uccellini and johnson (1979)
DESCRIPTION
Uccellini and Johnson (1979). Uccellini, L. W., and D. R. Johnson, 1979: The Coupling of Upper and Lower Tropospheric Jet Streaks and Implications for the Development of Severe Convective Storms. Mon. Wea. Rev . 107, 682–703. Purpose of paper: - PowerPoint PPT PresentationTRANSCRIPT
Uccellini and Johnson (1979)
Uccellini, L. W., and D. R. Johnson, 1979: The Coupling of Upper and Lower Tropospheric Jet Streaks and Implications for the Development of Severe Convective Storms. Mon. Wea. Rev. 107, 682–703.
Purpose of paper:
To determine how the transverse ageostrophic circulation about an upper tropospheric jetstreak influences the intensity of the low level jet and the development of severe convection
Typical severe weather scenario with upper and lower level jets
Methods:
1) Theory2) Numerical model3) Observation
indirect circulation associated with the exit region of a jetstreak
Contours (vertical motion in b/s)Arrows (ageostrophic circulation)Number under arrows (ageostrophic wind (m/s))
OUR GOAL:
Derive an equation that relates the ageostropic wind
on a low level theta surface to the pressure tendency. Low level pressure changes are forced by the upper level
jetstreak.
The equation we seek will theoretically relate an
accelerating low level jet to the ageostrophic circulation
induced by the upper level jetPs
decreasingPs
increasing
JET
THEORY
The theoretical development in this paper is cast in isentropic coordinates
gg
gg U
dt
dUU
t
U
dt
Ud
dt
Ud
U
dt
dUU
t
U
dt
Ud
dt
Ud
The (vector) expansion of the total derivative in isentropic coordinates
The geostrophic momentum approximation: We approximate U by Ug except in the advection term
We will apply the geostrophic momentum approximation in this paper: Assume that the wind can be approximated by its geostrophic value except when considering advection.
gg
gg U
dt
dUU
t
U
dt
Ud
dt
Ud
From before:
Use vector form of momentum equation
fvxdt
du
gfvx
)( gvvfdt
du
Recall in scalar notation
dt
UdkfUUU gag
1
agvdt
duf 1
Substitute from (1) into (2)
(1)
(2)
ggg
gag
U
dt
dkUkUUkU
t
UkfU
1
dt
Ud
Assume adiabatic flow and neglect second term
g
gag UkU
t
UkfU
1
0dt
d smallk
g
gag UkU
t
UkfU
1
Recall from ATMOS 403 that the geostrophic wind on a theta surface is related to the gradient of the Montgomery stream function: kfU g
1
With the assumptions made above, the ageostrophic wind is related to
1. the rate of change of the pressure gradient force (i.e. geostrophic wind) on a theta surface (the isallobaric component)
2. Advection/inertial forces
where the Montgomery stream function is given by
Put in the isallobaric term and it becomes….. gU
gzTC p
t
fU iag2
,
Isallobaric contribution to the ageostrophic wind
Hydrostatic equation in isentropic coordinates
pcR
p p
pc
/
0
L
S
p
dp
pc
cR
pSL
/
0
Integration of hydrostatic equation from surface to theta surface (L)
tp
pcd
t
p
p
pc
pc
Rc
tt
p
L
S
p cR
sp
cR
pp
pSL
/
0
1/
00
Time derivative of equation above:
tp
pcd
t
p
p
pc
pc
Rc
tt
p
L
S
p cR
sp
cR
pp
pSL
/
0
1/
00
Find expression for this term
ssps gzTc
scR
ssp
s gztp
p
tc
t
p
/
0
Substitute equation for theta
pcR
sss p
pT
/
0
And take derivative
01
00
/
0
t
p
p
p
pc
Rc
tp
pc
ts
c
R
s
p
sps
cR
sp
sp
p
Substitute in top equation: last RHS term in top cancels first RHS term on bottom
From last page…
t
p
p
p
p
Rd
t
p
p
pc
p
R
ts
c
R
ss
cR
pL
pL
S
p
1
00
1/
00
Simply by using expression for s
t
p
p
RTd
t
p
pp
pcR
tss
cR
pL L
S
p
0
/
0
1
t
fU iag2
,
Isallobaric contribution to the ageostrophic windFrom a while ago
Combine equations:
L
S
p
dt
p
pp
pc
t
p
p
RT
f
RU
cR
pss
iag
1/
002,
L
S
p
dt
p
pp
pc
t
p
p
T
f
RU
cR
pss
iag
1/
002,
The isallobaric component of the
ageostrophic circulation on an
isentropic surface L…
..is related tothe gradient
of the surfacepressure
tendency ..
