Momentum Budget of a Squall Line with Trailing Stratiform

Precipitation: Calculation with a High-Resolution Numerical Model.

Momentum Budget of a Squall Line with Trailing Stratiform

Precipitation: Calculation with a High-Resolution Numerical Model.

Yang, M.-J., and R. A. Houze Jr., 1996, J. Atmos. Sci., 53, 3629-3652.

Yang, M.-J., and R. A. Houze Jr., 1996, J. Atmos. Sci., 53, 3629-3652.

Introduction The separate roles of the convective and stratiform

precipitation regions have not been investigated in terms of how they may influence the largescale horizontal momentum field.

The objective of this study is thus to investigate the momentum budget of a two-dimensional squall line with leading-line/trailing-stratiform structure and thereby gain insight into the contributions of the convective and stratiform precipitation regions to the momentum transports over a largescale region containing the storm.

Introduction To achieve this objective, they make use of

the numerical simulation results for the 10-11 June 1985 squall line in PRE-STORM (Yang and Houze, 1995a,b).

Model description 2D nonhydrostatic cloud model (Klemp and

Wilhelmson, 1978; modified by Wilhelmson and Chen, 1982)

The model has a 314-km-wide fine mesh with 1-km resolution in the center of the domain.

The model domain translates with the storm such that the simulated storm is always within the fine mesh.

Model description The initial environmental conditions are

based on the 2331 UTC 10 june 1985 sounding obtained at Enid, Oklahoma, 4h before the squall line passed this station.

The model was integrated for 15h.

Initial stage

(7.5-8.5h)

Mature stage

(10-11h)

Slowly decaying stage

(12.5-13.5h)

CV: convective precipitation

SF: stratiform precipitation

RA: rear anvil

FA: forward anvil

Storm-relative horizontal windinflow

ascending FTR

descending RTFFTR flow

vertical velocity

updraft

downdraftweak vertical motion

forced by the strong convergence

caused by the release of latent heat of condensation

mesoscale updraft

mesoscale downdraft

mesoscale ascent and descent were weaker

by the release of latent heat

adiabatic temperature increase in the unsaturaed descent air

by latent cooling of evaporation and melting

reached -10K

reached -9K

potential temperature perturbation

wider, deeper, and stronger

produced by mesoscale downdraft

pressure perturbation

meso-γ-scale low

broadens and intensifies

continues to broadens

subsidence warming

subregional contributions to the large-scale mean horizontal and vertical velocity fields large-scale area A=ACV+ASF+ARA+AFA

a physical quantity I:

– σ:

FAFARARASFSFCVCV IIIII

vertical velocity [ I = w in (2) ]

mesoscale updraft

mesoscale downdraft

storm-relative horizontal velocity [ I = u - c in (2) ]

Time-averaged momentum equation

uss

svp

sss

Dz

uw

x

uu

xc

x

uc

t

u

t

u

0

TEN PGF HAD VAD TRB

time-averaged form: dtT

T

T 2

1

1

u-momentum equation

initial stage

ADV =HAD+VAD

u-momentum equation

mature stage

Area-averaged momentum budgets

ii

ui

i

si

i

ssi

i

vpis D

z

uw

x

uu

xc

t

u

0

area-averaged form: dxL

L

0

1

u-momentum equation

mature stage

FTR RTF

FTR RTF

u-momentum equation over the large-scale area A

once the system matures, the stratiform precipitation region determines the net momentum tendency of the large-scale area A.

formulation of momentum flux

wuwuwuwu ssss

0000

The total vertical flux of storm-relative horizontal momentum into three physically distinct parts:

Ttot Sm Se Te

Sm : transport by steady mean flow

Se : transport by standing eddies

Te : transport by transient eddies

vertical flux of storm-relative momentum

emss SSwuT 0

The 1-h averaged velocity field in the simulated storm thus behaves as if the storm were in a steady state.

All of the fluxes are transporting FTR momentum upward or RTF momentum downward.

negative

The wind vectors of:

(a) domain-averaged mean flow

(b) standing eddy

(c) total wind

mesoscale circulation

FTR + weak upward motion

vertical momentum flux by standing eddies Se

6.5

convective precipitation region

momentum flux by standing eddies Se

totcv FF 75.0~65.0

Large-scale momentum budget

emsvps S

zS

zu

xxc

t

u

00

2

0

11

TEN PGF HMF VMF VEF

The primary terms determining the large-scale momentum tendency TEN are PGF and (VMF+VEF).

And this two terms tend to oppose each other.

FTR RTF

RTF

FTR

PGF

VEF

Conclusions Decomposition of total momentum flux into

three physically distinct modes – transports by steady mean flow, standing eddies, and transient eddies – shows that in the middle to upper levels, the transport by steady mean flow contributes most of the total momentum flux.

The transport by standing eddies explains most of the total momentum flux in low to middle levels.

Conclusions summarizes the momentum balance

The net momentum tendencies are a delicate imbalance of strong terms of opposite sign.

RTF

FTR

RTF

Thanks

vertical convergence of momentum flux

mL

ms

ms

Pu

Lwu

z00

2

00

11

emss SSwuT 0

Moncrieff (1992)

follow =>

mL

ms

memtot

Pu

LSS

zT

z00

2

00

111

totTz

0

1

mL

ms

m

Pu

L00

21

Convective and Stratiform precipitation

The partition between the convective and stratiform precipitation regions is based on simulated surface rainfall rate.

The convective precipitation region either has a surface rainfall rate greater than or equal to 15 mm h-1, or the gradient of rainfall rate is greater than 5 mm h-1 km-1.

The surface precipitation region not satisfying these criteria is defined as the stratiform precipitation region.