Ensemble spreads and coupled error correlations in the Coupled ECMWF ReAnalysis for the 20th century (CERA-20C)

Xiangbo Feng, Keith Haines, and David Mulholland Department of Meteorology, University of Reading, UK

(Great thanks to Patrick Laloyaux and Eric Boisseson)

CDAW2016, Toulouse

Outline

1. Motivations

2. Methods and CERA-20C

3. Results at different time scales (short to long ranges)

4. Summary

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1. Motivations

• Towards 'strongly' coupled DA, which uses observational information from in one medium to alter increment in the other medium, based on the existing ‘weakly’ coupled DA system. This requires calculation of error covariances to control this spreading of information (the B matrix)

• To diagnose the behaviour of uncertainties (errors) in the atmosphere and ocean components of CERA-20C, which is designed as a long-term consistent climate reanalysis, and identify the physical processes behind.

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2. Method and CERA-20C • Ensemble Method

Ensemble anomalies from the mean in the background fields are treated as the background errors [Bannister, 2008].

B can be instantaneous (each day) or climatological (time average) matrix.

The ensemble mean represents the ‘truth’, while the ensemble spread (standard deviation of departures) is defined as the ‘uncertainty’.

• CERA-20C

An ensemble of 10 members of ocean-atmosphere coupled reanalysis for 1900-2010, based on ocean-atmosphere coupled system, coupling each hour. 4D-VAR and 3D-VAR are applied for atmosphere and ocean, with SST constrained by HadISST2 via a relaxation scheme. See details in Laloyaux et al. [2016].

SST and T2m (2-meter air temperature) are chosen to represent the ocean and atmosphere components.

Background fields in DA cycle are used, including daily background at different lead times in Jan 2006 and the monthly means of daily means of background (3hrs resolution) over 1900-2010.

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SST spread T2m spread

3.1 Ensemble spreads and correlations within 24hrs +24h background errors, based on daily ensemble, 1st-31st January 2006

Error correlations

• T2m spread is large in ITCZ and in areas of western boundary currents. • T2m spread based at middle latitudes is weather dependent, but SST is not. • Time scales of spreads are different. • Error correlations are varying at high frequency.

Green contour lines indicate MSLP for ensemble mean

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SST

T2m

+0h +24h +12h

• T2m spread based on daily scales is large in ITCZ and in areas with western boundary currents. • SST spread is large in summer and in upwelling regions • T2m uncertainty is growing with time, but SST is not

Time average of background spreads, daily ensemble, 1st-31st January 2006

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Time average of error correlations

• T2m-SST error correlations are stronger in summer regions and in regions of upwelling, corresponding to shallow MLD (mixed layer depth) except ITCZ.

• T2m-SST error correlations are reducing with longer forecast lead times. Coupling frequency is presumably responsible.

• Small-scale daily anomalies are also seen in error correlations. They are not weather related. Reasons remain unclear, but it might be due to different time scales of variability .

• suggests a time-varying B (climatological plus instantaneous).

Correlation anomaly on 1st Jan 2006

Green contour lines indicate MSLP for ensemble mean

+0h +24h +12h

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3.2 Ensemble spreads and correlations at monthly scales

SST T2m

January

Background errors, based on monthly ensemble, Jan. and July, 2006-2010 MLD

• Both show large-scale features of seasonality, with larger values in summer hemisphere. • SST spread > T2m spread, where MLD is shallow and ocean dynamics are strong, SST spread < T2m spread, where MLD is deep.

July

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January

July

• T2m-SST error correlations are enhanced with shallow MLD • But, in tropics, T2m-SST error correlations are reduced by convection (SST-T2m)

MLD Error correlation (T2m, SST) SST – T2m

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Colored by precipitation anomalies

Colored by MLD anomalies

Colored by precipitation anomalies Colored by MLD anomalies

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3.3 Long-term changes in ensemble spreads and correlations

Global average of background errors, based on monthly ensemble

AVHRR W.Ws.

• Spreads in the interface are gradually decreasing as more observations become available • Notable changes around WWs, 1980 and 2008 corresponding to abrupt data changes • Correlations are steadily increasing prior to1980, but reduced thereafter and then keep more straight

Thick lines show the 12month moving average

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Southern middle latitudes (30°S-60°S)

• Spread differences between T2m and SST are gradually decreasing, with sudden changes in 1980 • Atmosphere has very large uncertainties (over 0.4°C for T2m and 1m/s for v10) in early years • Wind errors take the role of determining T2m errors over SST in early years • Thermodynamic imbalance might be introduced in 1980 CDAW2016, Toulouse

Nino3.4 EI Nino La Nina

• Inter-annual variability related to ENSO is seen in T2m-SST error correlations, while it is not found in the spread • Deep convection moving with Pacific warm pool is responsible for weak correlations • During EI Nino,T2m errors are modulated by precipitation errors, whereas SST errors are related to MLD CDAW2016, Toulouse

Summary • Ensemble spreads and correlations between T2m and SST in CERA-20C are calculated at

different time scales, which are time-, region- and flow-dependent.

• CERA-20C produces a well defined coupled reanalysis, which shows consistent errors (ensemble departures) in the ocean-atmosphere interface, by the understanding of physics of air-sea interactions.

• MLD and atmospheric convection are responsible for T2m-SST error correlations. Wind errors also have impact in early years of the 20th century.

• T2m-SST error correlations are weakened when ocean and atmosphere spreads are changing inconsistently with time (e.g. 1980).

• For a possibility of moving CERA forward to a ‘strongly’ coupled DA system, B matrix should be able to capture the temporal changes in the coupled error covariances, which contains long-term, climatological and instantaneous information.

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In next • Calculate the localization parameters for T2m-SST error correlation, approximated with

MLD and precipitation/convection(?).

• Diagnose the cross error covariances between other ocean and atmosphere fields of CERA-20C (e.g. surface current and wind), and understand the physics behind.

• Identify model bias in CERA-20C (SAT), and understand if this could distort the shape of error distributions and further change the error covariances.

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Thanks!

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SST comparison between CERA-20C and HadISST2

Ensemble mean Ensemble spread

January

July

Time average

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Global average

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Ocean T spread cross equator section (5°N-5°S)

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corrcoef(T2m, 10v)

corrcoef(T2m, SST)

1901 2010 1960

Correlation between T2m and wind errors

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