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A Dynamical Interpretation of the Wind Field in Tropical Cyclones with the Consideration of Orographic Factors

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A Dynamical Interpretation of the Wind Field in Tropical Cyclones with the Consideration of Orographic Factors Vol.16 No.2 JOURNAL OF TROPICAL METEOROLOGY June 2010 Article ID: 1006-8775(2010) 02-0125-09 A DYNAMICAL INTERPRETATION OF THE WIND FIELD IN TROPICAL CYCLONES WITH THE CONSIDERATION OF OROGRAPHIC FACTORS 1 1 2 3 HAO Shi-feng (郝世峰) , PAN Jin-song (潘劲松) , YUE Cai-jun (岳彩军) , CUI Xiao-peng (崔晓鹏) , YANG 1 Shi-fang (杨诗芳) (1. Zhejiang Meteorology Observatory, Hangzhou 310017 China; 2. Shanghai Typhoon Institute of China Meteorological Administration, Shanghai 200030 China; 3. LACS, Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing 100029 China) Abstract: Based on the barotropic primitive equation in the polar coordinate system and the appropriate assumption, we obtained the mathematical equation of orographic forcing on unit mass air parcel. With the consideration of the frictional stress of the sea and land, supposing that parcel velocity in tropical cyclones is in linear variation and that the distribution of surface pressure is circular, a set of equations are derived, which describe the impact of orographic slope error, the central pressure error and position error of tropical cyclones on the wind field in the tropical cyclone. Typhoon Wipha (2007) is selected to verify the above interpretation method. The results show that the orographic slope, the frictional coefficient, the intensity and position of the cyclone are the important factors which have great influence on the interpretation of wind information about tropical cyclones. The dynamic interpretation method gives very good results, especially for the coastal area. It is applicable to improving the forecasts of the wind field in tropical cyclones. Key words: tropical cyclone; orographic slope; frictional stress; strong wind; dynamic interpretation CLC number: P444 Document code: A doi: 10.3969/j.issn.1006-8775.2010.02.004 1 INTRODUCTION cyclones. In order to improve numerical forecasts, a lot of efforts have been made to refine model capability, Tropical cyclones are intense synoptic systems enhance initial fields, etc. However, forecast errors are which occur over the tropical ocean. Since the inevitable since the permanent existence of data errors conventional synoptic observations over the ocean are and model errors. Then how to interpret products of rare and unreliable, it is difficult to know the true numerical forecasts and lessen the influence of the structure of tropical cyclones and associated above mentioned errors becomes an important task. characteristics. Although there exist plenty of satellite Presently, methods for interpretation of products of observations, it is still difficult to get very good results numerical forecasts mainly include statistical due to some reasons, such as difficulties in assimilation interpretation (such as MOS, PP and Kalman filter), technology. They are the most important reasons that synoptic interpretation, artificial intelligence lead to the difficulties of forecasts of tracks, intensities, interpretation, etc. While no matter which method to wind and rainfall associated with tropical cyclones. select, the key factors influencing the errors must be The disasters caused by tropical cyclones are taken into account. According to the particularity of mainly induced by strong wind and heavy rainfall. typhoons’ structure, some reasonable typhoon models Torrential rainfall, especially typhoon-induced are set up by incorporating the main factors which torrential rainfall, has been studied extensively by [1-5] influence the wind and pressure field of tropical many scholars at home and abroad , but few studies cyclones, such as the Fujita formula, Myers formula have been carried out on the strong wind of tropical and a tangential wind velocity profile scheme by Received date: 2009-12-11; revised date: 2010-03-02 Foundation item: National Basic Research Program of China (973 Program) (2009CB421505); major projects for science and technology development of Zhejiang province (2007C13G1610002); major promoting projects for new technology of China Meteorologycal Administration (09A13) Biography: HAO Shi-feng, senior engineer, M.S., mainly undertaking the research on numerical predication. E-mail for corresponding author: [email protected] PDF created with pdfFactory trial version www.pdffactory.com 126 Journal of Tropical Meteorology Vol.16 Williams in 1987, and applied to practical operations. 