recent progress in co 2 flux data assimilation

21 December, 2006LSCE

Recent progress in CO2 flux data assimilation

Ken Davis

Penn State/LSCE

with

D. Ricciuto, T. Hilton, A. Desai, P. Ciais, M. Reichstein, S. Piao


Outline

• Introduction and history. • Barriers to progress.• Evaluation or assimilation?• An example of flux data assimilation with the

aim of improving predictive capacity.• Progress towards understanding the spatial

and temporal statistics of ecosystem fluxes.


Introduction and history:Flux tower measurements in the story of

the global carbon cycle.


Overall goals: terrestrial carbon cycle science

“Bottom-up” methods• Build mechanistic, or

“bottom-up” models that can– Reproduce observed

spatial and temporal gradients in terrestrial fluxes (flux towers, atmospheric budgets).

– Predict future terrestrial fluxes

Attribution, prediction

“Top-down” methods• Quantify the non fossil fuel

global carbon budget• Observe spatial and

temporal patterns in the atmospheric CO2 budget and infer fluxes

Diagnosis, inference


Inherent spatial and temporal scales of methods of studying the carbon cycle

Methodological gap

Upscaling

Downscaling

Airborne flux

Chamber flux or exp plot Tower

flux

Forest inventory Inverse study

year

month

hour

day

Time Scale

Spatial Scale

(1m)2 = 10-4ha

(1000km)2 = 108ha

(100 km)2 = 10 6ha

(10k m)2 = 10 4ha

(1km)2 = 10 2ha

Rear th


Forest inventories, satellite land-surface observations commence.

Continuous flux tower measurements initiated at Harvard Forest.

Network of flux tower sites expands rapidly. Methodological research.

Many publications showing one year of flux observations from one site. Missing sink observed?

Publications covering a few years of data from individual sites. Climate-driven variability in terrestrial fluxes observed?

Forest inventory used to estimate large-scale, decadal C fluxes.

Publications comparing single years at multiple sites. No explicit spatial component.

Some publications attempt to merge multiple sites across space.

Atmospheric CO2 monitoring initiated.

N. Hemisphere terrestrial sink of CO2 inferred.

Strong interannual variability in global-scale terrestrial fluxes of CO2 observed.

20 year trends in the amplitude of the seasonal cycle of CO2 exchange observed in the N. hemisphere.

Attempts at continental to regional atmospheric inversions.

time

1950s-1980s

1990

Early 1990s

Mid to late 1990s

Early 2000s


Barriers to progress


• Flux tower footprints are very small (~1km2) compared to the globe.– Neither net annual fluxes nor interannual variability in

fluxes observed at flux towers can be readily linked to the observed global carbon balance.

– Mechanisms remain uncertain. Attribution has not been successful at regional to global scales.

x 107 = 1 PgC yr-1 ??= ± 1PgC yr-1 ??~1 km2

??


• Flux towers are limited in their time of record. Climate-driven trends and long-time scale processes are not well-constrained by these observations.– Detection of trends in flux tower time series is not

clear.– Ability to predict future fluxes is suspect. Decadal or

longer prediction remains highly uncertain for any spatial scale.

flux

time5-10 years of observations

Flux tower time series

Multi-decade terrestrial carbon cycle model prediction and uncertainty


• We cannot perform atmospheric inversions at small spatial and temporal scales– Too many unknowns, not enough data

• We are uncertain about how to interpolate flux tower data across space– Mechanisms governing spatial variability in fluxes are

uncertain

Regional diagnosis of terrestrial fluxes at any time scale remains uncertain.

100-1000 km domain

Is every flux independent in space and time?

Each grid box has a different flux for each time step.


Potential avenues for progressBarrier

• Lack of attribution of causes of large-scale fluxes. Limited spatial scale of a flux tower footprint.

• Inability to detect influence of climatic change, predict future fluxes.

• Uncertainty in how to aggregate fluxes over space. Inability to diagnose regional fluxes with confidence.

Potential solution• Map fluxes over space using a

numerical model aided by remote sensing and other spatial databases. Compare to atmospheric budgets.

• Maintain observations, add complementary observations (e.g. forest inventory), evaluate model skill.

• Study the spatial and temporal correlations in flux observations, flux-model differences.


Outline

• Introduction and history. • Barriers to progress.• Evaluation or assimilation?• An example of flux data assimilation with the aim of

improving predictive capacity.• Progress towards understanding the spatial and

temporal statistics of ecosystem fluxes.


Evaluation or assimilation?Flux tower observations

Terrestrial carbon cycle model

Atmospheric inversion fluxes

vs. vs.

