13 Z = Geptential height (m) = Lapse rate (6.5 K km -1 ) R = Gas cnstant fr dry air (287 Jkg -1 K) g = Acceleratin f gravity (9.8 ms -2 ) TS = Surface Temperature (K) p = Initial air pressure (Assumptin: 1013.25 hpa) p = Pressure at given pint (hpa) Geptential The use f pressure field as a vertical crdinate gives sme advantages t visualize bth the quasi-hrizntal pressure surfaces and the structures f the atmsphere. Geptential are used in synptic scale t analyze the mvement f air masses in isbaric crdinate. The values f geptential are btained as the ptential f gravity per unit mass at a certain gemetric height abve mean sea level. d gdz.....(34) = Geptential (m 2 s -2 ) g = Acceleratin f gravity (9.8 ms -2 ) z = Gemetric height (m) 3.3.4 Hrizntal Wind Prfile The appraching methds t analyze and apprximate wind mvement frm satellite imagery are cmmnly based n the mmentum equatins. The rientatin f a pressure gradient is used t simulate wind mvement and t evaluate wind field n each pressure level. In isbaric crdinate, the pressure gradient is replaced by the gradient f geptential in assumptin that neither frictins nr turbulence ccurs. Dv h Dt p fk ˆ Dv h Dt ˆ p fk v h = Hrizntal acceleratin = Gradient f geptential = The Crilis parameter...(35) V = Hrizntal wind cmpnents h Due t the fact that the Crilis frce is very weak near the equatr, the cmpnent f Crilis can be neglected s that the east-west wind cmpnent ( u ) and nrth-suth wind cmpnent ( v ) is expressed as: u t x The advective cmpnents were negligible since the satellite data used is in the frm f snapsht (dt=1 secnd). As the result btained is in the acceleratin frm and dt=1 secnd; the acceleratin can be thught as the speed f wind exactly at the time when the image was acquired. The magnitude f hrizntal wind can be fund by using simple vectr expressin (Stull 1995). V 2 2 ( u v )...(36). As fr the wind trajectry: v t y 360 = 90 v arctan... (37) C u 180 if U 180 C = Angular rtatin in full circle ( C 360 2 ) IV RESULTS AND DISCUSSION 4.1 Study Area The area analyzed by MODIS sensr n bard the Terra satellite fr this study is fcusing arund the muntain ranges lcated rughly in between 106 E and 107 E, 6.25 S and 6.85 S in the suthern part f West Java, Indnesia. The main reasn f chsing a particular area surrunded by muntains is simply due t the nticeable differences f surface temperature between the muntain s peak and the area with lesser height as it prvide sme aids t analyze the wind develpment. As the temperature at the surface heats the air abve it by cnductin, the heated air expands and becme less dense than the surrunding envirnment and s it rises. Later n, the differences f air density cause a pressure gradient between ne pint and anther, frcing the air t flw. 4.2 Preprcessing data The image acquired by MODIS sensr n bard the Terra satellite is gemetrically distrted due t the wide-angle swath and the Earth s curvature which lead t verlapping data errrs. The distrtin is s visible that it may affect image interpretatin; hence, verlapping parts need t be remved s that
14 Figure 12 Shuttle Radar Tpgraphy Missin (SRTM) data f the study area. MODIS data can be used effectively. Gemetric crrectin f MODIS data was carried ut using Mdistl in ENVI; the prcess f image restratin was dne by resampling the verlapping swaths then recnstructing the scene t prduce new image n a unifrm grid with equal pixel size. Three different statistical methds were used t measure the change f pixel value in MODIS L1B imagery after bwtie crrectin is applied. The Rt Mean Square Errr (RMSE) and Mean Abslute Errr (MAE) is used tgether t diagnse the variatin f errrs in bwtie crrectin while crrelatin cefficient is used t measure the strength and directin f a linear relatinship between Mdistl utputs and bserved values. As what is shwn in Table 1, very large errrs are unlikely t ccur during bwtie crrectin since the difference between RMSE and MAE is nt great enugh t indicate the presence f very large errrs. Thugh, there is sme variatin in the magnitude f the errrs that can be seen frm RMSE values which are bigger than MAE. The bserved values and Mdistl utputs is psitively crrelated as indicated by psitive values in crrelatin cefficient. Figure 13 MODIS data (RGB) befre and after bwtie crrectin.
