Data assimilation

Transcription

Data assimilation

Kompaktkurs: Atmosphärische Chemie und Dynamik, FZ Jülich 4.-8.10. 2011
Datenassimilation und Inversion
von Chemie-Transportmodellen
Hendrik Elbern
Rhenish Institute for Environmental Research at the
University of Cologne
and
Virt. Inst. for Inverse Modelling of Atmospheric Chemical
Composition
with contributions from the
RIU Chemical Data Assimilation Research group
5.10.2011
Contents
1. Objectives of data assimilation and inversion
2. Theoretical background
3. Meteorological examples
4. Stratospheric chemistry data assimilation
5. Tropospheric chemistry data assimilation and inversion
5.10.2011
1. Objectives of data assimilation and inversion
5.10.2011
Terminology
Inverse Modelling
The inverse modelling problem consists of using the actual result of
some measurements to infer the values of the parameters that
characterize the system.
A. Tarantola (2005)
5.10.2011
Data Assimilation
The ambitious and elusive goal of data assimilation is to
provide a dynamically consistent motion picture of the
atmosphere and oceans, in three space dimensions, with
known error bars.
M. Ghil and P. Malanotte-Rizzoli (1991)
5.10.2011
Objective of atmospheric data assimilation
•
"is to produce a regular,
physically consistent four
dimensional representation
of the state of the
atmosphere
• from a heterogeneous array
of in situ and remote
instruments
• which sample imperfectly
and irregularly in space and
time.
Data assimilation
• extracts the signal from noisy
observations (filtering)
•
interpolates in space and
time (interpolation) and
•
reconstructs state variables
that are not sampled by the
observation network
(completion).“ (Daley, 1997)
5.10.2011
2. Theoretical background
5.10.2011
Information sources and theories
declarative information:
•observations/retrievals
•forecasts
•“Climate” statistics,
•error statistics
procedural Information
differential equations
models
•contol theory
•statist. filter theory
•classical numerics
•optimisation algorith.
Interpolation
in space and time
Filter
error affected
data
Completion
non-observed
parameters
Advection
Information set
4D-consistent
process description
radiation
microphysic
s
gasphase
aqueous
phase
chem.
aerosol
s
Emissionen
Deposition
5.10.2011
Data assimilation has much of curve fitting!
y=ax+b
y
a
b{
|
0
|
1
x
5.10.2011
Characteristics in data assimilation,
in comparison to remote sensing retrievals
• high dimensional problem: dim (x) > 105
• highly underdetermined system (few observations with respect to
model freedom: dim(x)>>dim(y) )
• nonlinear dynamics
• constraints by physical laws are insufficient
5.10.2011
Advanced data assimilation is an application of the principles of Data
Analysis.
(As in satellite retrievals) we strive for estimating a latent,
not apparent parameter set x.
We dispose of
1. indirect information on the state and processes in terms of
manifest, though insufficient or inappropriate data y, and
2. a deterministic model M connecting x and y, in some way.
Bayes’ rule gives access to the probability of state x, given y and M
5.10.2011
Ad hoc (empirical) approaches (1)
Interpolation
5.10.2011
Optimality criteria: Which property can be attributed to our analysis
result?
(Need for quantification)
• maximum likelyhood:
 maximum of probability density function
• minimal variance: l2 norm
 parameters optimal, for which analysis error spread is minimal
(for Gaussian/normal and log-normal error distributions), Best
Linear Unbiased Estimate (BLUE)
• minimax norm (discrete cases)
• maximum entropy
5.10.2011
Data assimilation: Synergy of Information sources
example: 2 data sets with Gaussian distribution
(here: minimal variance= maximum likelihood)
Bayes’ rule:
Analysis (=estimation) BLUE
Best Linear Unbiased Estimate
xxb bb
xa yxoo a
a priori (=prediction or climatology)
