A background error covariance(BEC)matrix isintrinsically important in determining the level of influenceeach observation has on the analysis and howthis influence is distributed both spatially and amongdifferent analysis variables in data assimilation(DA).Compared to the variational DA approaches(Lorenc, 1986; Parrish and Derber, 1992; Barker et al., 2004), which generally use the time-invariant and nearlyhomogeneousBEC, ensemble techniques capture the“errors of the day” that usually propagate in timeon multiple scales from short term ensemble forecasts(e.g., Torn and Hakim, 2009; Zhang et al., 2009;Hamill et al., 2011a). One such approach is the ensembleKalman filter(EnKF), which was first proposedby Evensen(1994) and has been widely tested in numericalweather prediction(NWP)model experimentsagainst real data(e.g., Dowell et al., 2004; Meng and Zhang, 2008; Whitaker et al., 2008; Zhang et al., 2009;Liu et al., 2012).

The hybrid ensemble/variational DA incorporatesthe ensemble-produced BEC within a variationalframework. Studies by Hamill and Snyder(2000), Lorenc(2003), and Wang et al.(2007, 2008)havedemonstrated that the hybrid system has some potential to yield the “the best of two worlds” by improvingthe deterministic forecasts, due to the inclusion of theflow-dependent BEC and the st and alone EnKF witha small ensemble size.

Recently, the hybrid system has been used tostudy tropical cyclones(TCs)in global(Hamill et al., 2011b) and regional(Wang, 2011, hereafter W11;Li et al., 2012; Schwartz et al., 2013)modeling systemsassimilating real observations. All of the abovestudies found that the hybrid system produced morestatistically significant TC tracks and intensity forecaststhan those from three-dimensional variational(3DVAR)analyses. Among these studies, W11 reportedthat static BEC, in particular, was poorer thanthe flow-dependent BEC in observation-sparse regions.Schwartz et al.(2013)found that the hybrid systemwith the flow-dependent BEC produced comparabletrack forecasts to those from 3DVAR analyses withmultiple outer loops.

Different from the above studies, which focusedon comparisons between the hybrid and the variationalsystems that assimilate mainly conventional observations, this study explores the effect of satellite radianceassimilation in a hybrid framework on typhoonforecasting. Many of the operational NWP centers assimilateradiance data with variational DA methods.Several studies have also explored the impact of assimilatingradiance data for typhoon forecasting withinEnKF frameworks(Liu et al., 2012; Schwartz et al., 2012).

The impacts of radiance data on weather forecastingare known to be significant, especially for areasover oceans with sparse conventional observations(Liu et al., 2012). However, the impact of the radiancedata in the hybrid data assimilation system isnot clear. The purpose of this study is to explore theimpact of radiance assimilation on analyses and subsequentforecasts using the Weather Research and Forecastingmodel DA/ensemble transform Kalman filter(WRFDA/ETKF)hybrid system.

In this study, we choose the ETKF(Bishop et al., 2001)to update the ensemble perturbations, since itis relatively computationally inexpensive to solve theKalman filter equations in ensemble space and theyproduce skillful ensembles(W11). This work makesuse of radiance data including both microwave and infrared radiance data in the initialization of the TCenvironment. This work also differs from W11 in improvingthe inflation and fraction formula in the ETKFalgorithm to stabilize the ETKF when estimating theinflation factors with limited ensemble size. Moreover, sensitivities to vertical correlation localization matricesare also assessed.

The remainder of this paper is organized as follows.In Section 2, we provide a brief introduction tothe WRFDA ETKF/3DVAR hybrid system and radianceassimilation methodology. An overview of typhooncases and the experimental settings are given inSection 3. The results are presented in Section 4. Summary and future perspectives are presented in Section5.

