Reprint 1008

應用於業務數值天氣預報系統追蹤渦旋的改進算法

李子維 & 陳世倜

第二十六屆粵港澳氣象科技研討會 澳門，2012 年 1 月 17-19 日

應用於業務數值天氣預報系統追蹤渦旋的改進算法

李子維 陳世倜 香港天文台

摘要

香港天文台的新一代數值預報模式於 2010 年中開始投入業務運行。 新模式的水平分辨率得以大幅提高後，間中會在陸地上產生一些尺度 較小但強度顯著的背風低壓區。天文台原有的渦旋追蹤算法可能會將 該些小尺度系統誤當為熱帶氣旋的中心，並引致錯誤的熱帶氣旋預測 路徑。為此，天文台開發了一套新的渦旋追蹤算法，並在本文作詳細 介紹。新算法利用模式對平均海平面氣壓及 850 百帕的渦度場的預報 來正確找出熱帶氣旋的環流，從而定出熱帶氣旋的中心。本文透過 2010 年多個熱帶氣旋個案來展示新算法在追蹤旋轉中心的較優越表 現。

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An enhanced vortex tracker for the operational NWP system

Jeffrey Chi Wai Lee and S.T. Chan

Abstract

The Hong Kong Observatory’s new generation of numerical weather prediction model suite was put into operation in mid-2010. With a substantial increase in the horizontal resolution, the model suite occasionally produces small-scale yet prominent lee lows over land. The previous vortex tracker of the Observatory may mis-identify these small-scale features as the centre of tropical cyclones, failing to generate the correct tropical cyclone forecast tracks. A new vortex tracking algorithm was thus developed by the Observatory, the details of which are presented in this paper. Considering the mean sea level pressure field as well as the vorticity field at 850 hPa level, the new vortex tracker is able to correctly identify the circulation of tropical cyclones and hence the centres. This paper presents a number of tropical cyclone cases from 2010 to demonstrate the superior performance of the new vortex tracking algorithm.

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1. Introduction

Every year, an average of 12 tropical cyclones (TCs) occur over the [1], which is surrounded by a number of large landmasses, including the Mainland China and the island of Taiwan in the north, the in the east, Viet Nam in the west and Borneo in the south. The terrain of these landmasses are rather complex and peaks reaching 2000 m or above are not uncommon such as those found on and Mindanao of the Philippines and the Central Mountain Range on Taiwan. When a TC traverses across these rugged areas, lee lows are often formed which would potentially be mixed up with the centre of the TC. For many years, the Hong Kong Observatory (HKO) had been using a vortex tracker to track the TCs in the numerical weather prediction (NWP) model outputs by following the point of the lowest mean sea level pressure within the circulation of the TCs. The vortex tracker worked satisfactorily in the old days as the horizontal resolution of the models at that time was just too coarse to resolve the lee lows near the TCs.

In mid-2010, a new suite of high resolution NWP models based on the Non-Hydrostatic Model (NHM) adapted from the Japan Meteorological Agency was commissioned in HKO [2]. The so-called Meso-NHM, with a forecast range of 72 hours, is one of the two members of the new model suite. Among other things, it generates predictions on the track and intensity of TCs. With a high horizontal resolution of 10 km, the Meso-NHM is able to resolve the significant lee lows arising from the passage of TCs across rugged terrain. It was found that the old vortex tracker often mis-identified such lee lows as the centre of TCs, resulting in the generation of unrealistic forecast tracks. The old tracker sometimes also failed to depict the dissipation of a TC as it would continue to track some other low pressure systems as the centre of the TC following its dissipation. To tackle these problems, the vortex tracker has been enhanced by also referring to the 850 hPa vorticity field apart from the mean sea level pressure field. Compared with the vortex tracker developed by the European Centre for Medium-Range Weather Forecasts [3], the enhanced vortex tracker does not require additional model fields, including the winds at 850 hPa, 700 hPa and 500 hPa to determine the environmental steering flow. The enhanced vortex tracker is also less complicated than the GFDL vortex tracker in HWRF [4], and it always outputs the centre of a TC at a local minimum in the mean sea level pressure, while there is no such guarantee in the GFDL vortex tracker.

