VOLUME 21 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY APRIL 2004

Predicting Simultaneous Nadir Overpasses among Polar-Orbiting Meteorological Satellites for the Intersatellite Calibration of Radiometers

CHANGYONG CAO AND MICHAEL WEINREB NOAA/NESDIS/Of®ce of Research and Applications, Camp Springs, Maryland

HUI XU I.M. Systems Group, Kensington, Maryland

(Manuscript received 3 June 2003, in ®nal form 8 September 2003)

ABSTRACT A method for accurately predicting simultaneous nadir overpasses (SNOs) among different sun-synchronous polar-orbiting meteorological satellites is presented for intersatellite radiometer calibration. At each SNO, the radiometers on the two satellites view the earth and its atmosphere at nadir within a few seconds of each other, providing an ideal scenario for the intercalibration of radiometers. The basic mechanism and frequency of occurrences of such events are analyzed. Prediction using the Simpli®ed General Perturbations No. 4 (SGP4), an orbital model, is presented, and examples of SNOs among the NOAA-16, NOAA-17, Terra, and Aqua satellites are provided. Intersatellite calibration using this approach has the potential for achieving the calibration consistency and traceability required for long-term climate studies.

1. Introduction infrared-radiometer observations, which vary signi®- cantly with these parameters. As a result, uncertainties There is a need to intercalibrate the polar-orbiting in the intersatellite calibration are greatly reduced. Our radiometers on different satellites to achieve the con- studies show that this method is useful for the on- sistency and traceability required for long-term climate veri®cation of instrument performance for newly studies with the more than 20 yr of National Oceanic launched radiometers, as well as retrospective analyses and Atmospheric Administration (NOAA) satellite data. of historical data for constructing time series for climate In addition, the calibration of current operational radi- studies. The SNOs for polar-orbiting satellites occur ometers should be linked to those of the next-generation only near the earth's polar regions, which limits the meteorological satellites such as those of the National intercalibration to polar conditions. However, based on Polar-Orbiting Operational Environmental Satellite Sys- the principles discussed here, it is possible that in the tem (NPOESS). Many intercalibration studies have been done in the past. But most of them are limited to match- future, transfer radiometers identical to those on the up datasets acquired from different satellites with dis- polar orbiters can be launched into low-inclination similar instruments and that may have different obser- to provide better opportunities for calibration in the low- vation times and viewing geometries, and in many cases er latitudes with a variety of surfaces and atmospheres. rely on radiative transfer calculations to account for the observation differences. These restrictions introduce un- 2. Earth-orbiting satellites and orbital certainties in the intercomparisons. intersections In this study, we present a method for accurately pre- dicting the simultaneous nadir overpasses (SNOs) of The intersection of the orbital plane of an earth-or- two earth-orbiting satellites. At each SNO, radiometers biting satellite with the surface of the earth is a great from both satellites view the same place at the same circle. Every great circle of a sphere intersects all other time at nadir, thus eliminating uncertainties associated great circles of the sphere in exactly two points. There- with differences of atmospheric path, viewing geometry, fore, it is expected that the orbits of every pair of earth- and observation time. This is especially important for orbiting satellites have two points of intersection. In the case of two polar-orbiting satellites, the two intersec- Corresponding author address: Dr. Changyong Cao, NOAA/NES- tions always occur near the North and South Poles (typ- DIS/ORA, 5200 Auth Road, Camp Springs, MD 20746. ically in the ϩ70Њ to ϩ80Њ and Ϫ70Њ to Ϫ80Њ latitude E-mail: [email protected] zones). Although each satellite passes each intersection

᭧ 2004 American Meteorological Society 537

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC 538 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 21

