This study demonstrates the added benefits of assimilating the Advanced Technology Microwave Sounder (ATMS) radiances in the Hurricane Weather Research and Forecasting (HWRF) system to forecasts of four Atlantic hurricane cases that made landfall in 2012. In the National Centers for Environmental Prediction (NCEP) Gridpoint Statistical Interpolation data assimilation system, the HWRF model top is raised to ~0.5 hPa and the cold start embedded in the HWRF system is changed to a warm start. The ATMS data quality control (QC) procedure is examined and illustrated for its effectiveness in removing cloudy radiances of all the 22 ATMS channels using primarily the information from ATMS channels 1 and 2. For each hurricane case, two pairs of data assimilation and forecasting experiments are carried out and compared with and without including ATMS data. The only difference between the two pairs of experiments is that the second pair also includes data from several other polar-orbiting satellite instruments. It is shown that ATMS data assimilation in HWRF results in a consistent positive impact on the track and intensity forecasts of the four landfall hurricanes.
If you can't find a tool you're looking for, please click the link at the top of the page to "Go to old article view". Alternatively, view our Knowledge Base articles for additional help. Your feedback is important to us, so please let us know if you have comments or ideas for improvement.
 Satellite observations play a key role in Numerical Weather Prediction (NWP) systems. The development of fast radiative transfer models (RTM) has [McMillin and Fleming, 1976; Saunders et al., 1999, 2007; Weng, 2007] allowed for a direct assimilation of radiance measurements, instead of satellite retrieval products, from polar-orbiting satellites in operational NWP systems. Radiances at satellite-observed frequencies are calculated from a RTM for a given atmospheric state from a NWP model. The atmospheric state that serves as an RTM input is adjusted so that the NWP/RTM-simulated radiances fit the observations most closely of either the maximum likelihood or the minimum error variance.
 The Advanced Technology Microwave Sounder (ATMS) onboard Suomi National Polar orbiter Partnership (NPP) satellite provides the measurements of the atmospheric temperature and moisture profiles under almost all weather conditions except for heavy precipitation when the microwave sounding capability is degraded by a significant scattering effect from large raindrops and ice particles. ATMS combines and inherits most of the channels from its two predecessors: Advanced Microwave Sounding Unit-A (AMSU-A) and Microwave Humidity Sounder (MHS) onboard NOAA and Meteorological Operational Satellite Program of Europe (MetOP) satellites. New features of ATMS include a wider scan swath, a new low tropospheric temperature sounding channel, and two new water vapor sounding channels. The three newly added ATMS channels allow ATMS to provide more detailed information of vertical thermal and water vapor structures in the low troposphere, which is especially important for tropical cyclones (TCs) study. A simplification to cloud detection is bought by ATMS due to its temperature sounding and water vapor sounding data being at the same locations. The two low-frequency window channels (23.8 GHz and 31.4 GHz) are sensitive to liquid cloud and the two high-frequency window channels (88.2 GHz and 165.5 GHz) are sensitive to ice cloud. The four window channels can be used together to identify both liquid and ice cloud radiances. This is extremely important for TCs since clouds are populated within and around hurricanes. Therefore, ATMS will support a more rapid advance for improved short-range, regional TC forecast skills.
 Satellite data assimilation has been an active area of research since 1990s, especially for global NWP systems. Satellite passive infrared and microwave radiance observations are routinely assimilated into NWP systems at the National Centers for Environmental Prediction (NCEP) and European Centre of Medium-Range Weather Forecasts (ECMWF) [Eyre et al., 1993; Andersson et al., 1994; Derber and Wu, 1998; McNally et al., 2006]. Significant improvements in NWP global forecasts have been obtained from direct radiance assimilations [Eyre et al., 1993; Andersson et al., 1994]. In satellite radiance assimilation, QC and bias correction are critical and performed differently in each NWP system. Currently, satellite radiances that are either contaminated by cloud and/or precipitation or the forward calculations that are problematic in accuracy must be identified and eliminated through a proper QC procedure. Also, the biases of observations must be quantified and corrected since theoretically all data assimilation methods assume no bias. However, the model background fields may contain biases. Since only the sum of the observation and model biases is required for satellite data assimilation, the mean differences between the observed radiances and those simulated from the background fields are used for estimating the sum of the observation and model biases.
 The so-called limb effect primarily arises from the variation of the optical path length with scan angle for a cross-track scanning radiometer instrument (e.g., ATMS). Although this limb effect is modeled in a fast RTM, both the atmospheric inhomogeneity and the side-lobe effect introduced by the spacecraft radiation to satellite observations increase with scan angle. Therefore, a static scan-angle-dependent bias is anticipated for each ATMS channel [Weng et al., 2003; Zou et al., 2011]. Other than a static scan-angle bias scheme, Harris and Kelly  found a necessity of adding an air mass bias correction to a global scan correction, in which the air mass predictors are computed from the background field. The air mass correction represents a needed bias correction for the RTM simulated radiances. Recently, cloud- and rain-affected observations are also considered for assimilation at the European Centre for Medium-Range Weather Forecasts (ECMWF) [Bauer et al., 2006a, 2006b].
