Data-Driven Inference and Investigation of Thermosphere Dynamics andVariations

Piyush M. Mehta1, Richard Linares1, and Eric K. Sutton2

1Department of Aerospace Engineering and Mechanics, University of Minnesota, 2 Air Force Research Laboratory

Major Contributions

XNew methodology for data-driven inference andinvestigation of thermosphere dynamics and variations.

XReduced order modeling and self-consistent calibrationusing mass and number density observationssimultaneously.

Introduction

Modal decomposition or variance reduction methods offer anopportunity for data-driven investigation of thermospheredynamics and variations and for self-consistent calibrationof the thermosphere models. We develop the methodologyusing the MSIS model and infer oxygen-to-helium transi-tion as a validation by simultaneously assimilating discreteTIMED/GUVI and CHAMP/GRACE observations [1,2,3].

Methodology

We generate hourly model output (snapshots), xi, for eachinput sample generated using a latin-hypercube (F10.7 ∈[60, 250], Ap ∈ [0, 50], DOY ∈ [1, 365]) to cover the fullrange of inputs. We use a total of 365 + 8 (corner samples ofthe latin-hypercube) = 373 samples. A SVD decompositionis performed on the snapshot matrix, X = [x1, x2, . . . , xm], toderive the optimal set of basis vectors, U (X = USVT ), forO, O2, N2, and He. We do not tune N and H under the as-sumption that the CHAMP and GRACE observations do notcontain any signal about the minor species and that the par-tial pressure of H is negligible. The spatial basis vectors ormodes, U, can then be combined with time-dependent coef-ficients, c, such that x(s, t) =

∑ri=1 ci(t)Ui(s), where r is the

order or rank of truncation. The first (r = 3) modes for eachspecies captures more than 98% of the total variance. Thecoefficients, c, are derived by projecting the data, x, onto thespatial modes, U. We model their daily temporal variationsusing a sum of three cosine terms c(t) =

∑3i=1 ai cos(ωit+ζi)

and fit a, ω, ζ for each mode and species using Gaussian Pro-cess Regression for prediction at any new set of inputs.

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Measurement Intercalibration

Typically, reliable data assimilation requires the observationsto be intercalibrated. The CHAMP and GRACE observa-tions are first intercalibrated by multiplying the GRACEdensities with a yearly scale factor to match the mean andvariance of the observation-to-model ratio.

Figure: Observations/MSIS; CH = CHAMP, GR = GRACE, GR-S =GRACE Scaled, [mean,variance].

The GUVI number density and intercalibratedCHAMP/GRACE mass density observations are thencalibrated daily to the reference GUVI observation-to-modelvalue (based on mass density computed with O, N2, andO2) at ∼200 km, where the uncertainties are minimum.

Model or Measurement Calibration?

Intercalibration (IC) of observations accounts for biases withrespect to a given model; however, it keeps the calibrationfrom the true state by modifying the observations. The realgoal is to calibrate the model to the observations, even if itmeans relaxing certain model assumptions. We first validatethe data assimilation process with intercalibrated observa-tions for representative days (2002270 and 2007034 for highand low solar activity, respectively) using 3, 5, and 10 modes.We find that using 5 modes provides optimal results whileavoiding overfitting. We then perform assimilation w/o ICof the observations using 5 modes. All results presented arederived using 5 modes.