TABLE 1. Time between successive simultaneous nadir overpasses. Note that orbital periods are derived from two-line-elements with an of 27 Mar 2003. Time between successive SNOs (days) Perigee Apogee (km) (km) (min) NOAA-17 NOAA-16 NOAA-15 NOAA-14 Aqua NOAA-17 807 822 101.1722 NOAA-16 845 861 101.9885 8.78 NOAA-15 806 821 101.1050 105.71 8.11 NOAA-14 843 858 101.8884 10.00 72.10 9.13 Aqua 699 705 98.8293 2.96 2.21 3.05 2.28 Terra 701 703 98.8259 2.96 2.21 3.04 2.28 N/A once an orbit, for most orbits the two satellites do not ellites at inclination angles of 98.7Њ±98.8Њ so that the pass the same intersection at the same time. In fact, if orbital planes will precess eastward about 0.986Њ dayϪ1 both satellites are at the same altitude, they will have to keep pace with the earth's revolution around the sun the same orbital period, and they should never pass the (Rao et al. 1990). Since 1978, NOAA has successfully same orbital intersection at the same time (otherwise launched 11 polar-orbiting satellites (NOAA-6 to NOAA- they will collide). 17), with an average usable life of approximately 5 yr Kepler's third law implies that the higher the altitude in orbit for each. Since an AM satellite is generally at of a satellite, the longer its orbital period. Satellites at a lower altitude than the PM satellite, the AM satellite different altitudes have different angular velocities and has a shorter orbital period. For example, the nominal therefore different orbital periods. It follows then that orbital period for the AM satellite NOAA-17 is 101 min, as time goes by, the lower-altitude satellite will even- compared to 102 min for the PM satellite NOAA-16. tually catch up with the high-altitude satellite at the Therefore, NOAA-17 and -16 will pass the orbital in- orbital intersections, thus creating an SNO. When this tersections simultaneously with regularity. occurs, the radiometers from both satellites view the In general, assuming that two sun-synchronous polar- earth and its atmosphere at the same place and same orbiting satellites, S1 and S2, operate at altitudes h1 and time but from different altitudes. The difference in sat- h 2 (h 2 Ͼ h1) with orbital periods of ␶1 and ␶ 2 (␶2 Ͼ ␶1), ellite altitudes does not have signi®cant impact on the an SNO between them occurs when the orbital-period radiance comparison from the two radiometers on these time difference (␶ 2 Ϫ ␶1) accumulates over time and satellites, as long as the areas within the ®eld of view eventually amounts to ␶ 2. In other words, S1, having a are relatively uniform, because radiance is not a function higher velocity than S 2, eventually catches up with S 2. of the distance of measurement. Admittedly, the pixel The number of orbits required for S1 to catch up with sizes are slightly different due to the altitude differences, S 2 is ␶ 2/(␶ 2 Ϫ ␶1). Converting number of orbits to num- so when the temperature distribution within the ®eld of ber of days, we have the following formula for esti- view is not uniform, the larger pixels will have a slightly mating the SNO occurrences between two satellites: different average temperature from that of the smaller pixels. However, given a large number of match-up pix- T ϭ [␶22/(␶ Ϫ ␶ 1)] 1/ f 1, (1) els, the net effect of different pixel size is probably random and acts to increase the noise in the comparison. where T is time (days) between successive SNOs, ␶1 is This noise can be further reduced by averaging pixels. the orbital period (min) for S1 at h1, ␶ 2 is the orbital Finally, path radiance difference is negligible in the in- period (min) for S 2 at h 2, ␶2 Ͼ ␶1, h 2 Ͼ h1, and f 1 is tercomparison because there is no atmosphere between the number of orbits per day for S1 ( f 1 ϭ 1440 (min Ϫ1 the two satellites at different altitudes. day )/␶1). NOAA's Polar Operational Environmental Satellites For example, the time between successive SNOs for (POES) program typically employs two spacecraft in the NOAA-17 and -16 satellites is approximately 8 days. nearly circular sun-synchronous orbits at nominal alti- Similarly, NOAA-17 and Terra meet at their orbital in- tudes of 833 and 870 km. With their orbital planes ap- tersections about every 3 days. Table 1 shows the time proximately 90Њ apart, one has a 0730 or 1030 (for between successive SNOs for some selected polar-or- NOAA-17) local equator-crossing time in descending biting sun-synchronous meteorological satellites. It is node and the other a 1340 local equator-crossing time worth noting that even two PM satellites, such as NOAA- in ascending node. They are referred to as AM (morn- 14 and -16, have SNOs, although they occur much less ing) and PM (afternoon) satellites. A sun-synchronous frequently (every 72 days) because of their similar al- orbit ensures that the equator crossings always occur at titudes. the same local time. This is desirable as it provides The discussion above provides a basic understanding consistent scene illuminationÐa common mission re- of the mechanism of SNOs for earth-orbiting satellites. quirement for many meteorological and terrestrial ap- However, the accurate prediction of such events, in- plications. Such orbits are achieved by placing the sat- cluding the time, location, and nadir distance, cannot

