discrepancy between C(2-D) and C(3-D), but this subject goes beyond the scope of this paper. The main conclusion is that the asymmetry of deep convective tracer transports, as a typical feature, is more pronounced in 3-D than in 2-D. If far reaching vertical transport is of importance, 3-D simulations are required.

5. Conclusions

Two 3-D model studies of isolated midlatitude thunderstorms were performed to examine the vertical transport of inert trace gases. The net vertical tracer mixing was quantified and, for one case, described in terms of a transport matrix. Application of the transport matrix concept is illustrated in four examples.

The following conclusions may be drawn from the 3-D simulations: - The efficient vertical transport of inert trace gases through the whole tropo-

sphere by shortlived events that accompany deep convection is clearly demonstrated.

- Results from previous 2-D calculations are confirmed. Deep convection may reduce pollution in the boundary layer by 50%. Trace species may be transported from the ground to the tropopause in less than half an hour.

- Numerical simulation of a single cell embedded in a mesoscale convective system (NDTP, 28 June 1989) improved our understanding of the three dimensional structure of trace gas transport and observed ozone variability in the anvil region.

- The transport matrix concept allows an easy description of pollutant transport from distinct source layers.

- Deep convective tracer transport is highly asymmetric with stronger and far reaching upward transport.

- Vertical mass fluxes are less pronounced in 2-D than in 3-D and, therefore, weaken the typical asymmetric, upward dominated transport.

These conclusions are in accordance with earlier tracer transport studies of other authors (e.g. Lafore and Moncrieff, 1989; Langner et al., 1990; Scala et al., 1990). It is suggested that the transport matrix concept be used for studies of vertical subgrid scale transport of inert trace gases in global models. This is left to future work. The proposed matrix method for quantifying vertical transports provides


us a simple tool to describe inert tracer transports. It is also applicable to other conservative quantities in clouds, such as equivalent potential temperature and entropy.

Acknowledgements

The authors are grateful to Dr. H. HSller for his support in running the 3-D cloud model MESOSCOP for this study. Thanks are due to Dr. R. Dickerson for providing ozone measurement results of the NDTP case. This work was supported by the Bavarian Climate Research Program (BayFORKLIM), project No. B-III-5.

References

Alheit. R.R. and Hauf, T., 1992. Vertical transport of trace species by thunderstorms - - a transilient transport model. Ber. Bunsenges. Phys. Chem., 96: 501-510.

Boe, B.A. and Johnson, H.L., 1990. Destabilization antecedent to a tornadic northern High Plains mesoscale convective system: A case study. Preprints, 16th Conf. Severe Local Storms, Kananas- kis Park, Alberta, Canada, pp. 538-541.

Boe, B.A., Stith, J.L., Smith, P.L., Hirsch, J.H., Helsdon, J.R., Jr., Detwiler, A.G., Orville, H.D., Mann- ner, B.E., Reinking, R.F., Meitin, R.J. and Brown, R.A., 1992. The North Dakota Thunderstorm Project: A cooperative study of High Plains thunderstorms. Bull. Am. Meteorol. Soc., 73: 145- 160.

Chatfield, R.B. and Crutzen, P.J., 1984. Sulfur dioxide in remote oceanic air: Cloud tansport of reac- tive precursors. J. Geophys. Res., 89:7111-7132.

Cho. H.R., Niewiadomski, M., lribarne, J.V. and Melo, O., 1989. A model of the effect of cumulus clouds on the redistribution and transformation of pollutants. J. Geophys. Res., 94:12,895-12,910.

Costen, C., Tennille, G.M. and Levine, J.S., 1988. Cloud pumping in a one-dimensional photochemical model. J. Geophys. Res., 93: 15,941-15,954.

Dickerson, R.R., Huffman, G.J., Luke, W.T., Nunnermacker, L.J., Pickering, K.E., Leslie, A.C.D., Lindsey, C.G., Slinn, W.G.N., Kelly, T.J., Daum, P.H., Delany, A.C., Greenberg, J.P., Zimmer- man, P.R., Boatman, J.F., Ray, J.D. and Stedman, D.H., 1987. Thunderstorms: An important mechanism in the transport of air pollutants. Science, 235: 460-465.

Doddridge, B.G., Dickerson, R.R., Holland, Z.R., Cooper, J.N., Wardell, R.G., Paluch, O. and Wat- kins, J.G., 1991. Observations of tropospheric trace gases and meteorology in rural Virginia using an unattended monitoring system: Hurricane Hugo (1989), a case study. J. Geophys. Res., 96: 9341-9360.

Dye, J.E., Jones, J.J., Winn, W.P., Cerni, T.A., Gardiner, B., Lamb, D., Pitter, R.L., Hallet, J. and Saunders, C.P.R., 1986. Early electrification and precipitation development in a small, isolated Montana thunderstorm. J. Geophys. Res., 91 : 1231-1247.

