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Modeling a Microclimate within Vegetation

Modeling a Microclimate within Vegetation. Hisashi Hiraoka Academic Center for Computing and Media Studies Kyoto University. NATO ASI, KIEV 2004. 1. Outline. ◊ introduction • background • review • objective ◊ explanation of our microclimate model ◊ validation of the model

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Modeling a Microclimate within Vegetation

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  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 NATO ASI, KIEV 2004 2

  3. Introduction NATO ASI, KIEV 2004 3

  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) NATO ASI, KIEV 2004 4

  5. 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 NATO ASI, KIEV 2004 5

  6. 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 NATO ASI, KIEV 2004 6

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

  8. Outline of our microclimate model • turbulence model the present model [Table 1] • Ross’s radiation transfer model assumption 1: A scattering characteristic of a single leaf is of Lambertian type. Diffusion Approximation : surface harmonic series expanded up to the first-order • stomatal conductance model by Collatz et al. (1991) assumption 2: Vegetation is adequately supplied with water from soil. NATO ASI, KIEV 2004 8

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

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

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

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

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

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

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

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

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

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

  19. NATO ASI, KIEV 2004 The e equation : production from mean shear flow buoyancy vortex stretching molecular dissipation production from dispersive component turbulent diffusion turbulent diffusion molecular diffusion production from dispersive component production from mean flow 19

  20. The modeled terms: Modeling [Reynolds stress] [other turbulent fluxes] [the vegetation term in the e equation] dimensional analysis according to Launder production from dispersive component NATO ASI, KIEV 2004 20

  21. Table 2 The balances of heat, vapor and CO2 on leaves [a] Heat exchange between leaves and the surrounding air (1) short-wave radiations absorbed by leaves net long- wave radiation transpiration (latent heat) photosynthesis (sensible heat) sensible heat transfer between leaves and air [b] The balance of water vapor flux on leaves (2) transpiration rate [c] Net photosynthetic rate stomatal conductance (3) net photosynthetic rate NATO ASI, KIEV 2004 21

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

  23. Outline of stomatal conductance model by Collatz et al. Ball’s empirical equation (1) The value 1.6 means the ratio in molecular diffusivity of CO2 to H2O. (2) simplified Farquhar’s photosynthesis model (3) • The photosynthesis model was made on the basis of Rubisco enzyme reaction in Calvin cycle of C3 plant. • Refer to the paper by Collatz et al. (1991) for the details. NATO ASI, KIEV 2004 23

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

  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 NATO ASI, KIEV 2004 25

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

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

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

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

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

  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[m2/m3] 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 NATO ASI, KIEV 2004 31

  32. 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 [%] • CO2 mole fraction: 340 [mmol/mol] Figures: • Fig. 5 wind velocity vectors • Fig. 6 distribution of air temperature • Fig. 7 distribution of specific humidity • Fig. 8 distribution of CO2 mole fraction All figures are illustrated as graphs in (x-z) cross section through the center of the tree. NATO ASI, KIEV 2004 32

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

  34. Wind Velocity Vectors NATO ASI, KIEV 2004 34

  35. Wind Velocity Vectors NATO ASI, KIEV 2004 35

  36. Fig. 6 Distribution of air temperature NATO ASI, KIEV 2004 36

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

  38. Fig.8 Distribution of CO2 mole fraction NATO ASI, KIEV 2004 38

  39. Pressure Distribution NATO ASI, KIEV 2004 39

  40. 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. NATO ASI, KIEV 2004 40

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

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

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

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

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

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

  47. 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. NATO ASI, KIEV 2004 47

  48. Application of the model to a single tree (4) Results of computation: the others Figures: • Fig. 15 transpiration rate within foliage • Fig. 16 net CO2 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. NATO ASI, KIEV 2004 48

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

  50. Fig. 16 Net CO2 assimilation rate NATO ASI, KIEV 2004 50

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