from the variation of solar radiation caused by the absorption
and scattering influence of aerosol particles when it reaches
the land surface through atmosphere.
MODIS
has two types of
AOD
products (MOD04) at 10 km and 3 km spatial resolutions
retrieved by the Dark Target aerosol algorithm which is based
on the relationship of the satellite received top of atmosphere
(
TOA
) reflectance over cloud-free dark targets increasing with
AOD
(Levy
et al.,
2013; Remer
et al.,
2013). However,
AOD
products at rough resolution might introduce some errors and
cannot satisfy air pollution monitoring in a small area like
Hong Kong. In this paper,
MODIS AOD
data at 500 m resolution
is produced using the simplified aerosol retrieval algorithm
(
SARA
) developed by Bilal
et al.
(2013), which directly uses
the radiance transfer model (
RTM
) for
AOD
estimation instead
of a look-up table (
LUT
). The
SARA
method uses
MODIS
level 1
product (
MOD02HKM
) to calculate the
TOA
reflectance, geoloca-
tion product (
MOD03
) to obtain the solar and view angles, level
3 product (
MOD09GA
) to retrieve the daily surface reflectance,
and Aerosol Robotic Network (
AERONET
) data to obtain the
single scattering albedo (
SSA
) and asymmetric factor (
AF
) for
the day of the retrieval. All of the raw
MODIS
data for 500 m
AOD
retrieval were downloaded from the Level-1 and At-
mosphere Archive & Distribution System (
LAADS
) (
https://
ladsweb.nascom.nasa.gov
). While the
SSA
and
AF
data from
AERONET
at two stations (Hong_Kong_Sheung: 22.483°N,
114.116°E; Hong_Kong_PolyU: 22.303°N, 114.179°E) were
obtained from
AERONET
homepage (
gov/
). The mean values of
SSA
and
AF
from 2012 to 2014 are
0.95 and 0.7, respectively.
Meteorological Data
Some studies have demonstrated that the
PM2.5
concentration
variation is influenced by meteorological factors (Elminir,
2005; Tai, 2012; Wang and Ogawa, 2015). Therefore, the
meteorological data including pressure (hPa), temperature
(°C), relative humidity (
RH
) (%), wind speed (km/h) and wind
direction (°) are added to the model to improve the prediction
accuracy. The daily meteorological data at automatic weather
stations (shown by blue triangles in Figure 1) were download-
ed from the Hong Kong Observatory (
HKO
) (
URL
:
weather.gov.hk/cis/data/awsext_e.htm
). The meteorologi-
cal predictor values at
PM2.5
stations were derived from the
interpolation of meteorological stations at 500 m grid using
Inverse Distance Weighted (
IDW
) method.
Land Use Data
The
PM2.5
concentrations are also affected by some land use
factors, such as vegetation cover and traffic density (Chen
et
al.,
2012; Guo, 2003). In this study, the normalized difference
vegetation index (
NDVI
) is selected to represent the vegetation
cover and the total length of roads in 500 m buffer is employed
to represent the traffic density in the prediction model. The
NDVI
data were acquired from
MODIS
L3/L4 product (MOD13A)
from 2012 to 2014. The mean
NDVI
values in each month were
calculated and matched with
AOD
data. Table 1 lists the mean
NDVI
of three years and road length within the buffer of 500 m
radius of
PM2.5
stations. The stations of Tai Po, Sha Tin, Tap
Mun, and Tsuen Wan have relatively high
NDVI
values while
Central/Western, Causeway Bay, Central, and Mong Kok have
large road length values indicating heavy traffic.
Methodology
GTWR
Model
Considering heterogeneous spatial effects, Brunsdon
et
al.
(1996) and Fotheringham
et al.
(2002) proposed a local
regression model called geographically weighted regression
(
GWR
), which can capture the spatial variation of parameters.
Unlike the fixed parameters in global regression model, the
parameters in
GWR
are allowed to change with locations.
