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The Impact of Taiwan Topography on the Predictability of Typhoon Morakot’s
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Record-Breaking Rainfall: A High-Resolution Ensemble Simulation
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Xingqin Fang1,2, Ying-Hwa Kuo2,* and Anyu Wang1
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Department of Atmospheric Sciences, School of Environmental Sciences and
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Engineering, Sun Yat-Sen University, Guangzhou, China
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National Center for Atmospheric Research, Boulder, Colorado, USA
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To be submitted to Weather and Forecasting
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14 August 2010
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*
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Dr. Ying-Hwa Kuo
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Email: kuo@ucar.edu
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Address: NCAR, P. O. Box 3000, Boulder, CO 80307
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Phone: (303) 497-8910
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Corresponding author:
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Abstract
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From 6 to 10 August 2009, Typhoon Morakot brought record-breaking rainfall
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over southern Taiwan, with a maximum 96-h accumulated rainfall of 2,874 mm on
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the slope of the Central Mountain Range, causing heavy human casualty and severe
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property damage. In this study, we examine the impact of Taiwan topography on the
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extreme rainfall of Typhoon Morakot and the predictability of this rainfall with a
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high-resolution (4-km) ensemble simulation using the Advanced Research WRF
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(ARW) model. Ensemble prediction with realistic topography reproduces salient
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features of orographic precipitation. The 24-h and 96-h accumulated rainfall amount
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and distribution from the ensemble mean compares reasonably well with the observed
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precipitation. When the terrain of Taiwan is removed, the rainfall distribution is
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markedly changed suggesting the importance of the orography in determining the
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rainfall structure. Moreover, the peak 96-h rainfall amount is reduced to less than 20%,
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and the total rainfall amount over southern Taiwan is reduced to less than 60% of the
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experiments with Taiwan topography. Further analysis indicates that Taiwan’s
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topography substantially increases the variability of rainfall prediction. Analysis
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uncertainties as reflected in the perturbed initial state of the ensemble are amplified
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due to orographic influences on the typhoon circulation. As a result, significant
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variability occurs in storm track, timing and location of landfall, and storm intensities,
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which in turn, increases rainfall variability. These results suggest that accurate
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prediction of heavy precipitation at a specific location and at high temporal resolution
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for an event such as Typhoon Morakot over Taiwan is exceedingly difficult. The
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forecasting of such event would benefit from probabilistic prediction provided by a
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high-resolution mesoscale ensemble forecast system.
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Keywords: Typhoon Morakot, ensemble simulation, rainfall variability, rainfall
predictability, Taiwan topography
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1. Introduction
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Taiwan is an island that possesses complicated mesoscale topography. Its Central
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Mountain Range (CMR) has a dimension of about 200 km × 100 km, and includes
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many peaks that exceed 3,000 m. Heavy rainfall resulting from the orographic effects
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on the typhoon circulation associated with the CMR is one of the most serious threats
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to Taiwan. From August 6 to August 10, 2009, Typhoon Morakot brought
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extraordinary rainfall over Taiwan, breaking 50 years precipitation records and
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causing a loss of more than 700 people with an estimated property damage exceeding
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US$3.3 billion. Figure 1a and b show the analysis of the observed 96-h and 24-h
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rainfall, based on the hourly gauge data collected from about 450 automatic stations
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scattered throughout Taiwan. During the four-day period, more than half of southern
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Taiwan received more than 800 mm of accumulated rainfall (Fig. 1a). Some of the
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mountainous areas recorded more than 2,500 mm, with the maximum 96-h gauge
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value of 2,874 mm recorded at Chiayi County ending at 0000 UTC 10 August 2009
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(marked with the white star in Fig. 1a). From 0000 UTC 8 to 0000 UTC 9 August, the
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most intensive rainfall period, 1,504 mm was recorded at the same Chiayi County
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(marked with the white star in Fig. 1b).
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The westward moving Typhoon Morakot landed on central eastern Taiwan at
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around 1530 UTC 7 August 2009. Figure 2 shows the infrared cloud imagery of
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Typhoon Morakot before, during and after landfall. Although this was not a
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particularly intense storm (e.g., a category 2 storm), the size of its circulation was
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fairly large. In particular, the structure of its circulation possessed distinct asymmetry,
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with strong northwesterly, westerly or southwesterly flow sustained in its southern
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quadrants before, during and after landfall. Significant moisture flux and convergence
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resulting from the sustained westerly and southwesterly flows impinging upon the
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mountainous southern Taiwan produced continuous heavy rainfall over a very large
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area, causing severe flooding and landslides.
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Typhoon Morakot’s rainfall distribution (Fig. 1a, b) exhibited significant
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small-scale orographic rainfall features as a result of time-varying typhoon circulation
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impinging upon the fixed Taiwan mountains. In order to better understand the
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predictability of the extreme rainfall associated with Typhoon Morakot, it is important
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to understand the impact of Taiwan topography. Recently, many high-resolution
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sensitivity simulations were performed to study orographic effects on typhoon
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circulations for different typhoon cases (e.g., Jian and Wu 2008; Yang et al. 2008).
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Most of these studies are deterministic modeling studies. Previous studies have
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suggested that there are many sensitive parameters associated with the orographic
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effects on typhoon circulations. As reviewed by Wu and Kuo (1999), the behavior of
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a typhoon approaching Taiwan varies as a function of the intensity and size of the
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typhoon, as well as the environmental flow. The control parameters influencing the
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continuity and deflection of typhoon tracks are related to the typhoon strength and its
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structure, the scale, height and dimension of the mountain and the large-scale
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background features (Lin et al. 2002; Lin et al. 2005; Lin et al. 2006). As shown in
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Wu et al. (2002), even if the track is not sensitive to the existence of topography and
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is well simulated, the rainfall can be very sensitive to model resolution and
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topography. Besides, effects of planetary boundary layer physics, precipitation
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parameterization, impinging angles, and landfall location can significantly influence
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the orographic effects on typhoon circulations. Practical predictability is limited by
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uncertainties in both the initial states and the forecast models. For these reasons, it is
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necessary to investigate the impact of Taiwan topography on the typhoon mesoscale
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structures and precipitation forecasts from a stochastic perspective.
