Z
= Geopotential height m
= Lapse rate 6.5 K km
-1
R
= Gas constant for dry air 287 Jkg
-1
·K g
= Acceleration of gravity 9.8 ms
-2
TS
= Surface Temperature K
o
p = Initial air pressure
Assumption: 1013.25 hPa
p
= Pressure at given point hPa b
Geopotential The use of pressure field as a vertical
coordinate gives some advantages to visualize both the quasi-horizontal pressure surfaces
and the structures of the atmosphere. Geopotential are used in synoptic scale to
analyze the movement of air masses in isobaric
coordinate. The
values of
geopotential are obtained as the potential of gravity per unit mass at a certain geometric
height above mean sea level.
34 ..
.......... gdz
d
= Geopotential m
2
s
-2
g
= Acceleration of gravity 9.8 ms
-2
z
= Geometric height m
3.3.4 Horizontal Wind Profile
The approaching methods to analyze and approximate wind movement from satellite
imagery are commonly based on the momentum equations. The orientation of a
pressure gradient is used to simulate wind movement and to evaluate wind field on each
pressure level. In isobaric coordinate, the pressure gradient is replaced by the gradient
of geopotential in assumption that neither frictions nor turbulence occurs.
35 ..
.......... ˆ
h v
k f
p Dt
h v
D
Dt h
v D
= Horizontal acceleration
p
= Gradient of geopotential
k f ˆ
= The Coriolis parameter
h V
= Horizontal wind components Due to the fact that the Coriolis force is
very weak near the equator, the component of Coriolis can be neglected so that the east-west
wind component u and north-south wind component v is expressed as:
The advective components were negligible since the satellite data used is in the form of
snapshot dt=1 second. As the result obtained is in the acceleration form ms
-2
and dt=1 second; the acceleration can be thought as the
speed of wind exactly at the time when the image was acquired. The magnitude of
horizontal wind can be found by using simple vector expression Stull 1995.
36 ..
..........
2 2
v u
V
. As for the wind trajectory:
=
37 ..........
arctan 360
90 o
u v
C o
o
o o
180
if
o U
180
C
= Angular rotation in full circle
2 360
o C
IV RESULTS AND DISCUSSION
4.1
Study Area
The area analyzed by MODIS sensor on board the Terra satellite for this study is
focusing around the mountain ranges located roughly in between 106
o
E and 107
o
E, 6.25
o
S and 6.85
o
S in the southern part of West Java, Indonesia. The main reason of choosing a
particular area surrounded by mountains is simply due to the noticeable differences of
surface temperature between the mountain ’s
peak and the area with lesser height as it provide some aids to analyze the wind
development. As the temperature at the surface heats the air above it by conduction,
the heated air expands and become less dense than the surrounding environment and so it
rises. Later on, the differences of air density cause a pressure gradient between one point
and another, forcing the air to flow.
4.2 Preprocessing data
The image acquired by MODIS sensor on board the Terra satellite is geometrically
distorted due to the wide-angle swath and the Earth’s curvature which lead to overlapping
data errors. The distortion is so visible that it may affect image interpretation; hence,
overlapping parts need to be removed so that x
t u
y t
v
Figure 12 Shuttle Radar Topography Mission SRTM data of the study area.
MODIS data can be used effectively. Geometric correction of MODIS data was
carried out using Modistool in ENVI; the process of image restoration was done by
resampling the overlapping swaths then reconstructing the scene to produce new
image on a uniform grid with equal pixel size.
Three different statistical methods were used to measure the change of pixel value in
MODIS L1B imagery after bowtie correction is applied. The Root Mean Square Error
RMSE and Mean Absolute Error MAE is used together to diagnose the variation of
errors in bowtie correction while correlation coefficient is used to measure the strength and
direction of a linear relationship between Modistool outputs and observed values. As
what is shown in Table 1, very large errors are unlikely to occur during bowtie correction
since the difference between RMSE and MAE is not great enough to indicate the presence of
very large errors. Though, there is some variation in the magnitude of the errors that
can be seen from RMSE values which are bigger than MAE. The observed values and
Modistool outputs is positively correlated as indicated by positive values in correlation
coefficient.
a b Figure 13 MODIS data RGB before a and after b bowtie correction.
4.3 Surface Temperature
Infrared radiation is commonly used to remotely determine the global coverage of
surface temperature over the Earth’s surface. However, due to its limitation, the outgoing
infrared radiation from the surface cannot penetrate through clouds to reach the
satellite’s radiometer. Therefore, a cloud-free portion of the scene is used so that land
surface temperature is not mixed with cloud- top temperature. The brightness temperature
retrieved from TIR bands 31 and 32 of TerraMODIS L1B were used to measure the
surface temperature in assumption that the entire object is a perfect blackbody.
Figure 14 Linear regression of surface temperature in TIR bands 31 and 32.
The value
of surface
temperature calculated from TIR bands 31 and 32 is varied
but relatively similar. The relationship between these two bands is linear with 0.9934
coefficient of determination as shown in Figure 14. The value of surface temperature is
varied along with topography where high temperatures are more likely to be identified
in lowlands rather than in highlands as it can be clearly seen from Figure 15. The pattern of
surface temperature will vary depends on the amount of solar radiation absorbed by the
surface. It is related with the physical characteristics of the object. High surface
temperature of an object is generally associated with high emissivity, small heat
capacity, and high thermal conductivity. The rate at which surface temperature decreases
with height is very much affected by adiabatic process. When a parcel of air rises, it moves
into higher altitudes where the surrounding air pressure is lower than on the inside of the air
parcel itself. This pressure difference then causing the air parcel to expands and pushes
on the air around it. Since the work done by air parcel does not gain any heat exchange
Figure 15 The range of surface temperature in the study area K. Table 1 Comparison of statistical approaches in bowtie correction.
Statistics Band 1
Band 3 Band 4
Band 31 Band 32
RMSE 0.00960
0.00575 0.00689
0.15539 0.12670
MAE 0.00598
0.00278 0.00370
0.11067 0.09030
Correlation Coefficient 0.93401
0.92803 0.90951
0.97410 0.97072
K
