An Application of the Multi Physics Ensemble Kalman Filter to Typhoon Forecast

An Application of the Multi-Physics Ensemble Kalman Filter to Typhoon ForecastCHANH KIEU,1,3PHAMTHIMINH,2and HOANGTHIMAI2 Abstract—This study examines the roles of the multi-physics appr

An Application of the Multi-Physics Ensemble Kalman Filter to Typhoon Forecast

CHANH KIEU,1,3PHAMTHIMINH,2and HOANGTHIMAI2

Abstract—This study examines the roles of the multi-physics

approach in accounting for model errors for typhoon forecasts with

the local ensemble transform Kalman filter (LETKF) Experiments

with forecasts of Typhoon Conson (2010) using the weather

research and forecasting (WRF) model show that use of the WRF’s

multiple physical parameterization schemes to represent the model

uncertainties can help the LETKF provide better forecasts of

Typhoon Conson in terms of the forecast errors, the ensemble

spread, the root mean square errors, the cross-correlation between

mass and wind field as well as the coherent structure of the

ensemble spread along the storm center Sensitivity experiments

with the WRF model show that the optimum number of the

multi-physics ensemble is roughly equal to the number of combinations

of different physics schemes assigned in the multi-physics

ensemble Additional idealized experiments with the Lorenz

40-variable model to isolate the dual roles of the multi-physics

ensemble in correcting model errors and expanding the local

ensemble space show that the multi-physics approach appears to be

more essential in augmenting the local rank representation of the

LETKF algorithm rather than directly accounting for model errors

during the early cycles The results in this study suggest that the

multi-physics approach is a good option for short-range forecast

applications with full physics models in which the spinup of the

ensemble Kalman filter may take too long for the ensemble spread

to capture efficiently model errors and cross-correlations among

model variables.

Key words: LETKF, ensemble data assimilation,

multi-physics ensemble.

1 Introduction

Evaluating impacts of model internal

uncertain-ties in tropical cyclone (TC) forecasting models is a

challenging problem While there are many differentsources of errors related to observational errors,insufficient vortex initialization, or spurious correla-tions (see, e.g., DALEY,1993; ANDERSON,2007; BAEK

et al., 2006; LI et al., 2009), model deficienciesassociated with underrepresented physical processesare perhaps the main cause of the forecast errors in

TC models In particular, fast sub-grid processes such

as turbulence forcing or cloud microphysics arehighly variable under the TC extreme wind condi-tions that inadequate parameterizations of theseprocesses could impact considerably the TC track andintensity forecast skills Numerous studies haveshown that a simple change of microphysics scheme

or boundary parameterization could result in verydifferent forecasts even with the same initial condi-tion, especially for forecasts of high-impactmesoscale systems such as heavy rainfall or TCs(ZHU, 2005; VICH and ROMERO, 2010; BYUN et al.,

2007; LI and PU, 2009; IM et al., 2007; KIEU and

ZHANG,2010; PU,2011)

As a quick illustration, Fig 1 shows four 36-hforecasts of the accumulated rainfall over the Indo-china Peninsula, using the weather research andforecasting model (WRF-ARW, V3.2, SKAMARAOCK

et al., 2005) These forecasts are initialized with thesame boundary and initial condition valid at 1200UTC 13 July 2010 at which Typhoon (TY) Conson(2010) started to develop rapidly The initial andboundary conditions are taken from the NationalCenter for Environmental Prediction (NCEP) GlobalForecast System (GFS) forecast products All modelforecasts have similar model configurations except forfour different microphysics schemes including the Lin

et al., scheme, Kessler scheme, WSM 3-class simpleice scheme, and the WSM 5-class scheme One cannotice easily that both the magnitude and distribution

of accumulated precipitation differ substantially in the

1 Laboratory for Weather and Climate Forecasting, Hanoi

College of Science, Vietnam National University, Hanoi 10000,

Vietnam E-mail: chanhkq@vnu.edu.vn

2 Center for Environmental Fluid Dynamics, Hanoi College

of Science, Vietnam National University, Hanoi 10000, Vietnam.

