Regional Flux Estimation Regional Flux Estimation using the Ring of Towersusing the Ring of Towers

Scott Denning, Ken Davis, Scott Richardson, Marek Uliasz, Dusanka

Zupanski, Kathy Corbin, Andrew Schuh, Nick Parazoo,

Ian Baker, Tasha Miles, and Peter Rayner

Regional Fluxes are Hard!Regional Fluxes are Hard!

• Eddy covariance flux footprint is only a few hundred meters upwind

• Heterogeneity of fluxes too fine-grained to be captured, even by many flux towers– Temporal variations ~ hours to days– Spatial variations in annual mean

• Some have tried to “paint by numbers,” – measure flux in a few places and then apply

everywhere else using remote sensing

• Annual source/sink isn’t a result of vegetation type or LAI, but rather a complex mix of management history, soils, nutrients, topography not seen by RS

Temporal Variations in NEETemporal Variations in NEE

• Flux is nothing like a constant value to be estimated!• “Coherent” diurnal cycles?, but …• Day-to-day variability of ~ factor of 2 due to passing

weather disturbances

NEE @ WLEF

Pesky Variability in the Real Pesky Variability in the Real WorldWorld

• Managed forests, variable soils, suburban landscapes, urban parks

• Disturbance and succession: fires, harvest, etc• Crops: Wheat vs Corn vs Soybeans• Irrigation, fertilization, tillage practice• Wisconsin (ChEAS) flux towers

Attempt to “upscale” annual NEE over 40 km: – WLEF = a1 * WC + a2 * LC, – but only if a2 < 0– decorrelation length scale is very small

on annual NEE!

High-Frequency Variations in Space …

What Causes Long-Term Model What Causes Long-Term Model Bias?Bias?

• Parameters (maybe, but more likely to control variability than bias)

• State!– Respiration: soil carbon, coarse woody

debris– GPP: stand age, nutrient availability,

management

• Missing equations!

• Physiology is easier to model than site history and management

Our StrategyOur Strategy• Divide carbon balance into “fast” processes that

we know how to model, and “slow” processes that we don’t

• Use coupled model to simulate fluxes and resulting atmospheric CO2

• Measure real CO2 variations• Figure out where the air has been • Use mismatch between simulated and observed

CO2 to “correct” model biases for slow BGC

• GOAL: Time-varying maps of sources/sinks consistent with observed vegetation, fluxes, and CO2 as well as process knowledge

Observational ConstraintsObservational Constraints

• Satellite imagery & veg maps– spatial and seasonal variations

• Flux towers– Ecosystem physiology for different veg types– GPP, Resp, stomates, drought response

• Atmospheric CO2

– Average source/sink over large upstream area

Continental NEE and [CO2]Continental NEE and [CO2]

• Variance dominated by diurnal and seasonal cycles, but target is source/sink processes on interannual to decadal time scales

• Diurnal variations controlled locally by nocturnal stability (ecosystem resp is secondary!)

• Seasonal variations controlled hemispherically by phenology

• Synoptic variations controlled regionally, over scales of 100 - 1000 km. Target these.

wplsobs

frs

sgp

wkt

hrv

amtlef

ring

Seasonal and Synoptic Seasonal and Synoptic VariationsVariations

• Strong coherent seasonal cycle across stations

• SGP shows earlier drawdown (winter wheat), then relaxes to hemispheric signal

• Synoptic variance of 10-20 ppm, strongest in summer

• Events can be traced across multiple sites

• What causes these huge coherent changes?

Daily min [CO2], 2004

Lateral Boundary ForcingLateral Boundary Forcing

• Flask sampling shows N-S gradients of 5-10 ppm in [CO2] over Atlantic and Pacific

• Synoptic waves (weather) drive quasi-periodic reversals in meridional (v) wind with ~5 day frequency

• Expect synoptic variations of ~ 5 ppm over North America, unrelated to NEE!

