1. Introduction

Tropical cyclogenesis, tropical cyclone(TC)intensitychange and movement are controlled by manyenvironmental factors. The motion of a tropical stormis driven mostly by the large-scale environmental steering, which is defined as a weighted average of the environmentalwinds between 300 and 850 hPa(Carr and Elsberry, 1990; Velden and Leslie, 1991; Chan, 2005;Wu and Zou, 2008). Tropical cyclogenesis and TCintensification are affected by the vertical wind sheardefined by the wind difference between 200 and 850hPa. Although weak shear may aid genesis by forcingsynoptic-scale ascent in baroclinic environments(Bracken and Bosart, 2000; Davis and Bosart, 2006), strong vertical wind shears are detrimental to tropicalcyclogenesis(McBride and Zehr, 1981; Zehr, 1992) and impede TC intensification(DeMaria, 1996; Gallina and Velden, 2002). There are a number of hypothesesas to what causes the weakening of TC intensityin the presence of strong vertical wind shear.One hypothesis is that vertical wind shear acts to decreasethe efficiency of the hurricane heat engine byventilating the TC eyewall with low-entropy air at mid levels by eddy fluxes(Simpson and Riehl, 1958; Cram et al., 2007; Marin et al., 2009). Convective downdraftair originating outside eyewall and having thelow-entropy air due to evaporative cooling into theboundary layer is advected inwards into the sub-cloudlayer of the eyewall by the radial inflow(Powell, 1990;Riemer et al., 2010; Riemer and Montgomery, 2011).Tang and Emanuel(2012)developed a ventilation index, which is defined as product of the environmentalvertical wind shear and the non-dimensional midlevelentropy deficit divided by the potential intensity, forevaluating whether ventilation plays a detectable rolein current TC climatology. Steering flow, vertical windshear, an approaching upper-level trough, upper-leveleddy angular momentum flux convergence, stratosphericcooling, and quasi-biennial oscillation in thestratosphere are factors that involve atmospheric conditionsin the upper troposphere and the stratosphere.

The interaction of upper-level troughs and /or cutofflows with TCs is another important factor influencingTC intensification(Molinari and Vollaro, 2010;Leroux et al., 2013). An approaching trough may inducesignificant vertical wind shear, enhance the outflowpoleward of the storm, or introduce the cyclonicpotential vorticity(PV)into the TC core through advection.The vertical wind shear is usually detrimental and the PV advection into the TC core is usuallybeneficial to TC intensity(Leroux et al., 2013), and the asymmetric outflow increases the eddy angularmomentum flux convergence calculated at 200hPa over a 300–600-km radial range around the TCcenter(Molinari and Vollaro, 2010) and leads to TCintensification for storms whose intensity is well belowtheir maximum potential intensity(Pfeffer and Challa, 1981; Challa and Pfeffer, 1990; DeMaria et al., 1993;Bosart et al., 2000). The intensity of TCs could also beaffected by the stratospheric cooling associated withclimate change(Ramsay, 2013). With stratosphericcooling, the rising heated air would be able to rise evenhigher than normal and entering the stratosphere, narrowingthe eye of the storm. In turn, the outer rainb and sof the TC will retract, decreasing the size of thestorm while increasing its strength. A strong correlationbetween decreasing stratospheric temperatures and increasing hurricane intensity has been found from25-yr hurricane data records(Emanuel et al., 2013).Cooling near and above the model tropopause(about90 hPa)modifies the storm’s outflow temperature and could increase the potential intensity(PI)at a rateof 1 m s⁻¹ per degree cooling with fixed sea surfacetemperature(SST)(Emanuel, 1986; Bister and Emanuel, 1997). Chan(1995)noted a relationship betweenthe interannual variations in TC activity and the quasi-biennial oscillation in the stratosphere inthe western North Pacific. Modeling of TC track and those opposing effects of TC-trough interaction, stratospheric cooling, and the quasi-biennial oscillationin the stratosphere on the environmental factorsaffecting TC intensification requires a sufficiently highmodel top to fully capture these stratospheric features and their interactions with troposphere in hurricaneenvironments.

A large amount of remote sensing data from research and operational satellites becomes availablefor obtaining an improved description of the initialstate of the atmosphere in the upper troposphere and stratosphere. The primary source of data includesthose upper-level sounding channels from theAdvanced Microwave Sounding Unit-A(AMSU-A)onboardNOAA-18, NOAA-19, MetOp-A, and MetOp-B; the High resolution InfraRed Sounder(HIRS)onboardNOAA-19, MetOp-B, and MetOp-A; the hyperspectralAtmospheric Infrared Sounder(AIRS)onboardEOS Aqua; as well as the Advanced TechnologyMicrowave Sounder(ATMS) and the Cross-Track InfraredSounder(CrIS)onboard Suomi NPP(NationalPolar-orbiting Partnership)satellite. These six polarorbitingsatellites(NOAA-18, NOAA-19, MetOp-A, Aqua, MetOp-B, and Suomi NPP)provide microwave and infrared radiance observations to the NCEP operationalnumerical weather prediction(NWP)systemmore than 12 times daily. These satellite observationshave an excellent global coverage and good spatial resolutionvarying from about 15 km to around 100 km.However, the satellite radiation is contributed fromthe stratosphere and the assimilation of the data intoNWP requires that the model top be placed at a sufficientlyhigh altitude. For this reason, the ECMWF model top was raised from 10 hPa to about 0.1 hPa in1999(Untch et al., 1999).

