Scale-dependent localization in ensemble- variational data … · 2017. 9. 1. · Scale-dependent localization in ensemble-variational data assimilation: Application in global and

Scale-dependent localization in ensemble-variational data assimilation: Application in global and convective-scale systems Jean-François Carona, Étienne Arbogastb, Mark Buehnera, Thibaut Montmerleb, Yann Michelb and Benjamin Ménétrierb

aECCC bCNRM/Météo-France

Outline

1.  An approach to improve spa2al covariance localiza2on in EnVar : scale-‐dependent localiza2on (SDL)

2.  Applica2on in two EnVar-‐based DA systems a)  A simplified version of ECCC’s global opera2onal system b)  Meteo-‐France AROME convec2ve-‐scale system (R&D version)

Localisation

•  Spa2al covariance localiza2on is essen2al to obtain useful analyses with “small” ensembles (a 256-‐member ensemble is s2ll "small"!).

•  Currently, ECCC's EnVar uses simple localiza2on of ensemble covariances, similar to EnKF: single length scale in both horizontal and ver2cal localiza2ons based on Gaspari and Cohn (1999) 5th order piecewise ra2onal func2on.

•  Comparing various NWP studies, seems that the best amount of horizontal localiza2on depends on applica2on/resolu2on:

o  convec2ve-‐scale assimila2on: ~10km o  mesoscale assimila2on: ~100km o  global-‐scale assimila2on: ~1000km – 3000km (2800km at ECCC)

A one-‐size-‐fits-‐all approach for localiza2on does not seem appropriated for analysing a wide range of scales.

Scale-dependent localisation (SDL)

Defini2on: Simultaneously apply appropriate (i.e. different) localiza2on to different range of scales.

•  The approach can be applied to both horizontal and ver2cal localiza2on but this presenta2on will only focus on horizontal-‐scale-‐dependent horizontal localiza2on.

•  Pros: •  Seems appropriated for mul2-‐scale analysis. •  In limited-‐area: Could avoid the need of mul2-‐step or large-‐scale

blending approaches.

•  Cons: •  Adds more parameters to tuned. •  Increases the cost of the analysis step (at least in our formula2on).

Horizontal Scale Decomposition

Large scale

Medium scale

Small scale

2000 km 10000 km 500 km

Filter response func2ons for decomposing with respect to 3 horizontal scale ranges


Full Large scale

Small scale Medium scale

Perturba2ons for ensemble member #001 – Temperature at ~700hPa

0

-‐2

+2

0

-‐2

+2


Homogeneous horizontal correla2on

length scales

Large scale

Medium scale

Small scale

Full

6-‐h temperature perturba2on from 256-‐

member EnKF hP

a

km

Horizontal scale-‐dependent localiza2on leads to (implicit)…

ver2cal-‐level-‐dependent horizontal localiza2on


Waveband integrated variances

Large scale Medium scale

Small scale

6-‐h perturba2on from 256-‐member EnKF

hPa

Horizontal scale-‐dependent localiza2on leads to (implicit)… variable-‐dependent horizontal

localiza2on

T

All the scales

log(q)

•  The original ensemble covariances with localiza2on

LeeB !Tkk

kL ∑=

The basic idea (from Buehner and Shlyaeva, 2015, Tellus)

k: member index

Scale-dependent localisation (SDL)

•  With a scale-‐decompose ensemble

LeeB !∑∑∑=1 2

2,1,j j

Tjk

kjkL

•  With scale-‐dependent localiza2on

kjjk eFe =,F: filtering step j: scale index ∑=

jjkk ,ee

2,11 2

2,1, jjj j

Tjk

kjkSDL LeeB !∑∑∑=

EnVar with B1/2 preconditioning (ECCC)

•  Analysis increment computed from control vector (B1/2 precondi2oning) using:

( )∑∑=Δk j

kjjk ξLex 2/1, !

( )∑=Δk

kk ξLex 2/1!