observation
5.10.2011
5.10.2011
A 2 information bits example (1): Assumptions
5.10.2011
A 2 information bits example (2): estimation
5.10.2011
5.10.2011
5.10.2011
Single Observation, direct inversion
5.10.2011
Single observation, Minimisation
5.10.2011
Optimal Interpolation
Notation: Ide, K., P. Courtier, M. Ghil, and A. Lorenc,
Unified notation for data assimilation: operational sequential and variational,
J. Met. Soc. Jap., 75, 181--189, 1997.
5.10.2011
Types of assimilation algorithms:
“smoother” and filter
4D-var
Kalman Filter
5.10.2011
Sources of satellite trace gas observations:
•Limb sounding
instruments (trace gas
profiles, e.g. MIPAS on
ENVISAT)
•Occultation
•sun, moon, stars
•Nadir viewing instruments
-Total column content
- Profiles (coarse
vertical resolution)
5.10.2011
DA in the satellite data application chain
data
retrieval
level 0
detector tensions
level 1
spectra
prior
data
level 2
geolocated
geophysical parameters
radiance data
asimilation
inversion
geophysical
models
level 3
geophysical parameters
on regular grids
level 4
user applications
5.10.2011
The cost function to be minimized
5.10.2011
Transport-diffusion-reaction equation and its adjoint
5.10.2011
Staircase to the abyss:
Adjoint integration “backward in time”
How to make the
parameters of resolvents i
M(ti-1,ti) available in reverse
order??
back
5.10.2011
CONTRACE
Convective Transport
of Trace Gases into
the upper
Troposphere over
Europe: Budget and
Impact of Chemistry
Coord.: H.
Huntrieser,
DLR
flight path Nov.
14, 2001
5.10.2011
CONTRACE
Nov. 14, 2001 north (= home) bound
O3
CO
H2O2
1. guess
NO
assimilation result
observations
flight5.10.2011
height [km]
The 4D variational method:
Key development: construction of the adjoint code
forward model
backward model
(forward differential equation)
(backward differential equation)
algorithm
(solver)
adjoint algorithm
(adjoint solver)
code
adjoint code
5.10.2011
Kalman filter, basic equations
5.10.2011
Reduced rank Kalman filter (basic idea)
(Hanea, Heemink, Velders, 2004)
Appoximate covariance matrices
Pb,a (n x n) by a product of suitably low
ranked matrix Sb,a (n x p), and p << n .
Same procedure for the system noise
matrix Q with T (n x r).
The forecast step remains unchanged.
The forecast error covariance matrix rests
on 2 x p model integrations only!
The enlargement of p by r enforces
periodic reductions of columns (with
lowest ranked eigenvalues)
5.10.2011
Stratospheric chemistry data assimilation
CRISTA
5.10.2011
Worum geht es?
Bobachtung von
Spurengasen durch
Satellitensensoren
(z.B. MIPAS /
SCIAMACHY auf
ENVISAT)
Synoptische
Karte von
Spurengasverteilungen
SACADA
Assimilationssystem
5.10.2011
Icosahedral Grid vs. Conventional lat/lon Grid
•Separation of grid points 220-260
km, nearly homogeneous
•Equivalent resolution lat/lon grid
needs 2.0° x 2.4°
•10242 grid points per level
•13500 grid points per level
5.10.2011
SACADA Vertical Model Grid
Hybrid sigma /
pressure
coordinate
system
Assimilation
currently on 32
levels from 0.1 –
440 hPa (grey
shaded region)
5.10.2011
MIPAS FZK-IMK
ClONO2 retrieval example
Distribution of ClONO2 at 20 km
altitude in the Southern hemisphere
for 24 July 2002 and 3 days in
September 2002 (case study 1).
Note the pronounced collar structure
at the vortex edge.
