1. Modeling a Microclimate within Vegetation Hisashi Hiraoka Academic Center for Computing and Media Studies Kyoto University NATO ASI, KIEV 2004 1

2. Outline ◊ introduction background review objective ◊ explanation of our microclimate model ◊ validation of the model ◊ application of the model to a single tree the environment around the tree the heat budget within the tree 2

3. Introduction 3 NATO ASI, KIEV 2004

4. Background of this study numerically investigatng the effect of vegetation on a heat load of a building, thermal comfort, an urban thermal environment and the like. trees beside a house (heat load) roof garden (heat load, thermal comfort) garden (microclimate, thermal comfort) street trees (thermal comfort) park (microclimate, thermal comfort) wooded area in a city (urban thermal environment) woods (effect on urban thermal environment) forest (effect on urban thermal environment) 4

5. NATO ASI, KIEV 2004 Review of researches Waggoner and Reifsnyder (1968) Lemon et al. (1971) Goudriaan (1977) Norman (1979) Horie (1981) Meyers and Paw U (1987) Naot and Mahrer (1989) Kanda and Hino (1990) Necessary sub-models * turbulence model * radiation transfer model * stomatal conductance model * model for water uptake of root * model for heat and water diffusion in soil ◊ soil respiration model ◊ root respiration model 5

6. NATO ASI, KIEV 2004 Problems of the above models These models are not completely applicable to 3dim. Short wave radiation is not separated into PAR and the other. Objective of this study Proposing a model for simulating a microclimate within three- dimensional vegetation Examining the validity of the model by comparing with measurement Applying the model to a single model tree and investigating the microclimate produced by the tree 6

7. Microclimate Model for Vegetation 7 NATO ASI, KIEV 2004

8. Outline of our microclimate model turbulence modelthe present model [Table 1] Ross’s radiation transfer model assumption 1: A scattering characteristic of a single leaf is of Lambertian type. Diffusion Approximation stomatal conductance model by Collatz et al. (1991) assumption 2: Vegetation is adequately supplied with water from soil. 8 : surface harmonic series expanded up to the first-order

9. NATO ASI, KIEV 2004 Formulation of turbulence model (1)Basic equations are first ensemble-averaged and then spatially averaged. (2) The turbulence equations for dispersive component and real turbulent component are derived from the basic equation and the averaged equations. (3) These two kinds of equations are combined into the turbulence equation. (4) And the unknown quantities are modeled by the semi-empirical closure technique. 9

10. NATO ASI, KIEV 2004 Definition of spatial average: [formulas] (1) (2), where : the averaged volume : the fluid volume in : the i-th component of the velocity on leaf surface : filter function 10 G =1 in this study.

11. NATO ASI, KIEV 2004 An example of a filtering function (1 dimension) 11

12. NATO ASI, KIEV 2004 Symbols : instantaneous value of : ensemble mean of : spatial mean of : time fluctuation, or deviation from ensemble mean : deviation from spatial mean 12

13. NATO ASI, KIEV 2004 Table 1 Turbulence model for moist air within vegetation (1)(2) (3) (4)(5) (6) (7) : represents the vegetation terms which are originally expressed as leaf-surface integral except that in the  equation. : represents the modeled terms. 13 These terms are derived analytically from the basic equations by averaging spatially. drag force transpiration photosynthesis sensible heat heat transfer due to photosynthesis photosynthesis drag force

14. NATO ASI, KIEV 2004 The vegetation terms (1): leaf-surface integral, 14

15. NATO ASI, KIEV 2004 The vegetation term in the k equation (2): 15

16. The equation of k’: production from mean shear flow production from dispersive component viscous dissipation buoyancy molecular diffusion turbulent diffusionsurface integral term 16 NATO ASI, KIEV 2004 : Real turbulent component

17. The equation of k”: production from mean shear flow dissipation toward real turbulent component viscous dissipationbuoyancy production by drag force molecular diffusion turbulent diffusion 17 NATO ASI, KIEV 2004 : dispersive component of turbulent energy