Ebert, E.E., Schumann, U. and Stull, R.B., 1989. Nonlocal turbulent mixing in the convective boundary layer evaluated from Large-Eddy simulation. J. Atmos. Sci., 46:2178-2207.

Ehhalt, D.H., Rohrer, F. and Wahner, A., 1992. Sources and distribution of NOx in the upper troposphere at northern mid-latitudes. J. Geophys. Res., 97: 3725-3738.

Emanuel, K.A., 1991. A scheme for representing cumulus convection in large-scale models. J. Atmos. Sci., 48: 2313-2335.

Fankhauser, J.C., Barnes, G.M., Miller, L.J. and Roskowski, P.M., 1983. Photographic documenta- tion of some distinctive cloud forms observed beneath a large cumulonimbus. Bull. Am. Meteorol. Soc., 64: 450-462.

280 R.R. Albeit, T. Hauf /Atmospheric Research 33 (1994) 259-281

Fankhauser, J.C., 1988. Estimates of thunderstorm precipitation efficiency from field measurements in CCOPE. Mon. Weather Rev., 116: 663-684.

Feichter, J. and Crutzen, P.J., 1990. Parameterization of vertical tracer transport due to deep cumulus convection in a global transport model and its evaluation with 222Radon measurements. Tellus, 42B: 100-117.

Garstang, M., Scala, J., Greco, S., Harriss, R., Beck, S., Browell, E., Sachse, G., Gregory, G., Hill, G., Simpson, J., Tao, W.-K. and Torres, A., 1988. Trace gas exchanges and convective transports over the amazonian rain forest. J. Geophys. Res., 93:1528-1550.

Garstang, M., Scala, J.R., Simpson, J., Tao, W.-K., Thompson, A.M., Pickering, K.E. and Harris, R., 1989. Cumulus cloud model estimates of trace gas transports. Proc. Symposium on the Role of Clouds in Atmospheric Chemistry and Global Climate, January 30-February 3, Anaheim, Calif., pp. 260-263.

Garstang, M., Ulanski, S., Greco, S., Scala, J., Swap, R., Fitzjarrald, D., Martin, D., Browell, E., Ship- man, M., Connors, V., Harriss, R. and Talbot, R., 1990. Trace gas exchanges and convective transports over the amazonian rain forest. Bull. Am. Meteorol. Soc., 71: 19-32.

Geresdi, I., 1990. Two-dimensional simulation of a small hailstorm. Idrjfir~s, 94: 346-359. Hauf, T., 1993. Microphysical kinetics in phase space: The warm rain process. Atmos. Res.. 29: 55-

84. Helsdon, H.H. and Farley, R.D., 1987. A numerical modeling study of a Montana thunderstorm: 2.

Model results versus observations involving nonelectrical aspects. J. Geophys. Res., 92: 5645- 5659.

Heymsfield, A.J. and Miller, K.M., 1988. Water vapor and ice mass transported into the anvils of CCOPE thunderstorms: comparison with storm influx and rainout. J. Atmos. Sci., 45:3501-3514.

H~511er, H., 1986. Parameterization of cloud microphysical processes in a three-dimensional convective mesoscale model. DFVLR-Forschungsbericht, FB 86-02, 82 pp.

Hrller, H., 1988.3-d numerical modeling of deep convecUve clouds. In: WMO, Report of the second international cloud modelling workshop, Toulouse, 8-12 August 1988, TD 268, pp. 131 - 136.

Jacob, D.J. and Prather, M.J., 1990. Radon-222 as atest of convective transport in a general circulation model. Tellus, 42B: 118-134.

Kleinman, L.I. and Daum, P.H., 1991. Vertical distribution of aerosol particles, water vapor, and insoluble trace gases in convectively mixed air. J. Geophys. Res., 96: 991-1005.

Knight, C.A. (Editor), 1982. The Cooperative Convective Precipitation Experiment (CCOPE), 18 May-7 August 1981. Bull. Am. Meteorol. Soc., 63: 386-398.

Knight, C.A., 1990. Lagrangian modeling of the ice process: A first-echo case. J. Clim. Appl. Mete- orol., 29: 418-428.

Lafore, J.-P. and Moncrieff, M.W., 1989. A numerical investigation of the organization and interac- tion of the convective and stratiform regions of tropical squall lines. J. Atmos. Sci., 46: 521-544.

Langner, J., Rodhe, H. and Olofsson, M., 1990. Parameterization of subgrid scale vertical tracer transport in a global two dimensional model of the troposphere. J. Geophys. Res., 95:13,691 - 13,706.

Lelieveld, J. and Crutzen, P.J., 1990. Influences of cloud photochemical processes on tropospheric ozone. Nature, 343: 227-233.

Lelieveld, J. and Crutzen, P.J., 1991. The role of clouds in tropospheric photochemistry. J. Atmos. Chem., 12: 229-267.

