Data-model integration: Examples from belowground ecosystem ecology Kiona Ogle University of Wyoming...

Data-model integration:Data-model integration:Examples from Examples from

belowground ecosystem belowground ecosystem ecologyecology

Kiona OgleKiona OgleUniversity of WyomingUniversity of Wyoming

Departments of Botany & StatisticsDepartments of Botany & Statisticswww.uwyo.edu/oglelabwww.uwyo.edu/oglelab

Today’s TaskToday’s Task

• What are some ecological questions to which sensor network data could be applied?

• How would those data be used in models?

• Overview modeling of ecological data and processes.

Types of QuestionsTypes of Questions

• What are some ecological questions to which sensor network data could be applied?– Spatial & temporal processes

• Improved ecological understanding• More accurate prediction & forecasting

– Example problems• “Biogeochemical exchanges between the

atmosphere & biosphere”• How do environmental perturbations affect carbon

& water exchange?• Partitioning ecosystem processes & components• Linking processes & mechanisms operating at

multiple temporal & spatial scales

How to Address Such Questions?How to Address Such Questions?

• Couple data and models– Sensor network data

• Very rich– Real-time; large datasets; spatially extensive and/or

temporally intensive

• Heterogeneous– Different locations, processes, and conditions

– Models & data analysis• Less appropriate:

– “Classical” analyses that assume linearity and normality of data

– Design-based inference about patterns

• More appropriate: – Coupling of process-based models with diverse and rich

datasets– Model-based inference about patterns and mechanisms

Why Couple Data & Process Why Couple Data & Process Models?Models?

– Parameter estimation (or “model parameterization”)

• Quantification of uncertainty• Improved predictions and forecasts• Decision support, management, conservation

– Synthesize multiple types of data• Relate different system components to each other• Learn about important mechanisms

– Hypothesis generation• Use data-informed models to generate testable hypotheses• Inform sampling and network design

– Data analysis• Go beyond simple “classical” analyses• Explicit integration of multiple data types, diverse scales,

and nonlinear and non-Gaussian processes

How to Couple Data & Process How to Couple Data & Process Models?Models?

– Multiple approaches, for example:• Maximum likelihood-based models• Least squares, minimization of objective functions• Hierarchical Bayesian models

– Hierarchical Bayesian approach• Recall, from Jennifer’s talk …

( , , | )

( | , ) ( | ) ( , )

D P

D P D P

P Process Data

P Data Process P Process P

Observed data

Latent (or true) process Data parameters

Process parametersUnknown quantities

Posterior

Likelihood Probabilistic process modelPrior(s)

OutlineOutline• The process model:

– Types of ecological models– Building process models

• Examples from belowground ecosystem ecology:– Motivating issues– Ex 1: Estimating components of soil organic matter

decomposition– Ex 2: Deconvolution of soil respiration (i.e., CO2 efflux)– In both examples, highlight:

• Data sources• Process models• Data-model integration

• Implications of data-model integration for sensor network data & applications

Hierarchical Bayesian ModelHierarchical Bayesian Model

( , , | )

( | , ) ( | ) ( , )D P

D P D P

P Process Data


Observed data



Posterior


( | , ) :DP Data ProcessData = Latent process + observation error

( | ) :PP ProcessLatent process = Expected process + process error

Data model (likelihood)

Probabilistic process model

The “process model”

The Process ModelThe Process Model

• Conceptual model:– Systems diagrams– Graphical models

• Model formulation:– Explicit, mathematical eqn’s

• Systems equations• State-space equations

Conceptualmodel

Mathematicalmodel

Simulation model

Analyticaloutput

Numerical/simulation

output

The “process model”

Observedquantities

(data)

“Compare”

Unobservedor latent

quantities

“Predict”

Unobservedquantities

(parameters)

Outputs

Observedquantities

(driving variables)

Inputs

Types of Process ModelsTypes of Process Models

Deterministic Stochastic

Compartment models(differential or difference equn’s)

Matrix models

Reductionist models(include lots of details & components)

Holistic models(use general principles)

Static models Dynamic models

Distributed models(system depends on space & time)

Lumped models

Linear models Nonlinear models

Causal/mechanistic models Black box models

Analytical models Numerical/simulation models

Jorgensen (1986) Fundamentals of Ecological Modelling. 389 pp. Elsevier, Amsterdam.

