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