Utilization of terra/MODIS L1B data for analysis of horizontal wind profile in the troposphere

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GILANG ARIA SETA

DEPARTMENT OF GEOPHYSICS AND METEOROLOGY

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

INSTITUT PERTANIAN BOGOR

2012

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ABSTRACT

GILANG ARIA SETA. Utilization of Terra/MODIS L1B Data for Analysis of Horizontal Wind Profile in the Troposphere. Under the guidance of IDUNG RISDIYANTO, S.Si, M.Sc and Ir. HALIMURRAHMAN, M.T.

This study was concerned with horizontal wind derived from data collected with the Moderate-resolution Imaging Spectroradiometer (MODIS) on board the NASA’s Earth Observation System (EOS)-Terra satellite. The aim of this study is to develop a method for the estimation of horizontal wind movement in the troposphere based on Navier-Stokes equation. The method was applied to a calibrated and geolocated Terra/MODIS L1B 1 km data set. The data inputs to estimate surface temperature are retrieved from TIR (Thermal Infrared) bands 31 (10.780 m to 11.280 m) and 32 (11.770 m to 12.270 m). The obtained surface temperatures were later used to approximate geopotential height on a constant-pressure surface by using the modified Poisson equation. The main assumptions used are the hydrostatic equilibrium, ideal gas law, constant lapse rate and constant acceleration of gravity. Based on the distribution of geopotential height, the pressure gradient force is measured by the gradient of geopotential on an isobaric coordinate to present the horizontal wind profile. For certain topographic areas especially in the mountain ranges, there was a disadvantage of using pressure as a vertical coordinate which lead to inaccuracy. In spite of that, Terra/MODIS L1B data with 1 km spatial resolution can be used to estimate the horizontal wind movement in the troposphere.

Keyword: MODIS, Terra, Horizontal Wind, Equation of Motion, Surface Temperature, Geopotential Height

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GILANG ARIA SETA

Thesis

As one of the requirements to obtain a Bachelor's degree in science at the Faculty of Mathematics and Natural Sciences

DEPARTMENT OF GEOPHYSICS AND METEOROLOGY

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

INSTITUT PERTANIAN BOGOR

2012

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Title : Utilization of Terra/MODIS L1B Data for Analysis of Horizontal Wind Profile in the Troposphere.

Name : Gilang Aria Seta

Student ID : G24063219

Approved by

First Advisor Second Advisor

Idung Risdiyanto, S.Si, M.Sc Ir. Halimurrahman, M.T.

NIP. 19730823 199802 1 001 NIP. 19670503 011991 1 001

The Head Department of Geophysics and Meteorology Faculty of Mathematics and Natural Sciences

Institut Pertanian Bogor

Dr. Ir. Rini Hidayati, MS NIP. 19600305 198703 2 002

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This bachelor thesis is based upon studies conducted during the time in the Department of Geophysics and Meteorology, Faculty of Mathematics and Natural Sciences, Institut Pertanian Bogor, Indonesia. It’s been a great run as I’m truly blessed and deeply grateful for having had the opportunity to meet so many generous people who willingly shared their experience, knowledge and skills. The work presented in this thesis is dedicated to all of those people. Had it not been for their help and guidance, this thesis would have remained a dream. Thank you, I’m greatly indebted to each one of you that words fail me in trying to express it adequately.

First I would like to express my sincere gratitude to my leading advisors and mentors, Idung Risdiyanto and Halimurrahman for their guidance, patience, and steadfast encouragement to complete this thesis. Sonni Setiawan, Ahmad Faqih and Bregas Budianto for the discussion on the methods and also for all of the suggestions and constructive criticism. My labmate Diana Rumondang for helping me on how to handle MODIS extracted data. My good fellows, Sandro W. Lubis, Andi S. Muttaqin and Faiz R. Fajary for so many satisfying explanations on a variety of questions about the concept of dynamics and scripting language. Diki Septerian S. and Gema Nusantara for giving me detail and clear explanations about the concept of remote sensing and satellite imagery. Sigit D. Sasmito, Nizar Najmusakib, Uji Astrono P, Yunus Bahar, Getsa F. Salmon and also Yanto Ardiyanto for the insightful GIS lessons and tutors. Endy, who has been so kind as to provide me with his convenience linux derivative, ILOS. Ardhan, Jay and Gito Immanuel for their assistance with troubleshooting in linux, and also Raidinal Allifahrana for taking the time to read a draft version of this thesis and also for leaving comments and feedback. All of my friends and colleagues for supporting me and also everyone at the National Institute of Aeronautics and Space (LAPAN) and the Center for Climate Risk and Opportunity Management in South East Asia and Pacific (CCROM-SEAP) for the hospitality during my visitation.

A million thanks to Mom and Dad also my brother for all your blessings and loving supports, words does not seem sufficient and fail me once again in trying to describe how much I love you all. Last but not the least, all praise be to Allah the Almighty with His compassion and mercifulness for answering my prayers and giving me the strength, knowledge, ability, and courage to plod and struggle to accomplish this final task. The final word in this dedication goes to you. Yes, you, the one reading this. I don’t know who you are but I do hope that you will find some useful information inside this piece of work. For life is time and time is all there is. Live your life for as you think you shall become!

Bogor, November 2011

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ABOUT THE AUTHOR

Gilang Aria Seta was born in Surabaya on April 10th, 1988. After graduating from his senior highschool in 2006 he passed the selection into Institut Pertanian Bogor through SPMB (Seleksi Penerimaan Mahasiswa Baru). A year later, he entered the Faculty of Mathematics and Natural Sciences, studying in the Department of Geophysics and Meteorology. The major taken was Applied Meterorology and the minor was Information System. During his time of study, he was involved and active in various activities as a member of Himagreto, a student council of agricultural meteorology. He was also a teaching assistant for the course of Satellite Meteorology and a freelancer in software programming and GIS related jobs.

