1. Use of systems based models for the forecasting of space weather
S. N. Walker[1], T. Arber[2], K. Bennett[2], M. Liemohn[3], B. van der Holst[3], P. Wintoft[4], N. Y. Ganushkina[5], and M. A. Balikhin[1]
[1] Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK
[2] Dept Physics, University of Warwick, Coventry, UK
[3] Climate and Space Sciences Engineering, University of Michigan, Michigan, USA
[4] Swedish Institute of Space Physics, Lund, Sweden
[5] Finnish Meteorological Institute, Helsinki, Finland
Changes in the solar wind induce a response in the magnetosphere through a complex series of processes and interactions. The underlying philosophy used within numerical codes is to understand and model each process individually before conjugating them to model the overall system. The diversity and scales of the processes involved in such a chain is a major drawback for this kind of approach. Systems science proves a second, alternate route for modelling such process chains. These methodologies, which are data driven, study the evolution of a system as a whole, based on a set of system inputs. In contrast to other data driven methodologies, system science techniques can be used to probe the underlying physics and may also be used for the validation of numerical and analytical models.
This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No

2. Overview Modeling methodologies NARMAX modeling Kp
Electron fluxes at GEO
Electron dropout events
Dec 1st, 2017
ESWW 14, Oostende, Belgium

3. Modeling Methodologies
First principles, physics based models
Process 1
System
Process 2
Process n
Model 1
Model 2
Model n
Physical knowledge
Model of Complete System
Assumptions …
Dec 1st, 2017
ESWW 14, Oostende, Belgium

4. Modeling Methodologies
Neural Network Approach
Input data
Output data
System
Dec 1st, 2017
ESWW 14, Oostende, Belgium

5. Modeling Methodologies
Systems Approach
Input data
Output data
System
Physical knowledge
System outputs
System inputs
Noise/errors
F[] is a nonlinear function (polynomial, B-spline, radial basis function)
Dec 1st, 2017
ESWW 14, Oostende, Belgium

6. solar wind magnetosphereKp
Coupling
solar wind magnetosphere
Solar Wind at L1
V, Bs, VBs, p, √p Kp
Two approaches
Sliding window
Used to forecast 3, 6, 12, 24h ahead
Fixed length window to build model
Window moved 1 time step
Repeat
Direct approach
One model for each forecast horizon
Trained Jan-Jun 2000
Validate Jul-Dec 2000
Ayala Solares, J. R., et al. (2016), Modeling and prediction of global magnetic disturbance in near-Earth space: A case study for Kp index using NARX models, Space Weather, 14, 899–916, doi: /2016SW001463
Kp model
Inputs V Bs, VBs, p sqrt(p)
Output Kp
Two approaches
Sliding window – trains model and us recursively to forecast
fixed length data window (6 months)
Create model using this data
Make forecasts3, 6, 12, 24 hours ahead
Move window one time step
Repeat
Direct approach – separate model for each forecast horizon
Dec 1st, 2017
ESWW 14, Oostende, Belgium

7. Kp Sliding window models Direct models
Plots show results of forecasts for 3, 6, 12, and 24 hour ahead
Left sliding window method, right direct method
Tables show root mean square error, correlation, prediction efficiency
Main problem with model is forecast of low (Kp<=1 and )high (Kp>7) Kp values
Dec 1st, 2017
ESWW 14, Oostende, Belgium

8. GSO e- flux forecasts Models for 30-50 keV, 50-100 keV 100-200 keV,
>2MeV
View latest forecasts at
Dec 1st, 2017
ESWW 14, Oostende, Belgium

9. GSO e- flux forecasts Model comparison
One day ahead forecasted fluxes >2 MeV electrons compared with NOAA REFM
Prediction Efficiency
Correlation function
e- Flux
Log10(e- Flux)
Model PE
Corr
REFM
-1.31
0.73
0.70
0.85
SNB3GEO
0.63
0.82
0.77
0.89
Relativistic electron forecast model
Balikhin, M. A., et al. (2016), Comparative analysis of NOAA REFM and SNB3GEO tools for the forecast of the fluxes of high-energy electrons at GEO, Space Weather, 14, 22–31, doi: /2015SW
Dec 1st, 2017
ESWW 14, Oostende, Belgium