15 Table 1 Cmparisn f statistical appraches in bwtie crrectin. 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 Crrelatin Cefficient 0.93401 0.92803 0.90951 0.97410 0.97072 4.3 Surface Temperature Infrared radiatin is cmmnly used t remtely determine the glbal cverage f surface temperature ver the Earth s surface. Hwever, due t its limitatin, the utging infrared radiatin frm the surface cannt penetrate thrugh cluds t reach the satellite s radimeter. Therefre, a clud-free prtin f the scene is used s that land surface temperature is nt mixed with cludtp temperature. The brightness temperature retrieved frm TIR bands 31 and 32 f Terra/MODIS L1B were used t measure the surface temperature in assumptin that the entire bject is a perfect blackbdy. Figure 14 Linear regressin f surface temperature in TIR bands 31 and 32. The value f surface temperature calculated frm TIR bands 31 and 32 is varied but relatively similar. The relatinship between these tw bands is linear with 0.9934 cefficient f determinatin as shwn in Figure 14. The value f surface temperature is varied alng with tpgraphy where high temperatures are mre likely t be identified in lwlands rather than in highlands as it can be clearly seen frm Figure 15. The pattern f surface temperature will vary depends n the amunt f slar radiatin absrbed by the surface. It is related with the physical characteristics f the bject. High surface temperature f an bject is generally assciated with high emissivity, small heat capacity, and high thermal cnductivity. The rate at which surface temperature decreases with height is very much affected by adiabatic prcess. When a parcel f air rises, it mves int higher altitudes where the surrunding air pressure is lwer than n the inside f the air parcel itself. This pressure difference then causing the air parcel t expands and pushes n the air arund it. Since the wrk dne by air parcel des nt gain any heat exchange K Figure 15 The range f surface temperature in the study area (K).
16 frm the utside surrundings due t its lw thermal cnductivity, it lses energy and therefre its temperature decreases. The interactin that ccurs between the adiabatically cled air parcel and the bject s surface temperature smehw created a thermal equilibrium s that the surface temperatures in highlands tend t be smaller than the surface temperatures in lwlands. 4.4 Geptential and Geptential Height The measurements f geptential height are based n the surface temperature values retrieved frm the cmbinatin f Terra/MODIS L1B TIR bands 31 and 32. Each layer f geptential height between the pressure levels is reasnably represents f hw warm r cld a layer f the atmsphere is. Thus, the thickness f the atmsphere is measured by the height f geptential. It appears that a regin with high surface temperatures wuld have thicker layer than the regin with lwer surface temperatures. The fllwing figure are the vertical crss sectin f geptential height which passed thrugh the highest pint in the study area. Figure 16 Crss sectin f geptential height. The use f isbaric crdinates has a cmputatinal disadvantage where pressure levels near the surface intersect with muntain tpgraphy. The cmputatinal prblem lies in geptential which assumes that the Earth is a perfect sphere with perfectly flat and smth surface with n hills r muntains where the surface f zer geptential is cnsidered t be in equal height with the sea level. The results, cmpared with NCEP/NCAR data in appendix 7, des nt shw any significant difference with the nes that being prcessed frm Terra/MODIS L1B. The thickness f atmspheric layer, as represented by geptential height, is influenced by the cnditin f temperatures n the surface which is clsely assciated with air temperatures. Lw geptential height indicates the cld weather and dry air while high geptential height indicates the presence f warm weather and mist air. The analysis f geptential is fcused n tw different pressure levels f 200 hpa and 850 hpa. The analysis made fr these tw pressure levels are cmmnly used fr wind analysis since turbulence and frictin are relatively small in the level f 200 hpa whereas the atmspheric cnditins in the lwer level f 850 hpa are unstable as it is strngly influenced by surface cnditin. Mrever, the analysis n thse pressure levels is als useful t discver the center pint f cnvergence and t lcate the pint f lifting cndensatin level (LCL) at which a parcel f air is lifted dry adiabatically until it reaches saturatin and the water vapr within it is cndensed int water drplets that frm the clud. A surface f cnstant geptential as depicted in Figure 17 indicates a surface in which a parcel f air is mving withut underging any changes in its ptential energy that is required t vertically raise a unit mass f air frm ne pint t anther. Therefre, the variatins f gravity at Earth s surface bviusly have its influence n the geptential surface; but since gravity acceleratin in this study is assumed cnstant, the shape f geptential surface is nly determined by variatin f changes in altitude which are assciated with spatial distributin f temperature. Hence, it is bvius that geptential values in the level f 850 hpa are less than the nes in the upper-level regin f
