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Improving Ensemble-Based Quantitative Precipitation Forecast for Topography-Enhanced Typhoon Heavy Rainfall over Taiwan with a Modified Probability-Matching Technique
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Xingqin Fang * and Ying-Hwa Kuo
University Corporation for Atmospheric Research and National Center for Atmospheric Research,
Boulder, Colorado
Submitted to Monthly Weather Review
March 18, 2013
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18 *
Corresponding author:
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Dr. Xingqin Fang
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Email: fang@ucar.edu
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Address: UCAR, P. O. Box 3000, Boulder, CO 80307
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Phone: (303) 497-8983
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1
Abstract
2
In this paper, a modified probability-matching technique is developed for the
3 ensemble-based quantitative precipitation forecast (QPF) associated with landfalling
4 typhoons over Taiwan. The main features of this modified technique include a
5 resampling of the ensemble realizations, a rainfall pattern adjustment, and
6 bias-correction. Using this technique, a synthetic ensemble is created for the purpose
7 of rainfall prediction from a large-size (32 members), low-resolution (36 km)
8 ensemble and a small-size (8 members), high-resolution (4 km) ensemble. The rainfall
9 pattern is adjusted based on the precipitation distribution of 36-km and 4-km
10 ensembles. A bias-correction scheme is then applied to remove the known systematic
11 bias from the resampled 4-km ensemble realizations as part of the
12 probability-matching procedure. The modified probability-matching scheme is shown
13 to substantially reduce or eliminate the intrinsic model rainfall bias and to provide
14 better QPF guidance. The encouraging results suggest that this modified
15 probability-matching technique is a useful tool for the QPF of the
16 topography-enhanced typhoon heavy rainfall over Taiwan using ensemble forecasts at
17 dual resolutions .
18
1

1
1. Introduction
2
The Central Mountain Range (CMR) of Taiwan has a dimension of about 200
3 km × 100 km, and includes many peaks that exceed 3,000 m. Many previous studies,
4 based on either the deterministic approach (e.g., Lin et al. 2002; Jian and Wu 2008;
5
Yang et al. 2008) or the stochastic approach (Fang et al. 2011), have shown that the
6 rainfall pattern associated with landfalling typhoons is strongly modulated and also
7 that the rainfall amount is significantly enhanced by the topography of CMR. The
8 quantitative precipitation forecast (QPF) of a landfalling typhoon is a very
9 challenging problem due to the complicated orographic effects on the typhoon
10 circulation (Wu and Kuo 1999).
11
As shown in Fang et al. (2011), heavy rainfall is produced by a typhoon when its
12 inner and/or outer circulations interact with the CMR. The structure of rainfall
13 distribution is strongly tied to the relative position between the storm and the CMR.
14
Typhoon track must be predicted with sufficient accuracy for accurate forecast of
15 topography-enhanced typhoon rainfall. The good news is that typhoon track forecast
16 may not be overly sensitive to model resolutions when the model resolution is
17 sufficiently high enough to capture the main forcing mechanisms that control the
18 typhoon’s movement (many of our experiments have shown that a resolution of 36
19 km is sufficient for this purpose). Low-resolution (36 km) and high-resolution (4 km)
20 ensembles generally produce comparable ensemble mean track forecasts. However, as
21 shown in Wu et al. (2002), even if the track is well simulated, the rainfall can be very
22 sensitive to the model resolution and topography. A low-resolution model usually
2

1 misses the small-scale rainfall features and significantly under-predicts the rainfall
2 amount. Therefore, a high-resolution model is necessary to simulate the accurate
3 amount of the topography-enhanced typhoon rainfall. However, the 4-km model can
4 also have precipitation bias that is topographically locked (as shown in Fang et al.
5
2011), which requires remedy.
6
The ensemble forecasting has recently been applied to study the typhoon rainfall
7 events over Taiwan area due to the complicated uncertainty in both the initial states
8 and the model’s physical parameterizations, as well as the complicated orographic
9 effects of the CMR (e.g., Zhang et al. 2010; Fang et al. 2011; Li and Hong 2011;
10
Hong et al. 2012). For ensemble forecast of topography-enhanced typhoon heavy
11 rainfall over Taiwan, we are faced with the following challenges: 1) a large-size,
12 high-resolution ensemble is a desirable but expensive option; 2) a large-size,
13 low-resolution ensemble is affordable and could produce reasonable track forecast,
14 but most likely will systematically under-predict the precipitation amount.
15
Recognizing the fact that topography-enhanced typhoon heavy rainfall over Taiwan is
16 strongly tied to the relative position between the storm center and the CMR, we may
17 develop a new approach for a dual-resolution-ensemble-based typhoon QPF that is
18 computationally affordable.
19
In general, the simple ensemble mean (SM) usually provides a reasonable
20 estimate of the rain center, but the averaging process tends to smear the rain values so
21 that the peak rainfall is reduced and the areal coverage of light rain is artificially
22 expanded. Probability matching is an approach that can be used to blend data types
3

1 with different spatial and temporal properties, where usually one data type gives a
2 better spatial representation while the other data type has greater accuracy (Ebert
3
2001) .
Probability-matched ensemble mean (PM) is often used to restore the more
4 realistic rainfall amount. In the typical probability-matching technique, the PM has
5 the same spatial pattern as the SM and the same frequency distribution as the whole
6 ensemble. For typical rainfall situations that are not tied to topography, the PM
7 usually gives a more realistic peak rainfall amount. However, the performance of the
8
PM is dependent on the accuracy of the spatial distribution of the SM rainfall as well
9 as the frequency distribution of the ensemble. The application of traditional
10 probability-matching scheme in topographic rainfall is not straightforward as the
11 spatial distribution and the frequency distribution can be significantly distorted by
12 topography.
13
Another problem is that the storm positions after landfall could be significantly
14 dispersed as compared with those before landfall due to the complicated interactions
15 between the circulations of a typhoon and the CMR topography, as well as the
16 uncertainties in the model’s physical parameterizations in complicated mountainous
17 areas. In this situation, the spatial structure of the SM rainfall and the frequency
18 distribution of the ensemble may not be representative and, consequently, the
19 performance of the traditional probability-matching technique may be poor.
20
Furthermore, it has been noted that the high-resolution model may produce
21 excessive rainfall at the south tip of the CMR (see Fang et al. 2011). Although the
22 exact reason for this rainfall overprediction bias is still not clear, such
4

1 topography-locked rainfall bias will be amplified by the typical probability-matching
2 technique.
3
In this paper, we develop a modified probability-matching technique for
4 ensemble forecast of the topography-enhanced typhoon heavy rainfall over Taiwan.
5
The basic idea is to collect the track and rainfall forecast from a large-size,
6 low-resolution ensemble (LREN) and a small-size, high-resolution ensemble (HREN)
7 to reconstruct a synthetic rainfall ensemble (hereafter denoted by NEWEN). The
8 ultimate goal of this approach is to produce an improved ensemble-based QPF for
9 landfalling typhoons over Taiwan at affordable computational cost. Section 2
10 provides an overview of the demo case Typhoon Morakot (2009). Section 3 presents
11 the track and rainfall ensemble forecast results by the LREN and HREN, respectively.
12
Section 4 describes a modification to the probability-matching technique and the
13 procedure used to construct the NEWEN. Evaluation of the performance of the
14 probabilistic rainfall forecast produced by the LREN, HREN, and NEWEN is
15 presented in Section 5. Section 6 assesses the QPF performance of the ensemble mean
16 rainfall derived from the LREN, HREN, and NEWEN. Section 7 includes one more
17 case study of Typhoon Jangmi (2008). Conclusions and discussions are presented in
18
Section 8.
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20
2. Case overview of Typhoon Morakot (2009)
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From August 6 to August 10, 2009, Typhoon Morakot (2009) brought
22 extraordinary rainfall over Taiwan, breaking a 50-year precipitation record. As shown
5