 Recently, there are increasing concerns on a much enhanced satellite data assimilation effort for improved hurricane track and intensity forecasts. Early studies on satellite data assimilation for improved vortex initialization and hurricane prediction include those using a four-dimensional variational data assimilation system with either the Pennsylvania State University (PSU)/National Center for Atmospheric Research mesoscale model (known as MM5) [Zou and Xiao, 2000; Zou et al., 2001; Zhu et al., 2002] or the coupled Ocean Atmosphere Mesoscale Prediction System atmospheric model [Amerault et al., 2008, 2009]. In this study, we investigate impacts of assimilating the Advanced Technology Microwave Sounder (ATMS) data on hurricane track and intensity forecasts using Hurricane Weather Research and Forecast (WRF) system (known as the HWRF system) [Gopalakrishnan et al., 2011] and the National Centers for Environmental Prediction (NCEP) unified Gridpoint Statistical Interpolation (GSI) system for data assimilation [Derber and Wu, 1998; Wu et al., 2002]. In the GSI system, the Community Radiative Transfer Model (CRTM) developed by the U.S. Joint Center for Satellite Data Assimilation (JCSDA) [Weng, 2007; Han et al., 2007] is used as the observation operator for data assimilation of all satellite instruments.
 This paper is organized as follows: Section 2 describes main characteristics of ATMS and other satellite observations. A brief description of the HWRF system, the GSI system, hurricane cases, and experiment design are provided in sections 3–6. In section 7, the QC procedure, bias correction, and a comparison of the differences between ATMS observations and model simulations before (e.g., O-B) and after (e.g., O-A) data assimilation are described and presented. Section 8 assesses the added values of ATMS data on top of the combination of conventional, the Global Positioning System (GPS) radio occultation (RO) data, and the Advanced Scatterometer (ASCAT) surface wind observations. Experiments with and without several other satellite data (AMSU-A, Atmospheric Infrared Sounder (AIRS), and High-Resolution Infrared Radiation Sounder (HIRS)) are compared in terms of hurricane track and intensity forecasts. Section 9 provides summary and conclusions.
2 Satellite Observations
 ATMS is a cross-track microwave radiometer, which scans the Earth scene within ±52.7° with respect to the nadir direction. It has a total of 22 channels with channels 1–16 being designed for atmospheric temperature soundings above ~1 kPa and channels 17–22 for atmospheric humidity soundings in the troposphere below ~200 hPa. Fourteen of ATMS temperature sounding channels (ATMS channels 1–3 and 5–15) have the same frequencies as its predecessor AMSU-A (AMSU-A channels 1–14). The ATMS temperature channel 16 has slightly different frequency (88.2 GHz) from AMSU-A channel 15 (89.0 GHz). ATMS channel 4 is a new temperature sounding channel with its central frequency located at 51.76 GHz and contains temperature information in the lower troposphere (~700 hPa).
 Differences between ATMS humidity sounding channels and MHS are as follows: Two of ATMS humidity sounding channels (ATMS channels 20 and 22) have the same frequencies as its predecessor Microwave Humidity Sounder (MHS channels 4 and 5). The ATMS channels 17 (165.5 GHz) and 18 (183.31 ± 7.0 GHz) have slightly different frequencies from MHS channels 2 (157.0 GHz) and 3 (190.31 GHz). MHS channel 1 (89.0 GHz) is not kept by ATMS. The two new ATMS humidity channels 19 and 21 are located at 183.31 ± 4.5 GHz and 183.31 ± 1.8 GHz, respectively, for improving water vapor and precipitation retrievals. The weighting functions for the 22 ATMS channels were shown in Weng et al. .
 The ATMS channels 3–16 have a beam width of 2.2°, and that for ATMS surface channels 1 and 2 are 5.2°. The beam width is 3.3° for all AMSU-A channels. The ATMS humidity channels 17–22 have a beam width of 1.1° and is the same as MHS channels 1–5. The beam width differences between ATMS and AMSU-A channels result in significant differences in field-of-view (FOV) sizes between ATMS and AMSU-A [Weng et al., 2012]. Since ATMS temperature sounding channels have shorter integration time and therefore higher noise than AMSU-A, the ATMS observations from their overlapping FOVs are resampled to produce AMSU-A-like measurements so that all ATMS temperature sounding channels 1–16 have the same 3.3° beam width as that of AMSU-A [Satellite Applications Facility for Numerical Weather Prediction, 2011]. The resampled data from the 4th to 93rd FOVs at a five FOV interval are assimilated.
 Other satellite data assimilated include the Advance Microwave Sounding Unit-A (AMSU-A) onboard NOAA-18, NOAA-19, and MetOp-A, the hyperspectral Atmospheric Infrared Sounder (AIRS) onboard Aqua, and the High-Resolution Infrared Radiation Sounder (HIRS) onboard NOAA-19 and MetOp-A. AMSU-A is similar to ATMS. It is a cross-track scanning microwave radiometer for sounding the atmospheric temperature and provides a total of 15 channels. There are 12 channels in the frequency range from 50.3 to 57.3 GHz oxygen band for atmospheric temperature profiling from the Earth's surface to about 42 km (or 2 hPa). The other three channels are located at 89, 23.8, and 31.4 GHz. The AMSU-A FOV at nadir is about 48 km [Mo, 1996], and there are only a total of 30 FOVs from each scan.
