Past and future
changes in Sahel
rainfall: Possible
mechanisms
Kerry H. Cook
Department of Earth and Atmospheric Sciences
Cornell University
Ithaca NY
Present some of the dynamical processes that are
responsible for variability in the Sahel on all time
scales
paleoclimate – the African Humid Period
decadal (Samson Hagos)
interannual
intraseasonal
The African Humid Period
with Christina Patricola
African Humid Period
Present Day
AHP
Vegetation for (a) present day (b) and African Humid Period according to Hoelzmann et al.
(1998) with grassland - 7, shrubland - 8, savanna - 10, evergreen broadleaf forest - 13, and
desert -19.
Enhancement of the
westerly low-level jet is a
primary
moisture source.
Note that the southerly lowlevel southerly flow
is unchanged.
The African easterly jet is not a part of the AHP climate
The Monsoon Jump
with Samson Hagos
Coastal
“Sahel”
Smoothed rainfall in mm/day from TRMM (top) and FEWS (bottom)
2004
Coastal
Sahel
Daily rainfall in mm/day from TRMM
2002, 2003, 2005, 2006
Precipitation difference:
“Sahel” – “Coast”
Precipitation difference:
“Sahel” – “Coast”
monsoon onset
2002:
2003:
2004:
2005:
2006:
July 14
June 24
June 16
July 8
July 10
The regional model
captures the monsoon
jump
X
Pre-monsoon onset
A permanent sensible heating maximum exists from about 10N-12N:
relatively low albedo => shortwave radiation maximum and
net total radiative heating maximum
This sensible heating drives a shallow meridional circulation (Zhang
et al. 2006)
low-level moisture convergence
moisture transport into the middle layer (825 -525 hPa),
divergence
The radiative forcing increases through the spring and, near the
middle of May, the gradually increasing moisture supply from the
boundary layer begins condensing in the middle layer
=> condensation and precipitation increases in the continental
interior
Monsoon Onset
The condensational heating in the 825 - 525 hPa layer introduces
a meridional pressure gradient in this layer which results in an
inertial instability
=> coastal region becomes unfavorable for convergence
=> maximum precipitation abruptly shifts from the coast
into the Sahel
Eastern Sahel: Another "Monsoon Jump"
Two-Stage Monsoon Onset over Ethiopia
with Emily Riddle
Low-level 910 mb winds
Pre-onset
Mar 1 – Mar 31
Transitional
Apr 20 – May 15
Post-onset
Jun 1 – Jun 30
The precipitation dipole response
to SSTAs in the Gulf of Guinea
with Edward Vizy
Surface Temperature Anomalies
A prominent mode
of interannual
variability:
~ 25% of the years 1950 –
2000 are identified as dipole
years (12 years)
Extremely high correlation
with warm SSTAs in the
Gulf of Guinea during dipole
years
1984 Precipitation Anomalies
A north/south cross-section along the Greenwich meridian
Streamlines (v, wx10-2) and meridional velocity (m/s)
A north/south cross-section along the Greenwich meridian
Vertically-confined
monsoon inflow
AStreamlines
north/south cross-section
(v, wx10-2) and
along
meridional
the Greenwich
velocity
meridian
(m/s)
2nd selection criterion: Reasonable monsoon circulation
Subsidence over
the Gulf of
Guinea
Streamlines (v, wx10-2) and meridional velocity (m/s)
Southward mid-tropospheric
flow (African easterly jet)
Saharan high
thermal low
Streamlines (v, wx10-2) and meridional velocity (m/s)
Top: Climatological circulation
From a regional climate model.
Bottom: Circulation anomalies
associated with warming in the
Gulf of Guinea and the dipole
precipitation mode.
Anomalously high rainfall along
the Guinean coast occurs in
association with an increase in
the moisture content of the
monsoon inflow. Subsidence
over the Gulf of Guinea
suppresses the precipitation
anomaly over the ocean.
With warm SSTAs in the
Gulf of Guinea, the
southward outflow from the
Saharan high has a larger
meridional extent, and is
located closer to the surface.
These differences in the outflow
generate subsidence
and drying over the Sahel
due to shrinking of both
planetary and relative
vorticity.
Cold Air Surges and
Monsoon Breaks
with Edward (Ned) Vizy
What is a cold surge?
• Mid-tropospheric
ridge/trough pattern
• Shallow dome of cold
air with a sharp
temperature gradient
along it’s leading edge
• Typically moves along
topography, e.g., east
of the Rockies and
Andes
Fig 2. from Garreaud (2001): Conceptual model of
a cold surge moving from mid-latitudes
The climatology summer mid-tropospheric geopotential height field
does have the ridge/trough pattern
Topography (m) and June-August climatological 500 hPa geopotential
heights (m) and winds (m/s) from the NCEP2 reanalysis
The climatological summer mid-tropospheric height
field has the ridge/trough pattern
eastern
Mediterranean
Saharan
high
Topography (m) and June-August climatological 500 hPa geopotential
heights (m) and winds (m/s) from the NCEP2 reanalysis
A
B
C