It is well known that direct assimilation of satelliteinfrared(McNally et al., 2006) and microwave(Derber and Wu, 1998)radiances provided by thepolar-orbiting meteorological satellites out-performedthe assimilation of temperature and moisture retrievalsfor NWP forecasts. Radiance measurementsfrom different satellites instruments are now routinelyassimilated in operational global medium-range forecastmodeling systems, which have brought significantlypositive impacts on the medium-range forecast(3–7 days). Positive impacts of satellite data assimilationfor short-range forecasts using mesoscale regionalmodels have also been demonstrated by severalstudies. For examples, assimilation of AMSU-A radianceobservations and conventional observations usingthe HIgh Resolution Limited Area Model(HIRLAM)four-dimensional variational data assimilation(4DVar)consistently out-performed the HIRLAM 3D-Var, particularly for cases with strong mesoscale storm developments(Gustafsson et al., 2012). Using the sameHIRLAM 4D-Var, Stengel et al.(2009)demonstratedthe benefit of a regional NWP model’s analyses and forecasts gained by the assimilation of three of SEVIRI’sinfrared channels(i.e., the two water vaporchannels located at 6.2 and 7.3 μm, and the CO2channel placed around 13.4 μm). Montmerle et al.(2007)investigated the relative impact of geostationaryversus polar-orbiting satellites and their possiblecomplementarity using the Aladin/France operationalregional 3D-Var system at Meteo-France. Radianceobservations from the Spinning Enhanced Visible and Infrared Imager(SEVIRI)on board Meteosat-8; AMSU-A radiances from NOAA-15, NOAA-16, and AQUA; AMSU-B radiances from NOAA-16 and NOAA-17; and HIRS radiances from NOAA-17 and the Advanced Infrared Sounder(AIRS)on board theNOAA and AQUA satellites, were assimilated. Analyseswere strongly controlled by SEVIRI data in themiddle to high troposphere, resulting in a positiveimpact on forecast scores and predicted precipitationpatterns. Weng and Liu(2003)studied the forwardradiative transfer and Jacobian modeling in cloudyatmospheres, and Weng et al.(2007)employed rainaffectedmicrowave radiance observations for hurricanevortex analysis. Positive impacts of a 3D-Var assimilationof the Advanced Technology Microwave Sounder(ATMS)onboard Suomi NPP satellite on hurricaneforecasts have also been demonstrated(Zou et al., 2013). The wealth of more accurate remote sensingdata from research and operational satellites, the developmentof more sophisticated hurricane forecastingmodels, and the availability of more powerful computers, provide unprecedented opportunities to advancefurther our knowledge, underst and ing, and forecastskill of TCs.

This study investigates the impact of the altitudeof the model top on satellite radiance assimilation and the track and intensity forecasts of tropical storms usingthe Hurricane Weather Research and Forecasting(HWRF)system. In the following, a brief descriptionof data, the TC case, and the data assimilation and TC forecast model are provided in Section 2. Satelliteobservation instruments are introduced in Section 3.Impacts of model top on biases of satellite radiancesimulation by a radiative transfer model are describedin Section 4. Section 5 depicts the case and the HWRFexperiment setup. In Section 6, data assimilation resultsfrom the HWRF are discussed. Forecast resultsare presented in Section 7, in which how the tropicalstorm forecasts are affected by model tops are elaborated.Section 8 presents a summary of this study.

2. A brief description of the HWRF system

This study employs the HWRF system, which hasevolved from a single-domain system(Gopalakrishnan et al., 2011), to a doubly nested version(Bozeman et al., 2011; Pattanayak et al., 2011; Zhang et al., 2011;Yeh et al., 2012), and finally a triply nested version(Zhang et al., 2011). The triply nested 2012 version ofthe HWRF system is configured with a parent domainat 27-km horizontal resolution, an intermediate twowaymoving nesting domain at 9 km, and an innermosttwo-way moving nesting domain at 3 km. The parent, intermediate, and innermost domains have about750 × 750, 238 × 150, and 50 × 50 model grid points, respectively(Zhang et al., 2011). Both the intermediate and innermost domains are centered at the initialstorm location and configured to follow the projectedpath of the storm. All the three domains of theHWRF have the same 43 hybrid vertical levels withmore than 10 model levels located below 850 hPa and a model top located at about 50 hPa. The ghost domainhas the same spatial resolution as the intermediatedomain but is slightly larger than the intermediatedomain. The data assimilation has a model toplocated at 50 hPa in the 2012 HWRF version, whichis raised to 0.5 hPa in this study. It will be demonstratedthat a higher HWRF model top is required forHWRF to better assimilate those upper tropospheric and low stratospheric sounding channels even if theirweighting functions peak well below 50 hPa, as wellas for HWRF to fully describe the physical and dynamicalprocesses in the upper troposphere and thestratosphere that are important for the development, movement, and intensity change of tropical cyclones.

