1. New DA techniques and applications for stratospheric data sets
Patrick Laloyaux - Earth System Assimilation Section
Acknowledgement: Massimo Bonavita, Jacky Goddard, Niels Bormann, Heather Lawrence, Wei Han, Elias Holm, Simon Lang, Mike Fisher, Yannick Tremolet, Hans Hersbach, Dick dee and many others
In in Sept 2011
Out in June 2013
In in Nov 2016

2. Talk outline Different types of errors (bias-variance decomposition)
How to deal with systematic errors from observations and model in data assimilation?
Variational bias control (VarBC)
Weak constrant 4D-Var

3. 4D-Var formulations Bias-blind data assimilation
designed to correct the background with observations when errors are random with zero means
model is assumed to be perfect
Biases in reality
Observations (satellite miscalibrations)
Observation operator (approximations in radiative transfer calculations)
Model trajectory (inaccurate surface forcing, simplified representations of physics)
Initial value problem

4. Biases in observations
A possible to way to detect systematic errors in observations is to monitor the difference between the observations and the background (background departure)
Background departure with respect to the scan position of the satellite instrument
AMSUA channel 7
Mean Obs-FG
Limb
Nadir
Limb
Observations are unbiased for the nadir position, but biased for the limb position

5. Biases in observations
Timeseries of background departure (blue) for HIRS channel 5 on NOAA-14 and NOAA-16
HIRS channel 5 on NOAA-14 satellite has +2.0K radiance bias against FG
Same channel on NOAA-16 satellite has no radiance bias against FG
NOAA-14 channel 5 has an instrument bias

6. Biases in observation operators
Observation operators map geophysical variables to observation equivalents.
For satellites, the geophysical variables are converted in radiances using a radiative transfer model (RTTOV)
Background departure for two different spectroscopies used in the radiative transfer model
Mean Obs-FG
Channel number (HIRS)
The new spectroscopy (purple) reduce the bias in the radiative transfer model

7. Model for the observation biases
For each satellite/sensor/channel, a different bias model is built and depends on bias parameters and state vector
Predictors can correct biases that are constant, that depends on the atmospheric state or that depends on the scanning instrument
How to estimate the bias parameters?

8. 4D-Var formulations Bias-aware data assimilation (VarBC)
estimate simultaneously the initial condition and parameters of the observation bias model
the bias model copes with instrument miscalibration or systematic errors in the observation operator
the model is a strong constraint

9. Introduction of VarBC in operations
Analysis and background departures (mean and standard deviation) with respect to conventional temperature observations
Introduction of VarBC
in ECMWF operations
Reduction in the background and analysis biases

10. Why VarBC works well? More degrees of freedom to fit the observations
Errors in the difference (y – h(x)) arise from:
errors in the actual observations
errors in the observation operator
errors in the model background
There is no general method for separating these different error sources
we only have information about differences
there is no true reference in the real world!
We need to prevent VarBC to correct the model error. In a worst-case scenario, this could cause the assimilation to drift toward the model climate

11. Anchoring information for VarBC
Some observations are assumed to be biased free. This allow the VarBC scheme to disentangle the observation and the model errors
AMSU-A 14
GPSRO, radiosondes

12. AMSU-A Channel 14
What is happening if AMSU-A Channel 14 is not used as an anchor for VarBC?
Unrealistic drifts of VarBC because the presence of model bias in the stratosphere.
The difference between the observations and the model equivalents is completely absorbed by VarBC

13. Constrained VarBC
Apply VarBC to AMSU-A Channel 14, but with an extra constraint on the bias model
Known bias pattern are now captured, and unrealistic drifts are still avoided.
New AMSU-A 14 bias corrections
To be implemented in CY45R1 (AMSU-A 14/ ATMS 15)
W. Han, N. Bormann, H. Lawrence. 2016

14. Talk outline Different types of errors (bias-variance decomposition)
How to deal with systematic errors from observations and model in data assimilation?
Variational bias control (VarBC)
Weak constrant 4D-Var

15. Biases in model
Timeseries of background departure with respect to temperature from radiosondes at 100 hPa
Assimilating GPS-RO observations from December 2006 onwards reduce the cold bias in the model

16. Biases in model
Timeseries of estimated temperature model error after 12 hours [fc12h – an]
Pressure hPa
Nov 2016
Aug 2017
There are systematic differences between forecasts and analyses in the upper stratosphere
Estimating the systematic error in the model over a short period of time is not straightforward (disentangle model error and IC error)

17. Illustration of model biases in data assimilation
Assimilation of unbiased observations in a biased model (dashed curve is truth, solid curve is analysis).
Positive bias in the analysis, depending on the observation density
Algorithm that learns, after the first few analyses, that the model consistently overestimates the observation. It then uses this information to adjust subsequent model predictions
D. Dee, 2004

18. 4D-Var formulations
Bias-aware data assimilation (VarBC + Weak constraint)
Introduce additional controls to target an unbiased analysis and to move the assimilation away from a perfect-model trajectory
The model error represents the systematic error which develops in the model over the assimilation window
The model error covariance matrix Q constrains the model error field
Size on the control vector increased by ~25%
Y. Tremolet. 2006

19. Implemented in operations (22 Nov 2016, CY43R1)
Weak constraint 4D-Var has been implemented in operations
constant model forcing applied every hour
 only active above 40 hPa
Estimate the model error covariance matrix (Q)
run the ensemble forecasting system (ENS) with SPPT (51 members with the same initial condition for 20 days)
 differences after 12 hours are used to compute Q

20. Impact of weak constraint 4D-Var
Comparison between strong and weak constraint 4D-VAR.
Verification against GPS-RO (good for highlighting improvements in the stratosphere)

21. Impact of weak constraint 4D-Var
Comparison between strong and weak constraint 4D-VAR in the stratosphere. Verification against radiosondes.

22. Monitoring of the weak constraint 4D-Var in operations
Timeseries of estimated temperature model error after 12 hours [fc12h – an]
Pressure hPa
Timeseries of temperature model error estimated by the weak constraint 4D-Var
Pressure hPa
Nov 2016
Aug 2017
Negative (positive) model errors are corrected by positive (negative) forcings, especially in the upper stratosphere

23. Weak constraint 4D-Var in the troposphere
Model error variability for vorticity at 850hPa (September 2016)
Spurious day-to-day variability near airports
T399
T64
Q T399
Q T64
Aircraft observations are fitted in the 4D-Var by changing the model error
current model error covariance matrix contains small scales (T399)
new model error covariance matrix contains longer scales (T64)
localisation techniques and better set of ensemble forecasts to build Q

24. Summary and conclusions
4D-Var designed to correct the background with observations when errors are random with zero means
VarBC deals with systematic errors in observations and observation operators
Anchoring information is crucial to disentangle observation and model errors
Constrained VarBC allows to avoid anchoring of AMSU-A 14
Weak constraint 4D-Var deals with systematic errors in model
Performs well in the stratosphere but more work is required to disentangle background and model errors in the troposphere
Q matrix with longer correlation lengthscales and proper localisation is required