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TABLE OF CONTENTS

Page

LIST OF TABLES ... i

LIST OF FIGURES ... ii

LIST OF APPENDICES ... iii

I. INTRODUCTION 1.1 Background ... 1

1.2 Objective ... 1

II. LITERATURE REVIEW 2.1 Remote Sensing ... 1

2.1.1 Electromagnetic Principles ... 1

2.1.2 Blackbody Radiation ... 2

2.1.3 Bowtie Effect ... 3

2.1.4 Surface Temperature... 4

2.2 Dynamic Processes in the Atmosphere ... 5

2.2.1 Fundamental Forces ... 5

2.2.2 Forces in a Rotating Reference Frame ... 7

2.2.3 Structure of the Static Atmosphere ... 8

2.2.4 Horizontal Momentum Equations ... 10

III. METHODOLOGY 3.1 Location and Time ... 11

3.2 Tools and Materials ... 11

3.3 Data Processing ... 11

3.3.1 Bowtie Correction ... 11

3.3.2 Estimation of Surface Temperature... 12

3.3.3 Geopotential ... 12

3.3.4 Horizontal Wind Profile ... 13

IV. RESULTS AND DISCUSSION 4.1 Study Area ... 13

4.2 Preprocessing Data ... 13

4.3 Surface Temperature ... 15

4.4 Geopotential and Geopotential Height ... 16

4.5 Horizontal Wind Profile ... 17

V. CONCLUSIONS ... 21

REFERENCES ... 21

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LIST OF TABLES

Page

1. Comparison of statistical approaches in bowtie correction ... 15

2. Mean and standard deviation of geopotential height values ... 16

3. Decomposition of horizontal wind vectors into zonal and meridional components ... 19

4. Direction and acceleration profile of horizontal wind ... 20

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LIST OF FIGURES

Page

1. Electric (E) and magnetic (M) fields propagation at the speed of light (c) ... 2

2. Regions of electromagnetic spectrum ... 2

3. Emitted intensity of blackbody radiation and maximum wavelength at various temperatures ... 3

4. An example of bowtie effect in MODIS data ... 4

5. Morphology of the MODIS bowtie effect ... 4

6. Thexcomponent of the pressure gradient force acting on a infinitesimal parcel of air ... 5

7. An air parcel under the influence of Earth’s gravitational force ... 6

8. Vertical shearing stress on a volume of fluid element in thexdirection ... 7

9. Balance of vertical forces of the atmosphere in the state of hydrostatic balance ... 9

10. Slope of pressure surfaces in the x, z plane ... 10

11. Research flowchart ... 11

12. Shuttle Radar Topography Mission (SRTM) data of the study area ... 14

13. MODIS data (RGB) before (a) and after (b) bowtie correction ... 14

14. Linear regression of surface temperature in TIR bands 31 and 32 ... 15

15. The range of surface temperature in the study area ... 15

16. Cross section of geopotential height ... 16

17. Geopotential surface (m2s-2) in the level of 250 hPa (a) and 800 hPa (b) ... 17

18. The acceleration of zonal wind (m2s-2) in the level of 250 hPa (a) and 800 hPa (b) ... 18

19. The acceleration of meridional wind (m2s-2) in the level of 250 hPa (a) and 800 hPa (b) ... 19

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APPENDICES

Page

1. Derivation of geopotential height ... 24

2. Inverting Planck function to surface temperature ... 25

3. Example of ferret scripts (200 hPa) ... 25

4. Matlab resampling script ... 27

5. Terra/MODIS Specifications ... 27

6. True color image of Terra/MODIS (R, G, B: bands 1, 4, and 3) observed on October 1, 2006 (MOD021KM.A2006274.0315.005.2010183090822) ... 28

7. Distribution of geopotential height retrieved from NCEP/NCAR data ... 29

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I. INTRODUCTION 1.1Background

Wind forecasting in terms of either speed or direction is essential since the unevenly dispersed thermal energy on the Earth’s surface are distributed by winds. The winds play an important role in atmospheric stability (Kara et al. 2008) and influence surface heat and momentum fluxes over the ocean (Large and Pond 1981). It also correlates with the pattern of cloud movement which indirectly affects global distribution of precipitation and is also the primary factor in spreading pollutant in the atmosphere. Thus, it is noteworthy to measure the wind profile as it is the basic element of atmospheric circulation which influences other variables in the atmospheric system.

Various methods and techniques have been developed to provide continuous measurements of the condition in the atmosphere. Although the weather station will provide more detailed and accurate information about conditions within the atmosphere; in situ measurement is limited to a particular location and leaves some information gaps both spatially and temporarily. Therefore, alternative or complementary data source is needed to fill those gaps as well as to generate a more complete portrait of wind profile in the atmosphere.

The use of satellite-based technology at various spatial and temporal scales has proven to be useful and effective for observing the processes occurring both on the Earth’s surface and the atmosphere. The advancement of remote sensing instruments and techniques has enabled high-resolution imagery which provides global coverage of spectral reflectance and emmitance of radiation at frequent intervals per day that can be used for reliable wind measurement. Global ocean surface winds measurement using WindSat (Smith et al. 2006), correlation-based interpolation of NSCAT wind data (Polito et al. 2000), automated oceanic eddies detection (Dong et al. 2011), tropical instability waves and tropical instability vortices observation (Willet et al. 2006) and weather monitoring model (Risdiyanto 2001) are some past research associated with wind profile estimation based on remotely sensed data.

Different approaching methods to estimate wind profile were used in this study. The

horizontal wind vectors are derived from the momentum equations based on Newton’s second law of motion. Extracted satellite data from the Moderate-resolution Imaging Spectroradiometer (MODIS) were then utilized in calculating geopotential and pressure gradient force to describe the velocity and direction of air in motion at various heights in the troposphere.

1.2Objective

The purpose of this study is to develop a methodology in predicting horizontal wind movement and its meridional and zonal components using remotely sensed data. Terra/MODIS L1B product was used and the spatial characteristics of the vector fields were generated from the TIR (Thermal Infrared) bands data set.

II. LITERATURE REVIEW 2.1 Remote Sensing

According to Lillesand and Kiefer (1994), “Remote sensing is the science and art of obtaining information about an object, area, or phenomenon through the analysis of data acquired by a device that is not in contact with the object, area, or phenomenon under investigation.” Remote sensing techniques are based on the detection and measurement of electromagnetic radiation that is emitted or reflected from distance objects as wavelength to identify the physical properties of the objects detected. There are two types of sensors in remote sensing: passive sensors and active sensors. Passive sensors detect natural radiation that is being emitted or reflected by the objects. Reflected sunlight is the most common source of radiation measured by passive sensors whereas active sensors provide their own energy source and emits radiation to scan objects. These sensors are often mounted on satellites, making it possible to collect data from large, inaccessible, and even dangerous areas.

