THERMOSPHERE DENSITY CALIBRATION IN THE ORBIT DETERMINATION OF ERS-2 AND ENVISAT

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1 THERMOSPHERE DENSITY CALIBRATION IN THE ORBIT DETERMINATION OF ERS-2 AND ENVISAT Eelco Doornbos 1, Heiner Klinkrad 2, Remko Scharroo 3, and Pieter Visser 4 1 DEOS, TU Delft, Delft, The Netherlands 2 ESA/ESOC, Darmstadt, Germany 3 Altimetrics Inc., Cornish, NH, USA 4 DEOS, TU Delft, The Netherlands ABSTRACT The limited accuracy of empirical thermospheric density models is a major contributor to force model errors in orbit determination and orbit prediction for satellites such as ERS and Envisat. Although orbit accuracy has steadily improved due to advances in gravity field modeling and tracking systems, strong evidence of errors in density models have remained apparent in the orbit determination results, especially during high solar-activity periods. Using newly developed software, empirical density modeling accuracy can be enhanced. Two-Line Element (TLE) data of a large number of objects with perigee altitudes between km are used as input observations, which are converted to daily density values, averaged along their trajectories. These data are in turn used to adjust a set of daily correction parameters. In this study, the DORIS, SLR and radar altimeter data of ERS-2 and Envisat are used to evaluate the performance of density model calibration. A reduction from 23.5% to 17.1% RMS error was found by analyzing estimated density scale factors after adjusting the NRLMSISE-00 model using 10 parameters per day. These scale factors allow the reduction of long-period density model errors using tracking data. The remaining reduction in density model error over shorter periods, when using a calibrated model, causes only a modest improvement in the accuracy of ERS-2 precise orbits. Key words: orbit, drag, thermosphere, ERS-2, Envisat, SLR, DORIS, altimetry. 1. INTRODUCTION Orbit determination is an important task in both the production of science data and the operations of the ERS and Envisat satellites. Operational orbits are used to keep the satellite on its ground track [1] and to avoid collisions with space debris through manoeuvres [2]. Precise orbits based on tracking data from Satellite Laser Ranging (SLR) and the DORIS instrument on Envisat are required to convert altimeter measurements to sea level heights, or to combine SAR images into interferograms [3]. The Earth s atmospheric density decreases approximately exponentially with altitude, and is influenced strongly by the position and activity of the Sun. At around 800 km, aerodynamic drag is still a major perturbing force on the satellite orbit, especially during peak periods of the 11-year solar cycle, when increased extreme ultraviolet (EUV) radiation from the Sun causes this region of the atmosphere, called the thermosphere, to expand. The latest high activity period was between 1998 and Even during the current low activity period, when density is more than an order of magnitude lower than the maximum during the peak, its effects on the orbital motion are still easily detected using the DORIS system on Envisat or the SLR system used on both ERS satellites and Envisat. On Envisat, the DORIS tracking data is present almost continuously, which makes density modeling errors less critical than on ERS-2, were SLR is the only available tracking system. When cloudy weather or operational issues restrict laser ranging, long gaps in the tracking data can occur, during which the modeled accelerations completely determine the computed trajectory. This analysis concentrates mainly on ERS-2 orbit determination during 2003, when solar activity was steadily decreasing, while still showing some very large variations. 2. DENSITY MODELS The thermosphere density model developed by Jacchia [4] in the early 1970 s has been a standard for many years, and is still in use today for some applications. The French density model DTM [5] knows two revisions: DTM-94 [6] and DTM-2000 [7]. DTM-2000 can use either F 10.7 or Mg II as a solar activity input. Since the time series of Mg II has not been made available with the model, F 10.7 was used in this analysis. The MSIS series of models was Proc. Envisat Symposium 2007, Montreux, Switzerland April 2007 (ESA SP-636, July 2007)