 AIRS, one of the six instruments carried onboard the National Aeronautics and Space Administration's (NASA) Aqua satellite, is a hyperspectral infrared sounder providing a total of 2378 thermal infrared radiance observations across a spectrum from 3.7 to 15.4 µm. The spatial resolution for AIRS is 13.5 km at nadir [Aumann et al., 2003].
 HIRS is an atmospheric sounding instrument with one visible channel (0.6 µm), seven shortwave infrared channels (3.7–4.6 µm), and 12 longwave infrared channels (6.7–15 µm). It provides a nominal spatial resolution at nadir of 20.3 km in the visible and shortwave infrared channels and 18.9 km in the longwave infrared band, respectively. The HIRS/4 has the same number of channels as HIRS/3 except for an improvement in observation resolution. The nadir resolution for each channel is approximately 10 km.
 In summary, ATMS channels 1–16 and AMSU-A provide measurements at microwave frequencies below 60 GHz in an oxygen absorption band and ATMS channel 17–22 data are located at higher microwave frequencies above 89 GHz in a water vapor absorption band. The infrared channels from HIRS and AIRS have a mixed frequency distribution ranging from 4 to 15 µm. A spatial thinning is applied to ATMS, AIRS, AMSU, and MHS data. Details of the spatial thinning are provided in Appendix A.
3 The HWRF System
 The HWRF system was developed at NOAA's National Weather Service (NWS). The HWRF has a nonhydrostatic mesoscale model dynamic solver [Janjic et al., 2001, 2003]. The initial single-domain version of the HWRF system became an operational hurricane track and intensity guidance tool in 2007 [Gopalakrishnan et al., 2011]. A 3 km nesting domain was then added to the operational HWRF system for improved hurricane intensity forecasts [Zhang et al., 2011; Yeh et al., 2012; Pattanayak et al., 2011; Bozeman et al., 2011]. Finally, a triply nested version of the HWRF system was developed, which was configured with a parent domain of 27 km horizontal resolution with about 750 × 750 model grid points, an intermediate two-way telescopic moving nesting domain at 9 km with about 238 × 150 grid points, and an innermost two-way telescopic moving nesting domain at 3 km with about 50 × 50 grid points [Zhang et al., 2011]. Figure 1 shows the outer domain, the ghost domain, the middle nest, and the inner nest. The surface pressure field for tropical storm Beryl from the background field at 0000 UTC 27May 2012 within the outer domain is also shown. It is seen that the outer domain is reasonably large for capturing TC environmental flow evolution.
 The HWRF atmospheric model employs the following suite of advanced physics parameterization: Ferrier microphysics, NCEP global forecast system (GFS) boundary layer physics, GFS Simplified Arakawa-Schubert deep convection, and GFS shallow convection. The HWRF also includes the GFDL (Geophysical Fluid Dynamics Laboratory) surface physics, including GFDL land surface model and radiation, to account for air-sea interaction over warm water and under high wind conditions. The atmosphere component is coupled to the Princeton Ocean Model for all three domains, which employs feature-based initialization of loop current, warm and cold core eddies, and cold wake during the spin-up phase of the tropical cyclones. This version of the model also includes surface and boundary layer physics appropriate for higher resolution [Gopalakrishnan et al., 2012].
 The triply nested, 2012 version of the HWRF system is used for this study. Both the intermediate and innermost domains are centered at the initial storm location and configured to follow the projected path of the storm. The HWRF has 43 hybrid vertical levels with more than 10 model levels located below 850 hPa and a model top located at 50 hPa. The 50 hPa model top is too low for including many upper level ATMS channels in data assimilation. Figure 2a shows the weighting functions for all 22 ATMS channels, the pressures of the 43 vertical levels, and the pressure differences between two adjacent vertical levels. In order to include those high-level ATMS channels with their weighting functions peaking in the stratosphere, the model top is raised to 0.5 hPa, and the model levels are increased to 61 accordingly (Figure 2b).
 The vortex initialization in the HWRF is performed at the 9 km resolution domain, with model fields in the 3 km resolution domain being downscaled from those over the 9 km domain. It consists of merging a specified bogus vortex with an environmental field extracted from the GFS analysis at the beginning of the data assimilation cycle. Two prespecified symmetric vortices are made available, one for shallow or medium vortex and the other for a deep vortex. A storm size correction and an intensity correction are made to the prespecified vortex fields according to the storm size and intensity data provided by the tropical prediction center.
 The merged field with a corrected vortex and the GFS analysis environment is used as the background field for starting the data assimilation cycle of conventional and/or satellite observations at a 6 h interval. To eliminate complications associated with double uses of data, in this study, the 6 h HWRF forecasts are used as the background fields for the subsequent data assimilation experiments after the data assimilation cycle is initiated.
