As important as spectral and radiometric calibration, the geometric calibration is one of the requisites for the Suomi National Polar-Orbiting Partnership Cross-track Infrared Sounder (CrIS) Sensor Data Records (SDR). In this study, spatially collocated measurements from the Visible Infrared Imaging Radiometer Suite (VIIRS) band I5 are used to evaluate the geolocation performance of the CrIS SDR by taking advantage of high spatial resolution and accurate geolocation of VIIRS measurements. The basic idea is to find the best collocation position between VIIRS and CrIS measurements by shifting VIIRS images in the track and scan directions. The retrieved best collocation position is then used to evaluate the CrIS geolocation performance by assuming the VIIRS geolocation as a reference. Sensitivity tests show that the method can well detect geolocation errors of CrIS within 30° scan angle. When the method was applied to evaluate the geolocation performance of the CrIS SDR, geolocation errors that were caused by software coding errors were successfully identified. After this error was corrected and the engineering packets V35 were released, the geolocation accuracy is 0.347 ± 0.051 km (1σ) in the scan direction and 0.219 ± 0.073 km in the track direction at nadir.
 The successfully launched Suomi National Polar-orbiting Partnership (Suomi NPP) satellite in October 2011 (previously known as the National Polar-orbiting Operational Environmental Satellite System Preparatory Project) is a weather satellite to serve as a gap filler between NOAA's heritage Polar Operational Environmental Satellites and the new generation Joint Polar Satellite Systems (JPSS). Carried on Suomi NPP are five key instruments, that is, the Advanced Technology Microwave Sounder (ATMS), the Cross-track Infrared Sounder (CrIS), the Ozone Mapping and Profiler Suite, the Visible Infrared Imaging Radiometer Suite (VIIRS), and the Clouds and the Earth's Radiant Energy System (CERES). The CrIS on Soumi NPP is a Fourier transform spectrometer, providing sounding information of the atmosphere with 1305 spectral channels over three wavelength ranges: long-wave infrared (LWIR) (9.14–15.38 µm), middle-wave IR (MWIR) (5.71–8.26 µm), and short-wave IR (SWIR) (3.92–4.64 µm). Combined with ATMS, geolocated, radiometrically and spectrally calibrated radiances with annotated quality indicators from CrIS—the so-called Sensor Data Records (SDRs)—are used not only to retrieve atmospheric temperature and humidity profiles, but more importantly, to be directly assimilated into numerical weather prediction (NWP) models. Therefore, the data quality of the CrIS SDR is essential for producing accurate atmospheric profiles as well as for providing initial conditions for NWP models.
 After launch, an intensive postlaunch evaluation has been performed by the CrIS SDR team, focusing on validating its spectral, radiometric, and geometric calibration [Han et al., 2013]. Just as important as spectral (L. Strow et al., Spectral Calibration and Validation of the Cross-track Infrared Sounder on the Suomi NPP Satellite, submitted to Journal of Geophysical Research Atmospheres, 2013) and radiometric calibration [Tobin et al., 2013; (V. Zavyalov et al., Noise performance of the CrIS instrument, submitted to Journal of Geophysical Research: Atmospheres, 2013)], geometric calibration is also one of the requisites of the CrIS SDR. For instance, accurate and precise geolocation is required to coalign CrIS with ATMS in order to combine the ATMS and CrIS SDRs to atmospheric profile retrievals and data assimilation. Furthermore, good geometric calibration of the CrIS SDR is fundamental to potentially use VIIRS measurements for cloud flagging and scene feature detection. The spatial resolution of CrIS field of view (FOV) is 14.0 km at nadir. The designed specification for CrIS geolocation accuracy is less than 1.5 km for all the FOVs along scan angles, which are from a tenth to a hundredth of the FOV sizes varying with the scan angles. Therefore, evaluation of the postlaunch geolocation performance of the CrIS SDR has been listed as one of core tasks by the CrIS SDR team.
 Two methods are used to validate the geolocation of satellite measurements: (1) the coastline detection method and (2) the image coregistration method. The basic idea of the first method is to retrieve the coastline crossings with high thermal gradients (e.g., deserts adjacent to ocean) from clear-sky satellite measurements. The retrieved coastline is then compared with shoreline database with well-known geolocation information. The statistics are computed to identify systematic geolocation errors through different scenes. This method was initially developed for the Earth Radiation Budget Experiment scanner on the Earth Radiation Budget Satellite and the NOAA 9 spacecraft [Hoffman et al., 1987] and then was further applied for the Clouds and the Earth's Radiant Energy System (CERES) scanner [Smith et al., 2009], the Atmospheric Infrared Sounder on Aqua [Gregorich and Aumann, 2003], the Cloud-Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSOs) [Currey, 2002], and ATMS on Suomi NPP (K. Robinson et al., Advanced Technology Microwave Sounder (ATMS) Geolocation Analysis, submitted to Journal of Geophysical Research: Atmospheres, 2013). Another application is to use the difference between ascending and descending observations along the coastlines to quantify the geolocation errors for microwave instruments [Berg et al., 2013; Moradi et al., 2013]. However, for nonuniform spatial sampling satellite measurements (like CrIS, see Figure 1), a sensitivity test indicates that this method cannot effectively detect the geolocation bias because nonsymmetric errors are introduced when retrieving coastline crossings (see detailed discussion in section 5.3). As a result, the geolocation bias is averaged out after performing statistical computation.
 The second method relies on image registration with ground control points (GCPs), which are collected from high spatial resolution satellite measurements with well-known geolocation accuracy and landmark features (e.g., shorelines and islands) (see the papers in the study of Le Moigne et al. . Through radiometric and spatial transform, the GCP scenes are converted into corresponding satellite measurements, and they are then compared with satellite measurements to be validated. The differences in term of sensor orientation are determined to characterize the geolocation errors. For example, a library of land GCPs from Landsat Thematic Mapper has been developed and successfully used to evaluate the geolocation accuracy of imaging instruments, e.g., Moderate Resolution Imaging Spectroradiometer (MODIS) on Terra and Aqua [Wolfe et al., 2002] and VIIRS on Suomi NPP [Wolfe et al., 2013]. Furthermore, the MODIS GCPs (250 m resolution) were used to achieve subpixel geolocation accuracy of the advanced very high resolution radiometer (1 km resolution) [Khlopenkov et al., 2010]. While this method works well for imaging sensors, it is a challenge for a step and stare scanning instrument like CrIS due to its relative large footprint size and sampling gaps among FOVs (see Figure 1).
