Transcript Document

Task D4C1: Forecast errors in
clouds and precipitation
Thibaut Montmerle CNRM-GAME/GMAP
IODA-Med Meeting
16-17th of May, 2014
Outlines
1. Introduction
1. Modelization of B for specific
meteorological phenomena
1. Applications:
- Use of a heterogeneous B for DA in rain
- Assimilation of cloudy IR radiances
4. Conclusions and Perspectives
Introduction: DA in AROME
3h-cycled 3DVar (Seity et. Al 2011) :



 



T
1
1 o
b T
1
b
J x   J b  J o  x  x B x  x  y  H x R 1 y o  H x
2
2
The analysis is the solution of the BLUE :

x a  xb  BHT HBHT  R
 y  H x 
1
b
B has a profound impact on the analysis in VAR by :
• imposing the weight of the background, smoothing and spreading of
information from observation points through spatial covariances
• distributing information to other variables and imposing balance through
multivariate relationships
Practical difficulties:
• The “true” state needed to measure error against is unknown
• Because of its size ((108)2 for AROME), B can be neither estimated at
full rank nor stored explicitly
Introduction: B modeling
In AROME, use of the CVT formulation:
x  B1/ 2 
Following notation of Derber and Bouttier (1999) :
B1/2 = K P B1/2
S
• Kp is the balance operator allowing to output uncorrelated parameters
using balance constraints.
d x = KP c
æ
dz
ç
dh
ç
ç
ç (dT, d PS )
ç
dq
è
ö æ
÷ ç I
÷ ç MH
÷=ç
÷ ç NH
÷ è QH
ø
analytical linear balance operator
ensuring geostrophical balance
0 0 0
I 0 0
P I 0
R S I
æ
dz
öç
֍
dhu
֍
֍ dT, d PS
֍
øç
d qu
è
(
)
u
ö
÷ regression operators that
÷ adjust couplings with scales
÷
÷
÷
÷
Berre (2000)
ø
• BS is the spatial transform in spectral space, giving isotropic and
homogeneous increments:
B = SCST
S
Kp and BS are static and are deduced from an ensemble assimilation
(EDA, Brousseau et al. 2011a)
Introduction: limitations of the operational B
B strongly depends on weather regimes
Examples for an EDA that gathers anticyclonic and perturbed situations :
Spread of daily forecast
error of std deviations for q
Time evolutions of Z500, T500 and of
different background error standard
deviations at different levels
(Brousseau et al. 2011)
Modelization of B for specific meteorological phenomena
(Montmerle and Berre 2010)
EDA designed for LAM :
B Calibration
 Few cycles needed to get the full spectra of error variances
 High impact phenomena under-represented in the ensemble
Modelization of B for specific meteorological phenomena
Forecast errors are decomposed using features in the background
perturbations that correspond to a particular meteorological phenomena.
x*bi (qrz )
Example for
precipitation
Binary masks:
1
0
di,ppj
di,ccj
x*bi (qrz )
rain/rain
non rainy/non rainy
e f = x*b - x*b » éëGdijpp ùûe f + éëGdijcc ùûe f + éëGdijcp ùûe f
ij
i
j
ij
ij
(G : Gaussian blur)
ij
Application #1: use of a « rainy » B for DA of radar data
(Montmerle, MWR 2012)
Use of the heterogeneous formulation:
(Montmerle and Berre, 2010)