Lin, Y.L., Farley, R.D. and Orville, H.D., 1983. Bulk parameterization of the snow field in a cloud model. J. Clim. Appl. Meteorol., 22: 1065-1092.

Moncrieff, M.W., 1989. Dynamical models of the transport of momentum, gas and inert tracers by mesoscale convective systems. In: AMS, Proc. Symposium on the Role of Clouds in Atmospheric Chemistry and Global Climate, January 30 - February 3, Anaheim, Calif., pp. 264-269.

Musil, D.J., Christopher, S.A., Deola, R.A. and Smith, P.L., 1991. Some interior observations of southeastern Montana hailstorms. J. Clim. Appl. Meteorol., 30:1596-1612.

Murakami, M., 1990. Numerical modeling of dynamical and microphysical evolution of an isolated convective cloud - - The 19 July 1981 CCOPE cloud. J. Meteorol. Soc. Jpn., 68:107-128.

Orville, H.D., Kopp, F.J., Nair, U.S., Stith, J.L. and Rinehart, R., 1990. On the origin of ice in strong

R.R. Albeit, T. Hauf / Atmospheric Research 33 (1994) 259-281 281

convective cells. In: AMS, Preprints of the 1990 Conference on Cloud Physics, July 23 - 17, 1990, San Francisco, Calif., pp. 16-20.

Penner, J.E., Atherton, C.S., Dignon, J., Ghan, S. J., Walton, J.J. and Hameed, S., 1991. Tropospheric Nitrogen: A three-dimensional study of sources, distributions, and deposition. J. Geophys. Res., 96: 959-990.

Pickering, K.E., Dickerson, R.R., Luke, W.T. and Nunnermaker, L.J., 1989. Clear sky vertical profiles of trace gases as influenced by upstream convective activity. J. Geophys. Res,, 94:14,879-14,892.

Pickering, K.E., Thompson, A.M., Dickerson, R.R., Luke, W.T., McNamara, D.P., Greenberg, J.P. and Zimmerman, P.R., 1990. Model calculations of tropospheric ozone production potential following observed convective events. J. Geophys. Res., 95:14,049-14,062.

Pickering, K.E., Thompson, A.M., Scala, J.R., Tao, W.-K., Simpson, J. and Garstang, M., 1991. Pho- tochemical Ozone production in tropical sqall line convection during NASA Global Tropospheric Experiment/Amazon Boundary Layer Experiment 2A. J. Geophys. Res., 96:3099-3114.

Pickering, K.E., Thompson, A.M., Scala, J.R., Tao, W.-K. and Simpson, J., 1992a. Ozone production potential following convective redistribution ofbiomass burning emissions. J. Atmos. Chem., 14: 287-313.

Pickering, K.E., Thompson, A.M., Scala, J.R., Tao, W.-K. and Simpson, J., 1992b. Enhancement of free tropospheric ozone production by deep convection. In: AMS, Proc. Quadrennial Ozone Sym- posium, June 4 - June 13, Charlottesville, Virginia, USA.

Pickering, K.E., Scala, J.R., Thompson, A.M., Tao, W,-K. and Simpson, J., 1992c. A regional estimate of convective transport of CO from biomass burning. Geophys. Res. Lett., 19: 289-292.

Raymond, W.H. and Stull, R.B., 1990. Application of transilient turbulence theory to mesoscale numerical weather forecasting. Mon. Weather Rev., 118:2471-2499.

Scala, J.R., Garstang, M., Tao, W.-K., Pickering, K.E., Thompson, A.M., Simpson, J., Kirchhofl\ V.W.J.H., Browell, E.V., Sachse, G.W., Torres, A.L., Gregory, G.L,, Rasmussen, R.A. and Khalil, M.A.K., 1990. Cloud draft structure and trace gas transport. J. Geophys. Res., 95:17,015-17,030.

Schumann, U., Hauf, T., Htller, H., Schmidt, H. and Volkert, H., 1987. A mesoscale model for the simulation of turbulence, clouds and flow over mountains: Formulation and validation examples. Beitr. Phys. Atmos., 60:413-446.

Smolarkiewiez, P.K., 1984. A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comput. Phys., 54: 325-362.

Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology, Kluwer, 666 pp. Wang, W.-C., London, J., Isaksen, I., Shine, K., Ellingson, R. and Taylor, F,, 1992. Summary Report

of the IUGG-IAMAP Workshop MW5: Climatic Effects of Atmospheric Trace Constituents. Bull. Am. Meteorol. Soe., 73: 801-804.

Yang, H., Olaguer, E. and Tung, K.K., 1991. Simulation of the present-day atmospheric ozone, odd nitrogen, chlorine and other species using a coupled 2-D model in isentropic coordinates. J. At- mos. Sci., 48: 442-471.