Terrestrial model optimized to match the flux tower observations.

vs.

Flux estimates optimized to all available data sources

Carbon cycle data assimilation


An example of flux data assimilation with the aim of improving predictive capacity


Multi-year data assimilation at multiple flux tower sites

• Does data assimilation improve a terrestrial Does data assimilation improve a terrestrial carbon cycle model’s ability to simulate diurnal, carbon cycle model’s ability to simulate diurnal, synoptic, seasonal, interannual variability in fluxes? synoptic, seasonal, interannual variability in fluxes? What are the implications for predicting future What are the implications for predicting future fluxes?fluxes?• Can we simulate cross-site variability in fluxes?Can we simulate cross-site variability in fluxes?• Can we use a common set of model parameters Can we use a common set of model parameters for multiple sites?for multiple sites?• Are any model parameters poorly-constrained by Are any model parameters poorly-constrained by the flux data?the flux data?• What happens to carbon pools after assimilation?What happens to carbon pools after assimilation?

Ricciuto, Ph.D. dissertation, 2006.


Assimilation techniqueAssimilation technique• This is a potentially nonconvex problem, thus we chose a global optimization algorithm, Stochastic Evolutionary Ranking Strategy (SRES)

• Stochastic – difficult to guarantee convergence• Relatively fast method to find very good solution• No parametric uncertainty (unlike MCMC)

• Method:

- Twiddle all the knobs in the model until it matches all of the data.

– Start with initial population (parameter sets)– Evaluate goodness of fit (likelihood function)– Select best-fitting members (parameter sets)– Mutate these members, repeat until convergence “apparent”– Run three times for each tower, compare solutions


Tower sitesTower sites

Site-years analyzed

(37 total)

WLEF: 1997-2004

Harvard: 1992-2003

Howland: 1996-2003

UMBS: 1999-2003

M. Monroe: 1999-2003


Forcing: wind, [CO2], PAR, Tair,

precip

Wood(NL)

Wood(BL)

Leaf(BL)

Root (NL) Root (BL)

GPP (NL,BL)

Leaf(NL) NEE

NPP(NL,BL)

RH

RaRa

Soil carbon (CS)

Simplified TRIFFID ModelSimplified TRIFFID Model


Why TRIFFID?Why TRIFFID?• Dynamic Global Vegetation Model: Contains longer-term processes essential for decadal scale predictions.

• Used in Cox et al. (2000) – strong feedbacks. Are model parameters realistic? Is model structure appropriate?

Friedlingstein et al. (2006)

Cox et al. (2000)

Cox et al. (2000)

Friedlingstein et al. (2006)


Parameter name Units Default Lower bound

Upper bound

CS Soil carbon

kg C m-1 10.0 0.0 30.0

Q10H Heterotrophic respiration Q10

dimless 2.0 1.0 4.0

opt Optimal SWC for heterotrophic Q10

Vo l frac. 0.2 0.0 1.0

fac SWC dependence of RH

Dimless 0.8 0.0 1.0

c Critical SWC

Vo l frac. 0.30 0.0 1.0

w Wilting SWC

Vo l frac. 0.13 0.0 1.0

nl0BL Top leaf nitrogen content (BL)

kg N (kg C)-1

0.036 0.01 0.20

nl0 NL Top leaf nitrogen content (NL)

kg N (kg C)-1

0.030 0.01 0.20

BL BL Quantum efficiency

mol CO2 (mol PAR)-1

0.06 0.01 0.25

NL NL Quantum efficiency

mol CO2 (mol PAR)-1

0.06 0.01 0.25

Q10VM T-sensitivity of Vm

Dimless 2.0 1.0 4.0

TlowBL Lower Tleaf for BL photosynthesis

oC -5.0 -40.0 10.0

TlowNL Lower Tleaf for NL photosynthesis

oC -15.0 -40.0 10.0

TuppBL Upper Tleaf for BL photosynthesis

oC 33.0 10.0 50.0

TuppNL Upper Tleaf for NL photosynthesis

oC 28.0 10.0 50.0

Dc Critical humidity deficit

Kg (kg)-1 0.09 0.01 0.50

Rg Growth resp. coefficient

Dimless 0.25 0.05 1.00

Rdc Dark respiration coefficient

Dimless 0.015 0.003 0.075

Q10RD Dark respiration Q10

Dimless 2.0 1.0 4.0

Toff Critical Tleaf for leaf-off

oC 0.0 -30.0 30.0

off Critical moisture for leaf-off

Dimless 0.90 0.0 1.0

p Budburst/leafoff coefficient

yr-1 20.0 1.0 100.0

Twenty-two of TRIFFID’s (40?) parameters were chosen (by the seats of our pants) for optimization.

