比較建模與觀測落日時的天文折射現象

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(1)國立臺灣師範大學地球科學研究所碩士論文. 比較建模與觀測落日時的天文折射現象 Comparison of Modeled and Observed Astronomical Refraction of the Setting Sun. 研究生：吳育倫 Yu-Lun Wu. 指導教授：傅學海博士 Hsieh-Hai Fu. 中華民國一零一年一月.

(2) Abstract In this work, we try to calculate the astronomical refraction of the setting sun. The light path from a source outside the earth’s atmosphere is a curve due to the astronomical refraction, and this curve depends on the observed location and the angle between celestial body and the horizon, especially when the celestial body is near the horizon. The astronomical refraction is influenced by the density and temperature of the vertical atmosphere structure. The CWB rawinsonde observed data is used to construct the vertical density structure of the atmosphere. The sunset images taken on the September 17, 2011, October 17, 2011 and October 28, 2011 at Tamshui, and thes images are used as comparison of model and observed astronomical refraction of the setting sun. The difference of the model and the observed setting sun in minimum is -0.70" when the un-refracted incident angle is at 0.749674º above the real horizon, in maximum is 123.72" when the un-refracted incident angle is at 1.387341º above the real horizon.. Key Words: Astronomical Refraction, Sunset, Refraction, Atmosphere, Rawinsonde, Observe. I.

(3) 摘要. 在本研究中，我們嘗試計算得出落日時的天文折射現象。在光線通過大氣層的過程中，它會因為受到大氣層折射的影響而使光線的路徑逐漸彎曲，這即為天文折射現象。天文折射現象的彎曲程度受到天體的仰角所影響，在天頂時最小而在地平面時最大。天文折射現象是受到空氣的密度所影響，其與空氣的溫度和壓力息息相關，為了得到大氣的垂直密度結構，我們使用中央氣象局的雷文送（無線電探空儀）傳回的大氣垂直資料。我們用來比對的落日照片是在 2011 年 9 月 17 日，2011 年 10 月 17 日與 2011 年 10 月 28 日在淡水海邊所拍攝。將拍攝的落日與建模計算的落日仰角進行比對，兩者間的差異最小時是在天體仰角高度為 0.749674°時，差異量為-0.70"；兩者間差異量最大時是在天體仰角高度為 1.387341°時，差異量為 123.72"。. 關鍵字：天文折射、落日、折射、大氣層、雷文送、觀測. II.

(4) 致. 謝. 首先我要感謝我的指導教授傅學海老師，在我的修課及研究過程中給我許多意見與方向，激發我的思考，以及許多的指導與鼓勵，讓我能夠完成這篇論文，三年來感謝老師的諄諄教誨，給了我許多研究上的幫助。感謝口試委員管一政老師與林沛練老師，在百忙之中仍能抽空前來並給予指導與建議，讓我明白論文仍然不足需修該之處。感謝研究所的同學與學長姐及學弟妹們，經常一起熬夜拼進度與觀測的憲隆與翔宇，以及總是默默幫我們擋下許多瑣事的晟庭學長，還有經常來幫忙的鴻選、宗賢、心潔、姿穎、逸翔等人，還有既會抓我去打球又會幫我畫地圖的育群學弟，室友易儒、伯東與建勳，有你們在左右相伴，給予我在做論文這段期間許多的幫助。感謝峻鳴、牧笛、林怡、偉珊、為瀚這些瘦咖咖的成員還有濟榕、雅祺，在我苦悶的研究生涯中可以一起出野外爬山親近自然放鬆身心，讓我可以重獲戰力。孟遠、仕豪、百穗、榮倫、媺妼、儷芙這些老朋友也總是給予支持和鼓勵。以及實習學校的同事和師長們的勉勵，在你們的勉勵下我才能有今日。要感謝的人實在太多，總是會有族繁不及備載的親友師長們，最後要感謝仲元與我的家人們，時常體諒我晝夜顛倒的生活，感謝你們大家的支持與鼓勵，在你們的支持下我才能義無反顧的繼續努力，謝謝你們！. III.

(5) Contents 1. Introduction. ..........01. 2. Observation. ..........04. 3. Data Process. ..........13. 3-1. 3-2. Calibrate the altitude angle of the real sun (the unfracted sun) by the photo time. ..........13. The Central Weather rawinsonde data. ..........17. Bureau. (CWB). 3-3. The refraction index of the moist air. ..........18. 3-4. The refraction between each layer of the atmosphere. ..........24. The light path during the atmosphere. ..........27. 3-5 4. Result and Discussion. ..........29. 5. Conclusion. ..........44. 6. Reference. ..........46. 7. Appendix. ..........49. 7-A. The CWB rawinsonde data. ..........49. 7-B. The IDL source code. ..........60. 7-C. The observation without measured the real horizon.. ..........77. IV.

(6) List of Figures Fig 2-1.. The maximum distance of horizontal direction of the solar image (in pixel). ..........04. Fig 2-2.. The sea level in our image.. ..........07. Fig 2.3.. The scene while photo the setting sun. ..........09. Fig 2.4.. The difference of the water surface in the connected tubes looks from different height. ..........10. Fig 2.5.. The real horizon and the apparent sea level.. ..........11. Fig 2.6.. The location of the observation on the map.. ..........12. Fig. 3-1.. To calculate the angle θc from transit time to image time. ..........14. Fig. 3-2.. To calculate the angle θc to the altitude angle θx.. Fig 3-3.. The refraction between the boundaries of different layers. ..........24. Fig 3-4.. The light path of the astronomical refraction.. Fig 4-1.1.. The modeled sun and the observed sun on the image which was taken on September 17, 2011 morning. ..........30. Fig 4-1.2.. The height to pressure and the height to temperature figures which observed by CWB rawinsonde on 00:00 UT September 17, 2011. ..........31. V. ..........16. ..........27.

(7) List of Figures Fig 4-2.1.. The modeled sun and the observed sun on the image which was taken on September 17, 2011 evening. ..........32. Fig 4-2.2.. The height to pressure and the height to temperature figures which observed by CWB rawinsonde on 12:00 UT September 17, 2011.. .........33. Fig 4-3.1.. The modeled sun and the observed sun on the image which was taken on October 17, 2011 evening. ..........34. Fig 4-3.2.. The height to pressure and the height to temperature figures which observed by CWB rawinsonde on 12:00 UT October 17, 2011. ..........35. Fig 4-4.1.. The modeled sun and the observed sun on the image which was taken on October 28, 2011 evening. ..........36. Fig 4-4.2.. The height to pressure and the height to temperature figures which observed by CWB rawinsonde on 12:00 UT October 28, 2011. ..........37. VI.

(8) List of Tables Table.2-1. The equipment with the observe date. Table2-2.. ..........06. The Latitude, Longitude and the altitude with the observe date.. ..........08. Table 4-1. The result of the observation on September 17, 2011 morning.. ..........38. Table 4-2. The result of the observation on September 17, 2011 evening.. ..........39. Table 4-3. The result of the observation on October 17, 2011 evening.. ..........40. Table 4-4. The result of the observation on October 17, 2011 evening.. ..........41. VII.

(9) Introduction The difference of the position and shape of the observed setting sun and the model are compared, and the model of the setting sun is built in terms of the vertical atmosphere structure reconstructed from the Central Weather Bureau (CWB) rawinsonde data. The astronomical refraction model is established under the real weather condition, and the terrestrial refraction is gotten from the observation of the real horizontal level. The astronomical refraction could be improved in the field of archaeoastronomy, which often use some ancient monuments to align with the rising and setting of the celestial bodies (Schaefer, 1990), and it is also being improved in the field of astrometry. When stars separated 30″ at K band at a zenith angle 45°, the astronomical refraction could cause the relative astrometry accuracy up to 12,000 μas, it’s 120 times of desired accuracy (Joseph, 1998). Both of astronomical and terrestrial refraction causes the refraction correction angle to vary slightly for different frequencies. This refractive condition explains the observance of the “green spot” at sunset when the horizon is exceptionally clear. Although the refraction model presented here emphasizes visible refraction phenomena, a modified version can also be applied to the radio frequency for corrections on Global Position System (GPS) signals (Michael, 1996). The astronomical refraction had been known long before. About two thousand years ago, the astronomer Claudius Ptolemy of Alexandria, founds that the rising and setting point of celestial objects were deflected toward the North. Ptolemy indicated that this deflection was caused by. 1.

(10) reflection, and he also mentioned that the amount of refraction would decrease with increase altitude angle, and reaching to zero at the zenith (Smith, 1996). The Italian astronomer Gian Domenico Cassini according the Snell’s law, assumed the earth’s atmosphere were composed by the same density of gas, construct the “concentric spherical shell model” and the “plane parallel layer model”. Cassini using the amount of refraction to estimate the height of earth’s atmosphere as 6.82 km, the refractive index is 1.000284 while the radius of earth is 6377.36 km (Mahan, 1962). Sugawa suggest that the astronomical refraction has a seasonal variation, the minimum is occurred in the summer while the zenith angle is 85 , the refraction angle is about 08' 34".09, the maximum is occurred in the winter while the zenith angle is about 09'40".68. (Sugawa, 1955) The atmosphere of US standard model is used widely. In the 1962, Garfunkel used a piecewise linear representation of the atmosphere (Garfinkel, 1967), and Hao-jian Yan developed his scheme for a standard atmosphere (Yan, 1996), based on the model of US standard atmosphere. Thomas and Joseph were also used the US standard atmosphere into the astronomical refraction to simulate the solar rim of the real sun image (Thomas and Joseph, 1996). During the period of 1988 to 1989, Bradleye Schaefer observed the sunset in difference location on earth to estimate the astronomical refraction, the astronomical refraction is from 0.234 to 1.678 , and the mean is 0.64 (Schaefer, 1990) . Russell D. Sampson who use the camera to record the solar image. 2.

(11) and use the rawinsonde to contribute the vertical atmosphere structure and used into similar the astronomical refraction of the setting sun (Sampson, 2003), and tried to compared them on different seasons (Sampson, 2005) and at different longitude (Sampson, 2008) of the astronomical refraction of the setting sun. The relation between the refractive index and the air composition was modeled by experiments, which considered the temperature, pressure, relative humidity and the density of the CO2. This model is tested the air temperature from -40℃ to +100℃, and the pressure from 80 to 120 kPa and the relative humidity from 0 to 100%, and it should apply the wavelength from 300 nm to 1690 nm (Ciddor, 1996). In this work, a DSLR camera with Canon 400mm f/5.6 L lens to observed the setting/rising sun, and used the air refraction index model which established by Pholip E. Ciddor in 1996, and use the CWB rawinsonde data to structure the real vertical structure atmosphere to simulate and compared the astronomical refraction model with the observed setting sun.. 3.

