TRMM OVERFLIGHT FINDER ORBIT TRENDS AND ACCURACY NOTES: 4/13/2007

1. INTRODUCTION

This page explains how our TRMM satellite overflight estimates are made, the accuracy expected, and certain TRMM orbit characteristics.

A recent review of our predicted accuracy shows that we are often in error up to 75 seconds in time of overflight and 20 kilometers in cross track error. This accuracy should be good for several weeks into the future barring operational changes. If higher accuracy is needed in predictions, please contact us by e-mail (see below). It is now expected that TRMM satellite operations will be maintained at least through 2009.

For past orbits, the TRMM Overflight Finder uses TSDIS database information to fix the position of the overflight swath. A file of past orbit information is updated periodically. The date on the plot below tells when the last file updates have been made with the database historical data, and the predicted trend shown is updated as needed. The position and timing information for past orbits will be quite good, well within the resolution of the output lists--which are within 20 kilometers for cross track proximity, and within 1 minute in overflight times. See Section 5 of this discussion for notes about how the swath shape model influences the accuracies for past orbits. Note that past orbits are included in our database up through the day preceding that noted in Figure 1 below. This plot is nominally updated about twice a month.

2. HOW THE OVERFLIGHT FINDER ESTIMATES FUTURE OVERFLIGHTS

The TRMM Overflight Finder depends on two key average orbit properties, which are related:

• The average orbit nodal period
• The longitudinal westward drift of the ground track per orbit

Figure 1 below shows our projections for each orbit start time based on the average orbit nodal period, as shown relative to a linear fit to the data on orbit start times since the change in operating altitude was completed on August 22, 2001.

The large shift in time around orbit 38000 was due to the temporary suspension of orbit maintainance manuevers. This vividly illustrates how fast predictions can change without normal operations. During about 6 weeks of suspended orbit maintainance, the predictions from the old trends accumulated errors of about 30 minutes in time and up to about 500 kilometers in cross-track location error.

The recently increased spacing in the bouncing-ball-type path traced by the fit residuals is due to increased time between orbit adjusts which has resulted from the effects of decreasing atmospheric drag after the 2001 peak in the 11 year solar cycle. The features of this plot associated with the regular orbit adjusts are discussed further below with the historical trends.

Figure 1. Linear Fit to latest Orbit Start Times and projected long term fit.

A dotted line shows what is currently used to predict when the spacecraft will start future orbits. The line starts when the last trend prediction was implemented, and error bars are provided for a 20 kilometer equatorial cross track shift, corresponding to a 75 second timing shift.

The average orbit properties provide our basis for predicting the orbit trends ahead in time. While we don't expect the trends to shift significantly, changes could happen. Since the actual orbit properties long term depend partly on the regular orbit adjust operations, details of the operational planning can affect the long term trends. The trends have been known to change in the past for a variety of reasons, some of which are not well understood. The trends can be affected by changes in solar sunspot activity which affect the amount of atmospheric drag on the spacecraft, as well as by operational changes, or special events. Some examples of trend shifts are discussed in the historical review below. Noting how the orbit trends have shifted in the past clearly illustrates how orbit trend changes could readily lead to large prediction errors within a month or even less. (Note there are about 470 orbits per month.)

OLD HISTORICAL ORBIT TREND NOTES FOR OPERATIONS AT 350 km

The key orbit trends of concern are illustrated by showing the actual orbit start times compared to those predicted assuming an average orbit period. (These are the orbit start times as defined for TSDIS data granules, which are defined by when each orbit reaches the southernmost latitude. The orbit numbering is according to the TSDIS scheme.) This is plotted below for the entire mission up to the orbit altitude change as noted, and explanation follows of the features illustrated.

Figure 1b. Residuals from Linear Fit to Orbit Start Times for data at 350 km.

Some key features illustrated with the TRMM orbit trends are discussed:

• The orbit is re-adjusted regularly to maintain the operating altitude within a nominal range. Each orbit adjust is illustrated by a cusp of the "bouncing ball path" shown in the above figure. The nominal plan is to allow the orbit to decay through the altitude constraint "box" permitted by the mission specification, and schedule a reboost as it reaches the bottom of the box. (The orbit period gets shorter as the orbit decays. An orbit period plot shows a sawtooth function with jumps at the reboosts. The above plot shows the integral of the orbit periods, hence the bouncing ball type path.)

