An approach to dynamic control of sensor networks with

inferential ecosystem models

James S. Clark, Pankaj Agarwal, David Bell, Carla Ellis, Paul Flikkema, Alan Gelfand, Gabriel Katul,

Kamesh Munagala, Gavino Puggioni, Adam Silberstein, and Jun Yang

Duke University

Motivation

• Understanding forest response to global change– Climate, CO2, human disturbance

• Forces at many scales• Complex interactions, lagged

responses• Heterogeneous, incomplete data

CO2 fumigation of forests

Experimental hurricanes

Remote sensing

Heterogeneous data Individual seedlings

Some ‘data’ are model output

Wolosin, Agarwal, Chakraborty, Clark, Dietze, Schultz, Welsh

TDRMaturity obs

Data

Processes

Parameters

Hyperparameters

CanopyphotosCO2

treatmentSeed traps

Climate

Diameter increment

Height increment

Remote sensing

Canopy models

Survival

AllocationDispersal

MaturationFecundity

Height growth

Die-backDiametergrowth

Mortalityrisk

Observation errors Process uncertainty

Heterogeneity

Dynamics

Light

Canopystatus

Soilmoisture

Hierarchical models to infer processes, parameter values

p(unknowns|knowns) Spatio-temporal (no cycles)

10 11 12 13

Diameter (cm)

28 29 30 31

44 45 46 47

0 20 40 60 80 100 120

Clark, LaDeau, Ibanez Ecol Monogr (2004)

Random indiv effects

Year effects

Model error

Sources of variability/uncertainty in fecundity

Some example individuals

0

ln diam increment (cm)

02468 10 12

ln fecundity (seeds per yr) Trees per bin (n)

Red maple

Tulip poplar

01234 5

Canopy exposure (ln m2)

012345

Red maple Tulip poplar

Allocation

Inference on hidden variables

Can emerging modeling tools help control ecosystem sensor

networks?

Capacity to characterize factors affecting forests,

from physiology to population dynamics

Ecosystem models that could use it

• Physiology: PSN, respiration responses to weather, climate

• C/H2O/energy: Atmosphere/biosphere exchange (pool sizes, fluxes)

• Biodiversity: Differential demographic responses to weather/climate, CO2, H2O

Physiological responses to weather

H2O, N, P

H2O, CO2light, CO2

Temp

PSN Resp

Sap flux

Allocation

Fast, fine scales

H20/energy/C cycles respond to global change

H2O, N, P

H2O, CO2light, CO2

Temp

Fast, coarse scales

Prasad and Iverson

Biodiversity: demographic responses to weather/climate

Reproduction

Mortality

Growth

H2O, N, P

H2O, CO2light, CO2

Slow, fine & coarse scales

Sensors for ecosystem variables

Soil moistureWj,t

PrecipPt

EvapEj,t

TranspirTrj,t

DrainageDt

LightIj,t

TempTj,t

VPDVj,t

C/H2O/energy

Demography Biodiversity

Physiology

WisardNet

• Multihop, self-organizing network• Sensors: light, soil & air T, soil

moisture, sap flux• Tower weather station• Minimal in-network processing• Transmission expensive

Capacity

Unprecedented potential to collect data all the timeNew insight that can only come from fine grained data

The dynamic control problem

• What is an observation worth?– How to quantify learning?

• How to optimize it over competing models?

• The answer recognizes:– Transmission cost of an observation– Need to assess value in (near) real time

• Based on model(s)• Minimal in-network computation capacity• Use (mostly) local information

– Potential for periodic out-of-network input

Pattern ecosystem data

Where could a model stand in for data?

Slow variables

Predictable variables

Events

Less predictable

How to quantify learning?• Sensitivity of estimate to observation• Model dependent: Exploit

spatiotemporal structure, relationships with other variables

PAR at 3 nodes, 3 days: PSN/Resp modeling

observations

Real applications

• Multiple users, multiple models• Learning varies among models

Information needed at different scales

• C/H20/energy balance wants fine scale

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

May Jun Jul Aug

Volu

metr

ic s

oil

mois

ture

(%

)

The 2-mo drought of 2005

Soil moisture sensors in the EW network

gap

Models learn at different scales

Biodiversity: seasonal drought & demography

Differential sensitivity among species

Why invest in redundancy?

