modelled and measured stand transpiration and canopy conductance of an australian native forest rhys...
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Modelled and measured stand transpiration and canopy
conductance of an Australian native forest
Rhys Whitley1,2,3, Melanie Zeppel1,2,Belinda Medlyn4, Derek Eamus1,2
U T SUniversity of Technology, Sydney Institute for Water and Environmental
Resource Management
1Institute for Water and Environmental Resource Management, University of Technology Sydney2Department of Environmental Sciences, University of Technology Sydney
3Department of Physics and Advanced Materials, University of Technology Sydney4Department of Biological Sciences, Macquarie University
Talk Outline
A new method of estimating stand transpiration (Ec) as an alternative to Penman-Monteith (PM) equation
Comparing against the PM and an Artificial Neural Network (ANN)
Spatial variability of responses between ecosystems
Future Work
)/1(
)(
ca
apnc GG
DGCGRE
Methods of Modelling Transpiration
)()()( 321 fDfRfGG SMaxcc
)()(ˆ)( 321 fDfRfEE SMaxcc
Penman-Monteith Equation and Jarvis-Stewart Model.1. Needs measurements of Gc
2. Circular, Complex and Time Consuming
Directly expressed in the Jarvis-Stewart Model.1. Measurements in Ec
2. Retains Mechanistic value as Ec = GcD
Artificial Neural NetworkUsed as a statistical benchmark for the Jarvis models.
Defines an input map based onRS, D and
Defines a prediction map based on a linear regression between Ec and (RS, D and
1.0
x1
x2
xn
SOFM Network
Linear Mapping Network
Gives a prediction that indicates the ‘best’ possible fit given our data
Paringa Site: Liverpool Plains
0.8 ≤ LAI ≤ 1.2
Rainfall: ~ 600 mm
Shallow sandy soil with exposed sandstone
SpeciesDensity
(stems ha-1)
Basal area
(m2 ha-1)
Callitris glaucophylla
212.2 5.9
Eucalyptus crebra
42.2 14.5
SYDNEY
PARINGA
Methods of Collection
Greenspan sap flowsensors
4 sensors per tree 7 trees per species
2 species
Transpiration
Solar Radiation
Vapour Pressure Deficit
Soil MoistureContent
Weather station 100 m from tree stand
Theta probes at 10, 40 & 50 cm
Scaling to Stand Water Use
Stand water use is ….. sap velocity of the stand x sapwood area of the stand
Mean sap velocity for each species
Sapwood area of the stand estimated using the DBH vs. sapwood area relationship for each species
1 Jan 1 Feb 1 Jul 1 Aug 1 Sep
0200400600800
100012001400
0123456789
1 Jan 1 Feb 1 Jul 1 Aug 1 Sep56789
101112131415
020406080100120140160180200
1 Jan 1 Feb 1 Jul 1 Aug 1 Sep
0.00.51.01.52.02.53.0
S
ola
r R
adia
tio
n
(W m
-2)
RS D
Vap
ou
r Pressu
reD
eficit (kPa)
So
il M
ois
ture
Co
nte
nt
(mm
3 mm
-3) R
ainfall (m
m)
Sta
nd
Tra
nsp
irat
ion
(mm
d-1)
Ec
Measurement Time Series
Model Functional Dependencies
)exp()(ˆ 232 DkDkDf
)exp()( 22 DkDf
f1(RS )RS1000
1000 k1RS k1
f3()0
wC w1
, W,W C, C
Dependence of Gc and Ec onchanging solar radiation
Dependence of Gc on changingvapour pressure deficit
Dependence of Gc and Ec onchanging soil moisture content
Dependence of Ec on changingvapour pressure deficit
Parameterising the Model
0
200
400
600
800
1000
1200
1400
0:00:00 4:00:00 8:00:00 12:00:00 16:00:00 20:00:00
Sola
r R
ad
iati
on
RS (
Wm
-2)Filter the data set by removing….
a) Precipitation events
b) Hours where solar radiation is < 0i.e. between 0800-1600 hrs
Boundary Line Analysis
Quantile Regression
Heuristic Search Algorithms
We need to find the most likely values for the seasonal
response parameters
We need to use data that shows non-limiting response to Ec and Gc!