Figure 1 shows the parent domain, 3X domain, ghost domain, middle nest, and inner nest for forecastingthe track and intensity change of tropical stormDebby. The observed track and the surface pressurefield from the background field at 1800 UTC 27 June2012 within the parent domain are also shown. It isseen that the parent domain is sufficiently large fordescribing TC environmental flow evolution. Both theintermediate and innermost domains are centered atthe initial storm location and move on the projectedpath of the storm to capture storm’s inner core structures.The HWRF atmospheric model employs Ferriermicrophysics, NCEP global forecast system(GFS)planetary boundary layer physics, SAS deep convection and shallow convection, and Geophysical FluidDynamics Laboratory(GFDL)l and surface model and radiation. The atmosphere component is coupled tothe Princeton Ocean Model(POM)for all three do-mains(Gopalakrishnan et al., 2012).

The NCEP unified Gridpoint Statistical Interpolation(GSI)system employed by the HWRF for dataassimilation was described in Derber and Wu(1998) and Wu et al.(2002). A recursive filter was usedto obtain a non-homogenous grid-point representationof background errors in the GSI system(Wu et al., 2002; Purser et al., 2003a, b). The Community RadiativeTransfer Model(CRTM)developed by the USJoint Center for Satellite Data Assimilation(JCSDA)(Han et al., 2007; Weng, 2007)is used for simulationof all observations from satellite instruments. Satellitedata assimilation is carried out in both the parent and the ghost D2 domains at 27- and 9-km resolutions.

The quality control(QC)procedure for each typeof satellite data consists of several QC tests to removeoutliers under cloudy conditions, outliers associatedwith uncertainty in surface emissivity, and those fieldof views(FOVs)with mixed surface types. The GSIbias correction consists of a constant scan bias correction and an air mass bias correction. Spatial datathinning is applied to all ATMS, AMSU-A, HIRS, and AIRS instruments based on the spatial distance betweenobservation and the center of an analysis gridbox, the temporal difference between observation and analysis time, terrain height, surface type, etc. A detaileddescription of the QC, bias correction, and datathinning employed in GSI for ATMS can be found in Zou et al.(2013).

The vortex initialization is performed at the 9-km resolution 3X domain(see Fig. 1). A pre-specifiedbogus vortex is merged with an environmental fieldextracted from the GFS analysis. Once the 6-h dataassimilation cycle starts, the 6-h HWRF forecasts areused for extracting the environmental fields. Themerged field with a corrected vortex and the environmentfield are the background field for data assimilationthat employs the NCEP GSI analysis system.

3. Satellite observations

The AMSU-A onboard both the NOAA and EUMETSATpolar-orbiting satellites measures the atmosphericradiation in microwave frequency range from23 to 89 GHz. AMSU-A is a cross-track radiometer.The extreme scan position of the earth view to thebeam center is 48.3°. The cross-track size of AMSU-AFOV is 48 km at nadir and that at the outmost scanangle is 105 km. The AMSU-A instruments have 15channels, in which 3 channels are window channels.Figure 2 presents the normalized weighting functionsfor AMSU-A channels 1–15, which are overlapped ontothe 43 vertical levels of the HWRF model with itsmodel top located at 50 hPa and the 61 vertical levelswith its model top located at 0.5 hPa. It is pointedout that the peak of weighting function increases withscan angle. However, such a shift is much smaller forupper-level channels than for low level channels(seeFig. 2 in Zou et al., 2013). The radiative energymeasured by AMSU-A primarily comes from the emissionof oxygen whose concentration is nearly uniformlydistributed through the earth’s atmosphere. Each ofthe 12 sounding channels provides measurements of aweighted average of radiation emitted from a particularlayer of the atmosphere at a specified frequency.The 12 AMSU-A sounding channels are evenly distributedthroughout the earth’s atmosphere. Therefore, AMSU-A satellite instruments are ideal for remotelysounding the global atmospheric temperature.More details on the channel characteristics of AMSUAcan be found in Mo(1996) and the NOAA KLM(abbreviated for NOAA-15/16/17)User Guide^①.

