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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.
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
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
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
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.
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
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
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.