18. The equation of turbulent energy k: 18 NATO ASI, KIEV 2004 production from dispersive component dissipation toward real turbulent component

19. The  equation : 19 production from mean shear flowbuoyancy production from dispersive component vortex stretchingmolecular dissipation turbulent diffusion molecular diffusion production from mean flow production from dispersive component NATO ASI, KIEV 2004

20. The modeled terms: Modeling [Reynolds stress] [other turbulent fluxes] [the vegetation term in the  equation] 20 dimensional analysis according to Launder production from dispersive component

21. NATO ASI, KIEV 2004 Table 2 The balances of heat, vapor and CO 2 on leaves [a] Heat exchange between leaves and the surrounding air (1) [b] The balance of water vapor flux on leaves (2) [c] Net photosynthetic rate (3) 21 transpiration (latent heat) photosynthesis (sensible heat) sensible heat transfer between leaves and air short-wave radiations absorbed by leaves net long- wave radiation transpiration rate stomatal conductance net photosynthetic rate

22. NATO ASI, KIEV 2004 Ross’s radiation transfer models (Short wave radiation) (Long wave radiation) [symbols] : radiance, : distribution function of foliage area orientation : scattering function of leaf,: emissivity of leaf : leaf area density,: leaf temperature : direction of radiance : direction of leaf surface,: inner product 22

23. NATO ASI, KIEV 2004 Outline of stomatal conductance model by Collatz et al. (1) Ball’s empirical equation (2) The value 1.6 means the ratio in molecular diffusivity of CO 2 to H 2 O. (3) simplified Farquhar’s photosynthesis model The photosynthesis model was made on the basis of Rubisco enzyme reaction in Calvin cycle of C 3 plant. Refer to the paper by Collatz et al. (1991) for the details. 23

24. Verification of the Model 24 NATO ASI, KIEV 2004

25. Verification of the present model The measurement by Naot and Mahrer (1989) plant: cotton field (1.4m high, 1-dimension) location: Gilgal (25Km north of the Dead Sea), Israel period: August 18 - 20, 1987 (3 days) weather: fair during the period Comparison with the measurement physical quantities compared with the measurement (1) wind velocity at the height of 1.4m, and 2.5m (2) air temperature at the height of 1.4m (3) net radiant flux 25

26. NATO ASI, KIEV 2004 Fig. 1 Optimization of the coefficient c  p in the  equation the model by Svensson and Haggkvist (or Yamada): the present model: 26

27. NATO ASI, KIEV 2004 Fig. 2 Measured and calculated diurnal changes in wind velocity 27

28. NATO ASI, KIEV 2004 Fig. 3 Measured and calculated diurnal changes in air temperature at the height of 1.4m 28

29. NATO ASI, KIEV 2004 Fig. 4 Measured and calculated diurnal changes in net radiant flux 29

30. Application of the Model to a Single Model Tree 30 NATO ASI, KIEV 2004

31. Application of the model to a single tree (1) Outline of computation computational domain: 48m(x-axis)X30m(y-axis)X30m(z-axis) tree: 6m cubical foliage whose center is at a point(15m, 15m, 7m) leaf area density: 1[m 2 /m 3 ] distribution function of foliage area orientation: uniform leaf transmissivity: 0.1(PAR), 0.5(NIR) <- short wave reflectivity: 0.1(PAR), 0.4(NIR) <- short wave emissivity: 0.9 <- long wave sun: the solar altitude (h): 60 [degree] the atmospheric transmittance (P): 0.8 the diffused solar radiation: <- Berlarge’s equation PAR conversion factor at h=60: 0.425(direct), 0.7(diffuse) <- Ross the downward atmospheric radiation <- Brunt’s equation calculation method: FDM, SMAC, QUICK, Adams-Bashforth <- Bouguer’s equation 31

