task d4c1: forecast errors in clouds and precipitation thibaut montmerle cnrm-game/gmap ioda-med...
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Task D4C1: Forecast errors in clouds and precipitation
Thibaut Montmerle CNRM-GAME/GMAP
IODA-Med Meeting16-17th 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
3h-cycled 3DVar (Seity et. Al 2011) :
The analysis is the solution of the BLUE :
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
xyRxyxxBxxx oobb HHJJJTT
ob 11
2
1
2
1
Introduction: DA in AROME
bTTba xHyxx 1
RHBHBH
In AROME, use of the CVT formulation:
Following notation of Derber and Bouttier (1999) :
• Kp is the balance operator allowing to output uncorrelated parameters using balance constraints.
2/1Bx
Berre (2000)
analytical linear balance operator ensuring geostrophical balance
regression operators that adjust couplings with scales
Introduction: B modeling
• BS is the spatial transform in spectral space, giving isotropic and homogeneous increments:
Kp and BS are static and are deduced from an ensemble assimilation (EDA, Brousseau et al. 2011a)
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
Introduction: limitations of the operational B
(Brousseau et al. 2011)
Time evolutions of Z500, T500 and of different background error standard
deviations at different levels
EDA designed for LAM :
Few cycles needed to get the full spectra of error variancesHigh impact phenomena under-represented in the ensemble
B Calibration
Modelization of B for specific meteorological phenomena
(Montmerle and Berre 2010)
Forecast errors are decomposed using features in the background perturbations that correspond to a particular meteorological phenomena.
(G : Gaussian blur)
1 0
rain/rain non rainy/non rainy
Binary masks:
Modelization of B for specific meteorological phenomena
Example for precipitation
Use of the heterogeneous formulation: (Montmerle and Berre, 2010)
12/12/12
12/12/11
SDISF
SSDF
Application #1: use of a « rainy » B for DA of radar data(Montmerle, MWR 2012)
2
12/12
2/12
2/11
2/11
2/1
BFBFBx “Rain” “No Rain”
Vertical Cross section of q increments4 obs exp: Innovations of – 30% RH
At 800 and 500 hPa
Where F1 and F2 define the geographical areas where B1 and B2 are applied:
This formulation allows to consider simultaneously different BS and Kp that are representative of one particular meteorological phenomena
• Example for a real case: D is deduced from the reflectivity mosaic
Radar mosaic15th 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
B1 has shorter correlation lengths: increments have higher spatial resolutions in precipitation Potential increase of the spatial resolution of assimilated radar data
EXP OPER
Humidity increment at 600 hPa (g.kg-1) (zoom over SE France)
OperPrecipClear air
Dij >0.5
Application #1: use of a « rainy » B for DA of radar data
Cov(q, u)
Rain
convDivergence increments
EX
PO
PE
R
z = 800 hPa z = 400 hPa div
•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 troposphereVertical cross covariances
OPER
Application #1: use of a « rainy » B for DA of radar data
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:
% 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
Liquid cloud
Ice cloud
Flow-dependent vertical covariances :Use of mean contents to distort vertically climatological values
Error variances for rain and ice cloud
Mean contents vs. error std dev. “of the
day” for rain (left) and ice cld (right)
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
Background errors are reduced for ql and qi (as well as for T and q (not shown)), increments are coherently balanced for all variables.
Reduction of background error
variances for selections of high
opaque cloud (left) and low
liquid cloud (right)
Application #2: Assimilation of cloudy radiances in a 1DVar
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
Evolution of analyzed profiles using AROME 1D
Example for low semi-transparent
ice clouds:
Time evolution of integrated ice cloud contents (min)
Application #2: Assimilation of cloudy radiances in a 1DVar
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
Ensemble size
Degree of flow dependency
101 100
Static BC with balance relationships, homogeneous and isotropic covariances for unbalanced variables
EnVar: use of a spatially localized covariance matrix Be deduced from an ensemble, combined with BC
EnVar with more optimal localizations in Be
Static BC with covariances modulated by filtered values from an ensemble
One or several BC updated daily from an ensemble
Conclusions & perspectives
Thank you for your attention…
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, 409-422
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 cloud-affected 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.
References
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