ECMWF/EUMETSAT NWP-SAF
Satellite data assimilation Training
Course
14-18 Mar 2016
The estimation and
correction of
systematic errors
(with some examples from climate reanalysis)
ECMWF/EUMETSAT NWP-SAF Satellite data
assimilation Training Course
Why do we need to worry
about biases ?
J ( x)  ( x  xb)T B 1 ( x  xb) 
( y  H[ x])T R 1 ( y  H[ x])
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) ]
Why do we need to worry
about biases ?
ERA-40
Cosmic shower failure of MSU on NOAA-11
ERA-15
GLOBAL 200hPa temperature
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) ]
Example of a persistent mean
innovation suggesting a bias
AMSUA channel 14:
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
And what do they look like ?
•
Simple constant offset
•
Geographically / air-mass varying
•
Scan dependent
•
Time dependent
•
Satellite dependent
Scan variation of the bias:
NOAA-18 AMSUA temperature sounding channels
limb
nadir
limb
limb
limb
nadir
Time variation of the bias:
diurnal dependence of bias (K)
Seasonal dependence of bias (K)
drifting dependence of bias (K)
Dec 2004
date
June 2004
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.
Sources and Characteristics of
the bias:
INSTRUMENT
RADIATIVE
TRANSFER
SURFACE
EMISSIVITY
QC DATA
SELECTION
NWP
MODEL
AIR-MASS
SCAN
TIME
SATELLITE
Sources and Characteristics of
the bias:
INSTRUMENT
AIR-MASS
SCAN
TIME
SATELLITE
RADIATIVE
TRANSFER
YES
YES
YES
YES
SURFACE
EMISSIVITY
YES
YES
YES
NO
QC DATA
SELECTION
YES
YES
YES
NO
NWP
MODEL
YES
YES
YES
NO
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]
A predictor based bias
correction:
1. We pre- define a set of predictors [P1, P2, P3…]
2. 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..
Adaptive predictor based
bias correction:
1. We pre- define a set of predictors [P1, P2, P3…]
2. 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.
3. 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)
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
Internal adaptive predictor
based bias correction (VarBC)
J ( x)  ( x  xb)T B 1 ( x  xb) 
( y  H[ x]  C[ p1, p 2..])T R 1 ( y  H[ x]  C[ p1, p 2..]) 
J ( P)
Internal adaptive bias correction
Perform
analysis +
update bias
coefficients
Perform
analysis +
update bias
coefficients
Bias corrections of MSU2 in ERA-Interim
Jan 1989: Transition
between two separate
production streams
NOAA-14 recorded warmtarget temperature changes,
due to orbital drift (Grody et
al. 2004)
When bias corrections go
wrong
•
Correction of NWP model error
•
Under adaptive (Pinatubo)
•
Over adaptive
•
Interaction feedback with QC
When bias corrections go
wrong
•
Correction of NWP model error
•
Under adaptive (Pinatubo)
•
Over adaptive
•
Interaction feedback with QC
Correction of NWP model error
Our training sample is
mean
[ Yobs – H(Xb/a) ]
IASI channel 76
Correction of NWP model error
Our training sample is
mean
[ Yobs – H(Xb/a) ]
T799/L91
NOAA-16 AMSUA channel 14
VARBC
Bias correction anchored to zero in
Nov-07 for cycle 35R1
When bias corrections go
wrong
•
Correction of NWP model error
•
Under adaptive (Cosmic rays and Pinatubo)
•
Over adaptive
•
Interaction feedback with QC
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
Under adaptive correction
Our training sample is
mean
[ Yobs – H(Xb/a) ]
NOAA-10
NOAA-12
Under adaptive correction
Our training sample is
mean
[ Yobs – H(Xb/a) ]
When bias corrections go
wrong
•
Correction of NWP model error
•
Under adaptive (Pinatubo)
•
Over adaptive
•
Interaction feedback with QC
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]
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
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
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 !
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
•
Anchoring with zero bias correction
STATISTICS FOR RADIANCES FROM NOAA-16 / AMSU-A - 14
MEAN FIRST GUESS DEPARTURE (OBS-FG) (BCORR.) (ALL)
DATA PERIOD = 2004070912 - 2004073118 , HOUR = ALL
EXP = EPMX
Min: -12.983
Max: 20.55
Mean: -2.1263
AMSUA channel 14
150°W 120°W
90°W
60°W
30°W
0°
30°E
60°E
90°E
120°E
150°E
1000
2.7
60°N
60°N
30°N
30°N
2.1
1.5
0.9000
0.3000
0°
0°
-0.3000
30°S
30°S
-0.9
-1.5
60°S
60°S
-2.1
-2.7
-1000
150°W 120°W
90°W
60°W
30°W
0°
30°E
60°E
90°E
120°E
150°E
•
Anchoring with zero bias correction
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
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]
MEAN
MODE
ECMWF Data Monitoring and
Automated Alarm System
Why do we need an automatic system
??
Feedback info (ODB)
Past Statistics
Current Statistics
Per Data type, channel
Per Data type, channel
Set and adjusted manually
Hard limits
Soft limits
Detect slow drifts
Detect sudden changes
Anomaly detection
Various observation quantities
Ignore facility
Warning message
Web
E-mail
End
Interaction with QC
Our training sample is
mean
[ Yobs – H(Xb/a) ]