Variational Inversion of Hydrometeors
Using Passive Microwave Sensors
-Application to AMSU/MHS, SSMIS and ATMS-
S.-A. Boukabara, F. Iturbide-Sanchez, R. Chen, W. Chen, K. Garrett, C. Grassotti
F. Weng and R. Ferraro
NOAA/NESDIS
Camp Springs, Maryland, USA
17th International TOVS Study Conference (ITSC-17), Monterey, USA, April 14th-20th 2010
Contents
1
Overview of MiRS Algorithm
2
Concept of Cloud/Precip-clearing
3
Performance Assessment
4
Summary & Conclusion
2
1D-Variational Retrieval/Assimilation
Measured Radiances
MiRS Algorithm
Simulated Radiances
Comparison: Fit
Within Noise Level ?
Solution
Reached
No
Jacobians
Initial State Vector
Yes
Update
State Vector
Forward Operator
(CRTM)
Measurement
& RTM
Uncertainty
Matrix E
New State Vector
Geophysical
Mean
Background
Forecast
Climatology
Field (1D-Assimilation
(Retrieval Mode)
Mode)
Geophysical
Covariance
Matrix B
3
Quality Control of MIRS Outputs
2
ϕ
™ Convergence Metric:
B
K
1
E
T
K
B
K
T
K
B
B
S
™ Uncertainty matrix S:
⎛
⎜⎜
⎝
= − ×
× ×
+
⎞
⎟⎟
⎠
−
× ×
⎝
×
0
X
× ⎛⎜⎜ ︵ ︶ −
K
+
−
X
×
⎞
⎟⎟
⎠
Y
™ Average kernel A:
×
1 K
ED
T
K
A
⎛
⎜⎜
⎝
B
×
K
T
K
=
B
D
™ Contribution Functions D: indicate amount of noise amplification
happening for each parameter.
⎞
⎟⎟
⎠
= ×
ƒ If close to zero, retrieval coming essentially from
background
ƒ If close to unity, retrieval coming from radiances: No
artifacts from background
4
Parameters are Retrieved Simultaneously
If X is the set of parameters that impact
the radiances Ym, and F the Fwd Operator
Necessary Condition (but not sufficient)
If F(X) Does not Fit Ym within
Noise
X is not the solution
F(X) Fits Ym within Noise levels
X is a solution
X is the solution
All parameters are retrieved simultaneously to fit
all radiances together
Suggests it is not recommended to use independent algorithms for different
parameters, since they don’t guarantee the fit to the radiances
5
Contents
1
Overview of MiRS Algorithm
2
Concept of Cloud/Precip-clearing
3
Performance Assessment
4
Summary & Conclusion
6
All-Weather and All-Surfaces
sensor
Cl
ou
To handle surface-sensitive channels, we add the following in the state vector:
anc
e
gR
ad i
d- o
ri g
Ra
ina
ti n
dia
nc
e
gR
ad
ian
following in the state vector:
cte
d
• Temperature
• Sensing Frequency
••Absorption
and scattering properties of material
Moisture
To account
for cloud, rain,
ice, we add the
• Geometry
of material/wavelength
interaction
• Vertical
Distribution
• Cloud
(non-precipitating)
• Temperature of absorbing layers
• Liquid
• Pressure
at which Precipitation
wavelength/absorber interaction occurs
• Amount
of absorbent(s)
• Frozen
precipitation
• Shape, diameter, phase, mixture of scatterers.
ce
Sounding Retrieval:
Major Parameters for RT:
Up
wel
li n
Scattering Effect
Su
rf a
ce o ri
gi n
at i
ng
Ra
dia
nce
ng
elli
w
n
Dow
Su
rfa
c
e
anc
i
d
Ra
e-r
e
fle
• Skin temperature
Absorption
• Surface emissivity (proxy parameter for all surface parameters)
Scattering Effect
™
™
Instead of guessing and then removing the impact of cloud and rain and ice on TBs (very hard), MiRS
approach is to account for cloud, rain and ice within its state vector.
It is highly non-linear way of using cloud/rain/ice-impacted radiances.
