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Algorithm Theoretical Basis Document ESA AO/1-6367/10/NL/AF “GOCE+ Theme 3: Air density and wind retrieval using GOCE data” Algorithm Theoretical Basis Document Version 1.1 Eelco Doornbos – TU Delft Pieter Visser – TU Delft Georg Koppenwallner – HTG Bent Fritsche – HTG June 20, 2013 2 Contents 1 Introduction 7 1.1 About the project ................................. 7 1.2 Purpose of this document ............................ 7 2 Overall data flow 9 2.1 Data processing flow chart ............................ 9 2.2 Input products ................................... 9 2.2.1 EGG CCD (common-mode accelerations) ............... 9 2.2.2 EGG IAQ (attitude quaternions) .................... 11 2.2.3 SST PSO (precise science orbits) .................... 11 2.2.4 AUX NOM (ion engine thrust levels) ................. 11 2.2.5 GOCE mass ................................ 11 2.3 Space environment models ........................... 11 2.3.1 NRLMSISE-00 ............................... 11 2.3.2 HWM07 .................................. 12 2.3.3 Planetary ephemerides JPL DE405 ................... 13 2.4 Auxiliary input data ............................... 13 2.4.1 Solar and geomagnetic activity data .................. 13 2.4.2 Earth orientation parameters ...................... 14 2.5 Output products .................................. 14 3 Data calibration 15 3.1 Accelerometer and ion engine calibration using GPS data .......... 15 4 Non-gravitational force modeling 25 4.1 GOCE satellite geometry model ......................... 25 4.1.1 Modelling approach ........................... 25 4.1.2 Modelling GOCE ............................. 28 4.1.3 Reference frames ............................. 29 4.2 ANGARA two-phase approach ......................... 29 4.2.1 Aerodynamic analysis, Phase 1 ..................... 30 3 4.2.2 Aerodynamic analysis, Phase 2 ..................... 31 4.2.3 Radiation pressure analysis, Phase 1 .................. 31 4.2.4 Direct radiation pressure, Phase 2 ................... 32 4.2.5 Indirect radiation pressure, Phase 2 .................. 32 4.3 Integral and Monte-Carlo Test Particle methods ............... 35 4.3.1 Monte-Carlo Method ........................... 35 4.3.2 Integral Method .............................. 39 4.4 Summary ...................................... 42 5 Reference frame transformations 45 5.1 Reference frames ................................. 45 5.1.1 Local .................................... 45 5.1.2 Earth-fixed ................................. 45 5.1.3 Inertial ................................... 46 5.1.4 Orbit-fixed ................................. 46 5.1.5 Body-fixed ................................. 46 5.1.6 Pseudo body-fixed ............................ 48 5.2 Rotation matrices ................................. 48 5.2.1 Local to Earth-fixed ............................ 48 5.2.2 Inertial to earth-fixed ........................... 48 5.2.3 Inertial to orbit-fixed ........................... 48 5.2.4 Pseudo body-fixed to body-fixed .................... 48 5.2.5 Inertial to body-fixed ........................... 49 5.3 Quaternions, Euler angles and rotation matrices ............... 49 6 NRTDM data importing and (pre)processing routines 51 6.1 Data import .................................... 51 6.1.1 SP3FileToOrbitFiles ............................ 51 6.1.2 ImportASCIIFormatted ......................... 52 6.1.3 PolynomialCalibrationParameters ................... 53 6.2 Basic conversions ................................. 53 6.2.1 CalibrateAccelerometer ......................... 53 6.2.2 OrbitToGeo ................................ 55 6.2.3 WindCorotationSBF ........................... 56 6.2.4 QuaternionToEulerAnglesConvert ................... 56 6.2.5 GOCEThrusterAccel ........................... 57 6.3 Thermosphere model evaluation ........................ 58 6.3.1 GeoToDens ................................ 59 6.3.2 GeoToWind ................................ 59 6.3.3 WindLocalToSBF ............................. 60 6.3.4 WindSBFtoLocal ............................. 60 6.3.5 WindVectorProject ............................ 61 6.4 Force model evaluation .............................. 61 6.4.1 RadiationPressureProduct ........................ 61 6.4.2 ANGARA Earth radiation pressure environment model ...... 66 6.4.3 AccelerometerSubtract .......................... 68 6.5 Density and wind processing .......................... 69 6.5.1 DensityWindFromAccelerometerDirect ................ 69 4 6.5.2 CalibrateWithModel ........................... 76 6.5.3 DensityWindFromAccelerometerIterative ............... 76 6.6 Data editing and flagging ............................ 