exploring coupled atmosphere ocean data assimilation … · exploring coupled atmosphere‐ocean...
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Exploring Coupled Atmosphere‐Ocean Data Assimilation Strategies with an EnKF, a Low‐Order Model and CMIP5 data
Robert Tardif Gregory J. Hakim
Chris Snyder
University of Washington
NCAR
L
World Weather Open Science Conference 2014, Montréal
Motivation
Growing interest in near‐term (interannual to interdecadal) climate predictions (Meehl et al. 2009, 2013)
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Boundary‐valueproblem
Need accurate external forcings: ‐ solar variability,‐ greenhouse gases,‐ aerosols, …
Model errorInitial‐valueproblem
Models drift away from obs. (large biases) =>‐ Improve models‐ Parameter estimation‐ Post‐processing (bias correction)‐ Anomaly initialization
Skill of uninitialized forecasts limited to large scale externally forced climate variability(Sakaguchi et al. 2012)
For accurate predictions of internal variability: need coherent initialization of coupled
**low‐frequency** atmosphere & ocean
Challenges / overarching questions• Context: Interacting slow (ocean) & fast (atmosphere) components of
the climate system
• Challenges & overarching questions:o Unclear how to best initialize the coupled system
Q1: Traditional NWP‐style data assimilation (DA) appropriate?
o Slow has the memory but fewer observations than in fast Q2: Possible to initialize poorly observed or unobserved ocean?
Can obs. info. be effectively transferred to key unobserved variablesacross atmosphere‐ocean interface?
o Coherence between initial conditions of slow & fast relies on “cross‐media” covariances Q3: What do these look like? How to reliably estimate?
Fast component is “noisy” (i.e. high‐frequencies)…
o Practical considerations Q4: Can coupled DA be done at reasonable cost?
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Initialization approaches• Various methods considered so far:
1. Forcing ocean model with atmospheric reanalyses: no ocean DA2. Data assimilation (DA) performed independently in atmosphere &
ocean (i.e. combine independent atmospheric & oceanic reanalysis products)
3. Weakly coupled DA: Assimilation done separately in atmosphere & ocean but use fully coupled model to “carry” information forward
4. Fully coupled DA: w/ cross‐media covariances, still in infancy (Zhang et al. 2007, 2010)
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(simple)
(comprehensive)
Here, consider fully coupled ensemble DA
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DA strategies1) Assimilation of time‐averaged observations
Averaging over the noise: more robust estimation of cross‐media covariances?
2) Offline (i.e. “no‐cycling”) as cost‐effective DA alternative?Background ensemble from random draws of model states from long deterministic coupled model simulationi.e. climatological covariances (think EnOI) & background = climatology
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Cross‐media covariances: : obs. of fast ‐> noisy: state vector, including slowvariables Fast noise contaminates K
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Time‐average DA
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just update time‐mean
Time‐mean:
Deviations:
(Dirren & Hakim, GRL 2005; Huntley & Hakim, Clim. Dyn., 2010)
Time averaging & Kalman‐filter‐update operators linear and commute
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Full state:
[State vector] [Observations]
DA with simplified system• Use low‐order analogue of coupled North Atlantic climate system
o Analyses of Atlantic meridional overtuning ciculation (AMOC) as canonical problem Key component in decadal/centennial climate variability & predictability
Not well observed (i.e. important challenge for coupled DA)
1. Low‐order coupled atmosphere‐ocean model Cheap to run: allows multiple realizations over the attractor
2. Promising concepts tested using data from a comprehensive AOGCM (i.e. CCSM4) To assess robustness of results in realistic system
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Low‐order model
• From Roebber (1995)• Features:
Lorenz (1984, 1990) wave—mean‐flow model: fast chaotic atmosphere Stommel (1961) 3‐box model of overturning ocean: low‐frequency AMOC
variability (i.e. no wind‐driven gyre) Coupling:
upper ocean temperature affects mean flow & eddies (ocean ‐> atmosphere) hydrological cycle affects upper ocean salinity (atmosphere ‐> ocean)
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State vector: 10 variables!