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In this paper, we present results from high-resolution ensemble forecast
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experiments on Typhoon Morakot with and without Taiwan topography. Section 2
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presents the experiment design. Section 3 discusses the role of Taiwan topography in
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Typhoon Morakot’s extreme rainfall. Section 4 examines the rainfall variability
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impacted by Taiwan topography. Section 5 investigates the variability of the storm
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features impacted by Taiwan topography and their relationship with the rainfall
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variability. Section 6 discusses the ensemble probability prediction and the
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performance of the high-resolution ensemble simulation. Finally, conclusions are
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presented in section 7.
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2. Methodology
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a. Data and experiment design
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Two sets of 96-h 32-member ensemble forecast experiments initiated at 0000
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UTC of August 6, 2009 are performed with the WRF-ARW model, V3.1.1
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(Skamarock et al. 2008). Set 1 (hereafter referred to as EN0600) uses the real
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topography (at 30″ resolution) based on the Moderate Resolution Imaging
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Spectroradiometer (MODIS) landuse data, while Set 2 (hereafter referred to as
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NTEN0600) reduces the terrain height of Taiwan island to zero but still retains its
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land surface character. Terrain of everywhere else remains unchanged. The ensemble
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initial and boundary conditions (ICBC) are randomly perturbed from the
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high-resolution (0.225º×0.225º) European Centre for Medium-Range Weather
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Forecasts (ECMWF) analysis by adding analysis uncertainties based on WRF
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3DVAR background error covariance. Two corresponding deterministic simulations
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without any perturbations in the ICBC (hereafter ec0600 and ecNT0600) were
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performed for comparison. Figure 3 shows the model domain configuration and the
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geophysical height distribution, with the illustration for the removal of the Taiwan
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topography for sensitivity experiment. The 2-way interactive, triple nested domains
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include 36-km mesh (280×172), 12-km mesh (430×301), and 4-km mesh (364×322),
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respectively, extending vertically to the top at 20 hPa, with 36 η levels. The model
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physics include WSM5 microphysics (Hong et al. 2004; Hong and Lim 2006), YSU
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planetary boundary layer scheme (Hong et al. 2006; Hong 2007), Noah land surface
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model (Chen and Dudhia 2001), RRTM longwave radiation scheme (Mlawer et al.
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1997), Goddard shortwave radiation scheme (Chou and Suarez 1994), and BMJ
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cumulus convective parameterization (Betts 1986; Betts and Miller 1986; Janjic 1994;
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Janjic 2000). These physics schemes are used for all three meshes.
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b. Predictability measure
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The standard deviation (SD) between the ensemble members is often used to
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quantify the variability (i.e., the ensemble spread) of a particular variable. The SD is
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calculated as equation (1), and the associated root mean square error (RMSE) and
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mean error (ME) are defined as equations (2) and (3):
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M
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SD(i, j, t ) 
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RMSE (i, j, t ) 
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ME (i, j, t ) 
1
M
M
 R
m
m 1
1
M
M
 R
m 1
M
R
m 1
(i, j, t )  R (i, j, t ) 
m
m
2
(i, j, t )  O(i, j, t ) 
(i , j , t )  O (i , j , t ) 
(1)
2
(2)
(3)
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where, m denotes the ensemble member index, M the total number of the ensemble
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members, R the verification variable, R the ensemble mean, O the observation, i,
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and j the gridpoint two-dimensional spatial coordinate indices, and t the time
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coordinate index.
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Some authors (e.g., Mitchell et al. 2002; Zhang et al. 2006) use the root mean of
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difference total energy (RM-DTE) calculated from the model variables as a measure
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of the predictability in ensembles. In our study, we focus on the rainfall predictability
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within a targeted verification area, the worst hit area (hereafter referred to as HA) in
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Southern Taiwan, which is defined by the box in black in Fig. 1a. Its terrain is shown
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in Fig. 3. As pointed out by Jolliffe and Stephenson (2003), rainfall is a highly
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discontinuous variable with highly skewed distributions; it is very challenging to
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verify rainfall and measure rainfall variability using the instantaneous rainfall
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prediction on the model grid. Therefore, in order to reduce rainfall discontinuity, we
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use 3-h rainfall on the model grid as the basic verification variable; this is equivalent
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to performing time averaging before the calculation of the rainfall SD. The rainfall SD
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between the members of the ensemble simulation is used as a measure of rainfall
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predictability. Moreover, the SD of some other storm features, such as storm position
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storm intensity, etc., are used as measures of storm variability.
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3. The role of Taiwan topography in Typhoon Morakot’s extreme rainfall
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Figure 4 shows the spatial distribution of the simulated 96-h accumulated
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rainfall ending at 0000 UTC 10 August by the 32 ensemble members. Almost all
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members of EN0600 with Taiwan topography reproduce the key observed orographic
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rainfall features, with most of the precipitation concentrated along the windward side
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of the mountain, which is very different from the members of NTEN0600 without
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Taiwan topography. Almost all of the members of EN0600 predict 96-h accumulated
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rainfall over 2,500 mm; while only a few members of NTEN0600 produce 96-h
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accumulated rainfall exceeding 800 mm.
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Figure 1c and d show the spatial distribution of the simulated 96-h accumulated
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rainfall ending at 0000 UTC 10 August from the ensemble mean of EN0600 and
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NTEN0600, respectively. The EN0600 mean predicts three heavy rainfall areas with
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amount exceeding 800 mm (Fig. 1c) and several spots with amount over 2,500 mm.
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The rainfall extremes are distributed along the general orientation of the southern
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mountain range and on the windward slope, which closely resemble the observed
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orographic rainfall features shown in Fig. 1a. On the contrary, when the terrain of
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Taiwan is removed, the simulated rainfall is evenly distributed and exhibits no
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obvious local extremes (see Fig. 1d). The peak rainfall amount in NTEN0600 mean is
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only 616 mm, which is less than 20% of that (3,128 mm) in EN0600 mean.
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Table 1 shows some areal average statistics of 24-h and 96-h rainfall in the HA.
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The areal average 96-h accumulated rainfall in the HA is 917 mm for EN0600
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ensemble mean and 535 mm for NTEN0600. If we view the difference in the rainfall
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between EN0600 and NTEN0600 as “orographically additive rainfall” (or OAR), the
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areal average OAR in terms of 96-h total rainfall is 382 mm, which means that the
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total rainfall amount in the HA is increased by 70% by Taiwan topography.
