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Optimal Array Design for Enhancing Observations in the Tropical Indian Ocean

This study presents an ensemble-based optimal array design tailored for the tropical Indian Ocean. By utilizing Kalman filter theory, the research illustrates how the ensemble covariance can inform the mapping and analysis of observations, minimizing analysis error variance. The paper explores various model configurations, analyses basin-averaged theoretical variance reductions, and highlights practical applications of the proposed array design. Key insights on observation types, monitoring objectives, and constraints are discussed, providing a comprehensive framework for optimizing marine observations.

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Optimal Array Design for Enhancing Observations in the Tropical Indian Ocean

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  1. Optimal array design:Application to the tropical Indian Ocean Peter Oke November 2006 CSIRO Marine and Atmospheric Research http://www.cmar.csiro.au/staff/oke/ email: peter.oke@csiro.au

  2. Ensemble-based array designSakov and Oke Given a representative ensemble of anomalies: the ensemble covariance is given by: Using Kalman filter theory, the covariances of the ensemble can be used to map (or grid, or analyse) a vector of observations: Giving an analysis error covariance of:

  3. Ensemble-based array designSakov and Oke An optimal array minimises some norm of : We choose to minimise the analysis error variance: Given an observation, or an array of observations, we update the ensemble to reflect the reduced variance:

  4. Ensemble-based array design… in practice calculate optimal observation Representative ensemble update ensemble

  5. Ensemble-based array designModel configurations • ACOM2 ACOM3 OFAM • Model codeMOM2 MOM3 MOM4 • Zonal res.2o 0.5o 0.1-2o • Meridional res.0.5-1.5o 0.33o 0.1-2o • # vert. levels25 33 47 • Wind forcingNCEP/NCAR + FSUERS1/2 ERA40 • Heat flux ABLM + FC ABLM + FC ERA40 + FC • Shortwaveas above OLR + NCEP ERA40 • Freshwateras above Monthly analyses Levitus • Time period1982-1994 1992-2000 1992-2004

  6. Ensemble-based array designModel-based – Intraseasonal

  7. Ensemble-based array designModel-based – Intraseasonal • Table 1: The basin-averaged theoretical analysis error variance of IMLD (m2), and the percent reduction in parentheses • ACOM2 ACOM3 OFAM • Signal 15.2 22.7 49.3 • Proposed array12.3 (19%) 16.7 (26%) 36.6 (26%) • ACOM2 array11.5 (24%) 16.2 (29%) 36.6 (28%) • ACOM3 array11.9 (22%) 15.4 (32%) 35.8 (27%) • OFAM array12.1 (20%) 16.3 (28%) 33.6 (32%) • … in practice, the proposed array looks pretty good, and will probably perform as well as any objectively defined optimal array.

  8. Ensemble-based array designObservation-based – Intraseasonal to interannual

  9. Ensemble-based array designObservation-based – Intraseasonal to interannual • Table 2: The basin-averaged theoretical analysis error variance of GSLA (m2), and the percent reduction in parentheses • Variance (m2) • Signal 81.0 • Proposed array 34.9 (57%) • Unstructured array 27.1 (66%) • Structured array29.5 (64%)

  10. Ensemble-based array designCorrelation maps

  11. Ensemble-based array designSummary • We demonstrate how simple it is to calculate optimal observations given the system covariance. • In practice, if you have an ensemble that correctly represents the system covariance, it is easy to calculate the corresponding optimal observations. • We show an example application to the tropical Indian Ocean, using a: • model-based ensemble • observation-based ensemble Sakov, P., and Oke, P. R., 2006: Optimal array design: application to the tropical Indian Ocean. Monthly Weather Review, submitted.

  12. Key questions in observing system design • What types of observations can be made? • temperature and salinity from a mooring or glider • sea-level from a tide gauge station • surface currents from a HF radar array • What are the observations intended to monitor? • area-averaged temperature • El Nino Southern Oscillation • location of a front • What are the practical constraints? • cost • maintenance • What is the best “complete” representation of the field being observed and monitored? • model  temperature, sea-level, transport • observations  satellite sea surface temperature

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