 In this study, an intercalibration method of using spatially collocated measurements from VIIRS—an imaging instrument onboard the same satellite as CrIS—is used to evaluate geolocation accuracy of CrIS. The advantages of this intercalibration method are the following. First, VIIRS has a relatively fine spatial resolution (375 m at nadir for its imaging bands), and its geolocation accuracy is less than ~80.0 m [Wolfe et al., 2013]. Compared with the CrIS FOV size and geolocation accuracy specification, the geolocation for VIIRS can be treated as a reference to evaluate the geolocation of the CrIS SDR. Second, radiometric transformation from CrIS infrared (IR) spectra to VIIRS IR band radiances can be easily achieved by integrating CrIS spectra with VIIRS spectral response functions (SRFs). Third, sensor orientation is almost identical for CrIS and VIIRS because they are onboard the same satellite platform. Finally, the validation can be extended to any time at any locations.
 The paper is organized as follows: section 2 briefs CrIS instrument geometry and geolocation algorithm, section 3 describes the methodology, section 4 concentrates on sensitivity tests, section 5 presents the evaluation results, and section 6 concludes the paper.
2 CrIS Geolocation Algorithm
2.1 Instrument Geometry
 The Suomi NPP spacecraft orbits the Earth at a nominal altitude of 824 km in a Sun-synchronous orbit with an inclination of 98.7° and a mean period of 101 min (about 14 orbits per day). It has local equatorial crossing times of ∼1:30 P.M. and ~1:30 A.M. As a step-scan Fourier transform spectrometer, the radiation from the Earth and atmosphere is reflected into CrIS by a 45° mounted scan mirror rotating along two axes [JPSS Configuration Management Office, 2011; Kohrman and Luce, 2002; Stumpf and Overbeck, 2002]. CrIS takes 8 s for each scan sweep, each collecting 34 Fields of Regards (FORs). Among them, 30 are the Earth scenes, while 4 are the embedded space and blackbody calibration views. The scan mirror stepwise “stares” at the Earth step by step in the cross-track direction from −48.3° to +48.3 with a 3.3° step angle, equaling a 2200 km swath width on the Earth. At the same time, in order to compensate for in-track spacecraft motion, the scan mirror slightly moves backward in the track direction (saw teeth motion) so that the FOV footprint on the Earth surface is frozen during the sampling time (200 ms). Passing through the scene selection module (SSM), the radiation first reaches the Michelson interferometer positioned in front of the instrument. After the interference is constructed by the moving and fixed mirrors, a telescope (with an internal folding element) is responsible for collecting the collimated interferometer output into a converging beam. It is then spectrally split into three spectral regions and reaches the focal planes. Three field stops define the 3 × 3 detector array for each wavelength band, which are arrayed as 3 × 3 0.963° circles and separated by 1.1°. The energy transmitted from the Earth and atmosphere is then concentrated into the detectors by the condenser lens.
2.2 Geolocation Algorithms
 The goal of the CrIS geolocation algorithm is to map CrIS line-of-sight (LOS) pointing vectors to geodetic longitude and latitude on the Earth ellipsoid for each FOV at each scan position. Specifically, the CrIS geolocation calculation is divided into two parts, i.e., the sensor-specific algorithm and the spacecraft level algorithm. The sensor-specific algorithm computes CrIS LOS vectors relative to the spacecraft body frame (SBF) at a given UTC time. The detailed description can be found in the CrIS SDR Algorithm Theoretical Basis Document (ATBD) [JPSS Configuration Management Office, 2011]. The input data include (1) SSM in-track and cross-track servo errors, UTC timestamp, and FOR and FOV indexes from science data packets, and (2) timestamp bias, FOR in-track (pitch) and cross-track (roll) angles relative to nadir, instrument mounting angles from each reference system, and FOV position angles from engineering data packets. The algorithm begins with FOV position angles and goes through each rotation matrix and has the outputs of the CrIS FOV LOS vectors relative to the SBF coordinate system for each FOV at each scan position.
 The spacecraft level algorithm computes the intersection of those LOS vectors with the Earth ellipsoid to output geodetic longitude and latitude at a given universal time coordinated (UTC) time. This part of the algorithm is commonly used by all Soumi NPP instruments. The algorithm includes the following steps: (1) transformation of the LOS vector from the spacecraft coordinate to the orbital coordinate using the spacecraft attitude, (2) conversion of the LOS vector from the orbital coordinate to the Earth-centered inertial (ECI) coordinate systems based on the spacecraft's instantaneous ECI position and velocity vectors, (3) transformation of the LOS vector from ECI to the Earth Centered Rotational coordinate (also called the Earth-centered Earth-fixed (ECEF) coordinate), (4) computation of geodetic latitude and longitude through the Earth ellipsoid intersection algorithm, and (5) output of derived ellipsoid geolocation products, such as solar and sensor azimuth and zenith angles as well as the sensor range. The algorithm is described in the Joint Polar Satellite System (JPSS) Operational Algorithm Description (OAD) Document for Common Geolocation Software [JPSS Configuration Management Office, 2012a] and VIIRS geolocation ATBD [JPSS Configuration Management Office, 2012b].
 CrIS has three bands and each band has a focal plane. Only the detector position angles from the LWIR band are used for geolocation computation. The radial offsets of all 27 CrIS detectors from the interferometer axis are determined using the relative spectral calibration of these FOVs as discussed by L. Strow et al. (submitted manuscript, 2013). The spatial offsets of focal plane detectors between the LWIR and the MWIR/SWIR bands derived from relative frequency calibration can be used to connect the LW geolocation to the other two focal planes. The detector coregistration difference between the LWIR and either the MWIR or SWIR focal planes is less than 0.7% of the FOV, which is well within the 1.4% coregistration specification for CrIS focal planes.
