Transcript Horizonal Analysis, Forces, & Flows

Things to look for on the weather maps
Visible and IR satellite images (& radar too):
Look at cloud movements and locations - do
they correlate with what you would expect
from the surface or 500mb pressure patterns?
How can you distinguish between high and low
level clouds and between deep and shallow
clouds?
VIS
IR
Things to look for on the weather maps
Surface: Look for locations of high and low
pressure centers, warm and cold fronts,
regions of high winds, rain, snow, drylines, or
other significant weather.
Things to look for on the weather maps
850mb: Use this map to look at temperature
gradients, and to find regions of warm or cold
air advection. It is also important to look at
the moisture field and advection at this level
if available (low-level moisture).
Things to look for on the weather maps
500mb: Where are the troughs and ridges?
Where are the troughs and ridges in relation
to the high and low pressure systems on
surface maps (Positive Vorticity Advection &
Negative Vorticity Advection)?
Things to look for on the weather maps
300mb: Use this map to look for jet streaks,
or elongated pockets of very strong winds
embedded in the jet stream. Jet streaks
generally occur above regions of strong
temperature gradients that you would find on
the 850mb map. Why?
Forces
Forces govern the atmospheric motions
Pressure gradient force
Coriolis force
Gravity
Friction
Momentum equations
du
1 p

 2Ω  sin φ  v  2Ω  cos φ  w  Fx
dt
ρ x
dv
1 p

- 2Ω  sin φ  u  Fy
dt
ρ y
dw
1 p

 g  2Ω  cos φ  u  Fz
dt
ρ z
where Ω is the angular velocity of the Earth.
φ is the latitude.
Coriolis Force
A'
ball
O
*
A, B'
reference point
(fixed star)
B
A
*
B
O
v2 w d
v1
d
x
Ow
x<<d
Deflect to the right on the northern hemisphere, and to
the left on the southern hemisphere.
Coriolis Force
v1
O
v2 w d
d
x
w
x<<d
Given Coriolis acceleration a, the distance is
1
x = a • t2
2
Travel time:
t  d / v1
1 d
x  a   
2  v1 
2
ωd
1 d
dis tan ce, x  v2 t  ω  d  t 
 a 
v1
2  v1 
2
 a  2ωv1
2
Coriolis Force
N



z


is latitude angle
If w is that due to the earth’s rotation about
a local vertical axis, such that
ω = Ωz = Ω sin φ
Then
a = (2Ω sin φ) v1
= fv 1
(= Coriolis force if M = 1 kg)
where f = 2Ω sin φ (Coriolis parameter)
Forces
Forces govern the atmospheric motions
Pressure gradient force
Coriolis force
Gravity
Friction
Momentum equations
du
1 p

 2Ω  sin φ  v  2Ω  cos φ  w  Fx
dt
ρ x
dv
1 p

- 2Ω  sin φ  u  Fy
dt
ρ y
dw
1 p

 g  2Ω  cos φ  u  Fz
dt
ρ z
where Ω is the angular velocity of the Earth.
φ is the latitude.
Pressure Gradient & Pressure Gradient Force
960mb
1000mb
Positive pressure
gradient but
negative pressure
gradient force
in the x direction.
p
Δp