2.1.1 Electromagnetic Principles

The energy emitted or reflected by the object which recorded by satellite sensor is an electromagnetic radiation that passes through space at the speed of light in the form of sinusoidal waves. Electromagnetic radiation has electric and magnetic fields which oscillate in perpendicular phase at right angles to each other and the combined wave moves

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in a direction to both of the fields as shown in Figure 1. In wave model, the electromagnetic radiation is commonly associated with wavelength and frequency, expressed mathematically as:

) 1 ( .. ...  c f 

Where: f Wave’s frequency (Hz)

c



Speed of light (3 × 108 ms-1)



 Wavelength (m)

Figure 1 Electric (E) and magnetic (M) fields propagation at the speed of light (c) (CCRS 2003).

Based on quantum mechanics theory, electromagnetic radiation is described as a set of photons. Each photon contains a certain amount of energy that causes it to behave like a wave or a particle known as wave-particle duality. The energy of a photon is measured by using Planck-Einstein equation.

) 2 ( .. ... f h E Where: E Energy (J)



h Planck’s constant (6.626 × 10-34 Js-1)



f Wave’s frequency (Hz)

It can be concluded from equation (2) that the increase of photon energy is directly proportional to wave’s frequency; and the frequency itself is inversely proportional to wavelength (equation(1)). Given the relationship between wavelength and frequency, the energy of a photon can also be expressed in the equation where the energy of a photon is inversely proportional to wavelength.

) 3 ( .. ... 

c h E

The amount of energy contains in a photon defines the type of electromagnetic radiation. Based on its wavelength, frequency, and the amount of energy it carries, electromagnetic radiation is classified into the electromagnetic spectrum which consists of radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, x rays, and gamma rays.

Figure 2 Regions of electromagnetic spectrum

(http://science-edu.larc.nasa.gov).

2.1.2 Blackbody Radiation

Every substance that has temperature above absolute zero (0 K) emits electromagnetic radiation. The emitted radiation represents energy conversion from thermal energy into electromagnetic energy, also known as thermal radiation. Moreover, radiating substance also absorbs electromagnetic radiation to maintain its thermal equilibrium. If it absorbs and emits radiation at all wavelength, a substance is classified as a blackbody.

The curves shown in Figure 3 represent the emitted radiation of a blackbody at various temperatures; it shifts toward shorter wavelength and greater radiation intensity as temperature increases. Mathematically, the curve shape is given by Planck’s law of blackbody radiation.

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Figure 3 Emitted intensity of blackbody radiation and maximum wavelength at various temperatures (Salby 1996).





...(4) 1

/ 1 5

2 2

 

kT hc e hc B

 



Where: B_ = Blackbody radiation (Wm-2)

h = Planck’s constant (6.626 × 10-34 Js-1)

c = Speed of light (3 × 108 ms-1)  = Wavelength (m)

k = Boltzmann constant (1.380 ×10−23

JK-1)

T_{= Absolute Temperature (K)}

It follows that the peak wavelength of maximum radiation of a blackbody is inversely proportional to its absolute temperature when expressed as a function of a wavelength as stated in Wien’s displacement law.

) 5 ( .. ... max

T b  

Where: max₌Peak wavelength (m)

b ₌ Wien’s displacement

constant (2.897 × 10-3mK)

T

_{= Absolute Temperature (K)} The standard amount of radiaton emmited by a blackbody is derived by integrating the Planck function over the entire wavelength domain from 0 to ∞, represented by the area

under the curve as shown in Figure 3. As expressed by Stefan-Boltzmann law, total radiation emitted by a blackbody per unit surface area is directly proportional to the four power of its absolute temperature.

) 6 ( .. ... 4

T F

Where: F_{= Total radiation per unit surface}

area (Wm-2)

₌Stefan-Boltzmann constant (5.6704 x10-8 W m-2 K-4)

T_{= Absolute temperature (K)}

A true blackbody does not exist in nature. The amount of radiation emitted by a substance would not be the same as the absorbed radiation as it depends on its emissivity. The emissivity, ranged from 0 to 1; indicates a ratio of emitted radiation by a substance to radiation emitted by a blackbody at the same temperature. A blackbody would have an emissivity equal to one while any other substance would be less than that. Generally, the more reflective a substance is, the lower its emissivity where the Stefan-Boltzmann law is expressed as:

) 7 ( .. ... 4

T F

Where:  Emissivity of a substance

Most satellite sensors are based on these fundamental laws to distinguish objects by their spectral differences. It is also the same reason why certain satellite sensors are comprised in multispectral bands including the visible and infrared portions of electromagnetic spectrum to detect changes and interaction in the atmosphere, oceans, and the Earth’s surface. With specific techniques and algorithms, further processing on the information is used to meet end-user needs in various purposes.

2.1.3 Bowtie Effect

The Moderate Resolution Imaging Spectroradiometer (MODIS) instrument acquires image over a scan range of -55o to +55o at 705 km height. The length of each swath is 10 km at nadir and gradually becomes larger to the edge of the scene due to its large viewing angle (Gomez et al. 2004).

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Consequently, distortion occurs on the image as shown in Figure 4, known as the bowtie effect. The bowtie effect in MODIS data happens when the sensor scanning angle reach to 15o, as the angle increases the effect becomes more obvious (Wen 2008).

Figure 4 An example of bowtie effect in MODIS data (http://www.sat.dundee.ac.uk/). The bowtie effect causes a duplicated and sometimes triplicated view of the earth’s surface. Overlapping data need to be removed before applying any further process to obtain accurate results. Various algorithms have been developed to remove bowtie effect.Mainly there are two kinds of them; ephemeris method and non-Ephemeris method (Wen 2008). In Ephemeris method, geographic grid will be generated and the data will be matched to it based on its geographical coordinates with the bowtie effect eliminated at the same time. On the other hand, in non-Ephemeris method, the elimination of bowtie effect is done by removing the overlapped parts between neighbouring strips (Junhui 2004).

2.1.4 Surface Temperature

The surface temperature is considered as the temperature of the outer parts of an object. Whereas in satellite-based remote sensing; it is identified as the average temperature of a surface which is stored in a pixel. The amount of surface temperature that can be reached by an object is associated with its wavelength. Based on the blackbody radiation and as expressed by Planck’s law, the amount of energy emitted by a substance depends mainly on its temperature. Then, by inverting Planck’s function, it is possible to estimate surface temperature from brightness temperatures (Dash et al. 2002).

) 8 ( .. ... 1

5 2 2 ln

    

  

  

  

B hc k

hc T

Surface temperature is one of the key parameters in the physics of land surface processes which indicate surface-atmosphere interactions and energy fluxes between the atmosphere and the ground either on the regional or global scales (Sellers et al. 1988). It can be estimated from measuring thermal radiance which coming from the land surface by using satellite sensor. After appropriate aggregation and parameterization, the surface temperature retrieved from satellite data may be used to validate and improve the global meteorological prediction (Price 1982).

