Dynamical similarities and differences between cold fronts and density currents
Victoria Sinclair
University of Helsinki
15.08.2011 [email protected] www.atm.helsinki.fi/~vsinclai
Some cold fronts can be visually similar to density currents
Tower observations (Shapiro et al 1985)
w and θ
Model simulation of a cold front (dx = 2.5km)
Questions
• What is the force balance across a cold front?
• How does the force balance compare to theoretical predictions?
• Is the force balance across a cold front similar to that across a density current?
– Are cold fronts dynamically related to density currents?
Potential temperature, surface pressure and location of nested domains
3D Idealised experiments with WRF
3D baroclinic life cycle with nested domains
dx = 100km, 20km, 4km
WRF-ARW v3.2, Non-hydrostaticYSU BL scheme over a sea surfaceNo moistureSimulate a cold front and a density current
Drop a cold bubble and allow to spread
dx = 4km
Potential temperature, wind
Scale Analysis for fronts
l α β ACC
along
PGF alon
g
COR
along
ACC
across
PGF across
COR across
100km
1 0.1 1 1 1 0.01 1 1Semi – Geostrophic theory: we can neglect the acceleration only in the across front direction
(Hoskins and Bretherton, 1972)
dx = 100km Force balance across cold front
Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant acceleration
dx = 4km Force balance across cold front
Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant accelerationPurple: BL force
Along front forces z=100m
dx =100km dx = 20km dx = 4km
PGF COR
BL ACC
Across front forces z=100m
dx =100km dx = 20km dx = 4km
PGF COR
BL ACC
Cold front vs. Density Current
Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force
Across front z = 100m dx = 4km
Cold front Density current
Cold front vs. Density Current
Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force
Along front z = 100m dx = 4km
Cold front Density current
Conclusions
The force balance is resolution dependent
For the cold front at dx = 4km, PGF ≈ Coriolis force in the along front direction PGF >> Coriolis force in the across front direction
In the across front direction, the cold front force balance approaches that of the density current as resolution increases.
In the along front direction the cold front force balance differs to the density current force balance
Across the cold front, the unbalance pressure gradient force is likely due to enhanced horizontal buoyancy gradients.
Cold fronts have a large variety of structures
ΔT= 10K
Δt =5hrs
ΔT= 2K
Δt =30 mins
Temperature Temperature, pressure, rain rate
Density Current force balance
Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force
z = 1 km dx = 4km
Cold front force balance
Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force
z = 100m dx = 4km
Cold front force balance
Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force
z = 1 km dx = 4km
Scale Analysis - revisited
l α β ACC
along
PGF alon
g
COR
along
ACC
across
PGF across
COR across
20 km
7.5
0.5 1 1 0.13 1.8 3.3 1
Use U, V and l from the WRF simulation
Boundary layer processes are not included in Semi Geostrophic theory
Why do the results differ to theory?
Two assumptions
U/VV
115 20 7.5V ms l km 0.5
Scale Analysis - Hoskins and Bretherton (1972)
ACROSS FRONT
ALONG FRONT
Rossby number is assumed to be O(1)
Along front wind is assumed to be much greater than along fronts wind
∆x=100km. No Boundary layer scheme
Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant acceleration
What do these terms really mean?
u vDiv
x y
0u
t
0u
t
X
U
CF
Increases convergence
Strengthens front0u
t
0u
t
Decreases convergence
Weakens front
What do these terms really mean?
v u
x y
0v
t
0v
t
X
V
CF
Decreases vorticity0v
t
0v
t
Increases vorticity
Effect of resolution of frontal structure
The cross front scale decreases with increasing resolution and the wind shift becomes sharper
Potential temperature and wind barbs at z=100m
Effect of PBL on vertical structure of front
YSU PBL dx = 4kmNo PBL dx = 4kmPotential temperature (2K), system relative wind vectors.
Ascent is shaded. Descent contoured. Scales differ by a factor of 10
Density Current dx=4km.t=1.5 hours, z=100m, YSU BL scheme
Potential temperature and wind vectors
Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant accelerationPurple: BL force