3 I M Systems Group, NOAA/NWS/NCEP/EMC, Camp

Spring, MA 20746, USA.

 2013 Springer Basel

four forecasts (Fig.1), especially around and in the

eastern part of TY Conson where both the maximum

accumulation and the coverage of the rainfall vary

widely; for the Kesser and Lin et al., microphysics

scheme, the peaked rainfall exceeds 310 mm and is

confined mostly along-the-track of TY Conson while

the rest have distribution of rainfall extended farther

to the east of the Indochina Peninsular area

The diverse forecasts due to different physics schemes in the above simple exampledemonstrate one of many severe mesoscale weathersystems that are sensitive to forecasting models Asseen in Fig.1, the errors associated with such poorlyphysical representation could suppress any benefit ofobservational information assimilated into the model

micro-no matter how good the initial condition is This

Figure 1 Thirty six hours forecasts of the accumulated rainfall using the WRF model with the same initial and boundary condition but with different microphysics schemes including a Kessler microphysics scheme; b WSM 3-class simple ice scheme; c WSM 5-class scheme; and d Lin et al., microphysics scheme All simulations are configured with a single domain of 36-km resolution and initialized at 1200 UTC 12 July 2010 from

the GFS global input data and boundary updated every 6-h

poses some real challenge to any TC model in which

a single deterministic forecast could easily provide

bias track and intensity information Model errors are

thus essential and have to be considered properly in

any TC forecasting systems

The importance of model errors has been

recog-nized and examined extensively in previous studies

(e.g., ANDERSON and ANDERSON, 1999; HOUTEKAMER

et al.,2005; WHITAKERand HAMILL,2002; SZUNYOGH

et al.,2008; MENGand ZHANG,2007; LIet al.,2009;

Evensen,2009) For unbiased systems, ANDERSONand

ANDERSON(1999) proposed an approach in which the a

priori covariance matrix is enlarged every cycle by a

multiplicative factor k [ 1, the so-called

multiplica-tive covariance inflation technique This approach is

to some extent equivalent to an assumption that the

model error is proportional to the background

covariance by a factor of (k - 1), and, thus, bearing

all spatial structures of the priori covariance matrix In

another approach, MITCHELLand HOUTEKAMER(2000),

and HAMILLand WHITAKER(2005) suggested that one

can add a random distribution to the posteriori

anal-ysis perturbations such that the spread of the ensemble

and, consequently, the analysis covariance matrix are

augmented The additive and the multiplicative

inflation methods have been tested in various

assim-ilation systems and have proven to give encouraging

results (see, e.g., HOUTEKAMERet al.,2005; ANDERSON,

2007; WHITAKERand HAMILL,2002; SZUNYOGHet al.,

2008; HUNTet al.,2005; LIet al.,2009)

A somewhat different approach was introduced by

ZHANG et al (2004) in which modified analysis

per-turbations are computed by weighting the background

and newly-obtained analysis perturbations This

technique can be shown to be roughly equivalent to

degrading the quality of observations, i.e., to

increasing the observation errors, thus inflating the

posterior analysis To further enlarge the ensemble

spread, FUJITAet al (2007), MENGand ZHANG(2007),

KIEU et al (2012) proposed to employ multiple

physical parameterizations, which were demonstrated

to help improve the performance of the ensemble

Kalman filter (EnKF) for TC forecasts In addition to

the above approaches for the unbiased models, a

number of techniques that deal with the biased

models have been also developed (see, e.g., DEEand

KALNAY, 2008) A review of different model errorcorrection techniques in the presence of the modelbias can be found in LI et al (2009)