• Orbit adjusts can be seen occuring more frequently since the start of the mission. This is because of increased atmospheric drag on the spacecraft as solar sunspot activity has increased (which influences the atmospheric density at high altitudes). Initially reboosts occurred about every two weeks. The maximum drag on TRMM occurred at the solar activity maximum, reached in 2001. Reboosts were needed as often as every other day at that time. The rate of boosts have since fallen back as illustrated in the first plot of recent trends.

• The operational orbit maintainance procedure has been changed at a few times in the mission. Most dramatically in December of '98 (around orbit 6000) a change was made to do reboosts every 4 days regardless of solar activity to allow simpler scheduling. This meant that for several weeks the altitude was kept in the top half of it's altitude contraint box. This made the long term predictions originally estimated at this web site (approximately the first line segment fit) much less accurate. After various discussions about options and preferences, including TSDIS inputs, the orbit altitude maintainance strategy was switched back to the original plan.

• The sharp change in the trends around orbit 9300 on July 10, 1999 is not currently well understood, although solar activity changes have been mentioned as a possible culprit. Originally it was thought this period of slightly lower average altitude would be a temporary excursion, however this trend continued through August and into early September 1999. This shift has led us to reduce our previously advertised confidence in our predictions in the future.

• The sharp rise in the residuals starting at orbit 12014 are due to an extra reboost of TRMM for Y2K contingency planning. This was done so that reboosts would not be needed for at least a few days beyond the Y2K turnover in case spacecraft support problems were encountered. No problems were reported, but after this reboost TRMM then took more than a week for the orbit to decay back to its normal operating altitude. While at the higher altitude, the orbit period was a couple seconds longer than its normal range, causing the very sharp rise relative to the long term fit.

• A dotted line showed what was last predicted for when the spacecraft would start future orbits. Error bars show effects of a 20 kilometer equatorial cross track shift, corresponding to a 75 second timing shift. Of course these projections were no longer even close as the TRMM altitude was changed.

The accuracy of the overflight predictions based on these fits is discussed briefly as follows.

3. OVERFLIGHT PREDICTION ACCURACY ESTIMATION

The main error source currently of concern is how accurately we can estimate the start time and position of each orbit. (The overflight finder uses a fixed orbit model and swath shape within each orbit to get overflight times and swath positions, but the errors in that model are relatively small. See the further discussion in Section 5 below for notes about how the overflight finder works.)

There is a direct association between timing errors and position errors that allows us to get a pretty good estimate of cross-track position errors directly from this same plot (above). Although the position estimates come from a different source (see below), the errors are shown to be correlated closely as follows:

The error in our fit for position is approximately given by the amount that the Earth rotates under the satellite track during the error in our fit for timing. The Earth's rotation of 360 degress per day is just 0.25 degrees per minute. Near the equator there are about 112 kilometers per degree, so the earth surface moves about 28 kilometers per minute. This effect displaces the ground track and swath edge estimates in an East or West direction. If the spacecraft actually arrives later, the track is moved West.

The cross-track displacement magnitude is smaller than the East-West displacement because of the 35 degree inclination orbit of TRMM. Since the sine of 35 degrees is 0.57, the cross track displacement at the equator for a one minute timing error is 0.57 * 28 = 16 kilometers. At higher latitudes the cross-track component of the displacement is smaller. The cross-track position error is negligable near + or - 35 degrees latitude, around the top and bottom of the orbit track. Thus near these high latitudes, the timing may be in error, but the cross track error for the swath overlay will be quite small.

Based loosely on the past variablity of the trends, it is roughly estimated that the prediction errors can readily grow by about a minute in time per month or more, and thus by 20 kilometers or more in cross track position, with the position errors being worst near the equator. However we note that projecting the current orbit trends into the future has all the risks of any prediction of the future, and a number of spacecraft emergencies or reboost planning changes could affect the reality.

