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The Projects

The Projects. Control of DO across scales Langman et al. Beyond Odum Hanson et al. Surprise! Langman et al. Unprocessed Data. Hummingbird. Trout Bog. Allequash. Source: Owen Langman. Single Lake Wavelet Decompositions. Wavelet Transforms:

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The Projects

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  1. The Projects • Control of DO across scales • Langman et al. • Beyond Odum • Hanson et al. • Surprise! • Langman et al.

  2. Unprocessed Data Hummingbird Trout Bog Allequash Source: Owen Langman

  3. Single Lake Wavelet Decompositions Wavelet Transforms: A method of separating a signal into frequency components while preserving the time domain. Continuous Wavelet Transforms: A signal of finite length and energy is projected on a continuous family of frequency bands. Trout Bog; 24+ hr; DO, T Hummingbird; 2 hr; DO, U Allequash; 24 hr; DO, I Source: Owen Langman

  4. The effect of light on DO 30 25 20 15 10 5 1 Scale (hr) Lake area (ha) Source: Owen Langman

  5. The effect of wind on DO 30 25 20 15 10 5 1 Scale (hr) Lake area (ha) Source: Owen Langman

  6. P, Tair, U PAR Crystal Bog Dissolved Oxygen (mg/L) dO2/dt = GPP – R – Fatm + A (Odum 1956) MetDataWoodruffAirport.xls

  7. Pmax GPP = Pmax.* (1- exp(-IP * I / Pmax)) IP IR R0 (night time R) Simple model Complicated model(s) Gross Primary Productivity, Respiration P0 (always= 0) 0 0 Irradiance Figure X. Responses for ecosystem GPP and R as a function of irradiance. Parameters are per Table X.

  8. Test of the Ibeta (light history) parameter I original Beta = 0.1 Beta = 1 Beta = 10 Beta = 100 Effective I Time of day RunSimulation.m

  9. Processes: Night R GPP GPP Day R Light history • Use simulated data to determine which are identifiable. • Fit all the valid models for 3 lakes over one week. • Use AIC to discriminate among models.

  10. GPP R NEP Fatm Crystal Bog Irradiance • Models performed similarly • Biology explains diel • Much unexplained variability • Fatm similar to NEP DO observations, models (mg/L) Processes Day fraction GraphResults.m

  11. GPP R NEP Fatm Trout Bog Irradiance • Midnight surge unexplained • Complex model best • Fatm similar to NEP DO observations, models (mg/L) Processes Day fraction GraphResults.m

  12. GPP R NEP Fatm Trout Lake Irradiance • Complex model best • NEP >> Fatm • R remains elevated DO observations, models (mg/L) Processes Day fraction GraphResults.m

  13. Sparkling L. 2004 1-6 m Temperature (C)

  14. Surprise Theory Posterior PDF Prior PDF Kullback-Leibler divergence measures the difference between the distributions • Result: A quantitative single value measuring how unexpected the point is based on the amount of change from the prior to the posterior • Prior can be formed from historical data, existing models, or developed over a short training period from real time data • Capable of observing events at multiple temporal scales • Capable of observing events in 2D / 3D space Source: Owen Langman

  15. End

  16. Table X. AIC scores for each model for each lake. Model with the lowest AIC has the rank of 1. CompareModels.m => ResultsSummary.xls

  17. % Parameter sets ************************************ Parameters = [0 3.0 0.005 0.001 5 20 0.1]; % PO RO IP IR Pmax Ibeta Physics InitialDO = 7.5; Sigma = 0.1 mg L-1 d-1 Sigma = 1.0mg L-1 d-1 DO (mg L-1) Sigma = 20mg L-1 d-1 Day fraction

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