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Methods Model. The TECOS model is used as forward model to simulate carbon transfer among the carbon pools (Fig.1). In the model, ecosystem is simplified as a linear system, which can be represented by the following linear differential equation.

Effects of biometric data errors (SD) on parameter constraints

Uncertainty Analysis with Data-Model Assimilation at Duke FACE

AcknowledgementsThis study was financially supported by NSF and DOE. Thanks to Wenping Yuan, Jesse E. Bell, Xiaowen Wu and Jianzhong Lu for their help and useful discussions.

Fig.1 Diagram of carbon process on which the model equation is based.

Observed and simulated results comparison

Inverse approach. MCMC method was used to search parameters and construct

posterior distribution of these parameters. The likelihood function p(Z|c) is

represented by following equation with an assumption that each component being

independently and identically distributed over the observation times.

The probabilistic distribution of simulated pools

Conclusions• Measurement errors didn’t alter the values of maximum likelihood

estimates.• Measurement errors had significant effects on the probability distribution

function of parameters, which means they affected information retrieval.• The ranges of predicted pools increased with increase of measurement

errors.

Introduction Uncertainty in model forecasting of future changes in ecosystem services is unavoidable. It

is important to quantify uncertainty and to reveal its origination. The quantification of

uncertainties in forecasting affect public confidence on the predictions proposed by research

communities. The data-model assimilation techniques are powerful tools to evaluate the

uncertainties and show the factors controlling uncertainties in model prediction.

Ecological data, with the current limitations, hold the largest uncertainty in model

simulations. Especially in data-model assimilation, data can determine the uncertainties in new

knowledge. In this study, we evaluated the uncertainties induced by measurement errors with

the Markov Chain Monte Carlo (MCMC) approach. Our study is trying to reveal how

measurement errors between datasets result in uncertainties in simulation results and affect

prediction.

( )( ) ( ) ( )

dX tt ACX t BU t

dt

The carbon pools that are fluctuabale

Low measurement errors (SD) increased the

constraint of parameters, which means the

data with low measurement errors have

more information than those with high

errors. The parameters that were constrained

by data with ambient errors could be

constrained better with decreasing

measurement errors. However, those that

were not be constrained could not be

constrained by data with low errors either.

The carbon pools with long-term dynamics

Where, A is a transfer matrix, showing the carbon transfer among carbon pools. C is a diagonal matrix, representing turnover rate of the carbon pools. B shows the allocation of GPP in these pools. U(t) represents the carbon input at time t (GPP).ξ(t) is a environmental scalar, depending on temperature and soil moisture.

Uncertainties of predictions from the posterior parameter distribution

The simulated carbon content in foliage

(p1), woody (p2), fine roots (p3), microbial

(p6), slow SOM(p7), and passive SOM (p8)

pools are constrained well at three SD

levels. For metabolic litter pool, it is a

exponential distribution. For structural litter

(p5), reduced SD changed distribution

pattern. Overall, increased SD increased

ranges of predicted carbon content of these

pools.

For the relatively steady carbon

pools, which do not fluctuate with

short term conditions, the SD grows

steadily with time. And, higher SD

leads to high ranges of prediction

(Fig.5).

The standard deviations (SDs) of predictions are highly correlated with the SDs in observed data. Usually, if the observed SD is high, the predicted SD is also high and increase with years of prediction. However, there are two kinds of error propagation in the carbon pools.

The SDs of predicted carbon content in all of the 8 pools are highly related with

measured ones. The carbon content in long-term carbon pools increase steadily.

And, the simulated uncertainties increased significantly with time when there are

no observation data. However, for the pools which are sensitive to environmental

fluctuations, the carbon content doesn’t increase so much and the SDs increased

slowly either. Woody biomass

5000 6000 7000

5000

6000

7000

Fine roots

100 200 300 400 500100

200

300

400

500

Litter Fall

100 200 300 400 500 600

Sim

ulat

ed

100

200

300

400

500

Foliage biomass

350 400 450 500 550

Sim

ulat

ed

350

400

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500

550

Forest Floor C

400 600 800 1000 1200400

600

800

1000

1200Microbial C

0 50 100 150 200 2500

50

100

150

200

250

Slow SOM

Observed

2000 2200 2400

Sim

ulat

ed

2000

2100

2200

2300

2400

2500 Passive SOM

Observed

400 600 800 1000 1200400

600

800

1000

1200 Soil Respiration

Observed

0 1 2 3 4 5 6 70

1

2

3

4

5

6

7

Ensheng Weng, Chao Gao, Yiqi Luo University of Oklahoma, United States

E-mail: [email protected]

Fig.2 the effects of changes in SD on parameter constraint

Fig.3 the distribution of C pools’ carbon content at the end of 2005

Fig.4 comparison between observed data and simulated results

Simulated foliage biomass, woody biomass,

forest floor carbon, soil carbon, and soil

moisture agree with measured ones well.