(12) Observations We use the Canon EOS Camera with lens to observe the setting sun, the observed log as shown on Table.2-1. The image scale will be influenced by the CCD size and the focal length. The focal length is changed a little while the image is focused on a nearby object moving to a long-distant object, such as the Sun. To solve this problem, the maximum distance of horizontal direction of the solar image (in pixel) on image as the observed sun’s diameter (shown on the following figure), and calculated with the known sun diameter (in arcsec) which searched from JPL Horizon System as the image scale.. Fig 2-1. The maximum length of horizontal direction of the solar image (in pixel).. 4.

(13) The observed time is used the time recorded inside camera, adjusted by NTP (Network Time Protocol) program published by National Time and Frequency Standard Laboratory. The GPS time is also used to compare with the NTP time, and there is no difference between these two time-meters. Because of the camera’s time unit is only recorded to second, our accuracy of the time is 1 second which caused the altitude angle accuracy of the sun would be ±7.5".. 5.

(14) Table.2-1 The equipment with the observe date. The observed date with * means this observation is sunrise, and others are sunset Image Scale (arcsec/pixel). Observe date. Camera. Lens. May 8, 2009. Canon EOS 30D. Phoenix 80HD 2.723 f=480mm, F/5.6. June 1, 2010*. Canon EOS 50D. Canon EF 400mm 2.468 F/5.6 L. August 21, 2010. Canon EOS 50D. Canon EF 400mm 2.456 F/5.6 L. September 3, 2010. Canon EOS 50D. Canon EF 400mm 2.461 F/5.6 L. Canon. Canon EF 400mm. EOS 50D. F/5.6 L. September 25, 2010. Canon EOS 50D. Canon EF 400mm 2.460 F/5.6 L. October 12, 2010. Canon EOS 7D. Canon EF 400mm 2.246 F/5.6 L. September 17, 2011*. Canon EOS 7D. Canon EF 400mm 2.232 F/5.6 L. September 17, 2011. Canon EOS 7D. Canon EF 400mm 2.244 F/5.6 L. October 17, 2011. Canon EOS 7D. Canon EF 400mm 2.244 F/5.6 L. October 28, 2011. Canon EOS 7D. Canon EF 400mm 2.233 F/5.6 L. September 8, 2010. 6. 2.445.

(15) The time of sunrise and sunset will be directly influent in the observed location, and a GPS logger is used to show the data of location. The GPS logger, Holux M241 which uses MTK MT3318 GPS chipset, the accuracy of this GPS logger in location is less than 3 meters and the accuracy in altitude is less than 5 meters. The data of location gotten from GPS is accepted, because the altitude error less than 0.1 arcsec, and the image scale is larger than 2.2 arcsec/pixel.. The altitude error is. considered while use the visual horizon to define as the real horizon, it would cause 170" on altitude angle. The GPS data in 2011 are more reliable because the value of mean is used that the GPS data recorded continuously more than 30 minutes, while the location gotten from GPS is lower because the first value appeared was used before 2011. The images are rotated a small angle, 0.1° to 0.9°, according to the sea level of the image itself. But the sea level in our image is really wave line other than a straight line, so that the mean sea level is used.. Fig 2-2. is used.. The sea level in our image is not a straight line so that the mean sea level (the dashed line). 7.

(16) Table2-2. The Latitude, Longitude and the altitude with the observe date. Observe Date. Latitude. Longitude. Height (m). May 8, 2009. E 121°24'26.4". N 25°11'08.3". 11. June 1, 2010*. E 121°59'09.2". N 25°01'17.1". 15. August 21, 2010. E 121°24'26.4". N 25°11'08.5". 11. September 3, 2010. E 121°24'26.4". N 25°11'08.3". 9. September 8, 2010. E 121°24'26.3". N 25°11'08.3". 12. September 25, 2010. E 121°24'26.4". N 25°11'08.3". 11. October 12, 2010. E 121°24'26.4". N 25°11'08.3". 13. September 17, 2011*. E 121°59'35.5". N 25°00'01.6". 6. September 17, 2011. E 121°24'35.5". N 25°11'01.6". 5. October 17, 2011. E 121°24'35.5". N 25°11'01.6". 5. October 28, 2011. E 121°24'26.2". N 25°11'06.4". 5. 8.

(17) A much better method for finding the real horizon in the image field is used in each run of 2011. The sea level is not the real horizon because of the terrestrial refraction and the location height. If the altitude is higher than zero, the sea level of more distant will be seen, and it will be lower than real horizon. Furthermore, the apparent sea level will be higher than real sea level due to the terrestrial refraction. The terrestrial refraction makes the real sea level downer than the apparent sea level, and it would between 28.80" to 448.20" (Sampon, 2003).. 20m. Fig 2.3. The scene while photo the setting sun. The distance between camera to the nearby bottle is 20 meters, and the distance between the blue and red bottle is 8 meters. The camera was set at the same height of the water surface in the bottles.. 9.

(18) A connected tube is used to find the real horizon, and two bottles filling the water are connected with a long tube, 8-meter interval. The distance between of camera and the first bottle of connecting tube is 20 meters. The height of camera is adjusted to fit the same level of the surface of two bottles; that means the line along the center of camera image and the water surface of two bottles as the real horizon level.. In. order to distinguish these two bottles, the water is dyeing in color ink, closer is blue and the other is red.. The deviation between water surfaces. of two bottles is less than 1 mm.. Fig 2.4. The difference of the water surface in the connected tubes looks from different height, and the near bottle is dying in blue and the far bottle is dying in red. (a) While the camera is lower than the water level, the water in the near bottle would looks higher than the far bottle. (b) While the camera is higher than the water level, the water in the near bottle would look lower than the far bottle. (c) While the camera is at the same height of the water level, the water in the near and far bottles would at the same height. 10.

(19) Because of the focus, when we are focus on the sun or the sea level, even we let the aperture as F32.0 the closer bottles are still fuzzy. This makes error about 11.16" when we trying to determine the real horizon, but we couldn’t make the focus on the bottles because this will make the image scale changed.. Real Horizon. Visual Horizon Fig 2.5 The upside picture is the image when we adjust the camera at the same height with the water surface in the bottles, The water surface and the bottles are clear, but the sea surface is fuzzy. The right picture is adjust the focus on the sun, the bottles and water level are fuzzy but the sea level is clear, it makes error about 5 pixel to determine the place of the water surface.. We also use the rawinsonde data to construct the vertical structure of the atmosphere, the rawinsonde was launched by the Central Weather 11.

(20) Bureau (CWB) Banciao weather station where is 121° 26′ 1.57″ E, 24° 59′ 57.5″ N in GRS67 (121° 26.3′ 111″ E, 24° 59′ 51.02″ N in WGS84). The distance between the location rawinsonde launched to the location where we observed the setting sun is 17 km and to the location where we observed the rising sun is 61 km. The rawinsonde launched at 00 hour UT and 12 hour UT every day, it presence 2 to 3 hours delay of the time we observed the setting or rising sun.. Fig 2.6. This map shows the northern Taiwan coast and where the location we observed. The red triangle with the letter S marked is the location we observed the setting sun, where is nearby the Tamsui district, New Taipei city. The red triangle with the letter R marked is the location we observed the rising sun, where is nearby the Gongliao district, New Taipei city. The red circle with the letter C marked is the location where the Central Weather Bureau (CWB) launched the rawinsonde.. 12.

(21) Data Process 3-1. Calibrate the altitude angle of the real sun (the unfracted sun) by the photo time. The camera time had been set to the real local time, it would record the time in the EXIF information when we take the setting or the rising sun, so we can uses the photo time to calibrate the altitude angle of the real sun (the un-refracted sun). The transit time is from the Astronomical Almanac, which longitude is recorded at the 120˚ E. We calculated the transit time to the longitude of observe location by. Where the Transit time' is the transit time at the observe location, unit in hour, the Lon is the longitude of observe location, the Transit time is the transit time at the longitude 120˚ E, unit is in hour too. The St means the sun position at the transit time, the transit time is Tt and the coordinates of the sun at transit time is αt, δt. The S means the sun position at the image time, the image time is T and the coordinates of the sun at image time is α, δ.. The coordinates of the sun at the transit time. and the image time are come from the USNO website.. 13.

(22) Fig 3-1. To calculate the angle θc from the transit time to the image time, the red line is the celestial equator and the right ascension line which zenith angle is 90 ﾟ. St is the sun at the transit time, S is the sun at the image time, St’is the sun at the transit time coordinates rotate to the image time. The dα, dδ are the difference of the coordinates between the transit time to the image time.. The time units are transformed into hour.. The time between the. transit time to the image time is dT, which is dT=T-Tt, during this time the celestial body had rotated an angle αt where αt=dT×15 ˚. When a celestial object rotate from the transit time to the horizon, it needs rotate more than 90 ˚ when the declination is greater than 0˚ , and needs to rotate less than 90 ˚ when the declination is less than 0 ˚, so that when the celestial body is maintain at the same coordinate from the transit time to the set time, it needs rotate 90 ˚+δ ’ ˚, where δ’ is an angle related with the declination, which δ’ is , 14. 3-1.1.

(23) Where δ is the declination, φ is the longitude of the observe location. Therefore, when the sun is at the transit time coordinate α t, δt, it needs rotate 90 ˚+δt’ ˚, where δt’ comes from the formula 3-1.1. But the sun is not stay at the same position, during the image time , the sun had moved to the coordinate α, δ. The RA is inverse the rotate direction of the diurnal motion, which moved an angle dα which is dα=α-αt. The declination had also moved an angle dδ which is dδ=δ-δt. The angle dδ would cause an little angle dδ’ on the RA direction to calculate the rotate angle by diurnal motion from the sun transit to set, where dδ’= δ’-δt’, and also equal to. When at the transit time, the sun needs to rotate an angle 90˚+δ t’ to reach the horizon. When at the image time, it needs to rotate an angle θc to reach the horizon. Consider the coordinates of the sun at the transit time and the image time is not the same, the angleθc is. Finally need to transport the celestial coordinates into the horizontal coordinates, the Z is the zenith, the sun at image time is S, the declication The angle α=sin-1[(sinφ)/(cosδ)],. of the sun at the miage time is δ.. δL=sin-1[(sin)/(cosφ)], θ= sin-1(sinα sinδL), β=cos-1[cosφ cos(θc-θ)], Lx=sin-1[sinφ/sinβ], N=Lx+δ-90 ﾟ, the altitude angle of the sun at the image time θx= sin-1[sinβ/sinN].. 15.

