www.ec.gc.ca
One-Dimensional Variational
Assimilation of SSM/I
Observations in Rainy
Atmospheres at
Environment Canada (EC)
Science & Technology Branch
G. Deblonde
J.-F. Mahfouf
B. Bilodeau
D. Anselmo
6 October 2006
Motivation
• Development at EC of an assimilation system of
satellite radiances in cloudy and rainy regions (over
open oceans)
• Operational NWP centers
– JMA : Mesoscale 4D-Var assimilation of radar
precipitation
– NCEP : Global 3D-Var assimilation SSM/I and TMI
derived rainfall rates
– ECMWF : Towards a global 4D-Var assimilation of
SSM/I radiances in rainy areas
10/6/2006
• Two step method (1D-Var+4D-Var) operational since
Page 2006
2
June 2005 (Bauer et al.
a and b, QJRMS)
Proposed strategy
Marécal and Mahfouf (2000,2002) -SRR
Moreau et al. 2004 -Tb
Observations
MW Brightness
Temperature
Control variables
Profiles of T and Q
Observation operator (1)
Precipitation Schemes
1D-Var
Observations
Surface
Rainfall Rate
Observation operator (2)
Radiative Transfer Model
Integrated Water Vapor
10/6/2006
Page 3
QC
4D-Var
Experimental set-up
• Control variable : T and ln(q) profiles (58 levels)
• Observations : SSM/I brightness temperatures (Tb) or derived
surface rain rates (SRR) (Bauer et al. 2002)
• Observation operator :
– Moist physical processes : same as in EC global
forecast model (GEM) –jacobians obtained by finite
difference
– Radiative transfer model : RTTOV with scattering effects
(Bauer and Moreau, 2002) –jacobians obtained by adjoint
method
• Background error statistics : “NMC” method (lagged forecasts)
as in EC operational 4D-Var (incremental)
• Two case studies (40S-40N):
4
– Tropical Cyclone Zoe (F15) Page
& Typhoon
Chaba (F14)
10/6/2006
Background Term
•
Forecast Model:
– Global Environmental Multi-Scale (GEM) MESOGLOBAL -research
– Model Resolution: 0.45o longitude x 0.3o latitude grid
– 58 vertical levels, model lid at 10 hPa, time-step = 15 minutes
•
Moist physical schemes:
– Shallow Convection: KuoTrans -> only cloud liquid water
– Non-convective (or stratiform): CONSUN (Sundqvist variant)
– Deep Convection: Kain-Fritsch (CAPE) ->highly non-linear
•
12-h precipitation spin-up:
 1D-Var background field = 12-h forecast
10/6/2006
Page 5
Number of SSM/I Tb channels assimilated
Tb37V ! Tb37 H
P"
Tb37Vclear ! Tb37 Hclear
2
P &# % e
$2" / cos(! )
(Petty 1994)
•
P is a measure of visibility of sea-surface relative to expected value in
absence of clouds
P=0 => completely opaque rain cloud
P=1 => cloud-free ocean scene
If P > 0.15 ( =Transmittance > 0.4) then Use (19V,H,22V, 37 V,H)
Else Use 19V,H, 22V ONLY
!
