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  • View in gallery
    Fig. 1.

    Ensemble track predictions of Typhoon Megi (2016) in September and the associated total 24-h accumulated rainfall (0000 UTC 27 Sep–0000 UTC 28 Sep) for forecasts starting at (a) 1800 UTC 25 Sep, (b) 0800 UTC 26 Sep, and (c) 0000 UTC 27 Sep. The black and red lines in (a)–(c) are the ensemble mean track and the best track, respectively. (d) The CWB best track from 24 to 28 Sep (shown at left) and the rainfall observation (mm) during 0000 UTC 27 Sep–2200 UTC 27 Sep (shown at right).

  • View in gallery
    Fig. 2.

    Model domains use coarse mesh D1 (black) and fine mesh D2 (red) at a resolution of 15 and 5 km, respectively, with the contours for terrain height every 1000 m and the coastline (the outermost green dashed line). The horizontal and vertical coordinates are grid points in the east–west and north–south direction, respectively. The mountain peak of 3500-m height is located at grid point (185, 201), and the initial vortex center (denoted by the solid circle) is located at grid point (261, 201).

  • View in gallery
    Fig. 3.

    The simulated wind speed (shaded) of model domain D1 (401 × 401) in the north–south cross section through the vortex center for U1V2R2 with WDM6 at different times.

  • View in gallery
    Fig. 4.

    The simulated wind speed (shaded) of model domain D1 (401 × 401) in the north–south cross section through the vortex center for U1V4R3 with WDM6 at different times.

  • View in gallery
    Fig. 5.

    Total accumulated rainfall in 120 h for U1 = 4 m s−1 and U3 = 8 m s−1 with different cloud microphysics WSM6 or WDM6, (a) U1 (WSM6), (b) U1 (WDM6), (c) U3 (WSM6), and (d) U3 (WDM6). The horizontal (east–west) and vertical (north–south) scales of each panel (denoted below the bottom) are 125 and 225 km, respectively. The terrain height contours (solid) are at in interval of 1000 m. The red line indicates the vortex track near the surface.

  • View in gallery
    Fig. 6.

    Horizontal wind at 1 km and the associated dBZ for (from top to bottom) U1V1R1, U1V2R1, U1V3R1, and U1V4R1 with WSM6 at (a) 81, (b) 84, (c) 87, and (d) 90 h. Coordinates are grid numbers of the inner domain at a uniform grid interval of 5 km.

  • View in gallery
    Fig. 7.

    As in Fig. 6, but for (from top to bottom) U1V1R2, U1V2R2, U1V3R2, and U1V4R2 with WSM6.

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    Fig. 8.

    The 120-h accumulated rainfall with WSM6 for the experiments varying the initial maximum wind from 30 to 35 m s−1 denoted by (a) U1V3R2 (30 m s−1), (b) U1V3R2-a (31 m s−1), (c) U1V3R2-b (32 m s−1), (d) U1V3R2-c (33 m s−1), (e) U1V3R2-d (34 m s−1), and (f) U1V4R2 (35 m s−1).

  • View in gallery
    Fig. 9.

    The horizontal wind and the radar reflectivity at (from top to bottom) different times for the sensitivity experiments with the varying initial maximum wind as in Fig. 6 for (a) U1V3R2 (30 m s−1), (b) U1V3R2-a (31 m s−1), (c) U1V3R2-b (32 m s−1), (d) U1V3R2-c (33 m s−1), (e) U1V3R2-d (34 m s−1), and (f) U1V4R2 (35 m s−1).

  • View in gallery
    Fig. 10.

    The horizontal wind and the radar reflectivity with WSM6 at different times (39 and 42 h) for (a) U3V4R1, (b) U3V4R2, (c) U3V4R3, and (d) U3V4R4.

  • View in gallery
    Fig. 11.

    As in Fig. 5, but for double-sized terrain with WSM6 for (a) U1 (4 m s−1) and (b) U3 (8 m s−1). The horizontal (east–west) and vertical (north–south) scales of each panel are 225 and 325 km, respectively.

  • View in gallery
    Fig. 12.

    The averaged accumulated rainfall (mm) over the counted terrain heights above 100 m, where south, north, and all in the plots indicate the amounts over the northern half, southern half, and entire grid of the model terrain, and max is the maximum rainfall (mm) over all the counted terrain grid points, with respect to the experiments varying the vortex size. The maximum rainfall is referred to in the right coordinate.

  • View in gallery
    Fig. 13.

    As in Fig. 12, but with respect to the experiments varying the initial maximum wind of the vortex.

  • View in gallery
    Fig. 14.

    As in Fig. 12, but with respect to the experiments varying the initial steering wind speed.

  • View in gallery
    Fig. A1.

    The simulated tracks (lined dots) for the double rainfall sensitivity experiments of (a) CTL, (b) S4, (c) N4, (d) A330, (e) A300, (f) R120, (g) R160, (h) ST4, and (i) ST8 at an interval of one hour from 36 to 60 h. Contours are for terrain heights, from 1 m (the outer contour) and every 500-m interval. CTL uses U = 6 m s−1, Vmax = 40 m s−1, and R = 80 km; S4 and N4 are as in CTL, but with the initial vortex southward and northward shifted by four grids, respectively; A330 and A300 are as in CTL, but with the terrain rotated 330° and 300° clockwise (from the north), respectively; and R120 and R160 are as in CTL but with R = 120 km and R = 160 km, respectively. ST4 and ST8 use U = 4 m s−1 and U = 8 m s−1, respectively. The coordinates are grid points at a uniform interval of 5 km.

  • View in gallery
    Fig. A2.

    The 60-h accumulated rainfall (shaded colors in an interval of 100 mm) overlapped with the horizontal wind at 60 h for the double rainfall sensitivity experiments of (a) S4, (b) CTL, (c) N4, (d) A330, (e) A300, and (f) R160. Contours are for terrain heights, from 1 m (the outer contour) and every 1000-m interval. The coordinates are grid points at a uniform interval of 5 km.

  • View in gallery
    Fig. A3.

    The horizontal wind near the surface and accumulated rainfall (mm) in 6 h at (a) 36 and (b) 48 h for CTL. The black line at each panel is the 12-h backward trajectory of near-surface air parcel released near the surfaced from the time for the panel. Coordinates are grid numbers of the domain at a grid resolution of 15 km.

