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Modelled and measured stand transpiration and canopy conductance of an Australian native forest Rhys Whitley 1,2,3, Melanie Zeppel 1,2, Belinda Medlyn 4, Derek Eamus 1,2 U T S University of Technology, Sydney Institute for Water and Environmental Resource Management 1 Institute for Water and Environmental Resource Management, University of Technology Sydney 2 Department of Environmental Sciences, University of Technology Sydney 3 Department of Physics and Advanced Materials, University of Technology Sydney 4 Department of Biological Sciences, Macquarie University

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Talk Outline A new method of estimating stand transpiration (E c ) 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. 1.Needs measurements of G c 2.Circular, Complex and Time Consuming Directly expressed in the Jarvis-Stewart Model. 1.Measurements in E c 2.Retains Mechanistic value as E c = G c D

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Artificial Neural Network Used as a statistical benchmark for the Jarvis models. Defines an input map based on R S, D and Defines a prediction map based on a linear regression between E c and (R S, D and 1.0 x 1 x 2 x n SOFM Network Linear Mapping Network Gives a prediction that indicates the best possible fit given our data

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Paringa Site: Liverpool Plains 0.8 LAI 1.2 Rainfall: ~ 600 mm Shallow sandy soil with exposed sandstone Species Density (stems ha -1 ) Basal area (m 2 ha -1 ) Callitris glaucophylla Eucalyptus crebra SYDNEY PARINGA

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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 G c and E c on changing solar radiation Dependence of G c on changing vapour pressure deficit Dependence of G c and E c on changing soil moisture content Dependence of E c on changing vapour pressure deficit

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Parameterising the Model Filter the data set by removing…. a)Precipitation events b)Hours where solar radiation is < 0 i.e. between 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 E c and G c ! Monte-Carlo Markov-Chain Methods Methods of finding parameter values that are close to maximum likelihood

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Functional Relationships Jarvis-Stewart Model: for E c Jarvis-Stewart Model: for G c :

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Summer Winter

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Residuals and Correlation

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Optimisation Results Modified Jarvis Model (E c )Traditional Jarvis Model (G c ) ref max (mm hr -1 ) (0.0054) mm s -1 ( ) k 1 (W m -2 ) (39.67)257.99(47.76) k 2 (kPa) 1.08(0.02)-- k 3 (kPa) 0.44(0.04)0.39(0.01) θ W (mm 3 mm -3 ) 7.0*-7.14(0.12) θ C (mm 3 mm -3 ) 11.84(0.10)11.49(0.07) Measured Modified Jarvis Model Penman-MonteithANN E c total (mm) μ Ec (mm hr -1 ) R2R RMSE (mm hr -1 ) Results Summary

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Regions where the Jarvis model has been parameterised Japanese Conifer Amazonian Pasture & Rainforest Australian Eucalypt 1.Dolman et al Wright et al Sommer et al Harris et al Whitley et al Komatsu et al European Conifer and Poplar 1.Stewart Gash et al Granier & Loustau Zhang et al Bosveld & Bouten 2001

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Spatial Variability of Parameters

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Application of literature models MeasuredGranier & Loustau 1994Sommer et al E c total (mm) μ Ec (mm s -1 ) RMSE (mm s -1 ) Models from Granier & Loustau 1994 and Sommer et al were tested with our data and compared against our model

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Current and Future Work Traditional Jarvis Model Modified Jarvis Model Parameter Estimation Nonparametric Analysis Bayesian Analysis

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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 (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.

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

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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 TypeSpeciesReferences 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 Granier and Loustau 1994 Bosveld and Bouten 2001 Komatsu et al European Poplar Populus trichocarpa Populus tacamahaca Zhang et al Amazonian Rainforest Piptadenia suaveolens Licania micrantha Bocoa viridiflora Naucleopsis glabra Dolman et al Harris et al Amazonian Pasture Brachiaria decumbens Brachiaria humidicola Zea mays Vigna unguiculata Manihot esculenta Wright et al Sommer et al 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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Input Classification Map Architecture of SOLO 1.0 x 1 x 2 x n SOFM Network Linear Mapping Network v ji w ji I/O Prediction Map zjzj

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Setup of Models Jarvis-Stewart Model For G c : Jarvis-Stewart Model For E c :

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