Upcoming Example:Upcoming Example:Soil Carbon Cycle ModelSoil Carbon Cycle Model



Matrix models



Static models Dynamic models

Distributed models(system depends on space & time)

Lumped models




Source: Xu et al. (2006) Global Biogeochemical Cycles Vol. 20 GB2007.

Example Process ModelExample Process Model

Simplifiedsystems diagramof the soilcarbon cycle ina temperateforest

Pools or state variables

Flows of carbon


Model FormulationModel Formulation

( ) ( ) ( )d

t t u tdt

X AX B A: matrix of flux rates or

“carbon transfer coefficients” (parameters)

u(t): flux of carbon into the system(e.g., photosynthetic flux) (driving variable or modeled quantity)

B: vector of ‘allocation fractions’ (parameters)

X: vector of state variables (unobservable latent quantities, outputs)


Model FormulationModel Formulation

( ) ( ) ( )d

t t u tdt

X AX B

( )

( )

( )

( )

( )

X

X

AX

B

t

dt

Expected dttprocess

u t

u t

Observable(data)

How to Couple Data & Process How to Couple Data & Process Models?Models?

– Hierarchical Bayesian approach

( , , | )

( | , ) ( | ) ( , )

D P

D P D P

P Process Data


Observed data



Posterior


( | , ) :DP Data ProcessData = Latent process + observation error

( | ) :PP ProcessLatent process = Expected process + process error

Data model (likelihood)

Probabilistic process model

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

Tightly linked to aboveground system

BelowgroundBelowground• Little info• Difficult to measure• Aboveground measurements (helpful but limited)

Aboveground Aboveground • Lots of info• Easy to measure

Outstanding issuesOutstanding issues• Partitioning above- & belowground• Quantifying & partitioning belowground• Implications for ecosystem function• Examples: arid & semiarid systems

Figure from Kieft et al. (1998) Ecology 79:671-683

Belowground “Issues”Belowground “Issues”

Motivating Questions: Soil Carbon Cycle Motivating Questions: Soil Carbon Cycle

• From where in the soil is CO2 coming from?

• What are the relative contributions of autotrophs vs. heterotrophs?

• What factors control decomposition rates & heterotrophic activity?

• How does pulseprecipitationaffect sourcesof respiredCO2?

• Implications ofclimate changefor desert soilcarbon cycling?

Integrative ApproachIntegrative Approach

• Diverse data sources– Experimental & observational– Lab & field studies– Multiple scales– Varying “amounts” & “completeness”

• Process-based models– Key mechanisms, processes, components– Balance detail & simplicity– Multiple scales & interactions

• Statistical models: data-model integration– Hierarchical Bayesian framework– Mark chain Monte Carlo

Examples Presented TodayExamples Presented Today



Matrix models



Static models Dynamic models(implicit dependence on time)

Distributed models(implicit dependence on space & time)

Lumped models




Objectives:Objectives: 1.1. Identify soil & microbial processes affecting Identify soil & microbial processes affecting

decompositiondecomposition

2.2. Learn how vegetation (i.e., microsite) controls these Learn how vegetation (i.e., microsite) controls these processesprocesses

Ex 1: Soil organic matter Ex 1: Soil organic matter decompositiondecomposition

Experimental DesignExperimental Design

Mesquite shrublandin southern Arizona

Microsite types:1. bare ground2. grass3. small mesquite4. big mesquite

Bare ground Grass Small mesquite Big mesquite

3 cores (reps)

...

8 depths (layers)

...

Add water

Add sugar + water

Incubate at 25 oC

CO2

CO2

CO2 Measure CO2 efflux(soil respiration rate)at 24 & 48 hours


...

