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