Transcript Slide 1

A Case Study in Regional
Inverse Modeling
Andrew Schuh, Scott Denning, Marek Ulliasz Kathy Corbin, Nick Parazoo
The Question:
How is NEE distributed across domain in both
time and space
Deterministic Biosphere and
Transport Models
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SiB2.5 is used to predict carbon assimilation and
manage energy fluxes at the surface. MODIS
fPAR and LAI products are used to drive SiB2.5.
SiB2.5 is coupled to RAMS 5.0 which is used to
transport carbon dioxide. Meteorology is forced
with Eta 40km reanalysis data
Entire coupled model is run on 150 x 100 40km
grid over North America for the time period May
1,2004 through August 31, 2004.
How are observations “connected” to fluxes
Inversion Methods Available
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Bayesian Synthesis Inversion
• For many problems the quickest and easiest
method
• This basic bayesian posterior computation is at
core of many inversion methodologies
• However, computational concerns arise if the
dimensions of the problem get too large
Inversion Methods Available
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Kalman filtering techniques
• Reduces the effect of the time dimension of
inversion problem by putting in state space
framework and updating model in time.
• EnKF further reduces dimensional constraints
by effectively working with a sampled spatial
covariance structure. EnKF has also been
shown to have some desirable properties for
non-linear models.
Inversion Methods Available
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What about dealing with the spatial
structure of the problem in a hierarchical
way?
Inversion can take advantage of implicit
spatial structure inherent in many spatial
characterizations, like ecoregions
Covariance properties are propagated
through a hierarchical covariance
structure, independent within levels, thus
reducing dimensionality of the covariance
A possible hierarchy?
A possible hierarchy?
A possible hierarchy?
Hierarchical Model (Model Domain)
βI=1
βI=3
βI=2
LEVEL 2 ECOREGIONS
βI=4
LEVEL 1 ECOREGIONS
LEVEL 3 ECOREGIONS
βI=4,II=1 βI=4,II=2
βI,=4,II=3
βI=4,II=1,III=1 βI=4,II=1,III=2
βI=4,II=4
βI=4,II=1,III=3 βI=4,II=1,III=4
Data(likelihood):
y | X ,  III ,  ~ N X III ,  y 
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Level III ecoregions:  III | X  III ,  II ,   III ~ N X II ,   III
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Level II ecoregions:  II | X  II ,  I ,   II ~ N X I ,   II
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Level I ecoregions:  I |  0 ,   I ~ N  0 ,   I
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Example
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A backward in time lagrangian particle model (LPDM) was
used in conjunction with a 4 month SiB2.5Rams
simulation to produce “influence functions” for
assimilation and respiration for 34 towers.
Four afternoon observations each day for May 10, 2004 August 31, 2004 were used at each of the 34 towers.
Creationof Pseudo Bias Factors
Data(likelihood):
y | X ,  III ,  ~ N  X III ,1I 
Level III ecoregions:  III | X  III ,  II ,   III ~ N  X II ,0.001I 
Level II ecoregions:  II | X  II ,  I ,   II ~ N  X I ,0.04I 
Level I ecoregions:  I |  0 ,   I ~ N 0,0.2 I 
Results for Example
(via MCMC Gibbs Sampler)
Results for Example
(via MCMC Gibbs Sampler)
What about boundary conditions?
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Initial SiBRAMS run had constant carbon dioxide
for boundary conditions.
What effect might this have on the simulation?
How might corrections be made to these
boundary inflow terms?
Boundary conditions
Boundary conditions
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Initial results would seem to imply that boundary
conditions can be very important to regional scale
inversion using carbon dioxide concentrations
The boundaries also represent a large spatial area,
possibly contributing many unknowns to an often already
under constrained problem
In order to investigate this component, we begin by
investigating the modes of variability in simulated
boundary conditions.
Principal Components are generated, using PCTM (N.
Parazoo), for May 1, 2003 – August 31, 2003 and May
1,2004 – August 31, 2004. These provide “directions” of
maximal variability (in time) in the boundary conditions.
Principal Component Comparison 2003/2004
Boundary conditions
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The first principal component generally represents about
75% - 85% of the total variation over time with the
second representing another 3% - 6%.
The PCs appear to load nicely, particularly zonally. The
first principal component is capturing the changing zonal
gradient of carbon dioxide while the second appears to
capture gradients produced by synoptic activity along the
storm track in N.A.
This appears to be a promising dimension reduction of the
boundary influence and possibly robust interannually.
An obvious assumption here is that PCTM captures the
major modes of variability. Deficiencies in the transport
mechanisms of PCTM can not be expected to be captured
via these PCs.
Concluding Remarks and future directions
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Hierarchical inverse modeling offers many advantages
over traditional methods including an implicit spatial
correlation structure, multi-scale estimates of variance
and computationally efficient covariance
characterizations.
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Principal components appear to be a promising method of
parameterizing uncertainty in the boundary inflow terms
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Further directions:
- Nesting down to model grid resolution within regions of
interest
- Investigating real errors in boundary condition
estimates
- Applying real tower data