1. Integrating Fluxes of Carbon Dioxide and Water Vapor From Leaf to Canopy Scales Dennis Baldocchi Ecosystem Science Division/ESPM UC Berkeley

2. Outline Overview Leaf-Canopy Scaling and Integration Concepts Show Tests of Such Models over Multiple Time Scales Use the CANVEG Model to Ask Ecophysiological and Micrometeorological Questions Relating to Trace Gas Fluxes

3. Classes of Model Complexity The breadth and linkage of functional components that describe the biophysics of trace gas exchange. How driving variables are defined and used as inputs to non-linear model algorithms. The geometric abstraction of the canopy.

4. ESPM 111 Ecosystem Ecology System Complexity: Interconnection of Key Ecosystem Processes

5. Basics of Ecosystem Models

6. Processes and Linkages: Roles of Time and Space Scales

7. Examples: Non-Linear Biophysical Processes Leaf Temperature Transpiration Photosynthesis Respiration

8. Why Non-linearity is Important?

9. ESPM 111 Ecosystem Ecology Geometrical Abstraction of the Canopy One-Dimensional –Big-Leaf –Dual Source, Sun-Shade –2-Layer Vegetation and soil –Multi-Layered Two-Dimensional –Dual source sunlit and shaded Vegetated vs Bare Soil Three-Dimensional –Individual Plants and Trees After Hanson et al Ecol Appl 2004

10. Canopy Representation

11. ESPM 111 Ecosystem Ecology 3-d Representation of Canopy Qi Chen and D. Baldocchi

12. Big-Leaf Model

13. 2-Layer/Dual Source Models

14. Dual Source Model: Discrete Form Whole Canopy

15. ESPM 111 Ecosystem Ecology Role of Proper Model Abstraction

16. Multi-Layer Models

17. Quantifying Sources and Sinks Biology: a(z), C i, r s Physics: r b, C(z)

18. Weight Source/Sink by Fraction of Sunlit and Shaded Leaves and Their Environment

19. ESPM 111 Ecosystem Ecology Sun Angles and the probability of beam penetration, P 0 L: Leaf area Index G: direction cosine, leaf normal vs solar zenith angle Beer’s Law

20. ESPM 129 Biometeorology20 G functions for different leaf inclination angle distributions

21. Family of G-Functions ESPM 129 Biometeorology21 Computed Y. Ryu

22. ESPM 129 Biometeorology22 Extinction coefficients with different solar zenith angles

23. ESPM 129 Biometeorology23 Leaf Angle DistributionG, direction cosineK, extinction coefficient Horizontal cos(  ) 1 Vertical 2/π sin(  ) 2 tan(  / π ) Conical cos(  ) cos(  l )cos(  ) Spherical or random0.5 1/(2 cos(  )) Heliotropic1 1/ cos(  ) Ellipsoidal***

24. ESPM 129 Biometeorology24 The extinction coefficient, k, equals the fraction of hemi-surface leaf area (A) that is projected onto the horizontal (A h ), from a particular zenith angle.

25. ESPM 129 Biometeorology25 Light interception by Inclined leaves k= A h /A; it equals 1 As A h and A equal One another k goes to zero as A h goes to zero k goes to infinity As A h goes to infinity

26. ESPM 129 Biometeorology26 ,angle between leaf normal And solar zenith , solar elevation angle k, extinction coefficient G, G-function or direction cosine Define K in terms of Sun and Leaf Inclination Angles

27. ESPM 129 Biometeorology27 Project the area of a leaf normal to the sun’s beam (Ab) onto the horizontal (Ah). Project the area of a leaf onto the area normal to the solar beam

28. ESPM 129 Biometeorology28

29. ESPM 129 Biometeorology29 Voila’

30. ESPM 111 Ecosystem Ecology Probability of beam penetration with clumped and randomly distributed foliage , clumping coef Beer’s Law

