Modeling a Microclimate within Vegetation

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Modeling a Microclimate within Vegetation

• Hisashi Hiraoka
• Academic Center for Computing and Media Studies
• Kyoto University

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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
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Introduction
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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)
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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
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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
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Microclimate Model for Vegetation
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Outline of our microclimate model
turbulence model
the present model Table 1
Rosss 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.
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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.

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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.
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An example of a filtering function (1 dimension)
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Symbols
instantaneous value of
ensemble mean of
spatial mean of
time fluctuation, or deviation from ensemble
mean
deviation from spatial mean
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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.
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The vegetation terms (1) leaf-surface integral
,
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The vegetation term in the k equation (2)
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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
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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
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The equation of turbulent energy k
production from dispersive component
dissipation toward real turbulent component
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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
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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
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Table 2 The balances of heat, vapor and CO2 on
leaves
a Heat exchange between leaves and the
surrounding air
(1)
transpiration (latent heat)
photosynthesis (sensible heat)
short-wave radiations absorbed by leaves
net long- wave radiation
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
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Rosss 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
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Outline of stomatal conductance model by Collatz
et al.
Balls empirical equation
(1)
The value 1.6 means the ratio in molecular
diffusivity of CO2 to H2O.
(2)
simplified Farquhars 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.
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Verification of the Model
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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
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the model by Svensson and Haggkvist (or Yamada)
the present model
Fig. 1 Optimization of the coefficient cep in the
e equation
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Fig. 2 Measured and calculated diurnal changes
in wind velocity
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Fig. 3 Measured and calculated diurnal changes
in air temperature at the height of 1.4m
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Fig. 4 Measured and calculated diurnal changes
in net radiant flux
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Application of the Model to a Single Model Tree
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Application of the model to a single tree (1)
Outline of computation
computational domain 48m(x-axis)X30m(y-axis)X30
m(z-axis) tree 6m cubical foliage whose center
is at a point(15m, 15m, 7m) leaf area
density 1m2/m3 distribution
function of foliage area orientation uniform
leaf transmissivity 0.1(PAR), 0.5(NIR)
lt- short wave reflectivity
0.1(PAR), 0.4(NIR) lt- short wave
emissivity 0.9
lt- long wave sun the solar altitude (h) 60
degree the atmospheric
transmittance (P) 0.8 the diffused solar
radiation lt- Berlarges
equation PAR conversion factor at h60
0.425(direct), 0.7(diffuse) lt- Ross the
downward atmospheric radiation lt-
Brunts equation calculation method FDM, SMAC,
QUICK, Adams-Bashforth
lt- Bouguers equation
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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.
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m/s
Fig. 5 Wind velocity vectors
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Wind Velocity Vectors
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Wind Velocity Vectors
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Fig. 6 Distribution of air temperature
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Fig. 7 Distribution of specific humidity
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Fig.8 Distribution of CO2 mole fraction
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Pressure Distribution
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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.
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Fig. 9 PAR absorbed by leaves
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Fig. 10 NIR absorbed by leaves
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Fig. 11 Net long wave radiation
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Fig. 12 Distribution of latent heat
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Fig. 13 Distribution of sensible heat
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Fig. 14 Distribution of sensible heat of water
vapor due to transpiration
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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.
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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.
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Fig. 15 Transpiration rate within foliage
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Fig. 16 Net CO2 assimilation rate
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Fig. 17 Distribution of stomatal conductance
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Fig. 18 Distribution of leaf temperature
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Summary
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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.
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