Work Description

Date: 22 September, 2020

Dataset Title: Multifaceted Optimization Algorithm Version Dataset

Dataset Creators: D. A. Brandt, C. D. Bussy-Virat, A. J. Ridley

Dataset Contact: Daniel Brandt, branddan@umich.edu

Funding: Rackham Merit Fellowship, NRL Grant Number N00173-18-1-G00G, and NASA Grant #NNX15AJ20H (Michigan Space Grant)

Key Points:
- Empirical atmospheric models exhibit significant density underestimation during geomagnetic storms.
- A simple algorithm presents a new way of obtaining improved density model estimates from two-line elements describing satellite orbits.
- The technique is validated against Swarm GPS-derived densities during geomagnetic quiet and active times.

Research Overview:
Empirical models of the thermospheric density are routinely used to perform orbit maintenance, satellite collision avoidance, and estimate time and location of re-entry for spacecraft. These models have characteristic errors in the thermospheric density below 10% during geomagnetic quiet time, but are unable to reproduce the significant increase and subsequent recovery in the density observed during geomagnetic storms. Underestimation of the density during these conditions translates to errors in orbit propagation that reduce the accuracy of any resulting orbit predictions. These drawbacks risk the safety of astronauts and orbiting spacecraft, and also limit understanding of the physics of thermospheric density enhancements. Numerous CubeSats with publicly available ephemeris in the form of two-line element (TLEs) sets orbit in this region. We present the Multifaceted Optimization Algorithm (MOA), a method to estimate the thermospheric density by minimizing the error between a modeled trajectory and a set of TLEs. The algorithm first estimates a representative cross-sectional area for several reference CubeSats during the quiet time three weeks prior to the storm, and then estimates modifications to the inputs of the NRLMSISE-00 empirical density model in order to minimize the difference between the modeled and TLE-provided semi-major axis of the CubeSats. For validation, the median value of the modifications across all CubeSats are applied along31the Swarm spacecraft orbits. This results in orbit-averaged empirical densities below 10% error in magnitude during a geomagnetic storm, compared to errors in excess of 25% for uncalibrated NLRMSISE-00 when compared to Swarm GPS-derived densities.

Methodology:
The data are outputs from the Multifaceted Optimization Algorithm (MOA), along with the most recent version of the files that constitute the MOA source code.

Instrument and/or Software Specifications: N/A

Files contained here:
There are four .tar.gz files that must be uncompressed with the 'tar -xvf' command:
- Code.tar.gz contains various Python modules called upon by the rest of the MOA code
- MOA_OUT_1_sats_2017-05-23_2017-06-02_25.tar.gz contains raw MOA outputs for MOA runs that used the 25th percentile of the distribution of calibration satellite cross-sectional areas
- MOA_OUT_1_sats_2017-05-23_2017-06-02_50.tar.gz contains raw MOA outputs for MOA runs that used the 50th percentile of the distribution of calibration satellite cross-sectional areas
- MOA_OUT_1_sats_2017-05-23_2017-06-02_75.tar.gz contains raw MOA outputs for MOA runs that used the 75th percentile of the distribution of calibration satellite cross-sectional areas

The following Python scripts are required for generating figures that display the outputs from MOA, which include spacecraft cross-sectional areas, modified 10.7 cm solar radio flux (F10.7), modified geomagnetic activity (ap), and new model densities.

- MOA_comparator.py (computes median and mean values of modified F10.7 and ap across all calibration satellites)
- MOA_comparator_hist_lines.py (computes distribution and time-varying plots of calibration satellite cross-sectional areas)
- MOA_percentile_f107_compare.py (compares the modified F10.7 values calculated after MOA's use of the 25th, 50th, and 75th percentile of the cross-sectional areas)
- MOA_verify.py (computes new model densities)
- MOA_validate.py (called by MOA_verify.py)
- OMNIWeb_SWPC_plotter.py (downloads unaltered F10.7 and ap from NASA)

Several prerequisites are necessary before using any of the scripts:
- GNU Emacs
- Python 3.0+, Numpy 1.16
- spacepy (to work with NETCDF files, which requires a proper local build of HDF5)
- python wrapper for msise00 (courtesy of Dr. Michael Hirsch: https://pypi.org/project/msise00/, if on Linux, simply 'pip install msise00')

## GENERATING FIGURES ##

Unaltered F10.7 and ap as collected by NASA:
-----------------
(SWPC and OMNIWeb Geomagnetic Indices)
1. Open a terminal
2. type 'ipython' and hit 'enter' on the keyboard
3. type 'run OMNIWeb_SWPC_plotter.py' and hit 'enter' on the keyboard
4. type 'exit' and hit 'enter' on the keyboard to leave 'ipython'.
5. Figure 9a and 9b can are saved locally to 'OMNIWeb_SWPC_Geomagnetic_Indices_2017-05-23-2017-06-02.pdf'.
NOTE: Lines 38 and 39 are set to the dates '2017-05-23' and '2017-06-02', respectively, and must not be changed in order to be consistent with the figure in the paper.

