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**Rhys Whitley1,2,3, Melanie Zeppel1,2, Belinda Medlyn4, Derek Eamus1,2**

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 1Institute for Water and Environmental Resource Management, University of Technology Sydney 2Department of Environmental Sciences, University of Technology Sydney 3Department of Physics and Advanced Materials, University of Technology Sydney 4Department of Biological Sciences, Macquarie University U T S University of Technology, Sydney Institute for Water and Environmental Resource Management

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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

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**Methods of Modelling Transpiration**

Penman-Monteith Equation and Jarvis-Stewart Model. Needs measurements of Gc Circular, Complex and Time Consuming 1 Directly expressed in the Jarvis-Stewart Model. Measurements in Ec Retains Mechanistic value as Ec = GcD 2

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**Artificial Neural Network**

Used as a statistical benchmark for the Jarvis models. Defines an input map based on RS, D and q SOFM Network Defines a prediction map based on a linear regression between Ec and (RS, D and q) 1.0 x1 x2 xn Gives a prediction that indicates the ‘best’ possible fit given our data Linear Mapping Network

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**Paringa Site: Liverpool Plains**

SYDNEY PARINGA Rainfall: ~ 600 mm 0.8 ≤ LAI ≤ 1.2 Species Density (stems ha-1) Basal area (m2 ha-1) Callitris glaucophylla 212.2 5.9 Eucalyptus crebra 42.2 14.5 Shallow sandy soil with exposed sandstone

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**Weather station 100 m from tree stand**

Methods of Collection Greenspan sap flow sensors 4 sensors per tree 7 trees per species 2 species Transpiration Solar Radiation Vapour Pressure Deficit Soil Moisture Content Weather station 100 m from tree stand Theta probes at 10, 40 & 50 cm

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**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

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**Measurement Time Series**

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**Model Functional Dependencies**

Dependence of Gc and Ec on changing solar radiation Dependence of Gc on changing vapour pressure deficit Dependence of Ec on changing vapour pressure deficit Dependence of Gc and Ec on changing soil moisture content

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**Parameterising the Model**

1 We need to use data that shows non-limiting response to Ec and Gc! Filter the data set by removing…. Precipitation events Hours where solar radiation is < 0 i.e. between hrs 2 We need to find the most likely values for the seasonal response parameters Monte-Carlo Markov-Chain Methods Methods of finding parameter values that are close to maximum likelihood Heuristic Search Algorithms Quantile Regression Boundary Line Analysis

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**Functional Relationships**

Jarvis-Stewart Model: for Ec Jarvis-Stewart Model: for Gc:

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Summer Winter

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**Residuals and Correlation**

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**Modified Jarvis Model (Ec ) Traditional Jarvis Model (Gc )**

Optimisation Results Modified Jarvis Model (Ec ) Traditional Jarvis Model (Gc ) refmax (mm hr-1) 0.2667 (0.0054) mm s-1 ( ) 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) Results Summary Measured Modified Jarvis Model Penman-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 RMSE (mm hr-1) 0.028 0.030 0.021

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**Regions where the Jarvis model has been parameterised**

European Conifer and Poplar Japanese Conifer Komatsu et al. 2006 Stewart 1988 Gash et al. 1989 Granier & Loustau 1994 Zhang et al. 1997 Bosveld & Bouten 2001 Amazonian Pasture & Rainforest Dolman et al. 1991 Wright et al. 1995 Sommer et al. 2002 Harris et al. 2004 Australian Eucalypt Whitley et al. 2007

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**Spatial Variability of Parameters**

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**Application of literature models**

Models from Granier & Loustau 1994 and Sommer et al were tested with our data and compared against our model Measured Granier & Loustau 1994 Sommer et al. 2002 Ec total (mm) 110.52 37.45 μEc (mm s-1) 0.051 0.489 0.018 RMSE (mm s-1) - 0.952 0.056

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**Current and Future Work**

Traditional Jarvis Model Modified Jarvis Model Bayesian Analysis Nonparametric Analysis Parameter Estimation

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**the lab team at UTS for the data**

Acknowledgements Many thanks to Gab Abramowitz for lending his code and his help with SOLO. and the lab team at UTS for the data

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Thank you for your time

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Extra Slides

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Genetic Algorithms Are adaptive heuristic search algorithms based on natural selection and evolution. (Optimum Solution) 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.

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**Example: Genetic Algorithm Process**

Data Result Optimum Solutions Test 2min 2>2min Set population of random solutions Evaluation Cross-mix solutions Randomly select solutions Mutate

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**Bayesian Parameter Estimation**

Solve Bayes Theorem for the Jarvis model Uniform Prior Gaussian Likelihood

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**Spatial Variability of Parameters**

Forest Type Species References European Conifer Japanese Conifer Pinus sylvestris Pinus nigra var. maritima Pteridiura aquilinura (L.) Kuhn Pinus pinaster Ait. Pteridium aquiline Molinia coerule Pseudotsuga menziesii (Mirb.) Franco Cryptomeria japonica Stewart 1988 Gash et al. 1989 Granier and Loustau 1994 Bosveld and Bouten 2001 Komatsu et al. 2006 European Poplar Populus trichocarpa Populus tacamahaca Zhang et al. 1997 Amazonian Rainforest Piptadenia suaveolens Licania micrantha Bocoa viridiflora Naucleopsis glabra Dolman et al. 1991 Harris et al. 2004 Amazonian Pasture Brachiaria decumbens Brachiaria humidicola Zea mays Vigna unguiculata Manihot esculenta Wright et al. 1995 Sommer et al. 2002 Australian Eucalypt Eucalyptus crebra Callitris glaucophylla Whitley et al. 2007

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**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.

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**Linear Mapping Network**

Architecture of SOLO SOFM Network Input Classification Map wji I/O Prediction Map 1.0 x1 x2 xn zj vji Linear Mapping Network

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**Setup of Models Jarvis-Stewart Model Jarvis-Stewart Model For Gc:**

For Ec:

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