•  Varying amounts of smoothing applied to same set of amplitudes for a given member

Current (one-‐size-‐fits-‐all) Approach

Scale-‐dependent Approach (as in Buehner and Shlyaeva, 2015, Tellus)

where ek,j is scale j of normalized member k perturba2on

k: member index j: scale index

k: member index

Page 11

•  Analysis increment computed from control vector (B precondi2oning) using:

( )∑ Δ=Δk

ikko )( xeLex !!

•  Direct applica2on to the above formula2on

Current (one-‐size-‐fits-‐all) Approach

Scale-‐dependent Approach

j: scale index

k: member index

EnVar with B preconditioning (Meteo-France)

( )∑∑∑ Δ=Δ1 2

2,2,11, )(j j k

ijkjjjko xeLex !!

•  Reformula2on using B1/2 BT/2

( )∑∑=Δk j

kjjko ξLex 2/1, ! ∑ Δ=

jijk

Tjk )( ,2/ xeLξ !

Application in a global EnVar system: ECCC’s Global Determinisitic

Prediction System •  256 ensemble member @ 50km •  Localiza2on in spectral space •  Determini2c forecast @ 25 km

Scale-dependent covariance localization

Normalized temperature increments (correlation-like) at 700 hPa resulting from various B matrices.

Bnmc

Bens No hLoc Bens Std hLoc

Bens SD hLoc

hLoc: 1500km / 4000km / 10000km

700 hPa T observation at the center of Hurricane Gonzalo (October 2014) hLoc: 2800km

0

-‐1

+1

0

-‐1

+1

0

-‐1

+1

0

-‐1

+1

Impact in single observa3on DA experiments

Scale-dependent covariance localization Impact in single observa3on DA experiments

Bens No hLoc

Normalized temperature increments (correlation-like) at 700 hPa resulting from various B matrices.

Bnmc

Bens Std hLoc

Bens SD hLoc

hLoc: 1500km / 4000km / 10000km

700 hPa T observation at the center of a High Pressure

hLoc: 2800km

0

-‐1

+1

0

-‐1

+1

0

-‐1

+1

0

-‐1

+1

Scale-dependent covariance localization

•  2.5-month trialling (June-August 2014) in our global NWP system.

1)  Control experiment with hLoc = 2800 km, vLoc = 2 units of ln(p)

2)  Scale-‐Dependent experiment with a 3 horizontal-‐scale decomposi2on I.  Small scale uses hLoc = 1500 km II.  Medium scale uses hLoc = 2400 km III.  Large scale with uses = 3300 km

•  3DEnVar with 100% Bens used in both experiments

Ad hoc values!

Same vLoc (2 units of ln(p)) for every horizontal-‐scale

Forecast impact

Scale-dependent covariance localization Forecast impact

T+24h Northern E-T

Ø  Control

U

Z T

RH U

Z T

RH

Ø  Scale-‐Dependent

T+24h Southern E-T


T+72h Northern E-T

Ø  Control

U

Z T

RH U

Z T

RH


T+72h Southern E-T


T+120h Northern E-T

Ø  Control

U

Z T

RH U

Z T

RH


T+120h Southern E-T


T+168h Northern E-T

Ø  Control

U

Z T

RH U

Z T

RH


T+168h Southern E-T


Time series Northern E-T Time series Southern E-T

Std Dev for U at 250 hPa


Ø  Control Ø  Scale-‐Dependent


•  2 new 1.5-month trialling (June-July 2014) with a single localization approach (still using 3DEnVar with 100% Bens)

1)  hLoc = 2400 km (the value used for medium scale in SD hLoc)

2)  hLoc = 3300 km (the value used for large scale in SD hLoc)

Is it possible to do as good as SDL with a single localiza2on approach? Awer all, perhaps our one-‐size-‐fits-‐all horizontal localiza2on radius of 2800 km is not op2mal...





