Introduction to data assimilation in meteorology - ForOT Optical ...

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.
Initial state at t 0
state at t 0 +applet
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 10 4 VS 10 7 ‏.(‏ Need of an other
inf
ormation Background source : a previous x b forecast of the atmospheric state.
Observations y o Analysis at t 0

General ideas : assimilation cycle
Numerical model
integration
Background x b
Analysis x a
Observations y o
6 hr forecast
TIME
6 hr assimilation window

A simple case : estimation of the room temperature
information : 2 measurements T 1 et T 2
Best
Linear
Unbiased
Estimate
Minimise the objective function
8

Generalisation in meteorology
The Best Linear Unbiased Estimate :
x a = x b + applex
= x b + ((‏ BH T (HBH T +R) -1 (y o – H (x b
, d : difference between
optimal weighting
observations and
background
With :
B and R
resp
ectively background errors and observations errors covariance matrices
H : observation operator and H linear observation operator
Variational formulation : minimisation of the cost function
,
J(applex) = J b (applex) + J o (applex)
(‏applex = applex T B -1 applex + (d-Happlex) T R -1 (d-H

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 --x---x-- rmse
Temperature wind specific humidity

Objective scores : forecast compared to surface
observations
Improvement in the first hours of the forecast
Surface pressure
assimilation
Dynamical
adaptation
2m temperature
---------- Bias
--x---x-- rms

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

28
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

Cumulative rainfall, 18 July 2007 03-15 UTC
29
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…