Optimal array design: Application to the tropical Indian Ocean

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