1 Looping Tracks Associated with Tropical Cyclones Approaching an Isolated 2 Mountain

1 Looping Tracks Associated with Tropical Cyclones Approaching an Isolated 2 Mountain. Part I: Essential Parameters 3 4 5 Yi-Chih Huang1,@ and Yuh-Lang Lin2,3 6 7 8 1 Research Center for Environmental Changes, Academia Sinica, 9 Taipei, Taiwan 10 2Department of Physics 11 3Department of Energy & Environmental Systems 12 North Carolina A&T State University 13 Greensboro, North Carolina 14 15 16 17 18 19 May 7, 2017 20 Submitted for publication 21 22 23 24 25 26 27 28 29 30 @Corresponding author address: Dr. Yi-Chih Huang, Research Center for Environmental 31 Changes, Academia Sinica, 128 Academia Road, Section 2, Nankang, Taipei, 115, 32 Taiwan. 33 Email: dscpln@gate.sinica.edu.tw 1 34 Abstract 35 Essential parameters for making a looping track when a westward-moving tropical 36 cyclone (TC) approaches a mesoscale mountain are investigated by examining several key 37 nondimensional control parameters with a series of systematic, idealized numerical 38 experiments, such as U/Nh, Vmax/Nh, U/fLx, Vmax/fR, h/Lx, and R/Ly. Here U is the 39 uniform zonal wind velocity, N the Brunt-Vaisala frequency, h the mountain height, f the 40 Coriolis parameter, the maximum tangential velocity at a radius of from the 41 cyclone center and Lx is the halfwidth of the mountain in the east-west direction. It is 42 found that looping tracks (a) tend to occur under small U/Nh and U/fLx, moderate h/Lx, 43 and large Vmax/Nh, which correspond to slow movement (leading to subgeostrophic flow 44 associated with strong orographic blocking), moderate steepness, and strong tangential 45 wind associated with TC vortex; (b) are often accompanied by an area of perturbation high 46 pressure to the northeast of the mountain, which lasts for only a short period; and (c) do 47 not require the existence of a northerly jet. The nondimensional control parameters are 48 consolidated into a TC looping index (LI), ℎ, which is tested by several 49 historical looping and non-looping typhoons approaching Taiwan’s Central Mountain 50 Range (CMR) from east or southeast. It is found that LI < 0.0125 may serve as a criterion 51 for looping track to occur. 2 52 1. Introduction 53 When a tropical cyclone (TC) makes a looping track, its impacts on rainfall and 54 gusty wind are dramatic and much stronger than a nonlooping TC. A TC may make a 55 looping track when it is blocked by a synoptic cold front [e.g., Hurricanes Dennis (1999), 56 Catarina (2004), Nadine (2012), etc.] or by a mesoscale mountain [e.g., Typhoons 57 Fungwong (2002), Haitang (2005), Krosa (2007), Sinlaku (2008), etc.]. In previous 58 studies, several mechanisms have been proposed to explain looping tracks of typhoons 59 when they approached Taiwan’s Central Mountain Range (CMR), which include the lee 60 vortex-tropical cyclone interaction (Yeh et al. 2012), the channel effect (Jian and Wu, 2008; 61 Huang et al. 2011), the vortex-vortex interaction with another typhoon (Zhang et al. 2011; 62 Yang et al. 2008), the horizontal advection of potential vorticity (Yu et al. 2007), and the 63 advection by orographically blocked basic flow (Lin et al. 2016). 64 Jian and Wu (2008) investigated the looping track of Typhoon Haitang (2005) with 65 the Weather Research and Forecasting (WRF) modeling simulations, which found that a 66 low-level northerly jet is induced by the channeling effect between CMR and the TC 67 vortex. The channel effect was induced by terrain, as originally proposed by Lin et al. 68 (1999) for explaining the southward deflection of drifting vortex passing over CMR, 69 which shifts the strongest winds of the storm to the western side of the eyewall. Based 70 on real-case and idealized simulations of Typhoon Krosa (2007), Huang et al. (2011) found 71 that strong channel winds were intensified between the storm and the topography just 72 before looping occurred. The mountain height was considered as the most important 73 factor in causing the looping track, compared to surface properties, details of topographic 74 shapes, and cloud microphysics. Using piecewise potential vorticity inversion analysis 75 and numerical model simulations, Yeh et al. (2012) attributed the Haitang’s looping to the 76 binary vortex interaction in which a CMR-induced lee vortex and Typhoon Haitang (2005) 77 rotate around their system centers. This lee vortex - TC interaction mechanism suffers 78 from the fact that when a westward TC approaches Taiwan’s CMR, lee vortex and 79 northerly jet are often observed, but not looping tracks. Note that it takes time for a lee 80 vortex to develop when a TC approaches CMR, which may propose a causality problem 81 even though intuitively the lee vortex – TC interaction mechanism seems working, 82 however, there might be a causality problem. 83 Employing the potential vorticity diagnosis of numerically simulated results, C.