The Influence of Tree Crowns on Effective
Urban Thermal Anisotropy
Daniel R. Dyce1,2 J.A. Voogt1
1
Department of Geography, Western University
2 Toronto Region Conservation Authority
Urban thermal anisotropy
• The three dimensional structure of cities creates large
differences in radiometric temperature with view direction:
urban effective thermal anisotropy
• Limited observations available over select urban areas,
typically with low vegetation cover; model results also
typically ignore vegetation
Google Maps: Toulouse
Observed Toulouse: Lagouarde et al. 2010
Urban Trees: An important component of
urban surface structure
Note the location and relative height of urban vegetation
Boulevard trees
Yard trees
Photo: Bill Cobb SkylineScenes.com
How do tree crowns influence urban effective
thermal anisotropy?
• How does urban effective anisotropy change as we
add trees?
Incorporating Vegetation into a SSVM
SFC T
vV ==0.100.10
Tree Biophysical Descriptors
• Crown height
• Crown radius
• Trunk height
10
5
50
0
0
40
10
30
20
20
30
10
40
50
0

Use view factor analysis and solid angle geometry to calculate the integrated
brightness temperature based on surface-sensor-sun relations (Soux et al., 2004)

Trees are modelled as cuboid shapes consisting of plane-parallel cells
Vegetation Details
Leaf Biophysical Descriptors
• Foliage area density (mL)
• Leaf angle distribution
• Clumping Index (C)
• Foliage element width (fw)

Statistical gap probabilities determine the relative proportion of foliage and
surface ‘seen’ through tree crown gaps—used to weight surface view factors
Model Framework
SURFACE REPRESENTATION
GIS or internal regular
COMPONENT SURFACE
RADIANCES
Modelled or observed
SPATIAL AND
TEMPORAL
PARAMETERS
Date, time, location
TREE CROWN
PARAMETERS
Dimensions and
biophysical
BUILT SURFACE VIEW
FACTOR COMPUTATION
Contour integration
ESTIMATE REMOTELYDETECTED RADIANCE
Component radiances within
IFOV weighted by view factor
Model input parameters
CALCULATE SUNLIT AND SHADED
FOLIAGE PROPORTIONS
Modified 5-Scale model (Chen &
LebLanc 2001)
MODIFY VIEW FACTORS FOR
SURFACES SHADED BY TREE
CROWNS USING THE CROWN
GAP PROBABILITY
CALCULATE SUNLIT AND
SHADED LEAF RADIANCE
Leaf energy budget model
Model processes or calculations
SENSOR GEOMETRICAL
PARAMETERS
CONVERT TO REMOTELY-DETECTED
BRIGHTNESS TEMPERATURE
CALCULATE RADIANCE FOR SURFACES
SHADED BY TREE CROWNS
Weighted by gap probabilities for
direct beam and diffuse solar radiation
Tree Placement Options
BL
1. Regular, repeating block array surface
 Tree crowns located on the edge of
streets along the length of buildings;
relative dimensions: HT / BH, DBLD
SW
BH
HT
DBLD
λ𝑉 = Tree crown plan fraction
trees
2. GIS surface
 Specify individual tree crown centres
8
How does the addition of vegetation change anisotropy?
C
0
330
30
42
+
300
43
60
41
N
40
90
270
39
120
240
200 m
37
 = 0.0
150
210
V
180
36
Anisotropy =
2.071
C
0
330
Unvegetated (top)
Vegetated (bottom)
polar plots and
anisotropy for Vancouver
Sunset study area
(v = 0.062)
38
42
+
300
43
30
60
41
40
90
270
39
120
240
38
37
 = 0.062
150
210
V
Anisotropy =
4.732
180
36
How does the addition of vegetation change anisotropy?
• Lower Trad for every viewing
direction.
• DT is smallest at the hot spot
location and increases
elsewhere with off-nadir
viewing angle as Tmin
decreases
• Large (58%) increase in
modelled anisotropy relative
to its absolute magnitude
despite only a small tree
canopy increase (v = 0.06)
C
DTS (1200 LMST)
0
330
30
300
5.5
5
60
4.5
270
90
4
240
120
S
150
210
3.5
3
180
Difference due to addition
of vegetation
Vancouver: Sunset Residential Area
8
TIR
SUMVEG
6
Statistic
4
2
RMSE
1.06
3.65
1.06
0
RMSES
0.41
3.57
0.49
RMSEU
0.98
0.77
0.83
MAE
0.87
3.56
0.88
b (slope)
0.95
1.05
1.00
-6
a (intercept)
1.93
1.92
0.54
-8
d (Index of
agreement)
0.99
0.88
0.97
r2
0.96
0.98
0.92
-2
-4
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
DTS (C)
Model Evaluation
Flight 6
Flight 7
Flight 8
Test against airborne observations over the
Vancouver Sunset residential area.
8
TIR
SUMVEG
6
Statistic
4
2
RMSE
1.06
3.65
1.06
0
RMSES
0.41
3.57
0.49
RMSEU
0.98
0.77
0.83
MAE
0.87
3.56
0.88
b (slope)
0.95
1.05
1.00
-6
a (intercept)
1.93
1.92
0.54
-8
d (Index of
agreement)
0.99
0.88
0.97
r2
0.96
0.98
0.92
-2
-4
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
N-S
E-W
V-N
V-S
V-E
V-W
N-E
N-W
S-E
S-W
DTS (C)
Model Evaluation
Flight 6
Flight 7
Flight 8
Test against airborne observations over the
Vancouver Sunset residential area.
How does vegetation impact anisotropy for a range
of urban geometries?
• Suite of simulations:
–
–
–
–
p 0.15 – 0.4
v 0.0, 0.06, 0.13, 0.25, and 0.32.
HT/BT = 0.5, 1, 1.5
Summer solstice and equinox simulations at subtropical
and mid-latitude locations
– 0-60° ONA, 10° azimuthal steps; 12°FOV
• Use TUF3d (Krayenhoff & Voogt 2007) to specify built
surface temperatures
• Vegetation shaded temperatures – semi-empirically
determined
Anisotropy as a function of p and v
HT/BH = 1.00 (S = 24.15)
0.4
1.50
Low absolute 
MAX
16
14
0.35
1.25
P
12
0.3
1.00
No veg; max  at moderate p
0.25
8
0.75
H/W
0.2
0.15
0
10
6
Open geometry:  increases
4
0.1

