Current developments in data assimilation for numerical weather prediction in Canada: EnVar, EnKF and 4D-Var Mark Buehner 1, Josée Morneau 2 and Cecilien

Current developments in data assimilation for numerical weather prediction in Canada: EnVar, EnKF and 4D-Var

Mark Buehner1, Josée Morneau2 and Cecilien Charette1 1Data Assimilation and Satellite Meteorology Research Section2Data Assimilation and Quality Control Development Section

January, 2013

Page 2 – April 19, 2023

Contents

• Background and recent changes to the Canadian NWP systems

• The ensemble-variational (EnVar) data assimilation approach

• Recent results from using EnVar compared with standard 3D-Var and 4D-Var (but NO comparisons with 4D-Var-Bens or EnKF)

• Conclusions and next steps

Page 3 – April 19, 2023

Background• Environment Canada currently has 2 relatively independent state-of-

the-art global data assimilation systems

• 4D-Var (Gauthier et al 2007) and EnKF (Houtekamer et al 2009):

– both operational since 2005

– both use GEM forecast model and assimilate similar set of observations

– current effort towards unifying code of the two systems

• 4D-Var is used to initialize medium range global deterministic forecasts (GDPS)

• EnKF is used to initialize global ensemble forecasts (GEPS)

• Intercomparison of approaches and various hybrid configurations was performed in carefully controlled context: similar medium-range forecast quality from EnKF and 4D-Var analyses, 4D-Var-Ben best

• Results presented at WMO workshop on intercomparison of 4D-Var and EnKF, Buenos Aires, 2008 (Buehner et al 2010, MWR)

Summary of recent changes

Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov

2011 2012

Major improvements to DA of global and regional systems

New 10km/4DVar Regional Deterministic Prediction System…IBM Power7

Improvements to global & regional DA systems (Nov 2011)

New Satellite Data - 62 infrared channels from the IASI instrument on board the METOP satellite.- 7 microwave channels from the SSM/IS instrument on board the DMSP F16 satellite.- 1 water vapor channel from the GOES-W, METSAT-1R and both METEOSAT satellites. - Horizontal thinning of all satellite radiance data, previously done at 250 km (except 200 km for SSM/I) was reduced to 150 km, therefore adding much more satellite data to the systems.

Other Assimilation Changes- Moisture observations measured from properly equipped aircraft (AMDAR) are assimilated.- Unified satellite data bias correction scheme. Reduction of the time period to compute the bias corrections from 15 to 7 days. The same code is used for all radiance data.- Updated version of the RTTOV radiative transfer code for satellite radiance data.- New sea surface temperature analysis on a 0.2° grid.

Amount of data assimilated in the global system

- increase from ~1.9 million to ~4.2 million pieces of information per day.

Fig: GZ-500hPa anomaly correlations over the S. Hemisphere during the parallel run (Jan-Jun 2011): old vs new global system.

New IBM Power7• System was installed off-site • Migration of operational jobs took a year to complete • Fully operational since early May 2012

• 2 clusters; 8192 cores each• ~ 1/2 PFlops peak total • on average, performance gain per CPU about 2.7x compared to P5 CPU

Major upgrade of the Regional Deterministic Prediction System (RDPS)(Oct 2012)

Upgrade included:

• increase in resolution to 10 km from the previous 15 km

• 4D-Var data assimilation system replacing the previous 3D-Var

• important changes in the physics

Significant improvements in forecasts with most metrics throughout most of the atmosphere, especially:

• for the winter season

• for the lower portion of the atmosphere and at the surface

Fig: The red line indicates the domain covered by the RDPS.

Fig: Vertical profiles of bias (dashed lines) and error standard deviation (solid lines) of 48-h forecasts against radiosonde data, over Canada during the winter 2011, from the old (15km) versus new (10km) RDPS.