Table: RMS values. CH: CHAMP, GR: GRACE, GV: GUVI

Assimilate → CH GR CH+GR GV CH+GV GR+GV CH+GRValidate ↓ (%) (%) (%) (%) (%) (%) +GV (%)

2002270CH w/ IC 6.9 10.8 9.7 14.3 8.7 11.7 10.5GR w/ IC 16.3 10.0 10.1 14.1 15.2 10.8 10.7

CH w/o IC 6.2 12.0 9.1 14.8 9.5 13.5 12.4GR w/o IC 24.1 9.1 9.3 14.8 17.1 10.5 10.5

2007034CH w/ IC 7.5 16.8 10.7 27.6 8.8 16.1 10.7GR w/ IC 18.1 12.5 13.2 34.5 20.4 12.2 12.5

CH w/o IC 7.0 17.4 9.2 16.8 8.8 15.1 11.3GR w/o IC 29.1 11.2 11.7 18.4 22.7 11.5 12.1

Oxygen-to-Helium Transition

We use the methodology to infer He dynamics and O-to-Hetransition. Assimilation shows that the O-to-He transitionoccurs at significantly lower altitudes, as inferred by Thayeret. al., [4] using CHAMP and GRACE observations.

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Figure: Helium-to-Oxygen ratio on 2007034.The amount of O and He at higher altitudes differ signifi-cantly between the two different cases (w/ and w/o IC). Thisdifference is caused by the IC of observations with the casew/o IC providing the true state of the thermosphere. Forboth cases, MSIS underpredicts the amount of He at higheraltitudes in the winter polar region.

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Figure: He and O Assimilated/MSIS ratio on 2007034.The spatially and temporally averaged daily vertical pro-files of He and O are used to estimate the contribution oflower boundary composition and temperature effects underthe diffusive equilibrium assumption. Assimilating observa-tions with IC suggests over and underprediction by MSISclose to GRACE altitudes forO andHe, respectively. Assim-ilating without IC suggests that MSIS modelsHe accurately,however, significantly overpredicts O at GRACE altitudes.

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Figure: He and O vertical profile on 2007034.

Table: Contribution of composition and temperature variations125 km 500 km

(m−3) (m−3) (m−3) (m−3) Total % from fromMSIS Assimilated MSIS Assimilated Overprediction Comp Temp

w/ ICOxygen 1.27e17 1.49e17 3.87e12 3.18e12 21.7 -21.1 42.8Helium 4.47e13 4.61e13 1.88e12 2.46e12 -23.6 -2.4 -21.2

w/o ICOxygen 1.27e17 1.48e17 3.87e12 1.91e12 102.6 -33.5 136.1Helium 4.47e13 4.45e13 1.88e12 1.89e12 -0.5 0.5 -1.0

Storm-time Calibration

We also perform storm-time calibration to show that themethodology works effectively even during periods of highvariability; we perform assimilation on a 3-hourly time-scale.

Table: RMS values with and without IC (Intercalibration)w/ IC w/o IC

MSIS Assimilated MSIS AssimilatedAGU Storm, Days 348-350, 2006

CHAMP 49.1% 16.7% 60.5% 16.9%GRACE 81.8% 15.2% 105.1% 14.5%

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Figure: Calibration during the AGU storm, days 348-350, 2006

Conclusion

The developed method can be used for investigation and in-ference of thermosphere dynamics and variations and cali-bration of empirical models.

References[1] R. R. Meier and J. M. Picone, et. al.

Remote sensing of earth’s limb by timed/guvi: Retrieval of thermospheric composition and temperature.Earth and Space Science, 2(1):1–37, 2015.2014EA000035.

[2] Piyush M. Mehta, Andrew C. Walker, Eric K. Sutton, and Humberto C. Godinez.New density estimates derived using accelerometers on board the champ and grace satellites.Space Weather, 15(4):558–576, 2017.2016SW001562.

[3] Piyush M. Mehta and Richard Linares.A methodology for reduced order modeling and calibration of the upper atmosphere.Space Weather, 15(10):1270–1287, 2017.2017SW001642.

[4] J. P. Thayer, X. Liu, J. Lei, M. Pilinski, and A. G. Burns.The impact of helium on thermosphere mass density response to geomagnetic activity during the recent solar minimum.Journal of Geophysical Research: Space Physics, 117(A7):n/a–n/a, 2012.A07315.

Contact Information

•Email: piyushmukeshmehta@gmail.com•Phone: +1 (612) 481 7542

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