Shared vs unique data features (within nodes, among nodes)

Exploit relationships among variables/nodes?

Slow, predictable relationships?

Dij,t

Data from multiple sources Diameter data

Process: annual change in diameter

Parameters

Hyperparameters: spatio-temporal structure

Population heterogeneity

Mean growth

Dij,t-1 Dij,t+1

€

Dij,t(o)

€

Xij,t(o)

Increment data

Individualeffects

Year effectt-1

Year effectt

Year effectt+1

Diametererror

Incrementerror

Processerror

‘Data’ can be modeled

Clark, Wolosin, Dietze, Ibanez (in review)

i individualj standt year

‘Data’ can be modeled

Clark, Wolosin, Dietze, Ibanez (in review)

€

Dij,t(o)

€

Xij,t(o)

i individualj standt year

Capacity vs value

• Data may not contribute learning• A model can often predict data

– Reduces data value

• Different models (users) need different data

Controlling measurement• Inferential modeling out of network

– Ecosystem models have multiple variables, some are global (transmission)

– Data arrive faster than model convergence

• Periodic updating (from out of network)– parameter values– state variables

• Simple rules for local control– Use local variables– Models:

• Most recent estimates from gateway• Basic model: point prediction vs most recent value

In network data suppression

• An ‘acceptable error’ – Considers competing model needs

• Option 1: change?

• Option 2: change predictable?

€

y j,t − y j,t−1 < ε

€

y j,t − ˆ y j,t {X} j ,{ ˆ θ , ˆ X MF , X,Y}t , M I < ε

{X}j local information (no transmission){,X}t global info, periodically updated from full modelMI simplified, in-network model

{W,E,Tr,D}t

Data

Calibration data (sparse!)

Process

Parameters

Hyperparameters

heterogeneity

Processparameters

€

W j ,t(o)

Location effects

time effectt-1

time effectt

time effectt+1 Measurement

errorsProcess

error

{W,E,Tr,D}t-1 {W,E,Tr,D}t+1

Out-of-network model is complex

Outputs: sparse data and ‘posteriors’

Soil moisture example

• Simulated process, parameters unknown• Simulated data

– TDR calibration, error known (sparse)– 5 sensors, error/drift unknown (often dense, but

unreliable)

• Estimate process/parameters (Gibbs sampling)

• Use estimates for in-network processing– Point estimate only, periodic updating

• Transmit only when predictions exceed threshold

Model assumptions

€

yt+1 = f yt , pt ;θ( )eεt

f yt , pt ;θ( ) = yt + pt − ET yt ;θ1,θ2( ) − D yt ;θ3( )

εt ~ N 0,σ ε2

( )

€

ln z j,t+1( ) ~ N ln yt( ) 1+δ j t − t j( )( ),σ z2

( )

δ j ~ N 0,vδ( )

vδ ~ IG s1,s2( )

ln wt+1( ) ~ N ln yt( ),σ w2

( )

Process:

Sensor j:Rand eff:

TDR calibration:

€

p y{ },θ , δ{ },σ ε2 ,σ z

2 ,σ w2 z{ }, w{ }, p{ }( )Inference:

‘truth y’95% CI5 sensorscalibration

Colors:

Drift parameters {}Estimates and truth (dashed lines)

Dots:

Simulated process & dataNetwork

down

Process parameters Estimates and truth (dashed lines)

Field capacity

Evap const

Wilting point

Keepers (40%)Prediction error large

Increasing drift reduces predictive capacity

Lesson: model stands in for data

A framework

• Bayesification of ecosystem models: a currency for learning assessment

• Model-by-model error thresholds • In-network simplicity: point

predictions based on local info, periodic out-of-network inputs

• Out-of-network predictive distributions for all variables