Because the early TC development and subsequentintensification are challenging problems due to thesensitivity of the storm track and the intensity for fore-casting models, the case of TY Conson (2010) is chosen

in this study to examine the relative importance of themultiple physics (MP) and the multiplicative inflation(MI) in correcting model errors in the EnKF algorithm.The MI approach is currently considered as an effectivetreatment of model errors in many practical applications

of the EnKF in regional models While there are severalother techniques such as additive inflation or variousadaptive versions of the localization that are shown to bevaluable (see, e.g., ANDERSON,2007; BISHOPand HODYSS,

2009; MIYOSHI,2011), thorough validation of all theseinflation techniques is challenging in the context of theregional models with the full primitive equations set-tings Therefore, this study is limited to examining theperformances of the MP and MI approach for the ease ofimplementation and comparison A variant version ofthe EnKF, the so-called Local Ensemble TransformKalman Filter (LETKF), is adopted and implemented inthe WRF-ARW model system for our investigation.Recent studies have demonstrated that the LETKF is apotential candidate for various real-time global andregional applications (HUNTet al.,2005; SZUNYOGHet al.,

2008; MIYOSHIand YAMANE,2007; MIYOSHIand KUNII,

2012) By far, the MI approach and its related adaptivealgorithms are the most common method in accountingfor model errors in the LETKF (HUNTet al.,2005; LI

et al.,2009; MIYOSHI,2011) Thus, it is of significance toexamine the importance of the MP method against the

MI method in forecasting TCs with the LETKFalgorithm

Because a single case study could be exposed torepresentativeness errors that make it hard to apply tomore general situations, a series of complementaryidealized experiments with the Lorenz 40-variable(LORENZand EMANUEL,1998) whose model errors areassumed to be represented by a random forcingfunction will also be conducted Note again that themain objective of this study is to examine howthe multi-physics ensemble can help the LETKFalgorithm improve the TC forecasts relative tothe multiplicative covariance inflation technique

Therefore, potential representativeness errors arisen

from a single case are expected to be of secondary

importance for such relative comparison

In the next section, a quick overview of the

LETKF will be presented Section 3describes model

experiments and data Results are discussed in Sect

4 In Sect 5, some sensitivity experiments with the

idealized Lorenz 40-variable model are presented to

provide some further information into the dual role of

the multi-physics in the EnKF algorithm Discussions

and conclusions are given in the final section

2 LETKF Algorithm

Recent studies with LETKF have demonstrated

that this ensemble scheme is capable of handling a

wide range of scales and observation types (see, e.g.,

HUNT et al., 2005; SZUNYOGH et al., 2008; LI et al.,

2009; KIEU et al., 2012) The main advantage of

LETKF is that it allows for the analysis to be

com-puted locally in the space spanned by the forecast

ensemble members at each model grid point, which

reduces the computational cost and facilitates the

parallel computation efficiently

The key idea of the LETKF algorithm is to use the

background ensemble matrix as a transformation

operator from the model space spanned by the grid

points within a selected local patch to the ensemble

space spanned by the ensemble members, and

per-form the analysis in this ensemble space at each grid

point For a quick summary of the LETKF algorithm,

assume that a background ensemble fxbðiÞ: i¼

1; 2 .; kg are given, where k is the number of

ensemble members (assuming that we are doing

analysis at one instant of time, so no time index is

written explicitly) Following HUNTet al (2005), an

ensemble mean xb and an ensemble perturbation

matrix Xbare defined respectively as:

b¼1k

Xk i¼1

xbðiÞ

Xb¼ fxbð1Þ xb; xbð2Þ xb; ; xbðkÞ xbg: ð1Þ

Let x¼ xbþ Xbw, where w is a local vector in the

ensemble space, the local cost function to be

mini-mized in the ensemble space is given by:

J_ðwÞ ¼ ðk  1ÞwTfI  ðXbÞT½XbðXbÞT1Xbgw



wais orthogonal to N such that the cost function J_ðwÞ

is minimized, the mean analysis state and its sponding analysis error covariance matrix in theensemble space can be found as:

a

in the ensemblespace have a simple connection of Pa ¼ XbP_

a

ðXbÞT,the analysis ensemble perturbation matrix Xa can bechosen as follows:

