Why is there ascent on the cold
sid
ide off equator?
?
Meridional pressure gradient above the PBL:
wM
wy
V x ’v 2: sin T u
1 wv
#
2: sin T u
2 wwyy
2
1
Hydrostatic:
M PBL M R
o
wM pbl
wy
'p pbl
p
Tv pbl
'p pbl § wTv ·
wM
R
¨
¸
wy
p © wy ¹ pbl
'p pbl § wTv ·
1 wv
2: sin T u R
¨
¸
2 wy
p © wy ¹ pbl
2
2
PBL momentum:
V x ’v Fv
§ wM ·
¨
¸ 2: sin T u pblbl
© wy ¹ pbl
'p pbl § wTv ·
1 § wv 2 ·
1 § wv 2 ·
o ¨
¸ Fv # ¨
¸ R
¨
¸ 2: sin T u u pbl 2 © wy ¹ pbl
2 © wy ¹
p © wy ¹ pbl
|V|
v
Fv # CD
h
h ~ CD 'y
Fv dominant when
C
D
10
3
3
Thin frictionally dominated PBL:
Thin,
'p pblbl
|V|
CD
v#R
h
p
§ wTv ·
¨
¸ 2: sin T u © wy ¹ pbl
u constrained by angular momentum
conservation:
umiin
umax
:a
ª¬sin 2 T sin 2 T 0 º¼ ,
cos T
:a
2
sin T
cos T
4
Cold side of equator:
'p pbl § wTv ·
|V|
2
2
2
ª
T
T
T 0 º¼
sin
sin
CD
v#R
2:
a
tan
¨
¸
¬
h
p © wy ¹ pbl
Warm side of equator:
'p pbl § wTv ·
|V|
2
2
CD
v#R
¨
¸ 2: a tan T sin T
h
p © wy ¹ pbl
5
6
'p pbl
50 mb
7
'p pbl
100 mb
8
'p pbl
200 mb
9
January Zonal Mean OLR, Vertical and Meridional Wind, 19791993 from ECMWF
latitude
Contour interval 1 mm s-1
Shading Red Positive (Upward)
10
July Zonal Mean OLR, Vertical and
Meridional Wind, 19791993 from ECMWF
latitude
Contour interval 1 mm s-1
Shading Red Positive (Upward)
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Two--D primitive equation model
Two
• Parameterizations of
– convection
– fracti
tionall clloudiness
di
– radiation
– surface fluxes
• Ocean mixed layer energy budget
• Model forced by annual cycle of solar
radiation
• Available for class projects
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MIT OpenCourseWare
http://ocw.mit.edu
Spring 20
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