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+T
σ+σ
σ=Ta
22
22
21
21
σ
TT+
σ
TT=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…
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