Xa¼ Xb½ðk  1ÞP_a1=2: ð5ÞThe analysis ensemble xais finally obtained as:

xaðiÞ¼ xbþ Xbf waþ ½ðk  1ÞP_

aðiÞ

1=2g: ð6ÞDetailed handling of more general nonlinear andsynchronous observations in LETKF can be found

in HUNT et al (2005) It should be mentioned thatthe above formation is only valid in the absence ofmodel errors To take into account the modelerrors, Hunt et al (2005) suggested that a multi-plicative factor should be introduced in Eq (4)(specifically, the first factor on the rhs of Eq.4).This simple use of the multiplicative inflationintroduces no additional costs to the scheme, andhas been shown to be efficient in many applications

of the LETKF (e.g., LI et al.,2009; MIYOSHI,2011;

MIYOSHI and KUNII, 2012)

3 Experiment Descriptions

3.1 Overview of Typhoon Conson (2010)

Conson (2010) was the first typhoon of the 2010

typhoon season in the WPAC basin It originated

from a tropical disturbance east of the Philippines

around July 9 2010 The system reached the tropical

depression stage on July 11 and intensified quickly

into a severe tropical storm around July 12 as it

moved westward over favorable environmental

con-ditions By July 13, Conson attained the typhoon

*130 km h-1 It weakened substantially after

mak-ing landfall over the Philippines archipelago but

re-strengthened when it entered the South China Sea As

it approached Vietnam coastal line, it managed to

reach the typhoon stage again with the maximum

wind of *110 km k-1 right before crossing Hainan

Island Despite its fairly straight westward track, it

was somewhat surprising to notice that most model

guidance, including the GFS forecasts, had strong

right bias This caused a lot of confusion to

Hydro-Meteorological Service continued issuing advisories

that Conson would bear northward until later July 15

when the consensus forecasts from several guidance

models started to converge toward a track that headed

to the North of Vietnam Such persistent right biases

of the track forecasts appeared to be related to the

underestimation of the large-scale steering flow

associated with the western Pacific subtropical ridge

from the GFS model, which provided the global

boundary conditions for most of the regional models

As such, all of the downstream model applications

that were driving the GFS would suffer from the same

biases, leading to inaccurate advisories of Conson’s

track and intensity change

The impacts of Typhoon Conson were detrimental

across several countries including the Philippines,

Vietnam, China, and Laos In the Philippines, Conson

produced very heavy rains that triggered flooding

over a widespread area Seventy-six people were

reported to be killed across the area and 72 others are

listed as missing Damage was also announced in

Vietnam where several people were killed and 17

others were listed as missing In China, at least two

people have been killed due to wind-related incidents.The total damage over all countries was estimated atmore than US $100 million Understanding thesource of the bias as well as effectiveness of differentdata assimilation methods in improving the trackforecast of Typhoon Conson is, therefore, of signif-icance for future better preparation and typhoonforecasting

a large number of ensemble experiments conducted,the WRF model is configured with a single domain

of 36 km horizontal resolution and initialized withthe NCEP/GFS operational analysis The modeldomain covers an area of 3,700 km 9 3,700 kmwith 31 vertical levels, and it is centered in theSouth China Sea, to the East of Vietnam (Fig.1).The forecasted period spans the lifetime of TYConson from its earlier depression stage at 1200UTC 12 July 2010 to its near dissipation at 1200UTC 15 July 2010 after making landfall overVietnam