Surface
7
All-Weather:
Cloud/Precip-Clearing
™
™
™
Instead of guessing impact of cloud and rain and ice on TBs (very hard), MiRS approach is to account for cloud, rain and ice within its state vector.
Advantages:
ƒ
It is highly non-linear way of using cloud/rain/ice-impacted radiances
ƒ
Does not rely on cloud or rain uniform distribution
ƒ
Does not rely on cloud resolving models (added uncertainty, need to linearize, speed cost, etc)
Disadvantage:
ƒ
Results depend on assumptions made in RT (particle size, distribution, etc)
ƒ
Greater reliance on a robust, valid covariance matrix (flow dependent matrix becomes necessary: see poster by K. Garrett).
Is the
retrieval
stable?
Is the
approach
mathematically
valid?
Meas.
Ym
- EOF
decomposition
for all
profiles(or
(T,moderately
Q, C, R, I) and
™ The
PDF
of X is assumed
Gaussian
nonemissivity
vector.
Gaussian
it is a numerical
Nosince
Yes iterative process)
™ Operator Y able to Fit
simulate measurements-like
∆Y=Ym-Ys
Solution radiances
Is
the
solution
physically
consistent?
(between T, Q, C, R
™ Errors of the model and the instrumental noise
combined are
and I)
assumed (1) non-biased and (2) Normally distributed.
-Cov Matrix constraint
™ Forward
assumed
locally linear (or moderately non-Physicalmodel
Retrieval
& RT constraints
linear)
at each iteration.
-Convergence
(fitting Ym)
Jacobians-Jacobians to determine
Sim. Ys signals
T Q C R I
8
Solution-Reaching: Convergence
× − × ⎛⎜
⎝
−
X
Y
Previous version
( )⎞⎟⎠
m
Y
−
1
E
T
X
Y
ϕ = ⎛⎜⎝
m
Y
2
™ Convergence is reached everywhere: all surfaces, all weather
conditions including precipitating, icy conditions
™ A radiometric solution (whole state vector) is found even when
precip/ice present. With CRTM physical constraints.
( )⎞⎟⎠
Current version
(non convergence when precip/ice present)
9
Contents
1
Overview of MiRS Algorithm
2
Concept of Cloud/Precip-clearing
3
Performance Assessment
4
Summary & Conclusion
10
Hydrometeors Inversion Approach
MIRS Core Products
(from 1DVAR)
CLW, IWP and RWP
Sensor-independent
Function which
allows expanding
to all sensors easily
(pending 1DVAR
core products)
Hydrometeors are hard to
validate. RR is easier to
MIRS Rainfall Rate Algorithm
assess (wrt ground-based
radar, gauges). Assessing RR
+ a2RWP + a3IWP
RR = a1CLW
is an indirect validation
of
IWP, CLW, RWP.
MIRS Rainfall Rate
(mm/hr)
11
Rainfall Rate Assessment
MiRS Monthly composite (Metop-A)
MSPPS Monthly composite (Metop-A)
1DVAR
Heritage algorithm: based on physical regression
Significant reduction in Rain false alarm using MiRS, at surface transitions and edges
12
MiRS RR part of IPWG Intercomparison
(N. America, S. America and Australia sites)
No discontinuity at coasts (MiRS applies to both land and ocean)
This is an independent
assessment where
comparisons of MiRS RR
composites are made
against radar and gauges
data.
Image taken
taken from
from IPWG
IPWG web
web site:
site: credit
credit to
to John
DanielJanowiak
Villa
13
Image
MiRS RR Comparison to Gauges & Radar
Upper Limit set by the Rain Gauge to Rain Radar Comparison
14
Qualitative check of the
Cloudy/Rainy radiance handling
Cross-sectionsMiRS
of both
TRMM
and
MiRS products at 25 degrees North
Rain
Water
Path
TRMMcase
Rain/Ice
Profiles
A test
comparison
with TRMM rain/iceNotes:
product was conducted on 2010/02/02
Ice bottom
-The rain events were not captured exactly-Generally,
at the sameconsistent
time (shiftfeatures
noticed)
and MiRS (except for
-A qualitative assessment was Rain
done
vertical TRMM
cross-section
top on thebetween
-MiRS produces T(p), Q(p), cloud, rain and expected
ice profileshift)
-Purpose is to check if these products
behave
Vertical Cross
section physically
MiRS Rain/Ice Profiles
- Ice is found on top of liquid rain
Freezing level
MiRS Moisture
-Transition between frozen and liquid
is delineated by the freezing level
determined from the temperature
Vertical Cross section
profile.