8 depths (layers)

...

Add water

Add sugar + water

Incubate at 25 oC

CO2

CO2

CO2 Measure CO2 efflux(soil respiration rate)at 24 & 48 hours

Measure:Microbial biomassSoil organic carbonSoil nitrogen


• Full-factorial design:

• Microsite• 4 levels: bare, grass, small mesq, big mesq

• Soil layer• 8 levels: 0-2, 2-5, ..., 40-50 cm

• Substrate addition type• 2 levels: water only, sugar + water

• Incubation time• 2 levels: 24, 48 hrs

• Soil core or rep• 3 cores per microsite

• Stochastic data:

• Soil respiration rate• N = 359 (25 missing)

• Microbial biomass• N = 18 (14 missing)

• Soil organic carbon• N = 89 (7 missing)

Design & Data OverviewDesign & Data Overview

Some DataSome Data

Soil d

ep

th

microbesmicrobes soil Csoil C COCO22 flux flux

?? ?? datadata

Estimate microbial respiration (decomposition) parameters (i.e.,

process parameters)

Carbon substrate Micro

bial

biom

assR

esp

irati

on

Analysis ObjectivesAnalysis Objectives

biomass&

activity

Estimate microbial respiration (decomposition) parameters (i.e.,

process parameters)

Carbon substrate Micro

bial

biom

assR

esp

irati

on

Microbial biomass (B)

Resp

irati

on (

R)

Saturating carbon (C)

Low C

Michaelis-Menton type model:

Assume Ac related to “substrate quality”:

Ab

Ac

0 1max 0,

Ab B Ac CR

Ab B Ac CAc c c N

0 1max 0,Ac c c N

microbial “base-line” metabolic rate

microbial carbon-use efficiency

Process Model: Soil RespirationProcess Model: Soil Respiration

• Full-factorial design:

• Microsite• Soil layer• Substrate addition type• Incubation time• Soil core or rep

• Stochastic data:

• Soil respiration rate• Microbial biomass• Soil organic carbon

Soi

l dep

th

microbesmicrobes soil Csoil C COCO22

?? ?? datadata

NN

fixedfixed

B C R N

• Things to consider:

• Multiple data types• Nonlinear model• Missing data• Experimental design

0 1max 0,

Ab B Ac CR

Ab B Ac CAc c c N

Data-Model IntegrationData-Model Integration

somedata

somedata

( , , | ) ( | , ) ( | ) ( , ) D P D P D PP Process Data P Data Process P Process P

1. Let LR = log(R)

2. For microsite m, soil depth d, soil core r, substrate-addition type s, and time period t:

Observed rate Mean (“truth”)(latent process)

Observationprecision

(= 1/variance)

Data Model (Likelihood)Data Model (Likelihood)


1. Now, for the covariates...

2. For microsite m, soil depth d, and soil core r:

3. Note: the likelihoods are for both the observed and missing data

Observed Mean (“truth”)(latent process)

Observation precision(= 1/variance)

{ , , } { , }

{ , , } { , }

~ ,

~ ,

md r C md C

md r B md B

C Normal

B Normal



Likelihood components

Data parameters

Latent processes

{ , , , , } { , , , }

{ , , } { , }

{ , , } { , }

~ ,

~ ,

~ ,

md r s t LR md r s LR

md r C md C

md r B md B

LR Normal

C Normal

B Normal

, ,D LR C B

{ , , , } { , } { , }, ,LR md r s C md B mdLatent processes



Latent processes

Deterministic model for soil microbes & carbon contents

{ , , , } { , } { , }, ,LR md r s C md B mdLatent processes

*{ , } { , } { }

*{ , } { , } { }

C md md m

B md md m

c C

b B

Stochastic model for latent respiration

{ , , , } { , , }~ . ,LRLR md r s LR md sNormal

Probabilistic Process ModelProbabilistic Process Model


Specify expected process: Michaelis-Menten (process) model

{ , , , } { , , }~ . ,LRLR md r s LR md sNormal

{ , } { , } { , }

{ , } { , } { , }{ , , }

{ , }

water only.