5.10.2011
Results: Cost-functions for Oct. 21 – Oct. 26
c2- optimum
5.10.2011
Results: Cost-function for Oct. 27 – Nov. 14
c2- optimum
5.10.2011
Scatter plots for Nov. 13, 2003
HNO3
ClONO2
O3
Control Run
(after 23 days of
free integration
with SOKRATES
(2D) initial values)
23 days
consecutive
4D-var:
Background
Analysis
5.10.2011
Vergleichsbeispiel am DFD:
ROSE - SACADA
ROSE: 2.5°x3.8°
SACADA: ni32 = 2.25x2.25
5.10.2011
from Baier et al., 2006, EGU
poster
Results for ClONO2 at 7.6 hPa (~33 km), Nov. 13, 2003 12:00 UTC
Control Run (no
assimilation)
MIPAS Observations
Analysis
5.10.2011
Results for HNO3 at 28 hPa (~24 km), Nov. 4,
2003 12:00 UTC
Control Run (no
assimilation)
MIPAS Observations
Analysis
5.10.2011
water vapour assimilation
20. July 2003
~160 hPa
Integration start:
1. July,
no assimilation
after continuous assimilation
MIPAS water vapour retrievals
5.10.2011
Tropospheric chemistry
data assimilation and inversion
Rostock-Stuthof
5.10.2011
Objectives of air quality inverse modelling
• bring together air quality measurements and CTMs to provide optimal
spatio-temporal reconstructions of air quality parameters,
• estimate variability, sources, sinks, and trends
• provide better air quality predictions
• reconstruct past changes,
• act as a decision support system for protection measures (which
emissions are most critical?)
5.10.2011
Source types
• Gas phase
 NOx, volatile organic compounds (VOC),
 other anthropogenic
 biogenic (isoprenes, pinenes, …)
• Aerosol sources
 traffic, industrial, dwelling
 biomass burning
 mineral dust
 sea salt
5.10.2011
data
“Upgrade
to
information”
health
information
Satellite
retrievals
in situ
observations
Emission
inventories
legislation
Simulation of the
“atmospheric processor”
Meteo
data
GIS
data
cultural
heritage
farming
support
aviation
control
Chemical Weather System
science
5.10.2011
Processes in a complex chemistry-transport model
(EURopean Air pollution Dispersion model EURAD)
Meteorological Model
radiative transfer, winds, temperature, aqueous processes, cloud physics
condensation
evaporation
wet deposition
sublimation
CTM
transport
diffusion
chemical transformations
Gas phase
aqueous phase
aerosols
chemistry
dynamics
•nucleation
•coagulation
•sedimentation
•deliquescence
• ….
anthropogenic
+ biogenic
emissions
dry deposition
5.10.2011
Which constituents/complexity really matters?
• Human health:
 PM10, PM2.5, PM1 (= Particulate Matter )
 POPs (Persistent Organic Pollutants):
-
PAHs (Polycyclic Aromatic Hydrocarbons),
PCBs (PolyClorinated Biphenyls),
HCHs (HexaCloroHexanes),
benzene,
benzopyrene, ….
x
 m(r )dr
0
 Trace metals: Cd, Be, Co, Hg, Mo, Ni, Se, Sn, V, As, Cr, Cu, Mn, Zn, Pb
 Ozone, PAN, NO, NO2, SO2, CO
 Pollen
• Crops:
 Ozone
• Forests, lakes, other vulnerable ecosystems
 “Acid rain”
 ozone
5.10.2011
Special challenges of tropospheric chemistry inverse
modelling
The following problems prevail:
1.
strong influence of manifold processes including emissions and
deposition
2.
spatially highly variable “chemical regimes”
3.
chemical state observability (= “analyseability”) hampered by
manifold hydrocarbon species
4.
to maintain consistency across heterogeneous data sources:
satellite data and in situ observations
This invokes the application space-time inverse modelling algorithms
preserving the BLUE property (Best Linear Unbiased Estimator)
5.10.2011
State of the Art Examples
How are today’s services designed?
1.
2.
3.