To establish some general baseline about theperformance of different model error correctiontechniques, three experiments in which a fixednumber of 30 ensemble members are conducted Inthe first control experiment (NO), a specific set ofmodel physics in the WRF model including (a) theBetts–Miller–Janjic (BMJ) scheme cumulus parame-terization scheme (JANJIC, 2000); (b) the YonseiUniversity planetary boundary layer (PBL) parame-terization (HONG et al., 2006); (c) WRF Single-Moment 3-class (WSM3) microphysics scheme(HONG et al., 2004); and (d) the rapid radiativetransfer model (RRTM) scheme for both long-waveand short-wave radiations (MLAWERet al., 1997) areapplied for all ensemble members with no multipli-cative inflation at any analysis cycle This NOexperiment serves as a reference to evaluate theeffectiveness of the MI and MP approach

In the second experiment (MP), a spectrum of (1)

three microphysics schemes including the Kessler

scheme, the Lin et al., scheme, and the WSM3

scheme; (2) two PBL schemes including the YSU and

the Mellor–Yamada–Janjic (MYJ) scheme; (3) two

cumulus parameterizations schemes including the

Kain–Fritsch scheme, and the Betts–Miller–Janjic

scheme, and (4) two long-wave radiative schemes

including the RRTM and the Geophysical Fluid

Dynamics Laboratory (GFDL) longwave scheme are

used A total of 24 different combinations of these

physical options are formed and assigned to different

ensemble members in a sequence of permutations of

the above physical options.1 If the number of

ensemble members is larger than the number of the

combinations, the assignment will be repeated for the

next members There is no inflation invoked in the

MP experiment such that the increase of the ensemble

spread relative to the NO experiment can be

attrib-uted to the use of the multiple physics options

In the third experiment (MI), a multiplicative

inflation factor k = 1.8 is applied to the analysis

transformed covariance matrix P_

a

in Eq (4) Theinflation factor is kept constant for all cycles and the

same set of model physics as in the NO experiment is

used for all members such that the effectiveness of

the MI approach in correcting model errors can be

compared against that of the MP approach in a

transparent way The role of the MI approach is

examined further in a number of sensitivity

experi-ments in which the inflation factor varies from 1.0 to

6.5, which appears to be a typical range of the

inflation factor for the TC environment as shown in

MIYOSHI and KUNII (2012) These sensitivity

experi-ments are expected to provide some information

about the significance of the adaptive multiplicative

inflation in the LETKF Likewise, the effectiveness of

the MP approach can be investigated by varying the

number of ensemble members from 10 to 50 in

several additional sensitivity experiments See

Table1 for the list of experiments

Since there are no ensemble backgrounds for thefirst analysis cycle, cold-start background ensemblemembers are first initialized by adding a randomnoise with standard deviations of 3 m s-1 for wind,

3 K for temperature, and 3 9 10-3 kg kg-1 forspecific humidity into the GFS data 12-h earlier,i.e., at 0000 UTC 12 July The short 12-h forecasts ofthe cold-started members from 0000 UTC to 1200UTC 12 are then used as the initial background forthe first analysis cycle at 1200 UTC 12

3.3 Observation Data

To create observational data, a hypothetical truth

is formed by using the NCEP Final OperationalGlobal Analysis (FNL) dataset during the period thatencompasses the whole lifecycle of TY Conson(2010) Such FNL data represents roughly the truestate of the atmosphere and will be considered in thisstudy as a reference for later comparison After thetruth is obtained, bogused observations are generatedevery 6-h by assigning a random noise of a standarddeviation of 1 m s-1for the horizontal wind compo-nents, 1 K for temperature, and 10-3 kg kg-1for thespecific humidity to the truth at all of the grid pointsfrom surface up to level z = 13 km These bogusobservational data points are generated in the forms

of radiosonde columns in the LITTLE_R.2format; anydata levels that are below the terrain height will beeliminated As a step to orient the WRF-LETKFsystem to be consistent with the WRF assimilationsystem (WRFDA), all of the bogus observations areassigned observational errors that are based on theerror statistics imposed by the quality control com-ponent of the WRFDA system

Of the seven prognostic variables in the ARW model including the horizontal wind compo-nents, vertical velocity w, perturbation potentialtemperature, perturbation geopotential, surface pres-sure, and water vapor, then there are the variables thatare directly assimilated by the LETKF are the

WRF-1 In the WRF-ARW model, each physical parameterization

option has a designated number So, the 24 combinations of the

physical schemes are simply permutations of these options, which

are of the form (i, j, k, l) in which i [ [1, 2, 3] is for microphysical

scheme, j [ [2, 3] for the PBL schemes, k [ [1, 2] for the cumulus

schemes, and l [ [1, 2] for longwave radiation schemes.