sugar + water

B md md C md

B md md C mdLR md s

B md

Ab Acif s

Ab Ac

Ab if s

{ , } 0 1 { , }max 0,md mdAc c c N

Stochastic model for latent respiration

Microbial biomass (B)

Res

pir

atio

n (R

)

Saturating carbon (C)

Low C


Process components

Process parameters

* *{ , } { , } { } { } 0 1, , , , , , ,

LRP md md m mc b C B Abc c


{ , , , } { , , }

{ , } { , } { , }

{ , } { , } { , }{ , , }

{ , }

{ , } 0 1 { , }

*{ , } { , } { }

*{ , } { , } { }

~ . ,

.

max 0,

LRLR md r s LR md s

B md md C md

B md md C mdLR md s

M md

md md

C md md m

B md md m

Normal

Ab Acwater

Ab Ac

Ab sugar

Ac c c N

c C

b B


Data parameters

Process parameters

* *{ , } { , } { } { } 0 1, , , , , , ,



, ,D LR C B

Conjugate, relatively non-informative priors for precision terms

, , , ~ 0.01,0.001LRLR C B Gamma

Parameter Model (Priors)Parameter Model (Priors)

Data parameters

Process parameters

* *{ , } { , } { } { } 0 1, , , , , , ,



, ,D LR C B

Non-informative Dirichlet priors for relative distributions of microbes and carbon

{ ,.} { ,.}, ~ 1,1,1,...,1m mc b Dirichlet

Multivariate version of the beta distribution(with all parameters set to 1: multidimensional uniform)


Data parameters

Process parameters

* *{ , } { , } { } { } 0 1, , , , , , ,



, ,D LR C B

Relatively non-informative (diffuse) normal priors for the rest:

* *0 1 { } { }, ,ln ,ln ,ln ~ 0,0.0001m mc c C B Ab Normal



4 8 3 2 2 2

{ , , , , } { , , , }1 1 1 1 1

4 8 3 2 2

{ , , } { , } { , , } { , }1 1 1

exp2 2

exp exp2 2 2 2

ex2

( | , )

LR

LR LRmd r s t LR md r s

m d r s t

C C B Bmd r C md md r B md

m d r

D

LR

C B

P Data Process

0.0010.00

4 8 3 2 2

{ , , , } { , , }1 1 1

10.99 0.001 0.99 0.99 0.001 0.99

20 1

1

e e e e

0.0001 0.0001 0.

p

0001 0.0001exp 0 exp

.

02 2 2 2

2

CLR B LR

LR

LR

LR md r s LR md sm

C B

d r s

LR

c c

2

2

4 2 2* *{ } { }

1

0.0001 0.0001exp 0

2 2

0.0001 0.0001 0.0001 0.0001exp 0 exp 0

2 2 2 2m mm

Ab

B C

The PosteriorThe Posterior


4 8 3 2 2 2

{ , , , , } { , , , }1 1 1 1 1

4 8 3 2 2

{ , , } { , } { , , } { , }1 1 1

exp2 2

exp exp2 2 2 2

ex2

( | , )

LR

LR LRmd r s t LR md r s

m d r s t


m d r

D

LR

C B

P Data Process

0.0010.00

4 8 3 2 2

{ , , , } { , , }1 1 1

10.99 0.001 0.99 0.99 0.001 0.99

20 1

1

e e e e

0.0001 0.0001 0.

p

0001 0.0001exp 0 exp

.

