Observations for Carbon Data AssimilationScott Doney

Woods Hole Oceanographic Institution

Where does the “data” come from for “data assimilation”?

Atmospheric CO2 data•initial conditions•innovation terms•error covariance terms

Land and ocean carbon data•flux estimates for priors•process/mechanistic information

Data is NOT a black box!!

Atmospheric Inverse Modeling of CO2

Concentration(observedsamples)

Transport(modeled)

Sources &Sinks

(solved for)+ =

How data enters the problem (1)

Variational AssimilationAdjust model state “x” (atmospheric CO2 field) to minimize cost function J:

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J(x) =1

2(x − xb{ )T B−1(x − xb ) + yo − H(x)[ ]

TR−1 yo − H(x)[ ]}

Deviation of x from “background”

Deviation of x from “observations”

So where do we get:y0(t) data for innovation (model-data misfit)R data error covarianceB model error covariance

Some Issues to Ponder

Atmosphere CO2 drastically under-sampled•original design for marine background air•mostly discrete surface samples•NWP deg. freedom O(107); 6 hourly observations O(104-105)•CO2 weekly observations O(102-103)

Small signal on large background variability

•surface North-south difference ~2.5 ppmv•zonal continent to land contrast <1 ppmv•measurement precision•accuracy in time & across stations and networksreduce systematic biases!!

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yobs = y true + εobs

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εobs = εrandom + εsystematic

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E εobs1 ,εobs

2[ ] ≠ 0

Representativeness of data y0

•“footprint” of observation & mismatch with model grid•local heterogenity or point sources•aliasing of unresolved frequencies/wavenumbers (e.g., diurnal cycle)•data selection (i.e., exclude “unrepresentative” observations)

Some Issues to Ponder

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R = Rinstrument + Rrepresentativeness

CO2 Concentration in the Outer Damon Room, NCAR Mesa Lab, 2/7 – 2/9/06

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upBoard of Trustees Reception National Science

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ASP Reviews

Multiple Time/Space Scales DOE Terrestrial Carbon Modeling

GCM CarbonCentury

Decade

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Plot Tower Landscape Region Continent Globe

1-DBGC

TowerFlux

Aircraft Flux

Satellite GPP, NPP

TowerFootprint

OrbitingCarbon

Observatory

AtmosphericInversion

SPACE

GCM CarbonCentury

Decade

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Plot Tower Landscape Region Continent Globe

1-DBGC

TowerFlux

Aircraft Flux

Satellite GPP, NPP

TowerFootprint

OrbitingCarbon

Observatory

AtmosphericInversion

SPACE

In-situ Atmospheric Observing Network

Discrete surface flasks (~weekly)Continuous surface (hourly)observatoriesTall towers continuous (hourly)

Aircraft profiles (~weekly)

Surface Observatory

Seasonal CO2: Continental vs Oceanic Sites

•CO2 seasonal cycle attenuate, but still coherent, far away from source/sink region•Peak-trough amplitude of seasonal cycle ~ 30 ppmv (~10%)

TURC/NDVI Biosphere; Takahashi Ocean ; EDGAR Fossil Fuel [U. Karstens and M. Heimann, 2001]

Weather Cycles: CO2 is variable

10 ppmv

[LSCOP, 2002]

Modeled: one day in July

On T~5 days, x ~ 1000 kmCO2 variability in the boundary layer

~ 10 ppmv (3 %)

Diurnal CO2: Highly variable in boundary layer

•Diurnal cycle of photosynthesis and respiration > 60 ppmv (20%) diurnal cycle near surface

•Varying heights of the planetary boundary layer (varying mixing volumes)

Calm night: stably stratified boundary layer

Well-mixed PBL

Vertical Profiles (free troposphere)

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20062005 DATE

Aircraft Campaigns

COBRA 2000

Surface Fluxes => Atmospheric CO2

Orbiting Carbon Observatory(Planned Fall 2008 launch)

• Estimated accuracy for single column ~1.6 ppmv

• 1 x 1.5 km IFOV• 10 pixel wide

swath• 105 minute

polar orbit• 26º spacing in

longitude between swaths

• 16-day return time

How data enters the problem (2)

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xbi+1 = Φ(x i) + G(ui)

transport fluxes

Deviation of initial conditions from “prior”

Deviation of x from “observations”

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J(x) =1

2(x 0 − x prior

0{ )T B−1(x 0 − x prior

0 ) + yo − H(x)[ ]T

R−1 yo − H(x)[ ]

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+(u − uprior)T P−1(u − uprior )}

Deviation of fluxes from “prior”

Separating transport, initial conditions & surface fluxes

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xbi+1 = M(xa

i )Analysis at time i => forecast at time i+1

4D Variational methods: adjust initial conditions to better match future data

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x 0 ≠ x prior0

initial conditions

NEE = GPP – RecoNEE is measured at the tower

Ecosystem Respirationtypically based on nighttimeNEE & air temperature & ?

Reco = Rhetero + Rauto

GPPPhotosynthesis(Daytime only)

CO2

CO2

CO2

Adapted from Gilmanov et al.

Eddy-Flux TowersVertical velocity (mean and anomaly)

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w = w + ′ w

CO2 concentration (mean and anomaly)

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c = c + ′ c

Vertical CO2 flux

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wc = (w + ′ w )(c + ′ c )

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=w c + ′ w c + w ′ c + ′ w ′ c

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wc = w c + ′ w ′ c

FluxNet Tower Sites

Diurnal and Seasonal Cycle

Time-scale character of carbon fluxes

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Diurnal

Seasonal

1. Variability is at a maximum on the strongly forced time scales

2. They have an annual sum of ~0

3. Modeling the carbon storage time scales is much more difficult

Tall-TowerFootprint

(Wang, 2005)

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Mixed BL Deciduous

Mixed Dec/Con

Mixed Coniferous

Aspen

GrasslandPine

Urban/Dev/AgWater

Forest Inventory Analysis: Slow Process Observations

• Plot-scale measurement of carbon storage, age structure, growth rates: 170,000 plots in US!• Allows assessment of decadal trends in carbon storage

Air-Sea CO2 Flux Estimates

Takahashi

-undersampling & aliasing of surface water pCO2-transfer velocity k empirically derived from wind speed relationships

F = k s(pCO2air - pCO2

water) = kspCO2

ThermodynamicsKineticstransfer velocity

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Tracer N-2000Tracer Wat-91Tracer-WannRnC-14bombC-14 natk, 600 W-92k, 600 L&MS-86W-99

U10

(m/s)

Gas Transfer Velocity

Generating a Global Flux MapGenerating a Global Flux Map

Chavez et al.

In-Situ Sensors and Autonomous Platforms

Moorings/drifters (pCO2, pH, DIC, NO3)

Riser et al.

Profiling ARGO floats (also AUVs, caballed observatories)

-Global baseline (hydrography, transient tracers, nutrients, carbonate system)-Improved analytical techniques for inorganic carbon and alkalinity (±1-3 mol/kg or 0.05 to 0.15%)-Certified Reference Materials-Data management, quality control, & public data access

JGOFS/WOCE global survey (1980s and 1990s)

Ocean Inversion Method-Ocean is divided into n regions (n = 30, aggregated to 23)-Basis functions for ocean transport created by injecting dye tracer at surface in numerical models

• Basis functions are model simulated footprints of unit emissions from a number of fixed regions

• Estimate linear combination of basis functions that fits observations in a least squares sense.

Inversion is analogous to linear regression

footprintsfluxes obs

Premultiply both sides by inverse of A

Simple Inversion Technique

estimated fluxes