2 LITTLE_R is a legacy data format that was developed earlier to ingest observational data for the MM5 model This format

is adopted in the WRF-ARW as part of continued support for different observational format inputs More information about the LITTLE_R format can be found at: http://www.mmm.ucar edu/mm5/mm5v3/little_rv3.html

horizontal (u and v) winds, the potential temperature,

and the relative humidity The other three prognostics

variables are updated every cycle via

cross-correla-tions with the observed variables The degree to

which such prognostic variables can update

observa-tional information depends essentially on how the

ensemble cross-correlations are represented, and can

be used to evaluate the effectiveness of different

model error correction methods To minimize the

impacts of the homogeneous covariance localization,

the observational network is designed in such a way

that observations are given at all model grid points

for all cycles This partly removes the need of a

spatially adaptive localization, albeit the scale of the

localization still needs to be tuned at the initial time

for the best performance For the LETKF, a local

volume of 11 9 11 grid points in horizontal direction

and vertical extension of 0.2 (in r-coordinate) is

fixed, and the localization scale is chosen to be

700 km and kept constant in time

3.4 Boundary Condition

To ensure that each member has its own lateral

boundary condition consistent with its updated

anal-ysis, the WRFDA boundary routine is used to

generate boundaries for each ensemble member after

the ensemble analysis step is finished for every cycle

Because the GFS forecasts are outputted every 6-h,

the lateral boundary conditions are updated at the

same temporal period The roles of the lateral

boundaries in regional models should be especially

highlighted as our various experiments with different

types of boundary conditions show that idealized

boundaries tend to be detrimental to the TY

devel-opment (not shown) E.g., use of the open boundaries

destroys the coherent structure and development of

TY Conson after just two or three cycles This isbecause the convective instabilities needed to fuel the

TY growth appear to be radiated away from thedomain As a result, the storm dissipates and theensemble collapses (i.e., ensemble spread approacheszero) and drifts away from the truth quickly, thusreducing the capability of the ensemble filter inassimilating new observation

4 Results

4.1 Control Experiments

As a preliminary illustration of the performance

of the MI and MP approach in the forecasts of TYConson, Fig.2 shows the track forecast errorsaveraged from 1200 UTC 12–1200 UTC 13 and thetime series of the storm intensity valid at 1200 UTC

12 Note that this 12-h period rather than the entireforecast period is selected for the averaging shown inFig.2 because the TC track and intensity forecastsrequire tracking the point-like storm centers forwhich a systematical track bias can be carried overthe next cycles if it is not corrected for every cycle.Unless a vortex initialization scheme is used to re-correct the vortex center (or the initial condition iscontinuously updated from the GFS analysis), thestorm center will deviate gradually away from thebest track, leading to artificial accumulated track andintensity errors for the later cycles Since we have nobogus vortex component implemented in this work,any analysis of track or intensity forecast errors islimited to the first several cycles during which thestorm centers are located at the similar position as thetruth location from the FNL dataset

Table 1 List of experiments with the WRF-LETKF configuration Experiment Description

NO A single set of model physics; no inflation; 30 ensemble members

MP Combination of 24 physics options; no inflation; 30 ensemble members

MI A single set of model physics as in the NO experiment; inflation factor k = 1.8; 30 ensemble members MP–MI A combination of 24 physics options; inflation factor k = 1.8; 30 ensemble members