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Figure 5 shows the time series of some areal average statistics of the 3-h rainfall
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in the HA. The areal average OAR in terms of 3-h rainfall is positive during the entire
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96-h simulation period, with a maximum of about 25 mm. These results suggest that
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Taiwan topography substantially increases the precipitation and plays a key role in
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making Typhoon Morakot a record-breaking rainfall event.
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4. The rainfall variability in the HA impacted by Taiwan topography
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a. The areal average 24-h and 96-h rainfall SD in the HA
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If we view the difference in the SD between EN0600 and NTEN0600 as
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“orographically additive rainfall variability (or OARV)”, as shown in Table 1, the
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areal average 24-h rainfall OARV in the HA is positive for each of the four
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simulation days, and the areal average 96-h accumulated rainfall SD is significantly
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increased with the existence of Taiwan topography. The maximum OARV occurred
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on the third day, when the observed rainfall is also the greatest.
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b. The spatial distribution of 24-h and 96-h rainfall SD in the HA
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As shown in Fig. 6, significant 24-h and 96-h rainfall SD in the HA is induced by
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Taiwan topography, especially on the second and third simulation days. For instance,
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in EN0600, there exist two areas with SD exceeding 250 mm on the second day and
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three areas with SD exceeding 350 mm on the third day, while the maximum SD in
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NTEN0600 on these two days is less than 150 mm.
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c. The time series of areal average 3-h rainfall SD in the HA
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The areal average 3-h rainfall OARV in the HA is positive during the entire
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simulation period except for a short 9-h period from 15/7 to 00/8 (see the dotted curve
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in Fig. 5b). The OARV is about 5-8 mm on average before this 9-h period. After that,
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the OARV becomes even larger, with amounts exceeding 15 mm.
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The comparison of the time series of the SD (the dotted curves) and ensemble
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mean (the solid curves) of EN0600 and NTEN0600 in Fig. 5a shows that they are
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generally in phase with each other: the larger the ensemble mean, the larger the SD.
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However, it is not always the case in EN0600; they are out of phase during the 18-h
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period from 15/7 to 09/8, when the ensemble mean is near a peak while the SD is
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exhibiting a local minimum. This is unique in EN0600 and may be a result of
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orographic effects on typhoon circulations, which will be discussed later.
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According to the time evolution of the simulated areal average 3-h rainfall SD in
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the HA and its relationship with the ensemble mean shown in Fig. 5a, the total 96-h
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simulation period of EN0600 with Taiwan topography can be separated into 5 stages:
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stage one (30-h period from 00/6 to 06/7), the SD and ensemble mean are well in
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phase with each other, both reaching a local maximum from 21/6 to 00/7; stage two
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(9-h period from 06/7 to 15/7), the SD and ensemble mean have similar positive
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trends; stage three (18-h period from 15/7 to 09/8), the SD and ensemble mean are out
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of phase with each other, when the ensemble mean reaches its global maximum from
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21/7 to 00/8, while the SD reaches a local minimum; stage four (6-h period from 09/8
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to 15/8), large SD persists, although the ensemble mean decreases rapidly; stage five
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(33-h period from 15/8 to 00/10), the SD and ensemble mean both have similar
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decreasing trends.
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Obviously, the most significant OARV is at stage four and the first half of stage
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five (see the dotted curve in Fig. 5b). Note that this is also the period when the model
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significantly under-predicts the observed rainfall (see the dot-dashed curve in Fig. 5b).
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As will be shown later in Section 5, the storm (both in the observation and the
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simulation) has left Taiwan during this period.
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d. The spatial distribution of 3-h rainfall SD in the HA
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Figure 7 shows the spatial distribution of the simulated 3-h rainfall SD in the HA
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at 3-h intervals from 00/7 to 00/9 August. This two-day period is selected for detailed
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examination because it includes all of the five stages mentioned above as shown in
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Fig. 5a, and it is also the period when the simulated rainfall and rainfall variability are
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high.
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Consistent with the results of SD and OARV presented in Fig. 5, EN0600 has
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much larger rainfall variability than NTEN0600, in terms of the maximum SD values
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and the area coverage with SD at large thresholds. For example, for threshold of 40
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mm, EN0600 has a much larger areal coverage than NTEN0600 after 09/8, except for
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the short period from 15/7 to 03/8. For NTEN0600, there is only a brief period, from
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15/7 to 21/7, when the simulated typhoon rainbands propagate over the HA and
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produce significant rainfall and rainfall variability. The maximum 3-h rainfall SD in
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EN0600 is over 90 mm at the southern tip of the CMR from 12/7 to 15/7. For
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NTEN0600, there is also a region of large SD near the southern boundary of the HA,
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but the amount of SD is 10 mm less and it occurs 6-h later. The areas with SD
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exceeding 50 mm only exist for a very short period (12-h) in NTEN0600 in the
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southern part of the HA. On the contrary, in EN0600, regions with SD exceeding 50
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mm persist over a much longer period (36-h), and cover larger areas, with the
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distribution pattern changing with time. From 06/7 to 18/7, one large SD area is
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located at the northern part of the HA and the other one near the southern tip of the
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CMR; while from 03/8 to 00/9, a string of small areas with SD exceeding 50 mm are
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located along the mountain range. The distribution of large SD in EN0600 tends to
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orient along the CMR, showing the distinct orographic influence.
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e. The spatial correlation between the rainfall SD and ensemble mean in the HA
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As shown in Fig. 6 and Fig. 7, the rainfall SD generally matches well with its
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corresponding ensemble mean in terms of spatial distribution, for both EN0600 and
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NTEN0600. The orographically enhanced small-scale, large-value SD structures are
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consistent with the orographically enhanced small-scale structures of ensemble mean
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rainfall. This relationship suggests that the spatial distribution of the rainfall ensemble
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spread is not independent of the ensemble mean; the larger the mean, the larger the
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spread. Such relationship of ensemble mean precipitation and spread was discussed by
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Hamill and Colucci (1998). In our experiments, significant (at 99% confidence level
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with the student t-test) spatial correlation between the rainfall SD and ensemble mean
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in the HA exists in both EN0600 and NTEN0600. However, higher correlation exists
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in EN0600 with Taiwan topography (see Table 1).
