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