MI-sensitivity A single set of model physics as in the NO experiment; inflation factor k varying from 1.0 to 6.5; 30 members MP-sensitivity A combination of 24 physics options; no inflation; ensemble members varying from 10 to 50

One first sees in Fig.2 that although the track

errors in the MI experiment do not show much

improvement with respect to the NO experiment, the

MP experiment exhibits a noticeably better track

forecast with the track errors reduced about 20 % at

36-h lead time and longer during the selected period.This is because the broad spectrum of the physicsschemes in the MP experiment helps generate a range

of storms with different intensity, which interactdifferently with the steering environment (Fig.2b, c)

Figure 2

a Comparison of the track forecast errors between experiments with no model error correction (dark gray), the multiplicative inflation factor

of 1.8 (medium gray), multiple physics (light gray) b time series of the minimum sea level pressure for the MP experiment, and c similar to

b but for the MI experiment valid at 1200 UTC 15 JUL 2010 All experiments have 30 ensemble members

Unlike the MI ensemble in which all members show a

similar intensity with very minimum spread for the

entire forecasted period, the MP ensemble possesses

a much larger intensity spread with half of the

members showing higher intensity while the other

half possessing much weaker intensity Such

bifur-cation of the intensity seen in the MP ensemble is

attributed to the fact that the members with the Kain–

Fritsch cumulus scheme tend to produce storms with

much stronger intensity than those with the BMJ

scheme This is not limited to the selected cycle but

in fact observed very consistently in all experiments

conducted thus far with our WRF-LETKF system

Because of their stronger intensity and more

well-defined circulation, members with the Kain–Fristch

cumulus scheme are subject to larger northward bias

under the strong influence of the subtropical ridge

over Mainland China In contrast, the ensemble

members with the BMJ cumulus scheme have weaker

intensity and do not seem to be influenced much by

this northward steering, leading to an overall larger

ensemble spread and thus smaller ensemble mean

track errors as shown in Fig.2 Of course, any

analysis of the storm intensity at the 36-km resolution

should be cautioned as this coarse resolution may not

capture reliably the magnitude of the maximum

surface wind at any stage However, the mesoscale

characteristics are often sufficiently represented in

the model for the storms to experience a different

response to the large-scale steering flow under

different parameterizations This explains the ent performance in the track and intensity errors seen

differ-in Fig 2.Because the point-like metrics based on the TYtrack and intensity errors are rather sensitive to themodel resolution and could be subject to representa-tiveness errors, Fig 3 compares further the totalerrors between the MP and MI experiment Here, thetotal errors are defined as the volume-averagedenergy root mean squared errors (EME) as follows:

2ðU0U0þ V0V0þCp

T T

0T0Þ1=2; ð7Þwhere U, V are the zonal and meridional wind com-ponents, respectively, T is the temperature (in K unit),the prime denotes the differences between the anal-ysis and the truth valid at the same time, Cp is theconstant pressure heat capacity, T = 273 K is thereference temperature, and the average is taken overthe entire model grid mesh

Consistent with the track errors, the MP hasoverall better performance during the entire forecastperiod with the average EME error *0.2 m s-1 ascompared to 1.2 and 0.8 m s-1 in the NO and MIexperiment, respectively In particular, the MP EMEerrors reduce *80 % after just three cycles andmaintain a steady small magnitude afterward.Except for the first cold-started cycle, the smallerEME errors in the MP experiment are observed for a