Optimization with all parameters (one test case) did not significantly change our results.



• Does data assimilation improve a terrestrial Does data assimilation improve a terrestrial carbon cycle model’s ability to simulate carbon cycle model’s ability to simulate diurnal, diurnal, synoptic, seasonalsynoptic, seasonal, , interannualinterannual variability in fluxes? variability in fluxes?

Yes!Yes!

No!No!• What are the implications for predicting future What are the implications for predicting future fluxes?fluxes?

Little confidence in long-term predictions if Little confidence in long-term predictions if interannual variability cannot be simulated after interannual variability cannot be simulated after assimilating all available data.assimilating all available data.


Model performance:Model performance:Synoptic variabilitySynoptic variability

Our model reproduces daily sums of NEE reasonably well (example month: Sep 1997)


Model performance: Model performance: seasonal cycleseasonal cycle


Model performance:Model performance:Interannual variabilityInterannual variability


Timescales of modeled and observed fluxesTimescales of modeled and observed fluxes

Braswell et al. (2005)

• Analysis using SIPNET model: MCMC optimization with 26 parameters

• Fluxes at Harvard Forest:

• Largest variance in diurnal and seasonal cycles

• Optimized model fits these well

• Interannual variability:

• worst timescale for performance

• Model underestimates

• consistent with TRIFFID results

SeasonalSynoptic

Interannual

Diurnal


Hypotheses:

The model has a structural flaw that prevents it from being able to reproduces observed interannual variability in fluxes. Our best guess.

(If so, maybe the process that is missing is something that is very local, and the model does fine at large spatial scales? Probably not the case.)

OR

The observed interannual flux variability is insignificant or erroneous. Probably not the case.


Significant Interannual variability at WLEF

• fff

Uncertainty = gap-filling uncertainty + turbulent sampling uncertainty.

Random error: about 20 gC m-2

The range of interannual variability is therefore statistically significant at the 95% level.

Quantified systematic errors: Loss of very low frequency fluxes, choice of low-turbulence screening threshold, changes in flux levels: Also about 20 gC m-2 (for IAV).


• Eddy-covariance is a good method for characterizing interannual variability in fluxes.

• Sums may be biased due to advection, other systematic errors, but these (unquantified systematic) errors will not change much from year to year.


Observed interannual variability: only local processes? Probably not.

Gap-filled fluxes from the 5 sites used in TRIFFID analysis

Harvard and Howland: Coherent between 1996 and 2000, then breaks down.

UMBS and Morgan Monroe: coherent (similar PFT, climate)

WLEF: 2002 missing, coherent with UMBS and Morgan Monroe



• Can we simulate cross-site variability in fluxes?Can we simulate cross-site variability in fluxes?• Can we use a common set of model parameters Can we use a common set of model parameters for multiple sites?for multiple sites?

• Yes to both questions, if we let soil carbon and Yes to both questions, if we let soil carbon and leaf nitrogen (maximum photosynthetic rate) vary leaf nitrogen (maximum photosynthetic rate) vary across sites.across sites.

– this implies that these are quantities that must be this implies that these are quantities that must be mapped accurately in space and used as model inputs.mapped accurately in space and used as model inputs.– if they varied from year-to-year, we could also fit if they varied from year-to-year, we could also fit interannual variability, but what is the mechanism?interannual variability, but what is the mechanism?



Model performance: Model performance: Cross-site variabilityCross-site variability

• Site-specific variables, held constant in time.

• Soil carbon

• Leaf nitrogen (Vmax)

• Forest structure (needleaf or broadleaf, canopy height)



• Are any model parameters poorly-constrained by Are any model parameters poorly-constrained by the flux data?the flux data?

Yes. Respiration parameters.Yes. Respiration parameters.• What happens to carbon pools after assimilation?What happens to carbon pools after assimilation?

Out of equilibrium. Is this realistic? We don’t Out of equilibrium. Is this realistic? We don’t know…know…



Convergence diagnosticsConvergence diagnostics• Objective function = -1*log(likelihood)

• 3 runs generally converge for each site, but some slight disagreement

• Some model parameters converge

• photosynthesis

• phenology

• Some are poorly constrained

• Heterotrophic respiration

• Autotrophic respiration


Results of the joint parameter optimization, which uses observations from all sites as a data constraint. Well-constrained parameters are shown in bold, and are defined as v alues that are within 0.5% o f each other in all three SRES runs and are not edge-hitting.