The surface-leaving radiance is measured by satellite sensors in different spectral channel, most of the sensors are ranged in the infrared region since the temperature of every object on earth is higher than absolute temperature (0 K). The measurements are influenced by surface characteristics such as emmisivity and its geometric form (Voogt and Oke 2003) and also the distribution of

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temperature and emmisivity within a pixel and the spectral channel of measurement (Becker and Li 1995). Given that remote sensing of surface temperature are based on Planck’s law which relates to radiative energy emitted by a true blackbody, Planck’s function is multiplied by its emmisivity for natural objects which are non-blackbodies (Dash et al. 2002).

2.2 Dynamic Processes in the Atmosphere The ultimate cause of Earth’s winds is solar radiation. The amount of solar radiation received at the top of the atmosphere is not the same as the amount of radiation received at the Earth’s surface. When it travels through the atmosphere to the Earth’s surface, some of the incoming radiation is absorbed, reflected or scattered in all directions by clouds, atmospheric gases, vapours, and dust particles. These events caused the amount of solar radiation that reaches the Earth’s surface are not the same in all places. As the result, it heats the Earth’s surface differently. Uneven heating of the Earth’s surface then causes differences in air pressure at various locations that makes the wind blow from one point to the other as a fluid system in the atmosphere. 2.2.1Fundamental Forces

In the study of atmospheric dynamics, a fluid is treated as continuous medium (continuum) in which a point is a volume element that is very small compared to the total fluid volume but still contains a very large number of molecules (Holton 2004). Atmospheric motions are primarily caused by pressure gradient force along with the other fundamental forces such as gravitational force, and viscous force (friction). These forces, together with the apparent forces like centrifugal force and Coriolis force are the driving forces of the atmospheric motions. a. Pressure Gradient Force

The horizontal pressure gradient force in the equation of motion is the most vital part of dynamics that governs the forcing of the atmosphere (Parish et al. 2007). The force is a result of spatial differences in atmospheric pressure that causes air to move from high pressure regions to low pressure regions, resulting in wind from local to global scales. Assuming that an infinitesimal parcel of air has volumeδx δy δz is centered at the point x0, y0, z0; where the pressure is increasing from left to right as shown in Figure 6;

pressure gradient force can be expressed mathematically in Taylor series expansion as:

    2 0 x x p

p  higher order terms

Figure 6 Thexcomponent of the pressure gradient force acting on a infinitesimal parcel of air.

Neglecting the higher order terms in this expansion, the pressure force acting on the right and left sides of the parcel can be defined as: z y x x p p

F_Ax   

2 0            z y x x p p

FBx 

            2 0

Respectively, the net horizontal force acting on the parcel is the sum of F_Ax and F_Bx

z y x x p F F

F_X _Ax _Bx   

     

Since the mass (m) of the differential volume of the parcel is simply density () times volume; mρδx ρδy ρδz. Hence, the pressure gradient force per unit mass in x

component is: x p m x F      1

Similarly, the pressure gradient force per unit mass for yand zcomponents are:

y p m y F      1 z p m z F      1

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In three dimensional Cartesian coordinate directions, total pressure gradient force per unit mass is:

) 9 ( .. ... 1 p m p F    

The pressure gradient force is perpendicular to isobars. The greater the difference of pressure level between isobars, the stronger the pressure gradient force gets. Closely spaced isobars indicate stronger pressure gradient force than widely spaced one. The acceleration of air parcels depends mostly on the pressure gradient force; strong force will lead to high wind velocity while weak force will have resulted in low wind velocity. Since the motion of wind can occur in any direction, its vector can be broken down into vertical and horizontal components. Logically, as the atmospheric pressure decreases exponentially with increasing height, the air would rush off into space due to the vertical component of pressure gradient force. But instead of blowing the wind straight up, the wind is flowing horizontally in most cases because the air particles are being pulled down toward the earth due to gravity which progressively slows down or even stops the flow that occurs vertically.

b. Gravitational Force

The air parcels in the atmosphere are made of molecules of different gases which are influenced by Earth’s gravitational field. Newton’s law of universal gravitation states that every particle in the universe attracts each other with a force that directly proportional to the product of their masses and inversely proportional to the square of the distance between them. ) 10 ( .. ... ˆ 2 r r GMm g

F 

Where:

F = Gravitational force (kg m s-2) G_{= Gravitational} constant

(6.673x10-11 m3 kg-1 s-2)

M₌ First mass (kg)

m₌ _{Second mass (kg)}

r

_{= Distance between masses (m)}

Compared to Earth, the atmosphere is very thin. Its mass is concentrated and stratified vertically in the lowest 10 km of the Earth’s surface; which is less than 1% of the planet’s

radius (Salby 1996). Between two interacting objects, the gravitational force will get stronger as the mass of either objects increase and will get weaker as the separation distance between the objects increase. Thus, if M is the mass of Earth and m is a mass of an air parcel, the downward force exerted on an air parcel due to Earth’s gravitational attraction is:

) 11 ( .. ... ˆ 2 * r r GM g m g F   

As in dynamic meteorology, the height above mean sea level is used as a vertical coordinate. Then, by neglecting the bulges at the equator and assuming the Earth is in perfectly spherical shape; equation (11) can be rewritten as: ) 12 ( .. ... 2 1 * 0 ˆ 2 ) ( *            a z g r z a GM g

Where: g₀* = Gravitational force at mean sea level (kg m s-2)

z

= Height of an air parcel (m)

a = Radius of the Earth (m)

Figure 7 An air parcel under the influence of

Earth’s gravitational force.

Despite the fact that small variations of gravitational force with altitude are sometimes considered; for meterological applications

)

(za , these variations in the atmosphere are normally ignored so that gravitational force is simply treated as a constant

*) * (g g₀

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c. Viscous Force

As the air parcels are moving within the atmosphere, it movement leads to friction close to the Earth’s surface. This friction forced the air parcel to slow down and also changes its direction. There are at least two types of friction occur in the atmosphere; one that occurs between two surfaces as in between the atmosphere and the Earth’s surface; and molecular friction between air molecules called viscosity. Friction caused by viscosity is much less significant than the one caused between two surfaces. Molecular viscosity is negligible for the atmosphere below 100 km due to very weak viscous force; it is only matters in a thin layer within a few centimeters of the Earth’s surface where vertical shear is very large (Holton 2004).

