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Adaptive Ensemble Optimal Interpolation for Efficient Assimilation - - PowerPoint PPT Presentation

Nov 05, 2023 269 likes •480 views

Adaptive Ensemble Optimal Interpolation for Efficient Assimilation in the Red Sea Habib Toye 1 , Peng Zhan 1 , Furrukh Sana 1,2 , and Ibrahim Hoteit 1 1 King Abdullah University of Science and Technology, Thuwal, Saudi Arabia, 2 Harvard Medical

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Adaptive Ensemble Optimal Interpolation for Efficient Assimilation in the Red Sea

Habib Toye1, Peng Zhan1, Furrukh Sana1,2, and Ibrahim Hoteit1

1King Abdullah University of Science and Technology, Thuwal, Saudi Arabia, 2Harvard Medical School, Massachusetts General Hospital, USA

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Introduction – The Red Sea

1

  • Extensive evaporation (>2m/year)
  • One of the warmest and saltiest water

masses in the world

  • 2nd longest and 3rd largest coral reef system
  • Commercial highway
  • Source of food, water, and energy
  • ARAMCO is exploring it …
  • Impact on regional climate
  • Build an integrated data-driven modeling

system to study and predict the Red Sea circulation

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Model and Data

  • MITgcm 0.04°
  • ECMWF atmospheric forcing/ ECCO2 OBCS
  • Along-track merged SSH (RADS) every 3 days
  • 3-day midnight SST (AVHRR)
  • Data Assimilation Research Testbed (DART)

2

32oE 36oE 40oE 44oE 48oE 12oN 16oN 20oN 24oN 28oN

[aviso.altimetry.fr, 2014]

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3

!! = ! − !! !!

! = !! ! + ! (!! − ℎ(!! !))

Ensemble Kalman Filter (EnKF)

𝒚𝒋

𝒃 = 𝑩𝑼 𝒚𝒋 𝒈 − 𝒀𝒈 + 𝒀𝒃

EAKF

𝒀𝒃 = 𝚻𝒃 𝚻𝒈 ,𝟐𝒀𝒈 + 𝑰𝑼𝑺,𝟐𝒛 𝜯𝒃 = 𝚻𝒈 ,𝟐 + 𝑰𝑼𝑺,𝟐𝑰

,𝟐

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analysis

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1 2 3 Time Assimilation cycles (update + forcast) model advance model advance forecasts

Ensemble Optimal Interpolation (EnOI)

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Seasonal Variability

Yao et al. (2013 a, b) Smeed et al. (2004)

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DEU -- Adaptive EnOI

Forecast step: integrating only ONE mean at the forecast step. Before analysis: building the forecast ensemble by adding the anomalies to the forecasted mean.

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January February March December November October …

En1 En2 En12 En11 En10 … En3

LONG TERM SIMULATION Monthly dictionary

Conventional EnOI Seasonal EnOI

… … … …

Seasonal EnOI

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  • Through L2 norms on SST

To select the members that are closest to the forecast

  • Through an Orthogonal Matching Pursuit (OMP)

Other DEU Schemes

To update the ensemble X = [dj1, …, djN] at every assimilation step based on the latest forecast

OMP finds the members most correlated with the current residuals. (orthogonal projection of the signal onto the subspace spanned by the set of members selected so far)

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  • EAKF shows

smaller spreads in SSH, SST and temperature profiles

  • DEU exhibits

stronger eddy variability in the spread, suggesting the selected members describe different features

  • f eddy activities

Ensemble Spread (Feb-6-2006)

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Distribution of SSH (Feb-6-2006)

  • Ensemble spread is

small in EAKF and yeilds less increments

  • As anomaly of mean

flow, eddies information is described by Pf and can be introduced

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Schemes comparison

  • EAKF has larger analysis

RMSE than DEUs, due to the small ensemble spread

  • DEU analysis SSH RMSEs

are comparable to AVISO

  • SSH RMSEs are computed

against different sparse obs from what have been assimilated (nums & locations) SST SSH

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Statistics of SST (Feb-6-2006)

SEnOI L2 OMP

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Why larger ensembles?

Having more members enables:

  • Additional error directions (increased rank in Pf)
  • More robust correlations, and may be less localization
  • Better maintained ensemble spread, less inflation

Dual experiments have been carried for EAKF with ensemble size of

100 V.S. 1,000

(Forecast only: 22,000 3-day MITgcm runs 1100 members for 60d = 1 member for ~180yr)

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1000 members

100 members 100 members with cutoff

Prior Correlation - SST

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Prior Correlation - SSH

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1000 members

100 members 100 members with cutoff Long-range correlations vary in different variables, time, and locations, define adaptive localization scales for different variable?

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Prior Distribution

A larger ensemble seems to make the Monte Carlo-based approximation of the prior distribution more Gaussian.

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RMSE

The experiment with 1000 members has larger ensemble spread and smaller RMSE.

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  • The DEU schemes (SEnOI and L2) are able to provide reasonable

performance in the data assimilation experiments, at a small fraction of computing cost of EAKF.

  • EAKF with a larger ensemble size could significantly reduce the

spurious correlations, keep ensemble spread, and exhibit a more Gaussian prior, but it is too expensive!

  • Next: Hybrid-DEU with large ensembles

To Summarize

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Thank you!