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Topographic Rainfall of Tropical Cyclones past a Mountain Range as Categorized by Idealized Simulations

Ching-Yuang HuangDepartment of Atmospheric Sciences, National Central University, Jhongli, Taiwan

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Cher-Wei ChouWeatherRisk Explore Incorporation, Taipei, Taiwan

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Shu-Hua ChenDepartment of Land, Air, and Water Resources, University of California, Davis, Davis, California

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Jia-Hong XieCentral Weather Bureau, Taipei, Taiwan

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Abstract

Topographic rainfall induced by westbound tropical cyclones past an island mountain is investigated using an idealized Weather Research and Forecasting (WRF) Model. Idealized simulations with varying vortex core size R (100–250 km), vortex intensity Vmax (20–35 m s−1), and steering wind speed U (4–10 m s−1) are conducted. The results show that the geometric distributions of major rainfall over the island are not greatly sensitive to cloud microphysics schemes using either single momentum or double momentum. Major rainfall is produced over northeastern and southwestern slopes of the mountain for smaller U. As U is doubled, the rainfall, however, is considerably weakened or is present only over southwestern slopes. For smaller U, a bifurcation of island rainfall with a sudden change in intensity or geometric shifting exists within a tiny range of R or Vmax. When the bifurcation occurs with small track deviations, geometric distributions of major rainfall are also more sensitive to cloud microphysics schemes. Such formation of bifurcation or double-peak rainfall, however, is significantly reduced when the terrain size is doubled. Systematic experiments are conducted to relate the topographical rainfalls over the northern half, southern half, and the whole of the mountain slopes to varying R, Vmax, and U. Larger U tends to produce much larger southern rainfall than northern rainfall. The average and maximum rainfalls generally increase with increased Vmax, except for large R. The decrease of average rainfall and maximum rainfall with increased U is more evident for smaller R, while not necessarily true for larger R.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ching-Yuang Huang, hcy@atm.ncu.edu.tw

Abstract

Topographic rainfall induced by westbound tropical cyclones past an island mountain is investigated using an idealized Weather Research and Forecasting (WRF) Model. Idealized simulations with varying vortex core size R (100–250 km), vortex intensity Vmax (20–35 m s−1), and steering wind speed U (4–10 m s−1) are conducted. The results show that the geometric distributions of major rainfall over the island are not greatly sensitive to cloud microphysics schemes using either single momentum or double momentum. Major rainfall is produced over northeastern and southwestern slopes of the mountain for smaller U. As U is doubled, the rainfall, however, is considerably weakened or is present only over southwestern slopes. For smaller U, a bifurcation of island rainfall with a sudden change in intensity or geometric shifting exists within a tiny range of R or Vmax. When the bifurcation occurs with small track deviations, geometric distributions of major rainfall are also more sensitive to cloud microphysics schemes. Such formation of bifurcation or double-peak rainfall, however, is significantly reduced when the terrain size is doubled. Systematic experiments are conducted to relate the topographical rainfalls over the northern half, southern half, and the whole of the mountain slopes to varying R, Vmax, and U. Larger U tends to produce much larger southern rainfall than northern rainfall. The average and maximum rainfalls generally increase with increased Vmax, except for large R. The decrease of average rainfall and maximum rainfall with increased U is more evident for smaller R, while not necessarily true for larger R.

© 2019 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ching-Yuang Huang, hcy@atm.ncu.edu.tw

1. Introduction

Tropical cyclones moving past an isolated mountain have been widely investigated using observations and numerical models (e.g., Brand and Blelloch 1974; Chang 1982; Bender et al. 1987; Yeh and Elsberry 1993a,b; Lin et al. 1999, 2002, 2005; Kuo et al. 2001; Huang and Lin 2008; Jian and Wu 2008; Lin and Savage 2011; Huang et al. 2011; Wu et al. 2015; Tang and Chan 2015, 2016a,b; Huang et al. 2016; Hsu et al. 2018; Huang and Wu 2018). Topographical effects of a mesoscale mountain not only cause track deviations of approaching tropical cyclones but also enhance the rainfall over the mountain and thus greatly modify the rainfall distributions associated with the cyclones (e.g., Wu and Kuo 1999; Wu 2013). Wu and Kuo (1999) summarized the general characteristics of the typhoons impinging on Taiwan where the Central Mountain Range (CMR) peaks at 3.5 km and stretches about 300 km long and 100 km wide. One significant result of the rainfall produced by these impinging typhoons is that the distribution of major rainfall statistically resembles the contours of terrain height, often referred to as the “phase lock by terrain” mechanism. The geometric high asymmetry of the island rainfall exhibited in specific cases is statistically reduced, thus simply displaying the steepness effect of the slopes, regardless of being upwind or downwind.

The phase-locking mechanism provides a basic understanding of the topographic rainfall over the CMR associated with the typhoons from different impinging directions (e.g., Wu and Kuo 1999). However, the variability of intense rainfall over the terrain may sometimes be particularly large even for small track deviations, evident in observations as well as in predictions (e.g., Wu et al. 2002; Fang et al. 2011). One example is the event of moderate Typhoon Megi in late September 2016 that translated west-northwestward at a speed of 22 km h−1 prior to landfall at eastern Taiwan. Figure 1 shows the observed and predicted tracks and rainfalls associated with Megi based on about 20 ensemble forecasts using the Weather Research and Forecasting (WRF) Model with different physics schemes and initializations described by Hsiao et al. (2013). At an earlier initial time of 1800 UTC 25 September, prior to landfall, all the ensemble forecasts exhibit the west-northwestward movement of Megi, but with spreading tracks mostly southward biased (Fig. 1a). Most of the ensemble tracks remain to keep a similar west-northwestward movement, but still associated with southward track biases and landfall positions when initialized later at 0800 UTC 26 September (Fig. 1b). The ensemble mean forecast with these spreading tracks shows daily rainfall mostly at the east side of the CMR, while the observations exhibit two major rainfall regions over the northeastern and southwestern slopes of the CMR that are nearly disconnected (Fig. 1d). Note that the ensemble rainfall pattern during this stage is similar to the observed rainfall of Typhoon Bilis (2000) with a similar track as simulated by Lin et al. (2002). This double-peak rainfall pattern cannot be fully realized until the model forecast is initialized at 0000 UTC 27 September to obtain a more consistent ensemble mean track somewhat shifted northward to follow the best track (Fig. 1c). The official forecast by Central Weather Bureau (CWB) of Taiwan gives a west-northwestward track but without such northward shifting, thus leading to the underpredicted rainfall over southwestern Taiwan (figures not shown).

Fig. 1.
Fig. 1.

Ensemble track predictions of Typhoon Megi (2016) in September and the associated total 24-h accumulated rainfall (0000 UTC 27 Sep–0000 UTC 28 Sep) for forecasts starting at (a) 1800 UTC 25 Sep, (b) 0800 UTC 26 Sep, and (c) 0000 UTC 27 Sep. The black and red lines in (a)–(c) are the ensemble mean track and the best track, respectively. (d) The CWB best track from 24 to 28 Sep (shown at left) and the rainfall observation (mm) during 0000 UTC 27 Sep–2200 UTC 27 Sep (shown at right).

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

The above mechanisms controlling topographic rainfall over the CMR appear effective in a climatological sense. For example, Typhoon Soudelor in August 2015 also moved along a northwestward track with a landfall location very similar to Megi and showed a great resemblance of accumulated rainfall to Megi’s (figures not shown). For both Megi and Soudelor, variations of accumulated rainfall can be correlated with their tracks accompanying northward deflection prior to landfall. To understand the mechanisms of track deviations due to interaction with mountain topography, a number of numerical studies, as mentioned above, have utilized an idealized model to investigate the upstream track deflection of a westbound tropical cyclone past a mountain range similar to the CMR.