4. MORE ABOUT THE TRMM ORBIT

The TRMM altitude has been maintained within a fairly tight box at a nominal value of 350 kilometers for nearly the first 4 years of the mission. Actually it is the mean semi-major axis (using mean orbital elements) that was maintained within +/- 1.25 kilometers of 350 kilometers above the Earth equatorial radius (6378.14 km). The actual altitude above the oblate shaped Earth varied between 345 and 355 km during each orbit in a very regular pattern. The altitude constraint was chosen in coordination with the PR radar design, so that PR will rarely miss observations of the highest possible storm tops, and also the surface echo can be obtained across the swath. At nadir, echo return data also provide potential information to a useful altitude.

Since the orbit raising boost completed on August 22, 2001, the orbit has been maintained with a nominal mean altitude of 402.5 kilometers, with a mean semi-major axis with +/- 1.00 kilometers of 6780.64 (402.5 above 6378.14). The geodetic altitude above the oblate Earth will vary between about 397 and 408 kilometers.

5. MORE ABOUT HOW THE TRMM OVERFLIGHT FINDER WORKS

The TRMM Overflight Finder does not use Ephemeris predictions in a traditional approach to search for nearby overflights. Instead it uses a special efficient algorithm to determine if a given width swath intersects certain coordinates. The swath shape is a fixed model, and we use the "Longitude of Maximum Latitude (lon_of_max_lat)" as a single parameter to note where the highest latitude is reached for each TRMM orbit. This longitude location essentially tells us where to overlay our swath shape model on the map. The two dimensional latitude and longitude coordinates are translated using the swath shape model into conditions on the lon_of_max_lat such that the location will be inside the swath in either the ascending or descending segment of the orbit. The details of this algorithm were developed for the "Spatial Search" option which is available for TSDIS Science Users at the Remote Science Terminal (RST). The algorithm is described in a memo dated October 23, 1995 from Steve Bilanow. The swath shape model used for the search is analytic based on spherical trigonometry equations, and thus has differences from the actual TRMM swath shape due to Earth oblateness and spacecraft altitude variations. It is expected that the shape is accurate to within at least 20 kilometers though so that overflights can be identified to within this tolerance for a tabular summary of orbits within a certain distance of the ground site.

The TRMM Overflight Finder actually checks various swath widths, currently at 20 kilometer increments from 800 to 20, and determines what the smallest one is that contains a specified location. For each orbit, it has ranges that it checks for the lon_of_max_lat to determine first if an 800 kilometer swath would include the given location. Then it checks progressively tighter criteria on the lon_of_max_lat. If the point is missed at any smaller swath width, then the overflight proximity is noted as within the next larger swath in the TRMM Overflight List page.

For the map of the swath shown when the View Map button is selected, a different swath shape model used. This one is based on a typical orbit with the actual TRMM altitude variations and Earth oblate shape effects on the swath edges simulated with our geolocation software. The swath edge coordinates are stored in a file. Thus this model is better than the one used for the TRMM Overflight list search. Detailed analysis of the accuracy of both these swath shape model relative to the actual variablility of the TRMM attitude and orbit has not been pursued. However we think the swath shape errors are not significant for this application. The purpose of our site is to locate overflights within 20 kilometers, and illustrate them approximately for users to reliably get the real data at the located orbits. Users should allow for a few kilometers inaccuracy in the swath shape models. In addition, users should allow for the added uncertainty for predicting future orbits wherein the swath overlay can be displaced according to the orbit prediction accuracy discussed in Section 2 above.

For the lon_of_max_lat for each orbit in the past, we currently use a data file based on information stored in the TSDIS database. If problems are encountered in reading this file, then the user will see an error message the TSDIS developers of this page will be automatically notified of the problem. To show the general trends into the future, the longitude angles are extended -360 degrees at each date line crossing so a straight line can be fit. The residual errors from this fit are shown in the Figure 2 below for the pre-boost period.

Figure 2. Longitude of Maximum Latitude Residuals from Linear Fit.

6. MORE INFORMATION

Questions about the orbit modelling and the overflight predictions can be directed to Steve Bilanow or Michael Hensley at

or