4 The NCEP GSI and CRTM
 The NCEP GSI analysis system used in this study is a regional three-dimensional variational data assimilation (3-D-Var) system. A detailed description of the theory and development of the GSI system can be found in Wu et al. . The GSI analysis system is more advantageous than the earlier NCEP Spectral Statistical Interpolation (SSI) analysis system [Derber and Wu, 1998] in that it adapts more flexibly to situations where observations are greatly inhomogeneous in terms of their data density and quality. Through an application of recursive filters, the spectral definition of background errors in the SSI analysis system is replaced with a nonhomogenous grid point representation of background errors [Wu et al., 2002; Purser et al., 2003a, 2003b]. The GSI system is made available for the NWP community, and a GSI User's Guide (http://www.dtcenter.org/com-GSI/users/index.php) provides a step-by-step procedure for users to install, compile, and run the GSI system on different local computer systems.
 The CRTM is a fast radiative transfer model and was developed by the U.S. Joint JCSDA [Weng, 2007; Han et al., 2007]. It supports a large number of sensors onboard historical GOES/Polar Operational Environmental Satellite (POES) satellites, new sensors onboard Suomi National Polar orbiter Partnership (NPP), and future sensors from the Geostationary Operational Environmental Satellite-R Series and the Joint Polar Satellite System. It covers the microwave, infrared, and visible frequency regions. Specifically, it is capable of producing model simulations of radiances from all the instruments mentioned in section 2. The CRTM clear-sky radiance simulation requires vertical profiles of atmospheric temperature and water vapor, surface parameters (e.g., surface temperature and surface wind speed) and satellite geometry parameters as its input. For cloudy radiance simulations, vertical profiles of hydrometeor variables (e.g., cloud liquid water path and ice water path) are also required. The Jacobian module of CRTM is also developed and incorporated into the NCEP GSI system, allowing for an efficient calculation of gradients of a CRTM-simulated brightness temperature with respect to input variables.
5 Case Description
 Tropical storms Beryl and Debbie and hurricanes Isaac and Sandy that occurred in 2012 over Atlantic Ocean are selected for investigation. They were the four landfall cases. The best track of each of the cases is shown in Figure 3.
 Tropical storm Beryl developed from a tropical low on 22 May 2012 and became a subtropical storm on 26 May and a tropical storm on 27 May 2012. It first moved northeastward, then turned to move southwestward on 24 May, and finally made landfall around 0410 UTC 28 May near Jacksonville Beach, Florida. After landfall, Beryl moved northeastward across the northeastern Florida. Beryl was the strongest preseason tropical storm of record. Tropical storm Debby developed from a low-pressure system in the Gulf of Mexico on 23 June 2012. Debby turned from a northward movement to an east-northward movement on 24 June and made landfall in Florida on 26 June (Figure 3).
 Hurricane Isaac was initiated from a tropical wave in the west coast of Africa on 21 August 2012. It became a tropical storm later that day. Isaac moved westward before 25 August and northwestward afterward (Figure 3). Isaac remained as a tropical storm in the subsequent 7 days and intensified into a category 1 hurricane in the morning of 28 August before its landfall.
 Hurricane Sandy developed from a tropical wave in the western Caribbean Sea on 22 October 2012. It quickly strengthened and developed into a tropical storm on the same day. Sandy became a category 1 and 2 hurricane after 24 October. Sandy moved initially westward in the Caribbean Sea, northward over Bahamas, then northeastward when entering middle latitudes, and finally northwestward on 28 October (Figure 3). It made landfall near Atlantic City on 30 October. Hurricane Sandy was the largest Atlantic hurricane on record, which earned it a nickname Superstorm Sandy by the media and government agencies. It affected 24 states, resulting particularly severe damage in New Jersey and New York. It caused estimated damage at over $63 billion in U.S. and a casualty of at least 111 in U.S.
6 Experiment Setup
 A total of four numerical forecast experiments were carried out for each of the four cases. In the first experiment, only conventional data, the GPS RO data and ASCAT surface wind data are assimilated (CTRL1). The second experiment is the same as CTRL1 except for adding ATMS data (CTRL1 + ATMS). The third experiment, CTRL2, is the same as CTRL1 but includes, in addition, AMSU-A, AIRS, and HIRS data. The decision of including only radiance observations from AMSU-A, AIRS, and HIRS instruments but not MHS and GOES Sounder data is made based on a series of data-denying experiments conducted by Qin et al. . Qin et al.  showed that inclusions of MHS and GOES Imager data degraded the forecast skill of the all-satellite-data assimilation experiment. The fourth experiment, CTRL2 + ATMS, is the same as CTRL2 except for adding ATMS data (CTRL2 + ATMS). Data assimilation experiments are performed on both the parent and intermediate domains.
7 Data Assimilation
7.1 Quality Control
 The QC for ATMS data in GSI employs six parameters associated with cloud, water vapor, and temperatures, three parameters associated with surface emissivity estimated from ATMS observed and CRTM-simulated brightness temperatures, and one parameter related to the observation error. First, a cloud liquid water path (LWP) index () and a total precipitation water index () are calculated over ocean using the ATMS measurements at 23.8 (channel 1) and 31.4 GHz (channel 2) [Grody et al., 2001]:
where (i = 1, 2) represent the ith ATMS channel measurements, μ = cos θ with θ representing satellite zenith angle; ci (i = 1, 2, …, 5) are the regression coefficients for LWP whose values are set to 8.24, 2.622, 1.846, 0.754, and 2.265, respectively; and ti are the regression coefficients for TPW whose values are set to 247.92, 69.235, 44.177, 11.627, and 73.409, respectively. By replacing with (i = 1, 2) in equations (1) and (2), and are also calculated.