x  B   F B
1/ 2
1/ 2
1
1/ 2
1
1/ 2
2
F
1/ 2
2
B

 1 
 
 
 2
“Rain”
“No Rain”
Where F1 and F2 define the
geographical areas where B1 and
B2 are applied:
 F11/ 2  S D1/ 2S 1
 1/ 2
1 / 2 1
F2  SI  D S
 This formulation allows to consider
simultaneously different BS and Kp that
are representative of one particular
meteorological phenomena
Vertical Cross section of q increments
4 obs exp: Innovations of – 30% RH
At 800 and 500 hPa
Application #1: use of a « rainy » B for DA of radar data
• Example for a real case: D is deduced from the reflectivity mosaic
Radar mosaic
15th of June 2010 at 06 UTC
Resulting gridpoint mask
• In addition to conventional observations, DOW and profiles of RH, deduced
from radar reflectivities using a 1D Bayesian inversion (Caumont et al.,
2010), are also assimilated in precipitating areas.
Application #1: use of a « rainy » B for DA of radar data
Here: EXP:
B1=rain,
B2=OPER ,
D=radar mosaic
EXP
OPER
Dij >0.5
Humidity increment at 600 hPa (g.kg-1)
(zoom over SE France)
Oper
Precip
Clear air
B1 has shorter correlation lengths:
 increments have higher spatial resolutions
in precipitation
 Potential increase of the spatial resolution
of assimilated radar data
Application #1: use of a « rainy » B for DA of radar data
Cov(q, hu)
z = 800 hPa
z = 400 hPa
div
OPER
Vertical cross covariances
OPER
EXP
Rain
conv
Divergence increments
• Spin-up reduction correlated with the number of grid
points where B1 is applied
• Positive forecasts scores up to 24h for precipitation
and for T and q in the mid and lower troposphere
Application #2: Assimilation of cloudy radiances in a 1DVar
Liquid cloud
Computation of
background error
covariances for all
hydrometeors in clouds:
Analogously to Michel et al.
(2011), the mask-based
method and an extension of
Kp have been used:
ì
ï dT = dT
í d q = T0dT + d qu
ï d ql,i,r,s = T dT +T d q + d ql,i,r,s
1
2 u
u
î
Ice cloud
% of explained error variances
for ql (top) and qi (bottom)
Vertical covariances
between qi , ql and the
unbalanced humidity qu
Application #2: Assimilation of cloudy radiances in a 1DVar
Flow-dependent vertical covariances :
Use of mean contents to distort vertically
climatological values
Mean contents vs.
error std dev. “of the
day” for rain (left) and
ice cld (right)
Error variances
for rain and ice
cloud
Application #2: Assimilation of cloudy radiances in a 1DVar
Assimilation of IASI cloudy radiances (Martinet et al., 2013)
ql and qi have been added to the state vector of a1DVar, along with T and q
Reduction of
background error
variances for
selections of high
opaque cloud
(left) and low
liquid cloud (right)
 Background errors are reduced for ql and qi (as well as for T and q
(not shown)), increments are coherently balanced for all variables.
Application #2: Assimilation of cloudy radiances in a 1DVar
Evolution of analyzed profiles using AROME 1D
Example for low
semi-transparent
ice clouds:
Time evolution of integrated ice cloud contents (min)
 Thanks to the multivariate relationships and despite the spin-down,
integrated contents keep values greater than those forecasted by the
background and by other assimilation methods up to 3h
Conclusions & perspectives
 High impact weather phenomena (e.g convective precipitations, fog…)
are under-represented in ensembles that are used to compute
climatological Bc : DA of observations is clearly sub-optimal in these areas
 By using geographical masks based on features in background
perturbations from an EDA, specific Bc matrices can be computed and
used simultaneously in the VAR framework using the heterogeneous
formulation
 So far, combining radar data and “rainy” Bc leads to spin-up reduction
and to positive scores
 The formulation of the balance operator has been extended for all
hydrometeors that are represented in AROME in order to compute their
multivariate background error covariances using cloudy mask.
 The latter have been successfully exploited to analyzed cloud contents
from DA of cloudy radiances in a 1D framework.
Conclusions & perspectives
At CS and for LAM, Bc need to be updated frequently : the
set up of a daily ensemble is essential
Problems :
• need of perturbed LBCs
• the estimation and the representation of model error
• sampling noise is severe, especially at CS
• the computational cost !
Solutions :
•Cheaper ensembles in the limit of the “grey zone” (providing
that explicit convection is activated) : use of perturbations from
an AROME 4 km?
•Optimal filtering of forecast error parameters : B. Ménétrier’s
thesis
Conclusions & perspectives
Possible evolution of B in
operational NWP systems at CS
Degree of flow
dependency
One or several BC
updated daily from
an ensemble
Static BC with
balance relationships,
homogeneous and
isotropic covariances for
unbalanced variables
1
EnVar with more optimal
localizations in Be
EnVar: use of a spatially
localized covariance
matrix Be deduced from
an ensemble, combined
with BC
Static BC with
covariances modulated
by filtered values from an
ensemble
Ensemble size
10
100
Thank you for
your attention…
References
Brousseau, P.; Berre, L.; Bouttier, F. & Desroziers, G. : 2011. Background-error covariances for
a convective-scale data-assimilation system: AROME France 3D-Var. QJRMS., 137, 409422
Berre, L., 2000: Estimation of synoptic and mesoscale forecast error cavariances in a limited
area model. MWR. 128, 644–667.
Martinet et al 2013: Towards the use of microphysical variables for the assimilation of cloudaffected infrared radiance, QJRMS.
Ménétrier, B. and T. Montmerle, 2011 : Heterogeneous background error covariances for the
analysis of fog events. Quart. J. Roy. Meteor. Soc., 137, 2004–2013.
Michel, Y., Auligné T. and T. Montmerle, 2011 : Diagnosis of heterogeneous convectivescale
Background Error Covariances with the inclusion of hydrometeor variables. Mon. Wea Rev.,
138 (1), 101-120.
Montmerle T, Berre L. 2010. Diagnosis and formulation of heterogeneous background-error
covariances at themesoscale. QJRMS, 136, 1408–1420.
Montmerle T., 2012 : Optimization of the assimilation of radar data at convective scale using
specific background error covariances in precipitations. MWR, 140, 3495-3505.