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.

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(2)

   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.

An SNO occurs when D reaches a minimum (D_min) within a cycle such that D_min is smaller than a preset threshold. A perfect SNO is one for which D_min = 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 D_min is increased, which means allowing a longer difference between the times that the two satellites pass the same orbital intersection. But if D_min 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 D_min, which may vary depending on the specific requirements for a particular intercalibration.

From a practical point of view, the threshold for D_min 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 D_min 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 D_min 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 D_min 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 (D_min = 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.

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.