Effects of solar wind inhomogeneities on transit times of interplanetary shock waves

Long-term forecasting, greater than a few hours, of geomagnetic activity requires reasonably accurate estimates of the arrival times of interplanetary shock waves of solar origin. The shock waves travel through an inhomogencous interplanetary medium. Two major sources of uncertainty in estimates of arrival times are the variations of the velocity and the density of the ambient rnedium. The theory of propagation of strong shock waves through inhomogeneous media relates errors of estimate of shock arrival time to the inhomogeneities and shows that increases in the velocity along the Sun-Earth line lead to decreases in transit time and increases in the density lead to increases in transit time. The uncertainties in arrival time in both cases are proportional, in the linear approximation underlying the theory, to the perturbations or uncertainties in the velocity and density. The theory is applied to shock propagation through corotating inhomogeneities and used to calculate variances of arrival times using solar wind data. Four cases with different heliocentric radial dependences of density perturbation and fiducial shock speeds are considered. Numerical results based on NSSDC OMNI data give a variance of about 12-24 h for a fiducial transit time of 48 h, depending on the model for the inhomogeneities. In the most plausible model, in which the density inhomogeneitics deltap/p increase linearly with heliocentric radius and the fiducial shock speed is proportional to the inverse square root of the radius, the ratio of variance to transit time is about 0.25, independent of fiducial transit time. The results are in general agreement with observations, suggesting that much of the variance of observed transit times results from the influence of interplanetary inhomogencities. Published by Elsevier Science Ltd.