31. Random Spatial Distribution: Poisson Prob Distr. Prob of Beam Penetration Prob of Sunlit Leaf

32. Sunlit Leaf Area

33. Clumped Leaves

34. ESPM 129 Biometeorology34 L = 1.497 [P 0 ]=0.525 [ln(P 0 )]=-1.497 Ln[P 0 ]=-0.644 L*=0.644 Inverting LAI from Radiation Transfer Measurements L = 2.996 [P 0 ]=0.05 [ln(P 0 )]=-2.996 Ln[P 0 ]=-2.996 L*=2.996

35. Heterogeneous Canopies, Clumping and Radiative Transfer Youngryel Ryu, unpublished

36. Sunlit leaves are illuminated by direct and diffuse light Direct Light is Directional Diffuse Light is Isotropic and Hemispherical

37. Radiative Transfer Scheme After Norman, 1979 ESPM 228 Adv Topics Micromet & Biomet Downward Diffuse Upward Diffuse D U

38. Sources of Spatial Heterogeneity Vertical Variations in: –Leaf area index –Leaf inclination angles –Leaf Clumping –Leaf N + photosynthetic capacity –Stomatal conductance –Light, Temperature, Wind, Humidity, CO 2

39. Vertical Profiles in Leaf Area

40. Vertical Variation in Sunlight

41. Carboxylation Velocity Profiles

42. Turbulence Closure Schemes Lagrangian Eulerian –Zero Order, c(z)=constant –First Order, F=K dc/dz –Second Order and ++ (dc/dt, dw’c’/dt)

43. ESPM 228 Adv Topics Micromet & Biomet Higher Order Closure Equations and Unknowns

44. Lagrangian Near- and Far-Field Theory ESPM 228 Adv Topics Micromet & Biomet

45. Dispersion Matrix ESPM 228 AdvTopics Micromet & Biomet

46. Turbulent Mixing

47. Vertical Gradients in CO 2

48. Vertical Gradients in q and T

49. Physiology Photosynthesis Stomatal Conductance Transpiration Micrometeorology Leaf/Soil Energy Balance Radiative Transfer Lagrangian Turbulent Transfer CANOAK MODEL

50. CANOAK Schematic

51. ESPM 129 Biometeorology51 Leaf Energy Balance R: is shortwave solar energy, W m -2 L: is Longwave, terrestrial energy, W m -2  E: Latent Heat Flux Density, W m -2 H: Sensible Heat Flux Density, W m -2

52. ESPM 129 Biometeorology52 Leaf Energy Balance, Wet, Transpiring Leaf Net Radiation is balanced by the sum of Sensible and Latent Heat exchange

53. ESPM 129 Biometeorology53 Derivation 1: Leaf Energy Balance 2: Resistance Equations for H and E 3: Linearize T 4 and e s (T)

54. ESPM 129 Biometeorology54 Linearize with 1 st order Taylor’s Expansion Series

55. ESPM 129 Biometeorology55 Linearize the Saturation Vapor Pressure function

56. ESPM 228, Advanced Topics in Micromet and Biomet W c, the rate of carboxylation when ribulose bisphosphate (RuBP) is saturated W j, the carboxylation rate when RuBP regeneration is limited by electron transport. W p carboxylation rate with triose phosphate utilization

57. ESPM 228, Advanced Topics in Micromet and Biomet If W c is minimal, then: If W j is minimal, then If W p is minimal, then

58. ESPM 228, Advanced Topics in Micromet and Biomet Analytical Equation for Leaf Photosynthesis Baldocchi 1994 Tree Physiology

59. Model Parameters Leaf Area Index Photosynthetic Capacity, J max, V cmax Kinetics Basal Respiration, leaf/soil

60. ESPM 129 Biometeorology Seasonality in LAI, Deciduous Forests

61. ESPM 228, Advanced Topics in Micromet and Biomet Seasonality in V cmax Wilson et al. 2001 Tree Physiol

62. High V cmax must be Achieved in Seasonally- Droughted Ecosystems to attain Positive Carbon Balance Area under the Curves are Similar

63. ESPM 228, Advanced Topics in Micromet and Biomet Wullschleger, 1993 J Expt Bot J max and V cmax scale with one another

64. ESPM 228, Advanced Topics in Micromet and Biomet Practical Assessment for Vcmax in sites with many species and spatial variability

65. Vertical Variations in Vcmax, are they needed?

66. ESPM 228, Advanced Topics in Micromet and Biomet Temperature Response Curve E a or H a activation energy s: change in entropy H d : change in deactivation enthalpy R: Universal gas constant T: temperature, K Harley and Tenhunen; Bernacchi et al.