x
Δx
1 p
1 Δp


ρ x
ρ Δx
1000mb 960mb
Negative pressure
gradient but
positive pressure
gradient force
in the x direction.
Pressure gradient
Pressure gradient force
• Why do we want to know sea level pressure (SLP)?
• Why do we want to know pressure gradient?
Nature coordinate
s: along the wind direction
n: perpendicular to the wind direction,
positive to the left.
V
y
x
The nature coordinate can be obtained
by rotating the Cartesian Coordinate
until the x direction is along the wind
direction.
Then, x is in the s direction and y is in
the n direction.
And u=V and v=0
Estimate Pressure Gradient
How to calculate pressure gradient at point O?
P2
P2(xo,y2)
H
Po
P1
P2(x2,yo)
O
(x0,yo)
P1(x1,yo)
L
P1(xo,y1)
∇Hp =
Δp
Δp
î +
ĵ
Δx
Δy
| ∇Hp |=
Δp2 Δp2
+
Δx
Δy
Pressure Gradient & Pressure Gradient Force
How to calculate real distance Δx, Δy, Δn ?
1 o lat = ? km
Re
circumfere nce = 2πR e ,
where R e = 6371 km
=> 1o lat :
2π × 6371 km / 360o ≈111 km per degree
Dlat = lat2 – lat1
Dy= Dlat x 111 km per degree
Pressure Gradient & Pressure Gradient Force
How to calculate real distance Δx, Δy, Δn ?
Dx
r
Re
φ
r  Re  cos(lat)
circumfere nce = 2πr
1o long = 2π × 6371 km × cos(φ) / 360o
≈111 km × cos(φ)
Dlong = long2 – long1
Dx= Dlong x 111 km x cos(j)
Pressure Gradient & Pressure Gradient Force
Pressure gradient at point O:
P2
H
Po
P1
P1(x1,yo)
O
(x0,yo)
P2(x2,yo)
L
Δp p2  p1
p2  p1


Δx x2  x1 Δlong  111 km  cos( φ)
Pressure Gradient & Pressure Gradient Force
Pressure gradient at point O:
P2
P2(xo,y2)
H
Po
P1
O
(x0,yo)
L
P1(xo,y1)
Δp p2 - p1
p2 - p1
=
=
Δy y2 - y1 Δlat × 111 km
| ∇Hp |=
Δp2 Δp2
+
Δx
Δy
Pressure Gradient & Pressure Gradient Force
Or using the nature coordinates
P2
y2
H
Po
Δn
P1
O
(x0,yo)
P1(x3,y3)
(y4-y3)
x1
P2(x4,y4)
x2
(x4-x3)
L
y1
p2  p1
p 
Δn
Δn 
(x4  x3 )2  (y4  y3 )2 ,
shortest distance
Pressure Gradient
Horizontal pressure gradient vs.
vertical pressure gradient
p
  ρg ~ 10 kg m-2 s-2 in the lower atmosphere .
z
 Hp ~ 10  2 to 10 -3 kg m-2 s-2
Vertical pressure gradient force is much
greater than the horizontal one, but is
mostly balanced out by gravity. So, the
motion in the atmosphere is dominated by
horizontal winds.
Geostrophic flow (Vg)
The horizontal pressure gradient force (P)
is balanced by the Coriolis force (C).
P
.
988
P
992
P
.
996
1000
P
.
rest
.
Vg
C
C
C
O
1 ∂p
= -fVg , where f = 2Ω × sinφ
ρ ∂n
dVg
1 ∂p
1 ∂p
== 0, Vg = dt
ρ ∂s
fρ ∂n
Not happen often in the real world. If it does,
this is seen in large scale.
Gradient wind flow (VG)
P
VG
C
P
VG
C
VG < Vg
Subgeostrophic
1 ∂p
fVG > ρ ∂n
1 ∂p
fVg = ρ ∂n
=> VG > Vg
Supergeostrophic
If one uses geostrophic wind to approximate
gradient winds, what happens?
VG2
1 ∂p
= -fVG ;
ρ ∂n
R
dVG
1 ∂p
==0
dt
ρ ∂s
This is for large scale flow since
Coriolis force is important.
Gradient wind flow (VG)
500 mb Wind Vectors
Surface Weather Map
Any difference from the 500-mb one?
Because of what? Friction!
L
Friction
996
P
1000
P
P
V  Vg
V  Vg
V
V
F
F
1004
1008
P
F
C
geostrophic balance
C
C
unbalanced flow
C
balance with friction
Friction is proportional to the roughness of
the Earth’s surface and wind speed, and is
opposite to the wind moving direction.
Wind turns toward to the low pressure side !!!
Flow with friction
Divergence
Convergence
Good weather but
Stormy weather potentially bad for air quality
This is for large scale flow too
since Coriolis force is important.
Cyclostrophic wind flow
Vc
P
P
Vc
Vc2
1 p

ρ n
R
This is for small scale when Coriolis force is not
important!
This flow can exist only around a low pressure,
and the force needed to change the wind
direction is provided by the pressure gradient
force.
So, dust devils and tornadoes can turn either
cyclonically or anticyclonically.