1 in Fig. 1 of Fang et al. (2011), during this four-day period, more than 50% of rain
2 gauge stations over southern Taiwan received more than 800 mm of accumulated
3 rainfall; some stations over the mountainous areas recorded more than 2,500 mm,
4 with the maximum 96-h gauge value of 2,874 mm (about 9.4 feet) recorded at Chiayi
5
County. From 0000 UTC 8 to 0000 UTC 9 August, the most intensive rainfall period,
6
1,504 mm (about 4.9 feet) was recorded at the same Chiayi County.
7
As indicated in Fang et al. (2011), high-resolution ensemble forecasts of
8
Typhoon morakot with different combinations of moist physics would all have similar
9 significant overprediction of rainfall at the southern tip of the CMR (see their Figs. 1
10 and 9). This systematic bias is also observed in many other high-resolution
11 simulations of Typhoon Morakot (e.g., the 3-km simulation in Fig. 14 of Hall et al.
12
2013; the 3.33-km simulation in Fig.4 of Wu 2013, cf. Yen et al. 2011; the 4.5-km
13 ensemble simulations in Fig. 1 of Zhang et al. 2011). The reason for the
14 overprediction at the southern tip of the CMR is still not completely clear, which
15 might be related to the poor physical or dynamical representations of the complicated
16 topography of Taiwan in the model. However, it does warn us to investigate the
17 intrinsic bias in the high-resolution forecasts of such topography-enhanced heavy
18 rainfall as of Typhoon Morakot.
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20
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3. Track and rainfall ensemble forecast performance by the LREN and
21
HREN a. Experiment design of the LREN and HREN
6

1
The ensemble forecast experiments in this study use the Advanced Research
2
WRF (Weather Research and Forecasting) (ARW) model V3.3.1 (Skamarock et al.
3
2008) and the initial conditions (ICs) of the ensemble are obtained from WRF Data
4
Assimilation Research Testbed (DART) ensemble adjust Kalman filter (EAKF)
5 analysis ensemble. The model top is placed at 20 hPa with 64 η levels. The
6 triple-nested model domain configuration is shown in Fig.1, which includes a 36-km
7 mesh (280×172), a 12-km mesh (430×301), and a 4-km mesh (364×322). The
8
WRF/DART data assimilation is done only in the uttermost 36-km domain. For
9
Typhoon Morakot, the data assimilation was cold started at 0000 UTC August 5 2009
10 from the high-resolution (0.225º×0.225º) analysis of the European Centre for
11
Medium-Range Weather Forecasts (ECMWF). During the 24-h data assimilation
12 period, the traditional observation data and the GPS RO refractivity data (Anthes et al.
13
2008) were assimilation in 3-h cycling. This is to produce initial perturbations that are
14 both dynamically consistent and flow-dependent for the regional ensemble model.
15
The LREN is a 36-km low-resolution ensemble forecast with a single domain
16 that is identical to the data assimilation domain. The 32-member, 72-h ensemble
17 forecast is initiated at 0000 UTC August 6 2009 using the 32-member WRF/DART
18
EAKF analysis ensemble. The lateral boundary conditions (LBCs) are interpolated
19 from the ECMWF analysis perturbed by the WRF 3DVAR using the climatological
20 background error.
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The HREN is different from the LREN in the following aspects: 1) the HREN is
22 a two-way interactive, 36-12-4km triple-nested high-resolution ensemble forecast;
7

1 and 2) the HREN is a 8-member small-size ensemble forecast, which only utilizes the
2 leading 8 members of the 32-member WRF/DART EAKF analysis ensemble to save
3 the computational cost.
4
In this paper, the main verification area (hereafter denoted by VA) is identical to
5 the objective analysis area of the observed rainfall, that is, an area with latitudes from
6 22.0º to 25.2ºN, longitudes from 120.0º to 122.0ºE, and with a grid size of
7
0.02º×0.02º. The verification is performed also over the heavy-hit area (hereafter
8 denoted by HA) in the southern Taiwan, which is defined as an area of about 130×90
9 km
2
with latitudes from 22.50º to 23.74ºN, longitudes from 120.32º to 121.14ºE, and
10 with a grid size of 0.02º×0.02º. The domains of the HA and VA and their geophysical
11 background as resolved in the 4-km high-resolution model are shown in the zoomed
12 area of Fig. 1. Further more, the probability-matching process in this paper is carried
13 out within the VA.
14
15 b. Track forecast of the LREN and HREN
Figure 2 shows the forecast track of Typhoon Morakot by the LREN and HREN.
16
The LREN mean track is very close to the observed track (with a track error of less
17 than 50 km). We also find that the mean tracks of the LREN and HREN are generally
18 close to each other. Note that the storm positions in both the LREN and HREN spread
19 significantly after landfall.
20
21 c. Rainfall forecast of the LREN and HREN
Figure 3 shows the spatial distribution of the 3-h rainfall PM of the LREN and
22
HREN (denoted by LPM and HPM, respectively) and the observed 3-h rainfall at 3-h
8

1 intervals from 0000 UTC 6 to 0000 UTC 9 August 2009 over Taiwan. The LPM and
2
HPM present more realistic rainfall structures and amounts than the corresponding
3
SM (denoted by LSM and HSM, respectively, figures omitted). However, the LPM is
4 too smooth and consistently under-predicts the heavy rainfall, due in large part to the
5 low model resolution. The HPM has two obvious problems: on one hand, it produces
6 excessive rainfall at the south tip of the CMR, especially when the inner typhoon
7 circulations interact with the CMR; on the other hand, it generally under-predicts the
8 heavy rainfall after landfall (after 0009 UTC 8 August 2009) when the model storm
9 positions spread considerably and most of them have landed on or are close to the
10 mainland China.
11
12
4. The modified probability-matching technique and the formulation of
13
NEWEN
14 a.
The modified probability-matching technique
15
The main features of the modified probability-matching technique include: 1)
16 resampling a subset of the nearest LREN storm realizations (ignoring timing) for each
17 ensemble mean LREN storm position at each verification time (at 3-h intervals in this
18 paper); 2) resampling a subset of the nearest HREN storm realizations (ignoring
19 timing) for each selected LREN storm realization; 3) adjusting the rainfall pattern in
20 the SM of the selected HREN rainfall realizations using the rainfall distribution of the
21 corresponding LREN rainfall realization; 4) improving the representativeness of the
22 rainfall frequency distribution of the selected HREN rainfall realizations by correcting
9

1 the overprediction bias in the model; and 5) conducting probability-matching based
2 on the improved rainfall pattern and frequency distribution to reconstruct a synthetic
3
3-h rainfall ensemble at each verification time. The reconstructed rainfall ensemble by
4 this probability-matching technique is denoted as NEWEN.
5
There are two loops of iteration during the implementation of this modified
6 probability-matching technique. The outer loop is the time loop. Ensemble time series
7 of rainfall are constructed at a fixed time interval (currently, 3-h, but a shorter interval
8 is possible). The inner loop is the member loop. At each time point, the new
9 probability-matching technique is used repeatedly to build up members for the
10
NEWEN.
11
In other words, at a specific forecast time, the modified probability-matching
12 technique is repeatedly utilized to build up members of an ensemble , rather than used
13 only once to produce an ensemble mean as done in a typical probability-matching
14 technique.
15
Figure 4 is the scatter plots of the simulated storm positions of Typhoon Morakot
16 at 3-h intervals by the ensemble members of the LREN and HREN. Assisted by Fig. 4,
17 the new probability-matching technique can be described as below.
18 b.
The entire track realizations in the LREN and HREN

19
20
21

22
The entire realizations of the simulated storm positions of the LREN members are represented by the associated latitude and longitude pairs: LAT
LREN
 iel , itl

and
LON
LREN
 iel , itl

(see small red dots in Fig. 4) with itl

1, 2, ...
T , where iel

1, 2, ...
M
LR
and
M
LR

is the number of members in the LREN (set to 32 for this

10


1
2
3
4

5
6
7
8 study), and T is the length of the time series (set to 25 for the total 72-h simulation in 3-h intervals). The LREN mean track is expressed by

LONAVG
LREN
 
(see small black circles in Fig. 4) with
LATAVG
LREN it

1, 2, ...
T .
 
and

Similarly, the entire realizations of the simulated storm positions of the HREN members are represented by LAT
HREN
 ieh , ith

and LON
HREN
 ieh , ith

(see small blue dots in Fig. 4) with ieh

1, 2, ...
M
HR
and ith

1, 2, ...
T , where M
HR
is the
  number of members in the HREN (set to 8 for this study). Here, we are not overly
   concerned with the accuracy of the HREN mean track, as the ensemble size of the
9
HREN is too small.
10 c.
Selection of the LREN storm position realizations
11
At an arbitrary time it , the selected LREN storm position realizations that will
12
13 be used for further selection of the associated HREN storm position realizations

(ignoring the timing, see red circles in Fig.4) are those closest to the LREN mean
14 storm position at that time (see the large black circle in Fig. 4). The time for the
15 example shown in Fig. 4 is 1800 UTC 8 August 2009. The number of the LREN
16 storms to be selected is set to 16 in this study.
17
18 d.
Selection of the HREN storm position realizations
Similarly, for an arbitrary selected LREN storm position (see the red cross in Fig.
19
4), the selected HREN storm position realizations that will be used to extract the
20 associated high-resolution rainfall information are those with simulated storm
21 positions (again ignoring the timing, see blue circles in Fig.4) closest to the selected
22
LREN storm position realization. The example LREN storm position shown in Fig. 4
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1 is the sixth nearest storm from the LREN mean storm position at 1800 UTC 8 August
2
2009. The number of HREN storms to be selected is set to 8.
3 e.
The entire rainfall realizations in the LREN
6

7
4
5
The 3-h rainfall field of member iel of the LREN, at the time itl and the point ip can be represented by and ip

1, 2, ...
P , where
R
LREN
 iel , itl , ip

with iel

1, 2, ...
M
LR
, itl

1, 2, ...
T ,
P
 
is the number of the interpolated points in the VA.
  
