A New Empirical Model for Ionospheric Total Electron

ContentCole Tamburri1,2, Larisa Goncharenko2, William Rideout2, Anthea Coster2

1Boston College, 2MIT Haystack Observatory

American Geophysical Union Fall Meeting

9 December 2019

Introduction and Motivation• Forecasting the future state of the ionosphere is a fundamental challenge for near-space

environment research and operations

• The Space Weather Phase I Benchmarks (2017) cites the need for enhanced fundamental understanding of space weather and its drivers and improved predictive models

• Empirical ionospheric models still often outperform the theoretical models (Shim et al., 2011, 2012, 2017, 2018; Tsagouri et al., 2018)

• Significant effort in the community to develop new global or regional empirical models, in particular, models of Total Electron Content, TEC (Mukhtarov et al., 2013; Chen et al., 2015; Lean et al. 2016, 2019; Feng et al., 2019)• Most TEC models are based on GIM TEC data with 2 hrs resolution• Assumptions are used for areas with scarce or absent data

• Objective:• Develop an accurate, high-resolution empirical TEC model utilizing 20 years of data• Create a framework to study additional drivers• Use final model to study the variation of different parameters and their impact on TEC• Identify anomalies in TEC (and corresponding conditions) using final global model.

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Data Sources• TEC – GNSS, provided by CEDAR Madrigal

database.• Measured in TEC units (1 TECU = 1016

electrons/m2)• Available in 1o x 1o bins with 5 min temporal

resolution since 2000

• Solar Flux and delays• 10.7cm radio flux (F10.7) – CEDAR Madrigal

Database• Extreme Ultraviolet flux (EUV) – TIMED Solar

Extreme Ultraviolet Experiment (SEE)

• Geomagnetic Activity• Ap3 (3-hour Ap index), Kp (logarithmic), and

delays – CEDAR Madrigal Database

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Data Preparation

• Sidereal motion of satellites causes periodic artificial data variability in TEC data plots• More severe at solar minimum (absolute

error remains relatively the same)

• Regions of low GNSS coverage offer less data

• Goal: remove artificial variability while preserving reliable TEC variations

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UT

Ho

urs

Raw TEC at 45LAT, 0LON, 2011

UT

Ho

urs

TEC UnitsRaw TEC at 45LAT, 60LON, 2003

Examples of data problems in GNSS TEC data

Improving Data Quality• Hampel filter

• Vertical (13 point window, 1σ criterion)• Horizontal (3 point window, 3σ criterion)

• Cubic spline interpolant with low tolerance

• Iterative model-building - removal of points with:1. % data-model beyond 2σ of the mean2. Solar flux and delays < 0.007 W/m2

3. Ap3 and delays < 80

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Incremental result of process improving data quality

(a) Data before and (b) after filtering

Input Parameters: Solar Flux

• Indices available for use: EUV, F10.7• F10.7 – captures last solar cycle of

data well according to Mukhtarov et al. (2013)

• EUV – more comprehensive, able to identify smaller-scale disturbances

• Modulation by annual, semiannual, four-monthly, and three-monthly terms.

• Different delays investigated – not a moving 81-day average of solar flux

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Fit coefficients and p-values for EUV flux for 45oN, 0oE

Input Parameters: Geomagnetic Index and Solar Zenith Angle

• Geomagnetic index • Several available indices – Ap3, Kp, Dst

• 33-hour integral of Ap3 useful for storm-time (Araujo-Pradere et al. 2002)

• Longer-term delays statistically significant for general model – 3 hour, 24 hour, 48 hour, 72 hour

• Solar Zenith Angle• Potential to be used to describe seasonal

variation

• Less easily implemented into the model, no improvement in performance.

• Convenience of use – user can more easily input DOY (day-of-year) than solar zenith angle

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Fit coefficients and p-values for Ap3 index for 45oN, 0oE

Input Parameters: Final Selection

• EUV flux (linear and quadratic)• EUV delays: 1 day, 8 days, 24 days, 36 days• Ap3 index (linear and quadratic)• Ap3 delays: 3 hours, 24 hours, 48 hours (linear and quadratic),

72 hours• Seasonal terms: annual, semiannual, four-monthly, three-

monthly• Modulation of EUV linear term by annual, semiannual, three-

monthly terms• Modulation of EUV quadratic term by all periodic terms• Total number of predictors: 36

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Results and Model Performance• Final Model: Linear Regression

• Notable/unprecedented: developed at 45oN with 3o spatial resolution in longitude, 30 minute temporal resolution

• RMS Error of 1.78 TECU for whole model at 45LAT

• 3.387 TECU for Mukhartov. et al. (2013), ~2.9 TECU for Feng et al. (2019), 3.5 TECU for Lean et al. (2016)

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Model performance metrics for model at 45oN, 0oEMAPE = Mean Absolute Percentage ErrorRMSPE = Root Mean Square Percentage Error

Data and model for 45oN, 0oE

Model Performance – Comparison to IRI2012

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• IRI2012, low solar flux – 2008• IRI fails to show short-term variations as well as our

model, though this is less obvious during years of low solar flux

• IRI underestimates nighttime TEC• IRI fails to predict late-March increase in TEC

observed in data• IRI shows early summer peak slightly later than data

and our model (early June rather than late May)• Similar double-peaked structure during summer

months• Similar peak observed in mid-October, though

slightly more pronounced in our model.• RMSE

• IRI – 1.9714 TECU

• Version74 – 0.9008 TECU

Comparison of raw data, IRI2012, and new model, 2008

Model Performance – Comparison to IRI2012

• IRI2012, moderate/high solar flux – 2012• IRI fails to capture short-term variations in TEC• IRI predicts slightly earlier peak in midday TEC

during spring equinox• IRI predicts slightly later peak in midday TEC

during fall equinox • Midsummer peak in TEC reflected better by our

model than IRI• Similar double-peak structure during summer

months, though this is more pronounced in our model

• IRI overestimates daytime TEC, especially during the winter months

• RMSE• IRI – 4.2353 TECU

• Version74 – 1.9459 TECU

11Comparison of raw data, IRI2012, and new model, 2012

Seasonal and Longitudinal Features

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Prominent features in the new TEC model:• Strong semiannual anomaly• Spring equinoctial peak is higher than autumn equinoctial peak• Timing of equinoctial peaks vary with longitude• Significant longitudinal difference in diurnal behavior, especially during summer season

Summary

Acknowledgements

• This work was supported by the National Science Foundation through its generous Research Experience for Undergraduates program.

• Thanks to the MIT Haystack Observatory for development of the CEDAR Madrigal Database and to the TIMED SEE team for provision of EUV data.

• Finally, thanks to the entire MIT Haystack Observatory staff for graciously hosting my work for the summer and providing continued support. 13

• A new empirical model of TEC is developed based on GNSS data provided by Madrigal database• Current model is for 45oN• Input parameters include solar flux (EUV), geomagnetic activity (Ap3), seasonal variation and

modulation, and delay terms• 3 degree longitudinal resolution, 30 minute temporal resolution, low RMSE

• Comparison to IRI2012 shows better agreement with data, particularly during years of high solar flux• Model shows significant longitudinal features • Future work

• Continue diagnostics and compare to other models• Expand model to other latitudes with 3o x 3o spatial resolution and longer time period• Investigate additional drivers/independent variables• Identify anomalies using final model

References

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