(24) Fig 3-2. To calculate the angle θc from the celestial coordinates to the altitude θx on the horizontal coordinate.. 16.

(25) 3-2 The Central Weather Bureau (CWB) rawinsonde data The Central Weather Bureau (CWB) rawinsonde data had been auto calibrated into hundred different layers from 11 meters height to about 34000 meters height, in order to precise simulate the light path in each layer of the air, we use linear interpolation of each layer into 200 layers. Therefore the vertical structure of the atmosphere has been separate into 24000 to 28000 layers. The observation of rawinsonde carried out at 12:00 UT September 17, 2011 is only up to 17422 meters height, it may cause error about 30".. 17.

(26) 3-3 The refraction index of the moist air The refractivity of the air is decide by the density of the air, and the density of the air is decide by the pressure, temperature, and relative humidity of the air, especially by the pressure and temperature. We used the refractivity model made by Ciddor in 1996, which contained with pressure, temperature, relativity humidity and the CO2 density to construct the refractivity. The refractivity of the air n in this model which followed by:       n   a naxs  1   w nws  1  1 (A)   ws    axs   , ............................... where the  a is the density of the dry air while the pressure and the temperature is under the observation situation which is in the formula (c1), the  axs is the density of the dry air which is under the standard states which is in the formula (c2), the naxs means the refractivity of the dry air while under the standard states and which is in the formula (a), the  w is the density of the pure water vapor while the temperature and pressure is under the observe situation and which is in the formula (c3), the  ws is the density of the pure water vapor while under the standard states and which is in the formula (c4), the n ws is the refractivity of the pure water vapor while under the standard states but the relativity humidity is 100% and it is in the formula (b), the standard states is defined as the temperature t is 15C , the pressure P is 101325 pa, the relative humidity is 0% and the. density of the CO2 is at 450 ppm.. 18.

(27) The naxs means the refractivity of the dry air which is under the standard states, which comes from: naxs  {(nas  1)[1  0.534 106 ( xc  450)]}  1 ,. (a) ............................... where the  c is the density of CO2 which is under the observe situation, and nas is the refractivity of the dry air which is under the standard states but not contained with the CO2 , which is:  k1 k3   108  1 nas    2 2  k2     k0   ,. where the  is the reciprocal of the vacuum wavelength in inverse micrometers, the k 0 , k1 , k 2 , k 3 are the constants involved in the standard phase and group refractivity of dry air where k0  238.0185m2 , k1  5792105m2 , k2  57.362m2 and k3  167917m2 , the . in our. program is set as 1/550 nm-1, and the density of CO2  c is set as 450 ppm. The n ws means the refractivity of the pure water vapor while under the standard states, it comes from:.  . . nws  cf w0  w1 2  w2 4  w3 6 108  1. ,. (b) ............................... where the  is the reciprocal of the vacuum wavelength in inverse micrometers, the w0 , w1 , w2 , and w3 are the constants involved in the standard phase and group refractivity of water vapor with value, w0  295.235m2. ,. w1  2.6422m2. ,. w2  0.032380m 4. and. w3  0.004028m 2 , the cf = 1.022 is the correction factor finds by fitting the. 19.

(28) calculations to the measurements, and the  in our program is also set as 1/550 nm-1. The  means the density of the air, which comes from:  M   PM a    1  X w 1  w  ,  ZRT    M a .  . (c) ............................... Where P is the pressure in pa, T is the temperature in K, R is the gas constant which value is R  8.314510J mol 2 K 1 , M w is the molecular weight of the water vapor which is M w  0.018015kg / mol , M a is the molecular weight of the dry air which contained with  c ppm of CO2 , and. . . M a  10 3 28.9635  12.011  10 6  X c  400. kg / mol ,. due to the CWB. rawinsonde doesn’t detected the density of CO2 , all the observed value  c were set as the value 450 ppm., and the  w is the mole fraction of the water vapor which is in the moist air, which is: Xw . f h svp P ,. (c-a) ............................... where the h is the relative humidity in %, the P is the pressure in pa, the f    P  t 2 is the enhancement factor of water vapor in air,   1.0662 ,.   3.14  10 8 pa ,.   5.6  10 7 C 2. and t  T  273.15C , T is the. temperature in K, the svp is the saturation vapor pressure of water vapor in. air,. which. A  1.2378847  10 -5 K -2. is ,. svp  exp AT 2  BT  C  D / T  B  -1.9121316  10 -2 K -1. D  -6.3431645  10 3 K .. 20. ,. pa. ,. and. C  33.93711047. ,.

(29) The Z is the compressibility of the moist air, which is defined by:. . . 2. . . P P 2 2 Z  1  ( ) a0  a1t  a2t 2  b0  b1t X w  c0  c1t X w    d  eX w , ...(c-b) T T  . Where the  w is the mole fraction of the water vapor which is in the moist air and is in the formula (c-a), the P is the pressure in pa, T is the temperature in K, t is the temperature in C , a 0  1.58123  10 -6 KPa -1 , a 1  -2.9331  10 -8 Pa -1. , a 2  1.1043  10 -10 K -1 Pa -1 , b 0  5.707  10 -6 K Pa -1 ,. b1  -2.051  10 -8 Pa -1. ,. c 0  1.9898  10 -4 K Pa -1. ,. c1  -2.376  10 -6 Pa -1. ,. d  1.83  10 -11 K 2 Pa -2 and e  -0.765  10 -8 K 2 Pa -2 .. While Z is meaning the compressibility of the dry air, the temperature T is 288.15K, the pressure P is 1013.25 pa, the mole fraction of the water vapor which is in the moist air  w is 0. Put all of these values into the formula (c-b), and then get the compressibility of the dry air Z a . While Z is meaning the compressibility of the pure water vapor, the temperature T is 293.15K, the pressure P is 1333 pa, the mole fraction of the water vapor which is in the moist air  w is 1. Put all of these values into the formula (c-b), and then get the compressibility of the pure water vapor Z w . The  a in the formula (A) is the density of the dry air while the pressure and the temperature is under the observation situation. It is under the situation that the temperature T and the pressure P is the temperature and pressure in each layer of the air we recorded during observed by the rawinsonde, and the relative humidity h is 0%, the density of CO2  c is set. 21.

(30) as 450 ppm., and the compressibility of the moist air Z is equal to the compressibility of the dry air Z a . Put all of these values into the formula (c), and then get the density of the dry air  a , it is the formula (c1). The  axs in the formula (A) is the density of the dry air while the pressure and the temperature is under the standard states. It is under the situation that the temperature T is 15 C , the pressure P is 101325 pa, the relative humidity h is 0%, the density of CO2  c is set as 450 ppm., and the compressibility of the moist air Z is equal to the compressibility of the dry air Z a . Put all of these values into the formula (c), and then get the density of the dry air  axs , it is the formula (c2). The  w in the formula (A) is the density of the pure water vapor while the pressure and the temperature is under the observation situation. It is under the situation that the temperature T and the pressure P is the temperature and pressure in each layer of the air we recorded during observed by the rawinsonde, and the relative humidity h in each layer is observed by the rawinsonde, the density of CO2  c is set as 450 ppm., and the compressibility of the moist air Z is equal to the compressibility of the pure water vapor Z w . Put all of these values into the formula (c), and then get the density of the dry air  w , it is the formula (c3). The  ws in the formula (A) is the density of the pure water vapor which is under the standard states. It is under the situation that the temperature T is 15 C , the pressure P is 101325 pa, and the relative 22.

(31) humidity h is 100 %, the density of CO2  c is set as 450 ppm., and the compressibility of the moist air Z is equal to the compressibility of the pure water vapor Z w . Put all of these values into the formula (c), and then get the density of the dry air  ws , it is the formula (c4). Finally combined the density of the dry air while the pressure and the temperature is under the observation situation  a , the density of the dry air while the pressure and the temperature is under the standard states  axs , the density of the pure water vapor while the pressure and the temperature is under the observation situation  w , the density of the pure water vapor which is under the standard states  ws , the refraction index of the dry air which is under the standard states naxs , and the refraction index of the pure water vapor while under the standard states n ws into the formula (A), got the refractivity in the each layer of air n. We use the Central Weather Bureau (CWB) rawinsonde data which record the pressure, temperature and relative humidity respond to the height and use these data to establish different refraction index of each layer of atmosphere.. 23.

(32) 3-4 The refraction between each layer of the atmosphere While a light path incomes from outside of the atmosphere, it would has a incidence angle in the top of the atmosphere, and the light path would followed the snell’s law on the surface of two different layer of atmosphere, which is shows on the figure.. Fig 3-3. The refraction between the boundary of different layers.. The radius of the earth. is 6374248 meters, which is from the. ellipsoid defined by WGS84, use the latitude of the observe location to calculate the radius to the center of the ellipsoid as RE. The height of the observe location h is also considered, so the radius of the observe location to the center of the earth R is RE+h, we assumed the earth is a sphere 24.

(33) because in our model the difference from sphere to ellipsoid is quite small to ignore.. The. are the different thickness of the. vertical atmosphere layers described in the chapter 3-2, the different refraction index are described chapter 3-3, and the refraction index outside the atmosphere is set as. .. The process of the light path is followed the snell’s law, refractive at the boundary of the different layer of the atmosphere. The light path would be curved continuously till light-ray reach the ground. On the first boundary between the first layer of atmosphere to the space, the incidence angle is. and the refraction angle is. . In the first layer. of the atmosphere, we could calibrate the incidence angle. of the second. boundary between the first and second layer of the atmosphere. The Complementary. angle. of. the. incidence. is. and the incidence angle of the second. is. .. Summary all above, we get the relation the angles reponding to the light path during each layer of atmosphere: In the first layer:. , ,. In the second layer:. , ,. In the last second layer:. ,. 25.

(34) ,. …….(3-4). In the last layer: , where the. in the last layer is the is the altitude angle of the refracted sun. in the astronomical refraction model.. 26.