Based on the systematic experiments, Huang et al. (2016) by extending earlier works of Lin et al. (2005) and Huang and Lin (2008) have related the upstream track deflection to the dominant factor R/Ly (the nondimensional vortex size) with Ly (the mountain length scale in the direction normal to the vortex movement) and R (the radius of Vmax), among potential parameters including Lx (the mountain length scale in the direction of the vortex movement, h (the mountain height), U (the basic flow speed), Vmax (maximum tangential wind of the initial vortex), and N (environmental stability frequency). The basic-flow Froude number (U/Nh) was found to play no major role in the direction of track deflection, but influence significantly the degree of deflection. However, the duration of rainfall over the terrain is essentially dictated by the translation speed of the impinging typhoon. Thus, the intensity of steering flow plays an important role in the total rainfall production over the terrain, not only due to the duration of passage time over the terrain but also due to the track deflection (e.g., Chien and Kuo 2011; Wang et al. 2012).

Most of the above studies have focused on the upstream track deflection, although rainfall activities indeed are involved in their simulations. Since the associated rainfall of an impinging typhoon over the terrain is an essential product of typhoon forecasts, it is worthy of systematically investigating the geometric distributions of major rainfall over idealized topography so that the complexity of irregular mountain shapes can be simplified without loss of general understanding. Based on systematic experiments, this study is the first attempt to explore the sensitivity of the topographic rainfall with a statistical realization to several potential important parameters. Based on idealized experiments without a mountain and steering flow, Fovell et al. (2009) found that the tracks of tropical cyclones on a beta-plane are influenced by use of different cloud microphysics schemes that may give different cloud-radiation effects. Sensitivity of topographic rainfall to different cloud microphysics schemes will be investigated as well in this study. We will focus on a fixed mountain island with an idealized CMR and three chosen parameters (i.e., U, Vmax, and R). An idealized WRF Model with comprehensive physics is applied to investigate such variability and sensitivity of topographic rainfall with respect to these parameters. To reduce the freedom and dynamic complexity, we will not consider the beta effects as it will introduce additional beta drift to the vortex motion (e.g., Chan and Williams 1987; Tang and Chan 2015, 2016a,b) before it approaches to the mountain barrier.

This paper is organized as below. Numerical aspects are given in section 2 to introduce the numerical model and experiments in this study. Simulated rainfalls based on sensitivity experiments are presented in section 3. A bifurcation of island rainfall with a sudden geometric shifting or intensity change is also identified from the sensitivity experiments and is discussed in this section. In particular, factors affecting the double-peak rainfall formation as Megi exhibits are investigated. We have further conducted systematic experiments to relate areal average and maximum rainfall over the montane island to the three chosen parameters, U, Vmax, and R, in section 4. Finally, conclusions are given in section 5.

2. Numerical aspects

a. The numerical model

The WRF Model version 3.3.1 (http://wrf-model.org/index.php; Skamarock et al. 2008) is employed for the idealized experiments in this study. The WRF Model is nonhydrostatic in terrain-following coordinates. The model domain in this study includes two nested grids with the same 41 vertically stretched layers topped at 20-km height. The model simulations use the Yonsei University (YSU) planetary boundary layer (PBL) parameterization, the WRF single-moment 6-class graupel (WSM6) or double-moment 6-class cloud microphysics schemes (WDM6), and the modified Tiedtke cumulus parameterization (for the references of these parameterization schemes see the above WRF website). Radiative effects are not included in the simulations since the track deviation is mainly concerned near the topography at a short time scale.

All the simulations that are conducted in this study are considered on a constant-f plane at 23.5°N. A tropical sounding is used for model initial conditions as described in Huang et al. (2016). The sounding is conditionally stable below the tropopause and the relative humidity (RH) linearly decreases with height from 90% near the surface to 80% at 1 km and then to 30% at 10 km. Above 10 km, a constant RH of 30% is assumed. Environmental wind and moisture are assumed horizontally homogeneous. The steering flow condition can then be solved using thermal-wind balance. During the WRF Model integration, open boundary conditions are specified at all the lateral boundaries, while a 4-km sponge layer is imposed near the model top to absorb the reflected waves from the upper boundary. The initial sea surface temperature is set to 300.15 K and is fixed during the total 120-h model integration. The initial potential temperature near the surface is slightly warmer than that at the surface. This stable surface layer prevents the vortex from rapidly developing through convective instability.

b. Vortex initialization and experiments

The static vortex initialization scheme developed by Nolan (2011) was used to obtain the initial vortex in gradient-wind balance. The radial profile of the tangential wind is a modified Rankine vortex, which decays exponentially with height as described in Stern and Nolan (2011). The vortex is superimposed into the steering flow. The model takes some time to develop the Ekman flow in the planetary boundary layer. Thus, our experiment design ensures that the initial vortex is far away from a prescribed mountain so that the flow reaches a quasi-stationary state before the vortex is approaching to the mountain. In all the experiments, the mountain barrier is prescribed by a Gaussian function and is embedded in an island. For the surface type of each grid point, it is defined as a land surface if the terrain elevation is higher than 1 m; otherwise it is defined as a water surface. Both vortex initialization and terrain formulation are described in more detail in Huang et al. (2016).

In the experiments in Table 1, the steering flow U is varied as U1 = 4 m s−1, U2 = 6 m s−1, U3 = 8 m s−1, and U4 = 10 m s−1; the maximum tangential wind of the vortex Vmax as V1 = 20 m s−1, V2 = 25 m s−1, V3 = 30 m s−1, and V4 = 35 m s−1; and the radius of Vmax (R) as R1 = 100 km, R2 = 150 km, R3 = 200 km, and R4 = 250 km. Thus, experiment U1V2R3 stands for the initial vortex at an intensity of V2 and a core size of R3 under the steering flow of U1, and so on. Note that use of R1 beginning at 100 km may be slightly larger than many intense cyclones. Pu and Braun (2001) showed that use of R = 40 or 120 km only leads to minor differences in simulated hurricane tracks and intensities based on bogus data assimilation experiments. Therefore, we only consider some categorized representative radii of tropical cyclones as used in other idealized modeling studies (e.g., Lin et al. 2005).

Table 1.

Experiments for a typical cyclone (at size R and intensity V) past an island mountain with a peak of 3500 m. Here, Ux represents the steering flow speed (x = 1, 2, 3, 4) with U1 = 4 m s−1, U2 = 6 m s−1, U3 = 8 m s−1, and U4 = 10 m s−1. The WRF single-moment class-6 (WSM6) or double-moment (WDM6) cloud microphysics scheme is used.

Table 1.

The range of U from 4 to 10 m s−1 may cover most of the observational cyclone translational speeds (e.g., Yeh and Elsberry 1993a; Chien and Kuo 2011). The mountain range consists of a central peak h at a height of 3500 m and the length and width approximate to those of the CMR in Taiwan. The outer and inner grid meshes are shown in Fig. 2 with 401 × 401 grid points and 241 × 241 grid points at a uniform interval of 15 and 5 km, respectively. The vortex center and mountain peak are located on the grid points (261, 201) and (185, 201) in the outer domain, respectively, thus apart by 1140 km. In this study, we only consider moderate tropical cyclones at an intensity of V4 or weaker. This is because a more intense westbound tropical cyclone tends to deflect slightly northward before closing to the mountain, mainly in response to the associated moist asymmetric convection in the presence of the boundary layer as exhibited by Wu et al. (2015) and Huang et al. (2016). The rainfall distribution will be influenced by the landfall point where the produced rainfall will be more intense near the vortex speedy core. However, it is not feasible and convenient to control the initial latitudinal position of a vortex so that its landfall point can be as close as to the latitude of the central mountain (e.g., Huang et al. 2011; Wu et al. 2015; Tang and Chan 2015, 2016a,b). This also gives a reason why the constant-f plane is preferred in this study to eliminate the effects of beta drifting on landfalling position.

