Using data assimilation to improve understanding and forecasts of the

terrestrial carbon cycle

Mathew WilliamsSchool of GeoSciences, University of Edinburgh

And National Centre for Earth Observation

Source: CD Keeling, NOAA/ESRL

Mauna Loa CO2 record

300

310

320

330

340

350

360

370

380

390

400

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

Time

[CO

2]

Sampling at 3397 meters, well mixed free troposphere

60

90 90 650

120 GPP

RH

60

o

RA

0.1

0.4

Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997)

THE BIOLOGICAL GLOBAL CARBON CYCLE (1750)

Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr-1)

Soils

1580

Atmosphere

540

Deep ocean DOC 700

DIC 38000

Surface DOC 40 POC 7

Sediments 75,000,000

6

60

92 90 600

120? GPP

RH 1.4

60

Net destruction

of vegetation

RA

0.1

0.4

Source: Schlesinger (1997), Schimel et al. (1995), Reeburgh (1997)

THE MODERN GLOBAL CARBON CYCLE (2000)

Pools (billions of tonnes C) & fluxes ( billions of tonnes C yr-1)

Soils

1580

Atmosphere

720 (+3.2/yr)

Unattributed

C sink 1.6

Deep ocean DOC 700

DIC 38000

Surface DOC 40 POC 7

Sediments 75,000,000

Friedlingstein et al 2006: C4MIPIntercomparison of 11 coupledcarbon climate models

Problems with models

Poor parameterisation

Inaccurate initial conditions

Missing processes

Solution: make and break models with observations?

Space (km)

time

s

hr

day

month

yr

dec

0.1 1.0 10 100 1000 10000

FlaskSite

Time and space scales in ecological processes

Physiology

Climate change

Succession

Growth and phenology

Adaptation

Disturbance

Photosynthesis and respiration

Clim

ate

varia

bilit

y

OCO

Space (km)

time

s

hr

day

month

yr

dec

0.1 1.0 10 100 1000 10000

FluxTower

Aircraft

FlaskSite

FlaskSite

FieldStudies

MODIS

Time and space scales in ecological observations

Talltower

Observing networks: Flask [CO2]

Observing networks: CO2 Fluxes

FluxNet - ~200 eddy covariance systems

Harvard Forest [CO2]

340

350

360

370

380

390

400

410

420

0 30 60 90 120 150 180 210 240 270 300 330 360

Time (day of year 1998)

[CO

2 ]Harvard Forest

Mauna Loa

Source: Wofsy et al, Harvard Forest LTER

Hourly data ~5 m above canopy

Tall Tower ‘Angus’ CO2 CH4

N2OSF6

COH2

222Rn

at 222 m

at 50 m

T and RH at 220,100, 50 and 5 m agl

P, u and wind direction at 5 m agl

Li-7000 Agilent 6890 FID & ECD TGA3

ANSTO Radon

Photo: T Hill & T Wade

Landscape and regional ecology

Bark

ley e

t al,

[2

00

6]

SCIAMACHY CO2 [P Monks]MODIS EVI [NASA]

0-10

30-5050-70

90-110

130-150150 +

To nne s p e r he c ta re

C a rb o n C o nte nt

Airborne LIDAR biomass [C Nichol]

A range of Earth observation data

Improving estimates of C dynamics

MODELS OBSERVATIONS

FUSION

ANALYSIS

MODELS+ Capable of interpolation

& forecasts- Subjective & inaccurate?

OBSERVATIONS+Clear confidence limits

- Incomplete, patchy- Net fluxes

ANALYSIS+ Complete

+ Clear confidence limits+ Capable of forecasts

GPP Croot

Cwood

Cfoliage

Clitter

CSOM/CWD

Ra

Af

Ar

Aw

Lf

Lr

Lw

Rh

D

Modelling C exchanges

GPP Croot

Cwood

Cfoliage

Clitter

CSOM/CWD

Ra

Af

Ar

Aw

Lf

Lr

Lw

Rh

D

Photosynthesis &plant respiration

Phenology &allocation

Senescence & disturbance

Microbial &soil processes

Climate drivers

Non linear functionsof temperatureSimple linear functionsFeedback from Cf

Exploring model behaviour

Sensitivity to initial conditions Parameter sensitivity Steady state solutions

A master’s study by Tom Ilett– Supported by Sarah Dance, Jon Pitchford,

Nancy Nichols

Sensitivity of pools and NEE to altered initial conditions of Cf

Cr - roots Cw - wood

Clit - litter Csom – soil organic matter

NEE sensitivity to varying initial conditions over 3 years

Parameterdetails

Parametersensitivity

The steady state solution

For Cf = 0

The equilibria for the other stocks are linear functionsof G and Cf

Assume climate inputs are constants

There are three fixed points for GPP and Cf , for Cf 0; 50; 450.

Equilibrated values of other C stocks

Equilibrium value

(gC m-2)

Time to equilibrium (yrs)

G* 10.8 gC m-2 d-1

Cf* 450 <12

Cr* 290 <12

Cw* 37,000 250

Clit* 210 <12

Csom* 230,000 2000

NEE trajectories

12 yrs 250 yrs 2000 yrs

Evolution of NEE 0, time constant depends on stabilisation of Csom

Relationship between GPP, Cf and time – an indicator of phenology?

Convergence to attracting orbit for a 15 year projection.

Trajectories become darker as time progresses – final year is a black line

Combining models and observations

Are observations consistent among themselves and with the model?