(35) 3-5 The light path during the atmosphere We use the results calculated in 3-1 to calibrate the altitude angle of the unfracted sun (the real sun), but due to the refraction of the atmosphere, the light path is followed the real sun path which wouldn’t reach the observe place on the ground. If the light path reach the ground in front of the observe location, the incidence angle should add a little angle, , to correct the light path.. Fig. 3-4. The red line is the light path from the real sun, but due to the refraction of the atmosphere, the light path should a little higher than the red line, then the light path would be refracted then reach the ground where is the observer’s location.. The angle. is the original incidence angle on the top of the. atmosphere, which could calculate from the real sun’s altitude angle which had calculated in chapter 3-1. The. is. Then we could calculate the central angle. , which is. . We use the. as the incidence angle into chapter3-4 to calculate the 27.

(36) light path, and when the light path reach the ground, the refracted sun’s altitude. will be calculated, and all of the central angle. by summing. up the central angles during the process of the light path refracted in different layer of the atmosphere,. .. When the light path is followed the real sun’s light path (the red line in fig 3-5.1), the light path couldn’t reach the Observer’s position, it should followed the orange line path which had add a little angle to let the light path reaches the observer’s location. We add a little central angle. to let the light path reach the. observer’s location, due to the sun still not a real unlimited far object, the incidence angle should be changed to. while we add a little central. angle , and The angle. is comes from:. , Where the. is the distance between the earth and the sun at the photo. time calaulated from the USNO. The central angle. is restricted it conform to the equation, .. That means when the light path reach the ground, it is less than 0.556 meter around the observer’s real location.. 28.

(37) Result and Discussion At three dusk and at one dawn, the observations of the setting sun and rising sun with the measured real horizon, the images of seting/rising sun are compared with the model. However, there are six dusk and one dawn, only the images of setting/rising sun (without the measured real horizon) are also analyzed in the Appendix E.. For the observatioms of setting or rising sun without the real horizon, the sea level in the image is used as the real horizon, and it will derive the real horizon upper the sea level about 258.35" when the observer’s is at 5 meters height. The setting or rising sun without the measured real horizon ignored the terrestrial refraction which occurred the error of the real horizon is about 300".. 29.

(38) Fig 4-1.1. The refracted sun (blue) and the unfracted sun (pink), compared with the observed sun during the sunrise in September 17, 2011 with measured the real horizon. The pink dashed line is the real horizon from the observation, the green line is the apparent sea level at altitude=5 m and the green dashed line is the real sea level without the terrestrial refraction at altitude=5 m.. 30.

(39) Fig 4-1.2. The height to pressure fig (up) and the height to temperature fig (down) during observe at September 17, 2011 morning, the data is from the CWB rawinsonde which launched at 00:00 UT September 17, 2011.. 31.

(40) Fig 4-2.1. The refracted sun (blue) and the unfracted sun (pink), compared with the observed sun during the sunset in September 17, 2011 with measured the real horizon. The pink dashed line is the real horizon from the observation, the green line is the apparent sea level at altitude=5 m and the green dashed line is the real sea level without the terrestrial refraction at altitude=5 m.. 32.

(41) Fig 4-2.2. The height to pressure fig (up) and the height to temperature fig (down) during observe at September 17, 2011 night, the data is from the CWB rawinsonde which launched at 12:00 UT September 17, 2011.. 33.

(42) Fig 4-3.1. The refracted sun (blue) and the unfracted sun (pink), compared with the observed sun during the sunset in October 17, 2011 with measured the real horizon. The pink dashed line is the real horizon from the observation, the green line is the apparent sea level at altitude=5 m and the green dashed line is the real sea level without the terrestrial refraction at altitude=5 m.. 34.

(43) Fig 4-3.2. The height to pressure fig (up) and the height to temperature fig (down) during observe at October 17, 2011 night, the data is from the CWB rawinsonde which launched at 12:00 UT October 17, 2011. 35.

(44) Fig 4-4.1. The refracted sun (blue) and the unfracted sun (pink), compared with the observed sun during the sunset in October 28, 2011 with measured the real horizon. The pink dashed line is the real horizon from the observation, the green line is the apparent sea level at altitude=5 m and the green dashed line is the real sea level without the terrestrial refraction at altitude=5 m.. 36.

(45) Fig 4-4.2. The height to pressure fig (up) and the height to temperature fig (down) during observe at October 28, 2011 night, the data is from the CWB rawinsonde which launched at 12:00 UT October 28, 2011.. 37.

(46) Table 4-1. This table shows the unfracted incident angle, modeled refracted angle and the observed refracted angle on the different time during the observation on September 17, 2011 morning. The value means the altitude angle which is above the real horizon in degrees. The “Difference” means the difference between the modeled refraction angle and the observed angle in arcsec.. September 17, 2011 Sunrise Unfracted altitude. Modeled refracted. Observed refracted. Astronomical refraction. Difference. Upper limb. 1º 39' 2".85. 1º 56' 18".64. 1º 56' 12".88. 17' 10".02. 1' 31".19. Center. 1º 23 '8".28. 1º 41' 32".70. 1º 41' 27".02. 18' 18".74. 2' 09".41. Lower limb 1º 07' 13".70. 1º 26' 54".11. 1º 26' 45".53. 19' 34".83. 1' 40".11. Upper limb. 1º 48' 32".38. 2º 05' 01".57. 2º 05' 40".14. 17' 07".76. 0' 35".56. Center. 1º 32' 37".80. 1º 50' 14".70. 1º 51' 06".08. 18' 28".28. 0' 51".38. Lower limb 1º 16' 43".23. 1º 35' 31".69. 1º 36' 11".90. 19' 28".68. 0' 40".22. Upper limb. 1º 54' 38".49. 2º 10' 47".52. 2º 11' 08".63. 16' 09".02. 0' 21".11. Center. 1º 38' 43".92. 1º 55' 55".28. 1º 56' 06".55. 17' 11".36. 0' 11".27. Lower limb 1º 22' 49".35. 1º 41' 09".51. 1º 41' 42".43. 18' 20".16. 0' 32".92. Time. 21:48:10 UT. 21:48:52 UT. 21:49:19 UT. The mean of difference. 0' 57".02. The terrestrial refraction angle. 2' 15.59". 38.

(47) Table 4-2. This table shows the unfracted incident angle, modeled refracted angle and the observed refracted angle on the different time during the observation on September 17, 2011 evening. The value means the altitude angle which is above the real horizon in degrees. The “Difference” means the difference between the modeled refraction angle and the observed angle in arcsec.. September 17, 2011 Sunset Unfracted altitude. Modeled refracted. Observed refracted. Astronomical refraction. Difference. Upper limb. 1º 33' 10".31. 1º 50' 44".73. 1º 50' 30".95. 17' 20".64. 0' 02.86". Center. 1º 17' 15".86. 1º 36' 0".33. 1º 35' 46".17. 18' 30".60. 0' 16.31". Lower limb 1º 01' 21".42. 1º 21' 23".31. 1º 21' 08".69. 19' 47".27. 0' 11.23". Upper limb. 1º 11' 07".61. 1º 30' 51".71. 1º 31' 06".18. 18' 55".21. 0' 14.47". Center. 0º 56' 02".05. 1º 16' 16".87. 1º 16' 28".09. 20' 14".81. 0' 11.22". Lower limb 0º 40' 56".50. 1º 01' 50".38. 1º 01' 49".99. 21' 42".78. 0' 00.37". Upper limb. 0º 52' 29".20. 1º 13' 02".87. 1º 13' 13".16. 20' 33".67. 0' 10.26". Center. 0º 36' 34".75. 0º 58' 38".39. 0º 58' 55".14. 22' 03".64. 0' 16.75". Lower limb 0º 20' 40".31. 0º 44' 23".25. 0º 44' 43".84. 23' 42".95. 0' 20.59". Time. 09:50:44 UT. 09:49:18 UT. 09:47:44 UT. The mean of difference. 0' 11".57. The terrestrial refraction angle. 2' 10".45. 39.

(48) Table 4-3. This table shows the unfracted incident angle, modeled refracted angle and the observed refracted angle on the different time during the observation on October 17, 2011 evening. The value means the altitude angle which is above the real horizon in degrees. The “Difference” means the difference between the modeled refraction angle and the observed angle in arcsec.. October 17, 2011 Sunset Unfracted altitude. Modeled refracted. Observed refracted. Astronomical refraction. Difference. Upper limb. 1º 29' 09".21. 1º 46' 32".87. 1º 47' 28".10. 17' 23".67. 0' 55".22. Center. 1º 13' 06".36. 1º 31' 44".78. 1º 33' 6".26. 18' 38".43. 1' 21".47. Lower limb 0º 57' 03".51. 1º 17' 04".37. 1º 17' 39".33. 20' 00".86. 0' 34".96. Upper limb. 1º 02' 37".10. 1º 22' 56".32. 1º 23' 45".98. 20' 19".21. 0' 49".66. Center. 0º 46' 34".25. 1º 08' 20".78. 1º 9' 25".66. 21' 46".53. 1' 04".87. Lower limb 0º 30' 31".41. 0º 53' 53".96. 0º 54' 22".99. 23' 22".56. 0' 29".02. Upper limb. 0º 37' 38".36. 1º 00' 17".25. 1º 1' 14".61. 22' 38".89. 0' 57".37. Center. 0º 21' 35".51. 0º 45' 55".41. 0º 47' 15".92. 24' 19".91. 1' 20".50. 0º 31' 42".59. 0º 32' 48".14. 26' 09".92. 1' 05".56. Time. 09:16:57 UT. 09:18:52 UT. 09:20:44 UT. Lower limb 0º 5' 32".66 The mean of difference. 0' 57".63. The terrestrial refraction angle. 2' 23".89. 40.