① http://www2.ncdc.noaa.gov/docs/klm/c7/sec7-3

ATMS is a cross-track microwave radiometer, which scans the earth scene within ±52.7°with respectto the nadir direction. It has a total of 22channels with channels 1–16 designed for atmospherictemperature soundings below about 0.1 hPa and channels17–22 for atmospheric humidity soundings in thetroposphere below approximately 200 hPa(Weng et al., 2012, 2013). The ATMS weighting functions canbe found in Weng et al.(2012). Fourteen of ATMStemperature sounding channels(ATMS channels 1–3 and 5–15)have the same frequencies as its predecessorAMSU-A(AMSU-A channels 1–14). The ATMS temperaturechannel 16 has slightly different frequency(88.2 GHz)from AMSU-A channel 15(89.0 GHz).ATMS channel 4 is a new temperature-sounding channelwith its central frequency located at 51.76 GHz and contains temperature information in the lower troposphere(around 700 hPa). The ATMS channels 3–16have a beam width of 2.2°, and the ATMS surfacechannels 1–2 have a beam width of 5.2°. To reduce thedata noise due to a shorter integration time of ATMSFOV, the ATMS overlapping FOVs are re-sampled toAMSU-A-like observations(NWP SAF, 2011; Yang and Zou, 2013).

HIRS is a 20-channel atmospheric sounding instrumentwith channels 1–12 being located in the longwaveinfrared frequency range from 6.7 to 15 μm, channels 13–19 in the shortwave infrared range(3.7–4.6 μm), and channel 20 being a visible channel(0.6μm). HIRS provides a nominal spatial resolution of20.3 km at nadir in both the visible and shortwaveinfrared channels and 18.9 km in the longwave infraredchannels. The HIRS/4 has the same numberof channels as HIRS/3 except for an improvement inobservation resolution. The nadir resolution for eachHIRS/4 channels is approximately 10 km. Weightingfunctions for HIRS channels 1–19 overlapped onto theHWRF model levels(gray horizontal line)for the 43-level setup with its model top located at 50 hPa and the 61-level setup with its model top located at 0.5 hPaare provided in Fig. 3. It is seen that HIRS channels1–3 are upper-level channels with their peak weightingfunction located above 100 hPa.

AIRS is a hyperspectral infrared sounder providinga total of 2378 thermal infrared radiance observationsacross a spectrum from 3.7 to 15.4 μm.It is one of the six instruments carried onboardthe National Aeronautics and Space Administration’s(NASA)Aqua satellite. The spatial resolution forAIRS is 13.5 km at nadir(Aumann et al., 2003). Detailedinformation on AIRS instrument characteristicswas provided by Pagano et al.(2002). A total of281 AIRS channels are selected for data assimilationin the GSI incorporated in the HWRF. The weightingfunctions of these 281 channels are provided inFig. 4. There are more than 65 channels whoseweighting functions peak above 100 hPa(Figs. 4a and 4b). There are also several channels whose weighting functions peak below 500 hPa but have significant contributionfrom the atmosphere above 50 hPa(Figs.4c and 4d). A model top higher than 0.5 hPa withmore upper vertical levels is needed to fully resolveupper-level sounding channels of AMSU-A, ATMS, and AIRS.

4. Impacts of model top on biases of satellite radiance simulation by CRTM

The 3D-Var satellite data assimilation searchesfor a local minimum solution x^* of the following costfunction(Derber and Wu, 1998)

where x is a vector of the control variable, xb is a vectorof the background state variable, B is the backgrounderror covariance matrix; the vector y representsall observations including brightness temperatureobservations from all instruments; the nonlinearvector operator H(x)represents the forward observationoperator that simulates the observed quantitiesfor every given atmospheric state variable x, Ois the observation error covariance matrix, and F isthe error covariance matrix of the forward observationoperator and representativeness error. For satelliteradiance data assimilation, the Community RadiativeTransfer Model(CRTM)is chosen as H(x), which calculates the radiance at the top of the atmosphereat different channels from different instruments.The matrices H and H^T are the tangent linear operator and the adjoint operator of H(x), respectively.The state variable x in Eq.(1)includes the atmospherictemperature profile, water vapor profile, and surface parameters(e.g., sea surface temperature and surface emissivity). A climatology profile is taken asthe state variables in CRTM above the model top altitude, which is either 50 or 0.5 hPa in this study.The ozone profiles from the GFS background fieldsare used as input to CRTM in GSI. A series of surfaceemissivity/reflectivity models are implemented inCRTM for microwave channels over l and (Weng et al., 2001), ocean(Liu et al., 2011), and snow and sea ice(Yan et al., 2004), as well as infrared channels overl and (Carter, 2002) and ocean(Wu and Smith, 1997).

Statistically speaking, the analysis obtained byminimizing the cost function defined in Eq.(1)is themaximum likelihood estimate under the assumptionthat all observations(y), the background field(x_b), and the state variable x are unbiased. Thus, the nonzeromean of observation errors must be subtractedfrom the data. Since the differences between observations and model simulations, i.e., O − B, appeartogether in Eq.(1), only the difference of the observationerror mean(μ°) and the background error mean(μ^b)is required based on the following expression:

The difference of observation and model biases μ°−μ^b in Eq.(2)can be estimated based on a large sampleof O − B statistics since O − B = O − T −(B − T) =μ°−μ^b.

