CrIS Noise and Moldel Error Covariance

1

Introduction CrIS Noise Covariance Model Error Covariance Addtional Material

CrIS Noise and Moldel Error Covariance

L. Larrabee Strow, Howard Motteler, and Sergio De-SouzaMachado

UMBCDepartment of Physics and

Joint Center for Earth Systems Technology

STAR Science MeetingAug. 9, 2016

2


NWP Centers: CrIS Covariance Higher than IASI

Derive CrIS Noise Covariance

Using 1 day of ICT data, derive noise error covariance

Mimic?? NWP (Noise+Model) Error Covariance

Match ECMWF analysis/forecast to IASI, CrIS clear scenesConvert IASI observations (different noise) to CrISCompare bias error covariancesTry to convert CrIS error covariance to (IASI –> CrIS) errorcovariance and compare

Day: Jan 18, 2016SDR Code: CCAST standard

3


NWP Data Assimilation

Data assimilation ingests the observations y and minimizes acost function J

J = (x − xb)T B−1x (x − xb)+ (y − K(x))T (E + F)−1(y − K(x))

in order to find the best analysis increment to the modelbackground x − xb.

Bx : Background error covariance

K: CrIS RTA

E + F = R: Observation error covariance (often diagonal)

E: Instrument error covariance

F : Representativeness, nonlinearity, RTAcovariances

NPW centers are finding R is larger for CrIS than IASI. But this is generally

presented as correlations rather than covariances.

4


Present Status

A diagonal R was/is the norm in the past.

Many centers working towards off-diagonal R

This should lead to better use of sounder data, usinglower error estimates.

If practical, I hope this then leads to using morechannels, esp. for CrIS which has low noise, but slightlywider Jacobians

Recent Relevant Journal Articles

Effect of self-apodization correction on Cross-track Infrared Sounderradiance noise, Han et. al. (Applied Optics, 2015)

Infrared atmospheric sounder interferometer radiometric noise assessmentfrom spectral residuals, Carmine Serio et. al. (Applied Optics 2015)

Enhancing the impact of IASI observations through an updatedobservation-error covariance matrix, Niels Bormann etc. al (QJRMS 2016)

5


NWP “Correlation” Observations for CrIS, IASI

NRL CrIS/IASI Error Correlation

15#

IASI$vs$CrIS$Correla-ons$

ECMWF IASI Error Correlation

Updating IASI Observation-Error Covariance Matrix 1769

ozone and humidity channels. The initial assimilation choicesfor IASI are outlined in Collard and McNally (2009). The bulkof the assimilated data are observations unaffected by clouds,identified using the scheme of McNally and Watts (2003), whichlooks for cloud contamination based on evaluating background-departure signatures. The scheme has subsequently been refined,for instance, by taking into account information on clouds from acollocated imager (Eresmaa, 2014). The cloud-detection scheme isapplied to temperature-sounding channels; for the water-vapourand ozone band, the cloud screening is linked to the resultsfrom the temperature-sounding channels. Cloud-affected dataoriginating from completely overcast scenes are assimilated aswell, using the methods described in McNally (2009). No IASIradiances are currently used over land, primarily due to largeruncertainties for the skin temperature and surface-emissivityspecification, which also affects successful cloud detection. TheIASI observations are thinned to a resolution of 140 km.

Systematic errors between observed and modelled IASIobservations are removed through variational bias correction(e.g. Dee, 2004). The bias-correction models are similar to thoseused for other sounder radiances at ECMWF. They consist of alinear model for the air-mass bias, with a constant componentand four layer thicknesses calculated from the first guess aspredictors (1000–300, 200–50, 50–5, 10–1 hPa). Scan biasesare modelled through a third-order polynomial in the scanangle. No air-mass bias correction is used for some windowand lower sounding channels (380–1180 and 1820–2200), toavoid unwanted interaction between the cloud detection and thevariational bias correction (e.g. Auligne and McNally, 2007).

