bayesian deconvolution of belowground ecosystem processes kiona ogle university of wyoming
Post on 14-Jan-2016
35 Views
Preview:
DESCRIPTION
TRANSCRIPT
Bayesian Deconvolution of Bayesian Deconvolution of Belowground Ecosystem Belowground Ecosystem
ProcessesProcesses
Kiona OgleKiona Ogle
University of WyomingUniversity of WyomingDepartments of Botany & StatisticsDepartments of Botany & Statistics
Ecosystem ProcessesEcosystem Processes
Emphasis on aboveground
What about belowground?
NN
HH2200
HH2200
HH2200
CCCC
NN
PP
Biogeochemical CyclesBiogeochemical Cycles
NN
HH2200
HH2200
HH2200
CCCC
NN
PP
Biogeochemical CyclesBiogeochemical Cycles
Belowground system is critical to understanding and forecasting whole-
ecosystem behavior
Deconvolution of Belowground Deconvolution of Belowground ProcessesProcesses
• The water cycle• Partitioning plant water sources
• The carbon cycle• Partitioning soil respiration
• Data-model assimilation• Diverse data sources• Stable isotopes• Bayesian deconvolution framework
Today’sexample
ChallengesChallenges
• Patitioning sources of COPatitioning sources of CO22 fluxes fluxes
• Systems: soils & ecosystems
• Sources: autotrophs vs. heterotrophs
• Source contributions wrt soils:Source contributions wrt soils:• By soil depth (including litter)
• By species or functional group (autotrophs)
• Spatial variability
• Temporal dynamics
• Environmental drivers
CO2
Partitioning Soil RespirationPartitioning Soil Respiration
How does pulse precipitation affect sources of respired
CO2?
From where in the soil is CO2 coming
from?
????Relative contributions ofC3 roots (shrub), C4 roots (grass), and heterotrophs
(soil & litter)?
CO2
????????
????
CO2CO2
Bayesian Deconvolution Bayesian Deconvolution ApproachApproach
• Integrate multiple sources of Integrate multiple sources of informationinformation
• Diverse data sources
• Different temporal & spatial scales
• Literature information
• Lab & field studies
• Detailed flux modelsDetailed flux models• Respiration rates by source type & soil depth
• Dynamic models
• Mechanistic isotope mixing modelsMechanistic isotope mixing models• Multiple sources
The Deconvolution ProblemThe Deconvolution Problem
Isotope mixing model(multiple sources &
depths)
Relative contributions
(by source & depth)
Total flux(at soil
surface)
Flux model(source- & depth-
specific)
Mass profiles(substrate, microbes,
roots)
(Q10 Function, Energy of Activation)
( , )
( , )( )
ii
Tot
r z tp z t
R t
1 0
( ) ( , )source BN
Tot ii
R t r z t dz
/ /( , )i known measured estimatedM z t
????
13 13
1 0
( ) ( , ) ( , )source BN
Tot i ii
C t C z t p z t dz
( , ) , ( , ), ( , ), ( , )i i ir z t f SWC z t T z t M z t
Contributions by source (i ) and depth (z )? Temporal variability?
Source-specific respiration? Spatial & temporal variability?????
????
Theory & Process ModelsTheory & Process Models
What is i?(source-specific
parameters)
The Deconvolution ProblemThe Deconvolution ProblemObjectivesObjectives
Flux model(source- & depth-
specific)
( , ) , ( , ), ( , ), ( , )i i ir z t f SWC z t T z t M z tCovariate data
( , ) ( )
( ) ( , )i Tot
Tot i
r z t R t
R t p z t
Total soil flux
Contributions
How to estimate How to estimate ii, , rrii, and , and ppii??
