Observations and Ocean State Estimation: Impact, Sensitivity and Predictability
description
Transcript of Observations and Ocean State Estimation: Impact, Sensitivity and Predictability
![Page 1: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/1.jpg)
Observations and Ocean State Estimation:
Impact, Sensitivity and Predictability
Andy Moore University of California Santa Cruz
Hernan ArangoRutgers University
![Page 2: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/2.jpg)
Outline
• State estimation• Observation impact• Information content• Observation sensitivity• Forecast error and predictability• Examples from the California Current
![Page 3: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/3.jpg)
Ocean State Estimation and Data Assimilation
From Bayes’ Theorem:
Ocean state vector: T, , , ,T S u v x
a bx x Kd
Posterior Prior Gain Innovation
H bd y x
Obs Obsoperator
1T T K BH HBH RKalman gain:
Priorerrorcov
Obserrorcov
TLobs
operator
may includeocean dynamicsas in 4D-VarH
![Page 4: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/4.jpg)
Practicalities of 4D-Var
a bx x Kdidentified iteratively using 4D-Varax
Typically done using conjugate gradients (CG)
K K PracticalGain Matrix
Alternatively, view CG and 4D-Var as a function:
a bx x dK
4D-Var
![Page 5: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/5.jpg)
Two Views of 4D-Var
a bx x Kd
a bx x dKOR
Posterior Prior Innovation
![Page 6: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/6.jpg)
The Role of Observations
Q: What is the influence of the observations on the analysis?
Observation impact:TK
Observation sensitivity: T dK
Predictability: T d dK K
![Page 7: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/7.jpg)
Observation Impact
Consider a function I ax
T T
T T
T T
I I
I I
I I I I
I H I
b
b
b
a b
b x
a b x
b x
x x Kd
x d K x
x x d K x
y x K x
Q: How does each obs contribute to the analysis?
of the circulation:
![Page 8: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/8.jpg)
Observation Impact
1
1 i N i
N
g
I d d d g
g
i i id y H bx
Ti
ig I
bxK x
![Page 9: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/9.jpg)
Observation Sensitivity
Q: How does the analysis change if the observations change?
Consider again the function I ax
I I a bx x dK
Let y y y d d d
I I I a ax x
![Page 10: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/10.jpg)
TT
TT
=
I I I
I
I
I I
I I
a
a
a a
b
b
a x
x
x x
x d d
x d d d
x d d x
d d x
K
K K
K
K
Observation Sensitivity
![Page 11: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/11.jpg)
Observation Sensitivity
1
1 i N i
N
h
I d d d h
h
i id y
T
ii
h I ax
d xK
![Page 12: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/12.jpg)
Observations and Predictability
Q: How does each obs contribute to the forecast predictability?
Consider now an ensemble of forecastfunction values for obtained by perturbing priors and obs.
I I I f fx x x
I fx
Expected forecast error variance:
T2 2I I I I
f f
f
x xx E x
Forecasterror
covariance
![Page 13: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/13.jpg)
Observations and Predictability
TT
T
aa aE I H B I H
d dR
d d
KKM M
KK
Posteriorerror
covarianceTangentLinear4D-Var
AdjointLinear4D-Var
Tf fffE DMM
Forecasterror
covariance
diag , , ,f b f aD E B B B
Controlpriors
Tangentlinearmodel
where:
![Page 14: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/14.jpg)
The California Current
500m
37N
Mesoscaleeddies
![Page 15: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/15.jpg)
The California Current
30km, 10 km & 3 km grids, 30- 42 levels
Veneziani et al (2009)Broquet et al (2009)Moore et al (2010)
COAMPSforcing
ECCO openboundaryconditions
fb(t), Bf
bb(t), Bb
xb(0), Bx
Previous assimilationcycle
The Regional Ocean Modeling System (ROMS)
![Page 16: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/16.jpg)
Observations (y)
CalCOFI &GLOBEC
SST &SSH
ARGO
Ingleby andHuddleston (2007)
Data from Dan Costa
~90%
~10%TOPP Elephant Seals (APB)
EN3
![Page 17: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/17.jpg)
Observations
DataAssimilation
Posterior
Observations
DataAssimilation
Posterior
Observations
DataAssimilation
Posterior
prior prior prior
Sequential Data Assimilation: July 2002-Dec2004
7 days
Forecast Forecast Forecast
![Page 18: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/18.jpg)
CTD XBT
ARGO TOPP
All in situ data:July 2002 –Dec 2004
![Page 19: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/19.jpg)
Observation Impact
Q: How does each obs contribute to the analysis?
