Data-model Data-model assimilation for assimilation for
manipulative manipulative experiments experiments
Dr. Yiqi LuoDr. Yiqi Luo
Botany and microbiology Botany and microbiology departmentdepartment
University of Oklahoma, USAUniversity of Oklahoma, USA
Manipulative experiments
More manipulative experiments under planning by NEON and DOE
What is the nature of manipulative experiments?
How can we extrapolate results from
the Duke FACE experiment to
predict long-term, large-scale change
GPP
Leaves(X1)
Wood(X2)
Surface metabolicleaf litter (X4)
Soil metabolicroot litter (X7)
Surface microbes(X9)
Soil microbes(X10)
Wood litter(X6)
Surface structuralleaf litter (X5)
Soil structuralroot litter (X8)
Slow SOM (X11)
Passive SOM(X12)
CO2
CO2 CO2
CO2CO2
CO2
CO2CO2
CO2
CO2
CO2
CO2
CO2
CO2
CO2
Fine roots(X3)
CO2
CO2
Luo and Reynolds 1999
Luo and Reynolds 1999, Ecology, 80:1568-1583
Luo and Reynolds 1999
Observed C and N dynamics in FACE experiments are not applicable to natural ecosystems in response to a gradual CO2 increase.
0.8
1.0
1.2
1.4
1.6
1.8
0 2 4 6 8 10
Ch
an
ge
in
ph
oto
syn
the
sis
ControlGradural increasestep increase
A
0.8
1.0
1.2
1.4
1.6
1.8
0 2 4 6 8 10
B
0.7
0.8
0.9
1.0
1.1
0 2 4 6 8 10
Week after CO2 treatment
Ch
an
ge
in
le
af
nit
rog
en C
0.7
0.8
0.9
1.0
1.1
0 2 4 6 8 10Week after CO2 treatment
D
Microcosm Experiment
Hui et al. 2002
Luo et al. 2000
Duke FACE results
Luo 2001
Results of manipulative experiments can not be simply extrapolated to predict ecosystem responses to global change in the real world
Luo and Reynolds (1999)
“Rigorous analysis of (results from) step experiments requires not only statistical but also other new approaches, such as deconvolution and inverse modeling”
Data-model assimilation at Duke FACE
Applications
1. Soil C processes: Luo, et al. 20012. Transfer coefficients: Luo, et al. 20033. Uncertainty analysis, Xu et al. 20064. Forecasting of carbon sequestration
Tool development
1. Deconvolution (Luo et al. 2001)2. Adjoint function (White and Luo. 2002) 3. Stochastic inversion, Xu et al. 20064. Step-wise inversion, Wu et al. (in review) 5. Linear, nonlinear, ensemble Kalman Filter
(Gao et al. see poster)
Framework for Uncertainty analysis
Stochastic inversion
Variability in estimated parameter values
Forward model
Uncertainty in model predictions
Measurement errors
-15 -10 -5 0 5 10 150
0.05
0.1
0.15
0.2
0.25
观测误差( mol m-2 s-1)
频
率
误 差 分 布正 态 分 布双 边 指 数 分 布
Observation error (umol m-2 s-1)
Fre
qu
en
cy
Error distributionNorman DistributionDouble exponential distribution
-40 -30 -20 -10 0 10 200
50
100
150
200
GEE( mol m-2 s-1)
频
数
2.6 2.8 3 3.20
50
100
150
Re,ref
( mol m-1 s-1)
频
数F
req
uen
cy
Fre
qu
en
cy
半小时 日 月 季度 年0
20
40
60
80
100
120
NE
E/%
相对
不确
定性
TW__LSQTW__MLET__LSQT__MLE
Hour Day Month Year
Rel
a ti v
e un
c ert
aint
y (%
)
Multiple data sets
Tree biomass growthSoil respiration
Litter fall
Soil carbon
Foliage biomass
GPP
Leaf (X1) Wood (X3)
Metabolic litter (X4)
Microbes (X6)
Structure litter(X5)
Slow SOM (X7)
Passive SOM (X8)
CO2
CO2
CO2
CO2
CO2
CO2
CO2
CO2
BuAXdtdX
MCMC– Metropolis-Hastings algorithm
Mathematical and statistical procedure
1. Matrix to describe C flow
2. Mapping functions
Qj(A)(t) = qj(A)(t) • X(A)(t)
3. Cost function
4. Search method
jn
ij
ji
jm
jj tQtAQAJ
1
20
1
))())((()(
Root (X2)
400
500
600
700
800
900
400 500 600 700 800 900
Observed litterfall (g m-2 yr-1)
Mod
eled
litt
erfa
ll (g
m-2
yr-1
)
y = 1.036x + 2.301
R2 = 0.593
D
4.0
4.5
5.0
5.5
6.0
6.5
4.0 4.5 5.0 5.5 6.0 6.5
Observed woody biomass (kg m-2)
Mod
eled
woo
dy b
iom
ass
(kg
m-2
)
Ambient CO2
Elevated CO2
A
350
400
450
500
550
600
