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

The Projects

• Control of DO across scales – Langman et al.

• Beyond Odum– Hanson et al.

• Surprise!– Langman et al.

Dissolved Oxygen

8

8.1

8.2

8.3

8.4

8.5

8.6

8.7

8.8

8.9

9

Dissolved Oxygen

6.8

7

7.2

7.4

7.6

7.8

8

8.2

8.4

8.6

Dissolved Oxygen

2

2.5

3

3.5

4

4.5

5

5.5

6

Wind

0

0.5

1

1.5

2

2.5

3

3.5

4

Water Temperature

21.5

22

22.5

23

23.5

24

Irradiance

0

200

400

600

800

1000

1200

1400

1600

Hummingbird Trout Bog Allequash

Unprocessed Data

Source: Owen Langman

Single Lake Wavelet Decompositions

Hummingbird 150 Min. Decomposition

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

1 21 41 61 81 101 121 141 161 181 201 221 241 261 281 301 321

Time

Wind

DO

Trout Bog 1500 Min. Decomposition

-10.00

-8.00

-6.00

-4.00

-2.00

0.00

2.00

4.00

6.00

8.00

10.00

1 21 41 61 81 101 121 141 161 181 201 221

Time

Temp

DO

Allequash 1440 Min. Decomposition

-0.60

-0.40

-0.20

0.00

0.20

0.40

0.60

1 21 41 61 81 101 121 141 161 181 201 221 241

Time

Light

DO

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

The effect of light on DO

Lake area (ha)

Sca

le (

hr)

30

25

20

15

10

5

1

Source: Owen Langman

The effect of wind on DO

Lake area (ha)

Sca

le (

hr)

30

25

20

15

10

5

1

Source: Owen Langman

MetDataWoodruffAirport.xls

PAR

P, T

air,

U

0

5

10

15

20

25

30

232 232.5 233 233.5 234 234.5 235 235.5 236 236.5 237

0

500

1000

1500

2000AVG_PAR

TOT_PRECIP

AVG_AIR_TEMP

AVG_WIND_SPEED

Dis

solv

ed O

xyge

n (m

g/L) Crystal Bog

dO2/dt = GPP – R – Fatm + A (Odum 1956)

Irradiance

Gro

ss P

rim

ary

Prod

ucti

vity

, Res

pira

tion

0

0

P0 (always= 0)

R0 (night time R)

IP

IR

Simple modelComplicated model(s)

Figure X. Responses for ecosystem GPP and R as a function of irradiance. Parameters are per Table X.

Pmax

GPP = Pmax.* (1- exp(-IP * I / Pmax))

Time of day

Eff

ectiv

e I

I originalBeta = 0.1Beta = 1Beta = 10Beta = 100

Test of the Ibeta (light history) parameter

RunSimulation.m

Model R0 IP Pmax IR Ibeta

1 X X

2 X X X

3 X X X X

4 X X X X

5 X X X X X

Night R GPP GPP Day R Light 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.

0

500

1000

1500

2000

233 233.25 233.5 233.75 234

Crystal BogIr

radi

ance

DO

obs

erva

tion

s,

mod

els

(mg/

L)

Proc

esse

s

GPPRNEPFatm

Day fractionGraphResults.m

1. Models performed similarly2. Biology explains diel3. Much unexplained variability4. Fatm similar to NEP

0

500

1000

1500

2000

233 233.25 233.5 233.75 234

Trout BogIr

radi

ance

DO

obs

erva

tion

s,

mod

els

(mg/

L)

Proc

esse

s

GPPRNEPFatm

Day fractionGraphResults.m

1. Midnight surge unexplained2. Complex model best3. Fatm similar to NEP

0

500

1000

1500

2000

233 233.25 233.5 233.75 234

Trout LakeIr

radi

ance

DO

obs

erva

tion

s,

mod

els

(mg/

L)

Proc

esse

s

GPPRNEPFatm

Day fractionGraphResults.m

1. Complex model best2. NEP >> Fatm3. R remains elevated

Tem

pera

ture

(C

)Sparkling L. 20041-6 m

Surprise Theory

)(PD

dxxq

xpxpQPDKL

)(

)(ln)()|(

)|( QPD

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

End

CompareModels.m => ResultsSummary.xls

Table X. AIC scores for each model for each lake. Model with the lowest AIC has the rank of 1.

Lake Model AIC RankCB 1 298 3CB 2 233 4CB 3 228 1CB 4 302 5CB 5 231 2SP 1 -3551 5SP 2 -3606 3SP 3 -3645 2SP 4 -3570 7SP 5 -3655 1TB 1 -258 4TB 2 -273 3TB 3 -259 5TB 4 -495 2TB 5 -529 1TR 1 -17105 5TR 2 -18037 3TR 3 -18286 2TR 4 -17852 4TR 5 -19772 1

MeanR0 IP Pmax IR Ibeta Model RankX X 1 4.25X X X 2 3.25X X X X 3 2.50X X X X 4 4.50X X X X X 5 1.25

% Parameter sets ************************************Parameters = [0 3.0 0.005 0.001 5 20 0.1];% PO RO IP IR Pmax Ibeta PhysicsInitialDO = 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

(m

g L

-1)

Day fraction