Fig. 2.
Fig. 2.

Model domains use coarse mesh D1 (black) and fine mesh D2 (red) at a resolution of 15 and 5 km, respectively, with the contours for terrain height every 1000 m and the coastline (the outermost green dashed line). The horizontal and vertical coordinates are grid points in the east–west and north–south direction, respectively. The mountain peak of 3500-m height is located at grid point (185, 201), and the initial vortex center (denoted by the solid circle) is located at grid point (261, 201).

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

We examined the structural evolution of the simulated vortex at different V and R. The simulated evolving cyclones remain well organized with rather circular circulation above the boundary layer and move westward toward the mountain peak before closing to the mountain as shown in Huang et al. (2016). The wind speed of the evolving vortex in the north–south vertical cross section through the vortex center in U1V2R2 (with WDM6) indicates that the vortex core slightly weakens at the early stage due to the dynamic adjustment but then gradually intensifies with time in association with slight eyewall contraction as shown in Fig. 3. For comparison, the wind speed of the stronger and larger vortex in U1V4R3 (with WDM6) also exhibits reduced intensity at the earlier adjustment stage but followed by a gradual intensification with stronger eyewall development and contraction as shown in Fig. 4. However, this initial larger and stronger vortex remains to possess a larger core size with more intense flow that extends further outward than the initial smaller and weaker vortex in U1V2R2. In this study, it is intended to highlight the induced rainfall by such a slowly developing westbound vortex approaching to the central mountain peak.

Fig. 3.
Fig. 3.

The simulated wind speed (shaded) of model domain D1 (401 × 401) in the north–south cross section through the vortex center for U1V2R2 with WDM6 at different times.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

Fig. 4.
Fig. 4.

The simulated wind speed (shaded) of model domain D1 (401 × 401) in the north–south cross section through the vortex center for U1V4R3 with WDM6 at different times.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

Under calm steering flow, the imposed vortex in favorable environments can grow into a fast intensification stage with developed maximum wind speed over 80 m s−1 at a very short radius of about 30 km accompanied by eyewall contraction as shown in Stern et al. (2015). In the presence of steering flow, intense mature cyclones may also exhibit considerable variations in vertical development and intensity with time (e.g., Huang and Wu 2018). It is not feasible to control the developed core size and intensity of a translational intense vortex. Thus, use of initial larger R can help obtain a wider developed vortex circulation even associated with contraction of the maximum-wind radius with time. The initial vortex parameters may be used as “proxy” for the simulation results since the radius of the vortex maximum wind does vary with time in our experiments.

3. Results and discussion

a. Rainfall distribution

We first present the geometric distributions of the simulated rainfall in the vicinity of the island terrain. Figure 5 shows the total accumulated rainfall after 120 h for the experiments with the slower steering flow (U1 = 4 m s−1) and faster steering flow (U3 = 8 m s−1) and with different cloud microphysics schemes (WSM6 or WDM6). The vortex center defined as the position of minimum surface pressure perturbation is used to overlap the vortex track in each experiment in Fig. 5. The maximum accumulated rainfall of the simulation can exceed 800 mm in some of the experiments. Rainfall over 500 mm day−1 is defined as torrential heavy rainfall (the highest category) at CWB. For the slower steering flow, two concentrated rainfall zones over northern and southwestern slopes seem to be more favorably produced for smaller vortex core sizes when the WSM6 scheme is used, regardless of initial vortex intensity (Fig. 5a). These double rainfall peaks, however, significantly weaken or even diminish as the initial vortex core size becomes larger. The patterns of the major rainfall appear to display a large geometric shifting as the vortex core size or intensity is only slightly changed from some specific values, which cause “bifurcation” of the rainfall patterns since all the other model aspects are identical at the initial time. For example, bifurcation is evident in the rainfall patterns between U1V1R3 and U1V1R4, and between U1V4R3 and U1V4R4. As can be seen, such rainfall bifurcation may be attributed to the largely deviated tracks in some cases. For the pair of U1V1R3 and U1V1R4, the shifting of the major rainfall to the southern terrain for the latter is caused by the track shifting to further north. However, bifurcation remains effective for the pair of U1V4R3 and U1V4R4 with more similar tracks that deflect southward prior to landfall at southeastern mountain. We will further investigate the bifurcation processes for some pairs of the experiments later.

Fig. 5.
Fig. 5.

Total accumulated rainfall in 120 h for U1 = 4 m s−1 and U3 = 8 m s−1 with different cloud microphysics WSM6 or WDM6, (a) U1 (WSM6), (b) U1 (WDM6), (c) U3 (WSM6), and (d) U3 (WDM6). The horizontal (east–west) and vertical (north–south) scales of each panel (denoted below the bottom) are 125 and 225 km, respectively. The terrain height contours (solid) are at in interval of 1000 m. The red line indicates the vortex track near the surface.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

As the steering flow increases to 8 m s−1 (U3) in the experiments with the WSM6 scheme, the formation and intensity of double rainfall peaks are considerably reduced (Fig. 5c), except for the strongest vortex (as seen in the lowest row). The major rainfall becomes more concentrated near southern or southwestern terrain for the vortex cores at different intensities and sizes. The signal of rainfall bifurcation is not well revealed for the vortex under the stronger steering flow, which may be attributed to the rather uniform and similar tracks. As a result, the major rainfall, in general, is significantly reduced for the weakest vortex, regardless of the vortex core size (see the top row of Fig. 5c). It is clear that the amount of accumulated rainfall is partially dominated by the residency time of the intense vortex core so that the vortex at a faster moving speed cannot produce too much orographic rain. Thus, more intense rainfall is induced for the experiments with slower steering flow and stronger vortex as shown in the lowest row of Fig. 5a. For westward typhoons across central Taiwan, the most intense rainfall is frequently observed near the steepest southwestern slope of the CMR. We will discuss the rainfall processes in regard to the evolution of the vortex near the terrain in more detail later.

As cloud microphysics scheme is changed from WSM6 to WDM6, the geometric distributions of major rainfall in general is similar, despite some differences in rainfall intensity (Figs. 5a,c versus Figs. 5b,d). The tracks for most of the experiments with WSM6 or WDM6 are somewhat similar, but with larger variations near the terrain. The differences between the major rainfall of WSM6 and WDM6 experiments are reduced for the faster steering flow (Fig. 5c versus Fig. 5d). The previous rainfall bifurcation for some WSM6 experiments with slower steering flow remains unchanged for the corresponding WDM6 experiments. This may indicate that the major rainfall is more dominated by the dynamical processes rather than use of different microphysics schemes associated with the evolving vortex when strongly interacting with the mountain. The development of a tropical cyclone in the absence of steering flow is intimately related to cloud microphysics as illustrated by idealized experiments (Fovell et al. 2009). For our idealized experiments with a translational vortex, the evolving storms take rather straight tracks with similar intensities that are not greatly sensitive to cloud microphysics. Hereafter, we will focus on the simulated results with WSM6 to investigate the dynamical processes in the major rainfall over terrain and further identify the conditions for the formation of rainfall bifurcation.

