Optimal array design: Application to the tropical Indian Ocean Peter Oke November 2006 CSIRO Marine and Atmospheric Research

Ensemble-based array design Sakov 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:

Ensemble-based array design Sakov 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:

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

Ensemble-based array design Model configurations ACOM2 ACOM3 OFAM Model code MOM2 MOM3 MOM4 Zonal res. 2 o 0.5 o o Meridional res o 0.33 o o # vert. levels Wind forcing NCEP/NCAR + FSU ERS1/2 ERA40 Heat flux ABLM + FC ABLM + FCERA40 + FC Shortwave as aboveOLR + NCEP ERA40 Freshwater as above Monthly analyses Levitus Time period

Ensemble-based array design Model-based – Intraseasonal

Table 1: The basin-averaged theoretical analysis error variance of IMLD (m 2 ), and the percent reduction in parentheses ACOM2 ACOM3 OFAM Signal 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.

Ensemble-based array design Observation-based – Intraseasonal to interannual

Table 2: The basin-averaged theoretical analysis error variance of GSLA (m 2 ), and the percent reduction in parentheses Variance (m 2 ) Signal 81.0 Proposed array 34.9 (57%) Unstructured array 27.1 (66%) Structured array 29.5 (64%)

Ensemble-based array design Correlation maps

Ensemble-based array design Summary 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.

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