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This paper describes the enhanced vortex tracker. In Section 2, the formulation of the enhanced vortex tracker is introduced, followed by case comparison between the enhanced vortex tracker and the old tracker in Section 3. The conclusions are given in Section 4.

2. Formulation of the enhanced vortex tracker

TC is a weather system with a rotating column of air about its centre due to the low central pressure. The vertical extent of a TC depends on its strength and the stronger the TC, the higher will be its vertical extent. Over the sea or a flat terrain, the centre of a TC can be tracked by simply following the point of the lowest mean sea level pressure. Yet in high resolution models where the lee lows can become as deep as model TCs, one may have to also refer to the circulation sufficiently high above the ground in order to determine the correct location of the TCs.

One quantity that we may look at is the vorticity which is a measure of the degree of rotation of the TC wind field. However, the centre of a TC may not necessarily fall on the point of the maximum vorticity and an example is shown in Fig. 1 for the case of Severe (1011). Due to the higher surface friction over land, the winds at 850 hPa were generally stronger over the sea and, as a result, the region of the highest vorticities near the centre of Fanapi shifted towards the coastline. If the point of the maximum vorticity at 850 hPa is taken as the centre of a TC, the forecast track thus obtained will bias towards the coastline following the landfall of the TC.

Other than vorticity, the degree of rotation of the wind field can also be quantified by circulation (C), which is defined as:

, where Ur() is the wind field of the TC [5]. The line integral is taken along a circle centred at r0 with radius a . In the enhanced vortex tracker, we integrate the circulation with respect to to obtain the integrated circulation V :

It is this integrated circulation that we use in the enhanced vortex tracker to track the centre of TCs.

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The integrated circulation can be calculated from the vorticity ( ) by Stoke’s theorem and the formula is as shown below,

In the enhanced vortex tracker, we take a to be 200 km and the integral above 0 is evaluated numerically by simple summation of the relevant quantities.

When a TC crosses a rugged terrain, the surface winds could be significantly modified and the circulation centre may become ill-defined. On the other hand, the wind field at 850 hPa is less affected by the terrain and the circulation centre is more prominent. However, due to the presence of vertical wind shear, this circulation centre may not align right above the centre at surface. In view of this, the 850 hPa circulation centre is used as a first guess only. The enhanced vortex tracker will look for the nearest local minimum in the mean sea level pressure which is then identified as the centre of the TC. The detailed work flow of the enhanced vortex tracker is as follows:

(I) Take the analysis position of the TC from the forecaster as the first guess, look for the point of the highest integrated circulation at 850 hPa within 300 km of the first guess position. This highest integrated circulation must be greater than a pre-defined threshold, which is set at 600 (km)3s-1. (For comparison, an idealized perfectly circular TC with an average wind speed of 5 ms-1 within 200 km of its center has an integrated circulation of 200 (km)3s-1.) (II) Search for the nearest local minimum in the mean sea level pressure that is within 300 km of the position identified in (I). The mean sea level pressure of this local minimum must be lower than 1010 hPa. Take this location as the centre of the TC in the model analysis. (III) For the next forecast hour at 3 hours apart, take the current analysis/forecast location as the starting point, look for the point of the highest integrated circulation (with value greater than the same threshold as in (I)) at 850 hPa level using a searching radius of 300 km. (IV) Search for the nearest local minimum in the mean sea level pressure (with value less than 1010 hPa) that is within 300 km of both the position identified in (III) and the previous analysis/forecast position. Take this location as the centre of the TC. (V) Repeat (III) and (IV) until the end of the forecast range. If there is

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no pressure minimum/circulation maximum which satisfies the conditions in (III) and (IV), the TC is forecast to have dissipated and the tracker process will terminate.

A threshold value for the integrated circulation is introduced in order to: 1) distinguish the mostly surface-bound lee lows from genuine TC centres; and 2) detect the forecast dissipation of the TCs. The threshold was empirically set to optimize the performance. The thresholds for the searching radius are set to prevent the vortex tracker from mixing up different TCs in the model domain. The current setting works for most cases except for the case of Tropical Storm Namtheun (1008), which has its tracks mixed up with those from Severe Tropical Storm Lionrock (1006) in some model runs due to the predicted coalescence of the two systems by the model.