02 2 2 2

2

CLR B LR

LR

LR

LR md r s LR md sm

C B

d r s

LR

c c

2

2

4 2 2* *{ } { }

1

0.0001 0.0001exp 0

2 2

0.0001 0.0001 0.0001 0.0001exp 0 exp 0

2 2 2 2m mm

Ab

B C

No analytical solution for the joint posterior distribution

No analytical solution for most of the marginal distributions

Approximate the posterior: Markov chain Monte Carlo methods,implemented in WinBUGS

The PosteriorThe Posterior

Model Implementation: Model Implementation: WinBUGSWinBUGS

Model Goodness-of-fitModel Goodness-of-fit

[1,1]

[1,2]

[1,3]

[1,4]

box plot: parms.m[1,]

1.00E+3

2.00E+3

3.00E+3

4.00E+3

5.00E+3

[2,1]

[2,2][2,3]

[2,4]

box plot: parms.m[2,]

0.0

5.0

10.0

C* (total soil carbon, g C/m2) B* (microbial biomass, g dw/m2)

Bare Bigmesq.

Med.Mesq.

Grass Bare Bigmesq.

Med.Mesq.

Grass

Example ResultsExample Results

Example ResultsExample Results

[5,1,1][5,1,2]

[5,1,3]

[5,1,4]

[5,1,5]

[5,1,6]

[5,1,7] [5,1,8]

box plot: parms.md[5,1,]

0.0

0.05

0.1

0.15

0.2

[5,2,1]

[5,2,2]

[5,2,3]

[5,2,4]

[5,2,5]

[5,2,6][5,2,7]

[5,2,8]

box plot: parms.md[5,2,]

0.0

0.05

0.1

0.15

0.2

Bare ground Big mesquite

Soil depth (or layer)

Surface Deep Surface Deep

Rela

tive a

mou

nt

of

mic

rob

ial b

iom

ass

Sensitivity to Data SourcesSensitivity to Data Sources

• From where in the soil is CO2 coming from?

• What are the relative contributions of autotrophs vs. heterotrophs?

• What factors control decomposition rates & heterotrophic activity?

• How does pulseprecipitationaffect sourcesof respiredCO2?

• Multiple datasources

• lots• limited

Ex 2: Deconvolution of Soil Ex 2: Deconvolution of Soil RespirationRespiration

data

datadata

data

datadata

data

data

The Field SitesThe Field Sites

Sonoran Desert

San Pedro River Basin

Santa Rita Experimental Range

Stable Isotope TracersStable Isotope Tracers

CO2

CO2

1212CC

1212CC

1212CC1313CC

Source isotope

signatures

Respired CO2

signature

Important data source:facilitates “partitioning”

stochastic data Literature data

Data Source ExamplesData Source Examples

Datasets: field/lab pubs

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)

Potential sensor network data

Example DataExample Data

Day-1 0 2 6 14

Resp

iratio

n (

mol /

m2 /

s)

0

1

2

3

4

5

6Pre-monsoon Dry MonsoonWet Monsoon

Santa Rita pulse experiment

Res

pira

tion

(m

ol /

m2

/ s)

San Pedro automated flux measurements

San Pedro incubation experiment

-27

-25

-23

-21

-19

-17

-15

-13

-2 0 2 4 6 8 10 12 14 16

Day

d13C

of

resp

ired

CO

2 (

o/ o

o)

Santa Rita pulse experiment – d13C

Hierarchical Bayesian Model:Hierarchical Bayesian Model:Deconvolution ApproachDeconvolution Approach

• 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



( | ) ( | ) ( )j j jP Data L Data P


& Keeling plots)



Keeling plots)








types)


total mass)


total mass)


carbon, microbes)



covariate data





Bayesian DeconvolutionBayesian Deconvolution

d 13 ( ), ( ), ( , ), ( , ), ( , )Obs ObsTot Tot iData C t R t SWC z t T z t M z t

The Hierarchical Bayesian ModelThe Hierarchical Bayesian Model

Likelihood of data

(isotopes & soil flux)

d d

113 2

2

3 ( )

( )

( )~ ,

( )~ ,

ObsTot CTot

ObsTo Tot t R

C t No

R t N

C

R to

t

Latent processes: from isotope mixing model &

flux models

Functions of parameters

Some Likelihood ComponentsSome Likelihood Components

Define process models…

Observations(data)


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

????

d d

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

From previous “incubation/decomposition” study (Ex 1)

What is i?(source-specific

parameters)

The Deconvolution ProblemThe Deconvolution ProblemObjectivesObjectives


specific)

( , ) , ( , ), ( , ), ( , )i i ir z t f SWC z t T z t M z tCovariate data

( , )

( , ) ( )

( ) ( , )

i i

i Tot

Tot i

r z t

r z t R t

R t p z t

Total soil flux

Contributions

How to estimate How to estimate ii??