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC APRIL 2004 CAO ET AL. 539 be done without using orbital perturbation models, 2) Input the TLE of the ®rst satellite to the SGP4 model which is discussed next. and use its epoch as the starting date of prediction. 3) Given the time step (typically 1 s) and the time pe- riod of the prediction (in most cases less than a 3. Predicting SNOs using the Simpli®ed General week), run SGP4 at each time step to generate the Perturbations No. 4 dates, times, and locations of the satellite in latitude and longitude, and store them in an array. The 1-s Accurate prediction of the location of an earth-or- time step is preferred, to get a more precise location biting satellite at a given time requires the use of orbital of the SNO. This corresponds to a ground step size prediction models and appropriate input parameters. The of about 7 km for most polar-orbiting satellites. Simpli®ed General Perturbations No. 4 (SGP4) (Lane 4) Repeat steps 2 and 3 for the second satellite, using and Cranford 1969; Hoots and Roehrich 1988), devel- the same epoch and time step. This creates a list of oped and used by the North American Aerospace De- coordinates that match those for the ®rst satellite in fense Command (NORAD) for tracking all satellites in time. space, is a reasonably accurate and popular model avail- 5) Step through the latitude/longitude pairs in time se- able to the general public. The input to the SGP4 model quence, and compute the earth (ground) distance be- is contained in a two-line-element (TLE) set, which has tween the nadir points of the two satellites during information about the satellite and its orbit, such as the prediction period using the great circle distance satellite number, orbit inclination, eccentricity, argu- formula ment of perigee, derivatives of the , Ϫ1 BSTAR drag, , mean motion, and others. D ϭ R cos [sinl12sinl With a TLE, the SGP4 can predict the position and ϩ cosl cosl cos(m Ϫ m )], (2) velocity of the associated satellite for a given date and 12 2 1 time. TLE sets are released daily by NORAD for all where D is the ground distance (km) between the satellites, including all NOAA satellites since NOAA-6. nadir points of the two satellites; R is the mean earth The details of the SGP4 algorithm and the TLE (avail- radius (6378 km); l1 and l 2 are the latitudes (rad) of able online at http://celestrak.com) are beyond the scope the ®rst and second satellites, respectively; and m1 of this paper. This model is suf®ciently accurate for and m 2 are the longitudes (rad) of the ®rst and second predicting the SNOs, for which the required accuracy satellites, respectively. is on the order of a few kilometers, or within a few Equation (2) is a simpli®ed formula for estimating the pixels for most of NOAA's radiometers. ground distance, assuming a perfectly round earth. The To predict the SNOs of two earth-orbiting satellites, distance D at each time step shows how close the nadir the following algorithm is used. points of these two satellites are on the ground. A se- quential list of the distance D over a prediction period 1) Prepare the matching TLE pair for the two satellites; of many orbits will show that the nadir points of the since the precise satellite orbit is very dynamic, it two satellites approach or depart from each other reg- is important to use the TLE pair with epochs that ularly with a repeating cycle of T days determined by are closest to the time of prediction to avoid errors. Eq. (1). Also, ideally the TLEs for the two satellites should An SNO occurs when D reaches a minimum (Dmin) have the same epoch date. TLEs are usually released within a cycle such that D is smaller than a preset on a daily basis for all satellites; therefore, in most min threshold. A perfect SNO is one for which Dmin ϭ 0. cases, for a given pair of TLEs, the prediction is only However, in reality this does not occur often enough for necessary for a 1-day periodÐuntil the TLE pair for the purpose of intercalibrating radiometers. The number the next day becomes available. To predict the SNOs of SNOs will increase for a given prediction period if for an entire year, a series of TLE pairs must be the threshold for Dmin is increased, which means allow- prepared. ing a longer difference between the times that the two There are situations in which predictions for the next satellites pass the same orbital intersection. But if Dmin few days may be needed based on today's TLEs. For is too large (e.g.,Ͼ7000 km), it would mean that the example, one may need to schedule Advanced Very second satellite may have not passed the orbital inter- High Resolution Radiometer (AVHRR) local area section point until more than 15 min after the ®rst sat- coverage (LAC) data acquisitions, which may re- ellite did, and thus this may not qualify as a useful SNO. quire a 2-week lead time. In such cases, it should Therefore, there is a trade-off between the number of

be noted that the further in time from the TLE epoch, SNOs and the acceptable threshold for Dmin, which may the less accurate the prediction will become. Based vary depending on the speci®c requirements for a par- on our experience, forward prediction for a week is ticular intercalibration.

reasonably accurate, but errors may become unac- From a practical point of view, the threshold for Dmin ceptably large beyond a 2-week period if the TLE can be derived from the requirements on a time window. is not updated. A 30-s time window is generally acceptable for inter-

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC 540 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 21