Figure 3 Comparison of the volume-averaged energy root mean squared errors (EME) with no model error correction (dark gray), a fixed multiplicative

inflation factor k = 1.8 (medium gray), and multiple physics (light gray)

regardless of the domain size or the model

resolu-tion (cf also Fig 9) The outperformance of the MP

method during the entire period, especially for the

few early cycles, can be understood if one notes that

convective- to meso-scale instabilities often develop

rapidly during the incipient phase of model

integra-tion (TOTH and KALNAY,1997) Such development of

the uncertainties related to the instabilities at the

convective scale depends sensitively on the different

parameterization schemes used by the model With a

diverse set of physics schemes, the MP ensemble

could generate a large spread quickly after 12 h into

integration, allowing for the model errors associated

with physical representations to be captured more

efficiently

To investigate the MP and MI ensemble spread

more explicitly, Figs.4 and 5 show a series of

horizontal distributions of the ensemble spreads,

which are defined as the standard deviation of the

wind speed with respect to the ensemble mean, in the

MI and MP experiment Despite its fairly organized

structure in both coverage and amplitude, the MI

spread is in general small even near the storm center

where uncertainties are supposed to be the most

significant at the convective scale Because of the

inflation, it is seen that the analysis increments still

manage to capture some of the new observational

information at each cycle Apparently, the inflation is

essential to allow for such analysis to be updated

despite the small ensemble spread As long as the

spread does not completely collapse, the inflated

covariance always enhances the analysis

perturba-tions such that new observational information is

updated over the area where the spread is significant

Similar analyses of the ensemble spread versus

analysis update for the NO experiment confirm that

without the inflation, the analysis increments are

indeed very small and virtually negligible over the

entire domain after three cycles (not shown)

Although the MI analysis increments exhibit some

update of new observational information for every

cycle, it should be noted that the percentage of the

analysis increments relative to these increments

diminishes quickly in time in the MI experiment

(Fig.4e–h) Indeed, examining the observational

increments, shows that these increments keep

grow-ing in time because the model state is driftgrow-ing away

from the truth This is anticipated as the MI analysisincrements could not assimilate fully new observa-tional information at each cycle due to the smallensemble spread even after inflated (Fig.4) As aresult, the difference between the analyzed and thetrue states is accumulated every cycle, leading to agrowing deviation of the model state from the trueatmosphere toward the end of the forecasted period.Unlike the MI spread, the MP spread shows muchmore signal with time in both horizontal and verticalcross sections (Figs 5, 6) Specifically, the MPspread is more organized and could maintain wellthe structure of the uncertainties along the track of thestorm Inspecting the regions of strong wind conver-

representative in the first five cycles during whichmodel uncertainties related to convective instabilitiesdevelop rapidly, leading to a consistent and coherentstructure of the spread The clustering of the MPspread along the convergent areas seen in Fig.5implies that new observations are most updatedwithin these large spread areas but minimally used

in other areas where the ensemble spread is otherwisesmall The characteristically large concentration ofthe MP spread along the convergent zones does notseem to depend on the number of ensemble members

as this is seen for all ranges of the number ofensemble members

The difference in the MP and MI spread is evenmore apparent in the vertical cross sections (Fig.6).While the MI spread is confined mostly at the middlelevels, we observe that the MP spread could capturemodel uncertainties related to the TC physics fromthe surface up to 200 hPa Comparison of the analysisincrements in the MI and MP experiment shows thatthe MI method tends to be slightly more efficient atthe upper levels where the magnitude of the MI and

MP ensemble spread is somewhat similar, but it isless efficient than the MP approach from the surface

to *300 hPa where the MI spread is not sufficienteven after inflated Note that the performance of the

MP approach is somewhat degraded toward the end

of the forecast because the saturation of the ensemblespread affects the effectiveness of the LETKF.Therefore, the LETKF is no longer capable ofupdating new observations efficiently and the EMEerrors start to grow afterward (Fig 3)

Figure 4 Plane views at 900 hPa of a–d the ensemble spread with the inflation factor of 1.8 (shaded, m s -1 ) and zonal wind analysis increments (contoured at interval of 0.5 m s -1 ); and e–h rms wind speed errors (shaded) and observed zonal wind increments (contoured at interval of 0.5 m s -1 ) valid at 0000 UTC 13, 1200 UTC 13, 1200 UTC 14, and 1200 UTC 15 Superimposed are storm-relative flows

Figure 5 Similar to Fig 4 but for the multi-physics approach with no inflation