MOA Outputs 1:
----------
(Histograms of overlapping optimized areas)
1. Open a terminal
2. type 'ipython' and hit 'enter' on the keyboard
3. type 'run MOA_comparator_hist_lines.py' and hit 'enter' on the keyboard
4. type 'exit' and hit 'enter' on the keyboard to leave 'ipython'.
5. Figure 10 is saved to 'Optimized_Area_Histograms_10_sats_2017-05-09-2017-05-24_OMNIWEB.png' in the directory here: /MOA_OUT_1_sats_2017-05-23_2017-06-02_75/MOA_GRIDS_10_2017-05-23_2017-06-02_OMNIWEB
NOTE: No lines of this script ought to be changed.

MOA Outputs 2:
----------
(Linearly-interpolated F10.7 corrections for each percentile of optimized area)
1. Open a terminal
2. type 'ipython' and hit 'enter' on the keyboard
3. type 'run MOA_percentile_f107_compare.py' and hit 'enter' on the keyboard
4. Figure 12 is saved to 'MOA_percentiles_f107_compare_2017-05-23_to_2017-06-02_OMNIWEB.png' in the local working directory.
NOTE: As is the case for Figure 10, no lines of the script run for this figure should be changed.

MOA Outputs 3:
-------------------
(dSMA/dt across all Flock 3P satellites, static and linearly-interpolated F10.7 corrections, and F10.7 and ap corrections along with adjusted F10.7 and ap)
1. Open a terminal
2. type 'ipython' and hit 'enter' on the keyboard
3. type ' run MOA_comparator.py' and hit 'enter' on the keyboard
4. All figures are saved in the directory: 'MOA_OUT_1_sats_2017-05-23_2017-06-02_75/MOA_GRIDS_10_2017-05-23_2017-06-02_OMNIWEB'
5. Figure 9c is titled: 'MOA_comparisons_DSMA_10_2017-05-23-2017-06-02_OMNIWEB_75.png'
6. Figure 11 is titled: 'ALL_CORRECTIONS_2017-05-23_2017-06-02_OMNIWEB.png'
7. Figure 13 is titled: 'BIG_STACK_2017-05-23_2017-06-02_OMNIWEB.png'

New Model Densities:
-------------
(Orbit-averaged densities by percentile along SWARM-A and SWARM-B, and Orbit-averaged densities by MOA, MSISE00, and SWARM along SWARM-A and SWARM-B)
NOTE: All figures can be made by opening the terminal, starting ipython, and typing and entering 'run MOA_verify.py'. The only thing different between making each figure are the arguments in the script in lines 32, 33, and 41.

Figure 14a:
Line 32 = 'SWARM-A'
Line 33 = '39452'
Line 41 = 25
Figure saved locally to: 'VAL_SWARM-A_MOA_verify_ALL_SPLINES_COMP_2017-05-23-2017-2017-06-02_OMNIWEB_interp.png'

Figure 14b:
Line 32 = 'SWARM-B'
Line 33 = '39451'
Line 41 = 25
Figure saved locally to: 'VAL_SWARM-B_MOA_verify_ALL_SPLINES_COMP_2017-05-23-2017-2017-06-02_OMNIWEB_interp.png'

Figure 15a:
Line 32 = 'SWARM-A'
Line 33 = '39452'
Line 41 = 75
Figure saved locally to: 'VAL_SWARM-A_MOA_verify_SPLINES_2017-05-23-2017-2017-06-02_OMNIWEB_75_interp.png'

Figure 15b:
Line 32 = 'SWARM-B'
Line 33 = '39451'
Line 41 = 75
Figure saved locally to: 'VAL_SWARM-B_MOA_verify_SPLINES_2017-05-23-2017-2017-06-02_OMNIWEB_75_interp.png'

NOTE: Do not change any other lines in MOA_verify.py

Related Publication(s):
Brandt, D. A., et al. (2020). A Simple Method for Correcting Empirical Model Densities during Geomagnetic Storms Using Satellite Orbit Data. [Under review]

Use and Access:
This data set is made available under an Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license.

To Cite Data:
Brandt, D. A., Bussy-Virat, C. D., and Ridley, A. J. (2020), A Simple Method for Correcting Empirical Model Densities during Geomagnetic Storms Using Satellite Orbit Data [Data set]. University of Michigan - Deep Blue.