-Moisture increases in and around
the rain event
MiRS Temperature
TRMM (2A12) Rain Rate
- Suggests that these products are
reasonably constrained within
physical inversion
15
Contents
1
Overview of MiRS Algorithm
2
Concept of Cloud/Precip-clearing
3
Performance Assessment
4
Summary & Conclusion
16
Summary & Conclusion
™ MiRS is a generic retrieval/assimilation system (N18, N19,
Metop-A, DMSP F16/18 SSMIS). Being extended to
NPP/ATMS, TRMM/TMI and GPM/Mega-Tropiques
™ All parameters impacting TBs are retrieved simultaneously:
sounding, emissivity, skin temperature, cloud, rain, ice,
allowing point-to-point variation of emissivity over land
™ Final solution fits measurements (a necessary requirement).
™ Inclusion of hydrometeors in retrieval allows processing
cloud/rain –impacted radiances. Non-linear cloud-precip
clearing.
™ Physical Constraints are included through Covariance.
™ Assessment of hydrometeors performed using RR as proxy.
™ Results show that MiRS RR is consistent with established
algorithms perfs, with the added value of a physically
17
consistent solution.
BACKUP SECTION
18
X
(
Y
Y
)
E
T
X
)
m
0
x
x
K
0
x
y
x
y
︵ ︶︵ ︶
∂
=
™To find the optimal solution, solve for: ∂ =
⎡
⎤
︵
︶
︵
︶
=
+
−
⎢
⎥
™Assuming Linearity
⎣⎢
™This leads to iterative solution:
︶ ⎞⎟ +
⎠
n
X
Δ
n
K
−︵
︶ ⎞⎟ +
⎤
⎥
⎦
⎠
n
X
Δ
n
K
⎫
⎪⎡⎛
⎬⎢⎜
⎪⎣⎝
⎭
−︵
n
X
−
Y
+
⎞
⎟⎟
⎠
m
Y
⎛
⎜⎜
⎝
−
⎫
⎪⎪⎡⎛
⎬⎢⎜
⎪⎣⎝
⎪⎭
⎦⎥
n
X
−
−
1
E
More efficient
(1 inversion)
− +
⎞
⎟
⎟
⎠
Tn
K
B
n
K
Tn
K
B
1
n
X
Δ
+
⎧
= ⎪⎨
⎪
⎩
Y
m
Y
1
E
T
n
1K
n
K
1
E
T
n
K
1
B
1
n
X
Δ
+
=
⎧
⎪⎪⎛
⎨⎜⎜
⎪⎝
⎪⎩
0
X
X
J
X
'
J
⎤
Jacobians
& Radiance
−︵ ︶
× − × Simulation
−︵ ︶⎥
from Forward Operator: CRTM⎦
1
⎦ ⎣
(
Y
)⎤⎥ + ⎡⎢
×( −
m
−
Y
1 2
×
X0
X
)
1
−
B
(
T
X
J
︵ ︶= ⎡
⎢⎣
X0
X
1 2
Cost Function Minimization
™Cost Function to Minimize:
⎤
⎥⎦
Preferred when nChan << nParams (MW)
19
Importance of the Covariance Matrix
TPW Horizontal Field
ECMWF WV cross-section
21Rainy
Deg atmospheric profiles only,
Covariances using
rather than a Global climatology, had a significant impact
on performances. In the cases examined, the use of a
covariance matrix specific to precipitating conditions
MiRSsignal
WV Cross-section
helps to overcome the loss of radiometric
in the
Climatology Background
MiRS physical retrieval.
