Frontiers of Time Series Modeling 2: Nonparametric Approach to Knowledge Discovery Data Mining Approach to Space Weather Forecast T. Higuchi (Institute of Statistical Mathematics) S.-I. Ohtani (Johns Hopkins Univ./Applied Physics Lab. US)
Solar Wind Sun Earth Magnetosphere
Large-Scale Field-Aligned Current Structures Magnetic field Z Current sheet A Y X Satellite orbit Satellite Orbit Up Down Up Magnetic Pole
Space Weather Forecasting sun Solar Wind Monitoring Satellite Solar Wind Copyright JHU/APL Low Altitude Satellite Earth's Magnetosphere Solar Wind
Defense Meteorological Satellite Program Low Altitude 830 [km] Period about 100 [min.] Polar Orbit Sampling interval: 1 [second] Data Interval: 5 years 1983/12/06 1988/01/25 DMSP Satellite Coordinate System B=[Bx, By, Bz] x: radially downward y: parallel to the projection of the spacecraft velocity onto the plane perpendicular x Y Z X ' Sun Dayside Satellite Orbit Nightside x Center of the Earth
Coverage of Orbits of DPSP-F7 Magnetic Pole Dayside LSFAC MLT Mlat Nightside LSFAC FAC region
Flow chart of the Procedure Check of artificial noises Identification of LSFAC region from B z Minimum Principal Component Variance Analysis ( B y, B z ) ( B P, B A ) Polyline fitting Identify LSFAC region from B A Pick up candidates for node points a) Calculate auco-correlation b) Design lowpass filter c) Apply lowpass filter d) Detect local max. and min. points Select best nodes Node values are determined by least squares fit Optimal node number is selected by AIC Result
Polyline fit (First order B-spline) with Magnetic field Zvariable nodes A X Current sheet Satellite orbit Y A geophysical model can be represented by the polyline. Up Down Up Downward Upward A procedure is applied to 71,954 data files for the entire interval of satellite operation.
Polyline FAC Type, Intensity, Flow direction, depends on a) Time-dependent solar wind parameter b) Solar zenith angle c) Satellite orbit First-Order B-spline with J variable nodes Ex. J=4 (t,y ) 1 1 (t,y ) (Hiragi, Urakawa, and Tanabe (1985)) 2 2 (t,y ) 4 4 A plot of the magnetic perturbation can have any shape!! node position node value (t,y ) If T J=[ t 1, t 2,..., t J]' is given, an estimation of Y J=[ y 1, y 2,..., y J]' 3 3 is easy!
Design of Low-pass filter for each interval Equatorward LSFAC Poleward A A R (k)= (y - y)(y - y) n n+k Auto-correlation R (k) k* Preliminary determination of FAC interval from B A 0 k* k * k* Lag k design Lowpass Filter LF, LF, LF
Pick up of candidates for optimal node positions Smoothed curves obtained by applying a lowpass filter designed in each sub-interval by using information of auto-correlation. E I A E B ~ A E L A F I A F B ~ A P L A P I A P B ~ A : Local minimum and maximum points T = 10 E E E F F F P P P [ t1, t2, LA, t1, t2, t3 LA, t1, t2, t3 P ]
Determination of optimal node number SSR J = N ( B ) A, n B fit, n n = 1 2 SSR is a monotonously decreasing function with J. SSR alone does NOT determine J.
Fine adjustment of node positions: Results obtained by applying a linear low pass filter 1) Underestimate of an intensity of FAC 2) Overestimate of a width of FAC region
(Node position, Node value) = Width: I Height: ( t 1, g1) t, ) ( g 0 0 j H = t j = j+ 1 g t j+ 1 j ( t j, g j ) g j σ = N ( B ) A, n B fit, n n= 1 N 2, R fit = σ H max
R fit = σ H max R fit 8 Example: --Dayside --Northern hemisphere --3 current systems Day-side and 3 sheets LSFAC
Night-side LSFAC (Northern Hemisphere)
Four Large Scale FAC systems: (Ohtani et al., JGR, 1995) B L B A B A :Azimuthal component (maximum variance direction) B L : magnetic Latitudinal component (minimum variance direction)
Summary This procedure can make an important contribution to space weather and scientific research. The present procedure allows us to analyze an entire set of the DPSM-F7 data, and it can be easily applied to other datasets. The robustness of our procedure will allow us to conduct a statistical study of an unprecedented size, which will provide new insights into understanding the sun-earth physical connection.