3. Case Comparison between the enhanced vortex tracker and the old tracker

3.1 Forecast track for (1002), model run initialized at 18UTC 13th July 2010 Conson formed over the western North Pacific to the east of the Philippines on 12 July and crossed southern Luzon during the evening of 13 July. A prominent lee low was forecast to develop over northern Luzon by Meso-NHM (Fig. 2(b)). As a result, the old tracker misidentified the lee low as the centre of Conson, resulting in the generation of an unrealistic forecast track (red dashed track in Fig. 2(a)). The lee low then weakened and the old tracker jumped back to the centre of Conson in the later forecast hours. As shown in Fig. 2(d), the 850 hPa vorticity of the lee low was weak when compared with Conson and, therefore, the enhanced vortex tracker was able to distinguish the lee low from the centre of Conson for all forecast hours. The forecast track from the enhanced vortex tracker is shown in Fig. 2(c).

3.2 Forecast track for Typhoon Chanthu (1003), model run initialized at 00UTC 19th July 2010 The problem with the old tracker is most serious in this case. The old tracker was trapped by the lee lows over Luzon as the lee lows were so prominent that their central pressure were even lower than the forecast central pressure of Chanthu in the earlier stage of model integration (Fig. 3(a) and (b)). In the later forecast hours, the lee lows weakened but Chanthu had already moved too far away so that the old tracker was unable to jump back to the centre of Chanthu and kept tracking the strongest lee low over Luzon. Again, the 850 hPa vorticity associated with the lee lows were comparatively weak (Fig. 3(d)) and the enhanced vortex tracker

6 experienced no problem in compiling the correct forecast track (Fig. 3(c)).

3.3 Forecast track for Severe Tropical Storm Lionrock (1006), model run initialized at 00UTC 31st August 2010 This case illustrates the necessity of using the integrated circulation instead of simply the vorticity in locating the centre of a TC. The T+36h field of the mean sea level pressure and 850 hPa vorticity are shown in Fig. 4(a) and (b) respectively. There exist a few areas of low pressure in Fig. 4(a). The one near 24.5oN, 120oE was the forecast centre of Lionrock while those near 24.5oN, 121oE and 23.5oN, 121oE were lee lows formed due to the Central Mountain Range over Taiwan. The vorticity maximum identified was actually associated with the lee low near 23.5oN, 121oE. However, as this area of high vorticities was elongated in shape, the integrated circulation over this area was smaller than the one associated with Lionrock near 24.5oN, 120oE. As a result, the enhanced vortex tracker correctly identified the low pressure centre near 24.5oN, 120oE as the centre of Lionrock and produced a more accurate track (Fig. 4(d)) than that from the old tracker (shown in Fig. 4(c)).

3.4 Forecast track for Severe Typhoon Fanapi (1011), model run initialized at 06UTC 19th September, 2010 This case illustrates a common problem with the old tracker when a TC moves across Taiwan and becomes weakened after passing through the Central Mountain Range [6]. Lee lows sometimes develop over Taiwan with central pressure lower than that of the weakened TC. An example is shown in Fig. 5(a), in which Fanapi, with a central pressure of 990 hPa, was located near 24oN, 120oE. A prominent lee low developed near 24.5oN, 121oE and the pressure at centre fell to 989 hPa. As a result, the old vortex tracker misidentified the lee low as the centre of Fanapi and generated a jumpy forecast track as shown in Fig. 5(c). With the guidance from the 850 hPa circulation, the enhanced vortex tracker could successfully correct the erroneuos forecast track (Fig. 5(d)).

3.5 Forecast track for Super (1013), model run initialized at 12UTC 22nd October, 2010 This case aims to illustrate the improved handling of the dissipation of TCs by the enhanced vortex tracker. For those weak TCs, quite often the circulation at surface as captured by the models could be so weak that we can only apply a relatively loose pressure threshold for the vortex tracker to successfully identify and track the TCs. This problem, however, is less prominent for the circulation at upper-levels and therefore, a stricter condition can be applied to the integrated

7 circulation at 850 hPa. This gives the enhanced vortex tracker an advantage over the old tracker in handling the dissipation of TCs. In the case of Megi, which was forecast to dissipate over Fujian after making landfall, the enhanced vortex tracker correctly terminated the forecast track (Fig. 6(b)) while the old tracker continued to track some random low features following the dissipation of Megi (Fig. 6(a)).