4.
solvers of a deterministic transport-diffusion-reaction equation,
mostly operator-split-wise (except probably reaction-vert.
diffusion)
continental, or regional nest (1 km < Dx < 250 km horizontal
resolution)
tropospheric gas phase chemistry, 40-60 species, < 200 reactions
basic aerosol treatment of at least NH3, HNO3, H2SO4
5.10.2011
Special challenge: which is the appropriate scale for air quality
modelling?
• intercontinental / long range transport of pollutants
• many processes are local: point and line source emissions
• surface patterns/tesselation impacts skill
• boundary layer and convection simulation at least of like importance as in
meteorology
5.10.2011
Prognosis
www.eurad.uni-koeln.de
23 levels
lowest level: ca. 40 m
upper boundary ca. 15 km
Sequential nesting
Jülich example
Europe
ds = 125 km
Central Europe
ds = 25 km
NRW
ds = 5 km
ECHO
ds = 1 km
5.10.2011
Hemispheric forecast PM10
Incentives
•In readiness for
tropospheric satellite data
•boundary value provision
for continental scale models
for long range transported
constituents
high resolution version
150 x 150 grid
Dx = 125 km
5.10.2011
Daughter grids forecast 6.9.2005today
Europe Dx=125 km and central Europe Dx=25 km
5.10.2011
targeted regions
forecast 6.9.2005
5 km resolution
5.10.2011
NOx
1.5 x
0.6 x
1x
1.5 x
BERLIOZ
NOx-VOC
emissions
variation
ensemble
(21.7.1998,
15:00 UTC)
1x
0.6 x
0.6 x
1x
1.5 x
Note:
not
C-orthogonal,
not max.
sensitivities
aligned
VOCs
5.10.2011
concentration
Question: Which parameter to be optimized?
Hypothesis:
initial state and emission rates are least known
emission biased model state
observations
only initial value opt.
true state
joint opt.
only emission rate opt.
time
5.10.2011
Which model parameters should be
optimised?
• those that maximise the product (paucity of knowledge *
impact)
• tropospheric modelling:
Initial and boundary values
Emission Rates / Deposition Velocities
EURAD-CTM:
Grid Resolution
Reaction Rates
values and/or
• initial
Model Equations
• emission rates
• (boundary values)
5.10.2011
In the troposphere, for emission rates, the product (paucity of
knowledge*importance)
is high
5.10.2011
Treatment of the inverse problem
for emission rate inference
5.10.2011
Normalised diurnal cycle of anthropogenic surface emissions f(t)
emission(t)=f(t;location,species,day) * v(location,species)
day in {working day, Saturday, Sunday}
v optimization parameter
5.10.2011
Optimisation of emission rates
amplitude optimisation for each emitted species and grid cell
5.10.2011
Background emission rate covariance matrix D
5.10.2011
Mesoscale EURAD 4D-var inverse modelling system
4D-var configuration
Initial
values
gradient
EURAD
emission model
EEM
emission 1. guess
minimisation
meteorological
driver
MM5
emission rates
analysis
direct CTM
forecast
adjoint
CTM
observations
5.10.2011
2 level forward and backward integration scheme
time direction
forward integration
1. step 2. step 3. step 4. step 5. step 6. step 7. step 8. step 9. step
disk
store
recover
intermediate storage
Level 1
1. step 2. step 3. step 4. step 5. step 6. step 7. step 8. step 9. step
backward integration
5.10.2011
vert. Diffusion
Adjungierte
vert.Diffusion
vert.. Advekt
Adjungierte
vert. Advekt
horiz. Advekt y
Adjungierte
horiz. Advekt y
horiz. Advekt x
Adjungierte
horiz. Advekt x
Adjungierte
Chemie
Chemie
Chemie
horiz. Advekt x
horiz. Advekt y
vert.. Advekt
vert. Diffusion
horiz. Advekt x
horiz. Advekt y
vert.. Advekt
vert. Diffusion
horiz. Advekt x
Adjungierte
horiz. Advekt x
horiz. Advekt y
Adjungierte
horiz. Advekt y
vert.. Advekt
Adjungierte
vert. Advekt
vert. Diffusion
Adjungierte
vert.Diffusion
storage sequence: level 2, operator split
(each time step)
Level 1
Level 2
5.10.2011
Semi-rural measurement site Eggegebirge
7. August
8. August 1997
+ observations
no optimisation
initial value opt.