posterior likelihood process model prior
( | ) ( | ) ( | ) ( )P Data P Data Process P Process P
Bayesian DeconvolutionBayesian Deconvolution
13 ( ), ( ), ( , ), ( , ), ( , )Obs ObsTot Tot iData C t R t SWC z t T z t M z t
The Bayesian ModelThe Bayesian Model Statistical model(Bayesian probability
model)
Likelihood of data
(isotopes & soil flux)
113 2
2
3 ( )
( )
( )~ ,
( )~ ,
ObsTot CTot
ObsTo Tot t R
C t No
R t N
C
R to
t
From isotope mixing model & flux models
Functions of
i
The LikelihoodThe Likelihood
Goal: find values of i that result in “best” agreement b/w models
& data
From Keeling plots
From automated chambers
Bayesian DeconvolutionBayesian DeconvolutionPrior InformationPrior Information
Example: Example: Lloyd & Taylor (1994) model
( , ) , ( , ), ( , ), ( , )
1 1( , ) ( , ) exp
( , )
i i i
i i oo o
r z t f SWC z t T z t M z t
r z t r z t ET T z t T
Informative priors for EEoo and TToo:
304 308 312 316 215 220 225 230 235 240
~ 308.56,2Eo No ~ 227.13,10To No
Statistical model(Bayesian probability
model)
posterior likelihood process model prior
( | ) ( | ) ( | ) ( )P Data P Data Process P Process P
stochastic data Literature data
Data Source ExamplesData Source Examples
Soil Isotopes (δ13CTot)(automated chambers
& Keeling plots)
Soil CO2 flux(manual chambers)
Pool Isotopes (δ13Ci)(roots, soil, litter;
Keeling plots)
Soil CO2 flux(automated chambers)
Root respiration(in situ gas exchange)
Root distributions(arid systems,
different functionaltypes)
Soil carbon(arid systems;
total C)Root respiration
(arid systems,different functional
types)
Microbial mass(arid systems;
total mass)
Root mass(arid systems;
total mass)
Litter(arid systems; total mass,
carbon, microbes)
Soil temp & water(automated,
multiple locations,many depths)
covariate data
Soil samples(carbon content,C:N, root mass)
Soil incubations(root-free,
carbon substrate,microbial mass,
heterotrophic activity)
( | ) ( | )
( | ) ( )
P Data P Data Process
P Process P
ImplementationImplementation
• Markov chain Monte Carlo (MCMC)Markov chain Monte Carlo (MCMC)• Sample parameters (θi ) from posterior
• Posteriors for: θi’s, ri(z,t)’s, pi(z,t)’s, etc.
• Means, medians, uncertainty
• WinBUGSWinBUGS• Free software
• BUGS: Bayesians Using Gibbs Sampling
Example Deconvolution ResultsExample Deconvolution Results
05
1015202530
205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220
0.0
1.0
2.0
3.0
4.0
5.0
209 210 211 212 213 214 215 216 217
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Date
Tota
l ro
ot
resp
irati
on
(um
ol m
-2 s
-1)
Soil w
ate
r (v/v
)
Rain
(m
m)
Mesquite (C3 shrub)
Sacaton (C4 grass)
Soil water
Example Deconvolution ResultsExample Deconvolution Results
0.0
1.0
2.0
3.0
4.0
5.0
209 210 211 212 213 214 215 216 217
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Date
Tota
l ro
ot
resp
irati
on
(um
ol m
-2 s
-1)
Soil w
ate
r (v/v
)
0.00 0.10 0.20 0.00 0.10 0.20 0.00 0.10 0.20
Day 210 Day 213 Day 216
0-5
5-10
10-15
15-20
20-25
25-30
30-40
40-50
Dep
th (
cm)
0-5
5-10
10-15
15-20
20-25
25-30
30-40
40-50
0-5
5-10
10-15
15-20
20-25
25-30
30-40
40-50
Relative contributions by depth
Some IssuesSome Issues
Work-in-ProgressWork-in-Progress
• Uncertainty in Isotope dataUncertainty in Isotope data• Keeling plot intercepts
• Limited amount of data
• Indistiguishable source signatures
• Flux modelsFlux models• Alternative models
• Acclimation & temporally-varying parameters
• Interactions & feedbacks (e.g., soil water, temp)
• Spatial variability
The Inverse ProblemThe Inverse ProblemPlant water uptake Soil respiration
Isotope mixing model
Fractional contributions
Total flux
Fluxmodel
Substrate orroot profiles
( , )
( , )( )Tot
U z tq z t
U t
1 1 2 2( ) ( , ) (1 ) ( , )RA z Ga Ga
0
( ) ( , )B
TotU t U z t dz
(Q10 Function, Energy of Activation)
( , ) ( , )( , )
( )i i
iTot
r z t M z tp z t
R t
1 0
( ) ( , ) ( , )source BN
Tot i ii
R t r z t M z t dz
/ ?( , )i known measuredM z t
????