Note that, in order to be consistent, the rainfall from both the 36-km LREN and the

4-km HREN is interpolated to the same regular latitude and longitude grids that have
9 comparable horizontal resolution to the native resolution of the HREN. However, in
10 the subsequent discussion (Sections 5 and 6), when verified against the objectively
11 analyzed observations, all the model rainfall fields are interpolated to the same
12 observation analysis grids (ref. Section 2).
13 f.
The entire rainfall realizations in the HREN
14
15
16
17

18
Similarly, the 3-h rainfall field of member ieh of the HREN, at the time ith and the point ip can be represented by ieh

1, 2, ...
M
HR
, ith

1, 2, ...
T

, and ip

1, 2, ...
  g. The formulation of the NEWEN at a given time
P .
R
HREN
 ieh , ith , ip

with

Let

R
NEW EN
 ie , it , ip


represent the 3-h rainfall field of the member ie of the
19
20
21

22
NEWEN to be constructed at the time it and the point ip with ie

1, 2, ...
N ,
 it

1, 2, ...
T , and ip

1, 2, ...
P , where N is the number of members in the

 
NEWEN (set to 16); its construction is detailed in the eight steps below.


Step 1: Calculate the distance D
L
 iel , itl


between points
12


1
2

3
4
5
6
7

8
9

10
11
12
( LAT
LREN
( iel , itl ), LON
LREN
( iel , itl )) and point ( LATAVG
LREN
( it ), LONAVG
LREN
( it )).
Step 2: Sort the distance D
L
 iel , itl

in increasing order, and save the leading N pairs of indices of
  
,
  

with

Step 3: For an arbitrary member ie

1, 2, ...
N . ie , calculate the distance D
H

 ieh , ith

between points

( LAT
HREN

( ieh , ith ), LON

HREN
( ieh , ith ))

( LAT
LREN
( iel ( ie ), itl ( ie )), LON
LREN
( iel ( ie ), itl ( ie ))).

Step 4: Sort the distance D
H
and point
 ieh , ith

in increasing order, and save the leading
M pairs of indices of ( ieh ( im ), ith ( im )) with im

1, 2, ...
M , where im is the
 selected HREN storm position index and
 storm position realizations (set to 8).
Step 5:

Extract

M is the number of the selected HREN
 the LREN rainfall realization R
LSELECTED
  
R
LREN

( iel ( ie ), itl ( ie )), ip

for each selected LREN storm
13
14
15
16
17
18

19
20

21
22 position.

Step 6: Extract the HREN rainfall realizations R
HRESAMPLED
 im , ip


R
HREN
 ieh ( im ), ith ( im ), ip

with im

1, 2, ...
M for those associated HREN storm positions, and calculate the SM of R
HRESAMPLED
 im , ip

,
R

HRESAMPLED
 
, with im

1, 2, ...
M .

Step 7: Weight R
LSELECTED
 
and R
HRESAMPLED
 

to get a new rainfall pattern:
R
Pattern
  

W
L
* R
LSELECTED
  
W
H
* R
HRESAMPLED
 
, where W
L
and W
H
are the
  weighting factors of the low- and high- resolution rainfall patterns, respectively.
 
Step 8: Perform probability matching using the rainfall pattern in R
Pattern
 
and the rainfall frequency distribution in R
HRESAMPLED
 im , ip

. During the matching

13


1 process, remove values exceeding a certain percentile from R
HRESAMPLED
 im , ip

. This
2
3
4 is done to correct the topographically locked rainfall overprediction, which is known
 to exist at the southern tip of the CMR in this study. Thus, the probability-matched rainfall field R
NEW EN
 ie , it , ip

is constructed as an arbitrary member ie of the
5
6
7
8
NEWEN at a given time it .

In this paper, for the demo case Typhoon morakot,

W
L
and

W
H
are both set to be 0.5, and the bias-correction percentile is set to 99 for the after-landfall stage (i.e.,
  from 1200 UTC 8 to 0000 UTC 9 August 2009) and 97.5 for the other stages. Note
9 that the practical determination of these tunable parameters should be based on
10 reforecast of historical events.
11
12 h.
Some variants of the NEWEN
The NEWEN constructed by the above-described modified probability-matching
13 technique with the set parameters is hereafter denoted as NEWEN1, and for
14 comparison, four other variants are constructed: 1) NEWEN2, same as NEWEN1, but
15 without any pattern adjustment by the LREN, that is, W
L
and W
H
are set to 0.0 and
16
17
1.0, respectively; 2) NEWEN3, same as NEWEN1, but without bias-correction, that is,
  the bias-correction percentile is set to 100; 3) NEWEN4, same as NEWEN1, but with
18 neither weighting nor bias-correction; and 4) NEWEN5, same as NEWEN1, except
19 that it is constructed without probability-matching, that is, with rainfall members
20 constructed simply by the SM of the resampled HREN rainfall realizations in Step 6.
21
Table 1 summaries the experiment design of various NEWEN variants.
22
14

1
2
5. The performance of the probabilistic rainfall forecast a.
Definition of the ranked probability score
3
The ranked probability score (RPS; Epstein 1969; Murphy 1969; Murphy 1971;
4
Muller et al. 2005 ) is a score used to assess multi-category probability forecasts. In
5 this paper, the RPS is used to examine the probabilistic rainfall forecast performance
6 of the NEWEN variants. The RPS at the point ip and the time it with
7

8
9 it

1, 2, ...
T and ip

1, 2, ...
P is defined as
 


1
K

1 k
K 

1

FCDF k

 

OCDF k


2
, (1) where K is the number of rainfall categories, and FCDF k
and OCDF k
are the forecast and observed cumulative distribution function at category k , respectively.
11

 
In this paper, the rainfall categories are stratified by a set of rainfall bins
12
 determined by a series of percentages of the maximum observed rainfall at the
13 verification time in the VA. The rainfall bins vary from 0 to 100% in increments of
14
5%.
15
The RPS measures the sum of squared differences in cumulative probability
16 space for a multi-category probability forecast and indicates how well the probability
17 forecast predicts the category that the observations fall into. The RPS penalizes
18 forecasts less (more) severely when their probabilities are close to (further from) the
19 actual outcome. The RPS ranges from 0 to 1, with a perfect score being 0.
20 b.
The 3-h rainfall RPS by the LREN, HREN and NEWEN1
21
Figure 5 shows the time evolution of the 3-h rainfall RPS averaged over the land
22 area in the HA and VA by the LREN, HREN, and NEWEN1 for Typhoon Morakot.
15

1
As shown in Fig. 5, in both the HA and VA, NEWEN1 has a much smaller RPS when
2 compared with both the LREN and HREN during almost the entire simulation period.
3
In particular, in the HA (see Fig. 5a), NEWEN1 gives superior performance after 54-h
4
(i.e., 0600 UTC 8 August) forecast when the model storms start to leave Taiwan (see
5
Fig. 4) and when the model storm positions show significant spread.
6
Figure 6 shows the spatial distribution of the RPS for the 3-h rainfall from 1800
7
UTC to 2100 UTC on 8 August. The probabilistic forecast of the heavy rainfall of the
8
LREN around Chiayi County is very poor, with the RPS exceeding 0.6. The HREN is
9 better than LREN, but still has a poor probabilistic forecast at this heavy rainfall area,
10 with RPS exceeding 0.4. On the contrary, the RPS of NEWEN1 is mostly less than
11
0.4, and the total areal coverage with a RPS greater than 0.2 is very limited.
12
These results indicate that the new synthetic rainfall ensemble NEWEN1,
13 constructed from the modified probability-matching technique introduced in this
14 paper, outperforms both the LREN and HREN in terms of probabilistic forecast.
15
16 c.
The 3-h rainfall RPS by the NEWEN variants
Figure 7 shows the time evolution of the 3-h rainfall RPS averaged over the land
17 area in the HA by five NEWEN variants. The comparison of these five NEWEN
18 variants can further assess the effectiveness of the three remedies (i.e., resampling,
19 pattern adjustment, and bias-correction) adopted in the modified probability-matching
20 technique.
21
As shown in Fig. 7, among the five variants, NEWEN4 obviously performs the
22 worst during almost the entire simulation period, especially around the forecast time
16

