Transcript Document

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+t
Initial 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 ( reanalysis).
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.
Background xb
Analysis at t0
Observations yo
General ideas : assimilation cycle
Background xb
Numerical model
integration
Analysis xa
Observations yo
6 hr forecast
TIME
6 hr assimilation window
A simple case : estimation of the room temperature
information : 2 measurements T1 et T2
T1 = Tt + ε1,
E ε1  = 0,
T2 = Tt + ε2,
Eε1ε2  = 0
E ε2  = 0,
 
 
E ε22 = σ 22
E ε12 = σ12
Best
Linear
Unbiased
Estimate
σ 22
σ12
Ta = 2
T+ 2
T
2 1
2 2
σ1 + σ 2
σ1 + σ 2
σ12
= T1 + 2
(T1  T2 )
2
σ1 + σ 2
Minimise the objective function

T  T1 
J T  =
2
2
σ1

T  T2 
+
2
σ
2
2
8
Generalisation in meteorology

The Best Linear Unbiased Estimate :
xa
,
= xb +
= xb +
x
BHT (HBHT+R)-1 (yo – H (xb ))
optimal weighting

d : difference between
observations and
background
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)
= xT B-1 x
+
Jo (x)
+ (d-Hx)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

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
---------- Bias
Temperature
--x---x-- rmse
wind
specific humidity
Objective scores : forecast compared to surface
observations
 Improvement in the first hours of the forecast
Surface pressure
assimilation
Dynamical
adaptation
---------- Bias
--x---x-- rms
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
 24-h cumulative
rainfalls
 Better location
of the maximum
of precipitation
AROME in dynamical
adaptation
ALADIN
80 mm
Fog event, 7 february 2008


assimilation
Dynamical
adaptation
AROME low cloud cover at 9-h UTC
Fog is not simulated in spin-up mode
28
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
194 stations
Raingauges
measurements
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…