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Figure 8 is a scatter plot of the 3-h rainfall SD and ensemble mean in the HA at
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3-h intervals from 00/7 to 00/9 August. The correlation coefficient between the 3-h
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rainfall SD and ensemble mean is, in general, larger in EN0600 than in NTEN0600.
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The smaller regression coefficient of the 3-h rainfall SD against ensemble mean in
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EN0600 than in NTEN0600 may be related to the much larger rainfall amount in
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EN0600 with Taiwan topography. The correlation coefficient is relatively low
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(between 0.66 to 0.76) from 12/7 to 21/7, when the storm is very close to or on top of
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Taiwan in EN0600. Also, there is an obvious cluster separation in SD between large
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and small ensemble rainfall thresholds, with a very large range of rainfall SD
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occurring at smaller values of ensemble mean rainfall. The minimum regression
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coefficient of 0.18 in EN0600 occurs from 21/7 to 00/8, which is consistent with
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results shown in Fig. 5, with relatively small SD tied to the large ensemble mean
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rainfall.
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We note that the amplitude ratio between the SD and ensemble mean (or the SD
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normalized by the ensemble mean) may vary significantly in space. For instance, as
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shown in T00/6-00/10 of Fig. 6, of the several areas with large SD values, one area
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with SD exceeding 400 mm, located at the northern part of the HA (hereafter referred
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to as Area A), is tied to the ensemble mean precipitation of about 1,500 mm. On the
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other hand, another area with large SD values located at the southern tip of the CMR
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(hereafter referred to as Area B) is associated with ensemble mean precipitation of
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over 2,500 mm. These two areas have similar values of rainfall SD but with very
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different ensemble mean precipitation. The loci of Areas A and B are shown in Fig. 9.
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f. The rainfall predictability at specific locations
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Ensemble spread has been used as a measure to gauge flow dependent errors
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through the ensemble spread-skill relationship (see, e.g., Houtekamer 1993; Wobus
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and Kalnay 1995; Whitaker and Loughe 1998). However, this may not be applicable
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to a discontinuous variable with skewed distribution such as rainfall.
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Figure 9 shows the spatial distribution of the mean error (ME) of 24-h and 96-h
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accumulated rainfall in the HA in EN0600. The relationship between rainfall SD and
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magnitude and distribution of rainfall errors (as reflected in ME/RMSE) shown in
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Table 1, Fig. 5, Fig. 6 and Fig. 9 suggests that the rainfall SD can serve as an indicator
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for ensemble rainfall errors in some sense, at least for integrated quantities such as
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24-h or 96-h total rainfall. However, for rainfall forecast verification at a specific
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location and time, it may not be so simple.
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Two rain gauge stations within Areas A and B are selected to examine the 3-h
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rainfall SD and model rainfall prediction skills, respectively: Station A (23.51ºN,
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120.80ºE) at Chiayi County within Area A, which received the maximum 96-h gauge
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value shown in Fig. 1a; and Station B (22.59ºN, 120.60ºE) in Area B, which is near
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the maximum of model 96-h rainfall in Fig. 1c. Figure 10 shows the time series of
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selected 3-h rainfall statistics at these two stations. Significant orographically
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enhanced rainfall and rainfall variability (i.e., OAR and OARV) are introduced at
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both stations. The OARV values of these two stations are comparable, with relatively
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small values just after storm makes landfall, and the maximum value after the storm
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leaves Taiwan, consistent with the OARV curve in Fig. 5b. But, their OARs are quite
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different. The very large OAR at Station B is due to its orographically amplified
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erroneous heavy rainfall prediction.
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As shown in Fig. 10, the EN0600 ensemble mean significantly under-predicts the
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observed rainfall at Station A after 09/8 August but significantly over-predicts the
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rainfall at Station B, especially before 21/7 August. Although the ensemble spread has
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been used to estimate or predict large-scale flow dependent errors for traditional
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meteorological variables, this may not be applicable to rainfall. It is evident from Fig.
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10 that there is no clear relationship between model rainfall errors and rainfall SD at a
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fixed geographical location with high temporal resolution. The model rainfall RMSE
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at Station A varies significantly with time, and reaches extreme values after 09/8.
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However, there is no apparent time variation in SD around that time. Likewise, no
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clear relationship exists between the ensemble rainfall errors and the rainfall SD for
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Station B. It is very evident from Fig. 10 that when the model has large systematic
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errors, the SD among members will not adequately reflect these errors.
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5. The relationship between the variability of storm features and rainfall
variability
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Figure 11 shows the simulated tracks1 of Typhoon Morakot of EN0600 and
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NTEN0600 ensemble members. For EN0600, the model storm tracks follow generally
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the observed track well during the first 36-h simulation, until right before landfall. At
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about 50-km before landfall, the observed storm started to turn northwestward, and
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moved through northern Taiwan after making landfall. The model storms make
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landfall south of the observed landfall location, and have only a very slight
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northwestward turning after landfall. Consequently, the model storms move across
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central Taiwan, and the storm tracks deviate further away from the observed storm
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with time. The model storm tracks do not have a significant spread in the ensemble
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before the storms leave Taiwan. The systematic southward and westward storm track
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bias may account for, at least partially, the large model rainfall error at the Chiayi
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station on the third day (0000 UTC 8 - 9 August).
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The model storms in NTEN0600 behave similar to that of EN0600 before
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landfall for the first 30 h. However, at about 250 km before landfall, the model storms
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in NTEN0600 veer to the north of the observed track, as well as that of the model
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storms in EN0600. The model storms then move across Taiwan with nearly a straight
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westward track. For NTEN0600, the ensemble storm tracks start to diverge earlier
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than those in EN0600, at around landfall time. It is important to note that the tracks
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shown in Fig. 11 do not completely represent differences in storm positions with time.
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Some storms whose overall tracks look similar to each other may move slower or
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The tracks of the model storms are determined from a smoothed SLP field with
scales below 1000 km filtered. This is necessary to prevent the possibility of mixing
the typhoon center with transient mesolows created by topography.
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faster than the others.
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Figure 12 shows the time series of the storm track spread in EN0600 and
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NTEN0600. Note that the dispersion radius of storm position, the latitude spread and
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the longitude spread are calculated separately, because they are each important
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parameters when referring to the location of the storm relative to the fixed Taiwan
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topography.