1 of 36-42 h (1200 UTC 7 August to 1800 UTC 7 August) when the simulated typhoons
2 start to migrate over the northern part of Taiwan (see Fig. 4). In this environment,
3 similar to the results of Fang et al. (2011), members of the HREN produce very
4 narrow heavy rainfall stripes along the windward side of the CMR and significantly
5 overpredict the rainfall amount at the south tip of the CMR (figures omitted). The
6 poor performance suggests that without special remedies, the traditional
7 probability-matching process will not only fail to recover realistic peak rainfall, but
8 also amplify the overprediction bias and further lengthen the narrow rainfall pattern
9 over southern Taiwan. This is especially noticeable on the resampled rainfall
10 realizations.
11
With bias-correction (pattern adjustment), the probability-matching performance
12 is significantly improved in NEWEN2 (NEWEN3) in contrast to NEWEN4. This
13 illustrates that both bias-correction and pattern adjustment are effective.
14
As expected, the best performance is observed in NEWEN1 (see the red solid
15 line in Fig. 7) when bias-correction and pattern adjustment are used together. This
16 suggests that there is synergy between these two remedies.
17
When compared against NEWEN5, which is constructed without
18 probability-matching, it is found that benefits can always be gained from the
19 probability-matching technique if at least one of the two remedies is used (NEWEN1,
20
NEWEN2, or NEWEN3). However, if none of the remedies is used (NEWEN4), the
21 probability-matching technique would perform worse than the simple ensemble mean
22 method (NEWEN5).
17

1
What is the relative importance of using the two remedies? As shown in Fig.7,
2 the bias-correction (used in NEWEN2) gains more than the pattern adjustment (used
3 in NEWEN3) from the model forecast time of 18 h to 24 h (i.e., from 1800 UTC 6 to
4
0000 UTC 7 August, denoted as Period A), and from 45 h to 54 h (i.e., from 2100
5
UTC 7 to 0600 UTC 8 August, denoted as Period C); while the latter performs better
6 from 27 h to 42 h (i.e., from 0300 to 1800 UTC 7 August, denoted as Period B), and
7 from 57 h to 69 h (i.e., from 0900 UTC to 2100 UTC 8 August, denoted as Period D).
8
It should be noted that when referring to the observed typhoon track in Fig. 2 and
9 the observed 3-h rainfall evolution in Fig. 3, the above-mentioned Periods A, B, C,
10 and D are, in fact, the periods when the observed front outer, front inner, rear inner,
11 and rear outer typhoon rainbands interact with the southern part of the CMR,
12 respectively.
13
During these four different periods, on one hand, it can be shown that the moving
14 typhoon would produce a very different rainfall pattern and intensity over Taiwan
15 through its interactions with the topography of the CMR; on the other hand, it may
16 also show that the numerical model would have very different specific rainfall
17 forecasts at different resolutions for different rainfall processes due to its intrinsic but
18 imperfect representations of the precipitation physics and the complicated
19 typhoon-topography-interaction processes. This is why the relative importance of the
20 bias-correction and pattern adjustment varies with time.
21
Figure 7 suggests that the bias-correction is, in general, more important during
22
Periods A and C when the HREN tends to produce a more serious local
18

1 overprediction bias as the typhoon front outer and rear inner rainbands interact with
2 the topography; while pattern adjustment is relatively more important during Periods
3
B and D when the HREN tends to produce a more significant narrow rainfall pattern
4 by the typhoon front inner and rear outer rainbands. Obviously, coupling the broader
5 and smoother distribution of rainfall in the LREN members with the narrow rainfall
6 pattern along the windward side of the CWR in the HREN should help reproduce the
7 real rainfall pattern prior to the application of probability-matching.
8
Figure 8 shows the spatial distribution of the RPS for the 3-h rainfall ending at
9
1500 UTC 7 August by the NEWEN variants. This period is within Period B, and the
10 rainfall over Taiwan is produced by the front inner rainbands of the typhoon. When
11 compared against NEWEN4, pattern adjustment in NEWEN3 helps to reduce the RPS
12 significantly in the broader area, except the limited area near southern Taiwan, where
13 the bias-correction in NEWEN2 is most effective in reducing overprediction. When
14 compared against NEWEN5, which simply utilizes the SM of the resampled
15 realizations (Step 6), NEWEN1 shows that the modified probability-matching
16 technique, with both remedies applied, is superior to the simple mean method for the
17 resampled realizations; while NEWEN4, on the contrary, shows that the traditional
18 probability-matching technique, with neither remedy used, is inferior to the simple
19 mean method for the resampled realizations.
20
Figure 9 shows the spatial distribution of the RPS for the 3-h rainfall ending at
21
0600 UTC 8 August by the NEWEN variants. This period is within Period C, and the
22 rainfall over Taiwan is produced by the rear inner rainbands of the typhoon. This case
19

1 is similar to the one shown in Fig. 8, except that the bias-correction in NEWEN2 is
2 more effective than the pattern adjustment in NEWEN3.
3
It should be noted that the same resampling technique is applied to all the
4
NEWEN variants, including NEWEN5. As shown in Figs. 5 and 7, after the model
5 simulation time of 60 h (i.e., 1200 UTC 8 August), all the NEWEN variants have
6 similar RPS and perform better than the HREN without resampling. This implies that
7 the superior performance is mostly attributed to the resampling process in the
8 modified probability-matching technique. Note that the track ensemble forecast of the
9
LREN and HREN in this period has excessively large spread (see Fig. 2) and even the
10
HPM generally under-predicts the heavy rainfall (see Fig. 3). Under this
11 circumstance, the resampling is an effective technique to extract reasonable
12 probabilistic rainfall forecast information.
13
In short, the new 3-h rainfall ensemble constructed with the modified
14 probability-matching technique introduced in this paper can significantly improve the
15 probabilistic rainfall forecast for such topography-enhanced typhoon heavy rainfall
16 over Taiwan as of Typhoon Morakot.
17
18
19
6. The QPF performance of the ensemble mean
In Section 5, we show that the modified probability-matching technique can
20 construct a new rainfall ensemble with superior probabilistic rainfall forecast than the
21 original dual resolution ensembles. It would be desirable to assess its benefit in the
22
QPF. In this section, we compare the QPF performance of the ensemble mean rainfall
20

1 derived from the LREN, HREN, and NEWEN1.
2 a.
The QPF performance of the ensemble mean 3-h rainfall forecast
3
Figure 10 shows the spatial distribution of the 3-h rainfall PM of NEWEN1
4
(denoted by NPM) in 3-h intervals from 0000 UTC 6 to 0000 UTC 9 August 2009
5 over Taiwan for Typhoon Morakot. Compared with the observed 3-h rainfall shown
6 in Fig.3, the NPM obviously produces much more reasonable rainfall distributions
7 and amounts than both the LPM and HPM. In particular, the rainfall under-prediction
8 is mitigated around the observed maximum rainfall area, Chiayi County (see the black
9 star in Figs. 3 and 10).
10
The equitable threat score (ETS) is often used to quantitatively evaluate the
11 rainfall forecast skill of a numerical model (e.g., Anthes et al. 1989; Accadia et al.
12
2005; Tuleya et al. 2007; Cheung et al. 2008) . Here we use the ETS to verify the QPF
13 performance of the ensemble mean rainfall derived from the LREN, HREN, and
14
NEWEN1. Note that based on our model outputs in 3-h intervals, for the 3-h
15 accumulated rainfall, the ensemble mean can be extracted in two forms: the SM and
16 the PM.
17
18
19
As shown in Accadia et al. (2005), the ETS is defined by
ETS
 a
 a r a
 b
 c
 a r
, a r

( a
 b )

( a
 c ) a
 b
 c
 d
, (2) where a , b , c , and d are the categories of hits, false alarms, misses, and
21
22 correct no-rain forecasts, respectively, for a certain threshold, and a r
is a correction
    factor of the model hits expected from a random forecast . The ETS ranges from

1/3
 to 1, with a perfect score being 1.

