A Quasi-Physical Dynamic Reduced Order Model for Thermospheric Mass Density via Hermitian Space-Dynamic Mode Decomposition

Piyush M. Mehta, Richard Linares, Eric K. Sutton

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


Thermospheric mass density is a major driver of satellite drag, the largest source of uncertainty in accurately predicting the orbit of satellites in low Earth orbit (LEO) pertinent to space situational awareness. Most existing models for thermosphere are either physics based or empirical. Physics-based models offer the potential for good predictive/forecast capabilities but require dedicated parallel resources for real-time evaluation and data assimilative capabilities that are still under development. Empirical models are fast to evaluate but offer very limited forecasting abilities. This paper presents methodology for developing a reduced order dynamic model from high-dimensional physics-based models by capturing the underlying dynamical behavior. The quasi-physical reduced order model for thermospheric mass density is developed using a large dataset of Thermosphere-Ionosphere-Electrodynamics General Circulation Model (TIE-GCM) simulations spanning 12 years and covering a complete solar cycle. Toward this end, a new reduced order modeling approach, based on dynamic mode decomposition with control that uses the Hermitian space of the problem to derive the dynamic and input matrices in a tractable manner is developed. Results show that the reduced order model performs well in serving as a reduced order surrogate for TIE-GCM while almost always maintaining the forecast error to within 5% of the simulated densities after 24 hrs.

Original languageEnglish (US)
Pages (from-to)569-588
Number of pages20
JournalSpace Weather
Issue number5
StatePublished - May 2018

Bibliographical note

Funding Information:
The first two authors wish to acknowledge support of this work by the Air Force’s Office of Scientic Research under contract FA9550-18-1-0149 issued by Erik Blasch. The authors wish to acknowledge useful conversations related to DMD and reduced order modeling with Humberto Godinez of Los Alamos National Laboratory. The authors also wish to thank the anonymous reviewers for their helpful comments. The model can be downloaded at the University of Minnesota Digital Coservancy: http://hdl.handle.net/11299/194705.

Publisher Copyright:
©2018. American Geophysical Union. All Rights Reserved.


  • atmospheric drag
  • data assimilation
  • dynamic mode decomposition
  • forecasting
  • reduced order model


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