(49) Table 4-4. This table shows the unfracted incident angle, modeled refracted angle and the observed refracted angle on the different time during the observation on October 28, 2011 evening. The value means the altitude angle which is above the real horizon in degrees. The “Difference” means the difference between the modeled refraction angle and the observed angle in arcsec.. October 28, 2011 Sunset Unfracted altitude. Modeled refracted. Observed refracted. Astronomical refraction. Difference. Upper limb. 1º 17' 20".14. 1º 34' 54".70. 1º 34' 26".99. 17' 34".56. 0' 27".71. Center. 1º 01' 17".29. 1º 20' 09".77. 1º 19' 41".74. 18' 52".48. 0' 28".04. Lower limb 0º 45' 14".44. 1º 05' 33".17. 1º 04' 58".71. 20' 18".72. 0' 34".45. Upper limb. 0º 44' 55".93. 1º 06' 12".36. 1º 06' 23".84. 21' 16".43. 0' 11".48. Center. 0º 28' 53".08. 0º 51' 44".19. 0º 52' 06".80. 22' 51".11. 0' 22".61. Lower limb 0º 12' 50".23. 0º 37' 25".09. 0º 37' 38".55. 24' 34".85. 0' 13".47. Upper limb. 0º 13' 56".06. 0º 39' 07".40. 0º 39'06".34. 25' 16".43. 0' 01".06. Center. -0º 02' 06".78 0º 24' 55".53. 0º 25' 33".37. 27' 51".11. 0' 37".84. Lower limb -0º 18' 09".63 0º 10' 46".57. 0º 10' 53".50. 28' 34".85. 0' 06".93. Time. 09:08:35 UT. 09:10:59 UT. 09:13:17 UT. The mean of difference. 0' 20".40. The terrestrial refraction angle. 1' 08".55. 41.

(50) The difference between the modeled and the observed sun with the measured real horizon, the maximum is 2' 09".41, and the minimum is 0' 01".06. The mean of difference is 0' 11".57 on September 17 evening, is 0' 57".63 on October 17, 2011 evening, is 0' 20".40 on October 28, 2011 evening, and is 57".02 on September 17 morning. The terrestrial refraction is 2' 15.59" on September 17, 2011 morning, is 2' 10".45 on September 17, 2011 evening, is 2' 23".89 on October 17, 2011 evening, and is 1' 08".55 on October 28, 2011 evening. The difference between the observed and the modeled sun may cause by: (a) The time interval between the observation and the rawinsonde launch. (b) The uncertainty of the composition of the real atmosphere. (c) The accuracy of the time. (d) The accuracy of the measured real horizon. (e) The inappropriate operator during the observation The time between the observation and the rawinsonde launch is 2 to 3 hours delay after the sunset or sunrise, the temperature of the atmosphere might be changed after the sunset or sunrise, especially the atmosphere near the ground which influence the refraction most and also changed temperature most significant during this time. The composition of the atmosphere we use the rawinsonde to detect, but it is only detect the pressure, temperature, and the relativity humidity, we know nothing about the amount of the ice, water and the cloud during the light path go through the atmosphere. When the period of sunset, we notice that when the sun has been covered by an obvious cloud, the 42.

(51) position of the Sun would be changed significantly. It is reasonable supposed that the refraction may be influence by the unobvious cloud that can be detected by the rawinsonde. The accuracy of the time in this work is less than 1 second, about 15". If we could improve the record time to 0.1 second, it could significant reduce the error of the difference of position of the setting sun between the model and observation. The accuracy of the measured real horizon in this work is more than 12", if we could use the electric total station which accuracy is 2" to measure the altitude angle between the landscape to the sun in the same image, we could make the measured real horizon more accuracy. For the observations before year 2011, it is not take into account the shaking of the reflex mirror in the DSLR, and it is also caused about 60" uncertainty of the field. For the obaervations during the year 2011, the method of. the mirror lockup and remote control the camera by a. computer is used, and the shaking of the camera with lens is reduced a lot.. 43.

(52) Conclusion We used the Canon DSLR camera with 400mm lens to observed the setting sun at Tamshui and observed of the rising sun near the Gouliao, then compared with the astronomical refraction model which established by the CWB rawinsonde data. In our work, the difference between the observed sun and the modeled sun with the measured real horizon, is about from 0' 01".06 to 2' 09".41. The mean of difference is 0' 11".57 on September 17 evening, is 0' 57".63 on October 17, 2011 evening, is 0' 20".40 on October 28, 2011 evening, and is 57".02 on September 17 morning. Total in mean is 0' 36".65. The terrestrial refraction is 2' 15.59" on September 17, 2011 morning, is 2' 10".45 on September 17, 2011 evening, is 2' 23".89 on October 17, 2011 evening, and is 1' 08".55 on October 28, 2011 evening. Total in mean is 1' 59".62. The CWB rawinsonde data is used to construct the vertical atmosphere structure, but in fact, the structure of the atmosphere in different places will be different. The rawinsonde is also not stay up of the same place, when the rawinsonde is increasing its height, it is also pushed by the wind to the different direction, so that the atmosphere structure of the rawinsonde detected may be not responded the real structure of the atmosphere above the observation place, especially to the west direction from the west coast of Taiwan, because the rawinsonde in the stratosphere would pushed by the wind to the east direction of the observe location. In order to construct a better vertical atmosphere. 44.

(53) structure, the other rawinsonde data launched at locations nearby the direction of setting sun should be used to improve the model of atmosphere at different height, especially the upper atmosphere like the stratosphere. The rawinsonde is also launched at different time of observe the setting sun, late about 3 hours from the sun setting, and the structure of the atmosphere would change during this period.. The structure of the. atmosphere at the right time could be calculated with numerical weather model. The terrestrial refraction in this work could be measured, but it could not simulated because the pressure and the temperature near the ground changed complex, and the pressure and temperature changed in small scale could influence the result of the refraction. The Lidar technology could be used to find the density and temperature along the light path (W.N. Chen, 2002), and the atmosphere structure along the light path may be constructed, and position of setting sun in the model may be improved .. 45.

(54) Reference Auer L. H., “Astronomical Refraction: Conputational Method for All Zenith Angles,” AJ, 119:2472-2474 (2000). Attas M. and McMurry J., “Nailing the Equinox Sunrise,” JRASC, 93, 163A (1993). Bruton D., “Optical Determination of Atmospheric Temperature Profiles,” Ph.D. thesis (Department of Physics and Astronomy, University of Texas A&M University, 1996). Chen W. N., “The measurements and scattering propertites of aerosol, cirrus, and temperature between 10-30 km above Chung_li,” Ph.D. (Department of Physies, National Central University, 2002). Chen C. L., “The Derivations of the Four-Part Formulae and Its Inference in Spherical Trigonometry,” Maritime Quarterly, Vol. 16 No. 2, June 2007, pp. 67~84 (2007). Ciddor P. E., “Refractive index of air: new equations for the visible and infrared,” APPLIED OPTICS, Vol. 35, No. 9 (1996). Garfinkel B., “Astronomical Refraction in a Polytropic Atmosphere,” AJ, 72, 235G (1967). Gubler J. and Tytler D., “Differential Atmospheric Refraction and Limitations on the Relative Astrometric Accuracy of Large Telescope,” PASP, 110:738-746 (1998). Kireev S. V. and Sokolovskiy S. V., “Variations of refraction angles from observations of the Moon from space,” Applied Optics, Vol. 33, No. 36 (1994). Mahan A. I., “Astronomical Refraction-Some History and Theories,” Applied Optics, Vol 1, No. 4 (1962).. 46.

(55) Sampson R. D., “Astronomical Refraction And The Equinox Sunrise,” JRASC, 94:26 (2000). Sampson R. D., “Astronomical Refraction and the Equinox Sunrise,” RASC, 94:26S (2000). Sampson R. D., “Comparison of modelled and observed astronomical refraction,” Ph.D. thesis (Department of Earth and Atmospheric Sciences, University of Alberta, 2001). Sampson R. D., “Variability in the Astronomical Refraction of the Rising and the setting sun,” PASP, 115:1256-1261 (2003). Sampson R. D., “Comparison of modeled and observed astronomical refraction of the setting Sun,” Applied Optics, Vol. 42, No. 3 (2003). Sampson R. D., “Variability of observed low-altitude astronomical refraction (LAAR) from different geographic locations: progress toward a global map of LAAR variability,” Applied Optics, Vol. 44, No. 27 (2005). Sampson R. D., “Variability in low altitude astronomical refraction as a function of altitude,” Applied Optics, Vol.47, No.34 (2008). Schaefer B. E., “Refraction Near The Horizon,” PASP, 102, 7968 (1990). Schiebener P. and Straub J., “Refractive Index of Water and Steam as Function of Wavelength, Temperature and Density,” J. Phys. Chem. Ref. Data, Vol. 19, No. 3 (1990). Smith, M. A., “Ptolemy’s Theory of Visual Perception: an English Translation of the Optics,” Transaction of the American Philosophical Society, Vol, 86, Part 2, 300 pp (1996). Thomas M. E., “Astronomical Refraction,” Johns Hopkins APL Technical Digest, Volume 17, Number 3 (1996). Wei M., Lei Y. and Tie Q. X., “On Astronomical Atmospheric Refraction,”. 47.

(56) j-chinastron, 2008.10.011 (2008). Astronomical Almanac 2010, Central Weather Bureau, Ministry of Transportation and Communications, R.O.C. (2010) Astronomical Almanac 2011, Central Weather Bureau, Ministry of Transportation and Communications, R.O.C. (2011) Department of Defense World Geodetic System 1984 Its Definition and Relationships with Local Geodetic Systems, NIMA STOCK NO. DMATR83502WGS84, NSN 7643-01-402-0347 (2000).. 48.