Component fluxes

Bayesian DeconvolutionBayesian DeconvolutionThe Parameter Model (Priors)The Parameter Model (Priors)

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


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

Soil Temperature

Day of Year

190 200 210 220 230 240 250 260 270

Soi

l T (

oC

)

15

20

25

30

Soil Moisture

VW

C (

v/v)

0.04

0.08

0.12

Proportional Contribution of Respiration SourcesP

ropo

rtio

nal C

ontr

ibut

ion

0.000

0.005

0.010

0.015

0.020

0.025Heterotrophs (0-5 cm)Grass Roots (5-50 cm)Mesquite Roots (5-50 cm)

Results: Dynamic Source ContributionsResults: Dynamic Source ContributionsSan Pedro Site – Monsoon SeasonSan Pedro Site – Monsoon Season

Zoom-inZoom-in

Results: Root Respiration ResponsesResults: Root Respiration ResponsesZoom-in: July 27 – August 4Zoom-in: July 27 – August 4

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

Jul 27 Aug 4

Results: Contributions Vary by DepthResults: Contributions Vary by Depth

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

Mesquite (C3 shrub)

Sacaton (C4 grass)

Soil water

SummarySummary

• Sources of soil COSources of soil CO22 efflux efflux• Mesquite (shrub): major contributor, stable source

• Sacton (grass): minor contributor, threshold response

• Microbes (bare): minor contributor, coupled to pulses

• Deconvolution & data-model Deconvolution & data-model integrationintegration

• Soil depth (including litter)

• By species or functional groups

• Quantify spatial & temporal variability

• Incorporate environmental drivers

• Implications & applicationsImplications & applications• Identify mechanisms

• Predictions & forward modeling

Implications for Sensor Implications for Sensor NetworksNetworks– Parameter estimation (or “model

parameterization”)•Process models related to “biogeochemical exchanges between the atmosphere & biosphere”

•Quantification of uncertainty•Improved predictions and forecasts

– Synthesize data•Go beyond simple “classical” analyses•Explicit integration of multiple data types & scales•Relate different system components to each other•Learn about important mechanisms

– Hypothesis generation & sampling design•Use data-informed models to generate testable hypotheses

•Inform sampling and network design– Where (spatial), when (temporal), what

(components)?

Photo by Travis HuxmanPhoto by Travis HuxmanMonsoon flood, San Pedro River Basin; Sonoran desertMonsoon flood, San Pedro River Basin; Sonoran desert

Questions?Questions?

Soil Temperature

Day of Year

190 200 210 220 230 240 250 260 270

Soi

l T (

oC

)

15

20

25

30

Soil Moisture

VW

C (

v/v)

0.04

0.08

0.12

Proportional Contribution of Respiration Sources

Pro

port

iona

l Con

trib

utio

n

0.000

0.005

0.010

0.015

0.020

0.025Heterotrophs (0-5 cm)Grass Roots (5-50 cm)Mesquite Roots (5-50 cm)

Results: Dynamic Source ContributionsResults: Dynamic Source Contributions

Example WinBUGS OutputExample WinBUGS Outputparms[1] chains 1:2

iteration

1 2000 4000 6000

300.0

305.0

310.0

315.0

EO

parms[2] chains 1:2

iteration

1 2000 4000 6000

190.0

200.0

210.0

220.0

230.0

TO

Posteriorstatisticsparameter node mean sd 2.5% median 97.5% sampleEo parms[1] 307.7 1.205 305.2 307.7 309.9 1000To parms[2] 201.1 2.335 195.8 201.0 205.1 1000