 Then, a cloud LWP sensitivity index (GLWPindex) is calculated as follows
where αi is the scan-angle-dependent bias of the ith channel (i = 1, 2), (i = 1, 2) are the brightness temperature simulations of the ith channel, and is the 2 m surface air temperature from the background fields. Two more observation-minus-model indices, f1 and f2, are then calculated as follows:
 Three additional surface-emissivity-related parameters are calculated for ATMS channels 1–3:
where εi is the surface emissivity of the ith channel.
 The last parameter that is employed in the GSI QC algorithm is the modified observation error e′i, which is defined as follows:
 In equations (7) and (8), ei is the observation error of the i th channel (see Table 1), is the transmittance at the model top for the ith channel, , is the observation errors for cloudy radiance and is currently set to zero, and ftropic, fH2, and fH4 are defined as follows:
where ϕ is latitude and H is the terrain height.
Table 1. Prescribed Observation Error (σobs) and the Maximum Absolute Difference of Brightness Temperature Between the Observation and Background (|O − B|max)
|O − B|max (K)
|O − B|max (K)
 The QC procedure in the GSI system is implemented based on the values of the above 10 parameter calculated by equations (1) and (2) and (4)–(7), as well as the sum of the mixing ratios of cloud liquid water content and ice water content from the background field (i.e., ) is also used. It consists of the following nine tests:
 If qh > 0 and f2 > 1, data outside the latitudinal range [60°S, 60°N] are rejected for channels 1–7 and 16–22.
 If qh > 0, f2 ≤ 1, and f1 > 0.5, data outside the latitudinal range [60°S, 60°N] are rejected for channels 1–6 and 16–22 are rejected.
 If qh > 0 and , all data are rejected.
 If qh > 0 and either kg m−2 or kg m−2, data over ocean within the latitudinal range [60°S, 60°N] are rejected for channels 1–6 and 16–22.
 If qh = 0 and f2 > 1, data of channels 1–7 and 16–22 are rejected.
 If qh = 0, f2 ≤ 1, and f1 > 0.5, data of channels 1–6 and 16–22 are rejected.
 If qh = 0 and , all data are rejected, where ei,max is the maximum observation error (see Table 1).
 If qh = 0, f2 ≤ 1, f1 ≤ 0.5, but either r1 > 0.05, or r2 > 0.03, or r3 > 0.05, data over ocean of channels 1–6 and 16–22 are rejected.
 All data over a mixed surface are rejected, where a mixed surface is defined as a surface with none of the ocean, land, ice, or snow cover interpolated from the background field exceeding 99%.
 The ATMS channel 15 is not assimilated over both land and ocean. The first three QC tests remove outliers under cloudy conditions when model simulations greatly deviate from observations. The fourth QC test removes data points when either modeled () or observation retrieved () LWP is greater than 0.5 kg m−2. The last five QC tests remove outliers under cloudy conditions. The fifth and seventh tests identify outliers under clear-sky conditions when model simulations greatly deviate from observations. The sixth QC test considers not only the model and observation differences but also the sensitivity to LWP. The eighth test is used to remove outliers associated with uncertainty in surface emissivity. The ninth test is used to remove an FOV over which any single type of surface covers less than 99% of the FOV area.
 An example of data distributions retained and removed by the above QC procedure is provided in Figure 4. The brightness temperatures of the advanced very high resolution radiometer (AVHRR) channel 4 at 10.4 µm is used for showing the cloud distribution (Figure 4a). The O-B values of ATMS channel 19 for those data that pass GSI QC are provided in Figure 4b, and data points removed by different QC criteria are indicated in Figure 4c within and around Hurricane Sandy at 0600 ± 0300 UTC 26 October 2012. As expected, cloud is populated within and around Hurricane Sandy. However, there still are a lot of ATMS data distributed in clear-sky conditions within and around Hurricane Sandy. Most cloudy radiances (i.e., cross symbol sitting in clouds) are successfully identified and removed by the GSI QC procedure for ATMS data described above. Data points rejected by the GSI QC for this case are mostly by the fifth to the ninth QC criteria listed above.
7.2 Bias Correction
 Radiance measurements from meteorological satellites are not absolutely calibrated. Therefore, a global constant observation bias is expected with passive microwave data from a polar-orbiting satellite. For a cross-tracking satellite instrument, observations at large scan angles could be obstructed by the spacecraft radiation that is difficult to quantify. Therefore, an angular scan-dependent observation bias is also expected. Model simulations could also have biases. Although the limb effect of a cross-track instrument is modeled in a forward radiative transfer model, the atmospheric inhomogeneity arising from cloud and other sources within an FOV, which is not explicitly/accurately simulated in radiative transfer models, is larger at a larger scan angle. In addition, the altitude of the peak weighting function increases with scan angle and the atmospheric inhomogeneity within an FOV varies with altitude. The atmospheric radiative transfer models are more accurate near nadir than at large scan angles. Therefore, an angular scan-dependent model bias is expected.
