1. ECMWF/EUMETSAT NWP-SAF Satellite data assimilation Training Course
3-7 April 2017

2. ECMWF/EUMETSAT NWP-SAF Satellite data assimilation Training Course
The estimation and correction of systematic errors
(with some examples from climate reanalysis)
ECMWF/EUMETSAT NWP-SAF Satellite data assimilation Training Course

3. Why do we need to worry about biases ?
errors should be random and gaussian
Systematic errors must be removed otherwise biases will propagate in to the analysis (causing global damage in the case of satellites!). A bias in the radiances is defined as:
bias = mean [ Yobs – H(Xtrue) ]

4. Why do we need to worry about biases ?
ERA-40
Cosmic shower failure of MSU on NOAA-11
ERA-15
GLOBAL 200hPa temperature

5. The definition of a bias:
What we would like to quantify is:
mean [ Yobs – H(Xtrue) ]
But in practice all we can compute is the mean innovation :
mean [ Yobs – H(Xb) ]
…or the mean analysis residual :
mean [ Yobs – H(Xa) ]

6. Example of a persistent mean innovation suggesting a bias
AMSUA channel 14:

7. What can cause biases ? Instrument calibration / anomalies
Instrument characterisation
Radiative transfer model / spectroscopy
Surface emissivity model
Observation QC / selection / scale
NWP model used to diagnose bias

8. And what do they look like ?
Simple constant offset
Geographically / air-mass varying
Scan dependent
Time dependent
Satellite dependent

9. Scan variation of the bias:
NOAA-18 AMSUA temperature sounding channels
limb
limb
limb
limb
nadir
nadir

10. Time variation of the bias:
diurnal dependence of bias (K)
Seasonal dependence of bias (K)
drifting dependence of bias (K)
Dec date June 2004

11. Satellite dependence of the bias:
HIRS channel 5 (peaking around
600hPa on NOAA-14 satellite has
+2.0K radiance bias against model
HIRS channel 5 (peaking around
600hPa on NOAA-16 satellite has
no radiance bias against model.

12. Sources and Characteristics of the bias:
INSTRUMENT
AIR-MASS
SCAN
TIME
SATELLITE
RADIATIVE
TRANSFER
SURFACE
EMISSIVITY
QC DATA
SELECTION
NWP
MODEL

13. Sources and Characteristics of the bias:
INSTRUMENT
AIR-MASS
SCAN
TIME
SATELLITE
RADIATIVE
TRANSFER
YES
SURFACE
EMISSIVITY NO
QC DATA
SELECTION
NWP
MODEL

14. How do we correct for biases ?
The type of correction used must be suited to the types
of bias we have in our system and what we wish to correct (or perhaps more importantly what we do not wish to correct).
Simple constant offset C
Static air-mass predicted correction C[p1,p2,p3…]
Adaptive (in time) predicted correction C [p1,p2,p3….,t]

15. A predictor based bias correction:
We pre- define a set of predictors [P1, P2, P3…]
From a training sample of departures: [ Yobs – H(Xb/a)] we find the values of the predictor coefficients that best predict the mean component of the departures.
Predictors might be: mean temperature, TCWV, ozone, scan position, surface temperature etc..

16. Adaptive predictor based bias correction:
We pre- define a set of predictors [P1, P2, P3…]
From a training sample of departures: [ Yobs – H(Xb/a)] we find the values of the predictor coefficients that best predict the mean component of the departures.
The training sample will generally be the radiance departure statistics of the current assimilation window and the values of the predictor coefficients will be updated each analysis cycle (e.g. every 12 hours)

17. Adaptive predictor based bias correction:
External adaptive bias correction
Update bias coefficients
Perform analysis
Update bias coefficients
Perform analysis
Internal adaptive bias correction
Perform analysis + update bias
coefficients
Perform analysis + update bias
coefficients

18. Internal adaptive predictor based bias correction (VarBC)
Internal adaptive bias correction
Perform analysis + update bias
coefficients
Perform analysis + update bias
coefficients

19. Bias corrections of MSU2 in ERA-Interim
Jan 1989: Transition between two separate production streams
NOAA-14 recorded warm-target temperature changes, due to orbital drift (Grody et al. 2004)

20. When bias corrections go wrong
Correction of NWP model error
Under adaptive (Pinatubo)
Over adaptive
Interaction feedback with QC

21. When bias corrections go wrong
Correction of NWP model error
Under adaptive (Pinatubo)
Over adaptive
Interaction feedback with QC

22. Correction of NWP model error
Our training sample is
mean [ Yobs – H(Xb/a) ]
IASI channel 76

23. Correction of NWP model error
Our training sample is
mean [ Yobs – H(Xb/a) ]
Bias correction anchored to zero in Nov-07 for cycle 35R1
T799/L91
VARBC
NOAA-16 AMSUA channel 14

24. When bias corrections go wrong
Correction of NWP model error
Under adaptive (Cosmic rays and Pinatubo)
Over adaptive
Interaction feedback with QC

25. Under adaptive correction
Our training sample is
mean [ Yobs – H(Xb/a) ]
ERA-40
Cosmic shower failure of MSU on NOAA-11
ERA-15
200hPa temperature

26. Under adaptive correction
Our training sample is
mean [ Yobs – H(Xb/a) ]
NOAA-10
NOAA-12

27. Under adaptive correction
Our training sample is
mean [ Yobs – H(Xb/a) ]

28. When bias corrections go wrong
Correction of NWP model error
Under adaptive (Pinatubo)
Over adaptive
Interaction feedback with QC

29. Interaction with QC
Our training sample is
mean [ Yobs – H(Xb/a) ]

30. Interaction with QC
Our training sample is
mean [ Yobs – H(Xb/a) ]

31. Interaction with QC
Our training sample is
mean [ Yobs – H(Xb/a) ]

32. Interaction with QC
Our training sample is
mean [ Yobs – H(Xb/a) ]

33. How do we stop corrections going wrong :
Restrict number of predictors
Restrict values of predictors
Use of intelligent pattern predictors
Restrict time evolution of predictors
Anchoring
Use of the MODE

34. How do we stop corrections going wrong :
Restrict number of predictors
Restrict values of predictors
Use of intelligent pattern predictors
Restrict time evolution of predictors
Anchoring
Use of the MODE

35. A highly complex / adaptive correction of satellite temperature data has caused a strengthening of the N – S thermal gradient and degraded the U-component of wind, compared to a simple flat correction of the data.
Flat
bias
Complex
bias
With too many predictors the satellite data produces a mean analysis wind fit similar to a NO-SAT system !

36. How do we stop corrections going wrong :
Restrict number of predictors
Restrict values of predictors
Use of intelligent pattern predictors
Restrict time evolution of predictors
Anchoring
Use of the MODE

37. Anchoring with zero bias correction
AMSUA channel 14

38. Anchoring with zero bias correction

39. How do we stop corrections going wrong :
Restrict number of predictors
Restrict values of predictors
Use of intelligent pattern predictors
Restrict time evolution of predictors
Anchoring
Use of the MODE

40. Interaction with QC Our training sample is mean [ Yobs – H(Xb/a) ]
MODE
MEAN

41. ECMWF Data Monitoring and Automated Alarm System

47. Why do we need an automatic system ??

48. Various observation quantities
Feedback info (ODB)
Past Statistics
Per Data type, channel
Current Statistics
Per Data type, channel
Set and adjusted manually
Hard limits
Detect slow drifts
Soft limits
Detect sudden changes
Anomaly detection
Various observation quantities
Ignore facility
Warning message
Web

50. End

51. Interaction with QC
Our training sample is
mean [ Yobs – H(Xb/a) ]