2.3 CrIS Geolocation Uncertainty Tree
 The mapping accuracy requirement for the CrIS FOV is 1.5 km (radial, 1σ). Preflight analyses determined that the accuracy requirement would be met on orbit with significant margin (50%). As will be seen in the validation studies provided here, the FOV mapping accuracy does in fact meet the 1.5 km requirement. The contributors to the mapping knowledge uncertainty can be divided into two main components, dynamic and static components. The static components include error allocations in alignment at the instrument level and, additionally, for any shift that occurs during spacecraft installation. The dynamic components include allocation of uncertainties related to instrument drift and jitter for both in-track and cross-track directions, and uncertainties attributed to spacecraft thermal distortions and attitude determinations. The dynamic contribution is the smaller component of the mapping uncertainty, representing less than half of the total error budget. The dominant error contribution to geolocation knowledge is the static contribution, which includes uncertainties related to instrument boresight and instrument alignment reference, and the spacecraft attitude reference to the CrIS corner cube. Spacecraft position and timestamp errors are included in the error allocation but are very small contributors to the mapping knowledge uncertainty.
 The major steps of using VIIRS measurements to assess CrIS geolocation accuracy include the following: (1) CrIS spectral integration with VIIRS SRFs, (2) accurate computation of the CrIS FOV ground footprints, (3) spatial collocation of VIIRS pixels within the CrIS footprint, (4) definition of the cost function by shifting the VIIRS image in the along-track and cross-track directions, and (5) detection of CrIS geolocation accuracy by indentifying the minimum of the cost function (the best collocation position of VIIRS and CrIS measurements). These major steps are described below.
3.1 Spectral Integration
 The CrIS SDR radiances are measured at 1305 spectral channels over three wavelength bands, including long-wave IR band 1 (9.14–15.38 µm), middle-wave IR band 2 (5.71–8.26 µm), and short-wave IR band 3 (3.92–4.64 µm). In contrast to CrIS, VIIR is a whiskbroom scanning imaging radiometer, collecting visible and infrared imagery of the Earth through 22 spectral bands between 0.412 µm and 12.01 µm. These bands include 16 moderate resolution bands (M-bands) with a spatial resolution of 750 m at nadir, 5 imaging resolution bands (I-bands) with a 375 m at spatial resolution nadir, and 1 panchromatic day-night band (DNB) with a 750 m spatial resolution throughout the scan [JPSS Configuration Management Office, 2012b, 2012c]. For the purpose of geolocation assessment, it is better to use high spatial resolution I-bands than M-bands. The I-bands include three reflective solar bands (RSB) and two thermal emissive bands (TEB), all of which share the same geolocation data set. Among the two TEB I-bands, I5 band with 11.45 µm central wavelength is spectrally fully covered within the CrIS LWIR band spectrum, as shown in Figure 2. Therefore, the I5 band is used in this study.
 The purpose of spectral integration is to integrate the hyperspectral radiance spectrum from CrIS to match the narrowband VIIRS SRFs and make CrIS spectrum comparable with the VIIRS band radiance. Given the CrIS hyperspectral radiance R(ν) at each wave number ν, it can be integrated with the VIIRS SRF S(v) to generate the CrIS-simulated VIIRS IR band radiance L as
where ν1 and ν2 are the VIIRS I5 band-pass limits. The band radiances L can be converted into brightness temperatures (BT) using the Planck function. The VIIRS SRFs are obtained online at https://cs.star.nesdis.noaa.gov/NCC/SpectralResponseVIIRS. The band-averaged relative SRFs, which are averaged from the SRFs of 32 detectors and officially used in the Soumi NPP Interface Data Processing Segment (provided by Northrop Grumman Aerospace System), are used in this study. Although different versions of the VIIRS SRFs can be found on the above-mentioned website (including SRFs measured during the instrument-level testing and those measured during the spacecraft level testing), these differences for these SRFs are mainly located at the out-of-band regions or at the detector level on the order of less than 0.01%. At a band average level, the differences are negligible. The CrIS LWIR band contains 713 channels, covering from 655 to 1095 cm−1 (9.13–15.38 µm). The SRF for the I5 band is cut off at the range of 832.85–1040.80 cm−1. As a result, there are 333 spectral channels used to simulate VIIRS band I5. Finally, it is worth noting that the VIIRS rotating telescope assembly (RTA) is suffering the degradation due to tungsten contamination of RTA mirror coating since launch, which, however, only modulates the spectral response of RSB bands and does not affect on TEB bands [Cao et al., 2013]. Henceforward, except for those specially noted below, the CrIS BTs are referred to the simulated VIIRS BTs for the I5 band.
3.2 Computation of CrIS FOV Footprint
 After the radiometric transformation of CrIS spectra to match VIIRS band radiances, the next step is to spatially collocate VIIRS pixels within each CrIS FOV. To achieve this, the fundamental step is to accurately compute the CrIS FOV footprint projected on the Earth ellipsoid in form of geodetic latitude and longitude. Before proceeding to describe the details of the computation algorithm, we need to first define the coordinate systems in use. First, the Earth-centered inertial (ECI) system of coordinate has its origin located at the center mass of the Earth. In particular, one of commonly used ECI frames is defined with the Earth's Mean Equator and Equinox at 12:00 Terrestrial Time on 1 January 2000. The Earth Centered Rotational (ECR) coordinate—also known as the ECEF coordinate system—is the ECI adjusted for the Earth rotation, nutation, and precession in addition to the polar wander. It is important to note that all the computation is actually carried out in ECR coordinates. Furthermore, to be consistent with the VIIRS and CrIS geolocation algorithms, the World Geodetic System 1984 (WGS84) is used as a geodetic reference (datum) to characterize the Earth ellipsoid. The computation of CrIS FOVs' shape includes three major steps.
