Use of systems based models for the forecasting of space weather

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Presentation transcript:

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 637302.

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

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

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

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

solar wind magnetosphere Kp 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:10.1002/2016SW001463 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

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

GSO e- flux forecasts Models for 30-50 keV, 50-100 keV 100-200 keV, >2MeV View latest forecasts at https://ssg.group.shef.ac.uk/progress/html/ http://ssg.group.shef.ac.uk/ssg2013/proj_UOSSW.htm Dec 1st, 2017 ESWW 14, Oostende, Belgium

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:10.1002/2015SW001303. Dec 1st, 2017 ESWW 14, Oostende, Belgium

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 1.8-3.5 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:10.1002/jgra.50192. 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

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 100-400 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), 10.1002/2017JA024523 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:10.1002/2016JA022916. Dec 1st, 2017 ESWW 14, Oostende, Belgium

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:10.1029/2010GL045733 Dec 1st, 2017 ESWW 14, Oostende, Belgium

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 637302. Dec 1st, 2017 ESWW 14, Oostende, Belgium