Figure 8 Vertical shearing stress on a volume of fluid element in the x direction.

The viscous force acting in the x direction of δx δy δzvolume in Figure 8 is given by the net difference of stresses over y and z directions to the x component of the force per unit volume. To obtain the force per unit mass caused by vertical shear in the x direction, it is divided by the massρδx δy δzof the element:

              z u z z zx r F     1 1

If the dynamic viscosity coefficient,, is constant, the above equation may be simplified to

v

(



u

/



z

)

, where v/ is the kinematic viscosity coefficient. Since the wind movement may vary in all directions, it is written in three Cartesian coordinate directions as: u v z u y u x u v rx F 2 2 2 2 2 2 2           













 2 2 2 2 2 2 2           













v z v y v x v v ry F w v z w y w x w v rz F 2 2 2 2 2 2 2           













2.2.2 Forces in a Rotating Reference Frame

As it well known, Earth-based observer is considered to be in a non-inertial frame since the Earth is spinning on its axis. Therefore, Newton’s second law of motion has to be modified to describe the atmospheric motion in a rotating coordinate system. In spite of small angular velocity of Earth’s rotation, the effects caused by rotation of the reference frame are negligible; however, on some atmospheric motions at certain space and time scales, the effect of apparent forces is important and must be accounted for (Lynch and Cassano 2006).

a. Centrifugal Force

As an object is moving in a circular motion with radius r, its direction is continuously changing so that its velocity does not remain constant. To maintain its circular path, a net force; called the centripetal force is directed toward the curvature of the path. Thus, the centripetal acceleration is given by the rate of change of angular velocity. ) 13 ( .. ... 2 r ce a 

Where: a_ce= Centripetal acceleration (kg m s-2)

= Angular velocity (rad s-1 )

r

= Radius of curvature (m)

Newton’s third law of motion states that for every action there is an equal and opposite reaction. The centrifugal force is the equal counterpart force that is exerted in the opposite direction of the centripetal force; it is an apparent force invoked to make Newton’s second law of motion work in a rotating frame. The magnitude of centrifugal force acting on a body of mass m is given by:

) 14 ( .. ... 2 r m ce ma sf

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Viewed from a rotating frame of reference, the centrifugal force produced by Earth’s rotation is a result of the square of Earth’s angular velocity () times the position vector R from the Earth’s axis rotation. Closer to the equator, the centrifugal force produced by Earth’s rotation is stronger than at the poles where it reach the minimum. Similar with the gravitational force, the centrifugal force act on the center of mass of the object. The resultant of these body forces is known as gravity.

) 15 ( .. ... 2 * 0 R g

g  

Since the Earth is not a perfect sphere, *

g directed slightly away from the Earth’s center instead of pointing directly to it except at the equator and the poles where its surface are bulged out and flattened. Therefore, as the gravity, denotedg, is the resultant of both gravitational force and centrifugal force, the value of Earth’s gravity would vary at different place.

b. Coriolis Force

The Coriolis force is an apparent force that can only exists on any moving object situated on a rotating frame of reference; hence it disappears in a non accelerating inertial frame of reference. As the Earth rotates, the Coriolis force influences the wind movement from its intended path, causing it to undergo curved motion. The Coriolis force acts in a direction perpendicular to the object’s motion. It deflects wind to the right in the Northern Hemisphere, and to the left in the Southern Hemisphere. The Coriolis parameter is defined as: ) 16 ( ... )... sin(

2 



Where: f = Coriolis parameter = Earth’s angular velocity  = Latitude

The strength of Coriolis force varies with latitude. The magnitude of Coriolis force per unit mass acting on a horizontally moving air parcel is equal to the product of the Coriolis parameter and parcel’s velocity. The effect gets stronger as latitude increases, it reaches maximum at the poles and becomes zero at the equator. Likewise, at the same velocity, the wind that blows closer to the poles will be deflected more than the wind that blows near

the equator. In zonal and meridional components, the deflected motion caused by horizontal acceleration perpendicular to the motion’s path is given by

fv v Co Dt Du          ) sin( 2  fu u Co Dt Dv            ) sin( 2 

The acceleration caused by Coriolis force can be rearranged by combining the horizontal components in the vectorial form as in the below equation whereV represents horizontal velocity andkˆindicates vertical unit vector defined in positive upward direction.

) 17 ( .. ... V × kˆ 

 f Co Dt V D  













Though Coriolis force deflects the wind direction, it does not affect the wind speed. However, the effect of Coriolis force for masses that move over small distances is negligible; it is only significant over longer distances and larger regions. As the wind speed increases, the Coriolis force increases and greater deflection will occurs; hence, a strong wind blow will be deflected far from its intended path rather than slowly blowing wind.

2.2.3 Structure of the Static Atmosphere Thermodynamic processes that occur in the atmosphere involve the transfer of energy; the heat produced by thermal and mechanical processes then leads to changes in weather. All gases, including the mixture of gases in the atmosphere, are found closely approximate to the state of an ideal gas. The gas properties like pressure, temperature, mass and its volume are related to each other and determine the state of the gas.

) 18 ( .. ... T R m pV 

Where: p = Pressure (Pa) V = Volume (m3)

m = Mass (kg)

R = Gas Constant (J kg-1 K-1)

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The ideal gas constant,R, has different values for each particular gas or a mixture of gases. For dry air parcel that contains no water vapor, Rd= 287 J kg

-1

K-1. Since density =

m/ the ideal gas equation can be rewritten as:

In different case, the equation can also be modified by eliminating air density and replacing it with specific volume, , it is defined as the ratio of gas volume to its mass or simply the inverse of air density. The standard unit of specific volume is commonly expressed in m3 kg-1, depicting the volume occupied by one unit of mass at a given temperature and pressure.

) 20 ( .. ... T R p

In general, the thermodynamics properties of an air mass determine the particular weather condition in the atmosphere over the area in which the air mass covers. As an air mass travels from one place to another, it is being exposed to new environments and its thermodynamics properties may change gradually over time. These changes is then used as a fundamental to understand different atmospheric phenomenon ranging from the smallest cloud microphysical processes to the general circulation of the atmosphere (Wallace and Hobbs 2006).

a. The Hydrostatic Equation

The pressure of air in the atmosphere at any height is determined by the force per unit area exerted by the weight of air influenced by gravity that acts on its surface. Thus, as the atmospheric pressure decreases with increasing height, there will be an upward motion caused by the pressure gradient force.

Figure 9 Balance of vertical forces of the atmosphere in the state of hydrostatic balance.