 First, for a given CrIS FOV, the line-of-sight (LOS) vector LOS (that is the CrIS FOV pointing vector) and satellite position vector SAT are computed in ECR, as shown in Figure 3a. At point P where instrument LOS intersects with the WGS84 Earth ellipsoid, the CrIS geolocation product includes the geodetic latitude and longitude and satellite azimuth angle, zenith angle, and range (the distance from the satellite to the Earth ellipsoid). This information can be used to compute the vectors LOS and SAT through coordination conversions. Specifically, the vector R can be calculated as RX, RY, and RZ in ECR from latitude, longitude, and 0, respectively, through the transformation from the geodetic coordination system (expressed as latitude, longitude, and height) to ECR. The vector LOS in ECR can be computed in two steps. Using satellite azimuth angle, zenith angle, and range, the vector LOS is first calculated in the local East-North-Up (ENU) coordinates. The local ENU coordinate is formed from a plane tangent to the Earth's surface fixed to a specific location, and the east axis is labeled x, the north y, and the up z, by convention. After that, the vector LOS in ENU can be converted into ECR using the geocentric latitude (calculated from geodetic latitude) and longitude through the ENU-ECR transformation. When LOS and R are calculated, the satellite vector SAT can be derived as
 Second, given a vector LOS for any CrIS detector at any scan position, the CrIS detector is actually projected as a cone in celestial space with a constant solid angle of 0.963° with the vector LOS as its axis. As shown in Figure 3b, the task is, thus, simplified to compute the vector FOV, which rotates with the LOS from 0° to 360° with a 10° step angle. These 37 vectors present the CrIS circle detector projected in celestial space. In the theory of three-dimensional rotation, Rodrigues' rotation formula is an efficient algorithm for rotating a vector in space, given an axis and angle of rotation [Murray et al., 1994]. In particular, if V is a vector in a three-dimensional system and k is a unit vector describing an axis of rotation about which we want to rotate V by an angle θ (in a right-handed sense), the Rodrigues formula is
 Using the Rodrigues' rotation formula, the vector FOV in Figure 3b can be computed by rotating the vector LOS by a half of CrIS detector size angle φ (0.963°) along a unit vector , which is an arbitrarily defined unit vector and is orthogonal to LOS. It can be expressed as
 After that, the other 36 vector FOVi can be derived by rotating the vector FOV by 10° along the unit vector LOSunit step by step as
 In the final step, we need to find the intersection of 37 FOV vectors with the WGS84 Earth ellipsoid. Similar to Figure 3a, it can be determined using the basic Earth ellipsoid intersection algorithm as
where the vector SAT have been computed in equation (2), L is the slant range and needs to be resolved, and Ri is the vector from the Earth center to the intersection of the Earth ellipsoid through the unit vector and is expressed as RX, RY, and RZ in ECR. The equation for the ellipsoid Earth is as follows:
where a and b are semimajor and semiminor axes defined in WGS84. Equations (6) and (7) can be combined into a single quadratic equation for the slant range L. When there is an intersection, there are two real roots, and the smaller yields the visible intersection. When there is tangency, there is only one root, which is a valid solution. After that, the intersection of RX, RY, and RZ in ECR is transformed back to geodetic latitudes and longitudes. The 37 pairs of computed geodetic latitude and longitude represent the FOV footprint projected on the Earth surface.
 An example of computed CrIS FOV footprints is given in Figure 1 for an ascending orbit. It clearly shows that the FOV footprint in the nadir FOR are projected as a circle on the Earth while off-nadir FOV footprints are gradually changed to ellipses due to increased scan angles and the Earth's curvature. For example, the center FOV (FOV 5) is changed from a 14.0 km circle at nadir into an ellipse with major and minor axes of 43.6 km and 23.2 km at the end of scan. In addition, the FOVS at the end of scan are also rotated because of the 45° mounted scan mirror.
3.3 Collocation of VIIRS Pixels Within CrIS FOVs
 Given the computed CrIS FOV footprint in term of geodetic latitude and longitude, we can determine which VIIRS pixels fall within the closed FOV region by searching the VIIRS geolocation data. The geodetic latitudes and longitudes of CrIS FOV footprints and VIIRS measurements are simultaneously transformed to Cartesian (x, y) coordinates through the map projection. For any given VIIRS data point in the Cartesian (x, y) coordinates, there is a mature algorithm to determine whether it is within a closed CrIS FOV footprint. The radiance values of VIIRS pixels falling within a given CrIS FOV are averaged together. The averaged radiance is converted into BTs using the Planck function. Specially, when converting the radiances into BTs, the BTs are corrected by the individual channel response function using band correction coefficients (two coefficients for each channel). This allows the computation using a single Planck function calculation, rather than requiring the integration of the Planck function across the instrument SRF. This saves computational time compared to the full convolution. The BT value from spatially averaged VIIRS radiances is paired with the one from the CrIS-simulated VIIRS radiances from the same CrIS FOV. After spectral and spatial transformation, VIIRS and CrIS “see” the same target from the same satellite platform through the same spectral response.
 The Interface Data Processing Segment (IDPS) for the NPP mission processes the Raw Data Records (RDR) into SDR and generates two geolocation data sets for VIIRS I-bands, that is, the one with terrain correction and the other without terrain correction. The geolocation data without terrain correction are used in order to be consistent with CrIS.
3.4 Definition of Cost Function
 After the above steps (discussed in sections 3.1–3.3), the VIIRS and CrIS measurements are spatially and radiometrically matched. The remained task is to identify the CrIS geolocation accuracy using VIIRS geolocation as a reference. The following steps are used for this purpose:
 Arbitrarily select inhomogeneous CrIS granules with deep convective clouds over the tropical oceans. Our data analysis shows that randomly distributed cloudy scenes over tropical oceans have a large dynamic range (from 180 K to 320 K) and are very sensitive to the mismatch of the CrIS-VIIRS collocation, thus, suitable to detect possible CrIS geolocation errors relative to VIIRS. Each day, 14 CrIS cloudy granules over tropical oceans including 56 scans (~7.5 min) are arbitrarily selected. For the geolocation assessment at nadir, 4 nadir FORs (from FORs 13 to 16) at each scan including 36 CrIS FOVs are used to collocate with VIIRS. So each day, there are a total of 2160 pairs of VIIRS and CrIS collocated measurements.
 Collocate VIIRS pixels with CrIS FOVs and then compute spatially averaged radiances and simultaneously convert CrIS spectra into VIIRS band radiances using the methods as discussed in section 3.3. They are then converted into BTs using the Planck function with band correction.
 Calculate root-mean-square-errors (RMSEs) of paired CrIS VIIRS BTs over a statistical ensemble, collected over the selected cloudy scenes, including a total of 2160 pairs of VIIRS and CrIS collocated measurements.