The ETKF/3DVAR hybrid system is a componentof the WRFDA system(Barker et al., 2012). Thehybrid analysis increment δx is defined as the sum oftwo terms,

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where the first term δx_static is the increment associatedwith the 3DVAR static background covariance and the second term δx_flow-dep is the increment associatedwith the flow-dependent covariance given by

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where N is the ensemble number, αk is the extendedcontrol variable as defined by Lorenc(2003), and x'k isthe kth ensemble perturbation state vector. The symbol“°” denotes the Schur product(element by elementproduct)of the vectors αk and x'k. The correspondingcost function with respect to δx and αk to obtain theincrement is

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where δx is given by Eqs.(1) and (2), a is a vectorformed by concatenating N vectors αk, and Ais a block diagonal matrix that controls the spatialcorrelation of a, effectively performing localization ofthe ensemble BEC. H and H are the nonlinear and linearized observation operators, and d = y − Hδxbis the innovation vector, where xb denotes the background and y is the observations. In the WRFDAhybrid system, both the horizontal and vertical localizationsin A are applied. We found that the resultswere similar when we set the horizontal localizationradius to 500, 750, and 1000 km for the experimentsin this study. The results in the following sections arebased on 750-km horizontal localization radius. Thevertical localization was implemented through transformingthe extended control variable with empiricalorthogonal functions(EOFs; Li et al., 2012; Wang et al., 2014). The default vertical correlation c betweentwo levels(l1 and l2)in released WRFDA is defined as

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where M is the total model level number. The localizationradius is proportional to the modellevel index, indicating that the localization radii forthe lower levels were much smaller than those of thehigher levels. For radiance observations, a more advancedcorrelation method is

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in which a distance r is directly chosen as the localizationradius to fully spread the observation informationover the whole model space, even for the lowlevels, where z(l) is the height of the model level l. Forradiance assimilation, we conducted sensitivity experimentson vertical localization using Eqs.(4) and (5)with 4- and 8-km localization radii, respectively. Theresults were not sensitive to the vertical localizationschemes(figure omitted). Thus, we determined an 8-km radius for the hybrid model to conduct furthercomparisons with 3DVAR in the following sections.

The weights of the static covariance and flowdependentcovariance were determined by factors β₁ and β₂, with the constraint+= 1. For the experimentsin this study, we set = 0.5. We weightedthe BEC 50% toward the ensemble contribution, althoughwe achieved similar results using 75% and 25%.

In this study, ETKF was used to update the ensemble, estimating forecast error from the covariancematrix of the ensemble forecast perturbations(Bishop et al., 2001). ETKF was described by Wang et al.(2007)as

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where the ETKF transforms the matrix of forecastperturbations X^b into a matrix of analysis perturbationsX^a, whose columns contain N analysis perturbationsx_k^e by a transformation matrix T with theinflation factor Π. T is chosen to ensure the outputensemble error covariance to precisely equal the trueanalysis error covariance. The solution of T is given by

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where C contains the eigenvectors and Γ the eigenvaluesof the N × N matrix is the identity matrix, and ρc is the fraction factoraccounting for the projection of the forecast error inensemble space. For an ensemble size N of 100 orless, the computational cost of Eq.(7)is relativelylow. An enhanced inflation and eigenvector dependentfraction factor scheme(Xu et al., 2013b)was employedto increase the ensemble covariance to ameliorate theunderestimation of the analysis-error variance. Thisscheme is given by

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where the component of the vector p =(ρ(1), ρ(2), · · ·, ρ(N))is the fraction factor for eacheigenvector of the ensemble covariance matrix. Equation(8)is a refined form of Eq.(7). The fraction factorscorrect the inflation in proportion to the forecasterror variance projected onto a particular kth eigenvector.The adaptive fraction algorithm here aimsto ameliorate the problem by distinguishing between large and small background forecast errors, explainedby the different ensemble eigenvectors, instead of usinga constant fraction factor to rescale all the eigenvalues.In this study, observations used in ETKF whencalculating the transformation matrix were the sameas those in the hybrid system, filtered by strict qualitycontrol, and only radiosonde measurements were usedin estimating the inflation factor.

The procedure for the cycling ETKF/3DVAR hybridsystem includes six stages as follows.

(1)Generating the initial ensemble(20 membersin this study)by adding the NCEP Global ForecastSystem(GFS)analysis and correlated r and om perturbationsfollowing Torn et al.(2006) and Wanget al.(2008), before re-centering the ensemble withthe GFS analysis;(2)obtaining short-term ensembleforecasts from the initial ensemble in step(1);(3)calculating the ensemble mean and perturbations;(4)updating the ensemble mean and perturbations withthe 3DVAR and ETKF, respectively;(5)obtainingan analysis ensemble by adding the updated ensemblemean and perturbations; and (6)updating the lateralboundary conditions and lower boundaries beforeconducting short-term ensemble forecasts to the nextassimilation time or run a deterministic forecast todiagnose outputs from the analysis ensemble mean, and repeat from step(3).