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Variability in model
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Ocean: AMOC
Atmosphere: Zonal circulation
Ocean: Mainly centennial/millennialvariability; weaker decadal variability
Atmosphere: chaotic;Characteristic time scale (eddy damping) ~ 5 days
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Atmosphere—ocean covariability• Role of atmospheric observations in coupled DA
• Increase in covariability w.r.t. AMOC for annual & longer scales• Eddy “energy” (=X2+Y2) has more information than state variables
(atmosphere ‐> ocean coupling through hydrologic cycle)
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Correlations with AMOC vs averaging time
day
yearXYZ
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DA experiments• EnKF w/ perturbed obs. & inflation for calibrated ensembles• Perfect model framework: (obs. from “truth” w/ Gaussian noise added)• Obs. error stats: large SNR (to mimmick “reliable” modern obs). • 100‐member ensemble
• Compared: o daily DA (availability of observations) » frequent assimilation of
raw observations (i.e. NWP‐style DA)o time‐averaged DA (annual cycling)
o Data denial: from well‐observed ocean (except AMOC) to not observed at all (atmospheric obs. only)
o Cycling vs. “no‐cycling”
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DA results w/ cycling
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2
12
1
1
Na
i ii
N
ii
x xCE
x x
Coefficient of efficiency:
• Accuracy of AMOC analyses over 100 randomly chosen 50‐yr periods
CE = 1 : analysis error variance << climo. varianceCE = 0 : no information over climatology
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on ensemble mean
Cycling vs “No‐cycling”
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2
12
1
1
Na
i ii
N
ii
x xCE
x x
Coefficient of efficiency:
• Accuracy of AMOC analyses over 100 randomly chosen 50‐yr periods
• “No‐cycling”: background from random draws of coupled model states from prior long deterministic of the modelo Cheaper alternative (no fully coupled model ensemble)o DA based on climatological covariances (no “flow‐dependency”)
CE = 1 : analysis error variance << climo. varianceCE = 0 : no information over climatology
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on ensemble mean
“No‐cycling” DA w/ comprehensive AOGCM• Strategy: derive low‐order analogue using CCSM4 gridded output
o “Coarse‐grained” representation of the N. Atlantic climate system, but underlying complex (i.e. realistic) dynamics
o 1000‐yr “Last Millenium” CMIP5 simulation (pre‐industrial natural variability)o Low‐order variables: Ocean: T & S averaged over boxes [ upper (i.e. 200m) subpolar ocean ] Atmosphere: Eddy heat flux across 40oN & MSLP along transect at 40oN AMOC index: Max. value of overturning streamfunction in N. Atlantic
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monthly
10‐yr running mean
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Covariability in CCSM4• Correlations w.r.t. AMOC vs averaging time scale
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Subpolar ocean T, S
month decade
MSLP @ 40oN
Multi‐time scale DA• Assimilate obs. at appropriate time scale
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(Steiger et al. GRL submitted)
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End product is analysis of time averaged state over 2
Recover full state
Do update
Decompose at scale 1
Do update
Decompose at scale 2
Analyses over 1000 yrs100 members2 time scales:
1 = 50 yrs2 = 1 month
Single vs multi‐time scale DA
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w/ ocean DA
Atmosphere only DA
CE for ensemble mean analyses
monthly only50‐yr only50‐yr ocean T,S
or atmosphericmeridional
eddy heat flux+
monthly MSLP
Moving average (yrs)
Moving average (yrs)
CE (A
MOC)
CE (A
MOC)
Summary & conclusions• Q1: NWP‐style DA appropriate to initialize slow component?
A: Yes, if *sufficient* obs. in ocean• Q2: Possible to initialize poorly observed or unobserved ocean?
(i.e. ocean DA vs fully coupled DA)A: Yes, with time‐average DAo Frequent ocean DA slightly more effective when ocean is well‐observedo Fully coupled DA of time‐averaged obs. critical with poorly observed
ocean• Q3: How to reliably estimate cross‐media covariances?
A: Use time‐averaging over appropriate scaleo Averaging over “noise” in fast component = > enhanced covariability
• Q4: Simplified cost‐effective coupled DA available?A: Yes, “no‐cycling” DA (of time‐averaged obs.) cheap & viable
alternative
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