21

1
Figure 11 shows the time evolution of the ensemble mean 3-h rainfall ETS over
2 the land area in the VA derived from the SM and PM of the LREN, HREN, and
3
NEWEN1 (denoted by LSM, HSM, NSM, LPM, HPM, and NPM, respectively) for
4
Typhoon Morakot. The rainfall thresholds at different forecast times are shown in
5
Table 2. They are selected as different percentages of the maximum observed rainfall
6 values in the VA at different times.
7
It should be noted that although the SM and PM of both the LREN and HREN
8 are calculated on the regular latitude and longitude grids that have comparable
9 horizontal resolutions to the corresponding native model resolutions (36 km and 4 km,
10 respectively), they are interpolated onto the grid of the objectively analyzed rainfall
11
(with a horizontal resolution of about 2 km) for verification. This is done similarly for
12 the SM and PM of NEWEN1. Furthermore, the ETS is calculated only over the
13
Taiwan island in order to avoid the impact from the possible inaccurate rainfall
14 analysis outside the land area.
15
As shown in Fig. 11, the difference between the PM and SM varies in different
16 ensemble systems. In the LREN, the PM significantly outperforms the SM near the
17 rainfall centers, especially during a heavy rainfall period; in the HREN, the PM
18 generally outperforms the SM by improving the skill in heavy rainfall areas, as
19 expected; in the NEWEN1, the PM and SM generally have very similar performance,
20 which suggests that the resampling technique used in the modified
21 probability-matching technique for the construction of the NEWEN1 would reduce
22 the difference between the SM and PM. The large differences between the ETS of the
22

1
LPM and LSM demonstrate that in the circumstance that the 36-km low-resolution
2 model systematically under-predicts the heavy rainfall of Typhoon Morakot, great
3 benefit can be gained by the traditional probability-matching technique during the
4 rainfall post-process.
5
The comparison of the ETS evolution of the LPM (in Fig. 11d), HPM (in Fig.
6
11e), and NPM (in Fig. 11f) shows that the relative performance of the PM in
7 different ensemble systems varies with time. During the early simulation period (0-12
8 h), which is also the period with small rainfall amounts due to the relatively weak
9 simulated storms being located far away from Taiwan over the open sea, the LPM
10 perform the best. During the middle simulation period (15-57 h), which is also the
11 moderate rainfall period when the simulated storms develop, approach, make landfall,
12 and then leave Taiwan, the NPM and HPM have comparable performance, and they
13 both significantly outperform the LPM. During the final simulation period (60-72 h),
14 which is the period when Typhoon Morakot (2009) produced the heaviest observed
15 rainfall, and when the simulated ensemble storms with disperse positions have left
16 and moved far away from Taiwan, the NPM significantly outperforms both the LPM
17 and HPM.
18
The time evolution of the 3-h rainfall ETS of the LPM, HPM, and NPM, shown
19 in Figs. 11d, 11e, and 11f, is consistent with the time evolution of the 3-h rainfall RPS
20 of the LREN, HREN, and NEWEN1 shown in Fig. 5b. The consistent high ETS
21 values of the NPM and the low RPS values of NEWEN1 in the final simulation period
22
(66-72 h) further support the importance of the resampling process in the modified
23

1 probability-matching technique for the topography-enhanced typhoon heavy rainfall
2 that is usually underpredicted.
3
As shown in Fang et al. (2011), it is during this period that some members of the
4 high-resolution ensemble can produce topography-enhanced heavy rainfall by their
5 rear outer rainbands being embedded in the strong southwesterlies, while others do
6 not because of their unfavorable storm positions relative to the topography. In this
7 situation, the HSM will not only significantly underestimate the heavy rainfall
8 amount, but will also blur or smear the topographical features of rainfall spatial
9 distribution; such problem cannot be resolved by the typical probability-matching
10 method in the HPM. However, it can be effectively addressed by the modified
11 probability-matching technique introduced in this paper, mostly through the
12 resampling technique.
13
15 b. The QPF performance of the ensemble mean accumulated 24-h and 72-h
14 rainfall
To further demonstrate the benefit of the modified probability-matching
16 technique in the QPF of the accumulated rainfall with a longer period, the ensemble
17 mean accumulated 24-h and 72-h rainfall forecasts are verified. As a first step, it is
18 necessary to clarify the definition of the ensemble mean accumulated rainfall for
19 longer periods of accumulated rainfall, which is more complicated than the 3-h
20 accumulated rainfall that is the shortest period truncated by the model output
21 frequency.
22
Based on the 3-h accumulated rainfall ensemble time series of the LREN, HREN,
24

1 and NEWEN1, nine different kinds of ensemble mean accumulated 24-h or 72-h
2 rainfall can be defined as follows: 1) the LSM, SM of the accumulated 24-h or 72-h
3 rainfall of the LREN; 2) the HSM, SM of the accumulated 24-h or 72-h rainfall of the
4
HREN; 3) the NSM, SM of the accumulated 24-h or 72-h rainfall of the NEWEN1; 4)
5 the LPMa, sum of the 3-h rainfall LPM over time; 5) the HPMa, sum of the 3-h
6 rainfall HPM over time; 6) the NPMa, sum of the 3-h rainfall NPM over time; 7) the
7
LPMb, PM of the accumulated 24-h or 72-h rainfall members of the LREN; 8) the
8
HPMb, PM of the accumulated 24-h or 72-h rainfall members of the HREN; and 9)
9 the NPMb, PM of the accumulated 24-h or 72-h rainfall members of the NEWEN1.
10
Figure 12 shows the spatial distribution of the mean error (ME) of the simulated
11 ensemble mean accumulated 24-h and 72-h rainfall in the HA, derived by nine
12 different kinds of ensemble mean for Typhoon Morakot. As shown in Fig. 12, the
13
LSM, LPMa, and LPMb have a very large negative bias, especially at the
14 northwestern part of the HA (where the maximum observed rainfall was recorded);
15 the HSM also has considerable negative bias there; and the HPMa and HPMb have an
16 obviously positive bias at the south part of the HA (where the south tip of the CMR is
17 located). The NSM, NPMa, and NPMb significantly mitigate these biases.
18
Figure 13 shows the averaged ETS over the land area in the HA of the simulated
19 ensemble mean accumulated 24-h and 72-h rainfall derived by nine kinds of ensemble
20 mean for Typhoon Morakot. Figure 14 is the same as Fig. 13, except verified in the
21
VA.
22
Firstly, in both the HA and VA, the ensemble mean accumulated rainfall
25

1 forecasts of the NEWEN1 have a much larger ETS than those ensemble mean
2 accumulated rainfall forecasts of both the LREN and HREN, which demonstrates the
3 superior performance of the modified probability-matching technique.
4
Secondly, the differences among the three kinds of ensemble mean are different
5 for different ensemble systems. For NEWEN1, the three kinds of ensemble mean have
6 a very similar performance; however, for both the LREN and HREN, there are
7 significant discrepancies among them, especially for the 72-h accumulated rainfall as
8 well as for the final (D3) 24-h period. In all the three concerned ensemble systems,
9 the PM generally outperforms the SM, and the probability-matching works better on
10 shorter-time-scale (i.e., 3-h) accumulated rainfall ensemble than on the
11 longer-duration (i.e., 24-h and 72-h) accumulated rainfall ensemble.
12
Figure 15 compares the simulated ensemble mean accumulated 72-h rainfall
13 derived from the LPMa, HPMa, and NPMa against the observed rainfall for Typhoon
14
Morakot. The NPMa outperforms both the LPMa and HPMa in the following aspects:
15
1) it mitigates the negative bias at Chiayi County where a local maximum observed
16 rainfall was recorded; 2) it eliminates the erroneous excessive rainfall at the south tip
17 of the CMR in the high-resolution model; 3) it corrects the erroneous narrow heavy
18 rainfall distribution pattern over the southern part of Taiwan in the high-resolution
19 model; and 4) it reduces the positive bias over the northeast part of Taiwan. Note that
20 the 72-h HPMa has an incredible large value of 4885 mm. This is because the
21 traditional probability matching process used in the calculation of the 3-h HPM time
22 series (see Fig.3) exactly restores the maximum values within the entire ensemble
26

1 members, which add up to a very large value of the 72-h HPMa at the south tip of the
2
CMR. The maximum values of the 72-h HSM and HPMb are significantly smeared to
3
2592 mm and 3742 mm, respectively (figure omitted). However, compared with the
4 observation, these maximum values are all locked at the wrong location.
5
6
7
7. One more case study of Typhoon Jangmi (2008) a. Case overview of Typhoon Jangmi
8
Typhoon Jangmi (2008) is selected for one more case study to demonstrate the
9 robustness of the general idea suggested in this paper, and also to present the
10 flexibility and variety within the approach for different cases. From September 26 to
11
September 30, 2008, Typhoon Jangmi produced heavy rainfall over Taiwan, with the
12 maximum rainfall a little over 1000 mm. Although Typhoon Jangmi was much more
13 intense than Typhoon Morakt, partly due to its fast moving over Taiwan and quick
14 wakening after landfall, the maximum rainfall amount it produced over Taiwan is less
15 than half of that brought by Typhoon Morakot.
16 b. Ensemble forecast performance by the LREN and HREN for Typhoon Jangmi
17
The ensemble forecast experiments LREN and HREN for Typhoon Jangmi are
18
72-h forecasts from 1200 UTC 26 to 1200 UTC 29 September 2008.
19
Figure 16 shows the forecast track of Typhoon Jangmi by the LREN and HREN.
20
Note that due to the faster moving the Typhoon Jangmi, the 72-h forecast track covers
21 a larger plotting domain than that of Fig. 2. The LREN mean track captures the
22 observed track pretty well, however the HREN mean track has too slow moving
27