The community radiative transfer model(Han et al., 2006; Liu and Weng, 2006)was used as the observationoperator H in WRFDA for computing radiancesfrom the model profiles of temperature and moisture(Barker et al., 2012). A radiance observationwas rejected if the bias-corrected innovation(observationminus prior)exceeded either 15 K or 3σ0, whereσ0 is the specified observation error st and ard deviationfor brightness temperature. Radiance data overmixed surfaces(e.g., over coastal areas) and observationswith large scan angles(the first two pixels forAMSU-A radiances and the first four pixels for IASIradiances on the edge)were rejected. In these experiments, radiance data were used with a 90-km thinningmesh. Data within ±2 h of the analysis times were used and assumed to be valid at the analysis times.For the IASI infrared radiance data, the algorithm developedby McNally and Watts(2003)was used forcloud detection(Xu et al., 2013a).

The systematic errors for radiance observationswere corrected by modifying the observation operatorH as follows:

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where γ0 is the constant component of total bias, Ipthe number of the potentially state-dependent predictors, and p_i the predictors(the scan position, thesquare and cube of the scan position, the 1000–300- and 200–50-hPa layer thicknesses, surface skin temperature, and total column water vapor) and their coefficientsγ_i(Liu et al., 2012). The coefficients were updatedby a variational minimization process by includingthem as control variables(Derber and Wu, 1998;Auligné et al., 2007; Dee and Uppala, 2009).

To evaluate the impact of radiance data assimilationin the WRFDA ETKF/3DVAR hybrid systemwith flow-dependent background error, analysis/forecast experiments with radiance assimilation areperformed over the period from 18 July to 1 August2012, during which time typhoons Vicente and Saolaformed(Fig. 1).

Fig. 1. The WRF model domain and the 6-h tracks of Typhoon Vicente(black typhoon symbols)from 0000 UTC 20to 0000 UTC 25 July, and Typhoon Saola(red circles)from 1800 UTC 29 July to 0600 UTC 3 August. The snapshotof AMSU-A(orange dots from NOAA-18) and IASI(green dots from MetOp-A)radiance observations available withinthe assimilation window time of the first analysis time are denoted valid at(a)0600 UTC 18 and (b)0000 UTC 19 July2012, respectively.

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Typhoon Vicente was one of the most powerfulstorms to strike southern China in recent years, causingmajor damage to life and property. Vicente beganas a tropical depression on 18 July 2012, northeast ofthe Philippines. Vicente steadily moved into the SouthChina Sea, and gradually strengthened throughout 23July, at which point it changed course towards GuangdongProvince. Later on the same day, Vicente madel and fall over Taishan, Guangdong.

Typhoon Saola was a tropical cyclone that affectedthe Philippines and China(including the Taiwanregion). On 26 July, a tropical depression developedabout 1000 km to the southeast of Manila. On 28 July, it was upgraded to a tropical storm, and toa category-1 typhoon on 30 July. It was soon downgradedto a tropical storm late on 30 July. On 31 July, Saola developed again into a category-1 typhoon, and then to a category-2 typhoon early the next day. TyphoonSaola made l and fall over Taiwan at 1920 UTC1 August. On 2 August, Saola was downgraded to atropical storm and made l and fall again over Fujian at2250 UTC.

The WRF model(version 3.5; Skamarock et al., 2008)is employed in all forecast experiments. Thefollowing physical schemes are used: the WRF singlemoment5-class microphysics scheme(Hong et al., 2004); the Goddard shortwave(Chou and Suarez, 1994) and rapid radiative transfer model(RRTM)longwave(Mlawer et al., 1997)radiation schemes, including the refined upper boundary condition forRRTM(Cavallo et al., 2011), necessary when cyclingmodel tops above 50 hPa; the Yonsei Universityboundary layer scheme(Hong et al., 2006); theNoah l and surface model(Chen and Dudhia, 2001); and the Kain-Fritsch cumulus parameterization(Kain and Fritsch, 1990). The model domain for the experiments, as shown in Fig. 1, has an 18-km grid spacingon a 400 × 300 horizontal grid cell and 43 vertical levels, with the model top at 10 hPa.