If the model top is located too low(e.g., 50 hPa), radiances of many upper-level channels could be difficultto use. Significant temporally and spatially varyingbiases would be introduced for the assimilation ofthose channels that have a significant sensitivity tothe atmosphere above the model top. If these channelswere assimilated and adjusted during the assimilationprocess, signals in the satellite-observed radiancesfrom above the model top would be aliased, resultingin erroneous adjustments to model initial conditionswithin the model domain. The quality of forecastswould be reduced. It is thus important to have arelatively higher model top for the TC forecasts totake full advantage of upper-level radiance observations.

A quantitative assessment of the impact of modeltop altitude on model biases of satellite radiance simulationscan be illustrated for ATMS temperaturesounding channels. Figure 5a shows a global distributionof the differences of brightness temperature betweenobservations(O) and CRTM simulations(B)forATMS channel 15 during 0000–1200 UTC 20 December2011. The 64-level GFS fields were used as input toCRTM. The peak weighting function of ATMS channel15 is located at 2 hPa. The 64-level GFS model topis around 0.1 hPa. It is seen that the O–B differencesare within ±10 K. However, if the model top is locatedat 10 hPa, the CRTM will take the US st and ard profileabove 10 hPa as input to produce the simulatedATMS channel 15 brightness temperatures. The resultingdifferences of brightness temperature betweenobservations and CRTM simulations for ATMS channel15 are provided in Fig. 5b. The O–B differencescould exceed ±25 K in middle and high latitudes. Theupper-level information is crucial to assimilate upperlevelchannels.

Figure 6 presents the zonal mean temperature differencesbetween GFS 64-level forecast fields and theUS st and ard atmosphere above 10 hPa(Fig. 6a) and the zonal mean brightness temperature differences ofATMS channels 10–15 with and without the GFS fields above 10 hPa(Fig. 6b). The higher the channel’s peakweighting function and the higher the altitude, thelarger the O–B brightness temperature biases. Thelatter is caused by the differences between the GFSfields and the US st and ard atmosphere. If the modeltop is located at about 10 hPa, assimilation of ATMSchannels 13–15 is in question. This is because the impactof model top altitudes on model simulation ofthe ATMS upper-level channels is the smallest in thetropics.

5. Case description and the HWRF experiment setup

Tropical storm Debby occurred in 2012 over theGulf of Mexico, moved into the Atlantic Ocean, and isselected for this investigation. Debby developed froma low-pressure system in the Gulf of Mexico on 23 June 2012, then moved northeastward over the Gulf of Mexico.It turned into an eastward movement on June 24when approaching the Gulf coast. Debby made l and fallin Florida on June 26. It continued its eastwardmovement and went across Florida and moved intothe Atlantic Ocean. The NCEP operational HWRF5-day forecast tracks initialized on June 23 and 24produced a set of westward propagating tracks whenDebby moved northeastward. On June 25 and afterward, the operational HWRF model produced reasonablygood track forecasts. Therefore, the track predictionof tropical storm Debby before 25 June 2012 wasa major challenge.

Although the motion of a tropical storm is affectedby many factors, the primary driving force ofTC motion is the large-scale environmental steering(Elsberry, 1995; Wang et al., 1998; Chan, 2005). Inorder to see under what large-scale flow environmentthe tropical storm developed and moved, we examinethe geopotential and wind vector at 500 hPa using theNCEP global forecast system(GFS)6-h forecast fields(Fig. 7), which have a horizontal resolution of 0.3125°× 0.3125°, a temporal resolution of 6 h, and a totalof 64 vertical levels unevenly spaced from the earth’ssurface to about 0.1 hPa(Kleist et al., 2009). It isseen from Fig. 7 that the tropical storm Debby waslocated in between a subtropical trough its southeast and a midlatitude ridge its northwest. The anticyclonicflows on the west side of the subtropical high and on the east edge of the midlatitude ridge favoreda cyclonic flow development and a low-pressure systemin the Gulf of Mexico at 1800 UTC 23 June 2012.The midlatitude ridge experienced an enhanced developmentwith time, preventing Debby’s northwestwardmovement. The subtropical high gradually retreatedeastward and the northeast flow in the southwestwardbranch of the subtropical high and the midlatitudewesterly drove Debby to move eastward. It is thus anticipatedthat an accurate prediction of the size and position of the subtropical high is crucial for the trackprediction of Debby when the forecast model is initializedbefore 25 June 2012.

The model top of the HWRF data assimilation and forecast model is too low for including manyupper-level satellite channels in data assimilation. Toillustrate this, the 43 vertical levels are indicated in Figs.2–4 for weighting functions of AMSU-A, HIRS, and AIRS. The weighting function of a channel quantifiesthe relative contributions to the total measuredradiance from different levels of the atmosphere. Themeasured radiation is most sensitive to the atmospherictemperature at the altitude where weightingfunction reaches the maximum value. It is seen thata large portion of the weighting functions of manyupper-level channels are above the HWRF model top.In order to assimilate more upper-level channels withtheir weighting functions peaking in the upper troposphere and the stratosphere, the model top is raisedto 0.5 hPa, and model levels are increased to 61 accordingly(see right panels of Figs.2–4).

