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

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HummingbirdTrout BogAllequash Unprocessed Data Source: Owen Langman

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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. Hummingbird; 2 hr; DO, U Trout Bog; 24+ hr; DO, T Allequash; 24 hr; DO, I Source: Owen Langman

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

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

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MetDataWoodruffAirport.xls PAR P, Tair, U Dissolved Oxygen (mg/L) Crystal Bog dO 2 /dt = GPP – R – F atm + A (Odum 1956)

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

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

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ModelR0R0 IPP max IRIbeta 1XX 2XXX 3XXXX 4XXXX 5XXXXX Night RGPP Day RLight historyProcesses: 1.Use simulated data to determine which are identifiable. 2.Fit all the valid models for 3 lakes over one week. 3.Use AIC to discriminate among models.

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Crystal Bog Irradiance DO observations, models (mg/L) Processes GPP R NEP F atm Day fraction GraphResults.m 1.Models performed similarly 2.Biology explains diel 3.Much unexplained variability 4.Fatm similar to NEP

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Trout Bog Irradiance DO observations, models (mg/L) Processes GPP R NEP F atm Day fraction GraphResults.m 1.Midnight surge unexplained 2.Complex model best 3.Fatm similar to NEP

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Trout Lake Irradiance DO observations, models (mg/L) Processes GPP R NEP F atm Day fraction GraphResults.m 1.Complex model best 2.NEP >> Fatm 3.R remains elevated

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

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Surprise Theory Prior PDF Posterior 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

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End

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

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% 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 = 1.0 mg L -1 d -1 Sigma = 20 mg L -1 d -1 DO (mg L -1 ) Day fraction

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