Microwave and infrared radiance data are two majorsources of satellite data, and both are importantobservation types for data assimilation, especially forareas over oceans with sparse conventional observations.As two representative sources of microwave and infrared radiance data, AMSU-A and IASI(InfraredAtmospheric Sounding Interferometer)radiances arewidely studied in 3DVAR or EnKF frameworks(Mc-Nally, 2007; Liu et al., 2012; Schwartz et al., 2012;Xu et al., 2013a). In this study, five experimentsare carried out to assess the influences of AMSUA and IASI data on typhoon forecasts(Table 1), using both the 3DVAR and the ETKF/3DVAR hybridsystem. The first three experiments, denotedas CTRL, 3DVAR−AM, and HYBRID−AM are conductedto evaluate the AMSU-A data impacts. Theexperiment CTRL assimilates only conventional observationsfrom the NCEP operational global telecommunicationsystem dataset with 3DVAR. The experiment3DVAR−AM, similar to CTRL, assimilates AMSU-Aradiances from NOAA-18 and MetOp-A besides theconventional observations in CTRL. The experimentHYBRID−AM assimilates all observations from theexperiment 3DVAR−AM, but with the hybrid system.The distribution of AMSU-A observations available forthe first cycle time is shown in Fig. 1.

Table 1. Descriptions of experiments

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The IASI(Blumstein et al., 2004)is an advancedsensor, providing observational atmospheric temperature and humidity data with unprecedented accuracy and resolution. Xu et al.(2013a)found thatincluding IASI radiance data improved TC forecasts, especially for TC tracks in 3DVAR. Assimilation effectsof both AMSU-A and IASI radiances on typhoonsin the hybrid framework are explored to discover theextent to which IASI radiances will be complementaryor redundant to AMSU-A radiances in the hybridframework. Two extra experiments 3DVAR−AMIA and HYBIRD−AMIA are conducted, similar to experiments3DVAR−AM and HYBRID−AM, respectively, but also assimilate IASI radiances from MetOp-A withchannels around 15.0 μm.

Forecast-analysis experiments are carried out ona 6-h cycling basis. The data assimilation period isfrom 0600 UTC 18 July to 0000 UTC 1 August 2012.We compute the BEC statistics provided by the NMCmethod(Parrish and Derber, 1992)by using the differencesin the 24- and 12-h forecasts initiated fromGFS analyses at 0000 and 1200 UTC every day from1 to 30 July 2011. During this period, four typhoonsthat formed in the western Pacific Ocean struck easternChina. The BEC statistics could have been derivedfrom any one of these four. The backgroundensemble in the first analysis is provided by the 6-hensemble forecast initiated from the NCEP GFS 0.5°× 0.5° analysis at 0000 UTC 18 July. The forecastensemble is then re-centered about the GFS analysis, shifting the ensemble mean to preserve the perturbationsabout the mean. For the following cycles, the background is a 6-h WRF forecast from the previouscycle. The lateral boundary conditions for theWRF forecasts are also provided by the operationalGFS forecasts at 3-h intervals. In total, there are 56 analyses and forecasts during the period.

The key to ensemble-based DA is the use of anensemble to estimate the forecast error in a flow dependentmanner, so it is important to briefly examinethe ensemble performance. The ensemble spread ofwind and temperature at the 9th model level is shownin Fig. 2 after 2-day cycles valid at 0000 UTC 20 July, when Typhoon Vicente formed. The ensemble spreadreveals patterns that reflect features of the meteorologicalconditions and observation locations. Greatspread is found over western China, where few observationsare available to constrain the model. A localspread maximum is evident for wind speed and temperaturein the northeast of the Philippines, where theTCs moved, reflecting the uncertainty of TC prediction.

Fig. 2. Ensemble spread for(a)wind speed(m s−1) and (b)temperature(K)valid at 0000 UTC 20 July 2012 at the9th model level.