D
E

F
 
 p 
T Q  p 

     p  vT 

   
 v   pT   
t c p  po 
p
 po  p
A. Local rate of change of temperature (negligible)
B. Mean diabatic heating and cooling term (calculated as a
residual from the NCEP2)
C. Mean vertical advection of potential temperature term
D. Mean horizontal advection of temperature term (Zonal +
Meridional components)
E. Vertical transient term
F. Horizontal transient term
A
B

C
D
E
F

 
 p 
T Q  p 

     p  vT 

   
 v   pT   
t c p  po 
p
 po  p
850 hPa JJA
Thermodynamical
Budget Analysis
B
C
E+F
D
D
D
• Strong mid-tropospheric subsidence over the
eastern Mediterranean Sea
June-August Climatological Vertical-p velocity along 35N
NW Africa
E. Med Sea
Daily TRMM
rainfall rates
(mm/day) and
850 hPa wind
convergence
(contoured) for a
JULY 2005 cold
air surge event
Precipitation
climatology in
the current
generation of
climate models
1949 – 2000
JJAS
Coastal
“Sahel”
Daily rainfall in mm/day from TRMM (top) and FEWS (bottom)
2004
Coastal
Sahel
Smoothed rainfall in mm/day from TRMM (top) and FEWS (bottom)
2004
Coastal
Sahel
Daily rainfall in mm/day from TRMM
2002, 2003, 2005, 2006
Daily rainfall in mm/day from FEWS
2002, 2003, 2005, 2006
Precipitation difference:
“Sahel” – “Coast”
monsoon onset
2002:
2003:
2004:
2005:
2006:
July 14
June 24
June 16
July 8
July 10
The regional model
captures the monsoon
jump
Cold Surges
A type of monsoon break
Long term goal: Predicting monsoon onset
(monsoon jump)
Why does the jump occur?
What controls the timing of the monsoon
onset?
Does the timing of the onset correlate
with seasonal precipitation totals?
Is there a relationship with interannual
variability?
…. etc
Long term goal: Predicting monsoon onset
(monsoon jump)
Why does the jump occur?
What controls the timing of the monsoon
onset?
Does the timing of the onset correlate
with seasonal precipitation totals?
Is there a relationship with interannual
variability?
…. etc
The West Frican monsoon jump is a consequence of inertial
instability that develops in the coastal region
above the boundary layer (825 -525 hPa layer)
Hagos and Cook 2007: Dynamics of the West African
Monsoon Jump. J .Climate)
The West Frican monsoon jump is a consequence of inertial
instability that develops in the coastal region
above the boundary layer (825 -525 hPa layer)
Hagos and Cook 2007: Dynamics of the West African
Monsoon Jump. J .Climate)
A reminder about inertial instability …
Consider a geostrophic, zonal basic state flow in the
Northern Hemisphere.
ug ,2
Fp 
1
 f1u g ,1
y
u g ,1
F cor   f1ug ,1
Perturb the parcel to the north …
Fp 
ug ,2
u g ,1
 2
 f u g ,1
y
F cor   f 2ug ,1
Fp 
ug ,2
 2
 f 2u g ,2  f 2u g ,1
y
F cor   f 2ug ,1
u g ,1
Fp 
 2
 f 2u g ,1
y
the parcel will return southward (stable).
If F p  
 2
 f 2u g ,1
y
the parcel will continue northward (unstable).
If
So inertial instability is caused by an imbalance between
pressure gradient forces and inertial forces:
dv

