• Cao, C., , and Heidinger A. K. , 2002: Intercomparison of the longwave infrared channels of MODIS and AVHRR/NOAA-16 using simultaneous nadir observations at orbit intersections. Earth Observing Systems VII, William L. Barnes, Ed., Proc. SPIE,4814, 306–316.

    • Search Google Scholar
    • Export Citation
  • Heidinger, A. K., , Cao C. , , and Sullivan J. , 2002: Using Moderate Resolution Imaging Spectrometer (MODIS) to calibrate Advanced Very High Resolution Radiometer (AVHRR) reflectance channels. J. Geophys. Res.,107, 4702, doi:10.1029/ 2001JD002035.

    • Search Google Scholar
    • Export Citation
  • Hoots, F. R., , and Roehrich R. L. , 1988: Models for propagation of NORAD element sets. Aerospace Defense Command Spacetrack Rep. 3., Peterson AFB, CO, 90 pp.

    • Search Google Scholar
    • Export Citation
  • Lane, M. H., , and Cranford K. H. , 1969: An improved analytical drag theory for the artificial satellite problem. American Institute of Aeronautics and Astronautics paper 69-925, Reston, VA.

    • Search Google Scholar
    • Export Citation
  • Marshall, S. R., , and Patrick R. C. , 1997: Satellite Tool Kit user's manual. Analytical Graphics Inc., King of Prussia, PA, 471 pp.

  • Rao, P. K., , Holmes S. , , Anderson R. K. , , Winston J. S. , , and Lehr P. E. , 1990: Weather Satellites: Systems, Data, and Environmental Applications. Amer. Meteor. Soc., 503 pp.

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    Simultaneous (1 s) nadir overpass (SNO) between NOAA-16 and Terra

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

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  • 1 NOAA/NESDIS/Office of Research and Applications, Camp Springs, Maryland
  • 2 I.M. Systems Group, Kensington, Maryland
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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 Simplified General Perturbations No. 4 (SGP4), an orbital perturbation 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.

Corresponding author address: Dr. Changyong Cao, NOAA/NESDIS/ORA, 5200 Auth Road, Camp Springs, MD 20746. Email: changyong.cao@noaa.gov

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 Simplified General Perturbations No. 4 (SGP4), an orbital perturbation 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.

Corresponding author address: Dr. Changyong Cao, NOAA/NESDIS/ORA, 5200 Auth Road, Camp Springs, MD 20746. Email: changyong.cao@noaa.gov

1. Introduction

There is a need to intercalibrate the polar-orbiting radiometers on different satellites to achieve the consistency and traceability required for long-term climate studies with the more than 20 yr of National Oceanic and Atmospheric Administration (NOAA) satellite data. In addition, the calibration of current operational radiometers should be linked to those of the next-generation meteorological satellites such as those of the National Polar-Orbiting Operational Environmental Satellite System (NPOESS). Many intercalibration studies have been done in the past. But most of them are limited to match- up datasets acquired from different satellites with dissimilar instruments and that may have different observation times and viewing geometries, and in many cases rely on radiative transfer calculations to account for the observation differences. These restrictions introduce uncertainties in the intercomparisons.

In this study, we present a method for accurately predicting the simultaneous nadir overpasses (SNOs) of two earth-orbiting satellites. At each SNO, radiometers from both satellites view the same place at the same time at nadir, thus eliminating uncertainties associated with differences of atmospheric path, viewing geometry, and observation time. This is especially important for infrared-radiometer observations, which vary significantly with these parameters. As a result, uncertainties in the intersatellite calibration are greatly reduced. Our studies show that this method is useful for the on-orbit verification of instrument performance for newly launched radiometers, as well as retrospective analyses of historical data for constructing time series for climate studies. The SNOs for polar-orbiting satellites occur only near the earth's polar regions, which limits the intercalibration to polar conditions. However, based on the principles discussed here, it is possible that in the future, transfer radiometers identical to those on the polar orbiters can be launched into low-inclination orbits to provide better opportunities for calibration in the lower latitudes with a variety of surfaces and atmospheres.

2. Earth-orbiting satellites and orbital intersections

The intersection of the orbital plane of an earth-orbiting satellite with the surface of the earth is a great circle. Every great circle of a sphere intersects all other great circles of the sphere in exactly two points. Therefore, it is expected that the orbits of every pair of earth- orbiting satellites have two points of intersection. In the case of two polar-orbiting satellites, the two intersections always occur near the North and South Poles (typically in the +70° to +80° and −70° to −80° latitude zones). Although each satellite passes each intersection once an orbit, for most orbits the two satellites do not pass the same intersection at the same time. In fact, if both satellites are at the same altitude, they will have the same orbital period, and they should never pass the same orbital intersection at the same time (otherwise they will collide).