- 84 C. Yang et al. (2008) researched the binary interaction of Typhoons Fengshen (2002) and 3 85 Fungwong (2002). They found that in the earlier stage, the looping of Typhoon 86 Fungwong (2002) is mainly forced by Typhoon Fengshen (2002). Then a mutual 87 interaction occurs in the later stages. Additionally, the monsoon trough and subtropical 88 high pressure play a role in the binary interaction. Utilizing large-scale analyses, satellite 89 observations, and a nested, cloud-resolving simulation, Zhang et al. (2011) showed that 90 the vortex-vortex interaction with Typhoon Danas (2001) resulted in the looping track of 91 Typhoon Nari (2001). The interaction between Kuroshio Current and the vortex-vortex 92 interaction control the variable intensity of Typhoon Nari (2001) during the looping. 93 The vortex-vortex interaction also obstructs Nari accessing convective available potential 94 energy in the large-scale environment. While the vortex-vortex interaction mechanism 95 may work, it is not a necessary condition since TC looping did occur without the existence 96 of two nearby typhoons, such as Haitang (2005), Krosa (2007), Sinlaku (2009), etc. 97 Based on a typhoon model and potential vorticity (PV) budget analysis of 98 numerical simulations of Typhoon Haitang (2005), Yu et al. (2007) shed some lights on 99 the understanding of the movement of its looping track. Most of the time, the center of 100 Haitang moves to the region of maximum wavenumber one PV tendency, which is 101 predominantly caused by the horizontal advection and diabatic heating. The mid-level 102 warm air intrusion and the breakouts of low-level southwesterly jet lead to phase-lock 103 diabatic heating on the PV tendency field that eventually gives rise to the looping track of 104 Haitang. The sensitivity experiment suggested that the CMR may not be a crucial factor. 105 The horizontal advection and diabatic heating mechanism proposed by Yu et al. (2007) 106 for the looping track is appealing, nonetheless, a couple of questions may be raised: Why 107 are the two loopings over Taiwan Strait simulated by Yu et al. so different from 108 observations, and so much more distinct from the looping before landfall on Taiwan? Is 109 it possible that the unusual looping track was generated by the specific setting in the 110 numerical simulations? The sensitivity numerical experiments in M.-J. Yang et al. 111 (2008) showed that looping tracks were explained by the environmental steering flows 112 when the height of CMR was systematically increased. However, the dramatic change 113 of the steering flow from the control run to that with 75% terrain height remains 114 unexplained. Therefore, mechanisms for TC looping should be regarded as still not well 115 understood. 116 In summary, the key question for TC looping is: what are the environments 117 conducive to the formation of TC looping, or, specifically, what are the essential 4 118 dimensional and/or nondimensional parameters of the TC looping tracks when a TC 119 approaches a mesoscale mountain? Nondimensional parameters can simplify the 120 governing equations, provide insight on controlling factors and the nature of the problem, 121 and help predict the occurrence of TC looping. The investigation of nondimensional 122 parameters can be applied to various TC cases rather than only for a specific case. 123 Previously some key nondimensional parameters have been proposed to explain TC track 124 deflection and discontinuity (e.g., Lin et al. 1999, 2005). In this study, we plan to 125 conduct numerical simulations to investigate the ranges of essential nondimensional and 126 dimensional parameters associated with the TC looping. This will enhance our 127 understanding of the mechanisms for TC looping tracks caused by orographic forcing. 128 Furthermore, based on the essential nondimensional parameters and dimensional variables, 129 we will consolidate these parameters to construct a looping index for TCs. 130 The rest of this paper is organized as follows. The model description and 131 numerical experimental design can be found in section two. In the third section, we will 132 discuss the ranges of nondimensional parameters which control the TC looping, the related 133 regimes, basic physical fields, and a looping index. Conclusions are in the fourth section. 134 135 2. Numerical model description, and numerical experiment design 136 a. Model description 137 The numerical model utilized in this research is the Geophysical Fluid Dynamics 138 Model (GFDM) as described in Lin et al. (1999), which is based on three-dimensional, 139 primitive equations for a dry, stratified, hydrostatic, and Boussinesq fluid. There is no 140 cloud physics and planetary boundary layer included in this model. The governing 141 equations of the models are in the terrain-following coordinates (Gal-Chen and Somerville, 142 1975) and the characteristics of the GFDM are briefly summarized as follows: 143 The atmospheric variables are arranged on an Arakawa C staggered grid.

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