Introduction to data assimilation in meteorology

Pierre Brousseau, Ludovic Auger

ATMO 08,Alghero, 15-18 september 2008

Introduction Numerical weather-prediction systems provide

informative forecast of atmospheric variables. The accuracy of these forecasts depend on, among

other things, the initial conditions used.

state at t0+tInitial state at t0

Model integration

Introduction

The main goal of a meteorological data assimilation system is to produce an accurate image of the true state of the atmosphere at a given time, called analysis.

This analysis could also be used as a comprehensive and self-consistent diagnostic of the atmosphere ( re-analysis).

Outlines

General ideas on data assimilation Some kinds of observation A new meso-scale data assimilation system Assimilation experiments

Assimilated information : observations

Observation : a measurement of an atmospheric physical parameter.

Exemple :

Surface pressure measurements, 10 september 2008, 00 UTC

Assimilated information : background

Problems :– Lack of observation in some part of the atmosphere. – Observation number smaller than the numerical state

dimension (for AROME 104 VS 107). Need of an other information source : a previous

forecast of the atmospheric state.

Observations yo

Analysis at t0

Background xb

General ideas : assimilation cycle

Background xb

Observations yo

Analysis xa

TIME

6 hr assimilation window

Numerical model integration

6 hr forecast

information : 2 measurements T1 et T2

BestLinearUnbiasedEstimate

Minimise the objective function

)( 2122

21

21

1

222

21

21

122

21

22

TTσ+σ

σ+T=

Tσ+σ

σ+Tσ+σ

σ=Ta

22

22

21

21

σTT+

σTT=TJ

2

121

1

1,1

0,

σ=εE

=εE

ε+T=T t

2

222

2

2,2

0,

σ=εE

=εE

ε+T=T t

8

021 =εεE

A simple case : estimation of the room temperature

Generalisation in meteorology

The Best Linear Unbiased Estimate :

xa = xb + x= xb + BHT (HBHT+R)-1 (yo – H (xb ))

,

d : difference between observations and background

optimal weighting

With : B and R respectively background errors and observations

errors covariance matrices H : observation operator and H linear observation operator

Variational formulation : minimisation of the cost function

J(x) = Jb(x) + Jo (x) = xT B-1 x + (d-Hx)T R-1 (d-H x),

Background error statistics

Background-error statistics determine how observations modify the background to produce the analysis, filtering and propagating innovations.

B should contain some information about the uncertainty of the guess, which depends on :

– the model– the domain– the meteorological situation of the day (flow and initial conditions).

To determinate this uncertainty is a major problem in data assimilation

Outlines

General ideas on data assimilation Some kinds of observation A new meso-scale data assimilation system Assimilation experiments

Radiosonde observations Vertical profile of temperature, wind and humidity :

– very accurate– but only twice a day with an irregular spatial coverage

Satellite observations Instruments on :

– geostationnary satellite.– polar satellite.

Radiance measurements providing vertical profile of temperature and/or humidity (stratosphere and high-troposphere).

AMSU-A, 11 september 2008, 00 UTC (six hour assimilation window)

Satellite observations Observations not always available on limited domain AMSUB intrument, 11 september 2008

12 UTC : measurements from 2 satellites

00 UTC : no measurement

Surface observations Surface pressure, 2m temperature and humidity and 10m wind Very usefull to provide information on the low atmospheric layers 10 september 2008, 00 UTC

Radar observations Doppler-wind and reflectivity observations 10 september 2008, 00 UTC

Different kinds of observation Lots of observations which differ in :

– Measured parameter– spatial and temporal coverage– resolution

Observations informative for– large-scale model : ex : AMSU-A (Atmospheric sounder) :

resolution of 48 km.– Meso-scale model : ex : Doppler-wind measurement

Outlines

General ideas on data assimilation Different kinds of observation A new meso-scale data assimilation system Assimilation experiments

The AROME project AROME model will complete the french NWP system in 2008 :

– ARPEGE : global model (15 km over Europe)– ALADIN-France : regional model (10km)– AROME : mesoscale model (2.5km)

Aim : to improve local meteorological forecasts of potentially dangerous convective events (storms, unexpected floods, wind bursts...) and lower tropospheric phenomena (wind, temperature, turbulence, visibility...).

ARPEGE stretched grid and ALADIN-FRANCE domain

AROME France domain

Initial and lateral boundary conditions Lateral boundary

conditions for Limited Area Model provided during the forecast by : – a global model– a larger LAM

Initial conditions could be provided by :– a larger model

(dynamical adaptation)– A local data

assimilation system. Local data assimilation

systems for ALADIN and AROME

AROME data assimilation system Use a variational assimilation scheme 2 wind components, temperature, specific humidity and

surface pressure are analysed at the model resolution (2.5 km).

Use of a Rapid Update Cycle Forecasts initialized with more recent observations will be

more accurate Using high temporal and spatial frequency observations

(RADAR measurements for example) to the best possible advantage

Objective scores : analysis compared to radiosonde at 00 UTC

Temperature wind specific humidity

---------- Bias --x---x-- rmse

Analysis from the AROME RUC compared to ALADIN analysis show an important reduction of Root Mean Square Error and Bias for all parameters all over the troposphere except for the humidity field around 200 hPa

Objective scores : forecast compared to surface observations

assimilationDynamicaladaptation

---------- Bias--x---x-- rms

Improvement in the first hours of the forecast Surface pressure

2m temperature

First results

objective scores show that the general benefit of the AROME analysis appears during the first 12-h forecast ranges, then lateral conditions mostly take over the model solution.

Subjective evaluation confirms many forecast improvement during the first 12-h forecast ranges. In some particular cases, this benefit can also be observed after this range.

Outlines

General ideas on data assimilation Different kinds of observation A new meso-scale data assimilation system Assimilation experiments

Precipitating event, 5 october 2007

RADAR MEASUREMENT

AROME with assimilation

AROME in dynamical adaptation

ALADIN 80 mm

24-h cumulative rainfalls

Better location of the maximum of precipitation

Fog event, 7 february 2008

assimilation

Dynamical adaptation

AROME low cloud cover at 9-h UTC Fog is not simulated in spin-up

mode

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An observation influence study : ground-based GPS

Experiment in order to evaluate the influence of additional Ground-based GPS observations in AROME data assimilation system.

Use of 194 stations (blue star) + 84 additional stations (green circle).

Give information on integrated humidity profile

29

Cumulative rainfall, 18 July 2007 03-15 UTC

Raingauges measurements

194 stations

194 + 84 stations

Conclusion on data assimilation

Data assimilation provide an accurate image of the true state of the atmosphere at a given time in order to initialize numerical weather forecast using :– Observations– A previous forecast of the state of the atmosphere

Observations used are various and numerous and provide large and small scale information.

The use of a meso-scale data assimilation system improve Limited Area Model forecast accuracy up to 18 hours.

This system has been tested for one year and will be put into operation next month

Thank you for your attention…