Monte-Carlo Markov-ChainMethods
Methods of finding parameter values that are close to maximum
likelihood
Functional Relationships
0 200 400 600 800 1000 1200 1400
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.0
0.2
0.4
0.6
0.8
1.0
Solar Radiation (W m-2)
Sta
nd
Tra
nsp
irat
ion
(m
m h
r-1)
Vapour Pressure Deficit (kPa)
Soil Moisture Content (mm3 mm-3)
Ec/
Ec
max
Jarv
is-S
tew
art
Mo
de
l:
for
Ec
Jarv
is-S
tew
art
Mo
de
l:
for
Gc:
0 200 400 600 800 1000 1200 1400
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.0
0.2
0.4
0.6
0.8
1.0
Solar Radiation (W m-2)
Can
op
y C
on
du
ctan
ce (
mm
hr-1
)
Vapour Pressure Deficit (kPa)
Soil Moisture Content (mm3 mm-3)
Gc/
Gc
max
1 Jan 2 Jan 3 Jan 4 Jan 5 Jan 6 Jan 7 Jan
0.00
0.05
0.10
0.15
0.20
5 Feb 6 Feb 7 Feb 8 Feb 9 Feb 10 Feb 11 Feb 12 Feb
0.00
0.05
0.10
0.15
0.20
0.25
14 Jul 15 Jul 16 Jul 17 Jul 18 Jul 19 Jul 20 Jul 21 Jul
0.00
0.05
0.10
0.15
0.20
9 Sep 10 Sep 11 Sep 12 Sep 13 Sep 14 Sep 15 Sep 16 Sep
0.00
0.05
0.10
0.15
0.20
0.25
Sta
nd
Tra
ns
pir
ati
on
(m
m h
r-1)
Sapflow PM Jarvis ANN
Summer Winter
Residuals and Correlation
0 50 100 150 200 250 300 350-3
-2
-1
0
1
2
3
4
0 50 100 150 200 250 300 350
-4 -3 -2 -1 0 1 2 3 40
10
20
30
40
50
60
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80
90
100
110
120
Penman-Monteith Ec
Fre
qu
ency
Standard Deviation
Jarvis-Stewart Ec
-4 -3 -2 -1 0 1 2 3 4
Standard Deviation
Sta
nd
ard
Dev
iati
on
Time (Hrs)
Time (Hrs)
0.00
0.05
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0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.00 0.05 0.10 0.15 0.20 0.25 0.30
0.00
0.05
0.10
0.15
0.20
0.25
0.30
JS-m
od
el T
ran
spir
atio
n (
mm
hr-1
)
R2 = 0.87slope = 0.86
PM
T
ran
spir
atio
n (
mm
hr-1
) R2 = 0.86slope = 0.79
AN
N T
ran
spir
atio
n (
mm
hr-1
)
Sapflow Transpiration (mm hr-1)
R2 = 0.86 slope = 0.85
Optimisation Results
Modified Jarvis Model (Ec ) Traditional Jarvis Model (Gc )
refmax (mm hr-1) 0.2667 (0.0054) 0.00821mm s-1 (0.00012)
k1 (W m-2) 200.38 (39.67) 257.99 (47.76)
k2 (kPa) 1.08 (0.02) - -
k3 (kPa) 0.44 (0.04) 0.39 (0.01)
θW (mm3mm-3) 7.0* - 7.14 (0.12)
θC (mm3mm-3) 11.84 (0.10) 11.49 (0.07)
MeasuredModified
Jarvis ModelPenman-Monteith ANN
Ec total (mm) 110.52 84.03 74.91 110.70
μEc (mm hr-1) 0.051 0.039 0.040 0.052
R2 - 0.87 0.86 0.86
RMSE (mm hr-1) - 0.028 0.030 0.021
Results Summary
Regions where the Jarvis model has been parameterised
Japanese Conifer
Amazonian Pasture& Rainforest
Australian Eucalypt1. Dolman et al. 19912. Wright et al. 19953. Sommer et al. 20024. Harris et al. 2004
1. Whitley et al. 2007
1. Komatsu et al. 2006
European Conifer and Poplar
1. Stewart 19882. Gash et al. 19893. Granier & Loustau 19944. Zhang et al. 19975. Bosveld & Bouten 2001
0 1 2 3 4 5 6 7
0 5 10 15 20 25 30 35 40
0 200 400 600 800 10000.0
0.2
0.4
0.6
0.8
1.0
Vapour Pressure Deficit (kPa)
Whitley et al. 2007 Komatsu et al. 2006 Harris et al. 2004 Sommer et al. 2002 Zhang et al. 1997 Wright et al. 1995 Granier and Loustau 1994 Dolman et al. 1991
Specific Humidity Deficit (g kg-1)
Ec
/ Ec
max
Solar Radiation (W m-2)
Spatial Variability of Parameters
Application of literature models