b. Vortex circulation

We show the dynamic processes in the induced rainfall only for the U1 experiments (the slowest steering flow) with R1 and R2 since their associated rainfall is much more intense. Figure 6 shows the time evolution of the vortex circulation at 1-km height and the associated reflectivity (dBZ) for the experiments U1V1R1, U1V2R1, U1V3R1, and U1V4R1. Note that the total accumulated rainfall for these experiments with the smallest vortex (R1 = 100 km) exhibits a pattern of double rainfall peaks as seen in Fig. 5. As the vortex is closing to the eastern slope of the mountain, intense rainfall is mainly produced rightward of the track, regardless of the initial vortex intensity (see the leftmost column of Fig. 6). This is because the swirling flow of the inner core that strongly impinges on the northern slope produces the local major rainfall (Fig. 6a). As the vortex passes over the mountain and departs offshore from the island, intense rainfall is also produced over the southern and southwestern slopes (Figs. 6b–d). Cloud convection south of the vortex center becomes more intense as the vortex core is departing offshore to provide strong onshore flow near the southern mountain, which is the main cause of the other rainfall peak over the southwestern slope. The U1VxR1 experiments exhibit quite similar rainfall distribution and intensity, as already seen in Fig. 5a, since the intensity of the evolving vortex near the mountain does not vary greatly from V1 to V4 as shown in Fig. 4 of Huang et al. (2016).

Fig. 6.
Fig. 6.

Horizontal wind at 1 km and the associated dBZ for (from top to bottom) U1V1R1, U1V2R1, U1V3R1, and U1V4R1 with WSM6 at (a) 81, (b) 84, (c) 87, and (d) 90 h. Coordinates are grid numbers of the inner domain at a uniform grid interval of 5 km.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

As the initial vortex size increases to 150 km (R2), the major rainfall, however, exhibits quite different geometric patterns as shown in Fig. 7. At a larger vortex core, the intense cloud convection now is produced further north of the terrain for the weaker vortices (V1–V3), while the strongest vortex (V4) gives the major rainfall distribution in U1V4R2 (the lowest row) similar to those of the experiment with the smallest vortex (U1V4R1). The larger vortex (at a core size of 150 km) appears to be more asymmetric as it moves over the terrain and nearby, thus favoring intense convergence with the outer vortex flow to the further north. As the initial vortex is as intense as V4, the vortex core is more consolidated during the passage over the mountain. As the vortex core size further increases to 200 km (R3), the overall patterns (not shown) are similar to those with R2 (Fig. 7). This similarity can also be found in their accumulated rainfall in Fig. 5. For a stronger vortex (V2–V4), the largest vortex core size of 250 km (R4) leads to a somewhat destabilized vortex with stronger deformation as it is passing over the mountain. Consequently, the accumulated rainfall is quite different from those for the smaller vortex cores (R1–R3) that are more stabilized and well maintained during the passage over the terrain.

Fig. 7.
Fig. 7.

As in Fig. 6, but for (from top to bottom) U1V1R2, U1V2R2, U1V3R2, and U1V4R2 with WSM6.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

c. Bifurcation of rainfall

The snapshots of vortex circulation and reflectivity at different times in Figs. 6 and 7 have revealed a dramatic change in rainfall distributions qualified as “bifurcation” as the vortex parameters are only slightly changed within some range of R or V. The bifurcation can be easily identified from the rainfall patterns with a large geometric shifting or change in maximum intensity exceeding an e-folding ratio. To further identify the rainfall bifurcation that exists for some pairs of the experiments, we conducted sensitivity tests on tiny changes in the vortex intensity. Figure 8 shows the 120-h accumulated rainfall for the slowest-steering flow experiments with a vortex at a fixed core size of R2 but at different intensities varied by 1 m s−1 from 30 to 35 m s−1. As seen, significant bifurcation is induced from the vortex intensity of 30–32 m s−1, above which both intensity and distribution of the accumulated rainfall then are similar. How can the vortex bring so different rainfall distributions over the terrain only due to a tiny change in initial vortex intensity?

Fig. 8.
Fig. 8.

The 120-h accumulated rainfall with WSM6 for the experiments varying the initial maximum wind from 30 to 35 m s−1 denoted by (a) U1V3R2 (30 m s−1), (b) U1V3R2-a (31 m s−1), (c) U1V3R2-b (32 m s−1), (d) U1V3R2-c (33 m s−1), (e) U1V3R2-d (34 m s−1), and (f) U1V4R2 (35 m s−1).

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

To further understand the processes causing the rainfall bifurcation, we show the time evolution of the vortex circulation and associated reflectivity during the passage over the terrain for these intensity-sensitivity experiments in Fig. 9. The vortex appears to be more consolidated during the passage as the initial intensity increases to 32 m s−1 from 30 m s−1 (see U1V3R2-b in Fig. 9). When storms are close to landfall (e.g., at 81 h), the weakest vortex at V3 (U1V3R2) is elongated more north–southward than the stronger vortices so that the major cloud convection is produced further northeast of the terrain with much less rainfall over the northern slope of the mountain (see Fig. 8a). Major convection is rather similar for the vortex intensity at 32 m s−1 or higher and tends to shift to the southwestern part of the island near and after landfall. The vortex circulations in these experiments become more similar as the vortex core has departed offshore at 90 h. Consequently, the associated cloud convection changes to similar, roughly circular bands to the northwest of the mountain and over the central and southern mountain range for the vortex at 32 m s−1 or larger. This may explain why there exists a rainfall maximum over the southwestern slope of the mountain, leading to a distinguishable bifurcation near 31 m s−1 (Fig. 9a versus Fig. 9b). It is speculated that the bifurcation may be related to the simulated Froude number u/Nh, where u is the speed of the impinging wind contributed by both the environment and vortex (~30 m s−1) and N is the moist buoyancy frequency (~10−2 s−1 or smaller depending on the effects of latent heating associated with the moist air) around the critical value of 1 over which the flow may pass over the mountain ridge rather than be blocked or deflected ahead of the steep slope. Lin et al. (2005) showed that there exists a gray zone of 1.2–1.6 in the vortex Froude number (Vmax/Nh) below which the near-surface track of a westbound vortex past a mountain range (similar to the CMR) will be discontinuous, regardless of track deflection near landfall. This will in turn affect the geometry of the induced rainfall in response to the more intense vortex core whether or not passing over the central mountain, and the weaker outer circulation when passing over or around the mountain corners.

Fig. 9.
Fig. 9.

The horizontal wind and the radar reflectivity at (from top to bottom) different times for the sensitivity experiments with the varying initial maximum wind as in Fig. 6 for (a) U1V3R2 (30 m s−1), (b) U1V3R2-a (31 m s−1), (c) U1V3R2-b (32 m s−1), (d) U1V3R2-c (33 m s−1), (e) U1V3R2-d (34 m s−1), and (f) U1V4R2 (35 m s−1).