 On the other hand, all data assimilation systems are developed under the assumption that observation and forward model errors are unbiased. Therefore, any bias related to satellite instruments and forward models must be removed in satellite data assimilation. Therefore, it is important to have the ATMS data biases be properly quantified and removed prior to assimilation of ATMS data [Harris and Kelly, 2001; Zou et al., 2011; Weng et al., 2012].
 The GSI bias correction consists of the following three parts: (i) scan biases which are calculated as mean differences between observations and model simulations for each scan position, (ii) residual biases dependent on air mass distributions and geographical locations [Eyre, 1992], and (iii) residual biases that vary with time in both diurnal and seasonal scales [Auligné et al., 2007]. Specifically, the biases for the ith channel and the jth FOV of ATMS data, bi,j (i = 1, …, 22; j = 1, …, 96), consist of a static scan bias term (), an air mass-dependent bias term (), and an adaptive scan bias term () written as follows:
where αi,j is the static scan biases which are calculated as mean differences between observations and model simulations for each scan position; ωl (l = 1, …, 5) are the five bias correction coefficients for the five air mass predictors pi,j,l; and βi,j and γi,j,m (m = 1, …, M) are the scan angle and the polynomial coefficients up to the order of M, respectively. The adaptive scan bias term () is not applied for ATMS bias correction.
 The five air mass predictors are defined as follows:
where is the lapse rate of transmittance of the ith channel and the jth FOV and is the mean lapse rate of transmittance of the ith channel for all FOVs. Values of αi,j (i = 1, …, 22; j = 1, …, 96), (i = 1, …, 22), and ωl (l = 1, …, 5) are fixed and provided in the GSI input file.
 The lapse rate of transmittance that appears in equations (13d) and (13e) is calculated by the following expression:
where the subscript k indicates the kth vertical level, K is the total number of model levels, τi,k + 1 is the atmospheric transmittance of the ith channel integrated from the kth vertical level to the top of the atmosphere, and Tk is the atmospheric temperature at the kth vertical level.
 The biases of ATMS data bi,j described above are subtracted from the term , which appears in the cost function of the three-dimensional variational data assimilation method in the GSI system.
7.3 Comparison Between O-B and O-A Statistics
 Figure 5 shows the data count distributions as a function of the differences between ATMS data and background (O-B) or the differences between ATMS data and analysis (O-A) at the 8th, 13th, 18th, …, 93th ATMS FOVs for three tropospheric ATMS channels 6–8 (Figure 5a) and three stratospheric channels 9–11 (Figure 5b). The angular dependent biases and standard deviations are also plotted in Figure 5. It is seen that the (O-B) data spread is much broader than that of (O-A) for all ranges of (O-B) or (O-A) brightness temperature values. There is a scan-angle-dependent bias such as channels 7 and 11 in (O-B) distributions. The biases and standard deviations are significantly reduced at all scan angles. The (O-A) biases is nearly zero for all scan angles.
 Values of the mean and standard deviation of (O-B) and (O-A) at nadir for all ATMS channels assimilated in the experiment CTRL2 + ATMS for Hurricane Isaac are presented in Figure 6. The biases are reduced for all channels except for channels 13 and 18. The standard deviations of (O-A) are significantly reduced for all channels except for channel 14. This confirms a better fit of NWP model fields to ATMS observations resulting from data assimilation.
8 Impact of ATMS Data Assimilation on Track and Intensity Forecasts
8.1 Hurricane Isaac
 Impacts of ATMS data assimilation on hurricane track and intensity forecasts are examined in this section. First, we show daily variations of an added value of ATMS data to conventional data on Hurricane Isaac's track and intensity forecasts (Figures 7-10). Figure 7 shows the forecast tracks of Hurricane Isaac with model forecasts initialized at 0000 UTC and 1200 UTC during 22–28 August 2012 for CTRL1 and CTRL1 + ATMS. Forecast results initialized at 0600 UTC and 1800 UTC during the same time period from 22 to 28 August 2012 are similar and not included in Figure 7 for clarity. The forecast tracks have an overall eastward bias compared to the observed track. Impacts of ATMS data assimilation on track forecasts are seen for the forecast started at 0000 UTC 25 August, and become more significant on 26 August and afterward. While the center of the observed Hurricane Isaac moved over the Gulf of Mexico, the forecast tracks at 0000 UTC 25, 0000 UTC and 1200 UTC on August 26 are over the coastal land from the CTRL experiment. Such an error in forecast track will introduce a significant error in the intensity forecasts.
 Daily impacts of ATMS data assimilation on both track and intensity forecasts for Hurricane Isaac are provided in Figure 8. Specifically, an average of four 5 day forecasts initialized at 0000 UTC, 0600 UTC, 1200 UTC, and 1800 UTC on each day from 22 to 27 August 2012 is calculated as a function of forecast lead time for both the CTRL1 and CTRL1 + ATMS experiments. The track errors are relatively small at the beginning 3 days from 22 to 23 August 2012 for both experiments when Hurricane Isaac was in the open ocean. A rapid increase of track error with forecasting time occurred on 25 and 26 August for the CTRL1 experiment when Hurricane Isaac moved into Puerto Rico. The track errors exceed 400 nm and 600 nm when the forecast time reaches 96 h in the CTRL1 experiment. When ATMS data are added for data assimilation, the track errors remain around and below 200 nm even during the entire 5 day forecast period on 25, 26, and 27 August 2012. In other words, ATMS data assimilation had a marginal impact on Hurricane Isaac's track forecasts when the CTRL1 experiment has a reasonably good track forecast in the first 3 days. It has a significant positive impact on Hurricane Isaac's track forecasts when the CTRL1 experiment does not perform well. Impacts of ATMS data assimilation for intensity forecasts for Hurricane Isaac occur most significantly on 25 and 26 August 2012. Improvements of ATMS data to intensity forecasts occurred at the same time when track forecasts are improved for Hurricane Isaac.
