VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan,...
Transcript of VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan,...
![Page 1: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/1.jpg)
VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA
Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012
![Page 2: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/2.jpg)
MOTIVATION
• Radiosondes data often used as reference for other data • Radiosondes data, especially at high altitudes, are not
unbiased • Changes bias due to:
– Change of radiosonde
– Change of locations for the same radiosonde
– Other equipment changes • Vertically constant wind direction bias in many radiosondes • Unadjusted biases affect trends and observations usage • A bias adjustment, which takes into account all these
problems, is needed
![Page 3: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/3.jpg)
• Previous works:
– Radiosonde adjustment during ERA-INTERIM
• Current approach – Variational Bias correction (VarBC) – Possible bias models – Grouping of data (radiosonde types, elevation angles, …)
• Preliminary results • Conclusions
OUTLINE
![Page 4: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/4.jpg)
Wind • No adjustment is done for radiosonde winds
Temperature • Adjustment of annual mean bias
– Use of RAOBCORE (Haimberger et al. 2007, 2008) – Based on time series of individual stations – Detection of shifts in background departure – Adjustments can change temperature trends
• Adjustment of daily/seasonal bias – Method based on solar elevation adjustment (Andrae et al. 2004) – Based on station groups – Four classes of solar elevation – Adjustments calculated from the statistics of background departures
over the previous 12 months
ERA-Interim adjustment
![Page 5: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/5.jpg)
ERA-Interim adjustment
1960 1970 1980 1990 2000 2010−2
−1
0
1
2
[K]
6
SNHT CURVE
12h, 200 hPa
Trend 1979−2011:−0.14 ± 0.01 [K/10a]
0
100
200
300
400
500
600FIRST GUESS DEP.
1960 1970 1980 1990 2000 2010−2
−1
0
1
2
−2
−1
0
1
2
[K]
12h, 200 hPa
Trend 1979−2011: 0.03 ± 0.00 [K/10a]GLOBE BIAS CORR.
• Russian radiosonde, 12
UTC, 200hPa • Start from 1979, when
satellite data are available • First guess departure, using
uncorrected radiosondes • Bias correction to apply • Bias correction only until
2008, not applied any more • After 2008 less departure
but still existing, a bias adjustment is needed
• Limited departure probably due to changes on radiosondes dataset in the Russian federation
![Page 6: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/6.jpg)
• The observations are considered biased, a linear predictor model is used as observation operator in the 4DVAR equations:
• Introduction of a “bias term” in the variational cost function
• With xb and βb a priori estimations of model state and bias control parameters
• A large Bβ allows the parameter estimates to respond more quickly to the latest observation.
• The adjustment of the radiosondes depends on the resulting fit of the analysis to all other OBS, given the background from the model.
Variational Bias correction
![Page 7: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/7.jpg)
• Bias in observations can change during the time (wind and temperature)
• Seasonal and daily variations in bias exist (temperature)
• The bias model :
Must be chosen according to observations and physical origins of the bias.
• We assume the model unbiased, the presence of model bias attributes a wrong bias to the observations where there are not enough observations to correct the analysis
Variational Bias correction
b(x,β) = β0 + βii∑ pi (x)
![Page 8: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/8.jpg)
Wind direction bias
• Marion Island – Indian Ocean (extreme bias) – FG-departure wind direction compared to ERA-40 – 1978, 1982: Wind direction change throughout the
whole profile
Gruber and Haimberger, 2008
![Page 9: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/9.jpg)
Wind direction bias
Wide areas with wind direction bias over Asia
Isolated stations which have strong influences on the analysis
Gruber and Haimberger, 2008
• Due to constant vertical bias only a constant bias parameter is needed
• Constant wind direction bias parameter for the whole
profile of each station
b
![Page 10: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/10.jpg)
• One constant predictor • Problem:
– Model: u,v – Control variable in cost function: wind direction
• Transformation: From u,v Wind direction Bias model Bias back to u,v
Wind direction bias
![Page 11: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/11.jpg)
• Bethel, Alaska - 70219 • Athens, Greece - 16716 • Marion Island, Indian Ocean - 68994 • Aktynbinsk, Russia – 35229
• Evaluation of first experimental runs July and December 2011
• Test setup: – 15 degree wind direction bias added to 4 radiosonde
stations from day 4 onwards:
Wind test for bias correction
![Page 12: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/12.jpg)
Wind July 2011 Bethel, 70219
• 500 hPa but same bias over the whole profile
• To correct 15 degree • Bias correction around 2
degree after 31 days • The bias correction is in
the “right” direction but the amount is too low
OBSERVATIONS
BIAS CORRECTION
DEG
REE
D
EGR
EE
July
July
Bias + VarBC Control
![Page 13: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/13.jpg)
Wind July 2011 Marion Island, 68994
OBSERVATIONS
BIAS CORRECTION
DEG
REE
D
EGR
EE
• 500 hPa but same bias over the whole profile
• To correct 15 degree • Bias correction around 4
degree after 31 days • The bias correction is in
the “right” direction but the amount is too low
• In this case the correction is larger
July
July
Bias + VarBC Control
![Page 14: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/14.jpg)
First guess departure T
• Analysis of July 2011
• Average of first guess departure
• Results divided by station type
• Large differences between different station types (necessity of grouping)
• Different behaviour between stations at night and at large solar elevations
– Russian stations near 50 hPa positive departure for large solar angles, around 0 during the night
– Japanese and USA stations different path, positive departure in the upper levels
• Height dependencies are visible
• Bias depends on RS-type, pressure and solar angle
Night Θ < -7.5°
Θ > 22.5°
k
k
