1. Task 1 Definition of the AMSU+MHS measurement covariance

2. Overview The measurement error and error covariance for the millimetre-wave instruments was assessed by means of four independent methods: 1.Literature Study 2.Input from our consultant Bill Bell at UK Met Office UK Met Office diagnosed and operational measurement errors for AMSU-A and MHS 3.Input from ECMWF operational processing: Estimates of error covariance for AMSU-A and MHS through Hollingsworth/Lönnberg method Background error method Desroziers statistics 4.RAL method to estimate error covariance from comparison of bias corrected millimetre-wave measurements with forward model simulations based on observation state from infrared-only retrievals

3. Overview of AMSU Random Errors from Literature

4. Conclusions from Literature Review Some papers mix NEBT with systematic observation and forward model errors (apples and pears!). NEBT values in literature roughly consistent. Increased numbers (in some channels) for later publications. Some channels require bias correction (corrected in latest version of Lv1b data). Some channels have intermittent problems (abnormal bias or NEBT, so select dates accordingly) Most recent data of NEBT consistent with Met Office “diagnosed error”. All records of total measurement error from NWP analysis consistent with Met Office “operational error”.

5. RAL method of comparing MW measurements with simulations from IR only retrieval & PWLR 1.Get bias correction from mean of difference between observations and FM simulations based on IR-only retrieval. This gives the bias correction as a function of across-track scan position. 2.Estimate the measurement covariance (i.e. random errors) from the difference between bias-corrected MW observations and simulations based on IR-only retrievals. This is performed separately over land and sea. 3.Try two different methods to estimate the covariance: StdDev of Gaussian fit to histogram of all points (black lines). Estimated covariance is constructed using 3-sigma test to avoid outliers (red lines) – this is what we use. Self-consistency between the two methods is a cross- validation.

6. Observation – simulations from IR retrieval to provide MW bias correction Across-track scan index

7. Observation – simulations after MW bias correction

8. Observation covariance derived from MW residuals from IASI retrieval

9. ECMWF analysis of AMSU/MHS error covariance Analysis is based on covariances derived from pairs of First Guess and analysis departures Hollingsworth/Lönnberg: FG errors are spatially correlated, whereas observation errors are not. Background error: Subtracting scaled mapped background error cov. matrix from FG cov. Matrix. Desroziers: Consistency diagnostics of observation error characteristics. Mid-tropospheric to stratospheric channels for IASI, AMSU and MHS are uncorrelated and equal to NEBT. Surface channels observation errors exceed NEBT and are correlated. All three methods produce consistent results.

10. Error covariances by ECMWF Hollingsworth/Lönnberg Background error method Desroziers MHS AMSU-A SOME cross-correlation NO cross-correlation

11. ECMWF errors vs. RAL/MetOffice ECMWF errors consistent with RAL analysis and Met Office diagnosed errors. Met Office operational error includes contingency for model errors and cross- correlations (arguably too much according to Bormann and Bauer 2010). Desroziers (but not Hollingsworth/Lönneberg) found non-negligible cross- correlation errors for MHS only. RAL method results in slightly larger errors for window channels (channels 4-6) than other methods. In view of the first-order consistency of error datasets, the RAL method was chosen for the follow-on tasks because it ensures consistency with the infrared retrieval (and provides full covariance).