Kepler's third law implies that the higher the altitude of a satellite, the longer its orbital period. Satellites at different altitudes have different angular velocities and therefore different orbital periods. It follows then that as time goes by, the lower-altitude satellite will eventually catch up with the high-altitude satellite at the orbital intersections, thus creating an SNO. When this occurs, the radiometers from both satellites view the earth and its atmosphere at the same place and same time but from different altitudes. The difference in satellite altitudes does not have significant impact on the radiance comparison from the two radiometers on these satellites, as long as the areas within the field of view are relatively uniform, because radiance is not a function of the distance of measurement. Admittedly, the pixel sizes are slightly different due to the altitude differences, so when the temperature distribution within the field of view is not uniform, the larger pixels will have a slightly different average temperature from that of the smaller pixels. However, given a large number of match-up pixels, the net effect of different pixel size is probably random and acts to increase the noise in the comparison. This noise can be further reduced by averaging pixels. Finally, path radiance difference is negligible in the intercomparison because there is no atmosphere between the two satellites at different altitudes.

NOAA's Polar Operational Environmental Satellites (POES) program typically employs two spacecraft in nearly circular sun-synchronous orbits at nominal altitudes of 833 and 870 km. With their orbital planes approximately 90° apart, one has a 0730 or 1030 (for NOAA-17) local equator-crossing time in descending node and the other a 1340 local equator-crossing time in ascending node. They are referred to as AM (morning) and PM (afternoon) satellites. A sun-synchronous orbit ensures that the equator crossings always occur at the same local time. This is desirable as it provides consistent scene illumination—a common mission requirement for many meteorological and terrestrial applications. Such orbits are achieved by placing the satellites at inclination angles of 98.7°–98.8° so that the orbital planes will precess eastward about 0.986° day−1 to keep pace with the earth's revolution around the sun (Rao et al. 1990). Since 1978, NOAA has successfully launched 11 polar-orbiting satellites (NOAA-6 to NOAA- 17), with an average usable life of approximately 5 yr in orbit for each. Since an AM satellite is generally at a lower altitude than the PM satellite, the AM satellite has a shorter orbital period. For example, the nominal orbital period for the AM satellite NOAA-17 is 101 min, compared to 102 min for the PM satellite NOAA-16. Therefore, NOAA-17 and -16 will pass the orbital intersections simultaneously with regularity.

In general, assuming that two sun-synchronous polar- orbiting satellites, S1 and S2, operate at altitudes h1 and h2 (h2 > h1) with orbital periods of τ1 and τ2 (τ2 > τ1), an SNO between them occurs when the orbital-period time difference (τ2τ1) accumulates over time and eventually amounts to τ2. In other words, S1, having a higher velocity than S2, eventually catches up with S2. The number of orbits required for S1 to catch up with S2 is τ2/(τ2τ1). Converting number of orbits to number of days, we have the following formula for estimating the SNO occurrences between two satellites:
Tτ2τ2τ1f1
where T is time (days) between successive SNOs, τ1 is the orbital period (min) for S1 at h1, τ2 is the orbital period (min) for S2 at h2, τ2 > τ1, h2 > h1, and f1 is the number of orbits per day for S1 (f1 = 1440 (min day−1)/τ1).

For example, the time between successive SNOs for the NOAA-17 and -16 satellites is approximately 8 days. Similarly, NOAA-17 and Terra meet at their orbital intersections about every 3 days. Table 1 shows the time between successive SNOs for some selected polar-orbiting sun-synchronous meteorological satellites. It is worth noting that even two PM satellites, such as NOAA- 14 and -16, have SNOs, although they occur much less frequently (every 72 days) because of their similar altitudes.

The discussion above provides a basic understanding of the mechanism of SNOs for earth-orbiting satellites. However, the accurate prediction of such events, including the time, location, and nadir distance, cannot be done without using orbital perturbation models, which is discussed next.

