using data assimilation to improve understanding and forecasts of the terrestrial carbon cycle
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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
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