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?

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Biogeochemical CyclesBiogeochemical Cycles

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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