What processes are constrained by observations?

The Kalman Filter

MODEL At Ft+1 F´t+1OPERATOR

At+1

Dt+1

Assimilation

Initial state Forecast ObservationsPredictions

Analysis

P

Ensemble Kalman Filter

Drivers

0 365 730 1095-4

-3

-2

-1

0

1

2

0 365 730 1095-4

-2

0

2

Time (days, 1= 1 Jan 2000)

b) GPP data + model: -413±107 gC m-2

0 365 730 1095-4

-3

-2

-1

0

1

2

c) GPP & respiration data + model: -472 ±56 gC m-2NE

E (

g C

m-2 d

-1)

0 365 730 1095-4

-2

0

2

a) Model only: -251 ±197 g c m-2

d) All data: -419 ±29 g C m-2

Data brings confidence

Williams et al, GCB (2005)

= observation— = mean analysis| = SD of the analysis

Reflex experiment

Objectives: To compare the strengths and weaknesses of various model-data fusion techniques for estimating carbon model parameters and predicting carbon fluxes.

Real and synthetic observations from evergreen and deciduous ecosystems

Evergreen and deciduous models Multiple MDF techniques

www.carbonfusion.org

Participant Name – type of methodology

Code Prior Initial pools Convergence tests

Number of parameter sets produced

Number of model iterations

Programming language

E1 (stage 1)

MCMC Metropolis, then EnKF

Uniform Parameters to be estimated

Gelman and Rubin (1992)

~400000 ~1000000 Fortran

E1 (stage 2)

Evensen (2003)

PDFs from stage 1

PDFs from stage 1

n/a State only 8000 Fortran

E2 Ensemble Kalman filter

Evensen (2003)

gaussian Cr=Cfmax, Clit=0.5Cfmax, Clab=0.5Cfmax

n/a - ran EnKF 2 times with reinitialisation

~2000 800 Fortran90

U1 Unscented Kalman filter

Gove & Hollinger (2006)

gaussian From M3 n/a n/a n/a R

G1 Genetic algorithm Based on Haupt and Haupt (2004)

uniform Tuned with parameters

n/a ~100000 Fortran90

M1 MCMC – Metropolis Included in calibration

visual 300000 Fortran

M2 MCMC – Metropolis MCMC1 uniform Parameters to be estimated

Visual comparison of parameter PDFs from 2 chains

1000000 1000000 Fortran

M3 Simulated annealing-Metropolis

SAM uniform Parameters to be estimated

none 1000 ~250000 Fortran

M4 MCMC – Metropolis MCMC3 uniform Spinup to equilibrium of total C

Heidelberger and Welch (1983)

80000 ~300000 R

M5 Multiple complex MCMC – Metropolis

SCEM uniform Parameters to be estimated

Gelman and Rubin (1992)

~500000 150000 Matlab

Algorithms in the Reflex Experiment

Parameter constraint

Consistency among methodsConfidence intervals constrained by the dataConsistent with known “truth”

“truth”

Parameter retrieval for EV

ID Param d1 d2 d3 D Rank Biasp1 Td 0.26 0.36 0.75 0.87 11 1p2 Fg 0.30 0.41 0.02 0.51 6 3 Bp3 Fnf 0.07 0.49 0.00 0.50 5 4 Ap4 Fnrr 0.24 0.65 0.31 0.76 9 1p5 Tf 0.06 0.20 0.03 0.21 1 4 Ap6 Tw 0.22 0.40 0.69 0.83 10 0*p7 Tr 0.27 0.52 0.03 0.59 8 4p8 Tl 0.07 0.22 0.03 0.23 2 3p9 Ts 0.05 0.16 0.21 0.27 4 0*p10 Et 0.04 0.24 0.00 0.24 3 4p11 Pr 0.21 0.47 0.15 0.54 7 2 BMean 0.16 0.38 0.20 0.51d1. Consistency among methods: (m1,…,m9)/(pmax-pmin)d2. CIs constrained by the data: (CI1,…,CI9)/(pmax-pmin)d3. Consistent with truth : |t-(m1,…,m9)|/(pmax-pmin) mi=estimate by method i, p=prior, t=truth. D = (d1,d2,d3). A, B indicate correlations

Parameter summary

Parameters closely associated with foliage and gas exchange are better constrained

Parameters for wood and roots poorly constrained and even biased

Similar parameter D values for synthetic and true data

Correlated parameters were neither better nor worse constrained

Testing algorithms & their confidence

Fraction of successful annual flux tests (3 years x 2 sites, n=6)

Con

fiden

ce in

terv

al (

gC m

-2 y

r-1)

GPP Re NEE

Problems with soil organic matter…

And with woody C

State retrieval summary

Confidence interval estimates differed widely Some techniques balanced success with

narrow confidence intervals Some techniques allowed large slow pools to

diverge unrealistically

Conclusions

Attractor analysis is a useful technique for understanding C models

Model data fusion provides insights into information retrieval from noisy and incomplete observations

Challenges and opportunities: – introducing stochastic forcing– Linking other biogeochemical cycles– Designing optimal sensor networks– Theoretical understanding of plant process

Thank you

Time (days since 1 Jan 2000) Williams et al GCB (2005)

= observation— = mean analysis| = SD of the analysis

Time (days since 1 Jan 2000) Williams et al GCB (2005)

= observation— = mean analysis| = SD of the analysis