(57) Appendix A. The CWB rawinsonde data Table App-A-1. The CWB rawinsonde data at 00:00 UT September 17, 2011. 中央氣象局探空站氣象資料測站:466920 臺北 TAIPEI 時間：2011.09.17 00Z Levels : 141 經度：121°30' 24〞E 緯度：25°02' 23〞N [NLHMCWWAPP]=2550102305 T(℃) NO Si P(hPa) H(gpm) 1 1 1004.6 11 25.3 2 2 1003.1 24 24.9 3 10 1000 51 24.8 4 2 970 319 23.4 5 2 958.5 423 23.2 6 2 936.1 630 23.5 7 10 925 734 22.6 8 6 887 1098 20 9 2 884.4 1124 19.8 10 2 870.6 1260 20.2 11 2 866.2 1304 20 12 4 859.3 1373 18.9 13 2 854.2 1424 18.2 14 10 850 1466 18.3 15 2 839 1577 19.3 16 6 835.5 1613 19.2 17 6 821 1764 18.6 18 4 788.8 2105 17 19 2 783.1 2167 16.7 20 6 771.3 2296 16.8 21 2 762.9 2389 17.1 22 6 754.3 2486 16.9 23 6 707.6 3026 13.7 24 10 700 3117 13.1 25 2 555.3 5019 0.9 26 6 542.1 5210 -0.2 27 2 539.2 5254 0 28 2 534.6 5321 -0.6 29 6 524.2 5478 -1.5 30 2 520.8 5531 -2 31 2 509.2 5710 -1.7 32 10 500 5854 -2.5 33 6 478 6210 -4.2 34 6 456 6580 -6.3 35 6 447.7 6723 -7.3 36 10 400 7589 -13.1 37 6 391.9 7744 -13.9 38 6 385.5 7870 -14.7 39 2 380.6 7966 -14.7 40 4 376.1 8056 -15.5 41 6 336.1 8891 -22.5 42 2 335.1 8914 -22.7 43 2 326.4 9108 -24.5 44 6 325.7 9122 -24.6 45 2 323.6 9170 -24.9. 49. U(%) 74 75 75 83 75 59 61 73 74 45 42 64 77 75 30 25 18 26 27 18 11 9 8 8 20 10 4 28 17 26 4 3 3 1 2 1 1 1 1 6 26 25 63 57 31. Td(℃) WD(360°) WS(m/s) 20.3 185 0.9 20.1 0 0 20.1 0 0 20.3 211 1.8 18.6 17 1.8 15.1 28 3.7 14.6 19 3.1 15 18 3.7 15.1 18 4.1 7.8 25 7.9 6.8 23 9.4 11.9 21 11.5 14.2 30 10.7 13.8 38 9.5 1.5 47 7.7 -1.3 40 7.1 -6.1 11 6.5 -2.7 23 5.3 -2.5 20 5.3 -7.4 29 6.5 -13.4 22 7.4 -16.2 9 5.3 -19.8 27 5.3 -19.8 27 4.9 -19.9 283 4 -28.4 282 5.3 -37 288 6.3 -16.7 294 6.8 -23.4 318 5.1 -18.7 342 4.9 -40 297 1.9 -43 280 2.7 -42.8 215 5.2 -51.4 194 5.4 -51.1 165 5.9 -58.8 133 4 -59.4 166 5.4 -59.9 153 5.1 -59 143 3 -44.6 143 0.9 -37 191 5.4 -37.3 190 5.5 -29.6 164 6.8 -30.7 163 6.7 -37.3 166 6.3.

(58) 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106. 6 2 2 10 6 6 2 6 6 2 10 6 2 6 2 10 6 6 2 10 6 2 6 3 6 6 6 2 10 6 6 6 6 2 6 6 2 6 6 10 6 4 6 6 6 6 4 6 10 2 6 2 6 4 6 6 2 4 10 6 2. 315.4 314.2 309.9 300 297.9 289.9 284.2 282.2 257.1 255.2 250 247.3 220.4 202.1 200.3 200 185.1 160.1 155.4 150 130.7 130.5 117.8 115.2 112.3 108.2 102.4 100.1 100 95.7 90.2 86.6 83.4 81.8 81.1 78.9 74.9 73 70.9 70 68.7 67.2 66 61.7 57 54.7 53.9 51.6 50 48.9 47.3 47 43.4 40.2 37.4 32.7 31.3 30.8 30 29.9 29. 9355 9382 9483 9716 9767 9960 10101 10151 10799 10850 10993 11067 11845 12420 12479 12488 12989 13905 14087 14304 15126 15138 15731 15860 16007 16222 16538 16666 16674 16925 17268 17499 17714 17831 17877 18035 18342 18485 18653 18732 18837 18968 19076 19471 19955 20203 20294 20568 20757 20897 21098 21142 21639 22106 22566 23429 23698 23807 23972 23986 24188. -26.1 -26.3 -27 -28.9 -29.4 -31 -32.2 -32.4 -37.6 -38.1 -38.9 -39.3 -44.6 -49.6 -50.1 -50.1 -54.1 -61.7 -63.3 -65.4 -72.5 -72.7 -76.6 -77.4 -76.9 -76.3 -76.8 -77.2 -77.3 -76.8 -77.4 -76.7 -76.3 -74.9 -75.1 -75.1 -76.8 -75.9 -74 -74.3 -74.1 -73.1 -71.4 -69.4 -65.5 -64.2 -63.1 -61.8 -61.8 -61.4 -62.5 -62.7 -60.3 -58.4 -57.8 -55.3 -54 -54.1 -54.3 -54.2 -54.6. 50. 44 45 27 41 39 51 72 72 59 57 43 35 16 12 11 11 14 7 6 9 15 15 18 18 18 19 19 19 19 19 19 18 17 16 16 15 13 12 11 10 10 9 8 4 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -34.9 -34.9 -40.4 -38.2 -39.1 -37.9 -35.6 -35.8 -42.8 -43.4 -47 -49.1 -60.2 -67 -68 -68.1 -69.5 -80.8 -82.4 -82.2 -84.9 -84.9 -87.4 -88 -87.6 -86.8 -87.4 -87.8 -87.8 -87.2 -87.9 -87.5 -87.5 -86.6 -86.8 -87.4 -89.6 -89.2 -88.1 -88.6 -88.8 -88.7 -88 -89.5 -92.3 -93.8 -93.1 -92.2 -92.1 -91.9 -92.7 -92.8 -91.1 -89.7 -89.3 -87.6 -86.6 -86.7 -86.8 -86.7 -87. 205 207 206 212 214 190 201 205 201 203 218 228 234 227 230 230 257 202 204 194 162 162 203 190 165 186 141 142 141 137 64 84 64 73 74 54 62 63 89 88 88 102 113 101 131 80 74 49 63 73 96 96 87 98 116 110 97 91 78 77 83. 5.7 6 7.4 9.8 10.3 10.5 9.5 9.2 7.5 8 8.5 9.1 8.2 9.6 9.4 9.4 8.1 7.5 7.1 7 8.1 8.3 6.8 5.8 7.6 5.6 5.1 7.1 7.1 7.6 5.3 8.6 7.2 8.4 8.4 9.3 13.2 9.9 10.2 11.7 12.4 13.7 11.9 9.1 5.8 5.7 4.7 9.3 12.8 13.8 10.4 9.5 12.7 20.2 17.3 16.5 10.2 9.5 9.9 10 13.2.

(59) 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141. 4 6 2 6 6 6 6 4 6 10 2 6 6 2 6 6 2 6 2 6 4 6 6 6 10 6 6 6 2 6 6 2 6 6 20. 26.9 26 25.4 24 23.3 22 21.3 21.1 20.5 20 18.8 18.6 17 16.3 14.4 13.6 12.9 12.4 12 11.8 11 10.3 10.2 10.1 10 9.8 9.5 9.3 9.2 9.1 8.9 8.6 8.1 7.8 6.9. 24679 24888 25053 25425 25609 25982 26194 26259 26439 26609 27002 27064 27645 27940 28748 29158 29478 29784 29961 30067 30587 31001 31084 31139 31196 31299 31518 31681 31754 31836 31986 32224 32610 32913 33720. -50.9 -50 -49.3 -50 -49.4 -50 -50.7 -51.3 -51.9 -51.5 -52.6 -52.6 -49 -47.4 -46.2 -45.1 -44.7 -45.3 -46 -45.9 -44.3 -44.8 -45.2 -45.2 -45.5 -45.5 -45.3 -44.7 -44.8 -44.2 -41.7 -38.2 -37.8 -38.7 -37.3. 51. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -84.4 -83.8 -83.3 -83.8 -83.4 -83.8 -84.3 -84.7 -85.1 -84.9 -85.6 -85.7 -83.1 -82 -81.2 -80.3 -80.1 -80.5 -81 -81 -79.8 -80.2 -80.4 -80.5 -80.7 -80.6 -80.5 -80.1 -80.1 -79.8 -78 -75.6 -75.4 -75.9 -75. 100 110 95 73 82 46 53 62 90 82 72 72 108 104 94 128 110 148 147 153 80 6 9 20 42 95 105 57 46 38 53 52 55 56 21. 16.8 12.6 11.7 9.9 9 9.4 7.8 7.2 9.2 9 10.7 10.4 10 8.6 12.2 11.3 7.2 6 6.5 5.3 2.4 6.9 6.5 5.3 4.2 5.4 5.6 5.2 5.9 6.4 5.3 3.9 8.3 5.2 3.7.

(60) Table App-A-2. The CWB rawinsonde data at 12:00 UT September 17, 2011. 中央氣象局探空站氣象資料測站:466920 臺北 TAIPEI 時間：2011.09.17 12Z Levels : 72 經度：121°30' 24〞E 緯度：25°02' 23〞N [NLHMCWWAPP]=2550102315 T(℃) NO Si P(hPa) H(gpm) 1 1 1003.9 11 27.8 2 2 1002.4 25 27.8 3 10 1000 46 27.6 4 6 990.9 127 26.8 5 6 971.1 305 25.3 6 6 954.6 456 24.7 7 10 925 733 23.4 8 2 901 962 22 9 2 891.2 1058 23.2 10 4 870.1 1267 22.6 11 10 850 1469 21.5 12 6 834.5 1627 20.9 13 2 808.5 1900 19.9 14 4 795.3 2041 18.9 15 2 776.3 2248 17.4 16 6 752.7 2510 16 17 6 728.1 2791 14.6 18 2 722.3 2859 14.4 19 10 700 3122 12.4 20 2 613.6 4209 4.5 21 2 590.5 4521 2.8 22 6 571.7 4781 1.3 23 2 540.4 5235 -0.1 24 6 539.5 5247 -0.1 25 2 528.8 5407 -0.6 26 6 526.9 5437 -0.4 27 2 523 5496 -0.3 28 10 500 5854 -2.8 29 2 428.8 7056 -9 30 4 421.5 7190 -10 31 10 400 7590 -13.2 32 2 367.2 8237 -17.2 33 6 365.4 8274 -17.5 34 2 353.9 8512 -19.3 35 6 346.7 8665 -20.5 36 2 343.1 8743 -21.1 37 2 338 8853 -22.1 38 2 333.4 8954 -23 39 6 328.5 9062 -23.8 40 6 310 9483 -26.8 41 2 305.4 9590 -27.5 42 2 303.7 9630 -27.2 43 6 301.8 9676 -27.6 44 10 300 9719 -28 45 6 279.8 10214 -32 46 6 264.1 10621 -35.1 47 2 260 10729 -36.1 48 6 250.3 10992 -37.7 49 10 250 11000 -37.7 50 2 242.5 11209 -38.9 51 6 236.3 11388 -40.5. 52. U(%) 65 69 70 72 74 69 68 73 42 24 20 18 10 16 30 24 16 12 15 15 10 17 48 45 40 33 18 14 1 1 29 39 36 19 27 19 58 64 63 47 36 14 13 17 6 4 4 2 2 4 7. Td(℃) WD(360°) 20.6 83 21.5 95 21.6 95 21.3 97 20.4 91 18.7 66 17.3 83 16.9 124 9.4 85 1.3 342 -2.3 4 -4.6 16 -12.1 12 -7.6 18 -0.5 12 -4.4 8 -11.1 26 -14.4 26 -13.9 26 -20.2 9 -25.5 1 -21.2 353 -9.8 359 -10.5 359 -12.6 336 -14.8 331 -21.9 328 -26.4 346 -56.2 172 -56.6 0 -27.8 214 -27.9 229 -29 228 -37.1 191 -34.7 187 -38.9 195 -28.2 215 -28 228 -29 219 -34.7 214 -38.1 228 -46.6 233 -47.7 236 -45.6 234 -58.4 232 -63.5 253 -63.5 249 -70 232 -70.1 232 -66.4 242 -63.7 240. WS(m/s) 3.5 3.4 4.2 7 6.3 5.1 2.2 2.1 1.6 1 3.2 5.1 7.8 9.2 7.1 7 8.2 8.5 6.6 3.1 5.2 6.9 7.5 7.3 6.2 6 5.3 4.6 1.3 0 2.5 5.3 5.3 3.5 5.2 5.4 4.1 3.5 5.1 6.5 6.7 7.3 7.7 7.9 7.4 7.4 6.8 8.6 8.6 10 8.8.