• Regional inversions must specify correct time-varying lateral boundary conditions

Modeling & Analysis ToolsModeling & Analysis Tools(alphabet soup)(alphabet soup)

• Ecosystem model (Simple Biosphere, SiB)

• Weather and atmospheric transport (Regional Atmospheric Modeling System, RAMS)

• Large-scale inflow (Parameterized Chemical Transport Model, PCTM)

• Airmass trajectories(Lagrangian Particle Dispersion Model, LPDM)

• Optimization procedure to estimate persistent model biases upstream (Maximum Likelihood Ensemble Filter, MLEF)

Frontal Composites of Frontal Composites of WeatherWeather

GGρ =∇ρg∇∇ρ

• The time at which magnitude of gradient of density (ρ) changes the most rapidly defines the trough (minimum GG ρ, cold front) and ridge (maximum GG)

Frontal Locator Function

Oklahoma Wisconsin Alberta

Frontal COFrontal CO22 “Climatology”“Climatology” • Multiple cold fronts

averaged together (diurnal & seasonal cycle removed)

• Some sites show frontal drop in CO2, some show frontal rise … controls?

• Simulated shape and phase similar to observations

• What causes these?

wplsobs

frs

sgp

wkt

hrv

amtlef

ring

Deformational FlowDeformational Flow

• Anomalies organize along cold front

• dC/dx ~ 15ppm/3-5°

Dg

Dt

∂C∂x

+∂C∂y

⎛⎝⎜

⎞⎠⎟=−

∂ug

∂x∂C∂x

+∂vg

∂x∂C∂y

⎛⎝⎜

⎞⎠⎟−

∂ug

∂y∂C∂x

+∂vg

∂y∂C∂y

⎛⎝⎜

⎞⎠⎟

shear deformation- tracer field rotated by shear vorticity

stretching deformation- tracer field deformed by stretching

gradientstrength

ΔC

Δt= u

ΔC

Δx→ C day+1 =

uΔtΔC

Δx=

5ms−1 * 3600s * 24hr *15 ppm

5° *100km= 12 ppm

Ring of TowersRing of Towers

• inexpensive instruments deployed on six 75-m towers in 2004

• ~200 km radius

• 1-minute data May-August

Ring of Towers DataRing of Towers Datamid-day onlymid-day only June 9- July 5, 2004June 9- July 5, 2004

5 ppm over 200 kmu ~ 10 m/sΔz ~ 1500 m~ 13 mol m-2 s-1

Coupled Model: SiB-RAMS-Coupled Model: SiB-RAMS-LPDMLPDM

• SiB3 – Simple Biosphere Model [Sellers et al., 1996]– Calculates the transfer of energy, water, and carbon between the atmosphere

and the vegetated surface of the earth – Photosynthesis model of Farquhar et al. [1980] and stomatal model of Collatz

et al [1991, 1992] – Ecosystem respiration depends on soil temperature, water, FPAR, with pool

size chosen to enforce annual carbon balance– Parameters specified from MODIS Vegetation imagery (1 km)

• RAMS5 – Regional Atmospheric Modeling System– Comprehensive mesoscale meteorological modeling system (Cotton et al.,

2002), with telescoping, nested grid scheme– Bulk cloud microphysics parameterization– Meteorological fields initialized and lateral boundaries nudged using the NCEP

mesoscale Eta analysis (Δx = 40 km)– Deep cumulus after Grell (1995); Shallow cloud transports after Freitas (2001)– Lateral CO2 boundary condition from global SiB-PCTM analysis

• LPDM - Lagrangian Particle Dispersion Model– Backward-in time particle trajectories from receptors– Driven from 15-minute RAMS output

Average NEESiB-RAMS Simulated Net Ecosystem Exchange (NEE)SiB-RAMS Simulated Net Ecosystem Exchange (NEE)

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are needed to see this picture.

Back-trajectory AnalysisBack-trajectory Analysis• Release imaginary

“particles” every hour from each tower “receptor”

• Trace them backward in time, upstream, using flow fields saved from RAMS

• Count up where particles have been that reached receptor at each obs time

• Shows quantitatively how much each upstream grid cell contributed to observed CO2

• Partial derivative of CO2 at each tower and time with respect to fluxes at each grid cell and time

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are needed to see this picture.