Two data assimilation and forecast experimentswere carried out for tropical storm Debby(2012). Theonly difference between the two numerical experimentsis the model top, which results in different amountsof data assimilated. The model top is located at 50 and 0.5 hPa in experiments L43 and L61, respectively.The model domain information is provided in Fig. 1, in which the sea level pressure from the backgroundfield at 1800 UTC 23 June 2012 and the US NationalHurricane Center(NHC)best track from 1800 UTC20 to 1800 UTC 27 June are also shown. In bothexperiments L43 and L61, AMSU-A, ATMS, HIRS, and AIRS radiance observations, conventional data, the Global Positioning System(GPS)radio occultation(RO)data, and the Advanced Scatterometer ASCATsurface wind data are assimilated. The decisionof excluding MHS(Microwave Humidity Sounder) and GOES Sounder(GSN)data is made based on a seriesof data-denying experiments conducted by Qin et al.(2013). Qin et al.(2013)showed that the MHS and GOES imager radiance data assimilation could degradethe forecast skill. Data assimilation experimentsare performed on both the parent and intermediate domainsat 27- and 9-km resolution, respectively.

6. Data assimilation results

Data assimilation in HWRF/GSI is carried out at0000, 0600, 1200, and 1800 UTC, which is denoted ast₀. Observations within t₀ ± 1.5 h are assimilated at time t₀, and observations outside these time windowsare not assimilated in HWRF/GSI. On the otherh and , a polar-orbiting satellite provides global observationstwice daily, with the same local equator crossingtime(LECT). The polar-orbiting satellites NOAA-18, NOAA-19, Aqua, and Suomi NPP cover the afternoonorbits, and MetOp-A covers the mid-morningorbits. Therefore, satellite data coverage in a fixedHWRF parent model domain(see Fig. 1)from thesesatellites varies with the UTC time. An example isprovided in Fig. 8, which shows the spatial distributionsof AMSU-A channel 5 data from NOAA-19 and MetOp-A for experiment L61 with the following4-time windows: 0000±1.5, 0600±1.5, 1200±1.5, and 1800±1.5 UTC 24 June 2012. Data points fromAMSU-A onboard NOAA-19 and MetOp-A that pass QC and are assimilated in the HWRF/GSI for tropicalstorm Debby are indicated in orange and cyan, respectively.Data points that do not pass QC are indicatedin red dots for both NOAA-19 and MetOp-A. Thebrightness temperature observations of imager channel4 from GOES-13 at 2300 UTC 23 June, 0500, 1100, 1100 and 1700 UTC 24 June 2012 included in Fig. 8 providea rough reference for cloud distributions aroundDebby. It is seen that 1800 UTC has the best datacoverage among the 4 UTC times at which data assimilationis carried out. It is also found that cloudyradiances are removed reasonably well. There is adata void area in the central United States from midmorning and afternoon orbits.

Figure 9 shows data counts of ATMS radiance observationsassimilated at 0000, 0600, 1200, and 1800 UTC during the entire data assimilation cycle from23 to 29 June for tropical storm Debby in the parentdomain for both experiments L43 and L61. Verylittle data are available in the model domain at 0000UTC from an afternoon orbit Suomi NPP satellite.It is seen that more observations are assimilated forthe upper-level channels 8–13 in experiment L61 thanthose in experiment L43. The total number of satellitedata assimilated for different channels varies daily, which is a combined result of the UTC dependence ofsatellite data and the cloud distribution over the areaswith satellite data. Due to the presence of cloud in thetroposphere, less amount of the low and middle troposphericchannels(ATMS channels 1–6)are assimilatedthan the upper-level in experiment L61. The channeldependence of the data counts of AIRS radianceobservations assimilated at 3 UTC times(e.g., 0600, 1200, and 1800 UTC)during the data assimilation cyclefrom 23 to 29 June for tropical storm Debby is presentedin Fig. 10 for both experiments L43 and L61.The altitudes of peak weighting function for all AIRSchannels assimilated in both experiments are also indicated. It is seen that more upper-level channels and less middle and low tropospheric channels are assimilatedin experiment L61 compared with experimentL43. Being consistent with the fact that more afternoonorbit(e.g., AIRS)data are available at 1800 UTCas shown in Fig. 8, the amount of AIRS data assimilatedat 1800 UTC is largest within the HWRF domain.Very little and no data are assimilated at 1200 and 0000 UTC, respectively.

Figure 11 presents mean vertical profiles of temperature and specific humidity differences between experimentsL43 and L61 at 0600 and 1800 UTC from 23to 29 June 2012 for tropical storm Debby in the parentdomain. With a higher model top, middle and uppertropospheric water vapor tends to be less and uppertropospheric temperature tends to be lower, while low troposphere tends to be wetter and middle and lowtroposphere tends to be warmer.