2 developed in the late 1970 s and 1980 s. The MSIS-86 model [8] replaced Jacchia s model as a standard. Development of MSIS-series models has been continued at the Naval Research Lab (NRL) resulting in NRLMSISE- 00 [9]. The Jacchia-Bowman 2006 (JB2006) model [10] provides a major update to Jacchia s model. Innovative improvements in this model include the combined use of three proxies for the solar radiation energy input, and a new analysis of the semi-annual density variation. Another new development is thermospheric density model calibration. It has been demonstrated that drag data from a large number of objects can be assimilated to correct errors in a traditional model. A short history of development of such models is given in [11]. In this study, we have evaluated a version of the Near Real-Time Density Model (NRTDM) [12] for ERS-2 orbit determination. NRTDM makes use of Two-Line Element (TLE) data. NRTDM models were previously evaluated using TLE-derived densities from validation objects, which were not included in the calibration itself. This showed a reduction of relative density model error RMS over the year 2000 from around 30% to below 10%. For the analysis of ERS-2 orbit determination, we have used an NRTDM calibrated model that is based on an adjustment of NRLMSISE-00. Ten adjustment parameters are used: a single scale factor at 300 km, and a spherical harmonic expansion of degree and order 2 at 500 km, resulting in 9 additional parameters. Only the 9 parameters at 500 km affect the adjusted density at the altitude of ERS-2 and Envisat. The parameters were determined over the year 2003, using drag data from around 50 TLE objects with perigees between approximately 200 and 550 km. The applied model adjustments therefore imply an extrapolation of this data to the ERS-2 altitude of 800 km. Whether the improvement is still valid at the higher altitude is the subject of this investigation. 3. AERODYNAMIC MODELING The acceleration due to aerodynamic interaction is usually modeled in orbit determination software using a variant of the following equation: A 1 r D = f D C D m 2 ρv2 r u D (1) Here, ρ is the density from the density model. A is the frontal area of the satellite and m is its mass. C D is the drag coefficient, which describes the interaction between the atmospheric particles and the spacecraft surfaces. The quantity C D m A is the inverse of the ballistic coefficient. The velocity relative to the atmosphere is denoted by v r and can be calculated from the orbital velocity and a model of thermospheric winds. The unit vector u D denotes the direction of the acceleration, which is usually taken in a direction opposite the relative velocity if only drag is taken into account. Depending on the shape of the satellite, lift or sideways forces can also be Figure 1. ANGARA geometric model for aerodynamic calculations on ERS-2. generated, which will result in corresponding vector components in u D. Finally a time-dependent drag scale factor f D is usually applied when tracking data are available, in order to correct for errors in the other factors. The value of f D is then estimated as part of the orbit determination process, in order to make the computed orbit fit with the tracking observations. In a previous study [13], we made computations on detailed 3D models of ERS-2 (see Figure 1) and Envisat in the ANGARA analysis software, to compute accurate A values for the product C D m u D. These will be used in this study, together with the HWM-93 horizontal wind model [14], so that variations in f D will mainly represent errors in the density model. Time series of f D can therefore be used to analyze the accuracy of different drag models. 4. TIME SERIES OF DENSITY RATIOS Figure 2 shows the time series of 6-hourly f D values derived from SLR and DORIS tracking of Envisat and from SLR tracking of ERS-2. For comparison, at the bottom of the figure, the density ratio derived from TLE data for the Explorer-7 space debris object is also included. The time series for ERS-2 and Envisat are almost identical, due to their similar orbit geometry. The Envisat time series contains less noise, because of the availability of the dense DORIS tracking data, compared to the more sparse SLR data which is the only source of data that was used for ERS-2. There are a few peaks distinct to each satellite, which are probably due to manoeuvres. Orbit arcs containing manoeuvres have therefore been eliminated from further analysis. There are also some peaks, for instance in July and August, which are common to both ERS-2 and Envisat. These probably indicate short-term disturbances in the atmosphere, which are not represented in the density model. Another apparent feature in Figure 2 is the high-amplitude long-term variation, which is also present in the Explorer-7 series. These variations are similar to those in the F 10.7 solar activity proxy, suggesting

