input averaging time in secs average #sampling_classic input averaging time in secs median average #median input averaging time in secs root mean square #rms input window time in secs min() function #min input window time in secs max() function #max input window time in secs variance() function #var input window time in secs skewness() function #skew input averaging time in secs average #sliding_average input averaging time in secs root mean square #rms_sm input window time in secs min() function #min_sm input window time in secs max() function #max_sm input window time in secs variance() function #var_sm input window time in secs skewness() function #skew_sm input averaging time in secs smooths with a boxcar average #boxcar input time interval T in secs to delay by Delays array by T secs back (T < 0) and forth (T > 0)) #timeShift Cross product cross Angle between two vectors angle magnitude of a vector magnitude Dot product dot Magnitude magnitude Alfven velocity Valfven(density[cm^⁻3], mag[nT]) alfvenVelocity FAIRFIELD 1970 model of neutral sheet position Z = fairfield70(xyz_sm, x_ss) fairfield70 FAIRFIELD 1980 model of neutral sheet position Z = fairfield80(xyz_sm, x_ss) where xyz_sm are the solar magnetospheric coordinates of the spacecraft and x_ss is tilt angle fairfield80 Perreault and Akasofu 1978 model u = perreault78(E_mag, B_mag, theta_p) perreault78 NEWELL et al 2007 solar wind-magnetosphere coupling function d_phi/d_t = newell2007(mu, B_mag, theta) newell2007 Lopez 1990 model of magnetic latitude of the neutral sheet MLAT = lopez90(Kp, phi, R, DTA) where Kp is the 3-hour magnetic index, phi the magnetic local time in degrees (phi = 0° at midnight) R is the radial distance in RE and DTA is the dipole tilt angle lopez90 Absolute value abs Arc-cosine acos Natural logarithm log Logarithm to the base 10 log10 Arc-sine asin Arc-tangent atan Arc-tangent atan_2f Closest integer greater than or equal to its argument Ceil cosine cos Hyperbolic cosine cosh deriv() function with possibly unequal point spacing #deriv Natural exponential function exp Integer Fix Closest integer less than or equal to its argument Floor Sign Sign Sine sin Hyperbolic sine sinh Tangent tan Hyperbolic tangent tanh Square root sqrt