....contribution pSc[1,1,1] 0.00145 0.002904 -0.03455 6.34E-4 0.03565 1000by pSc[1,1,2] 0.8854 0.009694 0.8433 0.8853 0.9288 1000[date, pSc[1,1,3] 0.1132 0.009998 0.06992 0.1131 0.1558 1000plot, pSc[1,2,1] 0.00158 0.003157 -0.03353 6.685E-4 0.03607 1000source] pSc[1,2,2] 0.9721 0.008952 0.9297 0.9725 1.013 1000

pSc[1,2,3] 0.02636 0.008649 -0.01523 0.02622 0.0654 1000....

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


( , ) ( , )( , )

( )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

????

????

d d

d d

0

18 18

0

( ) ( ) ( , )

( ) ( ) ( , )

B

stem

B

stem

D t D z q z t dz

O t O z q z t dz

d d

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)


specific)

Mass profiles(substrate, microbes,

roots)


( , ) ( , )( , )

( )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


????

d d

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)

d d

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


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



( | ) ( | ) ( )j j jP Data P Data P


& Keeling plots)



Keeling plots)








types)


total mass)


total mass)


carbon, microbes)



covariate data





The Deconvolution ProblemThe Deconvolution 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


( , ) ( , )( , )

( )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


????

????

d d

d d

0

18 18

0

( ) ( ) ( , )

( ) ( ) ( , )

B

stem

B

stem

D t D z q z t dz

O t O z q z t dz

d d

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

Plant water uptake Soil respiration

1 1 2 2( ) ( , ) (1 ) ( , )

( , )

( , )

RA z Ga Ga

U z t

q z t

( , ) , ( , ), ( , )

( )

( , )

i i

Tot

i

r z t f SWC z t T z t

R t

p z t

What areω, 1, 1, 2, 2?

What isi?

Likelihood of data

d d

113 2

2

3 ( )

( )

( )~ ,

( )~ ,

ObsTot CTot

ObsTo Tot t R

C t No

R t N

C

R to

t

d

d

d

d

2

18 8 21

( )( )~ ,

( ))~ ,(

Obsstem D

Obsste

stem

stemm O

D t

O t

D t No

O t No

From isotope mixing model & flux model

The Deconvolution ProblemThe Deconvolution Problem

Types of data provides by sensor networks

• high-frequency tunable diode laser (TDL) measurement of the stable isotope

• eddy covariance for measuring concentrations and fluxes of gases (e.g., water vapor and CO2)

• soil environmental data: temperature, water content, water potential, etc.

• micro-met data: air temp, RH, vpd, light, wind speed, etc.