Measured Granier & Loustau 1994 Sommer et al. 2002
Ec total (mm) 110.52 1045.00 37.45
μEc (mm s-1) 0.051 0.489 0.018
RMSE (mm s-1) - 0.952 0.056
Models from Granier & Loustau 1994 and Sommer et al. 2002 were tested with our data and compared against our model
0 250 500 750 1000 1250 1500 1750 2000 2250 25000.00
0.04
0.08
0.12
0.16
0.20
0.24
0.28
0
1
2
3
4
5
6
Hours
Measured Ec Granier & Loustau 1994 Sommer et al. 2002
Sta
nd
Tra
nsp
irat
ion
(m
m h
r-1)
Current and Future Work
Traditional
Jarvis Model
ModifiedJarvis Model
ParameterEstimation
Nonparametric
Analysis
Bayesian Analysis
Acknowledgements
Many thanks to Gab Abramowitz for lending his code and his help with SOLO.
and
the lab team at UTS for the data
Thank you foryour time
Extra Slides
Genetic Algorithms
min2
(Optimum Solution)
• Are adaptive heuristic search algorithms based on natural selection and evolution.
• Powerful: Discovers optimum solutions rapidly for difficult high-dimensional problems.– e.g. 7 dimensional
parameter space.
• Searches this entire parameters space for the global minimum - optimum value.
DataResult
Optimum SolutionsTest
2min
2>2min
Set population of random solutions
Evaluation
Cross-mix solutions
Randomly select
solutionsMutate
Example: Genetic Algorithm Process
Bayesian Parameter Estimation
• Solve Bayes Theorem for the Jarvis model
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ii
Nki
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kikik
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IP
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)(
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)|(
)|(
),|()|(),|(
Uniform Prior
Gaussian Likelihood
Spatial Variability of ParametersForest Type Species References
European Conifer
Japanese Conifer
Pinus sylvestris
Pinus nigra var. maritimaPteridiura aquilinura (L.) KuhnPinus pinaster Ait.Pteridium aquilineMolinia coerulePseudotsuga menziesii (Mirb.) Franco
Cryptomeria japonica
Stewart 1988
Gash et al. 1989Granier and Loustau 1994Bosveld and Bouten 2001
Komatsu et al. 2006
European Poplar Populus trichocarpa Populus tacamahaca
Zhang et al. 1997
Amazonian Rainforest Piptadenia suaveolensLicania micranthaBocoa viridifloraNaucleopsis glabra
Dolman et al. 1991Harris et al. 2004
Amazonian Pasture Brachiaria decumbensBrachiaria humidicolaZea maysVigna unguiculataManihot esculenta
Wright et al. 1995Sommer et al. 2002
Australian Eucalypt Eucalyptus crebraCallitris glaucophylla
Whitley et al. 2007
Artificial Neural Network
• Uses a Self-Organising Feature Map (SOFM) and Self-Organising Linear Output Map (SOLO).
• SOFM trains and maps the input space.
• SOLO maps inputs into outputs using piecewise linear regression.
• Used as a statistical benchmark for the Jarvis models.
Input Classification Map
Architecture of SOLO
1.0
x1
x2
xn
SOFM Network
Linear Mapping Network
vji
wji
I/O Prediction Map
0
10
n
ijiijj vxvz
zj
Setup of Models
f1(RS )RS1000
1000 k1RS k1
f3()0
wC w1
, W,W C, C
)exp()(ˆ 232 DkDkDf )exp()( 22 DkDf
f1(RS )RS1000
1000 k1RS k1
f3()0
wC w1
, W,W C, C
Jarvis-Stewart Model
For Gc:
Jarvis-Stewart Model
For Ec: