Model-Based Extracted Water Desalination System for Carbon ...
Methods Model. The TECOS model is used as forward model to simulate carbon transfer among the carbon...
1
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 Acknowledgements This 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 t t 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. W oody biom ass 5000 6000 7000 5000 6000 7000 Fine roots 100 200 300 400 500 100 200 300 400 500 LitterFall 100 200 300 400 500 600 Simulated 100 200 300 400 500 Foliage biom ass 350 400 450 500 550 Simulated 350 400 450 500 550 ForestFloorC 400 600 800 1000 1200 400 600 800 1000 1200 M icrobial C 0 50 100 150 200 250 0 50 100 150 200 250 Slow SO M O bserved 2000 2200 2400 Simulated 2000 2100 2200 2300 2400 2500 Passive SO M O bserved 400 600 800 1000 1200 400 600 800 1000 1200 Soil R espiration O bserved 0 1 2 3 4 5 6 7 0 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 2 2 1 () () ( ) exp 2 n i i i Z t Xt PZc 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 O riginal SD Foliage biom ass (g C yr-1 m -2) 350 400 450 500 550 600 H alved SD D oubled SD Fine roots (g C yr-1 m -2) 250 300 350 Y D ata Y D ata yr 1995 2000 2005 2010 2015 M icrobial biom ass (g C m -2) 60 80 100 120 140 yr 1995 2000 2005 2010 2015 yr 1995 2000 2005 2010 2015 O riginal SD W oody biom ass (g C m -2) 4000 6000 8000 10000 12000 H alved SD D oubled SD LitterPool (g C m -2) 0 500 1000 1500 yr 1995 2000 2005 2010 2015 SOM (g C m -2) 2000 2500 3000 yr 1995 2000 2005 2010 2015 yr 1995 2000 2005 2010 2015 2020 c1 Pram etervalues *10 -3 0 1 2 3 4 5 Frequency 10 2 0 5 10 15 20 25 H alved SD O riginal SD D oubled S D c2 Param etervalues 10 -4 0.0 0.5 1.0 1.5 2.0 Frequency 10 2 0 2 4 6 8 10 12 14 16 c4 Param etervalues 10 -2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Frequency 10 2 0 2 4 6 8 10 c6 Param etervalues 0.1 0.2 0.3 0.4 0.5 Frequency 10 2 0 5 10 15 20 25 30 c7 P aram etervalues 10 -3 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Frequency 10 2 0 5 10 15 20 25 c8 Param etervalues 10 -6 0 2 4 6 8 Frequency 10 2 0 1 2 3 4 5 6 7 c3 P aram etervalues 10 -3 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Frequency 10 2 0 5 10 15 20 25 c5 P aram etervalues 10 -3 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Frequency 10 2 0 2 4 6 8 p1 300 400 500 600 700 800 Frequency 10 2 0 5 10 15 20 25 p2 5000 6000 7000 8000 9000 0 5 10 15 20 25 p3 100 200 300 400 500 Frequency 10 2 0 5 10 15 20 25 p4 100 200 300 400 500 0 5 10 15 20 25 p5 0 500 1000 1500 2000 Frequency 10 2 0 5 10 15 20 25 p6 0 50 100 150 200 0 5 10 15 20 25 p7 C arbon content(g C m -2 ) 1500 2000 2500 3000 3500 Frequency 10 2 0 5 10 15 20 25 halved SD O riginal S D doubled SD p8 C arbon content(g C m -2 ) 700 800 900 1000 1100 1200 1300 0 5 10 15 20 25
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Transcript of Methods Model. The TECOS model is used as forward model to simulate carbon transfer among the carbon...
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
450
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
Parameter values 10-34.0 4.5 5.0 5.5 6.0 6.5 7.0
Fre
qu
en
cy 1
02
0
5
10
15
20
25
c5
Parameter values 10-30.0 0.5 1.0 1.5 2.0 2.5 3.0
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