????
0
18 18
0
( ) ( ) ( , )
( ) ( ) ( , )
B
stem
B
stem
D t D z q z t dz
O t O z q z t dz
13 13
1 0
( ) ( , )source BN
Tot i ii
C t C p z t dz
( , ) ( ) ln ( )
( , ) ( , ) ( ) ( )root root
U z t RA z a RA z
z t k z t t k t
( , ) , ( , ), ( , )i ir z t f SWC z t T z t
The Inverse ProblemThe Inverse Problem
Isotope mixing model(multiple sources &
depths)
Relative contributions
(by source & depth)
Total flux(at soil
surface)
Flux model(source- & depth-
specific)
Mass profiles(substrate, microbes,
roots)
(Q10 Function, Energy of Activation)
( , ) ( , )( , )
( )i i
iTot
r z t M z tp z t
R t
1 0
( ) ( , ) ( , )source BN
Tot i ii
R t r z t M z t dz
/ ?( , )i known measuredM z t
????
13 13
1 0
( ) ( , ) ( , )source BN
Tot i ii
C t C z t p z t dz
( , ) , ( , ), ( , )i ir z t f SWC z t T z t
Contributions by source (i ) and depth (z )? Temporal variability?
????Source-specific respiration? Spatial & temporal variability?
What is i?(source-specific
parameters)
Likelihood of data
(isotopes & soil flux)
113 2
2
3 ( )
( )
( )~ ,
( )~ ,
ObsTot CTot
ObsTo Tot t R
C t No
R t N
C
R to
t
From isotope mixing model & flux models
The Deconvolution ProblemThe Deconvolution ProblemData-Model IntegrationData-Model Integration
Flux model(source- & depth-
specific)
( , ) , ( , ), ( , ), ( , )i i ir z t f SWC z t T z t M z tCovariate data
( , ) ( )
( ) ( , )i Tot
Tot i
r z t R t
R t p z t
Total soil flux
Contributions
Depend on
i
Isotopes: Tools for Isotopes: Tools for PartitioningPartitioning
• IsotopesIsotopes• δ13C of soil respired CO2 ( )
• δ13C of potential sources ( )
• Simple-linear mixing (SLM) modelSimple-linear mixing (SLM) model• Consider three potential sources
• By simple mass-balance:
• pi = relative contribution of source i
13soilC
13iC
13 13 13 131 1 2 2 3 3
1 2 31soilC p C p C p C
p p p
Limitations of SLM ModelsLimitations of SLM Models
• Nonidentifiability of Nonidentifiability of pi’s’s
• Estimate limited number of sources
• Range of potential values (e.g., Phillips & Gregg)
• Not constrained by mechanisms
• Lack mechanistic insightLack mechanistic insight• Controls on relative contributions
• Threshold responses
• Lack predictive capabilityLack predictive capability• Temporal reconstructions
• Spatial patterns
• Plant species or functional types
Limitations of SLM ModelsLimitations of SLM Models
• Don’t integrate other sources of Don’t integrate other sources of informationinformation
• Flux data
• Environmental drivers
• Source or pool characteristics
• Existing studies
• Complimentary lab studies
top related