3. Predicting SNOs using the Simplified General Perturbations No. 4

Accurate prediction of the location of an earth-orbiting satellite at a given time requires the use of orbital prediction models and appropriate input parameters. The Simplified General Perturbations No. 4 (SGP4) (Lane and Cranford 1969; Hoots and Roehrich 1988), developed and used by the North American Aerospace Defense Command (NORAD) for tracking all satellites in space, is a reasonably accurate and popular model available to the general public. The input to the SGP4 model is contained in a two-line-element (TLE) set, which has information about the satellite and its orbit, such as satellite number, orbit inclination, eccentricity, argument of perigee, derivatives of the mean motion, BSTAR drag, mean anomaly, mean motion, and others. With a TLE, the SGP4 can predict the position and velocity of the associated satellite for a given date and time. TLE sets are released daily by NORAD for all satellites, including all NOAA satellites since NOAA-6. The details of the SGP4 algorithm and the TLE (available online at http://celestrak.com) are beyond the scope of this paper. This model is sufficiently accurate for predicting the SNOs, for which the required accuracy is on the order of a few kilometers, or within a few pixels for most of NOAA's radiometers.

To predict the SNOs of two earth-orbiting satellites, the following algorithm is used.

  1. Prepare the matching TLE pair for the two satellites; since the precise satellite orbit is very dynamic, it is important to use the TLE pair with epochs that are closest to the time of prediction to avoid errors. Also, ideally the TLEs for the two satellites should have the same epoch date. TLEs are usually released on a daily basis for all satellites; therefore, in most cases, for a given pair of TLEs, the prediction is only necessary for a 1-day period—until the TLE pair for the next day becomes available. To predict the SNOs for an entire year, a series of TLE pairs must be prepared.There are situations in which predictions for the next few days may be needed based on today's TLEs. For example, one may need to schedule Advanced Very High Resolution Radiometer (AVHRR) local area coverage (LAC) data acquisitions, which may require a 2-week lead time. In such cases, it should be noted that the further in time from the TLE epoch, the less accurate the prediction will become. Based on our experience, forward prediction for a week is reasonably accurate, but errors may become unacceptably large beyond a 2-week period if the TLE is not updated.
  2. Input the TLE of the first satellite to the SGP4 model and use its epoch as the starting date of prediction.
  3. Given the time step (typically 1 s) and the time period of the prediction (in most cases less than a week), run SGP4 at each time step to generate the dates, times, and locations of the satellite in latitude and longitude, and store them in an array. The 1-s time step is preferred, to get a more precise location of the SNO. This corresponds to a ground step size of about 7 km for most polar-orbiting satellites.
  4. Repeat steps 2 and 3 for the second satellite, using the same epoch and time step. This creates a list of coordinates that match those for the first satellite in time.
  5. Step through the latitude/longitude pairs in time sequence, and compute the earth (ground) distance between the nadir points of the two satellites during the prediction period using the great circle distance formula
    DR−1l1l2l1l2m2m1
    where D is the ground distance (km) between the nadir points of the two satellites; R is the mean earth radius (6378 km); l1 and l2 are the latitudes (rad) of the first and second satellites, respectively; and m1 and m2 are the longitudes (rad) of the first and second satellites, respectively.
Equation (2) is a simplified formula for estimating the ground distance, assuming a perfectly round earth. The distance D at each time step shows how close the nadir points of these two satellites are on the ground. A sequential list of the distance D over a prediction period of many orbits will show that the nadir points of the two satellites approach or depart from each other regularly with a repeating cycle of T days determined by Eq. (1).

An SNO occurs when D reaches a minimum (Dmin) within a cycle such that Dmin is smaller than a preset threshold. A perfect SNO is one for which Dmin = 0. However, in reality this does not occur often enough for the purpose of intercalibrating radiometers. The number of SNOs will increase for a given prediction period if the threshold for Dmin is increased, which means allowing a longer difference between the times that the two satellites pass the same orbital intersection. But if Dmin is too large (e.g.,>7000 km), it would mean that the second satellite may have not passed the orbital intersection point until more than 15 min after the first satellite did, and thus this may not qualify as a useful SNO. Therefore, there is a trade-off between the number of SNOs and the acceptable threshold for Dmin, which may vary depending on the specific requirements for a particular intercalibration.

From a practical point of view, the threshold for Dmin can be derived from the requirements on a time window. A 30-s time window is generally acceptable for intercalibrating radiometers for meteorological applications. This is based on the assumption that, within this time period, clouds have not moved and the scene temperature has not changed significantly within the field of view of the radiometers. This 30 s in time corresponds to a separation of approximately 210 km on the ground, based on a satellite ground speed of ∼7 km s−1 along nadir. However, the actual distance between the nadir points of the two satellites is also affected by the angle between the two orbital planes, which varies between different satellites. The maximum nadir distance [thus the threshold for Dmin in Eq. (2)] occurs for two satellites moving in opposite directions, for which the nadir distance should be no greater than 420 km for a 30-s separation. Here the distance threshold for Dmin should be interpreted as the ground distance that the first satellite traveled past the orbital intersection point by the time the second satellite reached that point. However, it should be kept in mind, that, whatever the separation in time, the intercomparisons will involve data from the same location from both satellites; the use of Dmin is only a device for finding the near-simultaneous nadir overpasses. A smaller time window (<30 s) may be needed for some applications for better simultaneity at the cost of a reduced number of SNOs. It is worth noting that by using the 30-s time window we were able to find SNOs among meteorological satellites with a frequency of occurrence that is consistent with the predictions produced by Eq. (1).