 The maximum wind speeds and the minimum sea level pressure (SLP) of all the 5 day forecasts, four times a day for 22–29 August 2012, for Hurricane Isaac from CTRL1, CTRL2, CTRL1 + ATMS, and CTRL2 + ATMS are presented in Figures 9 and 10, respectively. The HWRF forecasts without satellite data assimilation tend to produce a stronger Isaac than the observed. Such a bias in intensity forecasts is reduced after satellite data are assimilated. Assimilating ATMS data reduces the spreads of both the maximum wind speed and minimum SLP from different 5 day forecasts throughout the time period of 22–29 August.
8.2 Hurricane Sandy
 The track forecast of Hurricane Sandy was a well-known challenge in 2012. Impacts of ATMS data assimilation on Hurricane Sandy's track forecasts are shown in Figures 11 and 12. Figure 11 is a “spaghetti” map showing the observed and model-predicted tracks of the 5 day forecasts initialized at 0000 UTC, 0600 UTC, 1200 UTC, and 1800 UTC from 23 to 29 October 2012 by the four experiments CTRL1, CTRL2, CTRL1 + ATMS, and CTRL2 + ATMS. The forecast tracks from the CTRL1 experiment have a systematic northeastward bias. Such a track bias is significantly reduced for forecasts initialized after 1200 UTC 26 October 2012. The forecast tracks from the CTRL2 + ATMS experiment follow the observed track most closely.
 In order to show forecast track differences between CTRL2 and CTRL2 + ATMS more clearly, the 5 day forecast tracks of Hurricane Sandy with the HWRF model forecasts initialized at 0000 UTC and 1200 UTC during the first 4 days (23–26 October) and the later 3 days (27–29 October) are separately presented in Figure 12. The observed track of Hurricane Sandy before and after 0000 UTC 27 October is plotted at 6 h interval by the hurricane symbol in two different colors (red and black). It is seen that the forecast tracks by the CTRL2 experiment before 25 October all moved northeastward while the observed track turned from its northeastward to northwestward moving directions. Assimilation of ATMS observations results in a much improved track prediction. The track of the CTRL2 + ATMS forecasts followed the observed track when the forecast model is initialized as early as 0000 UTC 25 October. The CTRL2 + ATMS experiment produced a reasonably good track forecast 1 day earlier than the CTRL2 experiment. The forecast tracks of both CTRL2 and CTRL2 + ATMS experiments made the right turn from their northeastward movement to a northwestward movement for all the forecasts initialized on 27–29 October. However, the landfall position from the CTRL2 + ATMS forecasts initialized on 27 October is more precise than that of the CTRL2 experiment.
 The largest difference in the track forecasts of Hurricane Sandy with and without ATMS data assimilation occurred for the forecasts initialized at 1200 UTC 26 October 2012. It is found that the improvement on track forecasts brought by ATMS data arises from a more realistic development of an Ω-shaped ridge in middle latitudes when Sandy moved into it. Figures 13a, 13b, 14a, and 14b show 72 h and 84 h forecasts of potential vorticity and wind distributions at 200 hPa valid at 1200 UTC 29 October and 0000 UTC 30 October 2012, respectively. For a benchmark comparison, the NCEP GFS analyses 1200 UTC 29 October and 0000 UTC 30 October 2012 are provided in Figures 13c and 14c, respectively. The model-predicted center positions for Hurricane Sandy are indicated in Figures 13a, 13b, 14a, and 14b, and the observed best track is indicated in Figures 13c and 14c. Based on the large-scale environmental flow pattern shown in Figures 13 and 14, it is pointed out that the track of Hurricane Sandy changed from a northeastward movement to a northwestward movement when it is moved into a middle latitude trough, or the westside neck of an Ω-shaped ridge downstream of the trough. The cyclonic flow of the trough, or the anticyclonic flow of the ridge, seems to contribute significantly to the northwestward movement of Hurricane Sandy. As seen in Figure 14c, Hurricane Sandy made landfall at 0000 UTC 30 October 2012.
 Improvements of Hurricane Sandy's track forecasts thus depend on how well these large-scale features in middle latitudes are forecasted by HWRF. Compared with the NCEP GFS analyses (Figures 13c and 14c), it is concluded that the large-scale flow patterns are better predicted by the CTRL2 + ATMS experiment (Figures 13b and 14b) than those by the CTRL experiment (Figures 13a and 14a). The model-predicted Ω-shaped ridge downstream north of Sandy is too weak in the CTRL2 experiment. In other words, the ATMS data assimilation contributes positively to the prediction of Hurricane Sandy's environmental flow.