0.2
V
0.3
Anisotropy as a function of p and v
HT/BH = 1.00 (S = 24.15)
0.4
MAX
16
1.50
14
0.35
1.25
P
12
0.3
1.00
10
0.25
8
0.75
H/W
0.2
0.15
0
Critical v
6
Open geometry:  increases
4
0.1

0.2
V
0.3
Further increases in v lead to
decreases in anisotropy
Anisotropy as a function of p and v
HT/BH = 1.00 (S = 24.15)
0.4
0.35
MAX
16
1.50
Compact geometry:  slight decrease
14
1.25
P
12
0.3
1.00
10
0.25
8
0.75
H/W
0.2
6
0.15
0
4
0.1

0.2
V
0.3
Increase relative tree height
HT/BHH=T/BH
1.00 =(1.00
0.50 =(0.50
= 24.15) HT/BH H
= 24.15) HT(/BH
= 1.50
( = 24.15)
C)H=T/BH
S
S
T/BH =S1.50

0.3
1.50
0.35
Compact geometry:  slight
decrease 1.00
0.3
MAX
16
0.25
0.25
0.75
14
12
1.00
10
8
0.2
0.15
0
0.15 4
0.3 0

0.2
V
0.25
0.2
6

16
1.50
0.2
V
s = 24.15°
14
12
10
0.75
0.1
16
14
Compact
0.35 geometry:1.25 slight
increase 12
1.00
0.3
1.25
0.2
0.1
0.4
1.50
1.25
P
P
0.35
0.4
P
0.4
MAX
8
10
8
0.75
6
6
0.15 4
0.3 0
4
0.1

0.2
V
0.3
Linking results to Local Climate Zones
Images from Stewart and Oke (2012)
Summary
• Representation of tree canopy improves model performance
• Addition of a small fraction of tree canopies led to large
relative changes in anisotropy for our test site
• Anisotropy changes depend on v in conjunction with P,
HT /BH and zenith angle.
– Low building densities, anisotropy increases with v and more so for
trees higher than buildings
– High building densities, anisotropy decreases as v increases
– As tree height increases relative to building height, anisotropy increases
Simplified Summary of Effects: HT/BH= 1
BL
SW
HT
BH
DBLD
Open Geometries: anisotropy increases with v sometimes up to a
critical value; the critical value of v decreases with increases in P
Compact Geometries: maximum anisotropy
occurs in the absence of tree crowns; crown
vegetation reduces contrast in Trad ;
A critical value of v depends on P
Sensitivity of Anisotropy to Tree Biophysical Parameters
 ( C)
P = 0.14
16
P = 0.28
14
P = 0.41
12
10
8
0
0.2
0.4
0.6
Clumping Index ( C)
0.8
1
Clumping index
1.2
15
10
5
0
0.5
1
1.5
2
2.5
3
mL (m )
-1
3.5
4
4.5
5
5.5
Foliage area density
18
16
 ( C)
These tests
use
HT = 1.5 BH
 ( C)
20
14
12
10
0
0.02
0.04
0.06
0.08
0.1
fw idth (m)
0.12
0.14
0.16
0.18
Foliage element width
Model Steps
• Define the urban surface and relative location and
dimensions of tree crowns
• Compute view factors for the ‘bare’ urban surface
• Add vegetation, identify surface patches that are partially
obscured by foliage
• Calculate sunlit and shaded leaf proportions (modified 5scale model Chen & LeBlanc 2001)
• Calculate sunlit and shaded leaf temperatures (Campbell &
Norman 1998 single leaf EBM)
• Calculate Pgap and weight view factors for surfaces shaded
by tree crowns by Pgap
• Determine Trad from component radiances weighted by
view factors in the FOV
Diurnal Variation of Anisotropy with Vegetation
14
 =0.11, H /BH=1.0
Influence of
roof shading
12
v
T
v =0.21, H T/BH=1.0
v
Effective Anisotropy (C)
“high density detached
residential” (λ𝑃 = 0.176) for
several λ𝑉 and 𝐻𝑇 /𝐵𝐻.
Geometric and radiative
surface properties from
Arnfield (1982).
 =0.21, H /BH=1.5
T
NV
10
Increasing v
8
6
No tree crowns
4
2
0
NV= No tree crowns
𝐻𝑇 /𝐵𝐻= Tree to building
height ratio
June 21
4
6
8
10
12
14
Time (LST)
16
18
20
22
24