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

Several pairs of the experiments with rainfall bifurcation can be clearly identified in Fig. 5, including (U1V1R1, U1V1R2), (U1V1R3, U1V1R4), (U1V3R2, U1V4R2), and (U1V4R3, U1V4R4). Note that the tracks of these pairs with rainfall bifurcation indeed are not much deviated. We find that the bifurcation for these pairs is mainly caused by the same mechanism discussed above. As illustrated in Fig. 9 for the experiment pair of (U1V3R2, U1V4R2), the bifurcation is induced as the two vortices in the pair take dramatically different structural evolutions during their passage over the terrain. Similar rainfall patterns and intensities are exhibited in U1V3R1 and U1V4R2 as well (see Fig. 5a), which involves required transitional changes in both V and R to prevent a bifurcation otherwise induced. Note that a transitional increase to R2 for U1V3R1 leads to a great reduction on the rainfall in U1V3R2, while a transitional increase to V4 from U1V3R2 leads to a large intensification of the rainfall in U1V4R2. These dramatic changes highlight a difficulty in a deterministic rainfall forecast when a small error in the estimated vortex parameters tends to cause the linear transition to bifurcation. As shown in Fig. 5b, similar bifurcation remains existent for the counterpart experiments with the double-moment cloud-microphysics scheme. Thus, the dynamic processes between the evolving vortex and the mountain play a more dominant role in induced rainfall bifurcation. The signal of bifurcation by varying vortex core size may be as important and strong as by varying vortex intensity as can be qualitatively identified from Fig. 5a.

d. Impact of increased steering flow speed

To illustrate the impact of increased steering flow speed on the rainfall near the terrain, the horizontal wind and radar reflectivity for the U3V4 group with WSM6 at different times (39 and 42 h) are shown in Fig. 10 for the strongest vortex of V4 that provides the prominent rainfall over the terrain (see Fig. 5c). Double-peak rainfall under the stronger steering flow of U3 is produced as in the slower-steering flow experiments, but with considerably reduced intensity again due to the shorter residence time. At 39 h, the northern rainfall near landfall is induced by the cyclonic upslope flow of the vortex circulation for all the vortex core sizes of R1–R4. Intense convection is also produced to the south and southwest of the mountain, except for the smallest-vortex experiment. As the vortex core moves over the mountain at 42 h, the southern rainfall is produced by the northwesterly flow of the inner vortex. The cloud convection is less organized around the outer annulus of the vortex as the vortex core size is increased, and becomes much weaker for an initial weaker vortex (figures not shown). This feature is quite different from the more organized convection around the inner vortex core for the slower-steering experiments (e.g., see Fig. 9f). For the stronger steering flow, as seen in Fig. 5c, stronger intensity of the vortex V appears to be a more dominant factor than smaller vortex core size R for the induced intense rainfall over the mountain.

Fig. 10.
Fig. 10.

The horizontal wind and the radar reflectivity with WSM6 at different times (39 and 42 h) for (a) U3V4R1, (b) U3V4R2, (c) U3V4R3, and (d) U3V4R4.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

e. Sensitivity to terrain size

The previous experiments use an island terrain similar to Taiwan terrain. Figure 11 shows the 120-h accumulated rainfall for the experiments as conducted in Fig. 5 but with the doubled length and width of the terrain and unchanged mountain height. The cloud microphysics scheme WDM6 is employed in the terrain-sensitivity experiments. The vortex deflects northward before landfall at the larger mountain and then rebounds southward near and after departure for the slowest steering flow U1, while the deflection before landfall is much reduced for the stronger steering flow U3 (not shown). As the terrain size is doubled in the presence of the slowest steering flow of U1, the double rainfall peaks are changed to one major rainfall along the southwest slope and the other weaker one over the northern terrain. The more intense southwestern rainfall results from the contributions from the lee flow convergence and upslope lifting of the outer vortex when the vortex is getting close to the mountain as well as from the upslope lifting of the vortex core as the vortex center is near and after departure.

Fig. 11.
Fig. 11.

As in Fig. 5, but for double-sized terrain with WSM6 for (a) U1 (4 m s−1) and (b) U3 (8 m s−1). The horizontal (east–west) and vertical (north–south) scales of each panel are 225 and 325 km, respectively.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

The dramatic change in rainfall distributions with varying vortex parameters that was seen in the previous experiments is greatly reduced for the larger mountain. As the steering flow is doubled to U3, only one single rainfall peak is produced near the southwestern slope (Fig. 11b). Little rainfall is produced over the northern and northeastern slopes in contrast to the prominent rainfall for U1. For U3, the rainfall patterns are similar with varying V and R. The major intense rainfall over the southwestern slope is mainly due to the lee convergence of the upslope flow of the inner vortex with the outer skirting flow when the impinging vortex deflects southward near landfall (not shown). As the vortex is departing offshore, the stronger flow of the vortex core impinges on the southwestern slope leading to more accumulation at the maximum rainfall region.

f. Sensitivity of double-peak rainfall formation

The previous experiments have clearly shown the formation of double rainfall peaks for a vortex westbound toward the mountain ridge. Sensitivity experiments of double-peak rainfall formation and intensity were conducted and are presented in the appendix with varying initial approaching directions and latitudinal departures of the vortex. It appears that the formation of double rainfall peaks is most influenced by the incidental angle of an approaching vortex, supporting the observed rainfall pattern for Typhoons Soudelor (2015) and Megi (2016) with similar northwestward tracks toward the central CMR.

4. Relationships of topographic rainfall with key parameters

One of the goals of this study is to identify the variations of the total rainfall over the terrain with respect to the key parameters, U, Vmax, and R, since they are much more concerned in the forecast. To reduce the degree of freedom, we will fix the terrain parameters (e.g., coastline, length, width and height) that may affect the vortex track as well and thus the local rainfall over the terrain. The island mountain fixed herein roughly resembles the CMR in Taiwan.

We focus on the statistics of the average rainfall over the northern half, southern half and whole grids of the model terrain, referred to as Rsouth, Rnorth, and Rall, respectively. The maximum rainfall over these grids is also counted as Rmax. However, only the terrain grids with an elevation height over 100 m is taken into account for a preferred consideration on the impact of the rainfall over steeper slopes. Figure 12 shows the average rainfall and maximum rainfall over the counted terrain grids for the experiments with varying vortex core size R. For U1V1, the four rainfall indices (Rsouth, Rnorth, Rall, and Rmax) follow the same trend with varying R, all slightly decreasing from R1 to R2 and then increasing toward R4 with a maximum rainfall Rmax near 1800 mm at R4. As the vortex intensity Vmax increases to V2, the U1V2 group also shows a decreasing trend with increased R, but then a very small upward trend from R3 to R4. The largest Rmax is about 1100 mm presented at R1. The results for the U1V3 group are quite similar to those for U1V2 group, while the U1V4 group gives the largest rainfall amounts of about 1400 mm at R2 which then significantly decreases to about 500 mm at R4. Thus, except for the weakest vortex (V1) which has maximum rainfall indices at R4, all the rainfall indices roughly show the decreased trends toward increased R for the U1 group.

Fig. 12.
Fig. 12.

