1. A Training Course on CO 2 Eddy Flux Data Analysis and Modeling Parameter Estimation: Practice Katherine Owen John Tenhunen Xiangming Xiao Institute of Geography and Natural Resources, Chinese Academy of Sciences, Beijing, China Institute for the Study of Earth, Oceans and Space, University of New Hampshire, USA Department of Plant Ecology, University of Bayreuth, Germany The Institute of Geography and Natural Resources, CAS, Beijing, China July 25, 2006

2. Practice: Parameter Estimation Many available methods. I will show: Hyperbolic Light Response Model Physiological Carboxylase-based Process Model both from Owen et al. 2006, Global Change Biology, submitted Outline 1. Inputs: data preparation 2. Running the program and potential problems 3. Outputs and potential problems 4. Examples

3. Practice: Parameter Estimation Inputs: Data preparation Input files for parameter estimation with the Hyperbolic Light Response Model (1): 1. Half-hourly meteorological and gas flux data (output file from flux partitioning and gap filling - “HE2001Processed.txt”)

4. Practice: Parameter Estimation Inputs: Data preparation Input files for parameter estimation with the Physiological Carboxylase-based Process Model (2): 1. Half-hourly meteorological and gas flux data (output file from flux partitioning and gap filling - “HE2001Processed.txt”) 2. Leaf Area Index (LAI) - either constant value or seasonally changing file (“HE2001.lai”) 3. Latitude & Longitude- to calculate sun angle 4. Physiological parameters - previously published values (eg. Leaf angle, Michaelis-Menton constant for oxygenation, Maximum rate of electron transport, etc.) for different vegetation types (“coni.gfx”)

5. Practice: Flux Partitioning & Gap Filling Inputs: Data preparation Review daily outputs from flux partitioning and gap filling - Are there problems? Do the results make sense? LAI file gfx file

6. Practice: Parameter Estimation Potential problems in running the program The Hyperbolic Light Response Model stops running: Fitter gets “stuck in a local minima” or can not converge on a solution due to high scatter in data (typical for winter or in periods with cut or harvests) - skip parameter estimation for the period The Physiological Carboxylase-based Process Model stops: Latitude & longitude were not defined LAI data file has a different number of days than meteorological and gas flux input file Fitter gets “stuck in a local minima” - skip parameter estimation for the period

7. Practice: Parameter Estimation How the Hyperbolic Light Response Model (1) works Use PPFD & un-gap filled NEE and non-linear least trimmed squares regression technique to iteratively calculate the , , and  for 10 day periods Set initial random values of , , and  Read in half- hourly meteorological & flux input file Output: optimal , , and  parameters for 10 day periods

8. Practice: Parameter Estimation Hyperbolic Light Response Model (1) Outputs Parameters:  Standard error of  and  Slope, intercept & r 2 of observed NEE vs. calculated NEE

9. Practice: Parameter Estimation: Outputs & Potential Problems: Hyperbolic Light Response Model (1) “abnormal”  results can be due to: Winter periods with little light response Strong scatter in NEE & PPFD relationship (due to cut or harvest) Poor starting values of  - results stuck in local minima We chose to eliminate “abnormal” results with:relative standard error > 0.6,  > 0.17,  > 100,  > 15

10. Practice: Parameter Estimation: How the Physiological Carboxylase-based Process Model (2) works Define LAI: constant or seasonally changing from file Calculate static geometric attributes of the canopy (diffuse & direct radiation on leaf surfaces-sunlit & shaded) Iteratively calculate energy balance throughout canopy (leaf temperature, incoming and outgoing shortwave & longwave radiation, estimated GPP) Define latitude, longitude, vegetation type gfx input file Read in half- hourly meteo & flux input file Output: (Vc uptake2* and alpha) or (Vc uptake1* ) parameters for 10 day periods

11. Practice: Parameter Estimation Carboxylase-based Process Model (2) Outputs Parameters: Vc uptake & alpha Standard error of Vc uptake & alpha Slope, intercept & r 2 of observed GPP vs. calculated GPP

12. Practice: Parameter Estimation Outputs & Potential Problems Carboxylase-based Process Model (2) “Abnormal” Vc uptake & alpha results can be due to: LAI of 0 Poor estimates of seasonal LAI harvests or cuts scatter or errors in data We chose to eliminate “abnormal” results with:relative standard error > 0.6, Vc uptake > 350, alpha > 0.17 Easter Bush, UK, 2005, LAI too low

13. Hesse, France Deciduous Beech Forest Fagus sylvatica experienced drought in 2003 Practice: Parameter Estimation Examples: Hesse, France

14. Practice: Parameter Estimation Examples: Hesse, France

15. Takayama, Japan Mountain Deciduous Forest Quercus crispula Blume, Betula ermanii Cham., Betula platyphylla Sukatchev var. japonica Hara Storm damage in 2004 Practice: Parameter Estimation Examples: Takayama, Japan

16. Practice: Parameter Estimation Examples: Takayama, Japan

17. Barrow, Alaska, USA Tundra Carex aquatilis spp. Stans, Eriophorum angustifolium, Dupontia fisheri, Poa artica Practice: Parameter Estimation Examples: Barrow, Alaska, USA

18. Practice: Parameter Estimation Examples: Barrow, Alaska, USA

19. Grillenburg, Germany Grassland Festuca pratensis, Alopecurus pratensis, Phleum pratensis Cut 2 or 3 times per year No grazing experienced drought in 2003 Practice: Parameter Estimation Examples: Grillenburg, Germany

20. Practice: Parameter Estimation Examples: Grillenburg, Germany