  fu 
dt
y
X
For example, in line with the idea of inertial instability, consider a parcel of air located at
point X on the zero contour of acceleration (Fig. 10a). Initially its acceleration is zero. Any
northward displacement would move the parcel into a region of positive net force and cause it to
accelerate further into the continent. Likewise, a parcel displaced southward is also accelerated
further southward. Therefore, because of inertial instability the coastal region (the region
surrounded by the contour of zero acceleration) becomes unfavorable for meridional
convergence in the end of May and the meridional wind convergence jumps into the continental
interior where convergence is sustainable.
Comparing Fig. 10b, which shows the sum of the first two right hand side terms of Eq.
(5), with Fig. 10a indicates that the change in sign of the meridional acceleration is related to a
change in the balance between the Coriolis and pressure gradient forces, while friction delays
the process by about three days. Thus, the condition for northward acceleration and the
associated shift in meridional convergence is a change in sign of -fu-dphi/dy For a geostrophic,
So inertial instability is caused by an imbalance between
pressure gradient forces and inertial forces:
 fu g
dv

  fu 
dt
y

dv
 f ug  u
dt

So inertial instability is caused by an imbalance between
pressure gradient forces and inertial forces:
 fu g
dv

  fu 
dt
y


dv
 f u g  u   fua
dt
Inertial instability is related to angular momentum and
vorticity by considering the stability of a parcel that is
displaced meridionally
y0 to y0   y
in the geostrophic, zonal background flow.
Apply the v-momentum equation at the new location for the
displaced parcel
dv
dt
y
0  y
 f  y0   y  u g  y0   y   u  y0   y  
But
since the parcel’s velocity at y0 is
u  y0   y   ug  y0   f  y the geostrophic background velocity
and
ug  y0   y   u g  y0  
So
dv
dt
or
ug
y
y
using a 1st order expansion
about y0
u g


 f u g  y0  
 y  u g  y0   f  y 
y
y  y


0
absolute vorticity
dv
dt
u g 

f f 
 y
y 
y  y

0
  f 
for v  0
and u  u g
For the application to the WAM jump, we are looking for the conditions
under which a northward displacement in the Northern Hemisphere is
unstable:
Unstable solution dv
dt
dv
dt
y
0  y
 0 for
f 0
and  y  0
u g 
u g

f f 
  0
  y  0 if f 
y 
y
y  y

0
This is the condition for
inertial instability
over West Africa relevant
to the monsoon onset
This is the theory, assuming
• purely zonal, geostrophic basic flow
• no friction
• neglected terms in Coriolis force/curvature, vertical velocity
But is this really what happens over northern
Africa to reposition the precipitation maximum in a relatively
short time?
Can’t tell (so far!) from the observations – not fine enough,
going to try using AMMA observations.
But we have a modeling study completed that I want to tell
you about, and how you the inertial instability at work.
du

 fv 
 Fx
dt
x
dv

  fu 
 Fy
dt
y
The regional model
captures the monsoon
jump
X
For example, in line with the idea of inertial instability, consider a parcel of air located at
point X on the zero contour of acceleration (Fig. 10a). Initially its acceleration is zero. Any
northward displacement would move the parcel into a region of positive net force and cause it to
accelerate further into the continent. Likewise, a parcel displaced southward is also accelerated
further southward. Therefore, because of inertial instability the coastal region (the region
surrounded by the contour of zero acceleration) becomes unfavorable for meridional
convergence in the end of May and the meridional wind convergence jumps into the continental
interior where convergence is sustainable.
Comparing Fig. 10b, which shows the sum of the first two right hand side terms of Eq.
(5), with Fig. 10a indicates that the change in sign of the meridional acceleration is related to a
change in the balance between the Coriolis and pressure gradient forces, while friction delays
the process by about three days. Thus, the condition for northward acceleration and the
associated shift in meridional convergence is a change in sign of -fu-dphi/dy For a geostrophic,
Because of the distribution of albedo and surface moisture availability, a
permanent sensible heating maximum exists around 10N. This sensible heating drives a
shallow meridional circulation (Zhang et al. 2006) and moisture convergence at that latitude.
During the second half of May, an imbalance between the moisture flux
from the boundary layer and divergence in the middle layer results in a net supply of
moisture and condensation (Figs. 5b and 7b). This condensation warms up the
continental middle layer, while the evaporation of rain and radiation cool the middle layer
along the coast (Fig. 11).
The resulting pressure gradient results in an inertial instability, which abruptly
shifts the meridional wind convergence maximum from the coast into the continental
interior on around May 29. This introduces a net total moisture convergence, net upward
moisture flux and condensation in the upper layer, and the enhancement of precipitation
in the continental interior (Figs. 10, 8, and 5a).
During the month of June, because of the shift of the meridional convergence into
the continent and downward flux of moisture into the boundary layer, upper layer
condensation and precipitation along the coast gradually disappear.
North/south circulation
in coupled GCMs with
reasonable precipitation
climatologies
NCEP/NCAR Reanalysis
Governing equations, neglecting friction and assuming that the
basic state is
v  u g iˆ
i.e., v = 0 and   0
x
Then the approximate momentum equations are
du
dy
 fv  f
 u  f  y
dt
dt
and
dv