emis. rate opt.
joint emis +
ini val opt.
assimilation interval
forecast
5.10.2011
Error statistics
bias (top), root mean square (bottom)
assimilation window
forecast
+ observations
no optimisation
initial value opt.
emis. rate opt.
assimilation window
joint emis +
ini val opt.
forecast
5.10.2011
Control and diagnostics
Which is the requested resolution?
BERLIOZ grid designs and observational sites
(20.21. 07.1998)
Dx=6 km
Dx=18 km
Dx=2 km
Dx=54 km
5.10.2011
Some BERLIOZ examples of
NOx assimilation (20.21. 07.1998)
NO
NO2
Time series for selected NOx
stations on nest 2.
+ observations,
-- - no assimilation,
-____ N1 assimilation (18 km),
-____N2 assimilation.(6 km),
-grey shading: assimilated
observations, others
forecasted.
5.10.2011
NO2,
(xylene (bottom), CO (top)
SO2 .
surface
Emission source estimates by inverse modelling
Optimised emission factors for Nest 3
height layer ~32-~70m
5.10.2011
Nest 2: (surface ozone)
(20.21. 07.1998)
without
assimilation
with assimilation
5.10.2011
# molec NO2/cm2
# molec NO2/cm2
Assimilation of GOME NO2 tropospheric columns, 5.8.1997
forecast without assimilation
NOAA ch 3 (near infrared)
post
assimilation
forecast
started:
5.8.97 06:00
UTC
# molec NO2
/cm2
GOME NO2 columns: Courtesy of A. Richter, IFE, U. Bremen
5.10.2011
NOAA 14
11:51 UTC
no assimilation
NO2 tropospheric column assimilation IFE:
Example: BERLIOZ episode 20.7.1998
with assimilation
GOME retieval
Courtesy: A. Richter, IFE Bremen
5.10.2011
IUP Bremen GOMEGOME forecast validation
no assimilation
with assimilation
20.7.98
ideal
forecast
forecast
verification
forecast
21.7.98
(not
assimilated)
5.10.2011
MOPITT tropospheric CO assimilation
retrieved 850
hPa
concentrations
in ppbV.
first guess at 11:00 UTC;.
4D-Var
analysis for the
same time;
850 hPa, 1 July. 2003
Note: Colour codes are not fully consistent!
5.10.2011
Aerosol observations
• In situ:
EEA Airbase: Database of groundstations of EU member
countries & states:
- 450 stations for PM10 (2003)
- No PM2.5. (4 stations in UK only)
 (national and federal observation networks, partly in near real
time)
• Satellite measurements:
SYNAER (SYNergetic AErosol Retrieval, DLR-DFD, [HolzerPopp et al., 2001])*
5.10.2011
SYNAER data
See details in next presentation M. Schrödter-Homscheit
SYNAER (SYNergetic AErosol Retrieval) has been developed
at DLR-DFD [Holzer-Popp et al., 2002]
• SYNAER provides a first step from aerosol optical
properties to chemical properties
• Information breakdown in terms of:
 water soluble
 water insoluble
 sea salt (accumulation mode)
 sea salt (coarse mode)
 soot
 minerals transported
5.10.2011
SYNAER scheme
• uses data from SCIAMACHY/AATSR (Envisat) & GOME2/AVHRR (METOP),
• calculates BLAOT (boundary layer aerosol optical thickness)
from radiometers
• calculate SCIAMACHY/GOME-2 spectra and select best fit
spectrum -> chosen mixture (assigning aerosol type
concentrations (40 reference mixtures))
• PMx calculation
5.10.2011
Typical data configuration by ENVISAT and in
situ
SYNAER PM10
retrievals
EEA PM10 stations (2003)
SYNAER retrievals are available near real-time
5.10.2011
EURAD Aerosol and Fire Emission model
5.10.2011
Parameterization of Fire Emissions
• Classification of landcover
IGBP Scheme
18 Categories
(International Geosphere-Biosphere Program)
Assignment of Fuel Load FL [g(C)/m2] (DM)
• Type of combustion
Assignment of Emission factors EF [g(Spec.)/kg(DM)]
• Climatic conditions
Assignment of burning efficiency BE [fract.]
