1
Supporting Information
2
S1. Ground emissivity retrieval
3
The ground emissivity was calculated as
4
ε = VFC × Rv × εv + (1- VFC) × Rs × εs + dε ,
(A1)
5
where εv is the mean emissivity of typical closed vegetation canopy (= 0.986) [Humes
6
et al., 1994] and εs is the emissivity of non-vegetated surface (= 0.995, 0.972, and
7
0.970 for water surface, soil surface, and impervious surface, respectively). If ε > εv, ε
8
= εv. The 30-m resolution land-use map of Beijing developed by Kuang [2011; 2012b]
9
was used to determine the type of non-vegetated land surface. The relative
10
temperature, Ri = (LSTi / LST)4, where i denotes land cover type: vegetation, water,
11
soil, or impervious surface. In this study, Ri was estimated with the empirical formula
12
developed by Qin et al. [2004]:
13
Rv = 0.9332 + 0.0585×VFC (land covered by vegetation canopy)
14
Rm = 0.9886 + 0.1287×VFC (impervious surface)
15
Rs = 0.9902 + 0.1068×VFC (other non-vegetated bare surface)
16
(A2)
According to Sobrino et al. [2004], dε was estimated as
17
dε = 0.0038×VFC
18
dε = 0.0038×(1 - VFC) (VFC > 0.5)
19
dε = 0.0019
(VFC < 0.5)
(A3)
(VFC = 0.5)
1
20
S2. Atmospheric transmittance retrieval
21
Based on numeric analysis, Qin et al. [2001] developed linear equations to
22
estimate atmospheric transmittance (τ) based on water vapor content (w, g cm-2) and
23
near-surface air temperature (T, ℃):
24
25
τ=a×w+b,
where
26
a = - 0.08007, b = 0.974290, if T ≥ 35℃ and w < 1.6;
27
a = - 0.11536, b = 1.031412, if T ≥ 35℃ and w ≥ 1.6;
28
a = - 0.09611, b = 0.982007, if T ≤ 18℃ and w < 1.6; and
29
a = - 0.14142, b = 1.053710, if T ≤ 18℃ and w ≥ 1.6.
30
This equation together with its parameters was used to calculate atmospheric
31
transmittance. When 18℃ < T < 35℃, the values of parameters a and b were
32
determined with a linear interpolation between the parameter values under 18℃ and
33
35℃. An estimation of w was provided by the MODIS atmospheric water product
34
MOD05_L2 (modis-atmos.gsfc.nasa.gov/MOD05_L2).
35
S3. Retrieval of radiation fluxes
36
37
38
(A4)
The net surface radiation flux (Rn) map of Beijing was developed according to
Niemelä et al. [2001a, 2001b]
𝑅𝑛 = (1 − 𝛼) ∗ 𝑅𝑠𝑑 + 𝜀 ∗ 𝑅𝑙𝑑 − 𝜀 ∗ 𝜎 ∗ 𝐿𝑆𝑇 4 ,
(A5)
2
39
where α is the surface albedo; ε is the emissivity, σ = 5.6704 × 10−8 W/m-2K-4 is the
40
Stefan-Boiltzmann constant; Rld is the downwelling longwave radiation; and Rsd is the
41
downwelling shortwave radiation. Rsd and Rld were calculated as
42
𝑅𝑠𝑑 = Gsc × 𝑐𝑜𝑠[𝜃] × 𝜏 × 𝑑
(A6)
43
𝑅𝑙𝑑 = 1.08 × [−ln(τ)]0.265 × σ × T 4 ,
(A7)
44
where Gsc = 1,367 W/m2 is the solar constant; 𝜃 is the solar zenith angle; 𝜏 is the
45
atmospheric transmittance; 𝑑 ≈ 1 + 0.03344 × cos(2𝜋 × 365.2422 − 0.049) is the
46
Sun–Earth distance, where jday is the Julian day (= 262 for our study period)
47
[Scharmer and Greif, 2000].