1 during the final 12 h simulation period. Large track spread booms in both the LREN
2 and HREN around and after landfall even the track spread over the open sea does not
3 grow too much.
4
Figure 17 shows the spatial distribution of the 3-h rainfall LPM, HPM and the
5 observed 3-h rainfall at 3-h intervals from 1200 UTC 26 to 1200 UTC 29 September
6
2009 over Taiwan. As compared with Fig. 2, similar smooth rainfall distribution issue
7 exits in the LPM for both Typhoon Jangmi and Typhoon Morakot; the HPM also has
8 similar local excessive rainfall problem for both cases, except that the main
9 overprediction bias for Typhoon Jangmi is at a broader northeastern mountain area,
10 rather than at the narrow south tip of the CMR. Further more, another difference
11 between the two typhoon cases is that in the final 9 h simulation period after landfall,
12 there is no heavy rainfall of Typhoon Jangmi.
13 c. The generation of the NEWEN1 for Typhoon Jangmi
14
For typhoon Jangmi, when constructing the new ensemble NEWEN1, W
L
and
15
16

17
W
H
are both set to be 0.5, the same as that for typhoon Morakot. The bias-correction
 percentile is set to 99 at the forecast early stage (before 0600 UTC 27 September) when the typhoon is still far away from Taiwan, 95 around the simulated landing
18 period (from 0300 UTC to 1500 UTC 28 September), and 97.5 for the other stages.
19
Thinking that Typhoon Jangmi has much less precipitation and the concentration of
20 the rainfall overprediction bias in the high-resolution model is not as serious as that
21 for Typhoon Morakot with extremely heavy rainfall (see Figs. 2 and 17), the bias
22 correction area should be more expanded for Typhoon Jangmi, therefore a little
28

1 smaller percentile parameter 95 is selected for Jangmi (2008) around the landing
2 period.
3
4 d. The performance of the probabilistic rainfall forecast for Typhoon Jangmi
Figure 18 shows the time evolution of the 3-h rainfall RPS averaged over the
5 land area in both the HA and VA by the LREN, HREN, and the five NEWEN variants
6 for Typhoon Jangmi. As shown in Figs. 18a and 18b, the NEWEN1 has much smaller
7
RPS than LREN and HREN from forecast time 45-63 h (i.e., from 0900 UTC 28 to
8
0300 UTC 29 September), which is just the period that the heaviest rainfall is
9 observed (referred to Fig. 17). However, it is also found in Figs. 18a and 18b that the
10
NEWEN1 has poor performance in the final 9 h simulation period. The reason for this
11 deficiency might be due to the sampling error resulted from the bias in the selected
12 high-resolution model realizations.
13
Figure 19 shows the scatter plots of the simulated storm positions of Typhoon
14
Jangmi at 3-h intervals by the ensemble members of the LREN and HREN. As an
15 example, the HREN realizations around the LREN average storm position at the final
16 simulation time (i.e., 1200 UTC 29 September 2008) are southwestward biased.
17
Nevertheless, the short-period deficiency for the small rainfall (referred to Fig. 17)
18 should have little impact on the general forecast performance of the NEWEN1, and
19 hopefully, increasing the ensemble size or the output frequency of the HREN in the
20 future should mitigate this deficiency.
21
Further more, as shown in Figs. 18c and 18d, if the new synthetic ensemble is
22 constructed from the resampled realizations using the PM (as shown in Table 1, this
29

1 refers to the NEWEN1-4), NEWEN4 and NEWEN2 generally have worse
2 performance than NEWEN1 and NEWEN3, which indicates the importance of the
3 pattern adjustment in the probability-matching process. This result is consistent with
4 that in Fig. 7b for Typhoon Morakot. The bias correction is also important to further
5 improve the new ensemble, but its relative importance varies with time, the
6 verification area as well as cases. Mostly, it is important especially for the extremely
7 heavy rainfall.
8
9 e. The QPF performance of the ensemble mean for Typhoon Jangmi
Figure 20 shows the averaged ETS over the land area in the HA of the simulated
10 ensemble mean accumulated 24-h and 72-h rainfall derived by nine kinds of ensemble
11 mean for Typhoon Jangmi. Figure 21 is the same as Fig. 20, except verified in the
12
VA. Note that the rainfall verification thresholds for Typhoon Jangmi are different
13 from those in Figs. 13 and 14 for Typhoon Morakot; they are adjusted to address the
14 much smaller rainfall of Typhoon Jangmi. It is found that in both the HA and VA, the
15 ensemble mean accumulated rainfall forecast derived from the new ensemble
16
NEWEN1 is superior to those derived from the original ensembles LREN and HREN.
17
As compared with Typhoon Morakot, there is much smaller discrepancy among
18 the three kinds of ensemble mean derived from the HREN for Typhoon Jangmi,
19 which implies smaller diversities within the high-resolution members for the smaller
20 rainfall amount of Typhoon Jangmi. However, there are still significant discrepancies
21 among the different kinds of ensemble mean derived from the LREN. Generally, the
22
PM outperforms the SM, only not as significant as for Typhoon Morakot.
30

1
Figure 22 compares the simulated ensemble mean accumulated 72-h rainfall
2 derived from the LPMa, HPMa, and NPMa against the observed rainfall for Typhoon
3
Jangmi. Note that we still retain the same color bar as in Fig. 15, just to show the
4 large differences between the rainfall values of the two cases. We also see that the
5 modified probability-matching technique helps to mitigate or eliminate the rainfall
6 biases in both the low- and high-resolution ensembles for Typhoon Jamgmi.
7
In a word, the above results for Typhoon Jangmi further confirm the
8 effectiveness of our suggested new approach for the topography-enhanced heavy
9 rainfall.
10
11
8. Conclusions and discussions
12
In this paper a modified probability-matching technique is introduced to improve
13 the ensemble-based quantitative precipitation forecast of the topography-enhanced
14 typhoon heavy rainfall over Taiwan. The basic idea is to construct a new synthetic
15 rainfall ensemble with the modified probability-matching technique to extract the
16 improved rainfall information from the dual low- and high-resolution ensembles that
17 have different systematic model biases for the topography-enhanced typhoon heavy
18 rainfall. The main features of the modified probability-matching technique include: (i)
19 resampling of the rainfall ensemble, (ii) rainfall pattern adjustment, and (iii)
20 bias-correction. Verification of the performances of the ensemble probabilistic rainfall
21 forecast and the ensemble mean rainfall forecast for a demo case Typhoon Morakot
22
(2009) with extremely heavy rainfall and another case Typhoon Jangmi (2008) with
31

19
20
21
22
13
14
15
16
17
18
3
4
1 moderately heavy rainfall led to the following conclusions:
2
1) Based on the affordable ensemble simulations from a large-size (32 members), low-resolution (36 km) ensemble and a small-size (8 members), high-resolution
(4 km) ensemble, valuable rainfall forecast information can be effectively
5
6
7
8
9 extracted from a new synthetic rainfall ensemble constructed with the modified probability-matching technique. The probabilistic rainfall forecast of the new ensemble outperforms both the low- and high-resolution ensembles, and the ensemble mean accumulated rainfall derived from the new ensemble is shown to mitigate or eliminate the intrinsic model rainfall bias in both the low- and
10 high-resolution ensembles, and therefore provide improved QPF guidance for the
11 topography-enhanced typhoon heavy rainfall.
12
2) The resampling process is an important step of this modified probability-matching technique. It can discard the outliers faraway from the mean track, reduce the smearing effect from storms with very different locations, and increase the similarity of the resampled realizations, and thus extract more realistic and representative rainfall pattern and values based on the reliable mean track forecast.
Of course, the effect of the resampling process should be sensitive to the error of the mean track forecast of the low-resolution ensemble that is used to anchor the searching and the bias in the selected high-resolution rainfall realizations. For the extremely heavy rainfall of Typhoon Morakot, the resampling process is very effective in extracting reasonable probabilistic rainfall forecast and ensemble mean forecast information that could be significantly
32