• plant ecophys/ecosystem data: sapflux, ET, albedo & reflectance

6 6

1 1

i ii i

i i i i

i ii i

i i

a cdPA R S E

dt c

dS a Ed S

dt c

d

d

Process modelsProcess models

State ID TABLENM "PLT_CN" PHYSCLCD "STATECD" "CYCLE""SUBCYCLE""UNITCD""COUNTYCD" "PLOT" "SUBP" "TREE" "CONDID"VA 229 TREE 23854928010661.00 21 51 3 2 1 1 13 2 1 1VA 407 TREE 23958646010661.00 21 51 3 4 1 1 19 1 5 1VA 408 TREE 23958646010661.00 21 51 3 4 1 1 19 1 6 1VA 1059 TREE 23958861010661.00 21 51 3 4 1 1 54 2 6 2VA 6768 TREE 23997965010661.00 22 51 3 5 2 7 9 2 4 1VA 7019 TREE 23906005010661.00 22 51 3 3 2 7 15 2 9 1VA 7111 TREE 23857072010661.00 22 51 3 2 2 7 16 2 7 1VA 8105 TREE 23805545010661.00 22 51 3 1 2 7 39 2 1 1VA 8539 TREE 23906968010661.00 22 51 3 3 3 9 9 1 3 1VA 12808 TREE 23807296010661.00 23 51 3 1 4 15 29 3 8 1VA 12810 TREE 23807296010661.00 23 51 3 1 4 15 29 3 10 1VA 13315 TREE 23858135010661.00 22 51 3 2 4 15 54 1 1 1VA 19399 TREE 23809332010661.00 22 51 3 1 2 19 23 3 4 1VA 19445 TREE 23909859010661.00 22 51 3 3 2 19 26 1 8 1VA 22050 TREE 23861227010661.00 23 51 3 2 5 21 8 2 5 1VA 22053 TREE 23861227010661.00 23 51 3 2 5 21 8 2 2 1VA 22060 TREE 23861227010661.00 23 51 3 2 5 21 8 1 4 1VA 22137 TREE 23910676010661.00 23 51 3 3 5 21 12 2 6 1VA 23519 TREE 23910590010661.00 23 51 3 3 5 21 39 2 5 1VA 26415 TREE 23911957010661.00 22 51 3 3 1 25 1 2 8 2VA 26783 TREE 23863007010661.00 21 51 3 2 1 25 7 2 3 1VA 28623 TREE 23862849010661.00 22 51 3 2 1 25 41 2 17 1VA 29299 TREE 24002221010661.00 24 51 3 5 1 25 54 3 6 1VA 29320 TREE 24002221010661.00 24 51 3 5 1 25 54 4 14 1VA 30129 TREE 23862787010661.00 22 51 3 2 1 25 69 3 6 1VA 30139 TREE 23862787010661.00 22 51 3 2 1 25 69 3 11 1VA 32119 TREE 23913201010661.00 23 51 3 3 5 27 42 3 2 1VA 34017 TREE 23813210010661.00 22 51 3 1 2 29 23 4 9 1VA 34329 TREE 23913514010661.00 22 51 3 3 2 29 29 1 4 1VA 34716 TREE 23914198010661.00 22 51 3 3 2 29 35 1 20 1VA 35041 TREE 24003030010661.00 22 51 3 5 2 29 41 3 2 1VA 36375 TREE 23813999010661.00 22 51 3 1 2 29 68 2 5 1VA 36410 TREE 23813999010661.00 22 51 3 1 2 29 68 3 7 1VA 36411 TREE 23813999010661.00 22 51 3 1 2 29 68 3 8 1

DataData

P

(|

X )

Statistical toolsStatistical toolsdata-model integrationdata-model integration

( | )

( | ) ( )( | ) ( )

P X

P X PP X P d

Key componentsKey components

The Process ModelThe Process Model

• Conceptual models:– Systems diagrams– Graphical models

• Model formulation:– Explicit, mathematical eqn’s

• Systems equations• State-space equations

“Compare”Observations

of real systemConceptual

modelMathematical

model

Simulation model

Analyticaloutput

Numerical/simulation

output

Observationaldata

Examples Presented TodayExamples Presented Today



Matrix models



Static models Dynamic models(implicit dependence on time)

Distributed models(implicit dependence on space & time)

Lumped models




Jorgensen (1986) Fundamentals of Ecological Modelling. 389 pp. Elsevier, Amsterdam.


Assuming conditional independence,likelihood of all data is:

4 8 3 2 2 2

{ , , , , } { , , , }1 1 1 1 1

4 8 3 2 2

{ , , } { , } { , , } { , }1 1 1

( | , ) exp2 2

exp exp2 2 2 2

LR LRD md r s t LR md r s

m d r s t


m d r

P Data Process LR

C B

Likelihood components

{ , , , , } { , , , }

{ , , } { , }

{ , , } { , }

~ ,

~ ,

~ ,

md r s t LR md r s LR

md r C md C

md r B md B

LR Normal

C Normal

B Normal


Data-model integration: Examples from belowground ecosystem ecology Kiona Ogle University of Wyoming...

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