67. Results and Discussion

68. Model Test: Hourly to Annual Time Scale

69. Model Test: Hourly Data

70. Model Test: Daily Integration

71. Time Scales of Interannual Variability

72. Decadal Scales of Variability

73. ESPM 228 Adv Topics Micromet & Biomet

74. Interannual Variability

75. ESPM 111 Ecosystem Ecology Hansen et al, 2004 Ecol Monograph Model Validation: Who is Right and Wrong, and Why? How Good is Good Enough?

76. NEE and Growing Season Length

77. Developing Simple Model from Complex One

78. Light Use Efficiency and Net Primary Productivity NPP=  f Q p

79. LUE and Leaf Area

80. LUE and Ps Capacity

81. Emergent Processes: Impact of Leaf Clumping on Canopy Light Response Curves

82. Role of Leaf Clumping on Annual C and H 2 O Fluxes

83. Interaction between Clumping and Leaf Area

84. How Sky Conditions Affect NEE?

87. Knohl and Baldocchi, 2008 JGR Biogeosci

89. Do We Need to Consider Canopy Microclimate [C] Feedbacks on Fluxes?

90. Isotopes Infer Leaf Temperatures of Tree Leaves are Constrained, ~ 21 C Helliker and Richter 2008 Nature Leaf Temperature Growing Season Temperature

91. Leaf Temperature, Modeled with CANOAK, as a Central Tendency near 20 C Canoak Model

92. Isotopes Evaluate a Flux-Weighted Temperature Transpiration (E) Weighted Leaf Temperature

93. Leaf size, CO 2 and Temperature: why oak leaves are small in CA and large in TN

94. Physiological Capacity and Leaf Temperature: Why Low Capacity Leaves Can’t Be Sunlit::or don’t leave the potted Laurel Tree in the Sun

95. Below Canopy Fluxes

96. Below Canopy Fluxes and Canopy Structure and Function

97. Impact of Thermal Stratification

98. Impact of Litter

99. Traverse radiometer system a b g f e d c 123 Study area

100. 8/5/2007 SimulationAVIRIS 5/12/2006 SimulationAVIRIS Simulated images (RGB composite) Kobayashi et al. unpublished

101. DOY 124 DOY 194 DOY 215 Comparison of simulated and tram-measured PAR and net radiation Hour PAR (obs.) PAR (Sim.) Kobayashi et al. unpublished

102. (W m-2) Downward PAR Upward PAR Net radiation Simulated understory (1m above the ground) radiations near the tram site Kobayashi et al. unpublished

103. Net radiation Sensible heat Latent heat Comparison of top of the tower net radiation, sensible heat and latent heat Kobayashi et al. unpublished

104. Ryu et al. unpublished UpScaling GPP Regionally with Sun-Shade Coupled Energy Balance Photosynthesis Model

105. Issues How Good is Good Enough? How Much Detail Is Enough? –Where and When can we Simplify? Assessing Errors and Variability in Model Parameters Constraining Model Parameters Assessing Errors in Driving Meteorological Conditions Biases in Test Data used to validate Models

106. Conclusions Biophysical Models that Couple Aspects of Micrometeorology, Ecophysiology and Biogeochemistry Produce Accurate and Constrained Fluxes of C and Energy, across Multiple Time Scales Models can be used to Interpret Field Data –LUE is affected by LAI, Clumping, direct/diffuse radiation, Ps capacity –NEE is affected by length of growing season –Interactions between leaf size, Ps capacity and position help leaves avoid lethal temperatures –Below canopy fluxes are affected by T stratification and litter

113. CO 2 Microclimate

114. Temperature Microclimate