(61) 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72. 6 6 6 10 2 6 6 10 2 6 6 6 6 6 2 6 6 12 6 6 20. 231.2 218.3 202.6 200 187.4 179.4 161.4 150 147.9 140 134.9 127.9 124.1 110.3 109.5 107.5 104.2 100 95.2 90.7 87.8. 11534 11921 12415 12500 12924 13201 13867 14318 14403 14736 14959 15272 15449 16129 16167 16272 16452 16686 16965 17237 17422. -41.9 -45.2 -48.9 -49.6 -52.7 -55.4 -61 -65.1 -65.9 -68.1 -69.7 -72.6 -74.2 -78.5 -78.8 -78 -78.6 -78.9 -79.7 -79.1 -78.3. 53. 9 10 5 5 4 9 13 14 14 14 14 15 15 19 20 21 23 25 27 27 27. -62.7 -64.4 -72.3 -72.8 -76.3 -73.6 -76.1 -78.9 -79.4 -81.3 -82.8 -85.2 -86.3 -88.7 -88.8 -87.8 -87.8 -87.6 -88 -87.3 -86.5. 222 241 201 201 195 193 208 200 200 179 197 171 177 154 151 131 131 107 135 84 85. 8.1 8.9 7.7 8 9.1 9.1 11 9.4 9.6 5.7 5.4 5.1 7 7.1 6.7 7.5 7.8 6.9 5.7 5.3 10.9.

(62) Table App-A-3. The CWB rawinsonde data at 12:00 UT October 17, 2011. 中央氣象局探空站氣象資料測站:466920 臺北 TAIPEI 時間：2011.10.17 12Z Levels : 125 經度：121°30' 24〞E 緯度：25°02' 23〞N [NLHMCWWAPP]=4550003214 T(℃) NO Si P(hPa) H(gpm) 1 1 1016.7 11 23.6 2 2 1015.1 25 23.6 3 10 1000 156 22.6 4 6 947.9 619 18.1 5 10 925 828 16.3 6 4 916.6 905 15.6 7 2 906.8 997 14.8 8 6 877.4 1275 13.3 9 10 850 1542 11.7 10 2 849 1552 11.6 11 2 837.2 1669 13.1 12 2 832.5 1717 12.9 13 2 830.2 1740 13.2 14 6 827 1773 13.4 15 2 824.6 1797 13.4 16 2 812.8 1919 14.5 17 4 801.1 2041 13.5 18 2 770.8 2365 11 19 6 769.6 2378 11 20 2 742.7 2675 10 21 2 732.4 2791 9.3 22 2 708.2 3068 7.7 23 6 704.2 3115 7.5 24 10 700 3165 7.3 25 2 675.6 3456 5.3 26 6 673.5 3482 5.2 27 2 634.2 3971 2.1 28 6 623.2 4112 1.4 29 2 592.2 4522 0.2 30 2 580.6 4680 0.4 31 2 506.8 5758 -6.7 32 2 501.9 5834 -5.9 33 10 500 5864 -6 34 2 491.6 5996 -6.6 35 6 469.5 6354 -8.5 36 2 449.9 6683 -10.5 37 6 408.6 7417 -15.4 38 10 400 7577 -16.6 39 6 374 8079 -19.4 40 2 370.3 8153 -19.8 41 6 328.3 9033 -26.6 42 6 309.5 9456 -30 43 10 300 9678 -31.9 44 10 250 10936 -42.8 45 2 248.8 10968 -43.1 46 2 219.4 11804 -48.8 47 10 200 12406 -53.6 48 6 187.5 12817 -56.6 49 4 174.6 13268 -59.9 50 6 158.5 13866 -64.5. 54. U(%) 63 60 62 76 79 82 84 81 99 99 43 43 70 82 85 62 63 89 89 30 58 70 69 69 81 80 66 62 48 27 40 22 21 11 9 7 8 7 3 3 9 33 33 45 46 7 9 8 9 16. Td(℃) WD(360°) 16.1 74 15.6 74 14.9 76 13.8 62 12.8 66 12.5 70 12.1 74 10.2 90 11.5 85 11.4 84 0.9 74 0.5 75 7.9 76 10.3 76 10.9 74 7.4 39 6.5 348 9.3 242 9.3 241 -6.6 283 1.4 306 2.5 299 2.3 294 2.1 288 2.3 263 2.1 261 -3.5 276 -5 278 -9.4 276 -16.3 275 -18.1 280 -24.2 278 -24.8 278 -31.9 276 -35.5 268 -39.5 264 -43 273 -44.5 270 -55.4 250 -54.4 250 -50.5 257 -41.1 273 -43 267 -50.1 266 -50.3 266 -69.6 268 -72.4 270 -75.5 278 -77.8 272 -77.7 261. WS(m/s) 3.8 3.2 6.1 10.1 10.8 11.1 10.5 8.5 6.7 6.7 6.7 6.2 5.8 5.1 4.6 1.9 1.4 5 5.1 4.1 4.2 4.7 5.1 5.5 7.3 7.5 8.6 9.4 13.2 15.4 15.4 16 16.2 17 18.3 18.2 17.6 17.8 16.1 16.7 15.7 19.4 19.8 23.3 22.9 22.9 23.5 22.2 25.6 24.7.

(63) 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111. 2 10 4 6 4 6 2 6 6 12 3 6 4 6 6 4 2 6 6 2 6 4 10 2 6 2 6 6 6 2 6 10 6 6 6 6 6 4 6 2 4 6 2 6 6 6 10 6 6 2 6 6 6 10 6 6 2 6 6 2 4. 151.9 150 132.8 119.6 115.1 114.1 111.6 107.6 103.7 100 99.2 97.7 95.6 93.6 89.8 88.4 87.6 84.1 81.3 79.9 79.1 70.9 70 62.5 60.9 58.7 56.9 53.1 51.6 51.4 50.2 50 47.4 45.3 43.6 42.1 40.8 39.9 37.5 37.3 36.3 35.3 35.1 33.9 31.5 30.7 30 29.4 27.9 27.5 25.3 23.1 20.8 20 18.8 17.8 17.5 16.9 16.5 15.9 15.3. 14122 14198 14927 15537 15760 15807 15934 16148 16356 16565 16610 16699 16822 16939 17178 17269 17318 17546 17747 17847 17907 18546 18625 19299 19453 19681 19876 20302 20478 20499 20641 20667 20991 21272 21521 21737 21935 22080 22455 22505 22662 22840 22875 23091 23568 23725 23871 24005 24332 24431 24965 25548 26249 26492 26904 27243 27376 27584 27774 27982 28261. -66.9 -67.1 -72.1 -75.5 -75.8 -76.1 -77 -76.5 -77.9 -78.8 -79.1 -78.7 -78.2 -78.3 -79.5 -80 -80.2 -76.7 -75.1 -73.1 -72.9 -71.5 -71.7 -68.6 -66.2 -63.5 -64 -63.2 -62.8 -62.6 -62.7 -62.8 -61 -60.5 -60 -59.5 -59.3 -58.6 -58.6 -58 -58.8 -59.8 -59.8 -57.8 -56.7 -56.3 -55.3 -55 -53.6 -52.7 -52.8 -52.1 -50.6 -50.2 -49.3 -48.7 -49.5 -48.6 -47.4 -45.8 -47. 55. 19 19 20 22 23 23 23 24 24 24 24 25 25 25 25 25 25 25 24 23 22 12 11 5 4 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -78.5 -78.6 -83 -85.2 -85.2 -85.5 -86.2 -85.7 -87 -87.7 -87.9 -87.4 -87 -87.1 -88.1 -88.6 -88.7 -85.5 -84.3 -82.9 -82.8 -85.4 -85.9 -87.7 -87.3 -88 -91.2 -93.2 -92.9 -92.8 -92.8 -92.8 -91.6 -91.3 -90.8 -90.5 -90.3 -89.9 -89.8 -89.5 -90 -90.7 -90.7 -89.3 -88.5 -88.2 -87.5 -87.3 -86.3 -85.7 -85.8 -85.3 -84.2 -83.9 -83.3 -82.9 -83.4 -82.8 -82 -80.8 -81.7. 268 269 276 281 248 241 241 251 238 257 262 263 240 219 221 231 239 277 273 299 311 0 208 265 305 4 63 106 89 89 108 108 73 107 104 139 116 123 115 111 63 31 35 82 91 80 96 102 88 86 89 64 73 69 71 46 47 61 42 48 49. 24.1 24.3 21.1 14 7.3 7.4 10.1 13.2 14 12.5 11 8 5.7 6.3 9.5 11.2 11.1 8.3 6.1 6.9 6.9 0 1.5 4.4 5.2 3.8 5.3 7.4 7 6.8 6.5 6.6 7.2 8.1 7.1 5.2 8 10.3 7.2 5.9 3.6 5.3 6.2 9.6 11 12.4 13.3 14 14.5 14.1 13.6 13.1 13.9 12.6 11.2 15 15.4 11.9 12 12.6 16.2.