FIG. 1. Simultaneous (1 s) nadir overpass (SNO) between NOAA-16 and Terra. calibrating radiometers for meteorological applications. the cost of a reduced number of SNOs. It is worth noting This is based on the assumption that, within this time that by using the 30-s time window we were able to period, clouds have not moved and the scene temper- ®nd SNOs among meteorological satellites with a fre- ature has not changed signi®cantly within the ®eld of quency of occurrence that is consistent with the pre- view of the radiometers. This 30 s in time corresponds dictions produced by Eq. (1). to a separation of approximately 210 km on the ground, based on a satellite ground speed of ϳ7kmsϪ1 along nadir. However, the actual distance between the nadir 4. Examples of predicted SNOs points of the two satellites is also affected by the angle To illustrate this procedure, we use an example SNO between the two orbital planes, which varies between between Terra (S1) and NOAA-16 (S2) on 21 March different satellites. The maximum nadir distance [thus 2003 (Fig. 1). In this case, a time step of 1 s was used. the threshold for Dmin in Eq. (2)] occurs for two satellites With TLEs for each satellite from 20 March 2003, a moving in opposite directions, for which the nadir dis- second-by-second sequence of the positions of the two tance should be no greater than 420 km for a 30-s sep- satellites and the nadir distance between them is pro- aration. Here the distance threshold for Dmin should be duced (see Table 2). For brevity only records with nadir interpreted as the ground distance that the ®rst satellite distances of less than 40 km are included in the table. traveled past the orbital intersection point by the time Clearly, these two satellites approached each other start- the second satellite reached that point. However, it ing at 2345:01 UTC on 21 March 2003. Three seconds should be kept in mind, that, whatever the separation later, at 2345:04 UTC, their nadir distance reached a in time, the intercomparisons will involve data from the minimum (Dmin ϭ 3 km), which is a very good SNO same location from both satellites; the use of Dmin is for intersatellite radiometer calibration. Then they only a device for ®nding the near-simultaneous nadir moved away from each other. Based on the prediction, overpasses. A smaller time window (Ͻ30 s) may be satellite data can be found and downloaded from the needed for some applications for better simultaneity at archive. It should be noted that the predictions are only used

TABLE 2. Satellite positions and nadir distance between Terra and for identifying the satellite data in the archive. As long NOAA-16 on 21 Mar 2003. as the correct dataset can be identi®ed based on the prediction, small errors in location and distance are tol- Nadir Time S lat/lon S lat/lon distance (km) erable because after the satellite data are acquired, the 2 1 precise point of orbital intersection can be found using 2345:01 UTC (71.1Њ, 186.6Њ) (71.4Њ, 186.6Њ) 33 the nadir pixel location embedded in the satellite data. 2345:02 UTC (71.2Њ, 186.5Њ) (71.3Њ, 186.5Њ) 21 2345:03 UTC (71.2Њ, 186.4Њ) (71.3Њ, 186.4Њ) 10 A pixel-by-pixel match between the two datasets can 2345:04 UTC (71.3Њ, 186.4Њ) (71.2Њ, 186.3Њ) 3 be done using the latitude/longitude information for 2345:05 UTC (71.3Њ, 186.3Њ) (71.2Њ, 186.2Њ) 14 each pixel, and the precise time difference for each pixel 2345:06 UTC (71.4Њ, 186.2Њ) (71.1Њ, 186.1Њ) 26 can also be determined. 2345:07 UTC (71.4Њ, 186.1Њ) (71.1Њ, 186.0Њ) 38 The following are examples of predictions (Table 3)