FCO2 (x, y, t) =R(x,y,t)−GPP(x,y,t)

Treatment of Variations for Treatment of Variations for InversionInversion

• Fine-scale variations (hourly, 20-km pixels) from weather forcing and satellite vegetation data as processed by forward model logic (SiB-RAMS)

• Multiplicative biases (caused by “slow” BGC that’s not in the model) derived by from observed hourly [CO2]

FCO2 (x, y, t) =βR(x,y)R(x,y,t)−βGPP (x,y)GPP(x,y,t)

SiB SiB

unknown!

unknown!

Ck ,m = βR,i, jRi, j ,nCRk,m,i, j ,n* + βA,i, jAi, j ,nCAk,m,i, j ,n

*( )i, j ,n∑ ΔtfΔxΔy+ CIN

Flux-convolved influence functions derived from SiB-RAMS

Maximum Likelihood Maximum Likelihood Ensemble Filter (MLEF)Ensemble Filter (MLEF)

• Closely related to Ensemble Kalman Filter• No adjoint, forward modeling of ensemble of

perturbed states or parameters• Propagate estimates of βGPP(x,y) and

βResp(x,y) along with (sample of) full covariance matrix

• Model “learns” about parameters, state variables, and covariance structure over each data assimilation cycle

• Explain on whiteboard?

Pseudodata Ring InversionsPseudodata Ring Inversions

• 6 short towers plus 396 m at WLEF

• 2-hour averaged data (from 1 min)

• SiB-RAMS nest at Δx=10 km

• LPDM on RAMS output, convolve with GPP and Resp, influence functions integrated for 10 days

• Add Gaussian noise to initial β’s and obs

• Estimate βGPP and βResp for 30x30 grid boxes

centered at WLEF at Δx=20 km

• Nunk = 30 x 30 x 2 = 1800

Synthetic “Ring” Experiment: Synthetic “Ring” Experiment: MLEFMLEF

• Solvefor β(x,y) on a 20-km grid

• “Truth” divided in half (E vs W)

• Noise added at different scales (8Δx N vs 4Δx S)

• Prior: β = 0.75

• Prior smoothing = 6Δx … solve6 towers, obs every 2 hours

β = 0.5_

β = 1.1_

Wow!

no info overGreat Lakes

MLEF Result after 70 DaysMLEF Result after 70 Days

• Easily finds E-W diffs

• Some skill locating anomalies

• Better N-S diff in covariance than prior

• No flux over lakes, so no skill there!

β

ββ

β

NACP “Mid-Continent Intensive” NACP “Mid-Continent Intensive” (2007)(2007)

31 Towers in 200731 Towers in 2007∂[CO2(t)]∂β (x,y)

Next Step: Predict Next Step: Predict ββ

• If we had a deterministic equation that predict the next β from the current βwe could improve our estimates over time

• Fold β into model state, not parameters• Spatial covariance would be based on

“model physics” rather than an assumed exponential decorrelation length

• Assimilation would progressively “learn” about both fluxes and covariance structure

Coupled Modeling and Assimilation SystemCoupled Modeling and Assimilation System

CSU RAMS

Radiation

Clouds

CO2 Transport and Mixing Ratio

Winds

Surface layerPrecipitation

PBL

(T, q)

Biogeochemistry

Microbial pools

Litter pools

Slow soil C

RootsWoodLeaves

passive soil C

allocation autotrophic resp

heterotrophic resp

SiB3

Snow (0-5 layers)

Photosynthesis

Soil T & moisture (10 layers)

Canopy air spaceSfc TLeaf T

H LE NEE

CO2

CO2

• Add C allocation and biogeochemistry to SiB-RAMS

• Parameterize using eddy covariance and satellite data

• Optimize model state variables, not parameters or unpredictable biases

• Propagate flux covariance using BGC instead of a persistence forecast