the projects control of do across scales –langman et al. beyond odum –hanson et al. surprise!...
TRANSCRIPT
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