 Shift the VIIRS image toward the along- and cross-track directions and then repeat steps 2 and 3. The cost function is defined as the RMSE varying with the number of shifted pixels in the along- and cross-track directions. Here x axis is defined as the VIIRS scan direction and y axis as the spacecraft velocity direction. The same rule is followed for both of the ascending and descending modes. Specifically, the position [nx, ny] designates that VIIRS image is shifted with nx pixels along the VIIRS scan direction and ny pixels along the spacecraft track direction. It is important to note that the VIIRS scan direction is actually opposite to CrIS [JPSS Configuration Management Office, 2011, 2012c].
 The minimum of the cost function represents the location where VIIRS best matches with CrIS. Since the VIIRS geolocation is treated as a reference, the position of the minimum value of the cost function in term of distance can be used to estimate the CrIS geolocation accuracy in the along-track and cross-track directions.
 Given in Figure 4 is an example of deriving the cost function step by step. CrIS and VIIRS I5 band granules over the tropical oceans are shown in Figures 4a and 4b, in which clouds are randomly distributed over ocean. Only nadir FOVs from FORs 13 to 16 are selected for collocation. Figure 4c shows scatterplots of VIIRS and CrIS BTs when one shifts the VIIRS granules by different numbers of pixels. From the position [1,1] to [5,8], the spread of the scatterplots of VIIRS BTs versus CrIS BTs quickly increases, indicated by the RMSE values of CrIS-VIIRS BT differences. The constructed cost function is given as a contour plot in Figure 4d.
3.5 Detection of CrIS Geolocation Accuracy
 The position of the minimum of the cost function represents the location where VIIRS measurements best match with CrIS, and thus, the final task is to identify the location of the cost function minimum. As shown in Figure 4d, the cost function is composed by 31 × 31 values, and the minimum value is actually located at the position of [1,1]. However, it is important to pin down the geolocation accuracy at a subpixel level. Using these 31 × 31 values, a contour map can be constructed using a standard procedure. 10 contour lines (or isolines) with values that are very close to the minimum value (beginning with the minimum value +0.005 K with a step of 0.001 K) are extracted from the contour map. Since each contour line can be treated as a closed ellipse, a fitting ellipse can be found, and the center of the ellipse reflects the minimum of the cost function. Based on this idea, as shown in Figure 4d, the 10 times of repeated fittings using 10 different contour lines give mean values of the minimum location of [1.023, 0.619] VIISR pixels with standard deviation of [0.003, 0.046] VIISR pixels. Considering the VIIRS pixel resolution as 388 × 371 m (along-scan by along-track) at nadir, the pair of [1.023, 0.619] can be converted to [397.0 m, 229.8 m]. Thus, these values can be interpreted as saying that, as revealed by this specific case, the CrIS FOV geolocation at nadir is estimated to be 397.0 m off along the VIIRS scan direction and 229.8 m off in the track direction when compared with VIIRS. However, CrIS geolocation accuracy should be evaluated through statistics with a large sample size rather than a simple case study, which is presented in section 5.
4 Sensitivity Test
4.1 Effects of Radiometric Discrepancy Between CrIS and VIIRS
 The CrIS-VIIRS BT differences are mostly dominated by imperfect spatial collocation between CrIS and VIIRS, but their radiometric discrepancy can also contribute a small part of the BT differences. First, radiance measurements from CrIS and VIIRS are separately calibrated based on their own onboard calibration targets. Consequently, their radiances are determined by each instrument's characteristics (for example, nonunity of blackbody emissivity and detector nonlinearity) as well as its calibration procedures. In addition, transformation from CrIS spectra to VIIRS band radiances may not be perfect. For example, the out-of-band spectral response is not considered because of the limited spectral coverage of CrIS (CrIS LWIR band 1 ends at 1095 cm−1 or 9.132 µm). While these factors can only result in CrIS-VIIRS BT difference on the order of 0.1 K, its effect on the geolocation assessment must be carefully studied to ensure that it does not bias the final results.
 Shown in Figure 5 are the contour plots for the same case as in Figure 4 but are separated as the standard deviation and mean of CrIS-VIIRS BT differences varying with shifted pixel number. To our best knowledge, the radiometric discrepancy between CrIS and VIIRS is a small systematic difference on the order of 0.1 K, which thus should be reflected by the mean of CrIS-VIIRS BT differences. On the other hand, since a very inhomogeneous scene is used, the spatial mismatch of CrIS and VIIRS should be dominated by the random errors, i.e., the standard deviation, in which the systematic difference between the two sensors is removed. Figure 5 clearly indicates that the standard deviation of CrIS-VIIRS BT shows the nearly identical pattern as the RMSE, whereas the contour from the mean is not sensitive to the shift of VIIRS pixels. Since we rely on spatial collocation to evaluate the geolocation accuracy of CrIS, it is under our expectation that the small radiometric discrepancy between CrIS and VIIRS has negligible effects on the geolocation assessment.
4.2 FOV-to-FOV Consistency
 As discussed in the Introduction, there are 3 × 3 detectors placed in the detector array. The parameters that characterize the detector positions are important not only for geolocation mapping but also for CrIS spectral calibration (L. Strow et al., submitted manuscript, 2013). After CrIS was launched, the positions of four side detectors and four corner ones relative to the central detector have been adjusted by a small amount in order to keep the consistent spectral calibration among FOVs. Therefore, it is important to check the FOV to FOV consistency for their geolocation consistency. Figure 6 gives the cost functions that are separated for different FOVs (the same case as in Figure 4), in which the locations of the minimum value are identified and listed. While the shapes of these cost functions are different from FOV to FOV, the detected minimum locations are generally consistent to each other, and the difference is within one VIIRS pixel. When we examine different cases, generally, the minimum locations are consistent to each other within 1 pixel (relative to the mean). On the other hand, the differences are randomly distributed and dependent on scenes. Apparent patterns cannot be easily identified. This indicates that these slight differences are mainly caused by the scene distribution in each FOV instead of possible geometric errors of detector position because systematic patterns that are related to geometric errors of detector position have not been found.