17 m 2 /s 2 m 2 /s 2 Figure 17 Geptential surface (m 2 s -2 ) in the level f 200 hpa and 850 hpa. 200 hpa. The cnturs f geptential als represent the pressure system in the atmsphere where the hrizntal pressure gradient frce becmes s strng when the cnturs are clse tgether and grw weaker as the cnturs farther apart. 4.5 Hrizntal Wind Prfile Wind develps as a result f spatial differences in atmspheric pressure due t the variatin f heating n the Earth s surface. As pressure gradient ccurs, the air flws frm an area f high tward an area f lw pressure. Similarly, it is equivalent fr pressure gradients measured at a cnstant altitude t gradients f geptential measured n a surface f cnstant pressure. Wind prpagates in all directin bth hrizntally and vertically. Hwever, the ccurrence f vertical winds are much less than the hrizntal nes as the pressure gradient frce that flwing upward is balanced by gravity frce in the ppsite directin. Since vertical mtin is an exceptinal case, the fcus f this study is n the hrizntal mtin that is respectively defined in znal and meridinal directin. The mvement f wind in isbaric crdinate is affected by gradients f geptential. The masses f air are mving frm lw geptential areas tward high geptential
18 areas as a gradient vectr always pints in the directin f greater values. Bth cmpnents f hrizntal winds has its psitive and negative velcities; psitive and negative znal velcities represents the easterly and westerly winds, while psitive and negative meridinal velcities represents nrtherly and sutherly winds. The results indicate that wind magnitudes in the level f 200 hpa are greater than the nes in the level f 850 hpa due t differences in geptential value. Hwever, bth in the level f 200 hpa and 850 hpa, the wind mvements went in the same directin as it is assumed that the factrs f turbulence flw and frictin near the Earth s surface is negligible in this study. Figure 18 The acceleratin f znal wind in the level f 200 hpa and 850 hpa. Figure 18 The acceleratin f znal wind in the level f 200 hpa and 850 hpa.
19 b Figure 19 The acceleratin f meridinal wind in the level f 200 hpa and 850. Table 3 Decmpsitin f hrizntal wind vectrs int znal and meridinal cmpnents. Level Cmpnent Dminant wind directin Max.acceleratin Min.acceleratin Average acceleratin 200 hpa Meridinal Nrth 2.109 3.162 x 10-5 2.165 x 10-1 Znal East 1.506 1.767 x 10-5 1.945 x 10-1 850 hpa Meridinal Nrth 0.2609 0.439 x 10-5 0.267 x 10-1 Znal East 0.1863 0.221 x 10-5 0.241 x 10-1 The hrizntal mmentum equatin used fr the mathematical apprach t derive wind vectrs frm Terra/MODIS L1B imagery is mainly riented n a shrt-term frecasting. The analysis f satellite-derived wind is meant t present the general infrmatin f the weather in which wind patterns at the surface are affected by upper level winds. The satellite-derived winds generated frm Terra/MODIS L1B imagery as what is shwn in Figure 20 are represented by twdimensinal vectr which express bth
20 Figure 20 Hrizntal wind prfile in the level f 200 hpa and 850 hpa Table 4 Directin and acceleratin prfile f hrizntal wind. Level Dminant wind directin Max.acceleratin Min.acceleratin Average acceleratin 200 hpa 180-225 2.115 5.457 x 10-3 3.241 x 10-1 850 hpa 180-225 0.264 0.152 x 10-3 0.407 x 10-1 magnitude and directin f hrizntal wind. Thicker vectrs indicate greater wind magnitudes and the arrws indicate the pint f wind directin, respectively. The figures implicitly shw a snapsht f pressure gradient which naturally directed frm high pressure areas t lw pressure areas. As stated in Newtn s secnd law f mtin, the acceleratin is equals t the sum f frces per unit mass. Fr synptic-scale mtin, the acceleratin is determined by pressure gradient frce, Crilis frce, and frictin. When these frces have cme int balance, it creates gestrphic current which make the winds flw parallel t isbars. Fr smaller-scale f mtin, such as the ne in