Dep. on: geolocation
Time-of-year /rel. Hum., Temp, Wind
• Area Burned AB [m2]
Overall emitted mass (Spec)
mSpec  FL  EFSpec  BE  AB
5.10.2011
EURAD – FIRE – MODEL  RACM
chemistry
EFM
52 Species
RACM
22 Gas & 4 Aerosol species
Gas-phase
CO2,CO,SO2,NH3, Isoprene,
Xylene,HCHO,CH4,Ethane, Ethene,
Formic-, Acetic acid
~
other Alkanes, Alkanols
Butadien
other Alkenes, Dienes
Aldehydes, Ketones
HC3, HC5, HC8
DIEN
OLT, OLI
ALD, KET
Terpenes
50% API
Nox
20% NO2 80% NO
50% LIM
Aerosols
TSP, PM2.5, EC, OC
PM2.5, EC, OC
Special
K, Hg, Furanes, Methyl halogenides
-
5.10.2011
Vegetation Classes for Fuel Load FL
estimation
EFM
EFM BE
EFM FL
IGBP
18 types of vegetation
5+1 Ecosystems
Evergreen Broadleaf
Tropical Forest
Evergreen Needleleaf
Deciduous Broadleaf
Mixed Forest
Burning efficiency
[frac]
Fuel Load
[kg(C)/m2]
0.85
30.0
Temperate Forest*
0.6
15.0
Deciduous Needleleaf
Boreal Forest
0.5
8.0
Shrublands
Wetlands
Woody Savanna
Crop/Natural Mosaic
Wooded Savanna
0.5
2.0
Savanna
Grass-,Croplands
Barren areas
Grassland
0.5
0.4
0
0.0
Water, Ice & Snow
No Vegetation
Urban
* north of 50° only Boreal Forest
5.10.2011
Input Data: Areas Burnt (AB)
Fire Locations (Hot Spots):
MODIS Web Fire Mapper
Further alternatives:
ESA World Fire Atlas
Environmental Agencies/Government/Institutes
Area Burned:
Satellite pictures (following confidence categories)
„Rule of thumb“:
Small Fires
1 ha
Large Fires
10 ha
Guessed from newspapers/news
5.10.2011
Example case: 13.07.2003
5.10.2011
in situ only
in situ & SYNAER
in situ & SYNAER
analysis increment
background
5.10.2011
How long does assimilation prevail?
~ ENVISAT overpass
~ assimilation time
Model run 12. – 14. July; Assimilation at 10 UTC
5.10.2011
How long do assimilation effects prevail?
No previous assimilation
assimilation on previous days 10 UTC
5.10.2011
Conclusions
• chemical weather inversions are high dimensional multiple
scale problems with transient constituents
• chemical inverse modelling rests on sparse and
heterogeneous observations, with variable error
characteristics (incl. error of representativity)
• initial value optimisation is insufficient, as at least emissions
are less known and more important for inversion
• the ability for inversion is therefore required to optimize
emission rates in the context of chemical conversions in a
high dimensional phase space
5.10.2011

Data assimilation

Transcription

Similar documents

"Operationelle Hydrologische Vorhersagen" 2010 Bern