Further details on the assimilation of IASI data can be foundin Collard and McNally (2009), with updates in McNally (2009),Han and McNally (2010), Dragani and McNally (2013) andEresmaa (2014).

3. Observation-error covariance derived from diagnostics

The observation-error covariance matrix used in this studyhas been derived using the departure-based diagnostic methodsapplied in Bormann et al. (2010), with some further adjustments.The derivation and the adjustments are described in more detailin Appendix A. The resulting matrix is shown in Figures 2and 3 in terms of the error standard deviation (σo) and aninterchannel error correlation matrix. Note that the diagnosedand adjusted observation error (dashed black line) is slightlyabove the standard deviation of background departures (dottedline) for some channels, due to the adjustments to the eigenvaluesdescribed in Appendix A. Spatial error correlations are neglected.

The unscaled covariance matrix shows the features commonto similar departure-based estimates (e.g. Garand et al., 2007;Bormann et al., 2010; Stewart et al., 2013), which are as follows:

(1) error standard deviations close to an average instrumentnoise estimate for upper tropospheric and stratospherictemperature sounding channels, with weak error correla-tions;

(2) error standard deviations much larger than the instrumentnoise for water-vapour channels, combined with significantinterchannel error correlations; and

(3) error standard deviations larger than the instrumentnoise for lower temperature sounding, window andozone channels, together with weaker, but still significant,interchannel error correlations.

Error correlations introduced through apodization are alsoapparent for neighbouring channels or near-neighbours, albeitsomewhat reduced compared with theoretical values as a resultof the adjustments described in Appendix A. It should be notedhere that the instrument noise estimate shown in Figure 2 hasbeen converted from radiance to brightness temperature spaceusing brightness temperatures for a standard atmospheric profile.As this conversion is nonlinear and the instrument noise is

Channel number

Est

imat

ed e

rror

[K]

16 70 104

131

157

179

199

222

246

267

286

308

331

362

389

457

921

1579

2889

5480

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

648.

75

662.

25

670.

75

677.

5

684

689.

5

694.

5

700.

25

706.

25

711.

5

716.

25

721.

75

727.

5

735.

25

742

759

875

1039

.5

1367

2014

.75

Wavenumber [cm–1]

Instrument noise

Operational observation error

Standard deviation of background departures

Diagnosed and adjusted observation error

Diagnosed and adjusted observation error times 1.75

Figure 2. Diagnosed and adjusted observation-error standard deviations (σo)for assimilated IASI channels (dashed black), together with an estimate for theinstrument noise (solid grey), the standard deviations of background departures(dotted) for the sample used to diagnose the observation-error covariance andthe observation-error standard deviations currently assumed in the operationalECMWF system (dashed grey). Also shown are the diagnosed and adjustedobservation-error standard deviations times an inflation factor of 1.75 (solidblack). The instrument noise has been converted from radiances to brightnesstemperatures using a mean scene temperature per channel. See the main text andAppendix A for further details about the derivation of the diagnosed observationerrors and the adjustments applied to them.

−0.2−0.15−0.1−0.0500.050.10.150.20.250.30.350.40.450.50.550.60.650.70.750.80.850.90.951

Channel number

Cha

nnel

num

ber

16 70 104

131

157

179

199

222

246

267

286

308

331

362

389

457

921

1579

2889

5480

16

70

104

131

157

179

199

222

246267286

308

331

362

389

457

921157928895480

648.

75

662.

25

670.

75

677.

5

684

689.

5

694.

5

700.

25

706.

2571

1.5

716.

25

721.

75

727.

5

735.

25

742

759

875

1039

.513

6720

14.7

5

Wavenumber [cm–1]

Figure 3. Observation-error correlations used in this study for assimilated IASIchannels. See main text and Appendix A for further details.

only constant in radiance space, the actual instrument noisein brightness temperature space is instead dependent on thescene temperature. This effect is not considered throughout thisarticle. Figure 2 also includes the currently assumed observationerror for IASI; this is significantly larger than that suggested bythese diagnostics, albeit it does not take into account any errorcorrelations.