The averaged accumulated rainfall (mm) over the counted terrain heights above 100 m, where south, north, and all in the plots indicate the amounts over the northern half, southern half, and entire grid of the model terrain, and max is the maximum rainfall (mm) over all the counted terrain grid points, with respect to the experiments varying the vortex size. The maximum rainfall is referred to in the right coordinate.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

Note that all the rainfall indices for V1 significantly drop for V2–V4 with the larger vortex core sizes of R3 and R4. Referring to Fig. 5a, this large jump appears as bifurcation in the presence of similar tracks for U1V1R4 and U1V2R4. A stronger large vortex crossing the terrain becomes less organized so that most of intense rainfall is not produced over the terrain. On the other hand, the accumulated rainfall over the terrain is also greatly reduced for U1V1R2 and U1V1R3 compared to U1V1R1. Comparing the top rows in Figs. 6 and 7, more intense rainfall over the terrain is found in U1V1R1 than in U1V1R2 as the former can maintain a smaller but more consolidated vortex core during the passage over the terrain than the latter. All simulated cyclones keep moving straight westward and make landfall at the island for these experiments (see Fig. 5). Thus, the rainfall bifurcation is not exclusively induced by track deviations, but can be also induced by vortex’s elongation and/or disorganization near and over the terrain.

The variations of the rainfall indices for the stronger steering flow (U3) are smaller than those for the weaker steering flow (U1). Rainfall indices for the U3V1 group are not sensitive to R, except for increased Rmax at larger R until R3. As seen, for the U3V1 and U3V2 groups (e.g., weaker vortices under stronger steering flow), Rsouth is much larger than Rnorth as also indicated in Fig. 5. For other groups with a stronger vortex (U3V3 and U3V4), the average indices are closer and larger than the U3V1 group. Both Rsouth and Rnorth are closer as Vmax increases, and do not vary greatly with R. More rainfall will be produced on the southern slope than the northern slope, except for the strongest vortex (V4) that shows slightly larger rainfall over the northern slope. Comparing the values of the four rainfall indices for both steering flows, we may find that these values for the slower flow (U1) are about two times as large as those for the faster flow (U3). This is also indicated by the observations that highlight the larger contribution from a longer storm residence time under slower steering flow.

Figure 13 shows the variations of the four rainfall indices with Vmax at a fixed vortex core size. For the U1R1 group, the rainfall indices are not sensitive to Vmax for the slower steering flow (U1). However, all the indices show a dramatic increase when Vmax increases from V3 to V4 in the U1R2 group. This trend is largely reduced for U1R3 and even becomes reversely decreased for U1R4. Such a significant reduction on the topographical rainfall associated with the strongest and largest vortex has been discussed before and can be attributed to the fact that the cyclone at this vortex core size is more subject to asymmetric elongation during the passage over the terrain. A large positive deviation of the northern rainfall from the southern rainfall exists for U1V3R4 (as also evident in Fig. 5a), which appears to result from its less southward track deflection near landfall. For the stronger steering flow (U3), the average rainfall indices show rather regular trends that slightly increase with increased Vmax. A jump in maximum rainfall is produced by V2 at R1–R3, while it disappears at R4. If we discard the decreasing trend of U1R4, we may find that the average rainfall indices indeed increase with increased Vmax for both steering flows, in spite of that the maximum rainfalls exhibit less linearity in their trends. This is expected since stronger cyclones should produce more average rainfall, while the largest rainfall over the mountain may not always be associated with the strongest but largest vortex.

Fig. 13.
Fig. 13.

As in Fig. 12, but with respect to the experiments varying the initial maximum wind of the vortex.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

Figure 14 shows the variations of the rainfall indices with steering flow speed U. We summarize the results only for the stronger vortex at V3 (left panels) and V4 (right panels) since the rainfall over the mountain is in general smaller for V1 and V2 (see Figs. 5a,c and 13). At the smallest vortex size (R1), both average rainfall and maximum rainfall tend to decrease with increased steering flow speed except for the reverse trend of southern rainfall. Although the three average rainfall indices for the vortex at V3 decrease toward U4, Rsouth indeed is largely raised up at U4 for the smallest vortex core at R1. It is noted that the maximum rainfall reversely increases toward U4 for the vortex core at R2. For further larger vortex core sizes (R3 and R4) at V3, the rainfall indices also roughly decrease with increased U. As the vortex intensity further increases to V4, all the rainfall indices tend to drop or level off toward U4. Note that for the V4R2 group all the rainfall indices give a rapid drop by a ratio of about three from U1 to U2 (with a small change of only 2 m s−1 in steering flow intensity), while a linear trend of all the rainfall indices is well exhibited with respect to U for the V4R1 group. For the larger vortex core at R3, a large increase in all the average rainfall indices as a kink structure evident in Fig. 14 can be partially attributed to the favorable flow of the vortex near and after landfall that is more incidental to upslope as shown for U3 in Fig. 10. However, as can also be realized from Fig. 5c, such enhancement on average rainfall is reduced for R4 (also see Fig. 12).

Fig. 14.
Fig. 14.

As in Fig. 12, but with respect to the experiments varying the initial steering wind speed.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

The idealized experiments highlight a scenario that faster-moving typhoons at a larger vortex core size, either stronger or weaker, may not always produce less rainfall than similar but slower-moving typhoons in terms of average and maximum rainfall indices. However, a linearly decreasing tend with increased translational speed in these rainfall indices is rather clear for the smallest vortex core size that was often associated with impinging intense typhoons.

5. Conclusions

Topographic rainfall associated with westbound tropical cyclones past an isolated island mountain is investigated using an idealized WRF Model. The idealized island mountain roughly resembles Taiwan’s terrain where the CMR is located roughly north–southward. Two nested domains at 15- and 5-km resolutions are employed for the outer and inner domains, respectively. Numerical experiments were conducted with combinations of different cloud microphysics schemes, steering flows, vortex core sizes, and vortex intensities.

The results from numerical experiments show that the geometric distributions of major rainfall over the island produced by impinging tropical cyclones with varying vortex core size R, vortex intensity Vmax, and steering wind speed U in general are similar for the two cloud microphysics schemes (single-momentum scheme WSM6 and double-momentum scheme WDM6). Major rainfall is produced over both the northeastern and southwestern slopes of the mountain to form double peaks for the weaker steering flow (e.g., at a speed of 4 m s−1). As the steering flow speed increases to 8 m s−1, most of the rainfall is significantly weakened or is produced mainly over the southwestern slope. It was found that the formation of double rainfall peaks is most influenced by the incidental angle of an approaching vortex. When the terrain size is doubled but with unchanged height, most of major rainfall is produced over the southwestern slope. The major rainfall over such larger terrain shifts more northward closer to the mountain peak for the weaker steering flow compared to that for the stronger steering flow.

There appears a bifurcation in major rainfall for the weaker steering flow, where the rainfall distribution and intensity over the terrain are suddenly changed within a tiny range of R and Vmax. Rainfall bifurcation is induced by the structural changes of the impinging vortex near and during landfall, thus intimately influenced by the track as well as initial vortex core size and intensity. When the bifurcation occurs, geometric distributions of major rainfall are also more sensitive to cloud microphysics schemes. However, the signal of bifurcation is significantly reduced as the terrain size is doubled. Consolidation and/or elongation of the vortex near and over the mountain are dynamically vital to the bifurcation of the induced rainfall. The elongated vortex circulation with stronger outer cyclonic flow enables more intense rainfall to occur further away from the mountain.