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC APRIL 2004 CAO ET AL. 541

TABLE 3. SNO examples for NOAA-16 and -17, Terra, and Aqua (TLE epoch: 16 Mar 2003). Date Time (UTC) Lat/lon Lat/lon Nadir distance (km) NOAA-16 vs NOAA-17 24 Mar 2003 1117:00 (72.3Њ, 11.5Њ) (72.5Њ, 12.9Њ) 54 2 Apr 2003 0701:30 (Ϫ72.1Њ, 255.8Њ) (Ϫ71.7Њ, 255.2Њ) 52 NOAA-16 vs Terra 17 Mar 2003 1327:00 (Ϫ70.7Њ, 161.7Њ) (Ϫ71.3Њ, 161.0Њ) 75 19 Mar 2003 1811:00 (Ϫ72.5Њ, 87.5Њ) (Ϫ72.3Њ, 91.6Њ) 139 21 Mar 2003 2345:00 (71.0Њ, 186.7Њ) (71.5Њ, 186.6Њ) 46 24 Mar 2003 0519:00 (Ϫ69.9Њ, 285.0Њ) (Ϫ70.7Њ, 282.0Њ) 143 26 Mar 2003 1003:00 (Ϫ71.8Њ, 211.0Њ) (Ϫ71.6Њ, 212.4Њ) 50 28 Mar 2003 1537:00 (70.2Њ, 310.1Њ) (70.7Њ, 307.5Њ) 110 30 Mar 2003 2021:00 (72.1Њ, 236.0Њ) (71.6Њ, 237.8Њ) 82 NOAA-17 vs Terra 18 Mar 2003 0414:00 (Ϫ80.1Њ, 330.9Њ) (Ϫ79.8Њ, 326.9Њ) 84 21 Mar 2003 0307:00 (Ϫ77.1Њ, 328.2Њ) (Ϫ77.4Њ, 330.8Њ) 72 24 Mar 2003 0245:30 (80.5Њ, 224.9Њ) (81.8Њ, 214.0Њ) 232 27 Mar 2003 0139:00 (80.8Њ, 200.0Њ) (80.8Њ, 195.1Њ) 87 NOAA-17 vs Aqua 18 Mar 2003 1334:30 (70.1Њ, 334.3Њ) (69.7Њ, 336.5Њ) 94 21 Mar 2003 1316:30 (Ϫ70.9Њ, 160.1Њ) (Ϫ72.1Њ, 157.5Њ) 158 24 Mar 2003 1208:00 (Ϫ71.3Њ, 177.9Њ) (Ϫ71.0Њ, 176.4Њ) 65 27 Mar 2003 1100:00 (Ϫ70.1Њ, 193.1Њ) (Ϫ71.6Њ, 192.4Њ) 169 30 Mar 2003 0951:30 (Ϫ70.5Њ, 210.8Њ) (Ϫ70.7Њ, 210.9Њ) 24 using this algorithm for SNOs among the latest NOAA, In previous studies, we have used the SNO in the sum- Terra, and Aqua satellites in mid-March 2003, with a mer of 2002 for the intercalibration of the longwave TLE epoch of 16 March 2003. infrared channels of AVHRR and the Moderate Reso- lution Imaging Spectroradiometer (MODIS) (Cao and a. NOAA-16 (PM) versus NOAA-17 (AM) Heidinger 2002; Heidinger et al. 2002). The results in Table 3 con®rm our earlier calculation that SNOs occur about every 8 days between NOAA- c. NOAA-17 (AM) versus Terra (AM) 16 and -17. It is also shown that SNOs can occur in It is clear from Tables 1 and 3 that two AM satellites both the North and South Pole regions, and both may also have SNOs if they are at different altitudes. In this be used for the intercalibration of radiometers. However, case, they occur about every 3 days. The frequent oc- there are signi®cant differences in the land cover and currence of SNOs between NOAA and MODIS-carrying atmosphere between these two regions, which may af- satellites is very fortunate. Establishing a long record fect calibration. In the Ϫ70Њ to Ϫ80Њ latitude zone, the of intersatellite calibration at the SNOs may provide the land cover is dominated by ice and snow all year round. basis for the calibration link between AVHRR and There may not be any water surface even during the MODIS, as well as the future Visible/Infrared Imager/ summer months. In contrast, for the ϩ70Њ to ϩ80Њ lat- Radiometer Suite (VIIRS) for NPOESS, in order to meet itude zone, the ice retreats in the summer and leaves the stringent calibration requirements for climate stud- some water surfaces in the Arctic Ocean. Water surfaces ies. are preferred calibration targets, especially for sea sur- face temperature, because of their relative spatial uni- formity, thermal inertia, and low re¯ectance. In addition, d. NOAA-17 (AM) versus Aqua (PM) water provides a good dynamic range for the calibration Both NOAA-17 and Aqua were launched in the sum- of the visible and near-infrared channels of AVHRR. mer of 2002. Aqua carries the Atmospheric Infrared Finally, the sun elevation angle is the highest in the Sounder (AIRS), a hyperspectral thermal infrared ra- summer months for the North Pole region, providing diometer for meteorological applications, and provides suf®cient solar illumination for calibrating these chan- many new opportunities for intersatellite calibration of nels. Therefore, the best calibration targets for the ap- sounders. We believe that the approach presented in this proach described in this paper may be found in the North paper is especially useful for infrared sounders, because Pole summer. the relatively spatially uniform upper atmosphere pro- vides a suitable target for intersatellite calibration. Also, b. NOAA-16 (PM) versus Terra (AM) collaborative studies between NOAA and National The SNOs between NOAA-16 and Terra occur every Aeronautics and Space Administration (NASA) scien- 2 days because of the large difference in their altitudes. tists are underway using AVHRR/NOAA-17 as a transfer