15
16
17
18
11
12
13
14
19
20
21
22
3
4
1
2 underpredicted even by the high-resolution realizations, particularly when the ensemble storm positions spread significantly (as often occurs after landfall). For typhoon Jangmi, the performance deterioration of the new ensemble is observed in a short period of the final 9 h simulation time. This problem might be
5
6
7 attributed to the overprdiction bias of the selected high-resolution realizations for the small rainfall of typhoon Jangmi in this period. Hopefully, increasing the ensemble size or the output frequency of the HREN in the future should mitigate
8
10 this sampling error.
9
3) Both high- and low-resolution ensembles are essential to this modified probability-matching technique. Mostly due to uncertainties in the model’s precipitation and boundary layer physical parameterizations in complex terrain, high- and low-resolution simulations tend to produce different systematic rainfall biases. By merging the broader and smoother rainfall distribution from a low-resolution ensemble with the rainfall pattern containing detailed features and structures from a high-resolution ensemble, a more realistic rainfall pattern emerges, which is important for the probability-matching process to work properly. On one hand, since the low-resolution and high-resolution ensembles share the same large-scale environment, the averaging can safely retain the large-scale rainfall variations. On the other hand, although the high-resolution ensembles can resolve more small-scale rainfall variations, some of such small scales could be contracted or shrunk locally by some special topography. These might be the physical rationales why the averaging has been helpful to extract
33

19
20
21
22
13
14
15
16
17
18
10
11
12
8
9
3
4
1 more reasonable rainfall pattern.
2
4) The bias correction is also important to further improve the new ensemble constructed by the modified probability-matching technique, but its relative importance varies with time, the verification area as well as cases. Mostly, it is
5 important especially for the extremely heavy rainfall.
6
5) In general, the probability-matching ensemble mean performs much better than the
7 simple ensemble mean (e.g., Ebert 2001) where averaging to produce the ensemble mean causes a large bias in rain area and a corresponding reduction in mean and maximum rain intensity; while using probability matching to reassign the ensemble mean rain rates using the rain frequency distribution produces improved results. For our demo case Typhoon Morakot with extremely heavy rainfall, it is true for both low-resolution and high-resolution model runs; for another case Typhoon Jangmi with moderate heavy rainfall, it is true for the low-resolution run. It should be noted that the application of the typical probability-matching technique may not perform well given the poor representation of rainfall pattern or rainfall distribution frequency in an ensemble. For example, for the high-resolution model runs the typical probability technique, via sharpening the area with systematic topography-locked positive bias, just ruins the forecast skill at those local areas. In addition, we found that, for our demo case Typhoon Morakot, the probability-matched ensemble mean accumulated rainfall derived with the probability-matching technique applied on a shorter-time-period (i.e., 3-h) accumulated rainfall ensemble performs better
34

1
2 than that derived with the probability-matching technique applied on a longer-duration (i.e., 24-h and 72-h) accumulated rainfall ensemble.
3
4
The demonstrated positive results from the modified probability-matching
5 technique are encouraging. This modified technique should be an effective approach
6 for the practical ensemble forecast of the topography-enhanced typhoon heavy rainfall
7 over Taiwan . Obviously, the skill of typhoon rainfall forecast is highly dependent on
8 the accuracy of track forecast. In fact, the performance of the derived ensemble mean
9 rainfall forecast by the modified probability-matching technique is strongly tied to the
10 ensemble mean track forecast. There are still tunable parameters in the proposed
11 modified probability-matching technique. We have demonstrated the application of
12 this technique for two different cases, but these parameters are by no means optimal
13 for general application of all landfall typhoons over Taiwan. For example, the
14 weighting factors of the low- and high- resolution rainfall patterns ( W
L
and W
H
)
15
16 need to be optimized, and the bias-correction percentile parameter should be adjusted
  based on statistics of the high-resolution ensemble simulation of many more storms,
17 as well as the simulated ensemble mean track and track spread. In addition, larger
18 ensemble size and higher frequency model rainfall outputs, i.e., a 1-h rainfall, could
19 potentially provide further improvement (the latter without requiring much more
20 computing resources). For hazard mitigation, quantitative precipitation forecast is
21 needed at both high temporal and high spatial resolution. The modified
22 probability-matching scheme can be further improved to meet the operational need.
23
35

1
Acknowledgement
2
This material is based upon work supported by the National Science Foundation
3 under CAS No. AGS-1033112. We thank Dr. Jing-Shan Hong at the Central Weather
4
Bureau (CWB) in Taiwan and Dr. Ling-Feng Hsiao at the Taiwan Typhoon and Flood
5
Research Institute (TTFRI) for fruitful discussions, and Dr. Der-Song Chen at TTFRI
6 for providing the rainfall observation data. We are also grateful to the three reviewers
7 for their constructive comments and suggestions that largely improve this paper.
8
9
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39

1
2
Table 1 . The experiment design of various NEWEN variants
Ensemble name
Feature
Resampling Pattern adjustment Bias-correction PM/SM
NEWEN1
NEWEN2
Yes
Yes
Yes
No
Yes
Yes
PM
PM
NEWEN3
NEWEN4
NEWEN5
Yes
Yes
Yes
Yes
No
N/A
No
No
N/A
PM
PM
SM
3
4
Table 2 . Thresholds of the 3-h rainfall (unit: mm) used in Fig. 10.
Percentage (%)
Forecast time (h)
45
48
51
54
57
30
33
36
39
42
60
63
66
69
72
15
18
21
24
27
3
6
9
12
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90
0.6 1.3 1.9 2.5 3.1 3.8 4.4 5.0 5.6 6.3 6.9 7.5 8.1 8.8 9.4 10.0 10.6 11.3
1.6 3.3 4.9 6.5 8.1 9.8 11.4 13.0 14.6 16.3 17.9 19.5 21.1 22.8 24.4 26.0 27.6 29.3
4.5 8.9 13.4 17.9 22.3 26.8 31.3 35.8 40.2 44.7 49.2 53.6 58.1 62.6 67.0 71.5 76.0 80.4
6.0 11.9 17.9 23.9 29.9 35.8 41.8 47.8 53.8 59.7 65.7 71.7 77.7 83.6 89.6 95.6 101.5 107.5
7.5 14.9 22.4 29.8 37.3 44.7 52.2 59.6 67.1 74.5 82.0 89.4 96.9 104.3 111.8 119.2 126.7 134.1
5.0 10.0 15.0 20.0 24.9 29.9 34.9 39.9 44.9 49.9 54.9 59.9 64.9 69.9 74.8 79.8 84.8 89.8
5.6 11.3 16.9 22.6 28.2 33.8 39.5 45.1 50.8 56.4 62.0 67.7 73.3 79.0 84.6 90.2 95.9 101.5
5.3 10.6 15.8 21.1 26.4 31.7 36.9 42.2 47.5 52.8 58.0 63.3 68.6 73.9 79.1 84.4 89.7 95.0
6.1 12.1 18.2 24.3 30.3 36.4 42.5 48.5 54.6 60.7 66.7 72.8 78.9 85.0 91.0 97.1 103.2 109.2
6.3 12.6 19.0 25.3 31.6 37.9 44.3 50.6 56.9 63.2 69.6 75.9 82.2 88.5 94.9 101.2 107.5 113.8
6.2 12.5 18.7 24.9 31.2 37.4 43.6 49.9 56.1 62.3 68.6 74.8 81.1 87.3 93.5 99.8 106.0 112.2
5.7 11.3 17.0 22.7 28.4 34.0 39.7 45.4 51.0 56.7 62.4 68.1 73.7 79.4 85.1 90.7 96.4 102.1
6.9 13.7 20.6 27.5 34.4 41.2 48.1 55.0 61.9 68.7 75.6 82.5 89.3 96.2 103.1 110.0 116.8 123.7
7.3 14.6 21.9 29.1 36.4 43.7 51.0 58.3 65.6 72.9 80.1 87.4 94.7 102.0 109.3 116.6 123.9 131.1
8.9 17.7 26.6 35.5 44.3 53.2 62.1 70.9 79.8 88.7 97.5 106.4 115.3 124.1 133.0 141.9 150.7 159.6
12.7 25.5 38.2 50.9 63.6 76.4 89.1 101.8 114.5 127.3 140.0 152.7 165.4 178.2 190.9 203.6 216.3 229.1
13.0 26.0 39.1 52.1 65.1 78.1 91.2 104.2 117.2 130.2 143.3 156.3 169.3 182.3 195.4 208.4 221.4 234.4
9.5 19.0 28.5 37.9 47.4 56.9 66.4 75.9 85.4 94.8 104.3 113.8 123.3 132.8 142.3 151.8 161.2 170.7
11.6 23.2 34.8 46.5 58.1 69.7 81.3 92.9 104.5 116.2 127.8 139.4 151.0 162.6 174.2 185.8 197.5 209.1
12.1 24.2 36.3 48.3 60.4 72.5 84.6 96.7 108.8 120.9 132.9 145.0 157.1 169.2 181.3 193.4 205.4 217.5
13.8 27.6 41.4 55.2 69.1 82.9 96.7 110.5 124.3 138.1 151.9 165.7 179.5 193.4 207.2 221.0 234.8 248.6
14.2 28.4 42.7 56.9 71.1 85.3 99.5 113.8 128.0 142.2 156.4 170.7 184.9 199.1 213.3 227.5 241.8 256.0
10.6 21.3 31.9 42.6 53.2 63.8 74.5 85.1 95.7 106.4 117.0 127.7 138.3 148.9 159.6 170.2 180.8 191.5
8.6 17.1 25.7 34.2 42.8 51.4 59.9 68.5 77.0 85.6 94.2 102.7 111.3 119.8 128.4 137.0 145.5 154.1
40