350 400 450 500 550 600
Observed foliage biomass (g m-2)
Mod
eled
fol
iage
bio
mas
s (g
m-2
)
y = 0.573x + 210.5
R2 = 0.527
C
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0.5 1.0 1.5 2.0 2.5 3.0 3.5
Observed soil carbon (kg m-2)
Mod
eled
soi
l car
bon
(kg
m-2
)
y = 1.001x + 0.012
R2 = 0.999
B
0
1
2
3
4
5
6
0 1 2 3 4 5 6Observed soil respiration (g m-2 d-1)
Mod
eled
soi
l res
pira
tion
(g m
-2 d
-1)
y = 0.754x + 0.433
R2 = 0.707
E
Luo et al. 2003, GBC
Criteria I: Data-model fitting
0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
x 10-4
0
50
100
150
200
250
300
350
400
Histogram of generated samples for c2
Range of c2
Sam
plin
g fr
eque
ncy
0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 0.022 0.024 0.0260
100
200
300
400
500
600
Histogram of generated samples for c3
Range of c3
Sam
plin
g fr
eque
ncy
Observed Data
Prior knowledge Posterior distribution
3 3.5 4 4.5 5 5.5 6 6.5
x 10-3
0
100
200
300
400
500
600
700
800
Histogram of generated samples for c5
Range of c5
Sam
plin
g fr
eque
ncy
Criteria II: Probability Distribution
Inverse model
Well-constrained
Edge-hitting
No-information
Xu et al. 2006, GBC
Uncertainty analysisVariability in estimated parameter values
Multiple data sets
Stochastic inversion
Variability in estimated parameter values
Xu et al. 2006, GBC
-3
0
3
6
9
-3 0 3 6 9
Residence time at ambient CO2 (ln)
Re
sid
en
ce ti
me
at e
leva
ted
CO2
(ln
)
ln (Y)=0.966 ln (X) + 0.215R2= 0.969
Luo et al. 2003, GBC
Model predictions
Multiple data sets
Stochastic inversion
Variability in estimated parameter values
Forward model
Uncertainty in model predictions 900 950 1000 10501800 2700 3600 4500
800 1600 2400 3200
160 240 320 4000.0
0.2
0.4
0.6
0.8
1.0
50 100 150 2000.0
0.2
0.4
0.6
0.8
1.0
Cum
ulat
ive
Pro
babi
lity
Dis
trib
utio
ns
Metabolic Litter(X3)
Structural Litter(X4)
Microbes(X5)
Slow SOM(X6)
Passive SOM(X7)
a
(c) (d)
(e) (f) (g)
Predicted Carbon Pool Sizes (g C m-2) in Year 2010
600 640 680 7200.0
0.2
0.4
0.6
0.8
1.0Foliage Biomass(X1)
7000 8000 9000 10000 11000
Under Elevated CO2Under Ambient CO2
WoodyBiomass (X2)
(a) (b)Xu et al. 2006, GBC
0
100
200
300
400
500
600
2000 2020 2040 2060 2080 2100
Year
Car
bo
n s
ink
(g C
m-2
yr-1
)
CO2 onlyForest regrowth
CO2 + forest regrowth
Estimated initial values of pools and residence times to partition C sink to two components caused by climate change and forest regrowth
Uncertainty Analysis
Measurement errors
Stochastic inversion
Variability in estimated parameter values
Forward model
Uncertainty in model predictions
1. Magnitudes (50%, 100%, and 200%) of measurement errors (Weng et al. poster)
2. Distributions (Normal vs. double exponential) of measurement errors of eddy-flux data (Liu et al. in review)
3. Different assimilation algorithms (least squares, maximal likelihood, and Kalman filter (Gao et al. poster)
4. Continental analysis on residence times (Tao Zhou et al. in review), Q10 values (Tao Zhou et al. in review, and their uncertainties (Xuhui Zhou et al. poster)
Applications
SummarySummary1.Data from manipulative
experiments can not be directly extrapolated to the real world. We have to extract information from data on fundamental processes
2.Model assimilation of multiple data sets is one of the best approaches to synthesis of experimental results with processing thinking and can better balance evidence from different lines.
http://bomi.ou.edu/luo
AcknowledgementIdea and math development
Luther WhiteJames ReynoldsS. LakshmivarahanDafeng HuiTao XuTao ZhouEnsheng WengChao GaoEnsheng WengLi ZhangMin Liu
Financial supportDOE TCP NSF
Data from the Duke FACE SchlesingerEllsworthFinziDeLuciaKatulOren