4.3 Effects of FOV Size
 When computing the FOV footprint, the CrIS FOV is treated as a 0.963°circle. This value is actually from CrIS engineering packets and also used for CrIS spectral calibration (L. Strow et al., submitted manuscript, 2013). However, in reality, the CrIS detectors have their own spatial response functions, namely, the spatial distribution of the contributions to the total radiance. The detector spatial response was measured during prelaunch testing. The FOV response widths were determined by performing three spot raster scans across the widest portion of each detector's response. The three spot raster scans were performed in both the cross-track and in-track directions. The response function is approximately a Gaussian distribution and is normalized by the peak value. A circle was then fitted to the 3%, 10%, 50%, and 70% response points obtained from the spot scans, and the response widths were reported from the diameters of the 3%, 10%, 50%, and 70% response circles. Shown in Figure 7 is the schematic diagram of the CrIS FOV spatial response, in which the data were obtained from the CrIS ATBD [JPSS Configuration Management Office, 2011]. The four different FOV sizes correspond to the four different spatial responses; 1.2380°, 1.1000°, 0.9420°, and 0.8735° equal 3%, 10%, 50%, and 70% of the peak response. Based on Figure 7, the FOV size of 0.963° actually corresponds to 44.7% of the peak response. Therefore, it is necessary to examine how the cost functions vary with different FOV sizes. Given in Figure 8 (the same case as in Figure 4), four FOV sizes including 1.1°, 0.963°, 0.942°, and 0.8735° are tested for the geolocation accuracy detection using the same CrIS granules. The results indicate that the minimum locations for different FOV sizes are almost identical while the differences are at a hundredth level. This suggests that the best collocation position between VIIRS and CrIS is not sensitive to the FOV size. Therefore, to be consistent with the CrIS spectral calibration, a value of 0.963° is used in this study.
4.4 Perturbation Tests at Nadir
 It is interesting to examine the ability of our proposed method to detect the geolocation accuracy of CrIS through a perturbation test. The question that we are trying to address is whether and how effectively the proposed method is able to capture the geolocation error, if there is an error in the geolocation data set. For this purpose, a series of perturbation tests are designed by intentionally adding systematic errors into the CrIS geolocation algorithm. The CrIS data sets with the perturbation of geolocation errors are regenerated, which are then examined using the VIIRS measurements to check whether the VIIRS-CrIS collocation method can detect the known perturbation errors. Note that the geolocation data produced by the original algorithm are used as the control run. The angles that we used for perturbation tests are the angles from spacecraft body frame (SBF) to Instrument Alignment Reference (IAR), including pitch, roll, and yaw angles [see Figure 48, JPSS Configuration Management Office, 2011]. The values of these angles are set as zero in CrIS engineering packets, which are used as the final step to compute the LOS vector relative to the spacecraft. Two experiments that examine the ability of the method to detect CrIS geolocation error at nadir are first performed. Only FOVs at nadir are used to collocate with VIIRS.
 The first experiment is to examine how well the method is able to detect geolocation errors in the track direction. It is well known that the perturbation of pitch angles will introduce in-track errors into geolocation data. In the sensitivity test, the pitch angle is gradually increased step by step by 0.0069° (0.1/830.0 rad) for 10 steps, which equals adding 100.0 m errors into the track direction. A scatterplot of perturbation distance and VIIRS-detected geolocation change in the along-track direction is shown in Figure 9. It clearly shows that the method can well capture the introduced in-track geolocation errors with the RMSE less than 10.0 m.
 The second experiment is to examine the ability of the method to detect geolocation in the scan direction. The perturbation of the roll angle will introduce geolocation errors in the scan direction, and the errors will grow with scan angles. Similar to the pitch angle perturbation, the roll angle is also increased step by step by 0.0069° for 10 steps. Figure 10 shows the scatterplot of perturbation distance and VIIRS-detected geolocation change in the scan track direction, indicating that the method can detect the perturbed in-scan geolocation errors with the RMSE of 34.0 m. As concluded by the two tests, the proposed method can well detect CrIS geolocation errors at nadir.
4.5 Perturbation Tests Off Nadir
 It is not enough to limit only nadir FOVs, and the method can be further extended to the off-nadir FOVs. The VIIRS detectors are rectangular, with the smaller dimension projecting along the scan. At nadir, three detector footprints are aggregated to form a single VIIRS “pixel”. Moving along the scan away from nadir, the detector footprints become larger both along track and along scan, due to geometric effects and the curvature of the Earth. The effects are much larger along scan. At around 32° in scan angle, the aggregation scheme is changed from 3:1 to 2:1. A similar switch from 2:1 to 1:1 aggregation occurs at 48°. The VIIRS scan consequently exhibits a pixel growth factor of only 2 both along track and along scan (0.8 km × 0.8 km at 56.063° scan angle), compared with a growth factor of 6 along scan without the use of the aggregation scheme [JPSS Configuration Management Office, 2012b]. This feature is clearly demonstrated in Figure 11, showing the VIIRS pixel size from I-bands varying with scan angles. In addition, a bow tie deletion scheme is also applied for VIIRS data, resulting in some of the samples in the overlap area to be excluded from the data. Specifically, 0 pixels are deleted at scan angles less than 31.59°, 2 pixels deleted at scan angles from 31.59 to 44.68°, and 4 pixels deleted at scan angles greater than 44.68°. Therefore, it is a challenge to extend our method to scan angles above 30°. Because of this, only FOVs from FOR 7 to FOR 24 (see red diamonds in Figure 11) within the 30° scan angle are used for off-nadir geolocation accuracy evaluation. Additionally, the corresponding VIIRS pixel sizes at these locations are saved in order to convert pixel shift to the distance.
 In the sensitivity test, the yaw angle from SBF to IAR is changed from the original value of 0.0 to 1.0/830.0 rad. Because of the yaw angle change, antisymmetric errors are introduced in the track direction. As shown by the black line in Figure 12, negative in-track biases slowly decrease from FORs 1 to 15 and then are close to zero at nadir. After that, in-track biases are changed to the positive values and increase from FORs 15 to 30. Only the measurements from FOR 7 to FOR 24 are used to examine whether the method can detect this antisymmetric pattern. The results are indicated by the black squares in Figure 12. Basically, the proposed method captures the antisymmetric pattern with the RMSE of 64 m, suggesting that it can also evaluate the geolocation errors along scan angles within ±30° scan angles.
