An approach to dynamic control of sensor networks with inferential ecosystem models James S. Clark,...
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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