Applied to an atmosphere at rest, the upward pressure gradient force is opposed by the downward pull of gravity. When there is a balance between these two forces, the atmosphere is in the state of hydrostatic equilibrium.For atmosphere in hydrostatic equilibrium, when forces are in balance, there is no net vertical force acting on it. Thus, there is no vertical acceleration occurs. The hydrostatic balance, as illustrated in Figure 9 is mathematically expressed as

) 21 ( .. ... dz g

dp 



Most of the time, the atmosphere approximates hydrostatic balance; however, this balance is not achieved for an intense small-scale system such as tornadoes and thunderstorms where the air rapidly accelerates in a vertical manner (Ahrens 2004). If the pressure of a fixed point on the Earth at height z is p(z), then the hydrostatic equation to an infinite height is given by

) 22 ( .. ... ) ( ) (



    z p z

p dp g



Since p()= 0, the pressure at height

z

, )

p , is equal to the weight of air and is the result of gravity force that acts on the air above its level. Hence, the air pressure at the mean sea level,p(0), would be 1013.25 hPa or 1.013 × 105 Pa; also known as 1 atmosphere (1 atm).

b. Geopotential

As gravity is a conservative force, the work done by gravity does not depend on its path and is identically zero (Lynch and Cassano 2006). Since the work done by gravity is equal to zero, it is represented as a gradient of a function; called geopotential. The geopotential is defined as the required work that must be done against gravity to raise a unit mass of air from sea level to a given height (Salby 1996).

) 23 ( .. ...

(

)

(







z

g

z

dz

The use of geopotential in momentum equations has the advantage to avoid using gas density, thus creating simpler equations. It is useful for most atmospheric applications since direct measurement of air density can be extremely difficult. If gravity were constant, a surface of geopotential at all places would be ) 19 ( .. ... T R p

(22)

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 ) ( 0 0 0



 

 zgdz

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:

 

x p z z z z z p p p x x x x p p p _                           1 1 0 0 1 1 0 0 ) ( ) ( ) ( ( 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

x x p

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 v_h uivj 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

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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_ ___ _  fk v_h _p 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.gov/data /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 Terra/MODIS 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.

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3.3.2 Estimation of Surface Temperature Thermal infrared sensing is normally applied to determine absolute or relative temperatures from a distance. The basic process is the same in all cases: using radiometers, sensors or thermal devices to sense radiation that is related to heat and relatable to temperature. Surface temperature from Terra/MODIS L1B data is retrieved from the combination of TIR 31 and 32 (Oguro et al. 2011). The steps taken are as follows:

(a) Conversion of Scaled Integer (SI) to Spectral Radiance (L )

In MODIS L1B data, each Earth View (EV) pixel is expressed as a 32-bit floating-point format. It is output as a 16-bit scaled integer (SI) in the scientific data sets (SDS) of the Hierarchical Data Format (HDF). The values are scaled to a range of 0 to 32767. Values greater than 32767 are invalid values which indicate missing pixels. The following expressions are used to convert scaled integer to spectral radiance (MCST 2003). ) 28 ( .. ... ) ( _ 

 Rscale SI Roffset

L  

) 29 ( .. ... 32767 min

max 



L L

scale

R  

) 30 ( .. ... min max min 32767     L L L offset R    



L

= Spectral radiance (Wm -2

µm-1sr-1) SI = Scaled integer value of 16

bits

integer data (dimensionless) 

scale

R = Radiance rescaling gain factor (Wm-2µm-1sr-1)



offset

R = Radiance rescaling offset factor (dimensionless)



min

L

= Observed spectral radiance scaled to 0 (Wm-2µm-1sr-1)



max

L

= Observed spectral radiance scaled to 32767 (Wm-2µm-1sr-1)

(b) Spectral Radiance (L ) conversion to Surface Temperature (TS)

Planck’s law of blackbody radiation is applied in TIR bands 31 and 32 of Terra/MODIS L1B to convert spectral radiance to brightness temperature (Rybicki

and Lightman 1979). By assuming that surface emmisivity is uniformly equal to one (



=1), brightness temperature is considered to be equal with surface temperature.

) 31 ( .. ... 1 ) 5 2 2 ln(       L hc k hc TS

TS = Surface temperature (K)

h = Planck’s constant (6.626 x 10-34 J s-1 ) c = Speed of light (2.998 x 108 m s-1)

k = Boltzmann constant

(1.38 x 10-23 JK1)



L = Spectral radiance (Wm-2µm-1sr-1)

 = Central wavelength of Terra/MODIS TIR (µm): Band 31: 11.03 µm Band 32: 12.02 µm To make it more convenient, the above equation is simplified as follow:

) 32 ( .. ... 1 ) 5 ln( 2 1       L K K TS

Where the constants are: k

K₁ 1.43877102mk 2

2 2hc

K  ₌1.19111016 Wm-2sr-1 3.3.3Geopotential

(a) Thickness of the Atmosphere

The concept of geopotential height is used to approximate the actual height of a pressure surface above mean sea level. In addition, it also used to estimate the vertical distribution of pressure in the atmosphere and the thickness of each layer. It is common that large-scale weather systems are analyzed in terms of geopotential height, and the winds are sometimes inferred from that field. The equation used to calculate geopotential height is a modification from Poisson’s equation (Risdiyanto 2001); it is derived from the hydrostatic equation and ideal gas law with the assumption that the acceleration of gravity and lapse rate is a single constant.

) 33 ( .. ... 1                     g R o p p TS Z  

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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)

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 (m2s-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 (u v

V  _.

As for the wind trajectory:

₌90 360 arctan _o...(37)

u v C

o_ ___

     o o 180

 if U180o

C_{= Angular rotation in full circle} (C360o2)

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 106o E and 107o E, 6.25o S and 6.85o 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       

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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)

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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 Terra/MODIS 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

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from the outside surroundings due to its low thermal conductivity, it loses energy and therefore its temperature decreases. The interaction that occurs between the adiabatically cooled air parcel and the object’s surface temperature somehow created a thermal equilibrium so that the surface temperatures in highlands tend to be smaller than the surface temperatures in lowlands. 4.4 Geopotential and Geopotential Height

The measurements of geopotential height are based on the surface temperature values retrieved from the combination of Terra/MODIS L1B TIR bands 31 and 32. Each layer of geopotential height between the pressure levels is reasonably represents of how warm or cold a layer of the atmosphere is. Thus, the thickness of the atmosphere is measured by the height of geopotential. It appears that a region with high surface temperatures would have thicker layer than the region with lower surface temperatures. The following figure are the vertical cross section of geopotential height which passed through the highest point in the study area.