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In a well-calibrated system, the ensemble meanroot-mean-square error(RMSE)compared to observations(or other reference)equals the “total spread”(Houtekamer et al., 2005). The forecast RMSEs, witha total spread aggregated between 0000 UTC 19 and 0000 UTC 31 July, and the static background error(defined as CV−5)calculated by the “gen−be” utilityin WRFDA(Wang et al., 2014)using the NMCmethod are shown in Figs. 3a and 3b. The forecastRMSEs are assessed by comparing the forecastensemble mean to the GFS analyses. We generate a200-member ensemble by sampling the background errorwith Gaussian noise using the r and om-cv facility inWRFDA. The static background errors in Fig. 3 areestimated based on the ensemble perturbations in the200 members. The averaged wind and temperature forecast RMSEs are less than 3 m s−1 and 1 K for mostlevels. For winds, the static BEC calculated with theNMC method is largely underestimated, also found by Wang et al.(2014), whereas the ensemble spread is inbetween the RMSEs and the static BEC. The ensemblelacks sufficient spread in temperature, especiallyfor the low levels. The increment from assimilation isprobably small where spread is small, indicating lessforecast uncertainty. The final BEC from the hybridsystem, as a mix of the flow-dependent and the staticBEC, plays an important role in the data assimilationprocedure.

Fig. 3. Static background error(CV−5), averaged forecast RMSEs against GFS analyses, and averaged ensemble spreadat 0000 UTC 19 July and 0000 UTC 1 August for(a)wind speed(m s−1) and (b)temperature(K).

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The mean differences between the 0000 and 1200UTC model analyses and corresponding ERA-Interimfields(model minus ERA-Interim)over the experimentalperiod are shown in Fig. 4 for temperature and wind speed. The CTRL analyses exhibit significantwarm biases(Fig. 4a)relative to the ERAInterimover most of the domain, especially along thetyphoon tracks, with larger bias values compared to HYBIRD−AM(3.28 versus 2.82), consistent with theresults of Liu et al.(2012). Past studies(e.g., Wang et al., 2011; Wang and Huang, 2012)have shown thatwind perturbation around TCs plays an important rolein TC movements. From Figs. 4c and 4f, it is clearthat HYBRID−AM shows the smallest bias comparedto both CTRL and 3DVAR−AM for both fields, evenover eastern China, where few observations are available, which is achieved through the BEC.

Fig. 4.(a, b, c)Averaged temperature(K) and (d, e, f)wind speed(m s−1)bias at the 9th model level for CTRL, 3DVAR−AM, and HYBRID−AM against the ERA-Interim over the period 0000 UTC 19 July and 0000 UTC 1 August.

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Figure 5 shows the 72-h track forecasts initializedat 0000 UTC 21 and 0000 UTC 31 July every 6 hours, respectively. The best track positions from the ChinaMeteorological Administration are also plotted(black dots). For the forecasts beginning at 0000 UTC 21July(Fig. 5a), the AMSU-A radiance has a positiveimpact on the track forecast from both 3DVAR−AM and HYBRID−AM, preventing the northward bias.The forecast track from HYBRID−AM agrees betterwith the best track than the CTRL and 3DVAR−AM.The worst track forecast occurs for Saola, with a significantnortheastward bias from both 3DVAR experiments.For the forecasts beginning at 0000 UTC31 July(Fig. 5b), the northeastward biases fromthe CTRL and 3DVAR−AM experiments are evident.However, even in these poor forecasts, the hybrid systemstill upgrades the track forecast, especially forthe first 36 hours, though the typhoons moved ratherfaster after making l and fall.

Fig. 5. 72-h track forecasts initialized at(a)0000 UTC 21 and (b)0000 UTC 31 July 2012 for BEST−TRACK, CTRL, 3DVAR−AM, and HYBRID−AM.

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To assess large-scale performance, 36-h forecastsare verified against a set of conventional observations(radiosondes and GeoAMV)in Fig. 6 from 0000 UTC20 to 0000 UTC 1 August. Inclusion of AMSU-A radiancedata has a positive impact on all the variablesin 3DVAR, except for slightly worse temperature forecastsat the very low and high levels. The hybrid experimentagrees better with the observations than the3DVAR experiment does at almost all levels for wind and temperature and at low levels for specific humidity.

Fig. 6. Vertical profiles of 36-h forecast RMSEs for(a)wind speed(m s−1), (b)temperature(K), and (c)specifichumidity(g kg−1), against conventional observations for CTRL, 3DVAR−AM, and HYBRID−AM. The numbers ofconventional observations are shown on the right of each panel.

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Figure 7 shows the absolute track errors of the typhoonsfor the two 3DVAR experiments(3DVAR−AM and 3DVAR−AMIA) and two hybrid experiments(HYBIRD−AM and HYBRID−AMIA). Consistentwith the results from Xu et al.(2013a), the IASI radiancehas a steady positive impact on the forecast skillwhen tracking the 3DVAR framework within approximatelythe first 54 hours. Generally, track forecastsfrom the hybrid scheme are better than or at leastcomparable to those from the 3DVAR system for mostforecast hours. HYBRID−AMIA improves the trackforecast for Typhoon Saola more significantly than forTyphoon Vicente in Fig. 7b.