4. Examples of predicted SNOs

To illustrate this procedure, we use an example SNO between Terra (S1) and NOAA-16 (S2) on 21 March 2003 (Fig. 1). In this case, a time step of 1 s was used. With TLEs for each satellite from 20 March 2003, a second-by-second sequence of the positions of the two satellites and the nadir distance between them is produced (see Table 2). For brevity only records with nadir distances of less than 40 km are included in the table. Clearly, these two satellites approached each other starting at 2345:01 UTC on 21 March 2003. Three seconds later, at 2345:04 UTC, their nadir distance reached a minimum (Dmin = 3 km), which is a very good SNO for intersatellite radiometer calibration. Then they moved away from each other. Based on the prediction, satellite data can be found and downloaded from the archive.

It should be noted that the predictions are only used for identifying the satellite data in the archive. As long as the correct dataset can be identified based on the prediction, small errors in location and distance are tolerable because after the satellite data are acquired, the precise point of orbital intersection can be found using the nadir pixel location embedded in the satellite data. A pixel-by-pixel match between the two datasets can be done using the latitude/longitude information for each pixel, and the precise time difference for each pixel can also be determined.

The following are examples of predictions (Table 3) using this algorithm for SNOs among the latest NOAA, Terra, and Aqua satellites in mid-March 2003, with a TLE epoch of 16 March 2003.

a. NOAA-16 (PM) versus NOAA-17 (AM)

The results in Table 3 confirm our earlier calculation that SNOs occur about every 8 days between NOAA- 16 and -17. It is also shown that SNOs can occur in both the North and South Pole regions, and both may be used for the intercalibration of radiometers. However, there are significant differences in the land cover and atmosphere between these two regions, which may affect calibration. In the −70° to −80° latitude zone, the land cover is dominated by ice and snow all year round. There may not be any water surface even during the summer months. In contrast, for the +70° to +80° latitude zone, the ice retreats in the summer and leaves some water surfaces in the Arctic Ocean. Water surfaces are preferred calibration targets, especially for sea surface temperature, because of their relative spatial uniformity, thermal inertia, and low reflectance. In addition, water provides a good dynamic range for the calibration of the visible and near-infrared channels of AVHRR. Finally, the sun elevation angle is the highest in the summer months for the North Pole region, providing sufficient solar illumination for calibrating these channels. Therefore, the best calibration targets for the approach described in this paper may be found in the North Pole summer.

b. NOAA-16 (PM) versus Terra (AM)

The SNOs between NOAA-16 and Terra occur every 2 days because of the large difference in their altitudes. In previous studies, we have used the SNO in the summer of 2002 for the intercalibration of the longwave infrared channels of AVHRR and the Moderate Resolution Imaging Spectroradiometer (MODIS) (Cao and Heidinger 2002; Heidinger et al. 2002).

c. NOAA-17 (AM) versus Terra (AM)

It is clear from Tables 1 and 3 that two AM satellites also have SNOs if they are at different altitudes. In this case, they occur about every 3 days. The frequent occurrence of SNOs between NOAA and MODIS-carrying satellites is very fortunate. Establishing a long record of intersatellite calibration at the SNOs may provide the basis for the calibration link between AVHRR and MODIS, as well as the future Visible/Infrared Imager/ Radiometer Suite (VIIRS) for NPOESS, in order to meet the stringent calibration requirements for climate studies.

d. NOAA-17 (AM) versus Aqua (PM)

Both NOAA-17 and Aqua were launched in the summer of 2002. Aqua carries the Atmospheric Infrared Sounder (AIRS), a hyperspectral thermal infrared radiometer for meteorological applications, and provides many new opportunities for intersatellite calibration of sounders. We believe that the approach presented in this paper is especially useful for infrared sounders, because the relatively spatially uniform upper atmosphere provides a suitable target for intersatellite calibration. Also, collaborative studies between NOAA and National Aeronautics and Space Administration (NASA) scientists are underway using AVHRR/NOAA-17 as a transfer radiometer to evaluate the calibration consistency between the MODIS on Terra and that on Aqua.