 The 84 h forecasts of total column integrated cloud condensate from the CTRL2 and CTRL2 + ATMS experiments valid at the time (i.e., 0000 UTC 30 October 2012) when Hurricane Sandy made landfall are provided in Figures 15a and 15b, respectively. For comparison, the observed brightness temperatures of channel 4 (10.7 mm) from GOES-13 at 0000 UTC 30 October 2012 are shown in Figure 15c. It is seen that the forecast from the CTRL2 + ATMS (Figure 15b) does a remarkable job in capturing the cloud structure of Hurricane Sandy (Figure 15c). It is also mentioned that the convective clouds near the tropic are quite well predicted in both CTRL2 and CTRL2 + ATMS experiments, although the CTRL2 + ATMS seems to have a slightly cloud coverage than that of CTRL2.
8.3 Averaged Impacts on Track and Intensity Forecasts
 The overall performance of hurricane forecasts with and without ATMS data for the four landfall storms in 2012 is presented in Figures 16 and 17. Variations of the mean forecast errors and standard deviations with the forecast time are compared between CTRL1 and CTRL1 + ATMS (Figure 16) and between CTRL2 and CTRL2 + ATMS (Figure 17). It is encouraging to find that mean errors for both track and intensity forecasts are consistently reduced by adding ATMS data into the HWRF data assimilation system. The standard deviations are also reduced except for the track forecasts from CTRL2 + ATMS. The slight degradation of standard deviations of track forecasts comes from a deteriorated track forecast for the tropical storm Debby. It is noticed that the track and intensity errors of CTRL2 are comparable with CTRL1. Further investigation on an optimal mix of different types of satellite data for hurricane data assimilation is warranted.
9 Summary and Conclusions
 The present study provides a preliminary assessment of the added values of ATMS microwave temperature and humidity sounding data to conventional and other satellite data for improved hurricane track and intensity forecasts using the HWRF system. The ATMS microwave radiance measurements are directly assimilated by the NCEP GSI system embedded in the HWRF system. Specifically, the added values of ATMS radiances to conventional data for improved tropical cyclones over Atlantic ocean are compared with a conventional data only experiment and with an experiment in which the conventional data and satellite data from the other three types of instruments (i.e., AMSU-A, AIRS, and HIRS). It is found that ATMS radiance data assimilation in the HWRF system contributes positively to both the track and intensity. The improvements brought by the ATMS data assimilation are more significant when the benchmark HWRF forecasts without incorporating ATMS data deviate more from the best track data.
 This study only investigates impacts of direct assimilation of ATMS radiance observations for four real tropical cyclone cases. Impacts of ATMS radiance assimilation experiments on hurricane track and intensity forecasts could be case-dependent and further improved. We plan to repeat these experiments for all Atlantic tropical storms in 2013 hurricane season to see if the conclusions from these case studies could be generalized. A similar study is being carried out to document the QC procedure and bias correction method employed in the GSI system and to assess the impacts of infrared radiance measurements at 1305 spectral channels from the Cross-track Infrared Sounder on hurricane track and intensity forecasts.
Appendix A: Spatial Data Thinning in GSI
 Spatial data thinning is applied to all ATMS, AMSU, MHS, and AIRS instruments. Factors considered in spatial data thinning are the spatial distance between observation and the center of an analysis grid box, the temporal difference between observation and analysis time, terrain height, surface type, LWP, and the difference of brightness temperature between two selected channels of each instrument. Following is a detailed description of the spatial thinning employed in GSI for ATMS.
 In a grid box in which there are more than one observations, only the observation with the smallest value of d × s + p is kept, others are rejected. The three parameters d, s, and p are defined as follows.
 The first parameter d is the spatial distance between each observation and the center of the analysis grid box in which the observation is located in the analysis grid point, is calculated:
where Δx and Δy are the distances in the x and y directions, respectively, between the observation location and the center of the analysis grid box in which the observation is located in, respectively.
 The second parameter (s) is calculated according to the difference between analysis time (ta) and observation time (to), terrain height (h), surface type (r):
where n is the total number of ATMS nonwindow channels whose observed brightness temperatures are outside the range of [50 K, 550 K]. There are five different surface types: Sea, land, sea ice, snow, and mixed surface. The values of r for these five different surface types are 0, 15, 10, 15, and 100, respectively.
 The third parameter (p) is related to the following two variables (qi and Lindex):
where is the brightness temperature observation of the ith channel, and is a scan-dependent bias of the ith channel, where FOV is the scan position of the observation.
 Over ocean, the parameter p is defined as p = 100 cos(α) × Lindex if Lindex > 0, q1 < 285 K, and q2 < 285 K; otherwise, p = 0. α is the satellite zenith angle. For other surface, p is defined as p = |q1 − q16| if |q1 − q16| ≤ 3K; otherwise, p = 100.
 A similar spatial data thinning is applied to AMSU, MHS, and AIRS instruments.
 Qin would like to acknowledge the support from Chinese Ministry of Science and Technology project 2010CB951600. This work was supported by NOAA JPSS Proving Ground Program and NSF project AGS-1037936.