32. NATO ASI, KIEV 2004 Application of the model to a single tree (2) Results of computation: the microclimate produced by the tree the atmospheric conditions: wind velocity: 2 [m/s] air temperature: 20 [C] relative humidity: 40 [%] CO 2 mole fraction: 340 [  mol/mol] Figures: Fig. 5 wind velocity vectors Fig. 6 distribution of air temperature Fig. 7 distribution of specific humidity Fig. 8 distribution of CO 2 mole fraction All figures are illustrated as graphs in (x-z) cross section through the center of the tree. 32

33. NATO ASI, KIEV 2004 Fig. 5 Wind velocity vectors [m/s] 33

34. Wind Velocity Vectors 34 NATO ASI, KIEV 2004

35. Wind Velocity Vectors 35 NATO ASI, KIEV 2004

36. Fig. 6 Distribution of air temperature 36

37. NATO ASI, KIEV 2004 Fig. 7 Distribution of specific humidity 37

38. NATO ASI, KIEV 2004 Fig.8 Distribution of CO 2 mole fraction 38

39. Pressure Distribution NATO ASI, KIEV 2004 39

40. NATO ASI, KIEV 2004 Application of the model to a single tree (3-1) Results of computation: the heat budget within foliage Figures: Fig. 9 PAR absorbed by leaves Fig. 10 NIR absorbed by leaves Fig. 11 net long wave radiation Fig. 12 distribution of latent heat Fig. 13 distribution of sensible heat Fig. 14 distribution of sensible heat of water vapor due to transpiration All figures are illustrated as graphs in (x-z) cross section through the center of the tree. 40

41. NATO ASI, KIEV 2004 Fig. 9 PAR absorbed by leaves 41

42. NATO ASI, KIEV 2004 Fig. 10 NIR absorbed by leaves 42

43. NATO ASI, KIEV 2004 Fig. 11 Net long wave radiation 43

44. NATO ASI, KIEV 2004 Fig. 12 Distribution of latent heat 44

45. NATO ASI, KIEV 2004 Fig. 13 Distribution of sensible heat 45

46. NATO ASI, KIEV 2004 Fig. 14 Distribution of sensible heat of water vapor due to transpiration 46

47. NATO ASI, KIEV 2004 Application of the model to a single tree (3-2) Summary of the heat budget within foliage A great deal of the short wave radiation absorbed by leaves is released through latent heat due to transpiration. Long wave radiation is not negligible. Air sensible heat (that is, heat convection term) is much less than latent heat. Sensible heat of water vapor due to transpiration is negligible. 47

48. NATO ASI, KIEV 2004 Application of the model to a single tree (4) Results of computation: the others Figures: Fig. 15 transpiration rate within foliage Fig. 16 net CO 2 assimilation rate Fig. 17 stomatal conductance Fig. 18 leaf temperature These figures are illustrated as graphs in a (x-z) cross section through the center of the tree. 48

49. NATO ASI, KIEV 2004 Fig. 15 Transpiration rate within foliage 49

50. NATO ASI, KIEV 2004 Fig. 16 Net CO 2 assimilation rate 50

51. NATO ASI, KIEV 2004 Fig. 17 Distribution of stomatal conductance 51

52. NATO ASI, KIEV 2004 Fig. 18 Distribution of leaf temperature 52

53. Summary 53 NATO ASI, KIEV 2004

54. Summary 1] The model for simulating a microclimate produced by three-dimensional vegetation was proposed. 2] The model was examined in comparison with the measurement. The results from the model agreed with the measurement. 3] The model was applied to a single model tree. And the heat budget within foliage was investigated. The results from the computation were: ◊ A great deal of the short wave radiation absorbed by leaves was released through latent heat due to transpiration. ◊ Long wave radiation was not negligible. ◊ Air sensible heat was much less than latent heat. ◊ Sensible heat of water vapor due to transpiration was negligible. This fact suggests that the results from a turbulence model for dry air are almost equal to those from the present model. 54