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For EN0600, the storm position spread increases sharply during 12/7-18/7
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August at around landfall time. By comparison with the storm position spread in
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NTEN0600, the impact of topography on the storm track spread becomes quite
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obvious. The difference between the two will be called orographically additive storm
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track variability (OASTV), which can be attributed to increased variability in the
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latitude and longitude directions. Although the storm ensemble mean propagation
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speed in the east-west direction is not significantly impacted by Taiwan topography,
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the storm position longitude variability substantially increases near the landfall time,
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which is probably due to variability in timing of landfall among ensemble members in
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EN0600. Figure 10b shows that between 00/7 to 18/7, the NTEN0600 ensemble mean
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shows a distinct northward track bias when compared with the observed track. Such
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bias is largely removed in EN0600 with the inclusion of topography. After 18/7 both
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EN0600 and NTEN0600 show southward and westward track bias, consistent with
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Fig. 11. There are little differences in storm position spread between EN0600 and
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NTEN0600 after 18/7 (after model storms leave Taiwan). The differences in position
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variability between these two sets of ensemble experiments in longitude and latitude
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directions appear to cancel each other.
2
The storm intensity is weakened around landfall time in both EN0600 and
3
NTEN0600, but it is weakened 3-5 hpa more with the impact of Taiwan topography;
4
and the orographically additive storm intensity variability (OASIV) around landfall
5
time is about 5-8 hpa (Fig. 12d). After landfall, the OASIV is negative when the
6
storms are moving towards the mainland, related perhaps to the significant impact of
7
the mainland topography on the more intense storms in NTEN0600 at that time.
8
To better understand the relationship between the variability of the storm
9
features and the rainfall variability over southern Taiwan impacted by Taiwan
10
topography, three 3-h periods, 12/7-15/7, 21/7-00/8 and 12/8-15/8 August in stage
11
two, three and four, respectively, are selected for further examination.
12
a. 12/7-15/7 August (model simulation time 36-h~39-h)
13
This period is around the time when the model storms make landfall, with very
14
large rainfall SD in the HA in both EN0600 and NTEN0600 (see Fig. 5a and Fig. 7).
15
Figure 13 shows the spatial distribution of the model 3-h rainfall and the associated
16
sea-level pressure (SLP) at 15/7 August. Both the inner and outer circulations of the
17
typhoon are moving over Taiwan during this period. The simulated SLP field and
18
rainfall distribution involved with the typhoon rainbands in EN0600 with Taiwan
19
topography are totally different from those in NTEN0600 without Taiwan
20
topography.
21
As noted by Lin et al. (1999), the low pressure and circulation centers tend to
22
split when a tropical cyclone passes over the CMR, which makes it difficult to trace
18
1
the path of the storm center. Based on the analysis of many historical typhoons
2
influencing Taiwan, Wang (1980) showed that when a typhoon passes over Taiwan,
3
its track may be continuous or discontinuous. When the center of a typhoon with a
4
discontinuous track is about to make landfall, a secondary center (or secondary low)
5
often forms on the lee side of the CMR. As the primary typhoon center above the
6
mountain moves over and becomes aligned with the secondary center, the secondary
7
low develops and replaces the original surface center. The formation of the secondary
8
center often influences the spatial distribution and intensity of local rainfall and makes
9
the rainfall forecast even more difficult. Some typhoons may experience a
10
“quasi-continuous track” phenomenon (Lee et al. 2008), in which the convective
11
bands and the circulation associated with the secondary low interact with the
12
topography to produce local heavy rainfall.
13
In our simulation with Taiwan topography, as shown in Tm1-32 in Fig. 13, the
14
typhoon circulations are significantly modulated by topography, and the formation of
15
a secondary low is clearly indicated by the minimum SLP. Most of the ensemble
16
members form a secondary low on the lee side over northwest Taiwan presumably
17
associated with orographic effects on the typhoon’s inner circulations. Before the
18
storm completely passes over the mountains, a low pressure trough extends southward
19
on the lee side over the southeast Taiwan seashore and a transient low-pressure center
20
shows up in some members. Together with the original low, a total of three lows show
21
up on the SLP map. This transient low pressure center can be slightly deeper than that
22
of the secondary low over the northwest Taiwan or even the main typhoon low-center,
19
1
as found in members 1, 10, 12, 17, 19, 20 and 28.
2
Due to variability in the timing of landfall and the orographic effects on the
3
typhoon circulations, the relative positions between the storms and the CMR vary
4
among the ensemble members, which in turn results in large rainfall variability. For
5
3-h rainfall exceeding 100 mm, the two areas with largest variability among Tm1-32
6
of Fig. 13 are the two regions, Areas A and B, with large SD in T00/7-00/8 and
7
T00/6-00/10 of Fig. 6 and T12/7-15/7 of Fig. 7. Obviously, the large rainfall SD
8
within Area A is related to the different positions of the inner typhoon circulation
9
relative to the CMR; while the even larger rainfall SD within Area B is related to the
10
larger diversity of the positions of the outer typhoon circulations relative to the
11
topography over southern Taiwan.
12
In sharp contrast, the storm track spread for ensemble members without Taiwan
13
topography is much smaller during the period of 12/7-15/7 (see Fig. 12), and no
14
secondary low is found in any member of NTm1-32 in Fig. 13. It is obvious that
15
without Taiwan topography, the typhoon circulation structure is not disturbed, and
16
both the inner and outer rainbands are intact. Neither the rainfall distribution nor its
17
variability exhibits any topographical influence.
18
b. 21/7-00/8 August (model simulation time 45-h~48-h)
19
During this period, the simulated storms in EN0600 with Taiwan topography
20
have a relative small rainfall SD concurrent with the greatest ensemble mean rainfall
21
in the HA. Figure 14 shows the distribution of the simulated 3-h rainfall during this
22
period and the associated SLP at 00/8 August in EN0600. The simulated storms are
20
1
about to leave or have just left the Taiwan island. On average, the storm is located on
2
the west coast of Taiwan with sizeable position spread. However, regardless of the
3
storm position spread, the typhoon circulations for almost all the members are
4
positioned very favorably for topographically enhanced precipitation, with broad and
5
strong moist southwesterly flows impinging upon the CMR at a very favorable angle.
