1. Task D4C1: Forecast errors in clouds and precipitation Thibaut Montmerle CNRM-GAME/GMAP IODA-Med Meeting 16-17th of May, 2014

2. 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

3. 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 ((10 8 ) 2 for AROME), B can be neither estimated at full rank nor stored explicitly Introduction: DA in AROME

4. In AROME, use of the CVT formulation: Following notation of Derber and Bouttier (1999) : K p is the balance operator allowing to output uncorrelated parameters using balance constraints. Berre (2000) analytical linear balance operator ensuring geostrophical balance regression operators that adjust couplings with scales Introduction: B modeling B S is the spatial transform in spectral space, giving isotropic and homogeneous increments: K p and B S are static and are deduced from an ensemble assimilation (EDA, Brousseau et al. 2011a)

5. 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

6. EDA designed for LAM :  Few cycles needed to get the full spectra of error variances  High impact phenomena under-represented in the ensemble B Calibration Modelization of B for specific meteorological phenomena (Montmerle and Berre 2010)

7. Forecast errors are decomposed using features in the background perturbations that correspond to a particular meteorological phenomena. (G : Gaussian blur) 1010 rain/rain non rainy/non rainy Binary masks: Modelization of B for specific meteorological phenomena Example for precipitation

8. Use of the heterogeneous formulation: (Montmerle and Berre, 2010) Application #1: use of a « rainy » B for DA of radar data (Montmerle, MWR 2012) “Rain” “No Rain” Vertical Cross section of q increments 4 obs exp: Innovations of – 30% RH At 800 and 500 hPa Where F 1 and F 2 define the geographical areas where B 1 and B 2 are applied:  This formulation allows to consider simultaneously different B S and K p that are representative of one particular meteorological phenomena

9. Example for a real case: D is deduced from the reflectivity mosaic Radar mosaic 15 th 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

10. Here: EXP: B 1 =rain, B 2 =OPER, D=radar mosaic B 1 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) Oper Precip Clear air D ij >0.5 Application #1: use of a « rainy » B for DA of radar data

11. Cov(  q,  u ) Rain conv Divergence increments EXP OPER z = 800 hPa z = 400 hPa div Spin-up reduction correlated with the number of grid points where B 1 is applied Positive forecasts scores up to 24h for precipitation and for T and q in the mid and lower troposphere Vertical cross covariances OPER Application #1: use of a « rainy » B for DA of radar data

12. Computation of background error covariances for all hydrometeors in clouds: Analogously to Michel et al. (2011), the mask-based method and an extension of K p have been used: % of explained error variances for q l (top) and q i (bottom) Vertical covariances between qi, ql and the unbalanced humidity q u Application #2: Assimilation of cloudy radiances in a 1DVar Liquid cloud Ice cloud

13. 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

14. Assimilation of IASI cloudy radiances (Martinet et al., 2013) q l and q i have been added to the state vector of a1DVar, along with T and q  Background errors are reduced for q l and q i (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

15.  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

16.  High impact weather phenomena (e.g convective precipitations, fog…) are under-represented in ensembles that are used to compute climatological B c : DA of observations is clearly sub-optimal in these areas  By using geographical masks based on features in background perturbations from an EDA, specific B c matrices can be computed and used simultaneously in the VAR framework using the heterogeneous formulation  So far, combining radar data and “rainy” B c 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

17. 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

18. Possible evolution of B in operational NWP systems at CS Ensemble size Degree of flow dependency 10 1 100 Static B C with balance relationships, homogeneous and isotropic covariances for unbalanced variables EnVar: use of a spatially localized covariance matrix B e deduced from an ensemble, combined with B C EnVar with more optimal localizations in B e Static B C with covariances modulated by filtered values from an ensemble One or several B C updated daily from an ensemble Conclusions & perspectives

19. Thank you for your attention…

20. 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