MiRS Rain Profile Cross-Section
MiRS WV Cross-section
Rain-Specific Background
20
MiRS General Overview
VerticalRadiances
Integration and Post-Processing
TPW
RWP
IWP
CLW
Temp. Profile
1DVAR
Outputs
Rapid
Algorithms
(Regression)
Humidity Profile
Advanced
1st Guess
Retrieval
Liq. Amount(1DVAR)
Prof
Vertical Vertical
Integration &
Integration
Post-processing
Ice. Amount Prof
selection
Rain Amount Prof
Emissivity Spectrum
MIRS
Products
Skin Temperature
Core Products
Post
Processing
(Algorithms)
-Sea Ice Concentration
-Snow Water Equivalent
-Snow Pack Properties
-Land Moisture/Wetness
-Rain Rate
-Snow Fall Rate
-Wind Speed/Vector
-Cloud Top
-Cloud Thickness
-Cloud phase
21
All-surfaces: Variational Handling of
Surface-Sensitive Channels
™ Similar to handling cloud and hydrometeors, MiRS approach to account
for surface-sensitivity of channels is by accounting for emissivity vector
within state vector.
™ Advantages:
ƒ Extend retrieval to all surfaces (only difference is background
covariance and mean used). Example: TPW over land.
ƒ Generating an emissivity vector product, clear from atmospheric
effects (used for a more accurate estimate of surface parameters)
ƒ Consistent treatment of all parameters globally (same methodology).
Example: RR is retrieved over ocean and land using the same code.
ƒ Greater physical distinction between Tskin and Emissivity (based on
physical Jacobians and different spectral signatures)
ƒ Allows a point to point variation of emissivity (useful for coasts, after
rain, etc)
™ Disadvantages:
ƒ Great emphasis must be given to the balance between different
parameters (so that emissivity does not become a sink hole for
variability due to other parameters such as cloud: hard)
ƒ Great constraint is put on the accuracy of emissivity
22
Assumptions Made in Solution Derivation
™The PDF of X is assumed Gaussian
™Operator Y able to simulate measurements-like
radiances
™Errors of the model and the instrumental noise
combined are assumed (1) non-biased and (2)
Normally distributed.
™Forward model assumed locally linear at each
iteration.
23
Retrieval in Reduced Space
(EOF Decomposition)
™All retrieval is done in EOF space, which allows:
ƒ Retrieval of profiles (T,Q, RR, etc): using a limited number of EOFs
ƒ More stable inversion: smaller matrix but also quasi-diagonal
ƒ Time saving: smaller matrix to invert
™Mathematical Basis:
ƒ EOF decomposition (or Eigenvalue Decomposition)
• By projecting back and forth Cov Matrx, Jacobians and X
L
B
T
L
Θ
=
× ×
Diagonal Matrix
Transf. Matrx
Covariance matrix
(used in reduced space retrieval)
(computed offline)
(geophysical space)
24
& (2) No risk of having unphysical negative values
Advantages: (1) Distributions made more Gaussian
Retrieval in Logarithm Space
P=416 mb
P=506 mb
P=606 mb
P=718 mb
P=810 mb
P=915 mb
P=506 mb
P=606 mb
P=718 mb
P=810 mb
x
J
×
x
x
g
o
L
∂
∂
=
∂
∂ ︵ ︶
P=915 mb
Rx
=
x
R
g
o
L
Jl
Applied to WV, Cloud and precip
P=416 mb
∂
= ×
∂ ︵ ︶
25
Challenges of Profiling in Active Areas
• Case of July 8th 2005
700 mb
DeltaT=3K
MHS footprint size at nadir
is 15 Kms.
But at this angles range
(around 28o), the were
MHS
4 Dropsondes
footprint is around 30 Kms
All these
dropped within 45 minutes and
are located within 10 kms from
each other
700 mb
Zoom in space (over the Hurricane Eye)
and Time (within 2 hours)
Temperature [K]
DeltaQ=4g/Kg
Water Vapor [g/Kg]
26
TPW Global Coverage
MiRS
GDAS
MiRS TPW Retrieval (zoom over CONUS)
Very similar features to GDAS
Smooth transition over coasts
27
No Discontinuities at Coast
28