  fu 
 f ug  u
dt
y


Governing equations, neglecting friction and assuming that the
basic state is
v  u g iˆ
i.e., v = 0 and   0
x
Then the approximate momentum equations are
du
dy
 fv  f
 u  f  y
dt
dt
fufug
g
and
dv

  fu 
 f ug  u
dt
y


Consider the stability of a parcel that is displaced meridionally from
y0
to
y0   y
in this geostrophic, zonal background flow. When it is displaced
northward (poleward) over West Africa, will it
return southward? = stable solution,
dv
0
dt
continue northward? = unstable solution, dv  0
dt
stay in the new location? = neutral solution
dv
0
dt
Evaluate the v-momentum equation at the new location for the
displaced parcel
dv
dt
y
0  y
 f  y0   y  u g  y0   y   u  y0   y  
Again, Holton’s derivation doesn’t distinguish between f at the
displaced location and the initial location:
f  y0   y   f 
dv
dt
y
0  y
 f u g  y0   y   u  y0   y  
The above equation provides a good physical interpretation of inertial
instability. If the displaced parcel’s zonal velocity is different from the
geostrophic zonal velocity at the new location, there will be a net
meridional acceleration because the velocity-dependent Coriolis force
will not balance the pressure gradient for in the new location.
Evaluate the v-momentum equation at the new location for the
displaced parcel
dv
dt
y
0  y
 f  y0   y  u g  y0   y   u  y0   y  
Again, Holton’s derivation doesn’t distinguish between f at the
displaced location and the initial location:
f  y0   y   f 
dv
dt
y
0  y
 f u g  y0   y   u  y0   y  
uageostrophic
The above equation provides a good physical interpretation of inertial
instability. If the displaced parcel’s zonal velocity is different from the
geostrophic zonal velocity at the new location, there will be a net
meridional acceleration because the velocity-dependent Coriolis force
will not balance the pressure gradient in the new location.
If the parcel velocity at the new location is greater than the
geostrophic velocity at the new location, then the parcel is
“super-rotating” and will be directed back toward the equator
by Coriolis accelerations. This is the stable case. If the parcel
velocity at the new location is less than the geostrophic velocity
at the new location, then the parcel is “sub-rotating” and will be
directed away from the equator by Coriolis accelerations.
This is the unstable case.
uageostrophic  0
stable
uageostrophic  0
unstable
Holton goes on to rewrite the above equation.
from the u-momentum equation,
u  y0   y   ug  y0   f  y since the parcel’s velocity at y is
0
the geostrophic background velocity
and
ug  y0   y   u g  y0  
So
dv
dt
ug
y
y
using a 1st order expansion
about y0
u g


 f u g  y0  
 y  u g  y0   f  y 
y
y  y


0
or
dv
dt
u g 

f f 
 y
y 
y  y

0
Why does this happen over West Afric and not over other places?
For example, does the South America monsoon onset this way? Is
this common in mid-latitude flows?
JJAS GPCP (1979 – 1999)
JJAS CRU (1961 – 1990)
JJAS GPCP (1979 – 1999)
JJAS CRU (1961 – 1990)
JJAS GPCP (1979 – 1999)
JJAS CRU (1961 – 1990)
JJAS GPCP (1979 – 1999)
JJAS CRU (1961 – 1990)
Summer Precipitation Climatology (mm/day)
Regional Model
A tropical, climate
version of MM5
grid spacing 90 km
23 vertical levels
time step 90 s