48
49
𝑗𝑑𝑎𝑦
The broadband land surface albedo (𝛼) was retrieved from Landsat TM5 with the
formula developed by Liang [2000]:
50
𝛼 = 0.356𝛼1 + 0.130𝛼3 + 0.373𝛼4 + 0.085𝛼5 + 0.072𝛼7 − 0.0018,
51
where 𝛼1 , 𝛼3 , 𝛼4 , 𝛼5 , and 𝛼7 are Landsat spectral albedos. Soil heat flux was
52
calculated using Bastiaanssen’s [1998] empirical formula
53
54
𝐺=
𝐿𝑆𝑇
𝛼
× (0.0038𝛼 + 0.0074𝛼 2 ) × (1 − 0.98 × 𝑁𝐷𝑉𝐼 4 ) × 𝑅𝑛 .
(A9)
Then H (sensible heat flux) and LE (latent heat flux) can be calculated as
55
LE = (Rn – G) /(1 + β)
56
H = LE × β
57
(A8)
(A10)
where β is the Bowen ratio.
3
58
S4. Estimating the contribution of shadow cooling to the
59
observed temperature difference between the high-rise
60
residential areas and the low-rise residential area in Beijing
61
Our Landsat TM-retrieved land surface temperature (LST, °C) indicated the
62
urban high-rise residential areas (UHR) were cooler than the low-rise residential areas
63
(ULR) in Beijing. This difference in LST could be caused by the higher green space
64
(which could dissipate latent heat effectively) coverage as well as by the higher
65
shadow (which had low LST) coverage in the UHR compared to the ULR. To
66
estimate the relative contribution of shadow cooling effect, we sampled 14 pairs of
67
UHR and ULR plots across the urban area of Beijing (Figure S2; Table S1). Each plot
68
had a 300×300 m2 area. Their overall LST temperatures were retrieved from the
69
2014 LST map developed in this study. The mean LST of shaded lands (LSTshaded)
70
was set to 15.26±1.21 °C, based on synchronously measured (using infrared camera)
71
LSTs of 30 randomly selected shadows in the study area. Then the relatively
72
contribution of the shadow cooling effect on the temperature difference (LSTULR-
73
LSTUHR) was calculated as:
74
shadow effect =
75
where sunlit denotes the temperature of sunlit surfaces, which was calculated as
76
𝐿𝑆𝑇𝑠𝑢𝑛𝑙𝑖𝑡 =
77
Where 𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒𝑠ℎ𝑎𝑑𝑜𝑤 is the coverage of shadows in each 300×300 m2 plot. The
78
79
(LSTUHR −LSTUHR )−(LSTULR,sunlit −LSTUHR,sunlit )
(LSTUHR −LSTUHR )
𝐿𝑆𝑇−𝐿𝑆𝑇𝑠ℎ𝑎𝑑𝑒𝑑 ×𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒𝑠ℎ𝑎𝑑𝑜𝑤
1−𝐶𝑜𝑣𝑒𝑟𝑎𝑔𝑒𝑠ℎ𝑎𝑑𝑜𝑤
(A11)
(A12)
shadow area (Ashadow) in a plot was estimated as
𝐴𝑠ℎ𝑎𝑑𝑜𝑤 = ∑(𝐴𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 × 𝐻𝑏𝑢𝑖𝑑𝑖𝑛𝑔 × cos(𝐴𝑠 ) × (1 − 𝛼))
(A13)
4
80
Where 𝐴𝑏𝑢𝑖𝑙𝑑𝑖𝑛𝑔 is the base area of a building, 𝐻𝑏𝑢𝑖𝑑𝑖𝑛𝑔 is the building height,
81
where cos(𝐴𝑠 ) was the sun azimuth, calculated using equation A14 according to De
82
and Maas (1992).
83
cos(A𝑠 ) = (sin(𝐻𝑠 ) × sin(φ) − sin(δ))/(cos(𝐻𝑠 ) × cos(φ))
84
Whereφ was the latitude, δ was the declination of sun, and 𝐻𝑠 was the solar
85
elevation angle at the satellite passing time. α is an empirical shading coefficient
86
(Table S2) estimated based on visual analysis on the relationship between shading and
87
building size in 181 random 90×90 m2 sample plots in Beijing (Figure S3).
88
(A14)
Our analysis indicated that shadows covered about 3.90% (2.8%-5.5%) of the
89
land surface in UHR areas, and 1.48% (0.9%-2.4%) of the land surface in ULR areas
90
(Table S1). The higher shadow coverage in the UHR contributed for 5% (1%-16%) of
91
its lower LST when compared with that of the ULR.
5
92
References
93
De J S, and Maas A J (1992) Measurement and analysis of thermal images sequences of
94
nature background. SPIE 1687, 265- 273.
