The Projects

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
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The effect of light on DO
30 25 20 15 10 5 1
Scale (hr)
Lake area (ha)
Source Owen Langman
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The effect of wind on DO
30 25 20 15 10 5 1
Scale (hr)
Lake area (ha)
Source Owen Langman
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P, Tair, U
PAR
Crystal Bog
Dissolved Oxygen (mg/L)
dO2/dt GPP R Fatm A (Odum 1956)
MetDataWoodruffAirport.xls
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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.
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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
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Night R
GPP
GPP
Day R
Light history
Processes

• 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.

11
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
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Trout Bog
Irradiance

• Midnight surge unexplained
• Complex model best
• Fatm similar to NEP

DO observations, models (mg/L)
Processes
Day fraction
GraphResults.m
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Trout Lake
Irradiance

• Complex model best
• NEP gtgt Fatm
• R remains elevated

DO observations, models (mg/L)
Processes
Day fraction
GraphResults.m
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Sparkling L. 2004 1-6 m
Temperature (C)
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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
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End
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Table X. AIC scores for each model for each lake.
Model with the lowest AIC has the rank of 1.
CompareModels.m gt ResultsSummary.xls
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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
DO (mg L-1)
Sigma 20 mg L-1 d-1
Day fraction