4. Conclusion

We presented the theoretical and numerical formulation of the enhanced vortex tracker and a number of TC cases from 2010 in this paper. The performance of the enhanced vortex tracker was found to be superior to the old tracker. The enhanced vortex tracker was put into operation in HKO at the beginning of the TC season in year 2011.

5. Acknowledgement

The authors would like to thank Mr. H.W. LEUNG and Mr. K.C. LEE for their assistance in preparing the datasets and figures used in this paper.

6. Reference [1] 胡文志、張文瀾、梁延剛，2005：西北太平洋熱帶氣旋活動的長期變化。第 十九屆粵港澳氣象科技研討會；廣東陽江，中國，2005 年 3 月 1-3 日 (in Chinese)。 [2] 黃偉健、周志堅，2010：天文台新一代數值天氣預報系統。第二十四屆粵港 澳氣象科技研討會；深圳，中國，2010 年 1 月 20-22 日 (in Chinese)。 [3] Van Der Grijn, G., 2002: Tropical cyclone forecasting at ECMWF: new products and validation. ECMWF Technical Memoranda No. 386. [http://www.ecmwf.int/publications/library/do/references/show?id=83940] [4] Gopalakrishnan, S., Q. Liu, T. Marchok, D. Sheinin, N. Surgi, M. Tong, V. Tallapragada, R. Tuleya, R. Yablonsky and X. Zhang, 2011: Hurricane Weather Research and Forecasting (HWRF) Model: 2011 Scientific Documentation. [5] Holton, J.R., 1992: An Introduction to Dynamic Meteorology, 3rd Ed. Academic Press. [6] Brand, S. and J.W. Blelloch, 1974: Changes in the Characteristics of Typhoons Crossing the Island of Taiwan. Mon. Wea. Rev., 102, 708-713.

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Fig. 1 Meso-NHM T+21h 850 hPa wind field valid at 15 UTC on 20th September 2010 depicting Severe Typhoon Fanapi (1011) near 24oN, 115oE. Region of higher vorticity lies to the south of the circulation centre.

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Lee low

Fig. 2 (a) The forecast track of Typhoon Conson (1002) for the Meso-NHM run at 18 UTC on 13th July 2010 by the old vortex tracker (dashed line in red) and the HKO warning track (black line). (b) T+6h mean sea level pressure valid at 00 UTC on 14th July 2010. (c) Same as (a) except that the forecast track is from the enhanced vortex tracker. (d) T+6h 850 hPa vorticity valid at 00 UTC on 14th July 2010.

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Lee low

Fig. 3 (a) The forecast track of Typhoon Chanthu (1003) for the Meso-NHM run at 00 UTC on 19th July 2010 by the old vortex tracker (dashed line in red) and the HKO warning track (black line). (b) T+6h mean sea level pressure valid at 06 UTC on 19th July 2010. (c) Same as (a) except that the forecast track is from the enhanced vortex tracker. (d) T+6h 850 hPa vorticity valid at 06 UTC on 19th July 2010.

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Fig. 4 (a) T+36h mean sea level pressure valid at 12 UTC on 1st September 2010. (b) T+36h 850 hPa vorticity valid at 12 UTC on 1st September 2010. (c) The forecast track of Severe Tropical Storm Lionrock (1006) for the Meso-NHM run at 00 UTC on 31st August 2010 by the old vortex tracker (dashed line in red) and the HKO warning track (black line). (d) Same as (c) except that the forecast track is from the enhanced vortex tracker.

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Fig. 5 (a) T+30h mean sea level pressure valid at 12 UTC on 19th September 2010. (b) T+30h 850 hPa vorticity valid at 12 UTC on 19th September 2010. (c) The forecast track of Severe Typhoon Fanapi (1011) for the Meso-NHM run at 06 UTC on 18th September 2010 by the old vortex tracker (dashed line in red) and the HKO warning track (black line). (d) Same as (c) except that the forecast track is from the enhanced vortex tracker.

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Fig. 6 (a) The forecast track of Super Typhoon Megi (1013) for the Meso-NHM run at 12 UTC on 22nd October 2010 by the old vortex tracker (dashed line in red) and the HKO warning track (black line). (b) Same as (a) except that the forecast track is from the enhanced vortex tracker.

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