The convergence of satellite data assimilation isdemonstrated in Figs. 12–16. Figures 12 and 13 provide the differences between observations and thebackground fields(O–B) and the differences betweenobservations and analysis fields(O–A)of ATMS channels5–12 at those data points that pass GSI QC and are assimilated at 1800 UTC 24 June 2012 in experimentsL61 and L43. Experiment L43 performs similarlyto experiment L61 for the middle troposphericATMS channels 5–7. Differences of brightness temperaturesbetween ATMS observations and model simulationsafter data assimilation(O–A; Figs. 12b and 12d)are significantly smaller than the O–B differences(Figs. 12a and 12c)for all ATMS channels 5–12 in experimentL61(Fig. 12). There is an area of positiveO–B difference near the center of tropical storm Debbyfor ATMS channels 8–9, indicating that the observedwarm core structure in the middle and upper troposphereis stronger than that in the model. Althougha significant amount of observations are removed forthe stratospheric ATMS channels 10–12, the convergenceof ATMS data assimilation in experiment L43(Fig. 13)for the remaining data kept by GSI QC isnot so good as those data assimilated in the L61 experiment.The differences O–A are larger than thedifferences O–B for the stratospheric ATMS channels10–12 in experiment L43, which is caused by adjustingthe temperature below the model top for radiation energycontributions from above the model top. As mentionedbefore, the US st and ard atmosphere is used inCRTM for brightness temperature simulations abovethe model top. The convergence of the low stratospheric and upper tropospheric ATMS channels 8–9 inexperiment L43 seems also affected by the model topdue to residual radiation energy contributions abovethe 50-hPa model top to these two channels. Therefore, it is concluded that the poor performance of theL43 compared to the L61 is not solely because of lowermodel top but also a poor quality control in assimilatingthe higher-level channels. A revised bias correctionmay be helpful for assimilation of those upper-levelchannels to fill the gap between observation and background. Further investigation on a revised bias correctionfor assimilation of upper-level channels with alow model top, which could be the case to save computationalcost, will be carried out to see if useful informationcan be provided into model initial conditionsinstead of simply removing these channels.

Figures 14 and 15 compare the data count distributionsas a function of scan angle and the differencesO–B or O–A from the 8th to 93th FOV at aninterval of 5 FOVs for ATMS channels 6–13 betweenexperiments L43(Fig. 15) and L61(Fig. 14). The angular-dependent biases and st and ard deviations arealso plotted in Figs. 14–15. In experiment L61(Fig. 14), the O–A data spread is much narrower than thatof O–B. The biases and st and ard deviations are significantlyreduced at all scan angles for all ATMS channels6–13. However, the O–A data spread becomes muchbroader than that of O–B for ATMS channels 9–13in experiment L43, which is consistent with Fig. 13.These results confirm an improved fit of NWP modelfields to ATMS observations through satellite data assimilationwhen the model top is raised from 50 to 0.5hPa, especially for upper-level channels. Similar resultsare obtained for AIRS data assimilation.

Figure 16 shows a channel-dependent reduction ofthe differences between AIRS observations and modelsimulated brightness temperatures after data assimilation, including all data assimilated during 23–29June for tropical storm Debby in experiments L43 and L61. The wavelength for each of the 281 AIRS channelsassimilated in both experiments is also indicatedin Fig. 16. Similar to what was seen in microwaveupper-level channels, the spread of the differences betweenobservations and model simulations is increasedby data assimilation for most AIRS channels whosepeak weighting functions are above 100 hPa when themodel top is located at 50 hPa(Fig. 16a). The modelsimulated brightness temperatures based on the analysiscompare more favorably to AIRS observations forthose channels whose wavelengths are between 6 and 10 μm and peak weighting function altitudes are below100 hPa. If the model top is raised to 0.5 hPa, thest and ard deviations of the differences between observations and model simulations are reduced for all channelsafter satellite data assimilation in experiment L61(Fig. 16b). Although more AIRS tropospheric channelsdata are assimilated in L43 than in L61(see Fig. 10), the convergence(i.e., fit to observations)of L61is consistently better than that of L43 for almost allAIRS channels assimilated(see Fig. 16c).

7. Forecast differences between the two model tops

The track forecasts by NWP models initialized 2–3 days before the l and fall of tropical storm Debby was a well-known challenge in 2012. The Debby predictedby the operational model moved westward while thereal storm moved eastward when the forecasts wereinitialized before 25 June 2012. Impacts of model topon Debby’s track forecasts are shown in Figs. 17 and 18. Figure 17 is a “spaghetti” map showing the observed and model predicted tracks of the 5-day forecastsinitialized at 1800 UTC 23 to 1200 UTC 25 June2012 by the two experiments L43 and L61. The forecasttracks from experiment L43 moved northwestwardbefore 0600 UTC 25 June while the observed trackmoved northeastward(Fig. 17a). Such a westwardtrack bias is significantly reduced for forecasts in experimentL61(Fig. 17b)except for the forecast initializedat 1800 UTC 23 and 24 June 2012. It is noticedthat the forecast initialized at 1800 UTC 24 June 2013has produced a track that deviates from the observedtrack more greatly than the forecasts initialized at earliertimes. The main reason is found to be associatedwith the fact that the model forecast initialized at 1800UTC 24 June has a weaker and narrower subtropicalhigh than those from other forecasts.

