scale-dependent localization in ensemble- variational data … · 2017. 9. 1. · scale-dependent...
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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
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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)
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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.
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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).
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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
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Horizontal Scale Decomposition
Full Large scale
Small scale Medium scale
Perturba2ons for ensemble member #001 – Temperature at ~700hPa
0
-‐2
+2
0
-‐2
+2
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Horizontal Scale Decomposition
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
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Horizontal Scale Decomposition
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)
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• 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 !∑∑∑=
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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
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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 !
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Application in a global EnVar system: ECCC’s Global Determinisitic
Prediction System • 256 ensemble member @ 50km • Localiza2on in spectral space • Determini2c forecast @ 25 km
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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
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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
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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
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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
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Scale-dependent covariance localization Forecast impact
T+72h Northern E-T
Ø Control
U
Z T
RH U
Z T
RH
Ø Scale-‐Dependent
T+72h Southern E-T
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Scale-dependent covariance localization Forecast impact
T+120h Northern E-T
Ø Control
U
Z T
RH U
Z T
RH
Ø Scale-‐Dependent
T+120h Southern E-T
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Scale-dependent covariance localization Forecast impact
T+168h Northern E-T
Ø Control
U
Z T
RH U
Z T
RH
Ø Scale-‐Dependent
T+168h Southern E-T
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Scale-dependent covariance localization Forecast impact
Time series Northern E-T Time series Southern E-T
Std Dev for U at 250 hPa
Std Dev for U at 250 hPa
Ø Control Ø Scale-‐Dependent
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Scale-dependent covariance localization Forecast impact
• 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...
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Scale-dependent covariance localization Forecast impact
Time series Northern E-T Time series Southern E-T
Std Dev for U at 250 hPa
Std Dev for U at 250 hPa
Ø Control (hLoc = 2800 km) Ø hLoc = 2400 km
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Scale-dependent covariance localization Forecast impact
Time series Northern E-T Time series Southern E-T
Std Dev for U at 250 hPa
Std Dev for U at 250 hPa
Ø Control (hLoc = 2800 km) Ø hLoc = 3300 km
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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.
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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
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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
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(Adhoc) scale-decomposition for AROME
Temperatutre perturba2ons at ~950 hPa for member #1. 3h forecast valid on 06 February 2016 at 00 UTC
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Pseudo-single obs - Frontal case
SP 250km
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Pseudo-single obs - Frontal case
SP-‐SDL 080/250/500km
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Pseudo-single obs - Convective case
SP 250km
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Pseudo-single obs - Convective case
SP-‐SDL 080/250/500km
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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
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Verification against aircraft
SP 075/150/300km vs SP 250km
2 weeks
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Verification against aircraft
SP 075/150/300km vs SP 250km
2 weeks
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Verification against aircraft
SP 075/150/300km vs SP 250km
2 weeks
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Verification against aircraft
SP 075/150/300km vs SP 250km
2 weeks
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Verification against aircraft
SP 075/150/300km vs SP 250km
2 weeks
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Verification against aircraft(+3 to +30h, 3h)
SP 075/150/300km vs SP 250km
2 weeks
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SP 075/150/300km vs SP 250km
Verification against aircraft (+1 to +10h, 1h)
2 weeks
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SP 300km vs SP 250km
Verification against aircraft (+3 to +30h, 3h)
2 weeks
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SP 200km vs SP 250km
Verification against aircraft (+3 to +30h, 3h)
2 weeks
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SP 150km vs SP 250km
Verification against aircraft (+3 to +30h, 3h)
2 weeks
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Full verification (+3 to +30h, 3h)
SP 075/150/300km vs SP 250km
1 month
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Full verification (+3 to +30h, 3h)
RF 075/150/300km vs RF 250km
1 month
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Impact on balance
RF-‐SDL RF SP-‐SDL SP
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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.