10. solar wind magnetosphere
Electron Fluxes at GSO
Coupling
solar wind magnetosphere
Solar Wind at L1
Electron Flux at GSO
Energy
Term 1
%ERR
Term 2
% ERR
90 keV
V(t)
97.0
V2(t)
2.7
127.5 keV
74.8
V(t-1)
22.2
172.5 keV
65.7
31.6
270 keV
97.5
V2(t-1)
2.3
407.5 keV
84.1
V(t-2)
13.7
625 keV
75.9
22.3
925 keV
96.2
N(t)
0.3
1.3 MeV
V2(t-2)
76.5
nV(t-1)
2.2
2.0 MeV
N(t-1)
53.7
13.6
MeV
51.5
N2(t-1)
15.1
Boynton, R. J., et al., (2013), The analysis of electron fluxes at geosynchronous orbit employing a NARMAX approach, J. Geophys. Res. Space Physics, 118, 1500–1513, doi: /jgra
All but top 2 enerfies – velocity is dominant control term for electron flux variance
Agree with Paulikas and Blake 1979, Geoff Reeves 2011
Top 2 energies previous days density is most important
ER > 50 % together with both energy models indicates not error
Velocity squared still appears in top 5 tmodel terms at these high energies
Coupling between density and velocity plays minor (3%) role
e.g. pV (nV3) or np (n2V2)
Bs found to have negligable influence < 0.1% - may be due to short time sale of dynamics associated with Bz ie hours rather than days for density, velicuty
Daily averaging probably hides Bz dynamics
Time delay also changes
Lower energies depend current velocity
Medium energies velocity previous day
Top energies V two – four days previously appears from analysis
i.E larger energies for larger time delays
Generally, Time delays in accordance with wpi and radial diffusion models – acceleration processes (WPI/radial diffusion) act on seed population, accelerating to high energies
However RD is slow process for particles to reach geostationary orbit– sqrt(time)
NARMAX results can be used to quantify dependence time delay and energy
Results show observed diffusion is a faster process due to interacton with local waves
Dec 1st, 2017
ESWW 14, Oostende, Belgium

11. Electron Flux dropouts
Which solar wind parameters/geomagnetic indices control the drop out of electron fluxes ?
L=4.2 (GPS orbit)
L=6.6 (GEO orbit)
Dropout selection criteria
Electron fluxes Sampled 4.1 < L < 4.3 in vicinity of magnetoc equator
Data from all satellits aeraged over 12 hours
18 Feb 2001 – 31 Dec 2016
L4.2 high energy dropouts more frequent than low energy
Dropouts appear larger at lower energy
Mediam magnitude of dropout also intreases with energy
20% dropouts mahgnetopause above L=8
25-40% dropouts at L 4.2 had no counterpart at L=6.6
Most Multi Mev droputs occur utside plasmapause
MARMAX
output – series of magnitue drops – flux before divided lower flux
Inputs sw vel, den, dypress, Bs, AE, Dst – lags t-0,to t-4 data points
Resuts indicat additionalloss mechanism at multi-MeV energies
Strongly dependant upon Bs, relatively indepenndent of mp shadowing
Suggests important role of priciptitation loss due to combined Chorus/EMIC in large number of evevnts studied
L 6.6
Dropouts less numrous between 63 keV and 650 keV
Dropout magnitude constant below 1 Mev, stringly increasing above
Factors
AE < 90keV
AE/density keV
pressure/density 128 < E < 925 keV
Dypress/Bs 1.3M-2M
Radial diffusion + shadowing not sole driving factor for al dropouts
>1MeV precipitation from EMIC and Chorus/hiss also effectivr, anso increased field line curvature during the disturbaabce
.1 – 1MeV radial diffusion coupled to MP shadowing related to increases in pressure, density
20-100keV chorus driven precipitation plus in/out radial diffusion during periods of high AE
L 4.2 additional loss mechanism for high energies
R. J. Boynton,1 D. Mourenas,2 M. A. Balikhin,1, Electron flux dropouts at L ∼ 4.2 from Global Positioning System satellites: Occurrences, magnitudes, and main driving factors Accepted J. Geophys. Res. (Space Physics), /2017JA024523
Boynton, R. J., D. Mourenas,and M. A. Balikhin (2016), Electron flux dropouts at Geostationary Earth Orbit: Occurrences, magnitudes,and main driving factors, J. Geophys. Res. Space Physics, 121, 8448–8461, doi: /2016JA
Dec 1st, 2017
ESWW 14, Oostende, Belgium

12. Coupling functions
Many solar wind-magnetosphere coupling functions have been proposed
NARMAX was used to determine the top 5 coupling functions
7 function + Dst
time lags (t-1), …, (t-5)
Solar wind input parameters
Dst output
Top 5 – percent NERR based on 7 models + Dst at lags t-1 to t-5 – total 40 parameter combinations
Selecting parameters from these coupling functions p1/2, n1/6, V, V4/3, Bs, BT sin4 and BT sin6 clock angle
Use NARMAX to rearrange these parameters
Larger number of possible expressions leads to lower percentages
Top 5 sets of parameters p1/2, n1/6, V, V4/3, Bs, BTsin4(θ/2) and BTsin6(θ/2) combined by NARMAX
Balikhin, M. A. et al. (2010), Data based quest for solar wind‐magnetosphere coupling function, Geophys. Res. Lett., 37, L24107, doi: /2010GL045733
Dec 1st, 2017
ESWW 14, Oostende, Belgium

13. Thank you for your attention
Summary
In the presentation it has been shown that the systems methodology NARMAX may be used to
Generate data based models for the forecast of space weather related parameters
Provide some insight in to the physical processes occurring within the system
Thank you for your attention
This project has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No
Dec 1st, 2017
ESWW 14, Oostende, Belgium