Fine roots are highly variable and sensitive

to environmental fluctuations. The data of

microbial biomass is very sparse (only

1996) and has high standard deviations. The

data of slow SOM is sparse and does not

increase significantly with time.

For the pools those are sensitive to

environmental fluctuation, the SD

does not increase so much with

simulation time. However, the SDs

still affect the ranges of prediction

(Fig.6).

Fig.6 the forecasting of carbon content in leaves, fine roots, and microbes

Data. The biometric and soil carbon data were collected from Duke FACE during

1996~2005. There were 9 datasets, including foliage biomass, woody biomass,

fine root biomass, microbial biomass, litter fall, forest floor carbon, organic soil

carbon, mineral soil carbon, and soil respiration. The gross primary production

(GPP) data were from the simulation results by MAESTRA model (1996 and

1997) and eddy flux.

Changes of standard deviations (SD) and model run. Three levels of SDs were

assigned: original, halved, and doubled, which were used to construct the

probability distribution of parameters for testing the effects of observed errors on

parameter constraint.

2

21

( ) ( )( ) exp

2

ni i

i

Z t X tP Z c

Fig.5 The forecasting of carbon content in woody biomass, litter, and soil

Leaves X1 Woody X2 Fine Roots X3

Metabolic Litter X4 Structural Litter X5

Microbes X6

Slow SOM X7

Passive SOM X8

GPP

Original SD

Fol

iage

bio

mas

s(g

C y

r-1

m-2

)

350

400

450

500

550

600 Halved SD Doubled SD

Fin

e ro

ots

(g C

yr-1

m-2

)

250

300

350

Y D

ata

Y D

ata

yr

1995 2000 2005 2010 2015

Mic

robi

al b

iom

ass

(g C

m-2

)

60

80

100

120

140

yr

1995 2000 2005 2010 2015

yr

1995 2000 2005 2010 2015

Original SD

Wo

od

y b

iom

ass

(g C

m-2

)

4000

6000

8000

10000

12000Halved SD Doubled SD

Litt

er

Poo

l(g

C m

-2)

0

500

1000

1500

yr

1995 2000 2005 2010 2015

SO

M(g

C m

-2)

2000

2500

3000

yr

1995 2000 2005 2010 2015

yr

1995 2000 2005 2010 2015 2020

c1

Prameter values *10-30 1 2 3 4 5

Fre

qu

en

cy 1

02

0

5

10

15

20

25

Halved SDOriginal SDDoubled SD

c2

Parameter values 10-40.0 0.5 1.0 1.5 2.0

Fre

qu

en

cy 1

02

02468

10121416

c4

Parameter values 10-20.0 0.5 1.0 1.5 2.0 2.5 3.0

Fre

qu

en

cy 1

02

0

2

4

6

8

10

c6

Parameter values0.1 0.2 0.3 0.4 0.5

Fre

qu

en

cy 1

02

05

1015202530

c7

Parameter values 10-30.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Fre

qu

en

cy 1

02

0

5

10

15

20

25c8

Parameter values 10-60 2 4 6 8

Fre

qu

en

cy 1

02

01234567

c3


Fre

qu

en

cy 1

02

0

5

10

15

20

25

c5


Fre

qu

en

cy 1

02

0

2

4

6

8

p1

300 400 500 600 700 800

Fre

quen

cy 1

02

05

10152025

p2

5000 6000 7000 8000 900005

10152025

p3

100 200 300 400 500

Fre

quen

cy 1

02

05

10152025

p4

100 200 300 400 50005

10152025

p5

0 500 1000 1500 2000

Fre

quen

cy 1

02

05

10152025

p6

0 50 100 150 20005

10152025

p7

Carbon content (g C m-2)

1500 2000 2500 3000 3500

Fre

quen

cy 1

02

05

10152025

halved SDOriginal SDdoubled SD

p8

Carbon content (g C m-2)

700 800 900 1000 1100 1200 130005

10152025