World Weather Open Science Conference.
Montreal, Canada, 16 to 21 August 2014
Experimenting with the LETKF
in a dispersion model coupled with the
Lorenz 96 model
Author: Félix Carrasco,
PhD Student at University of Buenos Aires,
Department of Atmospheric and Oceanic Sciences
[email protected]
In collaboration with: Juan Ruiz - Celeste Saulo - Axel Osses
Outline
Introduction.
The coupled Lorenz-Dispersion model.
Experiment Setup and definitions.
LETKF for model variables. Comparison between
online and offline.
LETKF to estimate Emissions.
Conclusion and future work.
Introduction
- We deal with two important data in the atmosphere/chemistry community:
Model and Observations, yet both of them contains errors.
Using both information in an optimal sense: Data Assimilation.
- Data Assimilation has been widely used in weather forecast and it has been
lately used in Atmospheric Chemistry for both chemical weather forecast and
source estimation.
- Chemical weather forecast has improved greatly the last decade using data
assimilation techniques also including operational implementations. Kukkonen
et al., 2012 (review Europe); Uno et al., 2003 (Japan); Constantinescu et al.,
2007.
- There has been great improves in order to estimate the emission (Inventory)
which usually have great uncertainties. Bocquet, 2011 (4Dvar); Kang et al.
(LETKF), 2011; Saide et al., 2011 (non Gaussian distribution).
Objective
Test the ability of the LETKF in simple transport model to improve estimation
of concentration and sources of atmospheric constituents in the context of
online and offline model.
Some ideas
- A good approach to test the ability of the technique is use simple models to
evaluate the performance before to implement in a more complex model.
- LETKF (Hunt et al. 2007) is a highly efficient and almost model independent
state-of-the art data assimilation technique that has been successfully applied
to several models.
Transport
Decay
Emission
Variable c20
Lorenz 96
Variable c40
-The idea is to coupled a trace
compound using the Lorenz
variables as the “wind” (Bocquet
& Sakov, 2013)
Variable c1
The coupled Lorenz-Dispersion model
Concentration of Lorenz 96 Coupled model
20
15
10
5
0
10
20
30
40
50
60
70
80
20
30
40
50
60
70
80
20
30
40
50
60
70
80
30
20
10
0
10
30
20
10
0
10
Time model with E=1,l =0.1
Concentration Lorenz 96 Coupled
20
40
35
X1
X6
c1
X2
Scheme
with N=6:
c5
X5
c2
X3
15
30
Variable cn
c6
25
10
20
15
5
10
5
c4
X4
c3
20
30
40
50
Time
60
70
Experiments setups and definitions
-The coupled model is resolved using a Four order Rungge-Kutta method with a
dT=0.01. We used N=40 variables for concentration and Lorenz variables (total
equal to 80) with the following parameter value for the model:
-Observations are generated from a long time model integration adding a
randomly distributed noise with STD equal to 1. Observations are assimilated
every five steps.
- To evaluate the performance we used the RMSE using the truth.
- We test the LETKF using a constant inflation factor and a localization scale.
Assimilated
Variable
...
...
Localization
Length
Experiments setups and definitions
- Two configuration model:
Offline Model
Online Model
Assimilation Cycle
Lorenz 96 +
Transport Model
Assimilation Cycle
MEAN
ENSEMBLE
Lorenz 96
Assimilation Cycle
Transport model
LETKF for optimal setup
Concentration RMSE
5
75
0.3
7
75
0.3
0.
4
0.
16
0.425
1
0.8
0.
1.
1.2
19
75
0.
3
8
10
12
14
Localization Length
01..8912
5
0.45
0. 3 7
0.425
75
0.3
6
5
4
0.3
5
0 .3
2
0.375
1.01
0.4
1.02
5
0.42
0.4
1.03
1
25
1.04
Online
Concentration
42
5
0.37
5
0.375
0.
0.425 4
1.05
0.425
0.4
Inflation factor
1.06
Online
Concentration
Ens Size=20
0.45
1.07
0.45
0. 3
1.08
- Variables shows high sensitivity to the
inflation parameter and localization scale.
0.425
1.09
0 .4
- Concentration and “wind” observations are
available at each grid point.
0.425
0.4
1.1
18
20
- Optimization of inflation and localization
scales for the concentration variables
- Less sensitivity to the inflation parameter and
to the localization scale.
- Optimal values for the wind variables
also good for the concentration variables
LETKF for optimal setup
- In the offline case, the RMSE values for
concentration variables are much higher than the
online case yet minor than the observation deviation.
- If the wind is not perturbed then a large part of the
uncertainty is missed ---> Higher optimal inflation
factor
Offline
Mean
Ens Size =10
Offline
ENS
- When we resolve the assimilation cycle
using the ensemble wind, the performance is
almost as good as in the online case.
LETKF for model variables
Online
Inflation factor: 1.02
Ensemble size: 20
Localization length: 6
Offline MEAN
Inflation factor: 1.8
Ensemble size: 10
Localization length: 4
Offline ENSEMBLE
Inflation factor: 1.02
Ensemble size: 10
Localization length: 2
- Large differences in
the RMSE even using
the optimal parameters
configuration
-Impact of concentration
upon wind analysis is
small
(At least when
observation density is
high)
LETKF for model variables
- We evaluated the performace of the three model for different observation densities.
- 100 experiments where performed for each observations densities randomly varying
the distribution of the observations.
- The large variability that is observed at low observation densities, is because the position of the
observation grid impacts directly on the performance of the data assimilation cycle
LETKF: Estimating sources
- Using the online model, we perform three experiments to test the ability of the LETKF
estimating the emission.
Inflation: 1.02
(Emission and
Concentration)
Localization: 6
Ensemble Size: 20
LETKF: Estimating sources
Two different emission scenarios:
Time Serie of RMSE.
Smooth spatial variabilty
Time Serie of RMSE.
High spatial variabilty
Inflation: 1.02 (Model);
1.01 (Emiss)
Localization: 6 (Wind);
3 (Concentration)
Ensemble Size: 20
Inflation: 1.02; 1.01
Localization: 6; 3
Ensemble Size: 20
Conclusion and Future work:
-We explore the abilities of one data assimilation technique (LETKF) in a simple
transport model for two model configuration.
- Results shows a good perfomance in estimating concentrations and wind in
both configuration with better perfomance when the uncertainty in the wind is
considered (Online and offline using ensemble).
- Results also shows a good perfomance in estimating emissions within
concentrations and wind with the online configuration. However the
performance of the filter is strongly sensitive to the spatial distribution of the
sources.
- Future work with this model is to explore using the rapid frequency Lorenz
variables model to study the impact of turbulence in the transport equation not
included in this formulation.
Thank You !
Questions?
Suggestions?
I like to thank the organizers for the travel grant that allow me to participate
in this WWOSC Conference.