3 Envisat ERS Explorer Jan Apr Jul Oct 2003 Figure 2. Time series, offset by 1.0 on the y-axis, of observed over NRLMSISE-00 model density ratios for ERS-2, Envisat and Explorer-7. Model Mean (%) RMS (%) Std. (%) Jacchia DTM (1978) MSIS DTM DTM NRLMSISE NRTDM JB Table 1. Mean, RMS and standard deviation of the relative error in density models for ERS-2 over the year that the imperfect correlation between this proxy and density is a large source of model error. These error features are not just present in the NRLMSISE-00 model. Figure 3 shows that other models show similar patterns. The density ratios of this figure are converted to relative errors, of which statistics are presented in Table 1. The relative errors in the table are calculated using the equation ρ o ρ m /ρ o 100 in which ρ o represents the observed density from SLR tracking and ρ m represents the model density. The new NRTDM calibrated model shows the lowest RMS error: 17.1% compared to the 23.5% of NRLMSISE-00, on which it is based. This improvement is considerable, although it is not as good as the results at lower altitudes. Figure 3 shows that most of the long-term error, of a month or longer, is no longer present in the NRTDM time series, although errors with a similar magnitude remain at shorter time-scales, of about two weeks or shorter. Model mean RMS stddev. JGM DGM-E EIGEN-GRACE01S EIGEN-CG03C EIGEN-GL04C Jacchia DTM (1978) MSIS DTM DTM NRLMSISE NRTDM JB Table 2. Crossover statistics for ERS-2 cycle 81, using several gravity models (computed using NRLMSISE- 00 densities) and density models (computed using the EIGEN-CG03C gravity model). Only crossovers over open ocean, with a maximum time difference of 5 days were used. The statistics are derived from 8531 crossover locations. 5. ORBIT QUALITY ANALYSIS In order to study the results on the orbit quality of ERS-2, a crossover analysis was performed for cycle 81 (January/February 2003). Table 2 shows the statistics. Crossover differences are formed by differencing the two altimetric sea level measurements from ascending and descending passes at the same location. These values therefore contain the sum of the natural sea surface variability and a number of errors in the altimetric processing, of

4 JB2006 NRTDM NRLMSISE-00 DTM-2000 DTM-94 MSIS DTM (1978) Jacchia 71 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2003 Figure 3. Time series, offset by 1.0 on the y-axis, of observed over modeled density ratios for eight density models from ERS-2 SLR tracking. Arcs containing manoeuvres have been omitted. which the orbit accuracy is just one. These numbers can therefore be interpreted to evaluate the relative accuracy of different models used in orbit determination, but they do not give any absolute information on orbit accuracy. The estimated scale factors f D, which were estimated for every 6-hour period, are effective in removing the effects of long-term errors in the density models. It is likely that the orbit errors due to density error represented in Table 2 therefore represent mainly shorter-period errors. To provide some context, the upper part of Table 2 shows a comparison between different gravity models, which have traditionally been the main driver for orbit accuracy improvement. The JGM-3 [15] and DGM-E04 [16] models were the state-of-the-art gravity models during the 1990 s, optimized for the TOPEX and ERS missions, respectively. The three generations of EIGEN models are all based on GRACE gravity data. The EIGEN-CG03C model [17] was used in the density analysis. Subsequent generations of GRACE-based gravity models only provide a modest improvement in ERS-2 orbit accuracy, which indicates that gravity model accuracy for this purpose is converging. The differences in the altimeter crossover statistics for different density models on the other hand do not show such a clear development. The magnitude of the differences between the models indicate that in the GRACEera, improvements in density modeling have become more important than improvements in gravity modeling for ERS-2 and Envisat orbit determination. For the period under investigation, the calibrated NRTDM model shows only slightly lower orbit errors in the crossovers than the NRLMSISE-00 model on which it is based. 6. CONCLUSIONS AND RECOMMENDATIONS The best choices for thermosphere density modeling in the orbit determination of ERS and Envisat are the MSIS- 86 or NRLMSISE-00 models and the new calibrated NRTDM model. The analysis of time series of scale factors suggest that the NRTDM calibration parameters determined from low-altitude TLE-derived density data can safely be applied to orbit determination at higher altitudes, although the calibration does not have the same level of effectiveness there. Large amplitude errors at periods of two weeks or shorter still remain. This could be due to the relatively poor temporal resolution of the TLE-derived density data. It is worthwhile investigating whether density observations derived from the accelerometers on CHAMP and GRACE could be included in the calibration. In order to improve accuracy at higher altitudes, it might also be feasible to use the density scale factors from ERS-2 and Envisat tracking in future versions of calibrated density models. Although the spacial sampling at this altitude is limited, the data from ERS and Envisat could help determine global variations with altitude, while the TLE data from lower heights could still help improving variations in the horizontal plane. REFERENCES [1] A. Rudolph, D. Kuijper, L. Ventimiglia, M.A. Garcia Matatoros, and P. Bargellini. Envisat orbit control - philosophy, experience and challenge. In H. Lacoste and L. Ouwehand, editors, Proceedings of the 2004 Envisat and ERS Symposium, 6-10 September 2004, Salzburg, Austria (ESA SP-572), [2] Heiner Klinkrad. Space Debris, models and risk analysis. Springer, 2006.

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