1
2
Figure captions:
6
7
3
Fig. 1.
The triple-nested model domain configuration. The zoomed area on the right
4
5 side shows the Taiwan geophysical height (color shaded, unit: m) resolved in the 4-km high-resolution innermost domain. The black box and white box in this zoomed area show the main verification area (VA) and the heavy-hit area
(HA), respectively.
14
15
16
10
11
12
13
8
Fig. 2.
The simulated track of individual ensemble members (green lines), and the
9 average track of the ensembles (red lines) of the LREN (left panel) and HREN
(right panel) for Typhoon Morakot (2009). The Japan Meteorological Agency
(JMA) best track (modified by analysis from the Central Weather Bureau in
Taiwan) is superimposed and represented as the thick black line (OBS) in each panel. The track is plotted from 0000 UTC 6 to 0000 UTC 9 August 2009, and the storm positions are shown as red circles at 0000 UTC 6 and 0000 UTC 8, blue circles at 1200 UTC 6 and 1200 UTC 8, black crosses at 0000UTC 7, cyan crosses at 1200 UTC 7, and black dots at 0000 UTC 9.
17
Fig. 3.
Spatial distribution of the 3-h rainfall LPM (left panel), HPM (middle panel)
18
19
20 and observations (right panel) (unit: mm, color shaded in levels as indicated in the color bar) for Typhoon Morakot in 3-h intervals from 0000 UTC 6 to 0000
UTC 9 August 2009 over Taiwan, labeled with LPM, HPM, and OBS,
41

1
2 respectively, and time stamped. The black star marks the location of Chiayi
County, where the maximum gauge rainfall was produced.
10
11
12
13
8
9
3
Fig. 4.
Scatter plots of the simulated storm positions of Typhoon Morakot in 3-h
4
5
6
7 intervals during the whole simulation period by the LREN and HREN, denoted by L_mem (H_mem) and marked by small red (blue) dots. The small black circles are the LREN simulated average storm positions (denoted by
L_avg). The red circles are the selected subset of the LREN storm positions
(denoted by L_selt) nearest to the LREN average storm position at an example time (here it is 1800 UTC 8 August 2009, denoted by T_exp and marked by the large black circle). The blue circles are the selected subset of the HREN storm positions (denoted by H_selt) nearest to the example member of the selected LREN storm positions (here it is member 6, denoted my M_exp and marked by the red cross).
14
Fig. 5.
Time evolution of the 3-h rainfall RPS averaged over the land area (a) in the
15
16
HA and (b) in the VA by the LREN, HREN, and NEWEN1 for Typhoon
Morakot.
17
Fig. 6.
Spatial distribution of the RPS for the 3-h rainfall ending at 2100 UTC 8
18
August 2009 for Typhoon Morakot by: (a) LREN; (b) HREN; (c) NEWEN1.
19
The black box shows the area of the HA.
20
Fig. 7.
Same as Fig. 5, except for the five NEWEN variants.
42

1
Fig. 8.
Spatial distribution of the RPS for the 3-h rainfall ending at 1500 UTC 7
2
August 2009 for Typhoon Morakot by the NEWEN variants: (a) NEWEN1;
3
(b) NEWEN2; (c) NEWEN3; (d) NEWEN4; and (e) NEWEN5.
4
Fig. 9.
Same as Fig. 8, except for 3-h rainfall ending at 0600 UTC 8 August 2009.
5
Fig. 10.
Spatial distribution of the 3-h rainfall NPM (unit: mm, color shaded in levels
6
7
8 as indicated in the color bar of Fig. 3) in 3-h intervals from 0000 UTC 6 to
0000 UTC 9 August 2009 over Taiwan for Typhoon Morakot, labeled with
NPM and time stamped.
9
Fig. 11.
Time evolution of the ensemble mean 3-h rainfall ETS over the land area in
10
11
12 the VA for Typhoon Morakot derived from: (a) LSM; (b) HSM; (c) NSM; (d)
LPM; (e) HPM; and (f) NPM with different percentages of the maximum observed rainfall in the VA as verification thresholds.
13
Fig. 12.
The spatial distribution of the mean error (ME) of the simulated ensemble
14
15
16
17 mean accumulated 24-h and 72-h rainfall in the HA (unit: mm, color shaded in levels as indicated in the color bar) derived from nine different kinds of ensemble mean for Typhoon Morakot (2009): row one labeled “D1” from
18
19
0000 UTC 6 to 0000 UTC 7 August; row two labeled “D2” from 0000 UTC 7 to 0000 UTC 8 August; row three labeled “D3” from 0000 UTC 8 to 0000
UTC 9 August; row four labeled “3Ds” from 0000 UTC 6 to 0000 UTC 9
20
August.
43

3
4
1
Fig. 13.
Averaged ETS over the land area in the HA of the simulated ensemble mean
2 accumulated 24-h and 72-h rainfall derived by nine different kinds of
5 ensemble mean for Typhoon Morakot (2009): (a) from 0000 UTC 6 to 0000
UTC 7 August; (b) from 0000 UTC 7 to 0000 UTC 8 August; (c) from 0000
UTC 8 to 0000 UTC 9 August; (d) from 0000 UTC 6 to 0000 UTC 9 August.
6
Fig. 14.
Same as Fig. 13, but in the VA.
9
10
7
Fig. 15.
The accumulated 72-h rainfall ending at 0000 UTC 9 August 2009 (unit: mm,
8 color shaded in levels as indicated in the color bar) as the simulated ensemble mean derived by (a) LPMa, (b) HPMa, and (c) NPMa, and (d) as observed for
Typhoon Morakot.
11
Fig. 16.
Same as Fig.2, but for Typhoon Jangmi (2008). The track is plotted from
12
13
1200 UTC 26 to 1200 UTC 29 September 2008, and the storm positions are shown as red circles at 1200 UTC 26 and 1200 UTC 28, blue circles at 0000
14
15
UTC 27 and 0000 UTC 29, black crosses at 1200 UTC 27, cyan crosses at
0000 UTC 28, and black dots at 1200 UTC 29.
16
Fig. 17.
Same as Fig.3, but for Typhoon Jangmi in 3-h intervals from 1200 UTC 26 to
17
1200 UTC 29 September 2008.
18
Fig. 18.
Time evolution of the 3-h rainfall RPS for Typhoon Jangmi: (a) averaged
19 over the land area in the HA by the LREN, HREN, and NEWEN1; (b)
20 averaged over the land area in the HA by the five NEWEN variants; (c)
44

1
2 averaged over the land area in the VA by the LREN, HREN, and NEWEN1;
(d) averaged over the land area in the VA by the five NEWEN variants.
8
9
3
Fig. 19.
Same as Fig.4, but for Typhoon Jangmi. The red circles are the selected
4
5
6
7 subset of the LREN storm positions (denoted by L_selt) nearest to the LREN average storm position at an example time (here it is 1200 UTC 29 September
2008, denoted by T_exp and marked by the large black circle). The blue circles are the selected subset of the HREN storm positions (denoted by
H_selt) nearest to the example member of the selected LREN storm positions
(here it is member 1, denoted my M_exp and marked by the red cross).
10
Fig. 20.
Same as Fig. 13, but for Typhoon Jangmi (2008): (a) from 1200 UTC 26 to
11
12
13
1200 UTC 27 September; (b) from 1200 UTC 27 to 1200 UTC 28 September;
(c) from 1200 UTC 28 to 1200 UTC 29 September; (d) from 1200 UTC 26 to
1200 UTC 29 September.
14
Fig. 21.
Same as Fig. 20, but in the VA.
15
Fig. 22.
Same as Fig.15, but the accumulated 72-h rainfall ending at 1200 UTC 29
16
September 2008 for Typhoon Jangmi.
45