Figure 18 shows geopotential height and wind vectorat 400 and 500 hPa from the analysis at 1800 UTC24 June and the 6-h forecast initialized at 1200 UTC24 June 2012 from experiment L61. The areas with thegeopotential at 400 hPa being greater than 7590 m and the geopotential at 500 hPa being greater than 5880m in the 6-h model forecast are significantly broaderthan those from the analysis at 1800 UTC 24 June2012. This would alter the environmental steering ofmodeled tropical storm Debby. A larger geopotentialheight value at the east side of the tropical stormfrom the 6-h forecast initialized at 1200 UTC(Figs.18b and 18d)corresponds to a stronger anticycloniccirculation. The southwestward flows on the west sideof the subtropical high would steer the storm to movenortheastward.

Although the motion of a tropical storm is affectedby many factors, the primary driving force ofTC motion is the large-scale environmental steering(Elsberry, 1995; Wang et al., 1998; Chan, 2005). Thesecondly important factor that controls TC motion isthe effect of the beta drift on TC motion, which notonly is much smaller than that of the steering flow, but also produces a systematic northwest track biasfrom the TC track. The northeastward movementof tropical storm Debby must therefore be controlled mostly by the environmental flow. Figure 19 providesthe 5-day forecast tracks as well as the steering flowcalculated from the deep layer mean environmentalflow of the HWRF model forecasts initialized at 1200(Fig. 19a) and 1800 UTC(Fig. 19b)24 June 2012 forexperiments L43 and L61 for tropical storm Debby.For steering flow calculation, the deep layer mean isfirst obtained(Carr and Elsberry, 1990; Velden and Leslie, 1991; Wu and Zhou, 2008). The vortex componentis then removed by using the Geophysical FluidDynamics Laboratory(GFDL)scheme(Kurihara et al., 1993). Finally, the environmental flow within aradius of 500 km from the storm center is averaged toobtain the steering flow. As shown in Fig. 19, the forecast tracks closely follow the steering flow, confirmingthat the Debby’s motion is mostly driven by theenvironmental steering flow. In experiment L61, thestorm initialized at 1800 UTC moved westward(Fig. 19b)while that from 1200 UTC followed a more realisticnortheastward track.

The forecast tracks from experiment L61 at otherUTC times followed the observed track more closely.The performance of all the 5-day forecasts for tropicalstorm Debby initialized from 1800 UTC 23 to 1200UTC 27 June 2012 is provided in Fig. 20. It is seenthat both the mean and the root-mean-square errorsof the track forecasts by experiment L61 are smallerthan those from experiment L43.

The overall performance of hurricane forecastswith two different model top altitudes for tropicalstorms Beryl and Debby and hurricanes Isaac and S and y that made l and fall in 2012 is presented in Fig. 21. The time period covered for Beryl, Debby, Isaac, and S and y is from 0000 UTC 23 to 1200 UTC 30 May, 1800 UTC 23 to 1800 UTC 29 June, 1800 UTC 21 to 1800 UTC 30 August, and 1800 UTC 22 to 1800 UTC29 October 2012, respectively. Variations of the meanforecast errors and st and ard deviations with the forecasttime are compared between experiments L43 and L61. It is found that the mean errors and st and ard deviationsfor both track and intensity forecasts of Beryl, Debby, Isaac, and S and y are reduced by raising themodel top of the HWRF data assimilation system.Further investigation on an optimal setup of differentvertical levels for improved satellite data assimilationfor hurricane track and intensity forecasts iswarranted.

8. Concluding remarks

The present study provides a preliminary assessmentof the benefits of having a higher model topin the HWRF/GSI system for both data assimilation and hurricane forecasts. Radiance measurements fromAMSU-A, ATMS, AIRS, and HIRS are directly assimilatedin the NCEP GSI system, which was adopted bythe HWRF system. Specifically, results from satelliteradiance assimilation(i.e., ATMS, AMSU-A, AIRS, and HIRS) and conventional data with two differentmodel top altitudes for the forecasts of tropical cyclonesin 2012 over the Atlantic Ocean are compared.It is found that satellite radiance data assimilationin the HWRF system with a higher model top improvesboth the track and intensity forecasts. Theimprovements brought by a higher model top for dataassimilation are more significant when the benchmarkHWRF forecasts with a lower model top deviate morefrom the best track data.

This study only investigates the impacts of directassimilation of satellite microwave and infrared radianceobservations for tropical storm Debby(as well asBeryl and hurricanes Isaac and S and y but not in muchdetail). Impacts of satellite radiance assimilation experimentswith an appropriately high model top onhurricane track and intensity forecasts could be casedependent and need to be further verified. We plan torepeat these experiments for more Atlantic and Pacifictropical storms in 2012 and 2013 hurricane seasons tosee if the conclusions from these limited case studies could be generalized.