GZ T

Upcoming NWP operational implementations b

y Ja

n 2

013

by

the

end

of

2013

Global Deterministic - resolution: from 33 km to 25 km

- new vertical coordinates / grid + improved physics

- 4D-Var analysis increments: from T108 to T180, ~100 km

Global EPS - resolution: from 100 km to 66 km

- analysis (EnKF): multi-scale (3x more assimilated data)

Regional EPS - resolution: from 33 km to 15 km

Global Deterministic - resolution: from 25 km to 15 km

- from lat-lon to Yin-Yang grid

- from 4D-Var to EnVar: main focus of this presentation

- resolution of increments: from 100 km to 50 km

- new sea-ice and land-surface analyses

Global EPS - resolution: from 66 km to 50 km

High-resolution System - single grid (2.5-km resolution) covering most of Canada

Major upgrade of the Global Deterministic Prediction System (GDPS)(expected to become operational in early 2012)

fore

cas

t m

od

el

horizontal resolution - from 33km to 25km - improvements seen in analysis cycle

dynamics- new vertical coordinate

- new vertical grid (from regular to Charney-Phillips)

- reduction of errors in stratosphere

- noise reduction; improved numerical stability and conservation properties

physics

orographic blocking

- amplification of bulk drag coefficient

- significant reduction of tropospheric errors in winter hemisphere

boundary layer

- turbulent hysteresis effect- reduction of errors associated with frontal inversions; improvement of upper-air scores

outer loop - from 33km to 25km

- more data (AMSU-A and Aircraft) due to increase of # bins

- all changes contributed to forecast improvements, roughly doubling the gain due to model changes

inner loop

TL / AD- from 160km to 100km

- t: from 45min (9 bins) to 18min (21 bins)

background error statistics

- from T108 to T180

minimization:# of iterations

- from 55 (30+25) to 65 (35+30)

DA

(4

Dv

ar)

Fig: Vertical profiles of bias (dashed lines) and error standard deviation (solid lines) of 120-h forecasts against radiosonde data, over the S. Hemisphere, during the summer 2011, from the old versus GDPS.

GZ T

Upgrade of Global & Regional Ensemble Prediction Systems(expected to become operational in early 2012)

Changes to the Global EnKF and EPS• multi-scale algorithm (horizontal localization varies vertically) • time-step: from 30 to 20min• horiz. resolution: from 100 to 66km• vertical levels: from 58 to 74• topography filter• reduced thinning of observations (2.7 X number of assimilated radiances)• improved dynamics and physics

Fig: Global verification (CRPS error) of temperature at 500hPa against radiosondes, ov OLD versus NEW GEPS, showing a gain in predictability of 12h and plus.

Changes to the Regional EPS

• Model component - horiz. resolution: from 33 to 15km - vertical levels from 28 to 40 - improved treatment of stochastic physical tendency perturbations to avoid unrealistic precipitation rates - improved boundary layer parameterization

• Assimilation component - no changes (i.e same initial conditions as the global EPS)

Model Dynamics: New approaches for global grids

Proposed Upgrades and Improvements to the MSC Data Processing for Radiosonde and Aircraft Data

• Increased volume of data: selection of observations according to model levels

• Revised observation error statistics

• Revised rejection criteria for radiosonde data based on those used at ECMWF

• Horizontal drift of radiosonde balloon taken into account in both data assimilation and verification systems

• Bias correction scheme for aircraft temperature reports

operationalproposed for both

radiosonde & aircraft

Impact of proposed changes

• General short-range forecast improvements above 500 hPa in both wind and temperature fields

• The temperature forecast biases are significantly improved due to the bias correction scheme for aircraft below 200 hPa and to the new rejection criteria for radiosonde humidity data above

wind speed temperature

12h

48h

Fig: Verification scores against radiosondes over the N. Hemisphere, Jan-Feb 2009 (dash = bias; solid = stde)

Page 14 – April 19, 2023

Role of Ensembles…

Global EnKF

Perturbed members of the globalprediction

system (GPS)

Control member of the

globalprediction

system (GPS)

GlobalEn-Var

Background error

covariances

2013-2017: Toward a Reorganization of the NWP Suites at Environment Canada

Regional EnKF

Perturbed members of the regionalprediction

system (RPS)

Control member of the

regionalprediction

system (RPS)

Regional En-Var ?