Parameter Published optimized Parameter published optimized CS (HV) 10.0 0.00 BL 0.06 0.0446 CS (HW) 10.0 5.59 NL 0.06 0.0239 CS (WL) 10.0 12.0 Q10VM 2.0 2.26 CS (MM) 10.0 0.00 TlowBL -5.0 -1.05 CS (UM) 10.0 2.97 TlowNL -15.0 50.0

Q10H 2.0 4.00 TuppBL 33.0 1.475 opt 0.55 0.447 TuppNL 28.0 30.0

fac 0.80 0.980 Dc 0.09 0.0246

c 0.30 0.216 Rg 0.25 0.005

w 0.13 0.00 Rdc 0.015 0.0143 nl0(HV) 0.036 0.112 Q10RD 2.0 1.515 nl0 (HW) 0.030 0.087 Toff 0.0 11.5 nl0(WL) 0.036 0.080 off 0.90 0.00 nl0 (MM) 0.036 0.083 p 20.0 15.8 nl0(UM) 0.036 0.113 -(Log L) N/A 465957


Parameter name Units Default Lower bound

Upper bound

CS Soil carbon

kg C m-1 10.0 0.0 30.0

Q10H Heterotrophic respiration Q10

dimless 2.0 1.0 4.0

opt Optimal SWC for heterotrophic Q10

Vo l frac. 0.2 0.0 1.0

fac SWC dependence of RH

Dimless 0.8 0.0 1.0

c Critical SWC

Vo l frac. 0.30 0.0 1.0

w Wilting SWC

Vo l frac. 0.13 0.0 1.0

nl0BL Top leaf nitrogen content (BL)

kg N (kg C)-1

0.036 0.01 0.20

nl0 NL Top leaf nitrogen content (NL)

kg N (kg C)-1

0.030 0.01 0.20

BL BL Quantum efficiency

mol CO2 (mol PAR)-1

0.06 0.01 0.25

NL NL Quantum efficiency

mol CO2 (mol PAR)-1

0.06 0.01 0.25

Q10VM T-sensitivity of Vm

Dimless 2.0 1.0 4.0

TlowBL Lower Tleaf for BL photosynthesis

oC -5.0 -40.0 10.0

TlowNL Lower Tleaf for NL photosynthesis

oC -15.0 -40.0 10.0

TuppBL Upper Tleaf for BL photosynthesis

oC 33.0 10.0 50.0

TuppNL Upper Tleaf for NL photosynthesis

oC 28.0 10.0 50.0

Dc Critical humidity deficit

Kg (kg)-1 0.09 0.01 0.50

Rg Growth resp. coefficient

Dimless 0.25 0.05 1.00

Rdc Dark respiration coefficient

Dimless 0.015 0.003 0.075

Q10RD Dark respiration Q10

Dimless 2.0 1.0 4.0

Toff Critical Tleaf for leaf-off

oC 0.0 -30.0 30.0

off Critical moisture for leaf-off

Dimless 0.90 0.0 1.0

p Budburst/leafoff coefficient

yr-1 20.0 1.0 100.0

Twenty-two of TRIFFID’s (40?) parameters were chosen (by the seats of our pants) for optimization.

Optimization with all parameters (one test case) did not significantly change our results.


How do we diagnose the potential model structural error?

• One way - limit the number of processes the model simulates - for example, cut out the soil hydrology by imposing observed soil moisture.


Comparison of observed vs. modeled NEE for two cases of the separate

assimilation at the WLEF tower: one using the observed soil water content (SWC) and one using the SWC from the simple bucket model in TRIFFID. Using the observed SWC improves the agreement of the model to observations, but most of the interannual variability is still not captured and the range of modeled variability is too small.


Forest inventories, satellite land-surface observations commence.

Continuous flux tower measurements initiated at Harvard Forest.

Network of flux tower sites expands rapidly. Methodological research.

Many publications showing one year of flux observations from one site. Missing sink observed?

Publications covering a few years of data from individual sites. Climate-driven variability in terrestrial fluxes observed?

Forest inventory used to estimate large-scale, decadal C fluxes.

Publications comparing single years at multiple sites. No explicit spatial component.

Some publications attempt to merge multiple sites across space.

Atmospheric CO2 monitoring initiated.

N. Hemisphere terrestrial sink of CO2 inferred.

Strong interannual variability in global-scale terrestrial fluxes of CO2 observed.

20 year trends in the amplitude of the seasonal cycle of CO2 exchange observed in the N. hemisphere.

Attempts at continental to regional atmospheric inversions.

time

1950s-1980s

1990

Early 1990s

Mid to late 1990s

Early 2000s


Potential avenues for progressBarrier

• Lack of attribution of causes of large-scale fluxes. Limited spatial scale of a flux tower footprint.