Ø  Control (hLoc = 2800 km) Ø  hLoc = 2400 km





Ø  Control (hLoc = 2800 km) Ø  hLoc = 3300 km

Scale-dependent covariance localization Impact on dynamical balance – Rota2onal Part

It is well know that localiza2on can disrupt the dynamical balance of the analysis increments. Does the SDL increase or decrease this problem?

rrrrrrrrrrrrr u

yf

xv

yu

yv

xu

xv

yu

yv

xu

xv

yu

yv

xuf ʹ′

∂

∂−⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

ʹ′∂

∂

ʹ′∂−

∂

ʹ′∂

∂

ʹ′∂+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂

∂

ʹ′∂−

∂

∂

∂

ʹ′∂+⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

ʹ′∂

∂

∂−

∂

ʹ′∂

∂

∂+ʹ′=Φʹ′∇ 22 ζ

Wind Mass

•  Rotational part: Charney’s (1955) nonlinear balance equation

Balance diagnos2cs as in Caron and Fillion (2010; MWR)

One conclusion from Caron and Fillion: Both horizontal and ver2cal localiza2on have significant deleterious effect on the rota2onal balance with the largest detrimental impact coming from the ver2cal localiza2on.

Scale-dependent covariance localization Impact on dynamical balance – Rota2onal Part

Ver2cal profile of average normalized departure from (n-‐l) balance

1.6 0.4

hLoc 2800 km SD hLoc

0.8 1.2

800

600

400

200

hPa

1000 1.6 0.4 0.8 1.2

Northern E-T Southern E-T

□ hLoc 3300 km ○ hLoc 2400 km

hLoc 2800 km SD hLoc

□ hLoc 3300 km ○ hLoc 2400 km

800

600

400

200

1000

Application in a convective-scale EnVar system:

Meteo-France’s AROME R&D version •  25 ensemble member @ 3.8km •  Localiza2on in spectral or gridpoint space •  Determini2c forecast @ 3.8 km

(Adhoc) scale-decomposition for AROME

Temperatutre perturba2ons at ~950 hPa for member #1. 3h forecast valid on 06 February 2016 at 00 UTC

Pseudo-single obs - Frontal case

SP 250km

Pseudo-single obs - Frontal case

SP-‐SDL 080/250/500km

Pseudo-single obs - Convective case

SP 250km

Pseudo-single obs - Convective case

SP-‐SDL 080/250/500km

Performed DA and forecast cycles

•  2 weeks trialling (February 2016) were used testing many horizontal localization lengtscale for both SDL and ‘one-size-fits-all’ approaches.

•  Extension to 1 month for both the control experiment and the best performing SDL configurations

•  Spectral and gridpoint (recursive fitler) localization were used/compared. •  The same horizontal-scale decomposition (3 wave band) was used in all

the SDL experiments. •  3-hourly DA cycle •  30-hour forecasts issued from 00, 06, 12 and18 UTC

Verification against aircraft

SP 075/150/300km vs SP 250km

2 weeks


SP 075/150/300km vs SP 250km

2 weeks


SP 075/150/300km vs SP 250km

2 weeks


SP 075/150/300km vs SP 250km

2 weeks


SP 075/150/300km vs SP 250km

2 weeks

Verification against aircraft(+3 to +30h, 3h)

SP 075/150/300km vs SP 250km

2 weeks

SP 075/150/300km vs SP 250km

Verification against aircraft (+1 to +10h, 1h)

2 weeks

SP 300km vs SP 250km


2 weeks



2 weeks



2 weeks

Full verification (+3 to +30h, 3h)

SP 075/150/300km vs SP 250km

1 month

Full verification (+3 to +30h, 3h)

RF 075/150/300km vs RF 250km

1 month

Impact on balance

RF-‐SDL RF SP-‐SDL SP

Summary and conclusion

•  SDL is feasible and straightforward to implement in EnVar, but more expensive than using single-scale localization.

–  In the SDL experiments reported here: 3x to 3.5x more expensive

•  Results using a horizontal-scale-dependent horizontal localization indicate small forecast improvements in both systems examined. However, the time-scales over which the SDL method impacted the forecasts are completely different:

–  Improvements up to day 5 were noticed in the global system, –  In the convective-scale system, they were limited mostly in the first 9 hours of the forecasts

•  In terms of dynamical balance, SDL seems to alleviate somewhat the imbalance generated by the localization.

•  Finding the optimal SDL setup is not straightforward. –  No objective approach has been found useful so far.

Documents

Scale-dependent localization in ensemble- variational data … · 2017. 9. 1. · Scale-dependent localization in ensemble-variational data assimilation: Application in global and