As evident from Figure 2, the diagnostics suggest a ratherlarge contribution from observation errors other than instrumentnoise for many channels. It is beyond the scope of this article toinvestigate the origin of these errors. Depending on the spectralregion, leading contributors are expected to be representativenesserror, cloud-screening error and radiative transfer error. It is likely

c⃝ 2016 Royal Meteorological Society Q. J. R. Meteorol. Soc. 142: 1767–1780 (2016)

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Noise Correlation

Following Han et. al., reproduce noise figures

Expand from 512 points to 1-day (either Jan 18 or 20,2016)

Do SVD analysis to determine correlated noise, about1-2% for Hamming (see Additional Material at end of talk)

Effect of hamming on covariance and correlationmatrices

Keep in mind:

noise =√(covi,i)

corri,j = covi,j√(covi,i·covj,j)

CrIS has lower noise than IASI

CrIS Hamming has lower noise than Sinc

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Noise Correlation Data Analysis

One day of ICT (blackbody) calibrated data.

Just substitude ICTi into SDR equation instead of ESi

Remove resulting slow variation in ICT B(T) with a31-point moving average smoother

For SVD correlated noise analysis divide by nominal noise

8


LongWave Noise Correlations

Sinc Noise Correlation Hamming Noise Correlation

These smoothed correlation matrices suggest off-diagonalcorrelated noise at the 2% level. Higher for hamming.

9


LongWave Noise Covariance

Sinc (or Hamming) Noise Covariance Hamming - Sinc Covariance

No difference between Sinc and Hamming off-diagonals!Lower Hamming noise increases off-diagonal correlations.

10


Other Sources of Correlation?

ICT environmental model? (in longwave ± -0.04 to -0.01K)ICT calibration variability, esp. over orbit?Small orbital calibration errors could produce thesecorrelations; TVAC results (day in the life?)IASI blackbody has a constant temperature

ICT Calibrated Temperature vs Time

0 5 10 15 20 25

Time (hours)

280.3

280.4

280.5

280.6

280.7

280.8

280.9

281

281.1

B(T

) in

K o

f IC

T

Scaled ICT T-sensor vs (ICT-SP) Counts

0 5 10 15 20 25

Hours

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

No

rma

lize

d U

nits

ICT-Sensor

ICT Counts

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Bias Correlation Data Analysis

Clear ocean scenes, tropical to keep F smaller

Convert IASI to CrIS ILS “IASI–>CrIS”

Modify CrIS to have “IASI–>CrIS” noise

Concentrate on 650-750 cm−1

F covariance clearly dominates rest of LW and MW (SST,water vapor)

??? Our F is larger than NWP and mixes background andobservation errors, and has no integration of the modelto the observation time, etc etc. We are using ECMWF3-hour forecast/analysis

??? Consequently, our results are, at most, only usefulfor relative comparisons

12


Clear Scene Locations for CrIS

Color is hour.

13


CrIS and IASI Clear Biases

800 1000 1200 1400 1600 1800 2000 2200 2400

Wavenumber (cm-1

)

-2

-1.5

-1

-0.5

0

0.5

1

1.5

Bia

s in

K

Night is similar, IASI 0.2K warmer in window region.

14


Bias Std and Noise

Bias Std

650 700 750

Wavenumber (cm-1)

0.1

0.2

0.3

0.4

0.5

0.6

Std

of

Bia

s in

K

IASI-->CrIS

CrIS

CrIS-Mod

IASI-Orig

Noise

650 700 750

Wavenumber (cm-1)

0

0.1

0.2

0.3

0.4

0.5

0.6

No

ise

in

K

IASI-CNES

IASI-Carmine

IASI-Carmine --> CrIS

CrIS

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Covariance Ratios (IASI/CrIS)

1000 1500 2000 2500

Wavenumber (cm-1)

0

1

2

3

4

5

6

Covariance R

atio o

f IA

SI/C

rIS

650 700 750

Wavenumber (cm-1)

