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On the usage of Principal Components Analysis (PCA) for the Prediction of Solar Energetic Particle (SEP) events

A. Papaioannou1, A. Anastasiadis1, A. Kouloumvakos2, M. Paassilta3, R. Vainio3, E. Valtonen3, A. Belov4, E. Eroshenko4, M. Abunina4, A. Abunin4

1IAASARS, National Observatory of Athens, Penteli, Greece 2IRAP, Université de Toulouse, CNRS, CNES, UPS, Toulouse, France

3Departement of Physics, University of Turku, Finland 4IZMIRAN, Troitsk, Moscow, Russia

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

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Distinction of 2 classes of events:

-Impulsive (small, frequent, presumably flare related)

- Gradual (large, rare, presumably fast CME related)

Impulsive Gradual

Impulsive Gradual

Credit: SOHO / NASA / ESA

Solar Energetic Particle (SEP) events

The origin of SEP events

Motivation

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Solar Energetic Particle (SEP) events

> We know that several inter-related quantities (solar) that describe (map) SEP events Can we make use of a higher-order combination of these quantities in order to classify and predict SEP events ?

Solar Energetic Particle (SEP) events

Motivation

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> Principal Component Analysis (PCA) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantities.

Principal Components Analysis (PCA)

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

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> PCA rotates the original data space such that the axes of the new coordinate system point into the directions of highest variance of the data

> 126 SEP events + 3599 non SEP events

> 6 variables > several different mappings

Application of the PCA

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

1. 2. 3. 4. 5. 6.

DATA MATRIX

> The variance plot shows how much variance in the dataset is explained by which PC (as bar) and how much variance is explained by the first n PCs (as line)

Application of the PCA

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

> PCA is a transformation of the old coordinate system (data grid) into the new coordinate system (PC), it can be estimated how much each of the old coordinates (columns of the data matrix. i.e. variables) contribute to each of the new ones (PCs) Loadings

Application of the PCA

> The values that the row vectors (observations/data) have in the component space

(PCs space) Scores

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Load

ings

> Radiation storms [S2 – S4] are closely related to SFs:

> of M and X magnitude

> mostly impulsive + short duration

> central, east & west

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

Score Plots l Classification of SEPs l Flares

> Radiation storms [S2 – S4] are closely related to:

> Fast and Halo CMEs

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

Score Plots l Classification of SEPs l CMEs

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> Apply Logistic Regression

# 1-parametric regression

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> Apply Logistic Regression

# 1-parameric regression

# multivariate regression

> Apply a probability threshold of 50% > Construct a contingency table > Calculate Categorical metrics (POD, FAR)

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

# multivariate regression

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> pth = 50 %

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> pth = 50 %

+ interaction terms

> Apply different probability thresholds of 25%, 50%, 75% > Construct a contingency table (pth = 50%) > Calculate Categorical metrics (POD, FAR)

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

# multivariate regression [+ interaction terms]

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> pth = 50 %

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

> pth = 50 %

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Application of the PCA

A possible index (I) for SEP nowcasting

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Conclusions

> PCA can be used for the:

• Classification the SEP events with respect to the characteristics of their parent solar drivers

• Prediction of the occurrence (or not) of an SEP event; utilizing logistic regression and the I index

Papaioannou et al, Solar Physics, 2018

> AP would like to acknowledge support from a post-doctoral IKY scholarship funded by the action “Supporting post-doctoral researchers” from the resources of the b.p. “Human Resources Development Education and Lifelong Learning” with Priority Axes 6, 8, 9 and co-funded by the European Social Fund and the Greek government. AA would further like to acknowledge the “SPECS: Solar Particle Events and foreCasting Studies” research grant of the National Observatory of Athens. MP and RV acknowledge the funding from the Academy of Finland (decision 267186). Research conducted by MP and RV was further supported by ESA contract 4000120480/17/NL/LF/hh

15th European Space Weather Week (ESWW15)

Session 6 Unveiling Current Challenges in Space Weather Forecasting Leuven

07.11.2018

Papaioannou et al, Solar Physics, 2018

Thank you

http://members.noa.gr/atpapaio/iky.html

Acknowledgement