95
Humes, K. S., W. P. Kustas, M. S. Moran, W. D. Nichols, and M. A. Weltz (1994),
96
Variability of emissivity and surface temperature over a sparsely vegetated surface, Water
97
Resour. Res., 30(5), 1299–1310, doi:10.1029/93WR03065.
98
Liang, S. (2000), Narrowband to broadband conversions of land surface albedo I Algorithms,
99
Remote Sens. Environ., 76, 213–238, doi:10.1109/LED.2010.2072901.
100
Qin, Z., W. Li, B. Xu, Z. Chen, and J. Liu (2004), The estimation of land surface emissivity
101
for Landsat TM6 [in Chinese with English abstract], Remote Sens. Land Resour., 61, 28–41.
102
Scharmer, K., and J. Greif (2000), The European Solar Radiation Atlas: Fundamentals and
103
Maps, vol. 1, Presses des MINES, Paris.
104
Yossarian, K (2000) Ground-plane Shadows, in Mark DeLoura, eds., Game Programming
105
Gems. Charles River Media. (Web link: http://www.gameprogramminggems.com/)
106
6
List of figures
Figure S1. An eddy tower in the high-rise built-up areas was surrounded by buildings
taller than 7 stories. Photo was taken in 2007 at the Institute of Atmospheric Physics
site (S4 in Table 1 and Figure 2).
Figure S2. Distribution of the 14 pair of UHR and ULR sites for the shadow cooling
effect analysis.
Figure S3. Sampling (a) high-rise building, (b) mid-rise building, and (c) low-rise
building to estimate the shading coefficient for each land type.
7
Table S1. Estimating the contribution of shadow cooling to the land surface temperature (LST, °C) difference between the urban high-rise
residential areas (UHR) and the urban low-rise residential areas (ULR) based on observations from 14 pair of UHR and ULR sites. The mean
LST of shaded lands was set to 15.26±1.21 °C, based on measurements of 30 randomly selected shadows in the study area.
Urban high-rise residential areas (UHR)
Sampling
sties
Urban low-rise residential areas (ULR)
LST difference between UHR and ULR
shadow
coverage
LSTUHR
LSTUHR,sunlit
shadow
coverage
LSTULR
LSTULR,sunlit
LSTULR LSTUHR
LSTULR,sunlit LSTUHR,sunlit
Contribution from
shadow cooling
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
3.14%
3.19%
4.95%
5.49%
3.99%
2.79%
3.09%
4.19%
3.08%
4.07%
4.19%
4.15%
5.13%
3.19%
27.27
28.01
26.15
26.33
28.01
25.1
26.51
28.04
26.19
24.4
25.61
27.46
23.44
26.82
27.66
28.43
26.72
26.97
28.54
25.38
26.87
28.60
26.54
24.79
26.06
27.99
23.88
27.20
1.34%
1.01%
1.39%
1.49%
1.32%
0.93%
2.06%
1.33%
2.01%
2.01%
0.95%
2.37%
1.28%
1.21%
31.63
40.45
31.58
30.92
30.52
29.35
29.34
30.23
30.85
30.85
29.96
32.54
31.92
32.68
31.85
40.71
31.81
31.16
30.72
29.48
29.64
30.43
31.17
31.17
30.10
32.96
32.14
32.89
4.36
12.44
5.43
4.59
2.51
4.25
2.83
2.19
4.66
6.45
4.35
5.08
8.48
5.86
Mean
3.90%
26.38
26.83
1.48%
31.63
31.87
5.25
4.19
12.28
5.09
4.18
2.18
4.10
2.77
1.83
4.63
6.38
4.04
4.97
8.25
5.69
5.04
4%
1%
6%
9%
13%
4%
2%
16%
1%
1%
7%
2%
3%
3%
5%
8
Table S2 Empirical shading coefficient for different building types
Type
Sample number
Max height (m)
Min height (m)
Average
height (m)
Max shading
coefficient
Min shading
coefficient
Average shading
coefficient
High-rise building
61
101
24
42
9.8
9.1
9.4
Mid-rise building
64
21
12
18
8.6
7.2
7.8
Low-rise building
56
9
2.5
3.5
7.1
0.3
3.9
9
Figure S1
10
Figure S2
11
Figure S3
12