Background error

covariances

High-res En-Var

High-resolution deterministic

prediction system

(HRDPS)

global system regional system

Page 15 – April 19, 2023

Ensemble-Variational assimilation: EnVar

• EnVar approach is currently being tested in the context of replacing 4D-Var in the operational Global Deterministic Prediction System

• EnVar uses a variational assimilation approach in combination with the already available 4D ensemble covariances from the EnKF

• By making use of the 4D ensembles, EnVar performs a 4D analysis without the need of the tangent-linear and adjoint of forecast model

• Consequently, it is more computationally efficient and easier to maintain/adapt than 4D-Var

• Hybrid covariances can be used in EnVar by averaging the ensemble covariances with the static NMC-method covariances

• Like 4D-Var, EnVar uses an incremental approach with:– analysis increment at the horizontal/temporal resolution of EnKF

ensembles– background state and analysis at the horizontal/temporal resolution of

the higher-resolution deterministic forecast model

Page 16 – April 19, 2023

• In 4D-Var the 3D analysis increment is evolved in time using the TL/AD forecast model (here included in H4D):

• In EnVar the background-error covariances and analysed state are explicitly 4-dimensional, resulting in cost function:

• Computations involving ensemble-based B4D can be more expensive than with Bnmc depending on ensemble size and spatial/ temporal resolution, but significant parallelization is possible

4D14D4D4Db4D

14Db4D4D 2

1)][()][(

2

1)( xBxyxHxRyxHxx TT HHJ

EnVar formulation

xBxyxHxRyxHxx 14Db4D

14Db4D 2

1)][()][(

2

1)( TT HHJ

Page 17 – April 19, 2023

4D error covariancesTemporal covariance evolution (explicit vs. implicit evolution)

EnKF and EnVar (4D B matrix):

4D-Var:

-3h 0h +3h

192 NLM integrations provide 4D background-error covariances

TL/AD inner loop integrations,2 outer loop iterations,then 3h NLM forecast

“analysis time”

Page 18 – April 19, 2023

EnVar: a possible replacement of 4D-Var

Overall, EnVar analysis ~6X faster than 4D-Var on half as many cpus, even though higher resolution increments

Wall-clock time of 4D-Var already close to allowable time limit; increasing number of processors has negligible impact

To progress with 4D-Var, significant work would be required to improve scalability of TL/AD versions of forecast model at resolutions and grid configuration used in 4D-Var

Current focus for model is on development of higher-resolution global Yin-Yang configuration that scales well

Decision made to try to replace 4D-Var with more efficient EnVar if EnVar is at least as good as current 4D-Var

Page 19 – April 19, 2023

• Current system (1-way dependence):

• GEPS relies on GDPS to perform quality control (background check) for all observations and bias correction for satellite radiance observations

Dependencies between global systems

Bgcheck+BC 4D-Var GEM (9h fcst)

GEM (9h fcst)EnKFxb xb

xbxb xb, obs

obsxa

xaGDPS:

GEPS:

Page 20 – April 19, 2023


• With EnVar (2-way dependence):

• 2-way dependence (EnVar uses EnKF ensemble of background states) increases complexity of overall system 2 systems have to be run simultaneously




xbxb xb, obs

obs

Bgcheck+BC EnVar GEM (9h fcst)


xbxb xb, obs

obsxb

xa

xa

xa

xa

GDPS:

GDPS:

GEPS:

GEPS:

Page 21 – April 19, 2023


• With EnVar (2-way dependence):

• Another possibility with EnVar (1-way dependence):




xbxb xb, obs

obs



xbxb xb, obs

obsxb



xbxb xb, obs

xb

Bgcheck+BC xb, obs

xa

xa

xa

xa

xa

xa

GDPS:

GDPS:

GDPS:

GEPS:

GEPS:

GEPS:

Page 22 – April 19, 2023

• Preconditioned cost function formulation at Environment Canada:

• In EnVar with hybrid covariances, the control vector () is composed of 2 vectors:

• The analysis increment is computed as (ek is k’th ensemble perturbation divided by sqrt(Nens-1) ):

• Better preconditioned than original “alpha control vector” formulation (with L-1 and 1/β in background term of J)

• Most, but maybe not all, applications of the approach use the better preconditioned formulation

EnVar formulation: Preconditioning

)()(2

1

2

1)( b4D

1b4D yξxHxRyξxHxξξξ HHJ TT

ens

nmc

ξ

ξξ

ens

1ens

1/22/1ensnmc

1/2nmc

2/1nmc

N

k

kk ξLeξBξx

ens

ens

1ens

ensNξ

ξ

ξ

ens

1ensnmcnmc

N

k

Tkk LeeBB

Page 23 – April 19, 2023

• radiosonde temperature observation at 500hPa

• observation at beginning of assimilation window (-3h)

• with same B, increments very similar from 4D-Var, EnKF

• contours are 500hPa GZ background state at 0h (ci=10m)

Single observation experimentsDifference in temporal covariance evolution

contour plots at 500 hPa

+

+ +

+

EnVar

Page 24 – April 19, 2023


• observation at middle of assimilation window (+0h)





+

+ +

+

EnVar

Page 25 – April 19, 2023


• observation at end of assimilation window (+3h)





+

+ +

+

EnVar

Page 26 – April 19, 2023

Experimental results:Configuration

EnVar tested in comparison with new version of forecast system currently being implemented in operations: • model top at 0.1hPa, 80 levels• model has ~25km grid spacing• 4D-Var analysis increments with ~100km grid spacing

EnVar experiments use ensemble members from new configuration of EnKF: • 192 members every 60min in 6-hour window• model top at 2hPa, 75 levels• model ~66km grid spacing EnVar increments ~66km

Page 27 – April 19, 2023

EnVar uses Hybrid Covariance MatrixModel top of EnKF is lower than GDPS

Bens and Bnmc are averaged in troposphere ½ & ½, tapering to 100% Bnmc at and above 6hPa (EnKF model top at 2hPa)

Bens scale factorBnmc scale factor

scale factor

pres

sure

Therefore, EnVar not expected to be better than 3D-Var above ~10-20hPa

Also tested 75% Bens and 25% Bnmc in troposphere, but results slightly worse

Also did preliminary tests with a full outer loop, but degraded the results

Page 28 – April 19, 2023

Forecast Results: EnVar vs. 3D-Var and 4D-VarRadiosonde verification scores – 6 weeks, Feb/Mar 2011

EnVar vs. 3D-Var120h forecastNorth extra-tropics

U |U|

GZ T

T-Td

Page 29 – April 19, 2023




U |U|

GZ T

T-Td

U |U|

GZ T

T-Td

Page 30 – April 19, 2023


EnVar vs. 3D-Var120h forecastSouth extra-tropics

U |U|

GZ T

T-Td

Page 31 – April 19, 2023




U |U|

GZ T

T-Td

U |U|

GZ T

T-Td

Page 32 – April 19, 2023

EnVar vs. 3D-Var24h forecastTropics


U |U|

GZ T

T-Td

Page 33 – April 19, 2023




U |U|

GZ T

T-Td

U |U|

GZ T

T-Td

Page 34 – April 19, 2023

Forecast Results: EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, Feb/Mar 2011

