a physical basis of goes sst retrieval prabhat koner andy harris jon mittaz eileen maturi
TRANSCRIPT
Summary
One year match up database ( Buoy & Satellite) has been analyzed to understand the retrieval problem of satellite measurement.
Various forms of errors and ambiguities for SST retrieval will be discuused.
110,000 night only data (GOES12 & Buoy) has been considered from this database to compare results with different choices of solution processes: RGR -> Regression OEM -> (KTSe
-1K+Sa-1)-1KTSe
-1 ΔY ML -> (KTSe
-1K)-1KTSe-1ΔY
RTLS -> (KTK+λR)KT ΔY (Regularized Total Least square)3.9 & 10.7 μm -> 2 channel3.9, 10.7 & 13.3 μm -> 3 channelTwo variables of SST & TCWV
Nomenclature
X -> state space parameters Y -> Measurements ΔY -> Residual (Measurements – forward model output) ΔX -> Update of state space variables δY -> Measurement noise δX -> Retrieval error Sa -> a priori/ background covariance Se -> measurement error covariance K -> Jacobian (derivative of forward model) κ(K) -> condition number of Jacobian (highest singular value/lowest singular
value) T -> Brightness temperature in satellite output BT -> Calculated Brightness temperature SSTg-> Sea Surface Temperature First Guess SSTb -> Sea Surface Temperature from Buoy measurement SSTrgr -> Sea Surface Temperature retrieval using regression SD -> Standard Deviation RMSE -> Root Mean Square Error.
SSTrgr=C0+∑Ci Ti ; C=a+b {sec(θ)-1}+…
Coefficients are derived from in situ buoy data or L4 bulk SST.
Validate with Buoy data
Bulk SST from Satellite measurement?
Historical Regressed based SST retrieval
Alternately we can use radiative transfer physics inverse model
Statistical (OEM) Deterministic (TLS)
Data & Measurement both uncertain
It can only estimate a posteriori probability density (parameters x’: “Best Guess”) by calculating Maximum likelihood P(x|y).
Measurement only uncertain Jacobian error is condidered in
cost funtion minimization. Retrieval in pixel level
Physical Retrieval
A posteriori
observationA priori
First we will see Pros-con of OEM
Global SST distributions match quite well, but…
…large differences between 1st guess and buoy SST are real
Shortcomings of OEM
A-priori based cloud screening algorithm (CSA) in place to constrain in image data
Paradox of OEM output
OEM=(KTSe-1K+Sa
-1)-1KTSe-1ΔY
Information comes from measurement and a priori covariance.
COV= (√Sa-1)-1ΔY
Sa=
By accident the choice Sa, COV retrieval is just adding residual of 3.9 μm channel with FG.
Covariance has no physical meaning
Add measurement increase noise into retrievals
12 0
0 0.15*TCWV2
To further investigate this issue, we calculate information content
H=-0.5 ln(I-AVK)Two measurement cannot produce more than 2 pieces of information.
Big Question?
OEM may be valid for linear problem, not applicable for inherently nonlinear RTE.
Condition number of Jacobian
The condition number of jacobian of most real life problem is high. Yields
δx <= κ (K) δy
K=randn(2); (κ(K) = 118) x=randn(2,1); [-1.35 0.97]
y=K*x For ii=1:100 error(:,ii)=0.01*randn(2,1); xrtv(:,ii)=K-1(y+error(:,ii)); End
Apart from model physics and measurement errors, the error due to κ(K) plays a role.
(KTSe-1K+Sa
-1)-1KTSe-1ΔY
Remedies: Reducing the condition number of inverted matrix
Regularization, constraints, scaling, weighting etc.
We use RTLS method. Uniquely solved in simulation
study.
Difficulty solve using satellite data, drive to further investigation
Online monitor ECMWFIt is not an instrument calibration problem or bias
Fast Forward Model Error
Need improvement of fast forward model.
Quality Flagging Algorithm
K=U∑VT -> Singular vector decompositionVT ∑1 -1U ΔY ->Principle Component solutionVT ∑n -1U ΔY ->Lowest singular value solution
Lowest singular value solution increases error in retrieval where measurement noise is high. Difference of two solutions is able identified bad retrieval.
Comparative results
Same data and model, results are different due to choice of solution methods
Results are based on single iteration. Second iteration may further improve the results for physical retrieval.
Conclusions
Radiative transfer can be successful used in retrieval of SST from satellite data if we pursue rigorous physics (accurate RTM) and mathematics
There is an ambiguity in the cost function minimization for nonlinear problems, i.e.
(Yδ-KX)TSe-1(Yδ-KX) + (X-Xa)TSa
-1(X-Xa)
does not apply if Y ≠ KX
Few DefinitionsModel: a simplified description of how the ‘real
world’ process behavesForward Model : the set of rules (mathematical
functions) that define the behaviour of the process (e.g. a set equation)Forward model of remote sensing Well understood but mathematically complex function Analytical derivative is almost impossible. Stable: On some appropriate scale a small change in
the input produces a small change in the outputInverse Model: quantities within the model structure
that need to be quantified from observation data Inverse model of remote sensing is ill-posed Is the solution we find unique? Observational, numerical and model errors often
cause the inverse problem to be unstable: a small change in the input produces a large change in the output
Forward Model
Absorption term
Emission term
Intensity of the background source
“Transmittance”between 0 and L
Spectral intensity observed at L
“Transmittance”between l and L
“Optical depth” L
xdxxLx ')'(),(
),0(
0),(),0( )()0()(
L LxL dexTBeILI
“Absorption coefficient”
Forward Model
Spectral intensity observed at L
“Absorption coefficient”
molec
m
lmlmkll1
),(),()(
“number density”
“Cross section”
“Volume Mixing Ratio”
lines
illiml pTimATimSlmk
1, ),,,,(),,(),(
“Line shape”“Line strength”
N
l
N
lk
kkllN
l
ll eeTlBeILI1 11
1,0
GENSPEC: line shape: Voigt: line Strength: HITRAN 2004