Dynamic control of sensor networks with inferential ecosystem models

1. Jim Clark, Environm, Biol, Stat Pankaj Agarwal, Comp Sci David Bell, Environment Carla Ellis, Comp Sci Paul Flikkema, EE, NAU Alan Gelfand, Stat Gabriel Katul, Environment Kamesh Munagala, Comp Sci Gavino Puggioni, Comp Sci Adam Silberstein, Comp Sci Jun Yang, Comp Sci Dynamic control of sensor networks with inferential ecosystem models

2. Motivation • Understanding forest response to global change (climate, CO2) • Forces at many scales • Complex interactions • lagged responses • Uneven data needs: occasionally dense, at different scales • Wireless networks can provide dense data, across landscapes

3. Ecosystem models that could use wireless data • 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

4. Physiological responses to weather Precip light, CO2 H2O, CO2 Resp PSN Temp Allocation Sap flux Fast, fine scales H2O, N, P

5. Sensors for ecosystem variables Demography Biodiversity Physiology Precip Pt Evap Ej,t Transpir Trj,t Light Ij,t C/H2O/energy Soil moisture Wj,t Temp Tj,t VPD Vj,t Drainage Dt

6. WisardNet: a wireless network • Multihop, self-organizing • Sensors for light, soil & air T, soil moisture, sap flux • Tower weather station • Minimal in-network processing sensor sensor gateway node Self-organizing wireless connections

7. Mapped stands • All life history stages • Seed rain • Seed banks • Seedlings • Saplings • Mature trees • Interventions • Canopy gaps • Nutrient additions • Herbivore exclosures • Fire • Environmental monitoring • Canopy photos • Soil moisture • Temperature • Wireless sensor networks • Remote sensing

8. Blackwood Division, Duke Forest sensor sensor node gateway Fluid topology

9. The goods and the bads The good: Potential to collect dense data Adapts to changing communication potential The bad: Most data uninformative, redundant, or both Battery life of weeks to months, depending on transmission rate Checking and replacing batteries is the primary maintenance cost of network

10. …the ugly Battery life at 13 nodes • Unreliable! Network partially down Failures Junk

11. A dynamic control problem • What is an observation worth? (How to quantify learning?) • 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

12. A framework for data collection • ‘Predict or collect’: • Transmit an observation if it could not have been predicted by a model. • Fast decisions (real-time) • Must rely on (mostly) local information • Minimize transmission

13. Predictability of ecosystem data Slow variables Where could a model stand in for data? Predictable variables Events Less predictable

14. Which observations are ‘informative’? Light Shared vs unique data features (within nodes, among nodes) Precipitation Exploit relationships among variables/nodes? Soil moisture Slow, predictable relationships?

15. Model-dependent learning • Exploit relations in space, time, and with other variables • Learning from previous data collection • If predictable, data have reduced value PAR at 3 nodes, 3 days observations

16. Controlling measurement with models Inferential modeling concerns Some parameters ‘local’, some ‘global’ Estimates of global parameters need transmission Data can’t arrive faster than model converges Simple rules for local control of transmission Rely mostly on local variables Periodic updating from out of network ‘Transmit if you can’t predict’

17. In network data suppression • An ‘acceptable error’,  • A standard reactive model based on change, • Alternative: is the observation ‘predictable’, {z}j local sensor data (no transmission) {, z, w}t global data, periodically updated from full model MF full, out-of-network model MI simplified, in-network model

18. Out-of-network model is complex Calibration data (sparse!) Sensor data zj,t Data {y,E,Tr,D}t-1 {y,E,Tr,D}t {y,E,Tr,D}t+1 Process Parameters Location effects Process parameters time effect t+1 time effect t-1 Measurement errors time effect t Process error heterogeneity Hyperparameters

19. Soil moisture example Simulated process, parameters unknown Simulated data TDR calibration, error known (sparse), 5 sensors, error/drift unknown (dense, but unreliable), Out-of-network estimate process/parameters Use estimates for in-network prediction Transmit only when predictions exceed threshold

20. Model summary Process: Sensor j: Rand eff: TDR calibration: Inference: Back to node j:

21. Simulated process & data ‘truth y’ 95% CI 5 sensors z Calibration w Colors: Red dots: Drift parameters {} Estimates and truth (dashed lines)

22. Estimates from training phase Process parameters  Estimates and truth (dashed lines)

23. Keepers based on acceptable error Transmit obs only if Increasing drift reduces predictive capacity From plug-in values: Keepers (40%), very few until drift accumulates

24. Better ‘data’, few ‘observations’ Known constraint on missing data Reanalysis model for missing data: ‘truth y’ 95% CI 5 sensors z Calibration w Colors: Red dots:

25. Additional variables

26. ‘Collect or predict’ • Inferential ecosystem models: a currency for learning assessment • In-network simplicity: point predictions based on local info, periodic out-of-network inputs • Out-of-network predictive distributions for all variables (‘reanalysis’ step) • A role for inference in data collection, not just data analysis

27. Advantages over ‘reactive’ data collection in wireless networks • ‘Change’ in a variable is not directly linked to its information content • Example: all soil moisture sensors may change at similar rates, making them largely redundant • ‘Predictability’ emphasizes change that contains information • The capacity to predict an observation summarizes its value and assures that it can be estimated to known precision in the reanalysis