6
Under this circumstance, the orographic effect produces almost identical heavy
7
rainfall that is closely tied to Taiwan topography. As a result, the 3-h rainfall in the
8
HA of almost each member is very large and the rainfall is distributed along the
9
mountain range in a very similar pattern (see Tm1-32 of Fig. 14); consequently, there
10
is a relatively small rainfall variability. This presents a unique situation in which
11
relatively small rainfall SD is associated with maximum ensemble mean rainfall when
12
the storm circulations are positioned at a very favorable position relative to Taiwan
13
topography.
14
As an illustration, Figs. 15a and 15b show the west-east and south-north cross
15
section for member 31 of EN0600 along the lines AB and CD as shown in Fig. 3.
16
Intensive convection occurs over a very large area along the west-east cross section
17
(see Fig. 15a). There are several low level westerly jets with speeds up to 36 m s-1
18
(see Fig. 15b), providing northward and upward moisture transport along the
19
windward slope of CMR (see Fig. 15a). Consequently, deep convection associated
20
with the inner rainband takes place on the northern end of the low level westerly jet
21
(see Fig. 15b). This is a very favorable environmental condition for orographically
22
enhanced convection and precipitation.
21
1
c. 12/8-15/8 August (model simulation time 60-h~63-h)
2
This period has the largest areal average rainfall SD in the HA (see Fig. 5) after
3
the simulated storm moves farther away from Taiwan. Figure 16 shows the
4
distribution of the simulated 3-h rainfall and the associated SLP at 15/8 August. At
5
this stage, the storm inner core has moved far enough away from Taiwan, such that
6
only the outer circulation can impact the precipitation forecast in the HA. Due to large
7
spread of the storm tracks in EN0600 (especially the longitude spread, see Fig. 12),
8
some members are now begin to be affected by the topography of mainland China,
9
and the rainfall SD in the HA consequently reaches a maximum. On one hand, some
10
members of EN0600, with the outer circulation at the back of the typhoon impinging
11
on the CMR, produce large amounts of precipitation. On the other hand, some
12
members have almost no precipitation over the HA; for these members the storm’s
13
circulation is no longer interacting with the CMR. The large storm spread in east-west
14
direction, amplified by the orographic effect, has resulted in very large rainfall
15
variability. Although the rainfall variability in NTEN0600 over the HA also reaches
16
its maximum at this period due to very large track spread, without the orographic
17
effect, the rainfall discrepancy among the dispersed members is not amplified and
18
thus the rainfall variability in NTEN0600 is much smaller than that in EN0600.
19
20
6. Probabilistic rainfall prediction
21
a. A rainfall probability forecast
22
An important advantage of ensemble prediction is its ability to provide
22
1
probabilistic forecasts and estimates of forecast uncertainties. Palmer (2002) gave an
2
example of an extratropical cyclone that devastated parts of Europe on 26 December
3
1999. Although the single deterministic prediction from ECMWF did not forecast the
4
storm, about a third of the ECMWF 50-member Ensemble Prediction System
5
produced intense cyclogenesis.
6
Based on the forecasts from our high-resolution ensemble system, the rainfall
7
probability distribution for different thresholds at different forecast periods are shown
8
in Fig. 17. Obviously, for an extreme rainfall event such as Typhoon Morakot,
9
probabilistic forecasts for high thresholds are very important, even if the probability is
10
small. For example, as shown in Fig. 17d, the south part of the observed main rainfall
11
area with 24-h rainfall ending at 0000 UTC 9 August over 1,000 mm in Southern
12
Taiwan is predicted by 30-60% of the members, and 10% of the members indicate
13
that such extraordinary rainfall could take place over the north part of HA (where the
14
maximum observed rainfall was recorded). This is important probability forecast
15
information that a single deterministic prediction cannot provide. Initialized with a
16
global ensemble Kalman filter data assimilation based on the NCEP Global Forecast
17
System (GFS), Zhang et al. (2010) also showed that cloud scale ensemble prediction
18
could provide useful probability forecast of precipitation for Typhoon Morakot.
19
b. The performance of the high-resolution ensemble simulation
20
As indicated by Roebber (2004), the accuracy of ensemble probabilistic forecasts
21
can be compromised by model biases. How well the ensemble (probability forecast)
22
performs depends on how well the "ensemble mean forecast" performs.
23
1
As shown in Figs. 1c, and 1e, the two forecasts of the 96-h accumulated rainfall
2
ending at 0000 UTC 10 August, one from EN0600 mean and another from the single
3
deterministic forecast ec0600, look so similar that it is difficult to differentiate one
4
from the other in the HA. However, if we look at their simulated time series of the
5
areal average 3-h rainfall in the HA (see Fig. 5a), it is evident that the EN0600 mean
6
outperforms ec0600 in the HA during most of the simulation period. From 00/6 to
7
00/8 August, both EN0600 mean and ec0600 overestimate the rainfall, but EN0600
8
mean is closer to the observation; from 00/8 to 06/9 August, both EN0600 and ec0600
9
underestimate the heavy rainfall. Again, EN0600 mean is closer to the observation.
10
Therefore, the superior performance of EN0600 mean over ec0600, obscured by the
11
96-h accumulated rainfall shown in Figs. 1c, and 1e, is nonetheless clearly reflected in
12
Fig. 5a.
13
14
7. Conclusions and discussions
15
This paper investigates the impact of Taiwan topography on the record-breaking
16
rainfall of Typhoon Morakot and its predictability through a high-resolution ensemble
17
simulation. Analysis of results from ensemble experiments with and without Taiwan
18
topography leads to the following conclusions:
19
a. Taiwan topography plays a key role in making Typhoon Morakot a
20
record-breaking rainfall event. With realistic topography, the high-resolution (4-km)
21
ensemble with the WRF-ARW model reproduced salient features of orographic
22
precipitation. The 96-h total rainfall amount and distribution from the ensemble mean
24
1
compares reasonably well with the observed precipitation. When the terrain of Taiwan
2
is removed, the orographic rainfall distribution features completely disappear and the
3
maximum 96-h accumulated rainfall amount is reduced to less than 20% and the total
4
rainfall amount in the HA is reduced to less than 60%. The orographically enhanced
5
rainfall in the HA reaches 25 mm and 382 mm for ensemble mean 3-h and 96-h
6
accumulated rainfall, respectively.
