1. Specifying the Combined Effect of Data and Representation Error for Altimetry Data Assimilation Alexey Kaplan and Mark A. Cane Lamont-Doherty Earth Observatory of Columbia University in collaboration with David W. Behringer, NOAA/NCEP/EMC 13th JCSDA Technical Review Meeting & Science Workshop on Satellite Data Assimilation 13-15 May 2015, NCWCP, College Park, MD

3. Function of Representation Error Let the “true” field T be modeled incompletely: T = T m + T r (Only T m part is modeled) Then the observation equation, as a constraint on the modeled part, will become T obs = H*T m + [ H*T r + e obs ] […] is “effective” observational error: it includes the representation error as well.

4. Altimetry Corrections Tidal signal removed by FES2004 tidal model AVISO Dynamic Atmospheric Correction: Static “Inverted Barometer” response to pressure removed using ECMWF pressure field Dynamic response to wind and pressure simulated by Mog2D FE barotropic model

5. Special role of scale-separation in estimating contributions to observational and representation error Variability at scales ~ a few model grid sizes: not resolved by the model, contributes to the representation error Variability at scales < 1 model grid size might not be sampled well by observations (observations within individual grids assumed aggregated)

6. A typical situation in global or basin-wide ocean modeling: Model: typical grid resolution – 30km x 60km Data: Sea surface height altimetry – 6km footprint; SST – 1-4-25km averages, depending on the product; In situ observations – local.

7. MOM3 ODA experiments by D.Behringer: CTL (no assim) TS (temp & sal profiles) TS + altimetry 8x2 binom filt to AVISO Altim fields (right col)

8. Effect of the spatial filtering on the TSA assim (left) and altim fields (right)

9. Eddy-related error in altimetry or model fields by Ponte et al (2007): Computed as std SSH difference between simulations with 1/8 and 1 deg spatial resolution

10. Approach here: find a separating filter, such that T m = F[T m ] T r = (I-F)[T] ~ (I-F)[T obs ] Connection to the Bob Miller’s approach (Richman et al., 2005 and followups): T r = (I-E*E T )*(T obs -T f ), where E are leading model EOFs. But E*E T *T f ~ T f, thus T r = (I-E*E T )*T obs In other words, E*E T ~ F behaves as a spatial filter (with a split at smaller scales than in Miller’s case)

11. Conclusions and Outlook CONCLUSIONS Systematic inter-comparison of the NCEP MOM3 ocean data assimilation experiments by D.Behringer were performed at monthly and pentadal resolutions. Error maps for the monthly gridded altimetry fields were reinterpreted as contributions to the MOM3 model representation error, due to the higher smoothness of model fields compared to the altimetry fields. Appropriate filters for identifying the representation error part in the altimetry data were designed.