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
CC
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upBoard of Trustees Reception National Science
Board Breakfast
ASP Reviews
Multiple Time/Space Scales DOE Terrestrial Carbon Modeling
GCM CarbonCentury
Decade
Y ear
Day
Hour
Plot Tower Landscape Region Continent Globe
1-DBGC
TowerFlux
Aircraft Flux
Satellite GPP, NPP
TowerFootprint
OrbitingCarbon
Observatory
AtmosphericInversion
SPACE
GCM CarbonCentury
Decade
Y ear
Day
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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)
384
372
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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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Lowland Shrub Wetla
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Forested Wetla
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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
0
20
40
60
80
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0 5 10 15 20
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
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