![Page 20: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/20.jpg)
Observation Impacts on Transport
7day average transport
I Transport increment
I
= (Posterior-Prior)
10km ROMS
![Page 21: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/21.jpg)
Example: 37N Transport
No assim
WithData
Assimilation
JAS time meanalongshore
Flow(10km, 42 lev)
CC
CC
CUC
CUC
CC = California CurrentCUC = California Under Current
![Page 22: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/22.jpg)
37NI
500mI
Poleward
Equatorward
Offshore
Onshore
Prior alongshore transport (CC+CUC+CJ)
Prior cross-shore transport
![Page 23: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/23.jpg)
Analysis Cycle – Observation Impacts
37NI
500mI
Poleward
Equatorward
Offshore
Onshore
Alongshoretransport
Cross-shoretransport
10km ROMS
rms
(Moore et al, 2011c)
![Page 24: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/24.jpg)
Sv (10-5)
Alongshore Transport Impacts
IGW
IGW
IGW
CTW(G)
AdjointCTW(GT)
SSH
GyreCirculation
![Page 25: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/25.jpg)
yObservation
vector
x
Degrees of Freedom (dof)
“Perfect World”dof ~ Nobs
yObservation
vector
xRedundancy
dof < Nobs
![Page 26: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/26.jpg)
Information Content of Obs
Degrees of freedom of obs (dof):
dof = Tr KH
30km
Only ~10% of obs contain independent info
Tr{KH}/Nobs vs assimilation cycle
Cardinali et al, 2004;Desroziers et al., 2009Bennett & McIntosh, 1982
upper & lower bounds
(Moore et al, 2011b)
![Page 27: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/27.jpg)
Observation Sensitivity
Q: How does the analysis change if the observations change?
Q: How does the analysis change if the observation array changes?
![Page 28: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/28.jpg)
Impact vs Sensitivity
Single 4D-Var cycle obs
Impact on 37N transport
Sensitivity of 37N transport to removing observations
![Page 29: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/29.jpg)
Observation Sensitivity: An OSSE
4D-Var change in 37N transport when all SSH removed
Change in 37N transport predicted by obs sensitivity
Change in 37N transport predicted by obs impact
![Page 30: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/30.jpg)
Observations
DataAssimilation
Posterior
Observations
DataAssimilation
Posterior
Observations
DataAssimilation
Posterior
prior prior prior
Sequential Data Assimilation: July 2002-Dec2004
7 days
Forecast Forecast Forecast
![Page 31: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/31.jpg)
Observations and Predictability
Q: How does each obs contribute to the forecast predictability?
![Page 32: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/32.jpg)
Forecast Ensembles
Small spread
Predictable
Large spread
Unpredictable
Expected uncertaintyof analysis
![Page 33: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/33.jpg)
Predictability
Analysis cycleending t0+7d
Analysis cycleending t0
t0 t0+7d t0+14dt0-7d
Forecast cycleending t0+14
Forecast cycleending t0+14
Forecastensemble
![Page 34: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/34.jpg)
Predictability
Alongshore transport
Cross-shore transport
2 2 2
14 7 14100 f f fr
0r positive impact of obs on predictability
![Page 35: Observations and Ocean State Estimation: Impact, Sensitivity and Predictability](https://reader034.fdocuments.us/reader034/viewer/2022051821/568159db550346895dc7297a/html5/thumbnails/35.jpg)
Summary
• In situ observations have a large impact on circulation estimates, despite small number.• Adjoint operators provide considerable utility for quantifying the impact and value of ocean observations.• Routine monitoring of adjoint-based diagnostics → real-time monitoring of observing array.• Quantification of the true value of observations.