79 5 6 Chapter 1 Introduction 1.1 About the project Accelerometers carried by low-Earth orbiters such as GOCE have the ability to provide highly detailed data for improving our understanding of thermospheric density and winds. Like its predecessor missions, CHAMP and GRACE, GOCE has not been de- signed for studies of the thermosphere. Nevertheless, the application to thermosphere studies of these earlier missions has resulted in density and wind data sets containing information at unprecedented levels of precision and coverage. The algorithms for pro- cessing the data of these these earlier missions have been adapted for GOCE, and will be presented here. 1.2 Purpose of this document The purpose of this document, according to the project’s Statement of Work, is as follows: “Algorithm Theoretical Basis Documents (ATBD): This document shall de- scribe into details all the algorithms, methods and models implemented for each Theme. The report shall include also all related data sources, process- ing steps and output data. In particular, the ATBD shall provide a complete description of all the algorithms, methods and models (both theoretical and technical) and corresponding input/output data flows, respectively. In ad- dition, this document shall report a scientific analysis of the results driving to specific development choices and trade-offs for all the algorithms imple- mented for developing the whole suite of target products. Technical consid- erations justifying the selected methodologies shall be also provided.” 7 8 Chapter 2 Overall data flow 2.1 Data processing flow chart Figure 2.1 shows an overview of the data processing. The processing starts with the import, pre-processing and calibration of the data. This results in four main data sources, on which the further processing is based: • Orbit • Attitude • Acceleration • Thruster actuation The processing involves the use of thermosphere models and satellite surface force mod- els, in combination with custom algorithms for the purpose of determining density and wind. This will be described in full detail in the remainder of this document. 2.2 Input products The following sections describe the origin of the GOCE input products that are used in the algorithms. 2.2.1 EGG CCD (common-mode accelerations) Common-mode acceleration measurements from the gradiometer instrument are used. The so-called sensitive pairs are used for each gradiometer axis. This data is obtained from the TU Delft HPF system, but is also readily available to GOCE users via the goce.esa.int website. 9 GOCE L1B and GOCE thruster L2 data actuation data Pre-processing and calibration Thruster Orbit Attitude Acceleration actuation Radiation Empirical density Empirical wind pressure model model evaluation model evaluation evaluation Modelled Modelled radiation composition, Modelled wind pressure temperature accelerations Compute initial Remove non- relative velocity aerodynamic accelerations Relative velocity Observed in SBF frame aerodynamic acceleration Aerodynamic Density and wind model evaluation processing Modelled density Density data Wind data Figure 2.1 Overview of the data processing in a single flow chart. Final and interme- diate data products are shown in yellow boxes. Standard data processing steps are blue, the use of thermosphere models is shown in green and the use of non-gravitational force models in brown. 10 2.2.2 EGG IAQ (attitude quaternions) Reconstructed attitude quaternion from the star cameras and gradiometer instrument are obtained from the TU Delft HPF system. This data is also readily available to GOCE users via the goce.esa.int website. 2.2.3 SST PSO (precise science orbits) The precise science orbit ephemeris is based on GPS satellite-to-satellite tracking data. It is obtained from the TU Delft HPF system, but is also readily available to GOCE users via the goce.esa.int website. 2.2.4 AUX NOM (ion engine thrust levels) The ion engine thrust level data is provided directly to the project team’s FTP site by ESA. The data come in XML files, which are parsed so that only a text file with a timeseries of 2.2.5 GOCE mass The GOCE mass as a function of time is available in a file named GOCE-Mass-Properties- COG-data.GOC, available for download from the goce.esa.int website. 2.3 Space environment models The NRTDM software incorporates several external models for the space environment. The following such models are applied in the GOCE data processing: • NRLMSISE-00 for atmospheric composition and temperature • HWM07 for in-track winds • Planetary ephemerides DE405 • Solar radiation pressure environment model (eclipse, varying Sun-Earth distance) from the ANGARA phase 2 code • Earth radiation pressure environment (Earth albedo and IR fluxes at the spacecraft) model adapted from the ANGARA phase 2 code 2.3.1 NRLMSISE-00 The NRLMSISE-00 model is the latest iteration of the MSIS series of models [Hedin et al., 1977a,b, 1979, Hedin, 1983, 1987, 1991] developed at NASA’s
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