EnVar vs. 3D-Var 48h forecast, global domain

no EnKF covariances

transitionzone

½ EnKF and½ NMCcovariances

U

GZ

RH

T

Page 35 – April 19, 2023


EnVar vs. 3D-Var EnVar vs. 4D-Var48h forecast, global domain

no EnKF covariances

transitionzone


no EnKF covariances

transitionzone


U

GZ

RH

T

U

GZ

RH

T

Page 36 – April 19, 2023


EnVar vs. 3D-Var 120h forecast, global domain

no EnKF covariances

transitionzone


U

GZ

RH

T

Page 37 – April 19, 2023


EnVar vs. 3D-Var EnVar vs. 4D-Var120h forecast, global domain

no EnKF covariances

transitionzone


no EnKF covariances

transitionzone


U

GZ

RH

T

U

GZ

RH

T

Page 38 – April 19, 2023


North extra-tropics 500hPa GZ correlation anomaly

EnVar vs. 3D-Var EnVar vs. 4D-Var

Page 39 – April 19, 2023


South extra-tropics 500hPa GZ correlation anomaly


This is the only significant degradation seen vs. 4D-Var in troposphere; Not in radiosonde scores because it originates from south of 45°S (see next slide)

Page 40 – April 19, 2023


120h forecast of 500hPa GZ - STDDEV

120h forecast of 500hPa GZ STDDEV - South extra-tropics

Page 41 – April 19, 2023


Tropics 250hPa U-wind STDDEV


Page 42 – April 19, 2023

Forecast Results: EnVar vs. 3D-Var and 4D-VarVerification against ERA-Interim analyses – 6 weeks, July-Aug 2011



Page 43 – April 19, 2023




Page 44 – April 19, 2023




Page 45 – April 19, 2023

Experimental results:4D-EnVar vs. 3D-EnVar

3D version of EnVar also tested: only uses EnKF flow-dependent ensembles valid at the centre of the 6h assimilation window, instead of every 60 minutes throughout the window

3D-EnVar compared with:

• 4D-EnVar: impact of 4D vs 3D covariances, and

• 3D-Var: impact of flow dependent vs stationary (NMC) covariances (both 3D)

Page 46 – April 19, 2023

Forecast Results: 4D-EnVar vs. 3D-EnVarVerification against ERA-Interim analyses – 4 weeks, Feb 2011


4D-EnVar vs. 3D-EnVar 3D-EnVar vs. 3D-Var

Page 47 – April 19, 2023

Forecast Results: 4D-EnVar vs. 3D-EnVar Verification against ERA-Interim analyses – 4 weeks, Feb 2011



Page 48 – April 19, 2023

Forecast Results: 4D-EnVar vs. 3D-En-Var Verification against ERA-Interim analyses – 4 weeks, Feb 2011



Page 49 – April 19, 2023

Conclusions

• Comparison of EnVar with 3D-Var and 4D-Var:– EnVar produces similar quality forecasts as 4D-Var below

~20hPa in extra-tropics, significantly improved in tropics

– above ~20hPa, scores similar to 3D-Var, worse than 4D-Var; potential benefit from raising EnKF model top to 0.1hPa

• EnVar is an attractive alternative to 4D-Var:– like EnKF, uses full nonlinear model dynamics/physics to evolve

covariances; no need to maintain TL/AD version of model

– instead, makes use of already available 4D ensembles

– more computationally efficient and easier to parallelize than 4D-Var for high spatial resolution and large data volumes

– computational saving allows increase in analysis resolution and volume of assimilated observations; more computational resources for EnKF and forecasts

Page 50 – April 19, 2023

Next Steps

• Finalize testing EnVar with goal of replacing 4D-Var in operational global prediction system during 2013 in combination with other changes:

– GEM global model on 15 km Yin-Yang grid

– CALDAS: new surface analysis system based on an EnKF

– modified satellite radiance bias correction scheme that gives conventional observations more influence on correction

– improved use of radiosonde and aircraft data

– additional AIRS/IASI channels and modified observation error variances for all radiances

– increased resolution of EnKF 66km 50km

• Testing of EnVar in regional prediction system as possible replacement of 4D-Var already started

Documents

Current developments in data assimilation for numerical weather prediction in Canada: EnVar, EnKF and 4D-Var Mark Buehner 1, Josée Morneau 2 and Cecilien