at the same height. But, since the value of gravity vary at different places; the altitude of
geopotential surface would also be different. The geopotential height is defined as
24 ..
.......... 1
z
gdz g
g z
Z
The concept of geopotential height is useful for approximating geometric height of
a constant-pressure surface in the atmosphere. The thickness of two surface levels can be
easily found by calculating the difference between geopotential heights.
c. Isobaric Coordinate System
For many applications associated with the governing dynamics of the atmospheric
motions, it is very common to transform the equations of motion from height Cartesian
coordinates x, y, z to isobaric coordinates x, y, p. As what it shown in hydrostatic
equation, pressure is related to geometric height by a single-valued monotonic function.
Pressure decreases monotonically with height that its surfaces never intersect; hence instead
of using height, pressure can be used as an alternative coordinate system.
Figure 10 Slope of pressure surfaces in the x, z plane.
As illustrated in Figure 10, the pressure difference between two lines of AB and BC
are particularly the same. Judging from the similarities it can be stated that:
p x
p z
z z
z z
p p
p x
x x
x p
p p
1 1
1 1
p x
z
x z
z p
x p
The subscripts are used to indicate variables which are being held constant during
differentiation. Taking the limits of
x
,
z
→ 0
p x
z
x z
z p
x p
and by using the hydrostatic balance equation to substitute the variables, it can be obtained
that
25 ........
1 p
x p
x z
g z
x p
Based on this outcome, the horizontal component of pressure gradient force can be
rewritten as
p x
x p
m x
F
1
p y
y p
m y
F
1
Given that pressure acts as the vertical
coordinate, it appears that density is no longer required for computing the pressure gradient
force; which is a great advantage as it simplifies
the equation
and indirectly
facilitates the observation. Thus, in isobaric coordinate system, the horizontal pressure
gradient force on a surface of constant pressure is determined by the gradient of
geopotential.
2.2.4 Horizontal Momentum Equations
In general, air motion comes from a balanced flow which is profoundly affected by
the the force of pressure gradient, Coriolis force and friction viscous force. For large-
scale movement of air in the atmosphere, viscosity is sufficiently small that frictions
near the Earth’s surface could be neglected. Therefore, the horizontal momentum equation
in height coordinates is given in the vectorial form as
26 ..
..........
1 ˆ
p h
h v
k f
Dt h
v D
Where
j v
i u
h v
is a horizontal velocity vector. The condition where the
forces acting on a parcel of air is in equilibrium with each other is considered as
Figure 11Research flowchart.
an idealization of atmospheric motion. In the form of isobaric coordinate, the horizontal
pressure gradient force can be transformed with the function of geopotential so that the
equation becomes
27 ..
..........
ˆ
p
h v
k f
Dt h
v D
It can be seen that the gradient of geopotential implicit the same horizontal wind
speed at all heights in the atmosphere whereas in height coordinates the velocity of
horizontal wind depends on the rate of pressure gradient which varies directly with
changes in air density.
III METHODOLOGY 3.1
Location and Time
The study
was conducted
in the
Laboratory of Meteorology and Atmospheric Pollution,
Department of Geophysics and Meteorology, Bogor Agricultural University and
in the Division of Climate Modelling,
National Institute of Aeronautics and Space LAPAN
Bandung from February until May 2011.
3.2 Tools and Materials
The sofwares used in this study are listed as follows:
ENVI 4.5, ER Mapper 7.1, Global Mapper v12, Ferret v6.7, ArcGIS 9.3,
Matlab R2010b,
Notepad++ 5.9,
Microsoft Office 2007 The materials consist of three main sources of
data: a. MODIS Terra level 1B L1B data;
covering Bogor and its surroundings. Data acquisition date: October 1,
2006. Band used: Thermal Infrared Bands TIR 31
10.780 m - 11.280 m and 32 11.770 m - 12.270
m. Spatial resolution: 1 km. http:ladsweb.nascom.nasa.govdata
search.html b. DEM data Digital Elevation Model
with 90 x 90 m spatial resolution http:srtm.csi.cgiar.org
3.3 Data Processing
The approaching method in this study is derived from the momentum equations based
on Newton’s second law of motion which
applied to TerraMODIS L1B data set. Generally, the steps taken can be seen in
Figure 11.
3.3.1 Bowtie Correction
The MODIS L1B data set contains calibrated
and geolocated
at-aperture radiances for 36 discrete bands covering the
part from 0.4
m to 14.4 m of
electromagnetic spectrum. These data were generated from MODIS level 1A scans of raw
radiance MOD01. Although the level 1B data have been calibrated and geolocated, it
needs to be corrected due to distortion caused by the characteristics of MODIS sensor and
the Earth’s curvature; known as the Bowtie effect. The elimination of bowtie effect was
done with Modistool in ENVI.