0

0.5

1

1.5

2

2.5

3

3.5

Co

va

ria

nce

Ra

tio

of

IAS

I/C

rIS

F covariances (Representativeness, RTA, etc.) constant between instruments

E covariances scale with instrument noise

Low noise implies higher off-diagonal correlations

16


Effective Model Error

650 700 750

Wavenumber (cm-1)

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Mo

de

l E

rro

r (K

)

CrIS

IASI-->CrIS

IASI model error up to 3X larger than CrIS??F =

√(std2 − inoise2)

17


CrIS vs IASI CorrelationsCrIS IASI

(CrIS + IASI Noise) - IASI (CrIS + IASI Std) - IASI

18


Day vs Night CorrelationsCrIS Night IASI Night

CrIS Day IASI Day

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Corrected Day CorrelationsCrIS IASI

(CrIS + IASI Noise) - IASI (CrIS + IASI Std) - IASI

20


Problem with LongWave IASI Biases?

0 5 10 15 20

Hour of Day

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Bia

s in

K

Blue: CrIS, Orange: IASI

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0 5 10 15 20

Hour of Day

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Bia

s in

K


22



0 5 10 15 20

Hour of Day

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Bia

s in

K


23


CrIS Radiometric Stability: dBT/dt Rates

600 800 1000 1200 1400 1600 1800

Wavenumber (cm-1)

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

dB

T/d

t in

K/y

ear

Blue: Observed Rate Red: Fit residuals

24


CrIS Stabliity from dBT/dt Rate Fits

Do an OEM fit of dBT/dt (K/year) CrIS rates for tropicalclear ocean spectra bias versus ERA.

Fits for T(z) and H2O (z) are close to ERA

OEM fit for CO2

CO2 CrIS = 2.45 ± 0.006 ppm/year (error is wrong)NOAA ESRL CO2 = 2.39 ± 0.09 ppm/year(NOAA ESRL CO2- CrIS CO2) = -0.002K/year ± 0.004K/year

OEM fit for CH4 (just final result)-0.0008 K/year ± 0.002 K/year

Need to include observation covariance to get correct OEMerrors!

25


Conclusions

How can NWP utilize low noise of CrIS?

Could CO2 be the cause of some of these correlations?Rd-do analysis in Spring when N/S gradient exists.

Need closer interactions between instrument, RTA, andNWP researchers?

If NWP includes observation covariances, can they nowincrease the number of channels used?

CrIS channels may have slightly higher correlations thanIASI, but maybe due to other IASI issues?

IASI calibration appears to vary slightly with some orbits?

JPSS-1 CrIS will have a better blackbody, will that changethese observations?

Exactly how well does the CrIS ICT temperature matchthe ICT emission over time? What can TVAC tell us?

26


Additional Material

SVD analysis of CrIS correlated noise is shown on the nextthree slides.

27


LongWave Noise Correlations

Sinc

600 700 800 900 1000 1100

Wavenumber (cm-1)

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

Fra

ction o

f N

ois

e

1

2

3

4

Hamming

600 700 800 900 1000 1100

Wavenumber (cm-1

)

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005Hamming

1

2

3

4

28


MidWave Noise Correlations

Sinc

1200 1300 1400 1500 1600 1700 1800

Wavenumber (cm-1

)

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

Arb

. U

nits

1

2

3

4

Hamming

1200 1300 1400 1500 1600 1700 1800

Wavenumber (cm-1

)

0.96

0.965

0.97

0.975

0.98

0.985

0.99

0.995

1

1.005

Arb

. U

nits

Hamming

1

2

3

4

29


ShortWave Noise Correlations

Sinc

2150 2200 2250 2300 2350 2400 2450 2500 2550

Wavenumber (cm-1

)

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

Arb

. U

nits

1

2

3

4

Hamming

2150 2200 2250 2300 2350 2400 2450 2500 2550

Wavenumber (cm-1

)

0.92

0.93

0.94

0.95

0.96

0.97

0.98

0.99

1

1.01

Arb

. U

nits

Hamming

1

2

3

4

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CrIS Noise and Moldel Error Covariance