4.6 VIIRS Geolocation Accuracy
 The geolocation from VIIRS I-bands is treated as a reference in this study. The accuracy of VIIRS geolocation has been comprehensively evaluated through the correlation between the GCP data sets from Landsat and the measurements from VIIRS band 1 [Wolfe et al., 2013]. Excluding some anomalies, the mean errors of VIIRS geolocation is about 26 m in the track direction and 13 m in the scan direction, and the RMSE is about 78 m and 60 m in the track and scan directions, respectively. It should be noted that there are offsets of band I5 from band I1 for band-to-band registration (6% of I-band horizontal scan interval), which are small and thus do not affect the overall assessment of CrIS geolocation [Wolfe et al., 2013]. Overall, compared to CrIS, the VIIRS geolocation errors are so small and thus can be neglected in our study.
5 Results and Discussion
5.1 Geolocation Accuracy Evaluations at Nadir
 Using the method discussed in section 3, a system has been set up to automatically track CrIS geolocation accuracy at nadir FOVs on a daily basis since 10 October 2012. Specifically, 14 CrIS granules with cloudy scenes over tropical oceans are arbitrarily selected in each day to detect the geolocation accuracy of CrIS. Figure 13 shows the CrIS SDR geolocation accuracy time series for nadir FOVs assessed by VIIRS, which are separated in the scan and track directions. It has been extended to 13 June 2013. In general, it clearly tracks the variation of the CrIS SDR geolocation accuracy caused by software updates and instrument changes (indicated by the red vertical dashed lines in Figure 13).
 Before 16 October 2012, the CrIS SDR suffered the geolocation errors of ~3.5 km in scan direction and ~2.7 km in the track direction caused by the CrIS geolocation software. This was identified when we first applied the method to the CrIS SDR in April 2012. Efforts were made by the authors to investigate the root causes of this geolocation error. It turned out that, the rotation matrix from IAR to Scene Selection Mirror mounting feet Frame (SSMF) was mistakenly applied two times in the IDPS software. After the new IDPS processing software (Version MX6.5) was released on 16 October 2012, in which the code bug was fixed in the geolocation module, the time series in the scan direction is close to the zero line, and the one in the track direction is less than 0.5 km.
 After 23 October 2012, the new engineering packet V35 was uploaded. Yaw and pitch angles from the interferometer boresight to SSMF were set to zero from the original values of (0.000526 and −0.000172) in radian unit. This update was suggested by the instrument vendor (ITT Exelis) because the misalignment from SSMF to the interferometer boresight has been considered in a different rotation matrix along the different scan positions. After this change, the geolocation error in the track direction was slightly reduced while the one in the scan direction was increased by 0.3–0.4 km.
 From 22 November to 11 December 2012, the CrIS geolocation error in the scan direction jumped up with ~0.3 km, but the one in the track direction did not change, which was caused by the artifact of geolocation error from VIIRS [Wolfe et al., 2013]. On 22 November 2012 at 1632 UTC, Suomi NPP VIIRS entered petulant mode. When the power was restored at 2207 UTC, the scan control electronics (SCE) was switched from side B to side A. At that time, geolocation look-up tables (LUTs) containing incorrect parameters for SCE side A introduced a nadir geolocation bias of ~325 m in the scan direction. Corrected LUTs were applied starting 11 December 2012 (data day 346) at 1918 UTC, and the geolocation products' accuracy returned to normal. The time series accurately captured this event (also shown in Figure 14).
 The results after 23 October 2012 are summarized in Figure 14, where the points caused by the VIIRS geolocation errors are extracted and shown in red colors. Excluding those caused by the VIIRS geolocation errors, the two histograms in the track and scan directions are given. In the scan direction, the geolocation accuracy is 0.347 ± 0.051 km (1σ) while it is 0.219 ± 0.073 km in the track direction.
 Figure 15 gives the CrIS FOV sizes varying with the FOR index in the track and scan directions. It shows that CrIS FOV size exponentially increase in the scan direction with scan angles. In other words, the CrIS FOV size at the end of the scan is 3.47 times in the scan direction and 1.74 times in the track direction compared to the nadir FOV. Given the designed specification of 1.5 km geolocation accuracy for all scan angles, it implies that the geolocation performance at nadir must be less than 0.433 km in the scan direction and 0.862 km in the track direction. Based on this error model, the geolocation accuracy at nadir that we found is smaller than the above values.
5.2 Geolocation Accuracy Off Nadir
 As discussed in section 4.5, the geolocation accuracy along scan angles can be directly evaluated within 30° from FORs 7 to 24. Similar to the geolocation assessment at nadir, a system is also set up to track the geolocation accuracy off nadir, but it only uses central FOV from FORs 7 to 24. The data from 10 January to 30 May 2013 have been accumulated. The results are summarized in Figure 16, separately in the track and scan directions. It is necessary to note that each point in Figure 16 actually represents the mean and standard deviations from an ensemble of cases.
 Based on Figure 16, asymmetric bias patterns can be found. Specifically, in the scan direction, the detected geolocation biases are close to zero from FOR 7 to FOR 15 while they increase from FOR 16 to 1.321 km at FOR 24. On the other hand, in the track direction, the bias is about −0.322 km at FOR 7, and it increases to 0.633 km at FOR 24. This pattern is similar to the one shown in Figure 12, a sensitivity test of the yaw angle perturbation, although the absolute values are larger in FORs 16–24 than those in FOR 7–15. This pattern may be caused by the fact that the yaw-dependent antisymmetry error is mixed with the pitch and roll errors (shown in Figure 14). It is possible that yaw-dependent antisymmetry pattern (similar to Figure 12) may show up once pitch and roll errors are first corrected. The results indicate that residual geolocation biases exist along the scan angle, and further adjustment is needed.
5.3 Cross Validation With Other Methods
 Two alternative methods for determining geolocation error were studied. These methods compared the measured positions of coastline positions determined from the CrIS radiance data to the coastlines listed in the GSHHS coastline database [Wessel and Smith, 1996]. The first method fits a cubic polynomial to four CrIS FOVs that cross a coastline. The geolocation error is then taken as a vector from the inflection point of the polynomial to the nearest point on the GSHHS coastline. In the second method, the radiance at each CrIS FOV is synthesized using a simplified land-sea model and compared to the CrIS measured radiances [Bennartz, 1999]. The modeled coastline is shifted back and forth in latitude and longitude directions until the best match with the CrIS measured radiances is obtained.