At the NOAA/National Environmental Satellite, Data, and Information Service (NESDIS)/Office of Research and Applications, SNOs between several pairs of meteorological satellites are predicted automatically on a weekly basis and can be found online at http://orbit-net.nesdis.noaa.gov/crad/sit/intercal. Also, historical SNOs among NOAA satellites are being generated for the retrospective intersatellite calibration of sounders and imagers beginning in 1980.

To ensure that the predicted times and locations of the SNOs are accurate, we have performed validations with the predicted SNOs. First, TLEs used in our predictions were fed into Satellite ToolKit (Marshall and Patrick 1997), a commercial satellite tracking software package (the mentioning of specific software does not constitute a commercial endorsement), and the simulation was run in a graphical environment, which verified that the satellites indeed approached each other at the SNOs, as we predicted. In addition, in several intercalibration studies (Cao and Heidinger 2002; Heidinger et al. 2002), we have successfully used the predicted SNO to find the datasets for intercomparing observations from AVHRR and MODIS. Our findings demonstrate that all predictions have been successful, though the accuracy decreases if the prediction is more than 2 weeks from the TLE epoch. Currently, the prediction is mainly used for finding the time window for the satellite orbit of interest in the intercalibration. A pixel-by-pixel match between the observations from the radiometer pairs is then performed using the location data embedded in the satellite data.

5. Concluding remarks

This paper presents a method for accurate prediction of simultaneous nadir overpasses (SNOs) among earth- orbiting satellites, with emphasis on the sun-synchronous polar-orbiting radiometers. At each SNO, radiometers on both satellites view the earth and its atmosphere at nadir at the same time, providing an ideal scenario for the intercalibration of radiometers aboard the two satellites. All earth-orbiting satellites at different altitudes have SNOs regularly and, therefore, can in theory be intercalibrated with this method. Prediction of SNOs with the Simplified General Perturbations No. 4 (SGP4) is presented, and examples of SNOs among the NOAA, 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.

Acknowledgments

The authors wish to thank Drs. Istvan Laszlo and Jerry Sullivan of NOAA/NESDIS for critical reviews of the manuscript, and the anonymous reviewers for their comments and suggestions. This study was partially funded by the Product Systems Development and Implementation program of NOAA/ NESDIS/OSD.

REFERENCES

  • Cao, C., , and Heidinger A. K. , 2002: Intercomparison of the longwave infrared channels of MODIS and AVHRR/NOAA-16 using simultaneous nadir observations at orbit intersections. Earth Observing Systems VII, William L. Barnes, Ed., Proc. SPIE,4814, 306–316.

    • Search Google Scholar
    • Export Citation
  • Heidinger, A. K., , Cao C. , , and Sullivan J. , 2002: Using Moderate Resolution Imaging Spectrometer (MODIS) to calibrate Advanced Very High Resolution Radiometer (AVHRR) reflectance channels. J. Geophys. Res.,107, 4702, doi:10.1029/ 2001JD002035.

    • Search Google Scholar
    • Export Citation
  • Hoots, F. R., , and Roehrich R. L. , 1988: Models for propagation of NORAD element sets. Aerospace Defense Command Spacetrack Rep. 3., Peterson AFB, CO, 90 pp.

    • Search Google Scholar
    • Export Citation
  • Lane, M. H., , and Cranford K. H. , 1969: An improved analytical drag theory for the artificial satellite problem. American Institute of Aeronautics and Astronautics paper 69-925, Reston, VA.

    • Search Google Scholar
    • Export Citation
  • Marshall, S. R., , and Patrick R. C. , 1997: Satellite Tool Kit user's manual. Analytical Graphics Inc., King of Prussia, PA, 471 pp.

  • Rao, P. K., , Holmes S. , , Anderson R. K. , , Winston J. S. , , and Lehr P. E. , 1990: Weather Satellites: Systems, Data, and Environmental Applications. Amer. Meteor. Soc., 503 pp.

    • Search Google Scholar
    • Export Citation
Fig. 1.
Fig. 1.

Simultaneous (1 s) nadir overpass (SNO) between NOAA-16 and Terra

Citation: Journal of Atmospheric and Oceanic Technology 21, 4; 10.1175/1520-0426(2004)021<0537:PSNOAP>2.0.CO;2

Table 1.

Time between successive simultaneous nadir overpasses. Note that orbital periods are derived from two-line-elements with an epoch of 27 Mar 2003

Table 1.
Table 2.

Satellite positions and nadir distance between Terra and NOAA-16 on 21 Mar 2003

Table 2.
Table 3.

SNO examples for NOAA-16 and -17, Terra, and Aqua (TLE epoch: 16 Mar 2003)

Table 3.
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