..and the integrated pressure tendencyBetween the surface and L
s,1s,2
L
0
t
ps
t
p
1
0
t
ps
JETEXIT
t
p
2
iagU ,
An existing low level jet will accelerate in this region, increasing shear and potential for severe weather
Model
Hybrid isentropic/sigma coordinate model used to simulate jetstreak circulations
L
lower 200 mb = coordinates
rest of atmosphere = coordinates
Initial conditions: functions designed to produce jetstreak
Mass flux divergence ( 10 g m-2 s-1)
in each quadrant of jetstreak as a function of altitude () from model
Solid (total), ageostrophic (dashed), geostrophic (dot dashed)
Air exiting column
Air entering column
ageostrophic component dominates
g
gag UkU
t
UkfU
1
Isallobaric term Inertial/advective term
Streamline analysis at the level of the jet streak due to the inertial advective term
At the level of the jetstreak, the pressure tendency is small (weak isallobaric effect), but advection/coriolis force effects are large
L
S
p
dt
p
pp
pc
t
p
p
RT
f
RU
cR
pss
iag
1/
002,
At low levels, the isallobaric effect dominates, creating the ageostrophic acceleration of the winds toward the north under the exit region of the jet
Ageostrophic flow forced by along stream variations in PGF at jetstream level
Isallobaric ageostrophic wind on a lower isentropic surface beneath jet
Entrance Exit
P P
Surface pressure falls in exit region lead to ascent of theta surfaces and isallobaric acceleration upward and northward along potential temp surface
Differential diabatic heating has the same effect
Cool here
Heat here(latent heatin convection)
Heating transportsmass from belowto above L
P on isentropic surf
P on isentropic surf
An example case study:
This study chosen because there was a jetstreak in the upper troposphere, but no low level jet in the lower atmosphere.
The development of the LLJ could be attributed to the isallobaric accelerations associated with the jetstreak circulation.
Surface charts for the 12 hour period
330 K isotachs and Mongomery streamfunction
300 K isotachs and Mongomery streamfunction
300 K pressure and mixing ratio
Jetstreak propagating eastward
No cross-jet flow here
SW 20 m/s LLJ between Kentucky and Pennsylvania flowing from 900 to 700 mb
Moist air intrusion
Downward extension ofUpper jetstreak
Another view of upper jetstreak and LLJ on isobaric surfaces
Note angle between the isotachs and height contours:
LLJ represents ageostrophic flow associated with isallobaric forcing
340 K
300 K
Surface
340 K
300 K
Surface
Mass tendencies in layers bounded by isentropes or surface
Green: increasing with timeRed: decreasing with time
12Z 10 May
00Z 11 May
Note the four quadrant jetstreak pattern
Actual data in cross section illustrating same effect
305 K
325 KPotential
temperature
Wind speed
J
J
L
S
p
dt
p
pp
pc
t
p
p
T
f
RU
cR
pss
iag
1/
002,
Evaluation of the integrated pressure tendency term in the equation for the isallobaric ageostrophic wind
on 300 K surface
iagU ,
L
S
p
dt
p
pp
pc
t
p
p
T
f
RU
cR
pss
iag
1/
002,
Term 1: Isallobaric wind
Term 3: Integrated
pressure tendencyTerm 2: Surface
pressure tendency
Further illustrates lower level ageostrophic flow induced by upper level jet streak
Cross sections from Omaha, Nebraska to Tetersboro, New Jersey
Normal wind
Moisture flux
Sensible Heat flux
Implications of coupled jet streaks for convective
storm development
Intensification of the LLJ by isallobaric forcing:
1) significantly increases lower atmospheric moisture flux
2) Significantly increases lower atmospheric sensible heat flux
3) enhances low level shear
THEREFORE:
enhances environment for severe storm development