 The inflection point of a polynomial method has the advantage of being straightforward but did not work well for CrIS due to nonuniform spatial sampling as was mentioned earlier. The CrIS detector focal plane has a 3 × 3 set of detector elements or FOVs for each band that is scanned back and forth to give a cross-track scan. In order to get four points for the fitting polynomial, it is always necessary to pick points from two different scan positions. Due to the design of the CrIS optics and scene selection mirror as the sensor scans away from nadir, the 3 × 3 ground footprints rotate. This rotation causes the relative spacing between FOVs in different FORs to change with off-nadir angle. A sensitivity study showed that the accuracy of the inflection point method degrades when nonuniform spatial sampling is present. An additional complication with this method is that when a geolocation error exists, the distance to the closest shoreline does not necessary represent the true geolocation error. Shoreline geometry is often chaotic, and a vector to the nearest coastline is often in the direction of the nearest outcropping of land instead of in the direction of the true error. This behavior tends to underestimate the geolocation error.
 Fitting a model of the coastline radiance to the CrIS radiance is more computationally intensive than the inflection point method but gave more consistent results. This method is not adversely affected by nonuniform spatial sampling or the complexity of shoreline geometry. It also has the advantage of not being dependent on the geolocation of VIIRS but has the disadvantages of being adversely affected by cloud cover and low land-sea radiance contrast.
 This simplified coastline model calculates a radiance for each CrIS FOV as indicated in equation (8):
where Rland and Rsea are the average radiance of the land and sea, respectively, found from averaging the radiances from FOVs that are well away from the shoreline. The land-sea fraction (lfrac) is calculated by integrating the CrIS FOV footprints across a digital map of the coastline as will be explained later. A standard chi-square (2) residual function is created by summing the residuals for each FOV as indicated in equation (9):
where RCrIS_FOV is the measured radiance for each FOV. The digital map is shifted in the north-south and east-west directions until the chi-square is minimized. After the geolocation error has been determined in north-south and east-west coordinates, it is then rotated into in-track and cross-track errors.
 As part of finding the land-sea fraction, a model of the CrIS footprints is required. For this model, several simplifications were performed with respect to the method described in section 3.2. The shape of the Earth is not a sphere but, instead, an ellipsoid bulging at the equator. However, within the area of a single FOV footprint, the Earth can be approximated well as a sphere. The IDPS software already calculates the intersection of the line-of-sight vector from the spacecraft to the center of each footprint on the geodetic surface. A spherical Earth was then assumed for calculating the rest of the footprint assuming a circular CrIS FOV of 0.963°.
 For computational purposes, a two-dimenstional grid was created centered on each CrIS FOV footprint. The grid had a 0.5 km sample space and was aligned in the cardinal directions. The CrIS FOV footprint was then projected onto this grid by setting each grid point within the footprint a value of one and the values outside, a value of zero. A Gaussian filter with a half width of 1 km was then convolved with the gridded FOV footprint to reduce aliasing. A similar procedure was performed for the coastline map. Grid points on land were given a value of one, and those on sea were given a value of zero. The coastline map was also Gaussian filtered. The product of the gridded CrIS footprint and the gridded coastline map properly normalized gives the land fraction.
 Due to the necessity of finding cloud-free coastlines and maintaining near-constant conditions for the coastline model, the continuous regions used is this study were quite small, typically on the order of 400 × 400 km. Even though the standard deviation between runs was about 1.3 km, the method was clearly able to detect the change in geolocation that occurred due to the IDPS software update that occurred on 16 October 2012 (see Figure 13). Results from this costal modeling method are consistent with the results from the VIIRS cross comparison method.
5.4 Issues and Future Work
 The assessments indicate that the CrIS geolocation accuracy is 0.344 ± 0.056 km in the scan direction and 0.224 ± 0.080 km in the track direction at nadir. More important, Figure 13 clearly shows that the geolocation error in the scan direction jumped up with 0.3–0.4 km after the adjustment of yaw and pitch angles from interferometer boresight to SSMF. It indicates that there is still a room to adjust these angles to further improve geolocation accuracy at nadir. Furthermore, asymmetric bias patterns that are revealed in Figure 16 could be further reduced through additional adjustment, which is now being investigated by the authors.
 Just as important as spectral and radiometric calibration, the geometric calibration is also one of the requisites for the CrIS SDR. In this study, an intercalibration method of using spatially collocated VIIRS measurements from I5 band is used to evaluate the geolocation performance of the CrIS SDR. The major steps include (1) CrIS spectral integration with VIIRS SRFs, (2) accurate computation of the CrIS FOV ground footprints, (3) spatial collocation of VIIRS pixels with CrIS, (4) definition of the cost function by shifting the VIIRS image in the track and scan directions, and (5) detection of CrIS geolocation accuracy by statistically indentifying the minimum position of the cost function (the best collocation position of VIIRS and CrIS measurements). The best collocated position of VIIRS and CrIS measurements is then used to estimate the CrIS geolocation accuracy. A series of sensitivity tests have been carried out regarding to the radiometric discrepancy, FOV to FOV consistency, FOV size, and the perturbation of pitch, roll, and yaw angles. The results indicate that the method is able to detect possible geolocation errors of the CrIS SDR within the 30° scan angle.
 We applied this method to evaluate the geolocation performance of the CrIS SDR. The geolocation errors that were caused by the software coding errors were successfully identified by this method. After this error was corrected and the engineer packets V35 were released, the geolocation accuracy is 0.347 ± 0.051 km (1σ) in the scan direction and 0.219 ± 0.073 km in the track direction at nadir. Asymmetric bias patterns are found along the scan angles within 30° scan angle in the track and scan directions. In the scan direction, the detected geolocation biases are close to zero from FOR 7 to FOR 15, while they increase from FOR 16 and reach 1.321 km at FOR 24. In the track direction, an antisymmetric pattern is revealed. The bias is −0.322 km at FOR 7 and increases to 0.633 km at FOR 24. Angle adjustment is being studied to further improve the CrIS geolocation accuracy in the future.
 This study is funded by the NOAA JPSS Program Office. Likun Wang is also partially supported by NOAA grant NA09NES4400006 (Cooperative Institute for Climate and Satellites (CICS)) at the University of Maryland/ESSIC. The manuscript contents are solely the opinions of the authors and do not constitute a statement of policy, decision, or position on behalf of NOAA or the U.S. government.