Figure 16 Cross section of geopotential height.

The use of isobaric coordinates has a computational disadvantage where pressure levels near the surface intersect with mountain topography. The computational problem lies in geopotential which assumes that the Earth is a perfect sphere with perfectly flat and smooth surface with no hills or mountains where the surface of zero geopotential is considered to be in equal height with the sea level. The results, compared with NCEP/NCAR data in appendix 7, does not show any significant difference with the ones that being processed from Terra/MODIS L1B. The thickness of atmospheric layer, as represented by geopotential height, is influenced by the condition of temperatures on the surface which is closely associated with air temperatures. Low geopotential height indicates the cold weather and dry air while high geopotential height indicates the presence of warm weather and moist air.

The analysis of geopotential is focused on two different pressure levels of 200 hPa and 850 hPa. The analysis made for these two pressure levels are commonly used for wind analysis since turbulence and friction are relatively small in the level of 200 hPa whereas the atmospheric conditions in the lower level of 850 hPa are unstable as it is strongly influenced by surface condition. Moreover, the analysis on those pressure levels is also useful to discover the center point of convergence and to locate the point of lifting condensation level (LCL) at which a parcel of air is lifted dry adiabatically until it reaches saturation and the water vapor within it is condensed into water droplets that form the cloud.

A surface of constant geopotential as depicted in Figure 17 indicates a surface in which a parcel of air is moving without undergoing any changes in its potential energy that is required to vertically raise a unit mass of air from one point to another. Therefore,

the variations of gravity at Earth’s surface

obviously have its influence on the geopotential surface; but since gravity acceleration in this study is assumed constant, the shape of geopotential surface is only determined by variation of changes in altitude which are associated with spatial distribution of temperature. Hence, it is obvious that geopotential values in the level of 850 hPa are less than the ones in the upper-level region of

(29)

(a)

(a) (b)

(b)

Figure 17 Geopotential surface (m2s-2) in the level of 200 hPa (a) and 850 hPa (b).

200 hPa. The contours of geopotential also represent the pressure system in the atmosphere where the horizontal pressure gradient force becomes so strong when the contours are close together and grow weaker as the contours farther apart.

4.5 Horizontal Wind Profile

Wind develops as a result of spatial differences in atmospheric pressure due to the variation of heating on the Earth’s surface. As pressure gradient occurs, the air flows from an area of high toward an area of low pressure. Similarly, it is equivalent for pressure gradients measured at a constant altitude to

gradients of geopotential measured on a surface of constant pressure. Wind propagates in all direction both horizontally and vertically. However, the occurrence of vertical winds are much less than the horizontal ones as the pressure gradient force that flowing upward is balanced by gravity force in the opposite direction. Since vertical motion is an exceptional case, the focus of this study is on the horizontal motion that is respectively defined in zonal and meridional direction. The movement of wind in isobaric coordinate is affected by gradients of geopotential. The masses of air are moving from low geopotential areas toward high geopotential

m2_/s2 m2_/s2

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areas as a gradient vector always points in the direction of greater values. Both components of horizontal winds has its positive and negative velocities; positive and negative zonal velocities represents the easterly and westerly winds, while positive and negative meridional velocities represents northerly and southerly winds. The results indicate that wind

magnitudes in the level of 200 hPa are greater than the ones in the level of 850 hPa due to differences in geopotential value. However, both in the level of 200 hPa and 850 hPa, the wind movements went in the same direction as it is assumed that the factors of turbulence flow and friction near the Earth’s surface is negligible in this study.

(a)

(b)

Figure 18 The acceleration of zonal wind (ms-2) in the level of 200 hPa (a) and 850 hPa (b).

(b)

Figure 18 The acceleration of zonal wind (ms-2) in the level of 200 hPa (a) and 850 hPa (b).

m/s2

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(a)

(b)

Figure 19 The acceleration of meridional wind (ms-2) in the level of 200 hPa (a) and 850 (b). Table 3 Decomposition of horizontal wind vectors into zonal and meridional components.

Level Component Dominant wind direction

Max.acceleration (ms-2)

Min.acceleration (ms-2)

Average acceleration

(ms-2) 200 hPa Meridional North 2.109 3.162 x 10-5 2.165 x 10-1

Zonal East 1.506 1.767 x 10-5 1.945 x 10-1

850 hPa Meridional North 0.2609 0.439 x 10-5 0.267 x 10-1

Zonal East 0.1863 0.221 x 10-5 0.241 x 10-1

The horizontal momentum equation used for the mathematical approach to derive wind vectors from Terra/MODIS L1B imagery is mainly oriented on a short-term forecasting. The analysis of satellite-derived wind is meant to present the general information of the

weather in which wind patterns at the surface are affected by upper level winds. The satellite-derived winds generated from Terra/MODIS L1B imagery as what is shown in Figure 20 are represented by twodimensional vector which express both

m/s2

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(a)

(b)

Figure 20 Horizontal wind profile (ms-2) in the level of 200 hPa (a) and 850 hPa (b) Table 4 Direction and acceleration profile of horizontal wind.

Level Dominant wind direction

Max.acceleration (ms-2)

Min.acceleration (ms-2)

Average acceleration

(ms-2) 200 hPa 180o-225o 2.115 5.457 x 10-3 3.241 x 10-1

850 hPa 180o-225o 0.264 0.152 x 10-3 0.407 x 10-1

magnitude and direction of horizontal wind. Thicker vectors indicate greater wind magnitudes and the arrows indicate the point of wind direction, respectively. The figures implicitly show a snapshot of pressure gradient which naturally directed from high pressure areas to low pressure areas. As stated in Newton’s second law of motion,

the acceleration is equals to the sum of forces per unit mass. For synoptic-scale motion, the acceleration is determined by pressure gradient force, Coriolis force, and friction. When these forces have come into balance, it creates geostrophic current which make the winds flow parallel to isobars. For smaller-scale of motion, such as the one in

m/s2

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this study which areas are also near the equator, the Coriolis force is so small that its effect is almost negligible. As the Coriolis force is not strong enough to create geostrophic balance with other forces, the only significant horizontal force acting on the air parcel were the pressure gradient force. So instead of blowing parallel with the isobars, the air parcel accelerates toward lower pressure in response to the net force. The magnitudes of horizontal wind are stronger in the upper pressure level of 200 hPa rather than in the lower pressure level of 850 hPa as what it shown in Table 5. The strong winds are associated with great pressure gradient where the wind magnitudes are directly proportional to the rate of pressure gradient that varies directly with changes in air density with altitude.