• Inability to detect influence of climatic change, predict future fluxes.

• Uncertainty in how to aggregate fluxes over space. Inability to diagnose regional fluxes with confidence.

Potential solution• Map fluxes over space using a

numerical model aided by remote sensing and other spatial databases. Compare to atmospheric budgets.

• Maintain observations, add complementary observations (e.g. forest inventory), evaluate model skill.

• Study the spatial and temporal correlations in flux observations, flux-model differences.


Outline

• Introduction and history. • Barriers to progress.• Evaluation or assimilation?• An example of flux data assimilation with the aim of

improving predictive capacity.• Progress towards understanding the spatial and

temporal statistics of ecosystem fluxes.


Sabbatical plans

• Examine the space-time statistics of flux observations and flux-model residuals for selected study areas:– ChEAS - many towers, very different stand types,

very similar climate - nearly colocated– Plant functional type clusters - same stand types,

varying climate/spatial separation. Europe, North America.

• Use both optimized and non-optimized ecosystem models.


Sabbatical results• Incomplete driver data preparation (but I haven’t

given up!)• A nice workshop - plans to initiate FLUXCOM• A couple of good plots from my students• A bit of ORCHIDEE-AmeriFlux comparison

• Lots of good CO2-relevant discussions of boundary layer meteorology (which I hope to continue)

• Many family dinners together• My kids learned a lot of French!


Observed interannual variability: only local processes? Probably not.

Gap-filled fluxes from the 5 sites used in TRIFFID analysis

Harvard and Howland: Coherent between 1996 and 2000, then breaks down.

UMBS and Morgan Monroe: coherent (similar PFT, climate)

WLEF: 2002 missing, coherent with UMBS and Morgan Monroe


Northern Wisconsin - ChEAS (Chequamegon Ecosystem-Atmosphere Study)

18 flux measurement sites and the WLEF trace gas measurementsFirst “ring of towers” regional inversion experimentAbundant ancillary data - remote sensing of surface, ground-based plant physiological and biometric data, atmospheric profiling


7 day block averaged fluxes

1 year block averaged fluxes


Another view of spatial Another view of spatial correlation of fluxescorrelation of fluxes

Chevallier et al (2006): no correlation at any spatial scale in model-data residuals

Daily average fluxes

Mixed vegetation types

Model is not optimized for the observed fluxes


Climatic Gradients in European Fluxes

Reichstein, Papale et al.GRL, in press

cf. also Valentini et al. (2000)Law et al. (2002)

Index Water Availability Ea/Ep (mm/mm) Mean annual temperature (°C)

Continental

Interannual

Southern sites - water limited Northern sites - temperature limited


Climatic Gradients in North American Fluxes

Color indicates plant functional type. Each small symbol is a site-year.


Findings - flux data only• Very similar flux vs. climate spatial slopes over Europe and North

America.• Both GPP and TER positively correlate with annual temperature

and water availability.• Cross-site NEE dependency on climate is weak (compensating

gradients of TER, GPP - effects of management, for example, become more prominent).

• Results broadly similar to Law et al (2002), but this analysis limited to forested systems, benefits from longer time series.

• Interannual variability at sites does not appear to follow the cross-site climatic gradient in fluxes.

• Does ORCHIDEE produce similar spatial gradients? Analyses underway.


What controls IAV in GPP ?Model suggests that GPP variability is determined by :Temperature in the North and by rainfall in the South

Maps of R2(GPP-Temperature) minus R2(GPP-Precipitation)

Is this also observed in eddy-covariance time series ?

Analyses in progress.


Interannual variability is smaller than cross-sitespatial variability: ORCHIDEE and observations

North America

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

GPP TER NEE

Std Dev (Kg m-2 yr-1)

Spatial-continental

Interannual

ORCHIDEE Spatial-continental

ORCHIDEEInterannual


conclusions

• Prediction appears to be difficult. Model development needed?

• Spatial gradients in fluxes seem much more tractable to model, and reasonably coherent in space (at long time scales).

• Continued analyses required!


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WLEF tall tower (447m)CO2 and H2O flux measurements at: 30, 122 and 396 mCO2 mixing ratio measurements at: 11, 30, 76, 122, 244 and 396 m

WLEF flux and mixing ratio observatory


Region: Flat, heterogeneous, forested, managed, rich in wetlands, low in humans

4 meter 30 meter 1 kilometer

recent progress in co 2 flux data assimilation

Documents

terrestrial fluxes flux

years of data

year of flux observations

network of flux tower

flux tower time series

observed global carbon

global carbon cycle

atmospheric co2 budget