Fig. 7. Mean absolute track errors as a function of forecast lead time for(a)Vicente from 0000 UTC 20 to 1800 UTC 21July 2012, and (b)Saola from 0000 UTC 30 to 1800 UTC 31 July 2012 for experiments 3DVAR−AM, 3DVAR−AMIA, HYBRID−AM, and HYBRID−AMIA.

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Similar to Fig. 6, Fig. 8 displays theRMSE profiles of the 36-h forecasts verified againsta set of conventional observations. Consistent withthe results from Xu et al.(2013a), experiment3DVAR−AMIA has smaller RMSEs for temperature, wind, and specific humidity at most levels comparedto 3DVAR−AM. Radiance assimilation in the hybridsystem dramatically improves forecasts of all variablesconsistently. The assimilation IASI radiance data canupgrade forecasts of wind and specific humidity at almostall levels. The RMSEs from HYBRID−AM and HYBRID−AMIA are comparable for the temperatureforecast. One possible reason why the IASI data give better results in 3DVAR, but less promising results inthe hybrid system is that, as an advanced data assimilationsystem, the hybrid system can make betteruse of limited observation information compared to3DVAR. When more observations are assimilated inthe hybrid system, the positive impacts are not significant, since the analyses from the hybrid system withonly conventional and AMSU-A data are already satisfactory.

Fig. 8. As in Fig. 6, but for experiments 3DVAR−AM, 3DVAR−AMIA, HYBRID−AM, and HYBRID−AMIA.

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In this study, the WRFDA ETKF/3DVAR hybridsystem is used to predict two typhoons using AMSUA and IASI radiance data. The vertical localization schemes are considered for radiance assimilation inthe hybrid system. The results show that ETKF hassome skill in updating the ensemble perturbations and maintaining the ensemble spread, corresponding to theforecast errors, especially for wind. The hybrid schemeprovides a flow dependent background error with respectto the TC environment based on the ensembleperformance. Model output is compared to TC“best tracks” and conventional observations. AMSUAradiance data have slight positive impacts on thetrack forecast with the 3DVAR method. Typhoontrack forecast skills are greatly improved when the hybridscheme is employed. For 36-h forecasts, the hybridscheme has lower RMSEs for wind, temperatureat most levels, and specific humidity for at low levels, compared to 3DVAR.

The assimilation of both AMSU-A and IASI radiancedata in the ETKF/3DVAR hybrid system isalso conducted. On average, the use of the IASI radiancedata in the hybrid system upgrades the track, wind, and specific humidity forecast compared to theexperiment without the IASI radiance in the hybridsystem, but less significantly and consistently thanthe use of IASI radiances in 3DVAR compared to theexperiment without IASI radiance in 3DVAR.

In this study, we use ETKF/3DVAR hybrid toinvestigate two typhoon cases. To assess the impactof radiance assimilation in the framework ofETKF/3DVAR hybrid on TCs, additional studieswith more cases over extended periods are needed. Asradiances are important in improving the quality ofinitial conditions of NWP systems, especially for TCforecasts, effective use of more radiance observationsfrom other sensors should also be considered for futurestudies. Only track forecasts are emphasized in thisstudy, since the intensity forecasts are not encouragingdue to limitations of NWP in model dynamics, physicalparameterizations, spatial resolution, etc. Furtherinvestigations into the use of the ETKF/3DVAR hybridradiance data assimilation system for typhoonintensity forecasts are ongoing and will be reported infuture papers.

As ETKF solves the Kalman filter equation in theensemble space without localization, a single inflationfactor is applied domain-wide. Sampling errors caneasily cause instability issues(Bowler et al., 2008), especiallyfor large non-physical perturbations. Furtherwork is also planned to improve the inflation schemesin regional sub-domains or in a scale-dependent manner, to stabilize the ETKF scheme.

Acknowledgments. NCAR is sponsored by theUS National Science Foundation. Any opinions, findings, and conclusions or recommendations expressedin this publication are those of the authors and donot necessarily reflect the views of the US NationalScience Foundation.