(64) 112 113 114 115 116 117 118 119 120 121 122 123 124 125. 2 6 2 6 6 6 10 6 2 2 4 2 6 20. 15 14.7 13.4 13.2 12.3 11.8 10 9.5 9.4 8.8 8.5 7.7 6.9 6.5. 28386 28539 29140 29264 29723 29972 31086 31418 31525 31960 32143 32794 33514 33908. -47 -46.4 -43.5 -43.7 -45.6 -45.2 -48.5 -49 -49.2 -45.5 -47 -48.8 -46.4 -45.4. 56. 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -81.7 -81.3 -79.3 -79.4 -80.8 -80.5 -82.7 -83.1 -83.2 -80.7 -81.7 -82.9 -81.3 -80.6. 57 67 33 26 26 44 31 21 23 22 53 138 29 63. 15.2 12.8 9.9 11.2 8.7 6 3.4 6.4 6.4 2.6 1.6 4 9 11.8.

(65) Table App-A-4. The CWB rawinsonde data at 12:00 UT October 28, 2011. 中央氣象局探空站氣象資料測站:466920 臺北 TAIPEI 時間：2011.10.28 12Z Levels : 137 經度：121°30' 24〞E 緯度：25°02' 23〞N [NLHMCWWAPP]=2560002210 T(℃) NO Si P(hPa) H(gpm) U(%) 1 1 1016.7 11 23.6 2 2 1014.8 27 23.5 3 6 1005.3 110 22.8 4 10 1000 156 22.4 5 6 989.9 244 21.6 6 6 952 582 18.9 7 10 925 829 17 8 2 921.8 858 16.8 9 2 888.9 1168 15.2 10 6 853.3 1515 13.8 11 10 850 1548 13.6 12 6 840.4 1644 13.2 13 2 839.3 1654 13.1 14 2 811.6 1938 13.9 15 4 810.3 1951 13.9 16 2 786.7 2200 11.8 17 2 772 2358 11.3 18 2 763.2 2453 10.6 19 6 756.1 2531 10.5 20 6 744.8 2657 9.9 21 2 728.4 2842 9 22 6 725.6 2873 8.9 23 2 704.9 3112 8.6 24 6 700.9 3159 8.3 25 10 700 3170 8.2 26 2 672.8 3496 5.7 27 6 648.4 3798 3.8 28 6 635 3967 2.6 29 6 609.6 4297 1.3 30 2 583.2 4652 -1.2 31 2 574.2 4775 -0.3 32 6 567 4876 -0.4 33 6 551.6 5097 -1.2 34 2 542.9 5223 -1.7 35 6 518.1 5594 -4.4 36 2 504.9 5796 -5.7 37 2 501.7 5847 -6.1 38 10 500 5873 -6.3 39 2 492.7 5987 -6.6 40 2 476.7 6245 -8.3 41 2 465.6 6426 -9.3 42 6 456.6 6577 -10.5 43 6 441 6844 -12.9 44 6 434.7 6952 -13.7 45 2 429.1 7051 -14.4 46 2 424.7 7129 -14.4 47 10 400 7581 -18 48 2 374.5 8070 -22.2 49 2 348.8 8589 -25.1 50 6 344.6 8677 -26 51 2 331.5 8956 -28.1. 57. 78 74 75 76 79 84 86 87 89 85 88 89 89 61 59 73 52 67 47 37 22 27 37 36 37 69 65 70 54 55 44 44 39 35 35 27 39 37 20 36 17 22 35 37 37 15 29 33 20 22 26. Td(℃) WD(360°) WS(m/s) 19.5 81 4.2 18.7 76 3.6 18.2 73 5.6 18.1 81 6 17.9 94 7.5 16.2 72 12.9 14.8 86 10.1 14.7 85 10 13.4 98 9.9 11.4 108 8.4 11.7 112 7.7 11.4 132 5.2 11.3 134 4.8 6.5 27 1 6.1 11 0.9 7.1 257 2.6 1.9 259 4 4.7 238 5.8 -0.2 256 6.7 -4.1 250 5.1 -11.4 270 4.9 -9.1 269 5.2 -5.4 249 4.8 -5.8 248 5.1 -5.6 248 5.2 0.4 287 5 -2.2 330 5.7 -2.4 302 7.3 -7 276 5.1 -9 281 6.5 -11.1 286 5.5 -11.1 293 6 -13.3 272 6.3 -15.1 271 6.8 -17.7 283 10.1 -21.9 268 8.6 -18 264 9.6 -18.7 262 9.9 -25.7 250 8.8 -20.7 239 9.4 -29.7 236 9.4 -28 222 10.8 -25.3 241 11.4 -25.4 225 11.6 -25.9 231 11.5 -35.2 233 12.2 -31.8 240 14.6 -34 240 13.7 -41.7 255 18.3 -41.6 259 18.4 -41.9 256 17.3.

(66) 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112. 2 2 10 4 10 6 2 2 4 2 6 10 6 2 6 10 6 6 4 6 6 3 12 6 6 4 2 2 6 2 2 10 2 2 4 6 10 6 2 6 2 6 6 6 2 6 6 6 4 6 6 6 10 6 6 6 4 6 6 6 6. 319.6 303.6 300 269.6 250 230.6 223.7 220 217.9 210.3 203.8 200 190.5 178.1 161.7 150 133.1 124.2 120.1 118.7 111.6 108.3 100 97.7 91.5 87.9 87.6 79 78.3 74.3 73.3 70 69.5 61 57.3 50.5 50 48.7 48.1 45.7 45 42.5 40.7 39.3 38.5 37.9 37 35.5 33.6 32.6 32.1 30.3 30 29.9 28.1 27.1 25.5 23.7 21.9 21.2 20.7. 9217 9580 9664 10403 10911 11446 11644 11755 11815 12046 12248 12370 12682 13109 13711 14174 14895 15303 15501 15573 15932 16106 16564 16696 17081 17310 17333 17931 17985 18284 18364 18640 18684 19468 19843 20605 20665 20822 20904 21222 21318 21670 21944 22152 22291 22378 22538 22793 23143 23342 23435 23802 23871 23887 24293 24513 24919 25397 25904 26118 26286. -30.4 -33.3 -34.1 -40.3 -44.5 -49.3 -50.9 -51.4 -51 -51.6 -53.2 -54.3 -55.8 -57 -62.1 -64.7 -69.3 -72.1 -72.2 -72.6 -75.4 -76.7 -76.7 -75.1 -75.1 -74.2 -73.8 -76.7 -76.4 -74.7 -70.4 -69 -68.7 -69.2 -67.5 -64.6 -64.8 -63.9 -63.8 -60.8 -59.4 -60.9 -60.1 -59.5 -59 -59.1 -57.8 -55.9 -55.7 -55.2 -55.2 -55.8 -55.2 -55.2 -53.9 -53.7 -53.1 -50.2 -50.4 -50 -49.6. 58. 60 63 60 49 42 29 31 25 18 5 8 12 13 4 5 6 7 7 7 7 8 9 11 12 12 12 12 12 12 12 11 8 8 3 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -35.8 -38.1 -39.2 -46.9 -52.4 -59.6 -60.7 -62.9 -64.9 -74.1 -72.6 -70.9 -71.7 -79.7 -82.5 -83.7 -86.5 -89 -88.9 -89.3 -91 -91.6 -90.3 -88.7 -88.4 -87.7 -87.3 -89.9 -89.7 -88.2 -84.9 -85.4 -85.5 -91.1 -92.1 -94.1 -94.3 -93.7 -93.6 -91.4 -90.5 -91.5 -90.9 -90.5 -90.2 -90.2 -89.3 -87.9 -87.8 -87.5 -87.5 -87.9 -87.5 -87.5 -86.5 -86.4 -86 -84 -84.1 -83.8 -83.5. 262 265 265 266 263 269 264 262 261 250 244 245 258 255 253 253 251 243 225 219 236 232 238 229 273 280 278 232 236 260 283 238 201 139 0 48 58 99 105 27 36 69 71 104 109 108 84 100 81 80 97 92 80 77 116 76 72 47 71 58 79. 19.1 19.7 19.7 21.6 16.6 17.7 15 14 13.6 14.2 16.6 16.1 17.6 16.3 20.2 15.2 12.5 12.7 11.1 11.6 13.3 15.9 13.5 13.4 5.7 1.3 1.3 7.1 7.7 2.7 3.8 1.2 1.5 1.9 0 5.1 5.7 8 7.2 5.2 8.6 10.9 6.7 12 9.6 6.7 6 5.9 4 5.1 6.2 6.4 5.1 5.1 6.6 6.8 4.2 11.9 9.6 8.8 6.2.

(67) 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137. 10 2 6 2 6 6 6 6 6 4 2 6 6 6 6 10 6 6 2 6 6 2 6 6 20. 20 19.8 19.4 18.3 18.1 17.6 16.7 16 15.3 14.7 12.9 12.4 11.5 10.8 10.2 10 9.7 8.8 8.5 8.5 7.9 7.7 7.2 6.8 6.8. 26498 26564 26685 27069 27142 27349 27690 27949 28249 28530 29379 29652 30135 30590 30917 31071 31298 31936 32165 32175 32605 32816 33231 33587 33599. -49.2 -48 -48.3 -50.4 -50.4 -50.3 -49.4 -48.4 -48.9 -47.6 -44.9 -46 -46.9 -47.7 -47.7 -46.5 -47.5 -48 -49 -49 -46.1 -44.4 -46.4 -47.5 -47.3. 59. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. -83.2 -82.4 -82.6 -84.1 -84.1 -84 -83.4 -82.7 -83.1 -82.1 -80.2 -81 -81.6 -82.2 -82.2 -81.4 -82 -82.4 -83.1 -83.1 -81.1 -79.9 -81.3 -82.1 -81.9. 64 59 53 51 51 35 50 14 21 0 344 327 335 309 308 324 329 308 321 321 297 308 318 296 999. 9.9 10.7 11.1 9.7 9.7 9.4 8.4 8.7 5.2 0 7.4 5.2 6 7 9.8 13.2 12.3 16.2 13.4 13.2 12.5 15.3 12.3 6 999.9.