Huang
et al.
(2010) extended the traditional
GWR
to geographi-
cally and temporally weighted regression (
GTWR
) by intro-
ducing temporal variability, which aims to process data with
spatio-temporal nonstationarity. It allows the relationship
between dependent and independent variables to vary over
space and time by constructing weighting matrix based on
spatio-temporal distance. By incorporating
AOD
, meteorologi-
cal and land-use variables, a
GTWR
model for
PM2.5
concentra-
tions prediction is established as following:
(
)
*
,
H
t
(
)
(
)
t P
*
,
(
)
PM
t
t AOD
t T
i
i i i
i i i
i
i i i
i
2 5
0
1
2
3
. ( )
, ,
, , *
, , *
=
(
)
+
(
)
+
(
)
+
β
µ
ν
β
µ
ν
β
µ
ν
β
µ
ν
β
µ
ν
β
µ
ν
β
µ
ν
i i i
i
i i i
i
i i i
i
i i
t R
WS
t
, ,
, *
, ,
,
+
+
+
4
5
6
i
i
i i i
i
i i i
i
i
WD
t NDVI
t RL
+
(
)
+
(
)
+
*
, , *
, , *
β
µ
ν
β
µ
ν
ε
7
8
(1)
where,
PM2.5
(
i
)
is the estimated
PM2.5
concentration of sample
i
, (
μ
i
,
ν
i
,
t
i
) denotes the space-time location,
β
0
is the intercept,
β
1
…
β
8
are the coefficients of variable
AOD
(
AOD
i
), temperature
(
T
i
), pressure (
P
i
), relative humidity (
RH
i
), wind speed (
WS
i
),
wind direction (
WD
i
),
NDVI
(
NDVI
i
), total road length in 500 m
buffer (
RL
i
) respectively,
ε
i
is the random error. The values of
β
0
…
β
8
change with space-time locations, indicating the rela-
tionship between
PM2.5
concentrations and other influencing
factors changes with space-time locations.
In order to estimate these localized coefficients, it is as-
sumed that the samples closer to point
i
have greater influ-
ence on estimation of
β
than those samples far from point
i
.
Based on this assumption, the parameter
β
of point
i
at space-
time location (
μ
i
,
ν
i
,
t
i
) can be estimated as:
W t
(
)
W t
(
)
(
)
ˆ , ,
, ,
, ,
.
β µ ν
µ
ν
µ
ν
i i i
T
i i i
T
i i i
t
X
X X
PM
=
−
1
2 5
(2)
where, X is a vector consisting of all predictors,
W
(
μ
i
,
ν
i
,
t
i
) is a
diagonal matrix whose diagonal values (
ω
ij
) are the spatio-temp-
oral weights of the observations for point
i
. The weight matrix
is calculated for each point
i
to estimate the parameter
β
.
Since the strength of relationships between locations
diminishes as separation increases, the weight
ω
ij
is decided
using the Gaussian distance decay-based function, where the
weight of observation point to estimation point decreases ac-
cording to the Gaussian curve as their distance increases:
ω
ij
ij
ST
ST
d
h
= −
exp[
(
)
]
2
2
(3)
Table 1. The land use variables for
PM2.5
stations.
PM2.5 stations
NDVI
Road length in 500 m buffer (m)
Central/Western 0.143
33991.477
Eastern
0.430
23158.388
Kwai Chung
0.350
24605.851
Kwun Tong
0.195
23094.983
Sham Shui Po 0.197
25583.889
Tai Po
0.480
21782.273
Sha Tin
0.498
21147.150
Tap Mun
0.511
3575.484
Tsuen Wan
0.453
29459.528
Tung Chung
0.271
21025.090
Yuen Lung
0.397
22255.272
Causeway Bay 0.184
33953.057
Central
0.283
35330.545
Mong Kok
0.248
35417.386
PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING
December 2018
763
