1. Evaluating Sub-Grid Variability of Surface Fluxes with a Cellular Automata Model─Wet/Dry DaisyWorld
Dennis Baldocchi & James Dorsey
Department of Environmental Science, Policy and Management
University of California, Berkeley
Monique Leclerc
University of Georgia, Griffin

2. Outline Why Sub-Grid Variability is a Problem? 2-D DaisyWorld Model
Cellular Automata
Results & Discussion
Spatial Scaling and Variance
Overlay Flux Footprints on 2-d Daisyworld Energy Flux Grid to assess Spatial Sampling Errors and Energy Balance Closure

3. Upscaling Fluxes over Heterogeneous Canopies, e.g. Savannas
What is the Expected Value of the Energy Flux from this Heterogeneous
1 km grid, the scale of a MODIS Pixel?

4. Assessing Spatial Averages: a la ‘Reynolds’ Decomposition of Penman-Monteith Equation

5. Sub-Grid Variability: at MODIS and IKONOS scales

6. Wet/Dry Daisy World
Baldocchi et al, Tellus, 2005

7. Cellular Automata (CA) Rules: 2d Daisy World
If cell bare, compute probability of birth
Based on temperature of central, bare cell
Based on temperature of surrounding neighbors
Based on temperature of neighbor, picked at random
If ‘daisy’ is born, decide if it is ‘wet’ or ‘dry’ and assigned it values of albedo and stomatal conductance based on
Properties of neighbor, picked at random
Properties of the dominating neighbor

9. dry
wet
Bare

10. Latent Heat Exchange

11. Heterogeneity follows Power Law Scaling with size of Averaging Window

12. Scaling Rules and Tools: Does sET scale with sT?

13. Errors in ET Scaling

14. Radiometer vs Flux Footprints
3-d Lagrangian Footprint Model, with canopy
Langevin Eq: Thomson Model
Turbulence Fields: 3rd Order Closure Model, Pyles and Paw U

15. Tonzi Ranch

16. Vaira Ranch

17. Eddy covariance footprints and ecosystem representativeness
Further work
Improvements to the turbulence closure scheme used in the Lagrangian footprint model are underway.
DaisyWorld simulations of larger and more heterogeneous ecosystems
Use of MODIS and GIS data to perform representativeness assessments for several US Ameriflux sites.

19. Eddy covariance footprints and ecosystem representativeness
Footprint representation
Newly developed Lagrangian stochastic footprint model was run for a 1 m canopy and 3 m measurement height. Half a million trajectories were integrated to calculate the source probability density.
The footprint calculation was run using the same grid geometry as the DaisyWorld simulation to allow convolution of the results.
The EC “tower” was placed in different locations in the simulated ecosystem, and the EC system's view of the ecosystem was calculated.
Results are histograms of the ratio of measurement simulations to ecosystem activity.

20. Eddy covariance footprints and ecosystem representativeness
Results
Histograms show water vapour flux closure. Values of 100% denote a representative measurement. Each histogram shows 500 separate tower locations within the simulated ecosystem.
Closure probability for heterogeneity length scale
Lh = 1 m

21. Eddy covariance footprints and ecosystem representativeness
Results
Closure probability for heterogeneity length scale
Lh = 2 m
Closure probability for heterogeneity length scale
Lh = 4 m