7
b. Rainfall variability is substantially enhanced by Taiwan’s topography. The
8
standard deviation of areal averaged rainfall in the HA among members of the
9
ensemble system is increased by up to 15 mm and 75 mm for 3-h and 96-h
10
accumulated rainfall, respectively, as a result of topography. For a single grid-point
11
rainfall prediction, the variability can be more than doubled, with a value less than
12
150 mm for no terrain experiment and more than 400 mm with terrain. The spatial
13
distribution of rainfall variability is strongly modulated by the underlying topography.
14
c. The relationship between the ensemble mean precipitation and rainfall
15
variability is complex and time varying. There is no simple linear relationship
16
between the amount of ensemble mean precipitation and the rainfall variability. There
17
exists a unique period when the ensemble mean precipitation reaches its maximum,
18
while the rainfall variability is having a local minimum. This is the time when the
19
storm is located over the west coast of Taiwan, and shortly after it left Taiwan, a
20
period when the typhoon circulations are positioned most favorably relative to
21
Taiwan’s topography for producing topographic precipitation.
22
d. It is not possible to use the rainfall forecast standard deviation to estimate
25
1
model rainfall forecast error at high temporal and spatial resolution. Although
2
ensemble spread has been considered a useful variable to measure flow dependent
3
model forecast uncertainties for large-scale variables, this does not seem to apply for
4
rainfall prediction. The high temporal and spatial variability of rainfall, coupled with
5
enhanced variability due to topography, prevents the use of rainfall ensemble spread
6
as a useful measurement of model rainfall forecast errors. This is especially true when
7
the model exhibits significant systematic bias in certain specific regions. We do note
8
that for integrated quantities, such as 96-h accumulated rainfall, this relationship
9
becomes more robust. For example, the correlation coefficient for rainfall standard
10
deviation and rainfall RMSE is 0.63.
11
e. The orograhic effects on typhoon circulations amplify uncertainties in the
12
initial model states and substantially increase variability in storm track, positions,
13
storm propagation speed, landfall location and timing, and the detailed pressure
14
structures (e.g., secondary lows) among the ensemble members. The variability in
15
these mesoscale storm features, in return, result in significant variability in rainfall.
16
The topographically enhanced variability is particularly robust near the time of
17
landfall. This makes it practically impossible to make an accurate quantitative
18
precipitation forecast at a specific location for a land-falling typhoon over Taiwan.
19
f. Probabilistic rainfall prediction derived from the high-resolution ensemble
20
system does show some skill in estimating where significant rainfall may take place.
21
For example, the 90% probability of accumulated rainfall exceeding 1000 mm
22
between 00/7 and 00/9 match well with the contour of the observed 1000 mm. In
26
1
comparison with one single deterministic forecast, the ensemble mean is shown to
2
possess superior skill in forecasting precipitation.
3
Careful evaluation of the ensemble mean prediction with observations also
4
points out some notable deficiencies. This includes a westward and southward track
5
bias after landfall, significant under-prediction of the rainfall over Chiayi county and
6
significant over-prediction of rainfall over southern Taiwan over the mountain ridge.
7
The significant under-prediction of rainfall after 0600 UTC 8 August by the ensemble
8
mean may be attributed, at least partially, to the systematic track bias. Further efforts
9
should be devoted to improving the performance of the model, including model
10
initialization, precipitation parameterization, and treatment of topography.
11
Acknowledgement:
12
We thank Central Weather Bureau for providing the rainfall data for this study.
13
We appreciate Ed Tollerud, John Gyakum, and Ling-Feng Hsiao for reading an earlier
14
version of the manuscripts, and offering many thoughtful comments. This work is
15
partially supported by the National Science Foundation, Division of Atmospheric and
16
Geospace Sciences CSA-0939962, under Cooperative Agreement No. AGS-0918398.
17
This work is also supported in part by the NOAA’s Hurricane Forecast Improvement
18
Project (HFIP) through the Developmental Testbed Center.
27
1
2
3
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1
2
Table 1. Areal average statistical measures of 24-h and 96-h rainfall in the
HA
Rainfall variables
Areal average measures
Analyzed observation (OBS) (mm)
EN0600_mean (mm)
NTEN0600_mean (mm)
OAR* (mm)
EN0600_SD (mm)
NTEN0600_SD (mm)
OARV** (mm)
Correlation coefficient of SD and
ensemble mean in EN0600
Correlation coefficient of SD and
ensemble mean in NTEN0600
EN0600_RMSE (mm)
EN0600_ME (mm)
EN0600_RMSE/EN0600_SD (%)
Correlation coefficient of
EN0600_SD and EN0600_RMSE
24-h
rainfall
(00/600/7)
24-h
rainfall
(00/700/8)
24-h
rainfall
(00/800/9)
24-h
rainfall
(00/900/10)
96-h
rainfall
(00/600/10)
84
129
55
75
39
27
12
0.87
321
383
277
107
115
91
24
0.75
625
356
191
165
183
114
69
0.97
179
48
12
36
32
11
21
0.79
1209
917
535
382
216
142
74
0.86
0.79
0.48
0.89
0.62
0.22
76
45
1.97
0.78
171
62
1.49
0.69
358
-269
1.96
0.58
141
-131
4.47
0.41
470
-293
2.18
0.63
3
4
5
6
7
*
OAR denotes orographically additive rainfall, the rainfall difference between
EN0600 and NTEN0600
**
OARV denotes orographically additive rainfall variability, the rainfall
variability difference between EN0600 and NTEN0600
8
34
1
Figure captions:
2
Fig. 1. The spatial distribution of Typhoon Morakot’s rainfall over Taiwan and
3
surrounding islands (unit: mm): objective analysis of the observed 96-h
4
accumulated rainfall ending at 0000 UTC 10 August (a) and 24-h
5
accumulated rainfall ending at 0000 UTC 9 August (b); the simulated
6
96-h accumulated rainfall ending at 0000 UTC 10 August by EN0600
7
mean (c), NTEN0600 mean (d), and ec0600 (e). The white star mark
8
shows the maximum gauge value, 2874 mm in (a) and 1504 mm in (b).
9
The box in black in (a) is the worst hit area (HA), with latitudes from
10
22.50ºN to 23.74ºN and longitudes from 120.32ºE to 121.14ºE (about
11
130×90 square km).