V CONCLUSION

The obtained results show that Terra/MODIS L1B data with 1 km spatial resolution used in this study; which was acquired on October 1, 2006 at 10:30 AM local time, can be used to estimate the horizontal wind movement in the troposphere. The average acceleration of horizontal wind in the level of 200 hPa and 850 hPa is respectively 3.241 x 10-1 ms-2 and 0.407 x 10-1 ms-2. However, it should be noticed that wind trajectory keeps changing from its initial direction as the air parcel rapidly accelerates toward lower pressure. Therefore, the initial wind velocity is required as to improve and yield a more accurate forecasting. As for the analysis of geopotential height, the results retrieved from the processing of Terra/MODIS L1B does not show any significant diference with the ones retrieved from NCEP/NCAR data. The momentum equation used in isobaric coordinates has a certain computational disadvantages in an area surrounded by the mountains where the pressure surface cannot effectively adjust to topographical factors. Therefore, some adjustment on the equations and coordinate system needs to be done to get more accurate results. As this study is still in early stage of development, it is expected for future study to validate the results with in situ data such as radiosonde and also to minimize the assumptions as to include turbulent flow and friction to get a better analysis on the surface wind.

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(1)

(a)

(a) (b)

(b)

Figure 17 Geopotential surface (m2s-2) in the level of 200 hPa (a) and 850 hPa (b).

4.5 Horizontal Wind Profile

m2_/s2

(2)

(a)

(b)

Figure 18 The acceleration of zonal wind (ms-2) in the level of 200 hPa (a) and 850 hPa (b).

(b)

Figure 18 The acceleration of zonal wind (ms-2) in the level of 200 hPa (a) and 850 hPa (b).

m/s2

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(a)

(b)

Figure 19 The acceleration of meridional wind (ms-2) in the level of 200 hPa (a) and 850 (b). Table 3 Decomposition of horizontal wind vectors into zonal and meridional components.

Level Component Dominant wind direction

Max.acceleration (ms-2)

Min.acceleration (ms-2)

Average acceleration

(ms-2) 200 hPa Meridional North 2.109 3.162 x 10-5 2.165 x 10-1

Zonal East 1.506 1.767 x 10-5 1.945 x 10-1

850 hPa Meridional North 0.2609 0.439 x 10-5 0.267 x 10-1

Zonal East 0.1863 0.221 x 10-5 0.241 x 10-1

m/s2

(4)

(a)

(b)

Figure 20 Horizontal wind profile (ms-2) in the level of 200 hPa (a) and 850 hPa (b) Table 4 Direction and acceleration profile of horizontal wind.

Level Dominant wind direction

Max.acceleration (ms-2)

Min.acceleration (ms-2)

Average acceleration

(ms-2) 200 hPa 180o-225o 2.115 5.457 x 10-3 3.241 x 10-1 850 hPa 180o-225o 0.264 0.152 x 10-3 0.407 x 10-1 magnitude and direction of horizontal wind.

Thicker vectors indicate greater wind magnitudes and the arrows indicate the point of wind direction, respectively. The figures implicitly show a snapshot of pressure gradient which naturally directed from high pressure areas to low pressure areas. As stated in Newton’s second law of motion,

m/s2

(5)

GILANG ARIA SETA

DEPARTMENT OF GEOPHYSICS AND METEOROLOGY

FACULTY OF MATHEMATICS AND NATURAL SCIENCES

INSTITUT PERTANIAN BOGOR

2012

(6)

Lillesand TM, Kiefer RW. 1994. Remote

Sensing and Image Interpretation. 3rd

Edition. New York: John Wiley. Lynch AH, Cassano JJ. 2006. Applied

Atmospheric Dynamics. West Sussex:

J. Wiley and Sons.

MODIS Characterization Support Team (MCST). 2005. MODIS Level 1B

Algorithm Theoretical Basis

Document. USA: NASA/Goddard

Space Flight Center.

Oguro Y, Ito S, Tsuchiya K. 2011. Comparisons of Brightness Temperatures of Landsat-7/ETM+ and Terra/MODIS around Hotien Oasis in the Taklimakan Desert.

Applied and Environmental Soil

Science. Vol. 2011: Article ID

948135

Parish TR, Burkhart MD, Rodi AR. 2007. Determination of the Horizontal Pressure Gradient Force Using Global Positioning System on board an Instrumented Aircraft.J. of Atm.

and Oceanic Tech. 24, (3).

Polito, Paulo S, Liu WT, Tang W, 2000. Correlation-Based Interpolation of NSCAT Wind Data. J. Atmos.

Oceanic Technol. 17: 1128–1138.

Price JC. 1982. On the use of satellite data to infer surface ﬂuxes at meteorological scales. Journal of Applied

Meteorology. 21:1111–1122.

Risdiyanto. 2001. Weather monitoring

model based on satellite data [Master

Thesis]. Bogor: MIT-Program, Pascasarjana-IPB.

Rybicki GB, Lightman AP. 1979. Radiative

Processes in Astrophysics. USA:

John Wiley and Sons.

Salby ML. 1996. Fundamentals of

Atmospheric Physics. USA:

Academic Press.

Sellers PJ, Hall FG, Asrar G, Strebel DE, Murphy RE. 1λ88. The ﬁrst ISLSCP Field Experiment (FIFE). Bulletin of

the American Meteorology Society.

69:22–27.

Smith CK, Bettenhausen M, Gaiser PW. 2006. A Statistical Approach to WindSat Ocean Surface Wind Vector Retrieval. IEEE Geoscience And

Remote Sensing Letters.

3(1):164-168.

Stull RB. 1995. Meteorology Today for Scientist and Engineers: A Technical

Companion Book. USA: West

Publishing Company Co.

Voogt JA, Oke TR. 2003. Thermal remote sensing of urban climates. Remote

Sensing of Environment. 86:370-384

Wallace JM, Hobbs PV. 2006. Atmospheric

Science: An Introductory Survey. 2nd

Edition. USA: Academic Press. Wen X. 2008. A new prompt algorithm for

removing the bowtie effect of MODIS L1B data. The International Archives of the Photogrammetry,

Remote Sensing and Spatial

Information Sciences. 37:Part B3b.

Willett CS, Leben RR, Lavin MF. 2006. Eddies and tropical instability waves in the eastern tropical Pacific: A review. Progress in Oceanography. 69: 218–238.