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC 542 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 21 radiometer to evaluate the calibration consistency be- ometers on both satellites view the earth and its at- tween the MODIS on Terra and that on Aqua. mosphere at nadir at the same time, providing an ideal At the NOAA/National Environmental Satellite, Data, scenario for the intercalibration of radiometers aboard and Information Service (NESDIS)/Of®ce of Research the two satellites. All earth-orbiting satellites at different and Applications, SNOs between several pairs of me- altitudes have SNOs regularly and, therefore, can in teorological satellites are predicted automatically on a theory be intercalibrated with this method. Prediction weekly basis and can be found online at http://orbit-net. of SNOs with the Simpli®ed General Perturbations No. nesdis.noaa.gov/crad/sit/intercal. Also, historical SNOs 4 (SGP4) is presented, and examples of SNOs among among NOAA satellites are being generated for the ret- the NOAA, Terra, and Aqua satellites are provided. rospective intersatellite calibration of sounders and im- Intersatellite calibration using this approach has the po- agers beginning in 1980. tential for achieving the calibration consistency and To ensure that the predicted times and locations of traceability required for long-term climate studies. the SNOs are accurate, we have performed validations with the predicted SNOs. First, TLEs used in our pre- Acknowledgments. The authors wish to thank Drs. dictions were fed into Satellite ToolKit (Marshall and Istvan Laszlo and Jerry Sullivan of NOAA/NESDIS for Patrick 1997), a commercial satellite tracking software critical reviews of the manuscript, and the anonymous package (the mentioning of speci®c software does not reviewers for their comments and suggestions. This constitute a commercial endorsement), and the simu- study was partially funded by the Product Systems De- lation was run in a graphical environment, which ver- velopment and Implementation program of NOAA/ i®ed that the satellites indeed approached each other at NESDIS/OSD. the SNOs, as we predicted. In addition, in several in- tercalibration studies (Cao and Heidinger 2002; Hei- REFERENCES dinger et al. 2002), we have successfully used the pre- dicted SNO to ®nd the datasets for intercomparing ob- Cao, C., and A. K. Heidinger, 2002: Intercomparison of the longwave servations from AVHRR and MODIS. Our ®ndings infrared channels of MODIS and AVHRR/NOAA-16 using si- multaneous nadir observations at orbit intersections. Earth Ob- demonstrate that all predictions have been successful, serving Systems VII, William L. Barnes, Ed., Proc. SPIE, 4814, though the accuracy decreases if the prediction is more 306±316. than 2 weeks from the TLE epoch. Currently, the pre- Heidinger, A. K., C. Cao, and J. Sullivan, 2002: Using Moderate diction is mainly used for ®nding the time window for Resolution Imaging Spectrometer (MODIS) to calibrate Ad- vanced Very High Resolution Radiometer (AVHRR) re¯ectance the satellite orbit of interest in the intercalibration. A channels. J. Geophys. Res., 107, 4702, doi:10.1029/ pixel-by-pixel match between the observations from the 2001JD002035. radiometer pairs is then performed using the location Hoots, F. R., and R. L. Roehrich, 1988: Models for propagation of data embedded in the satellite data. NORAD element sets. Aerospace Defense Command Spacetrack Rep. 3., Peterson AFB, CO, 90 pp. Lane, M. H., and K. H., Cranford,1969: An improved analytical drag 5. Concluding remarks theory for the arti®cial satellite problem. American Institute of Aeronautics and Astronautics paper 69-925, Reston, VA. This paper presents a method for accurate prediction Marshall, S. R., and R. C. Patrick, 1997: Satellite Tool Kit user's manual. Analytical Graphics Inc., King of Prussia, PA, 471 pp. of simultaneous nadir overpasses (SNOs) among earth- Rao, P. K., S. Holmes, R. K. Anderson, J. S. Winston, and P. E. Lehr, orbiting satellites, with emphasis on the sun-synchro- 1990: Weather Satellites: Systems, Data, and Environmental Ap- nous polar-orbiting radiometers. At each SNO, radi- plications. Amer. Meteor. Soc., 503 pp.

Unauthenticated | Downloaded 10/03/21 12:15 AM UTC