Systematic experiments were conducted to relate the maximum and average accumulated rainfall over the northern half, southern half, and the whole of the montane grids with respect to varying R (100–250 km), Vmax (20–35 m s−1), and U (4–10 m s−1). The grids counted herein are over the mountain slopes at an altitude above 100 m. In general, the average rainfall and maximum rainfall over the slopes for the faster steering flow (8 m s−1) are approximately half of those for the slower steering flow (4 m s−1). However, a linear trend in rainfall accumulation with respect to vortex core size is not clearly exhibited, possibly because of that the track near and after landfall is more sensitive to vortex core size as found in other studies (e.g., Lin et al. 2005; Huang et al. 2016). The stronger steering flow tends to produce a more asymmetric rainfall pattern, in which southern rainfall is much larger than northern rainfall. On the other hand, the average and maximum rainfalls do increase with increased vortex intensity, except for the largest vortex core size of 250 km that causes the vortex to be desymmetrized and disorganized near landfall and over the mountain. Finally, the maximum rainfall does exhibit a linear decrease with increased steering flow speed, however, only for the smallest vortex core size of 100 km. This indicates that faster moving cyclones at a larger vortex core size may not necessarily produce smaller average and maximum rainfall amounts over the mountain than similar but slower moving cyclones.

Based on the idealized experiments, the topographical rainfall formation, intensity, and distribution crucially depend on a combination of the vortex track, landfall position and the structure of the vortex circulation, and are intimately related to the three key parameters, R, Vmax, and U. From the systematic experiments with respect to R, Vmax, and U, this study provides useful qualitative information on variations of topographic rainfall associated with westbound tropical cyclones past an island mountain range. The variability of the induced rainfall is relatively larger for varying vortex core size than for varying the others, possibly due to the fact that a vortex core size over 150 km used in this study is larger than observed intense cyclones and is subject to vortex reorganization near the topography. Nevertheless, the exhibited nonlinear variations of the induced rainfall with the three key parameters complicate the formulation of possible nondimensional parameters for controlling the major rainfall over similar topography.

Acknowledgments

This study was supported by the Ministry of Science and Technology (MOST) in Taiwan. We appreciate Dr. D. Nolan for his idealized WRF codes for use. Model development team at Taiwan Typhoon Flood Research Institute (TTFRI) helped provide the WRF ensemble forecasts.

APPENDIX

Sensitivity Experiments for the Formation of Double Rainfall Peaks

We conducted several experiments for exploring the sensitivity of the double-peak rainfall formation in the appendix. The initial vortex center and mountain peak are 900 km apart. The control experiment CTL uses U = 6 m s−1, V = 40 m s−1, and R = 80 km with the constant Coriolis parameter at 23.5°N, which mimics the environmental steering and vortex conditions of Megi (2016). To simulate varying approaching directions of a vortex on a constant-f plane, the island mountain is rotated clockwise (from the north). All the vortices keep a straight westward movement before closing to the mountain as shown in Fig. A1. Southward deflection of the track near landfall increases with decreased U, but less affected by increased R (e.g., from 80 to 160 km). Southward deflection is enhanced for an initial northward-shifted vortex in N4 (four grids more northward than CTL; Fig. A1c) but almost disappears for an initial southward-shifted vortex in S4 (four grids more southward than CTL; Fig. A1b). When the vortex moves northwestward in A330 or north-northwestward in A300 (A330 and A300 are as in CTL, but with the terrain rotated 330° and 300° clockwise from the north, respectively) toward the mountain ridge, the tracks appear to deflect rightward before landfall and then leftward after landfall over the mountain (Figs. A1d,e).

Fig. A1.
Fig. A1.

The simulated tracks (lined dots) for the double rainfall sensitivity experiments of (a) CTL, (b) S4, (c) N4, (d) A330, (e) A300, (f) R120, (g) R160, (h) ST4, and (i) ST8 at an interval of one hour from 36 to 60 h. Contours are for terrain heights, from 1 m (the outer contour) and every 500-m interval. CTL uses U = 6 m s−1, Vmax = 40 m s−1, and R = 80 km; S4 and N4 are as in CTL, but with the initial vortex southward and northward shifted by four grids, respectively; A330 and A300 are as in CTL, but with the terrain rotated 330° and 300° clockwise (from the north), respectively; and R120 and R160 are as in CTL but with R = 120 km and R = 160 km, respectively. ST4 and ST8 use U = 4 m s−1 and U = 8 m s−1, respectively. The coordinates are grid points at a uniform interval of 5 km.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

The simulated results exhibit double rainfall peaks as shown in Fig. A2, some of which are clearer for CTL, S4, N4, and R160 (as in CTL but with R = 160 km). Variations of the double rainfall peaks are associated with the initial slightly southward or northward shifted tracks (S4 and N4) that lead to enhanced northern or southern rainfall, respectively. Indeed, the rainfall pattern and intensity captured by S4 (Fig. A2b) agree best with the rainfall of Megi as its associated track is closest to the best track. For CTL, the track is slightly north of the centerline of the mountain range so that the northern rainfall maximum is considerably stronger than the southern one. The rainfall accumulation is roughly proportional to reverse of the typhoon translational speed, but approximately preserving the formation of the double rainfall peaks (figures not shown). Increasing R to 160 km may somewhat reduce the intensity of the double rainfall peaks, but without largely affecting the geometric formation (Fig. A2f). However, the incidental direction of the translational vortex plays a more significant role, which results in gradually weakened formation of double rainfall peaks as the northward direction in A330 is increased in A300.

Fig. A2.
Fig. A2.

The 60-h accumulated rainfall (shaded colors in an interval of 100 mm) overlapped with the horizontal wind at 60 h for the double rainfall sensitivity experiments of (a) S4, (b) CTL, (c) N4, (d) A330, (e) A300, and (f) R160. Contours are for terrain heights, from 1 m (the outer contour) and every 1000-m interval. The coordinates are grid points at a uniform interval of 5 km.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

To explore the double-peak rainfall formation, Fig. A3 shows the induced rainfall and backward trajectories released near the mountain slope surface for CTL before and after landfall. As the cyclone is approaching the mountain, rain is produced by the incoming cyclonic flow over the northeastern slope and by the outer skirting flow over the southwestern slope. Near and after landfall, intense rainfall is produced by the stronger inner vortex over the northeastern slope as well as the southwestern slope. As the vortex moves offshore, the outer skirting of the vortex is still producing some rain over the mountain range (not shown). Similar mechanism of the double rainfall formation is found for N4, but the southwestern rainfall peak is less pronounced for S4 as seen in Fig. A2. For S4, the departing vortex core is too close to the mountain peak (see Fig. A1) so that the upslope lifting of the incoming flow over the mountain range is weaker and produces less rainfall than both CTL and N4.

Fig. A3.
Fig. A3.

The horizontal wind near the surface and accumulated rainfall (mm) in 6 h at (a) 36 and (b) 48 h for CTL. The black line at each panel is the 12-h backward trajectory of near-surface air parcel released near the surfaced from the time for the panel. Coordinates are grid numbers of the domain at a grid resolution of 15 km.

Citation: Weather and Forecasting 35, 1; 10.1175/WAF-D-19-0120.1.35.1.test

For comparing the mechanism of the double-peak formation, two real cases, Soudelor (2015) and Megi (2016) were simulated using WRF with three nested domains at horizontal resolution of 45, 15, and 5 km, respectively. The formation of double-peak rainfall in both cases is well captured with similar backward trajectories as indicated by the idealized experiment CTL (figures not shown).

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