2 [6] [7] ìdvr vq ¶f Zou and Xiao and Pu and Braun constructed ï-fvFq-=-+r Bogus schemes by using typhoon models and ïdtrr¶ assimilated them into initial fields, which improved ïdvvv 1 ¶f qq+r+fvF=-+, (1) forecasts. These simplified typhoon models could í r q ï dtrr¶q describe the main characteristics of typhoons since they ï¶f ® have the key factors. While the wind fields of these ï+Ñ·(f -=ghv)0 typhoon models are mainly symmetric, which are î¶t different from those of actual typhoons with apparent in which Fr and Fq are the frictional stress, h is asymmetric features, Lei and Chen [8] showed that the the height of terrain, and all other notations here are distributions of the physical fields associated with conventional in the meteorological context. The typhoons are often asymmetric due to the influences of subscripts “q ” and “ r ” indicate the tangential and the moving speed, frictional stress and environmental radial directions, respectively. Supposing that the synoptic systems. Many researches have focused on the geopotential equation of Eq.(1) is for stationary motion, asymmetric structures of typhoons at home and abroad. [9] ¶f Zhang and Sui put forward a model of wind fields of = 0 , and the distribution of geopotential height in typhoons by considering frictions in stable state in ¶t 1989, and discussed it under ideal conditions. Hu et al. tropical cyclones is circular, namely the zero order [10] and Huang et al. [11] further studied the model, ¶f approximation[13, 14], = 0 , the geopotential verified it by using wind fields of real typhoon cases r¶q and pointed out that this model was applicable in equation can be expressed as: describing the asymmetric distribution of wind fields of ¶f ®® tropical cyclones. vr =v·Ñgh-()f -Ñhgv. (2) In the previous work, researches are mainly ¶r restricted to the wind field of tropical cyclones on the By introducing the equation of continuity, Eq.(2) sea level. Hao et al[12] studied the dynamical can be further written as interpretation of wind field of tropical cyclones over ¶f ® v=v·Ñ+ghgw (3) the sea. Due to not considering the orographical factors, rs¶r their researches show that the interpretation effect is where w is the vertical velocity over the surface, not good on land, and the wind field on islands was not s which is the sum of vertical velocity caused by improved after the tropical cyclone landfalling. In this [15] paper, a dynamical interpretation method of wind fields orographic uplift and frictional effect , C ® of tropical cyclones, in which orographical factors wx=d +vh·Ñ , where x is the vorticity over were considered, is proposed by combining the method s f proposed by Hao with operational forecasts and by the surface, and C is the drag coefficient. By analyzing the key factors influencing wind fields in d tropical cyclones. substituting ws into Eq.(3) we obtain ¶f gCg¶¶hh =d x ++2()vv v ¹ 0 . (4) 2 DYNAMICAL INTERPRETATION ¶rvfvq rr¶¶q r r METHOD OF WIND FIELDS IN TROPICAL rr CYCLONES In Eq.(4), the second term expresses the radial orographic forcing on unit mass air parcel in tropical 2.1 Correction equation of numerical forecasts of cyclones on the condition that the atmosphere is wind fields in tropical cyclones barotropic, which is associated with the orographic slope, wind speed, and the angle between the wind By setting the center of tropical cyclones as the direction and orographic slope. Set the second term of origin of polar coordinates, the barotropical primitive Eq.(4) as equations of any air parcel in tropical cyclones could g¶¶hh be expressed as: frr=+2()vvq . (5) vrrr¶¶q Because the direction of forcing caused by the orographic slope and the orographic gradient are collinear, the tangential forcing caused by the orographic slope is PDF crea126t ed with pdfFactory trial version www.pdffactory.com No.2 HAO Shi-feng (郝世峰), PAN Jin-song (潘劲松) et al. 127 g¶h¶¶hh suitable to study the wind field over land surface f=+2[vv()21()]- . (6) qqvr¶qq¶¶rrr directly, they were introduced into the primitive r equation as modified terms as follows: As Eqs. (5 & 6) were obtained on the condition that the atmosphere is barotropic, which are not 2 ìdvrvq12¶pg¶¶hh ï-fvqq-=--d ()v++vFrr ïdtrrq¶rvrr¶¶ í r (7) dvvv 12¶pg¶h¶¶hh ïqq+r+fv=--d[v()21()]-++vF ï rrqq îdtrr¶qvrr¶qq¶¶rr 1 ¶p tropical cyclones is circular, -=0 , considering where d is the modified coefficient. r ¶q Supposing that parcel velocity takes on linear the influence of the speed of movement of tropical variation in tropical cyclones, that is, [16] cyclones, vs , on the cyclonic curvature radius r , dvr dvq = Cr , =-Cq are constants, further and setting the counter-clockwise direction to be dt dt positive, the frictional stress to be proportional to the supposing that the distribution of sea level pressure in square of wind speed and k to be frictional coefficient. Eq.(7) could be further written as: 2 ìvqqvvscosa 12¶pg¶¶hh 22 ï ++fvq=+d ()vqq+vr+kvrv++vCrr ïrrrq¶rvrr¶¶ í r (8) vvvv cosa2g¶h¶¶hh ïrq+rs +fv=-d[v()2()]-1+v-kvv22++vC ï rqrrqqq îrrvrr¶qq¶¶rr where a is the angle between the moving direction of ¶h Ng= 2d , and Q=+vv22, Eq.(8) can be tropical cyclones and the tangential direction of parcels. ¶r q r 1 ¶p ¶h By setting p = , Mg= 2d , expressed alternatively as: r ¶r r¶q 2 ìvqqvvscosa 1 ï++fvqq=p +()vM+vrN++kvrrQC ïrrv í r . (9) vvvv cosa 1 ïqr+rs +fv=-()vM21N- +vM-+kvQC ï rrqqq îrrvr Since the orographic slope is constant, obtain the influence of the error of the orographic slope ¶NM on wind speed as follows: MN22+=const , we can obtain =- .
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