10/6/2006
Page 6
Brightness Temperature (K)
at 19 GHz V 2002 12 27 000 UTC
GEM Mesoglobal 12h Forecast
SSM/I F15 Observations
K
10/6/2006
Page 7
Tropical Cyclone Zoe
Experiments
1D-Var Tb Observation Error (K)
10/6/2006
Page 8
70
60
Observation Error (K)
• 1D-Var Tb – Small Observation
Errors (SOE)
– (O+F) = 3 K for V channels &
6 K for H channels (as in
Moreau et al. 2004)
• 1D-Var Tb – Large Observation
Errors (LOE)
– (O+F) = HBHT
• 1D-Var SRR (Surface Rainfall
Rate) –Observation error
provided by retrieval algorithm
50
40
SOE
LOE
30
20
10
0
19v 19h
22v 37v 37h
SSM/I channel
Zoe Case: 0000 UTC 27 Dec 2002
(HBHT)1/2 in Kelvin
19V
19H
22V
37V
37H
10/6/2006
N=1414 for 3 channels –more opaque
N=3098 for 5 channels –less opaque
Page 9
TC Zoe: Analyzed Surface Rain Rate (mm/h)
1D-Var LOE
1D-Var SOE
b)
a)
d)
c
)
1D-Var SRR
10/6/2006
PATER observations SSM/I F15
Page 10
Analyzed fields vs SSM/I retrievals based
on regression equations
O=SRR (Bauer et al. 2002 , PATER)
3
2.5
O=IWV (Alishouse et al. 1990)
8
1
Tb SOE(N=4512)
Tb LOE (N=4288)
0.5
0
-0.5
6
SRR (N=4038)
(O-P) bias
(O-P) SD
(O-A) bias
NON-RAINY IWV (kg/m2)
SRR (mm/h)
2
1.5
(O-A) SD
-1
-1.5
LWP (kg/m2)
-2
4
2
0
(O-P) bias
-2
-4
-6
0.8
-8
0.6
-10
0.4
0.2
0
(O-P) bias
(O-P) SD
(O-A) bias
(O-A) SD
Tb SOE (N=4507)
Tb LOE (N=4283)
SRR (N=4034)
-0.2
-0.4
-0.6
O=LWP (Weng & Grody, 1994)
10/6/2006
Page 11
(O-P) SD
(O-A) bias
(O-A) SD
Tb SOE (N=1242)
Tb LOE (N=1166)
SRR (N=1840)
Integrated Wapor Vapor (IWV) increments
(kgm-2)
Increment = (Analysis-Background)
6
5
4
3
2
1
0
-1
-2
-3
10/6/2006
TROPICAL CYCLONE ZOE
Tb SOE
Tb LOE
Tb LOE2
SRR
Mean
SD
Page 12
IWV Increments (kg/m2)
IWV Increments (kg/m2)
TYPHOON CHABA CASE
7
6
5
4
3
2
1
0
-1
-2
-3
Tb SOE
Tb LOE
Tb LOE2
SRR
Mean
SD
Analyzed IWV error estimate
A = [ B-1 + HTR-1H ] -1, Rodgers (2000)
Chaba
Zoe
Tb SOE
10%
5%
Tb SOE
TB LOE
10%
10%
5%
SRR
SRR
10%
10/6/2006
10%
Page 13
Tb LOE
10%
Size of temperature and humidity
increments (normalized by background
errors) for Zoe
(Analysis-Background)
lnQ
lnQ
lnQ T
T
lnQ
1D-Var Tb LOE
10/6/2006
T
1D-Var Tb SOE
Page 14
T
Conclusions
•
•
•
•
•
•
•
•
1D-Var Tb and SRR developed (RTTOVSCATT-SSM/I or TMI) with GEM moist physical
schemes
Successful analyses for Tropical Cyclone Zoe and Typhoon Chaba (> 95% convergence).
1D-Var Tb SOE experiment: weight given to observations is too large and leads to large water
vapor increments.
Largest contribution of observation error comes from the moist physics (in particular deep
convection scheme) and hence affects the 1D-Var behavior
– Explicit scheme favored (larger sensitivity to humidity)
Assimilation of Tb, rather than SRR, should be favored in the variational assimilation context due
to the direct dependence of Tb on cloud liquid water path and integrated water vapor.
Correlation of observation error between different channels is important for five channel set (less
opaque atmosphere implies more parameters to define).
Applying moist physical schemes (“linearized”) from other NWP centers (developed specifically
for DA) not trivial because schemes need to be tuned for model of center. Evaluate the impact of
assimilating 1D-Var IWV in the EC global 4D-Var
– Need to improve the computing efficiency of the 1D-Var
– Tb bias correction
Paper accepted to appear in Monthly Weather Review
10/6/2006
Page 15
www.ec.gc.ca
10/6/2006
Page 16