![Page 15: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/15.jpg)
1. Bias model
– First approach, seems suitable for US and Japanese radiosondes at some periods
– Not suitable for vertically nonlinear bias profiles
2. No functional relationships, instead estimate bias parameters for pressure layers, solar elevations and station groups – More bias parameters need to be estimated
3. First results (test) using only a vertically constant bias parameter valid for all solar elevations
Radiosonde temperature bias correction
b
b
![Page 16: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/16.jpg)
12 UTC 00 UTC
![Page 17: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/17.jpg)
1. Bias model
– First approach, seems suitable for US and Japanese radiosondes at some periods
– Not suitable for vertically nonlinear bias profiles
2. No functional relationships, instead estimate β0 for different pressure layers, solar elevations and station groups – More bias parameters need to be estimated
3. First results (test) using only a vertically constant bias parameter valid for all solar elevations
Radiosonde temperature bias correction
b
b
![Page 18: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/18.jpg)
-0.006-0.005-0.004-0.003-0.002-0.001
00.0010.0020.0030.0040.0050.0060.007
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series bias correction 20hPa
all Russia USA Japan
Magics 2.14.11 (64 bit) - lxa15 - ermm - Thu Apr 12 12:05:24 2012
NIGHT
-0.0010
0.0010.0020.0030.0040.0050.0060.0070.0080.009
0.010.0110.0120.0130.014
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series bias correction 20hPa
all Russia USA Japan
Magics 2.14.11 (64 bit) - lxa15 - ermm - Thu Apr 12 11:57:32 2012
SOLAR ELEVATION > 22.5°
• Time series for vertical mean bias correction
• Generally very small bias corrections
• For higher solar elevations larger bias corrections
• Radiosonde types with larger first-guess departure (Russia) have also the higher bias corrections
• The bias corrections are in the “right” direction but the amount is too low
Bias adjustment
![Page 19: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/19.jpg)
First-guess departure T bias correction
0.01
0.02
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series biascorrection 23921
bias correction23921
Magics 2.14.11 (64 bit) - lxa15 - ermm - Tue Apr 17 14:32:44 2012
-2
0
2
4
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series fg departure 23921
fg departure 23921
Magics 2.14.11 (64 bit) - lxa15 - ermm - Tue Apr 17 11:44:50 2012
• Station 23921, Russia
• Vertically averaged first guess departure positive at most times
• We expect a bias correction which converges to a positive value of about 0.4K
• The bias correction for this station increases until a value around 0.02K and then decreases (negative fg-departure)
• The bias correction is in the “right” direction but the amount is too low
• B too small?
• This is just a start, much development still needed
<T>=0.389 K
![Page 20: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/20.jpg)
CONCLUSIONS AND OUTLOOK
• Variational bias correction for temperature for radiosondes is far away from
a final solution. For wind a constant parameter could be sufficient • A different approach as in ERA-INTERIM • First results: too small bias corrections but in the right directions • VarBC can be applied where RAOBCORE detects the shifts • Anchoring using “trusted” radiosondes and nowadays GPS data
Temperature • Use of a “physical approach” (function of predictors) taking into account
grouping of radiosondes • Different predictors and functions for different groups have to be tested
(work in progress)
Wind • The Bias is normally quite constant over the whole profile • Larger Bβ in order to have faster adjustments
![Page 21: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/21.jpg)
![Page 22: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/22.jpg)
QUESTIONS
• Definition of the matrix Bβ
• RMS
• Examples Temp
![Page 23: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/23.jpg)
DEFINITION OF Bb
• We do not know the actual error covariances of β (Bβ) • We use Bb to control the adaptivity of the bias parameters:
– Increase Bb for faster bias adjustments; decrease for slower adjustments
• We take diagonal Bβ related to the diagonal of R:
for i=1,…,Nj number of predictors for the variable j
• In this way the part in the cost function related to the bias parameter background constraint for the variable j has the same weight as Mj new observations.
![Page 24: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/24.jpg)
RMS first guess departure T
• The negative departures do not counteract the positive departures
• RMS give more weight to the larger first guess departure
• The Russian stations has larger RMS in the upper levels and near 200 hPa
• Japanese’s stations RMS in the upper levels larger for higher solar angles
• USA stations better than Russian’s and Japanese’s for Θ > 22.5°
• Groups for different stations are desirable
1000
2000
5000
10000
20000
50000
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
Vertical profile RMS first guess departure < 7.5
all
Russia
USA
Japan
Magics 2.14.11 (64 bit) - lxa15 - ermm - Wed Apr 11 16:05:48 2012
1000
2000
5000
10000
20000
50000
-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
Vertical profile RMS first guess departure > 22.5
all
Russia
USA
Japan
Magics 2.14.11 (64 bit) - lxa15 - ermm - Wed Apr 11 16:01:42 2012
Night Θ < -7.5°
Θ > 22.5°
![Page 25: VARIATIONAL BIAS CORRECTION FOR … · VARIATIONAL BIAS CORRECTION FOR RADIOSONDE DATA Marco Milan, Christina Tavolato, Leopold Heimberger Washington 9/05/2012](https://reader031.fdocuments.us/reader031/viewer/2022022021/5b9f59cc09d3f2083f8cff3c/html5/thumbnails/25.jpg)
First-guess departure bias correction
• Station 27730, Russia
• Vertical averaged first guess departure change from positive to negative
• The negative bias corrections could counteract the positive
• The bias corrections could be too slow
-1
0
1
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series fg departure 27730
fg departure 27730
Magics 2.14.11 (64 bit) - lxa15 - ermm - Tue Apr 17 11:44:47 2012
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
0.011
0.012
0.013
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31Jul
2011
time series biascorrection 27730
bias correction27730
Magics 2.14.11 (64 bit) - lxa15 - ermm - Tue Apr 17 14:32:41 2012
<T>=0.137K