12
Fig. 2. The Dvorak BD curve enhanced (a-f) and color enhanced (g and h)
13
infrared cloud imageries (from
14
http://rammb.cira.colostate.edu/products/tc_realtime) of Typhoon
15
Morakot before, during and after landfall at: (a) 1530 UTC 6 August; (b)
16
0030 UTC 7 August; (c) and (g) 1530 UTC 7 August; (d) 0030 UTC 8
17
August; (e) 1530 UTC 8 August; (f) and (h) 1530 UTC 9 August. The two
18
yellow circles in (a)-(f) have radii of 1 and 2 degrees latitude around the
19
storm center respectively.
20
21
Fig. 3. The model domain configuration and the geophysical height distribution
(color shaded, unit: m) with the terrain of Taiwan removed for
35
1
sensitivity simulation. The zoomed area in the red box shows the real
2
Taiwan geophysical height, lines AB and CD are the cross section lines
3
used in section 5, and the box in white in this zoomed area is the
4
targeted verification area.
5
Fig. 4. The spatial distribution of the simulated 96-h accumulated rainfall
6
ending at 0000 UTC 10 August over Taiwan and surrounding islands
7
(unit: mm) by the 32 ensemble members of EN0600 (labelled by
8
Tm1-32) and NTEN0600 (labelled by NTm1-32).
9
Fig. 5. The time series of some areal average statistical measures of the 3-h
10
rainfall in the HA estimated from the ensemble members (unit: mm): (a)
11
minimum, lower quartile, median, upper quartile and maximum
12
depicted by the blue wide (red narrow) box-and-whisker plot for
13
EN0600 (NTEN0600), SD, and 3-h rainfall from ensemble mean, ec0600
14
and the analyzed observation (OBS); (b) OAR, OARV, ME and RMSE of
15
EN0600. The time axis indicates the ending time of each 3-h interval,
16
and the triangles separate the total simulation period into different
17
stages.
18
Fig. 6. The spatial distribution of the 24-h and 96-h accumulated rainfall SD
19
(unit: mm, color shaded in levels as in the color bar), ensemble mean
20
(unit: mm, contoured in levels of 10, 30, 50, 70, 100, 150, 200, 300, 400,
21
500, 800, 1000, 1200, 1500, 2000 and 2500 mm) for EN0600 and
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1
NTEN0600 (labelled by “T” and “NT”, respectively, and time stamp) in
2
the HA.
3
Fig. 7. The spatial distribution of the 3-h rainfall SD (unit: mm, color shaded in
4
levels as in the color bar), ensemble mean (unit: mm, contoured in levels
5
of 10, 30, 50, 70, 100, 150 and 200 mm) for EN0600 and NTEN0600
6
(labelled by “T” and “NT”, respectively, and time stamp) in 3-h intervals
7
from 00/7 to 00/9 August in the HA.
8
9
Fig. 8. The scatter plot of the 3-h rainfall SD (Y axis, unit: mm) and ensemble
mean (X axis, unit: mm) for EN0600 and NTEN0600 (labelled by “T” and
10
“NT”, respectively, and time stamp) in 3-h intervals from 00/7 to 00/9
11
August in the HA.
12
Fig. 9. The spatial distribution of the 24-h and 96-h accumulated rainfall ME
13
(unit: mm) in the HA in EN0600: (a) 00/6-00/7; (b) 00/7-00/8; (c)
14
00/8-00/9; (d) 00/9-00/10; (e) 00/6-00/10. The blue (red) box
15
illustrates Area A (B).
16
Fig. 10. The time series of some 3-h rainfall statistical measures (unit: mm) at:
17
(a) Station A; (b) Station B. See text for station descriptions and
18
locations.
19
Fig. 11. The simulated track of ensemble members (green lines), the single
20
deterministic simulation (blue line), and the average track of the
21
ensembles (red line) of EN0600 (top) and NTEN060 (bottom). The JMA
37
1
best track (modified by analysis from Taiwan Central Weather Bureau)
2
is superimposed as the thick black line labelled OBS. The track is plotted
3
from 00/6 to 06/9 August, and the storm positions are shown by the red
4
circles at 00/6, 00/7 and 00/8, blue circles at 12/6 and 12/7, black
5
circles at 12/8 and cyan circles at 00/9.
6
Fig. 12. The time series of storm track and intensity spread and related
7
ensemble mean in EN0600 and NTEN0600: (a) storm center position
8
dispersion radius (relative to the ensemble mean position, unit: km); (b)
9
storm center latitude (unit: degree); (c) storm center longitude (unit:
10
11
degree); (d) storm center minimum SLP (unit: hpa).
Fig. 13. The spacial distribution of the simulated 3-h rainfall rate (colored
12
shade, unit: mm) at 12/7-15/7 August for the ensemble members of
13
EN0600 (labelled by Tm1-32) and NTEN0600 (labeled by NTm1-32).
14
The associated sea level pressure (blue contours, unit: hPa) and the
15
observed typhoon center (black dot) at the end of this period is
16
superimposed.
17
Fig. 14. Same as Fig. 13, but for EN0600 at 21/7-00/8 August.
18
Fig. 15. West-east cross section along line AB in Fig. 3 of reflectivity (color
19
shaded, unit: dbz), wind bar (u, w) (m s-1, 0.05 m s-1) with one full bar of
20
10 unit and meridional wind v (blue line, unit: m s-1) for member 31 of
21
EN0600 (a); south-north cross section along line CD in Fig. 3 of
38
1
reflectivity (clour shaded, unit: dbz), wind bar (v, w) (m s-1, 0.05 m s-1)
2
with one full bar of 10 unit and zonal wind u (blue line, unit: m s-1) for
3
member 31 of EN0600 (b). X axis is the model grid number with grid
4
length of 4 km.
5
Fig. 16. Same as Fig. 13, but for 12/8-15/8 August.
6
Fig. 17. The rainfall probability distribution (%) exceeding the thresholds of (a)
7
500, (b) 1000 mm for 24-h rainfall ending at 0000 UTC 8 August; (c)
8
500, (d) 1000 mm for 24-h rainfall ending at 0000 UTC 9 August; (e)
9
1000, (f) 1500 mm for 48-h rainfall ending at 0000 UTC 9 August; (g)
10
1500, (h) 2500 mm for 96-h rainfall ending at 0000 UTC 10 August
11
estimated from the 32 members of EN0600. The observed rainfall at the
12
corresponding threshold is shown by the blue line, and the black star
13
indicates the automatic observation station at which the maximum 96-h
14
accumulated rainfall occurred.
15
39