Z. K. Smith

Improvements to the HAF solar wind model for space weather predictions

We have assembled and tested, in real time, a space weather modeling system that starts at the Sun and extends to the Earth through a set of coupled, modular components. We describe recent efforts to improve the Hakamada-Akasofu-Fry (HAF) solar wind model that is presently used in our geomagnetic storm prediction system. We also present some results of these improvement efforts. In a related paper, Akasofu [2001] discusses the results of the first 2 decades using this system as a research tool and for space weather predictions. One key goal of our efforts is to provide quantitative forecasts of geoeffective solar wind conditions at the L1 satellite point and at Earth. Notably, we are addressing a key problem for space weather research: the prediction of the north-south component (Bz) of the interplanetary magnetic field. This parameter is important for the transfer of energy from the solar wind to the terrestrial environment that results in space weather impacts upon society. We describe internal improvements, the incorporation of timely and accurate boundary conditions based upon solar observations, and the prediction of solar wind speed, density, magnetic field, and dynamic pressure. HAF model predictions of shock arrival time at the L1 satellite location are compared with the prediction skill of the two operational shock propagation models: the interplanetary shock propagation model (ISPM) and the shock-time-of-arrival (STOA) model. We also show model simulations of shock propagation compared with interplanetary scintillation observations. Our modeling results provide a new appreciation of the importance of accurately characterizing event drivers and for the influences of the background heliospheric plasma on propagating interplanetary disturbances.

MHD study of temporal and spatial evolution of simulated interplanetary shocks in the ecliptic plane within 1 AU

We utilize a 21/2-D MHD time-dependent model to perform a parametric study of interplanetary shock propagation to 1 AU. The input conditions are represented by the following variables:(1) initial shock velocity, (2) duration of the driving pulse, and (3) width of the pulse at the near-Sun position (18 solar radii). The total net energy added to the solar wind was calculated for each pulse. The forward shocks travel time to, and the peak dynamic pressure at, 1 AU as a function of location along the shock front have been studied over a range of total input pulse energies from 1029 to 1032 ergs. For input pulses with modest angular width and temporal duration, we find that the propagation of the resulting interplanetary fast forward shock waves depends primarily upon the net input energy. The dependence of the transit time upon energy is a power law with a -1/3 index which corresponds to the classical, piston driven case. Reverse shocks are also formed behind all but the lowest energy shocks. Their properties, although also a function of input energy, depend upon the specific values of the input pulse shock velocity, width and duration. We also briefly discuss the propagation of the shocks out to 1 AU, and the conditions for which the interplanetary shocks depart from being symmetric about the input pulse central meridian due to magnetic and dynamic effects.

Propagation of an interplanetary shock along the heliospheric plasma sheet

Propagation of an interplanetary shock along the heliospheric plasma sheet (HPS) is simulated using a high-resolution numerical MHD model in the meridional plane. The ambient solar wind contains two opposite orientations of the interplanetary magnetic field above and below the equatorial plane. These regions are separated by a thin transition layer that represents the heliospheric current sheet contained within the HPS, A pulse is introduced at the inner boundary (0.1 AU) into this steady state to initiate the interplanetary shock. The HPS with its weaker intensity of the magnetic field, larger mass density, and slower flow velocity modifies the global shock structure. A dimple is formed at the forward shock front, a reverse dimple is formed at the reverse shock, and the contact discontinuity is significantly distorted. Weak compression of the HPS occurs beyond the forward shock front due to the postshock increase of the azimuthal magnetic pressure. Although slight collimation of mass flow takes place toward the axis of the HPS, an antisunward protrusion (“pimple”) within the shock fronts dimple did not form in our simulation.

Performance of interplanetary shock prediction models: STOA and ISPM

Abstract The shock time of arrival (STOA) model and the interplanetary shock propagation model (ISPM) give predictions of the time of arrival and strength of solar-initiated interplanetary shocks. This paper presents the first operational predictions made of interplanetary shocks that follow solar events. The time interval of this study was February 1997–March 1999 (the rise of Solar Cycle 23). The results are presented in contingency-table form (whether or not a shock was predicted and/or observed) and also as the time differences (errors) between the predicted and observed shock arrivals. These results are compared to the accuracies that would be obtained using a constant, representative value (Rule of Thumb or R-T) for the transit time. The results show the percentage of successful predictions to within an accuracy of 12 h of shocks for the STOA, ISPM and R-T are 53, 58, and 33%, respectively. The corresponding root mean square (rms) errors of the shock arrival times are 15.0, 15.1 and 14.8 h. Note that the rms heavily weights outlying points, so although only 3 of the ISPM-predictions were off by more than 12 h, the ISPM rms is worse than that for STOA and R-T models; both of which had prediction errors >|12| h for eight events. Statistics presented in this paper not only show the capabilities of these models, but also allow for comparison to future shock-arrival forecasting models. These results may be considered as reference metrics in evaluating forecasting skill. The relationship of the interplanetary shocks to geomagnetic activity is also briefly considered.

Simulation of magnetic cloud propagation in the inner heliosphere in two-dimensions: 1. A loop perpendicular to the ecliptic plane

We present results of simulations of a magnetic clouds evolution during its passage from the solar vicinity (18 solar radii) to approximately 1 AU using a two-dimensional MHD code. The cloud is a cylinder perpendicular to the ecliptic plane. The external flow is explicitly considered self-consistently. Our results show that the magnetic cloud retains its basic topology up to 1 AU, although it is distorted due to radially expanding solar wind and magnetic field lines bending. The magnetic cloud expands, faster near the Sun, and faster in the azimuthal direction than in the radial one; its extent is approximately 1.5–2× larger in the azimuthal direction. Magnetic clouds reach approximately the same asymptotic propagation velocity (higher than the background solar wind velocity) despite our assumptions of various initial conditions for their release. Recorded time profiles of the magnetic field magnitude, velocity, and temperature at one point, which would be measured by a hypothetical spacecraft, are qualitatively in agreement with observed profiles. The simulations qualitatively confirm the behavior of magnetic clouds derived from some observations, so they support the interpretations of some magnetic cloud phenomena as magnetically closed regions in the solar wind.

The influence of the large-scale interplanetary shock structure on a low-energy particle event

We have developed a numerical model to study the influence of the large-scale shock topology on the associated low-energy (less than 2 MeV) particle event upstream of the shock. It includes particle injection at the solar corona, two-dimensional MHD simulation of the propagation of the shock, modeling of particle propagation through the interplanetary medium, and particle injection at the shock. The model does not attempt to simulate the physical processes of shock particle acceleration, therefore the injection at the shock is represented by a numerical source function in the equation that describes particle propagation

MHD simulation of an interaction of a shock wave with a magnetic cloud

Interplanetary shock waves, propagating in the heliosphere faster than earlier-emitted coronal ejecta, penetrate them and modify their parameters during this interaction. Using two and one half dimensional MHD simulations, we show how a magnetic cloud (flux rope) propagating with a speed 3 times higher than the ambient solar wind is affected by an even faster traveling shock wave overtaking the cloud. The magnetic field increases inside the cloud during the interaction as it is compressed in the radial direction and becomes very oblate. The cloud is also accelerated and moves faster, as a whole, while both shocks (driven by the cloud and the faster interplanetary shock) merge upstream of the cloud. This interaction may be a rather common phenomenon due to the frequency of coronal mass ejections and occurrence of shock waves during periods of high solar activity.

Magnetohydrodynamic modelling of interplanetary disturbances between the Sun and Earth

A time-dependent, nonplanar, two-dimensional magnetohydrodynamic computer model is used to simulate a series, separately examined, of solar flare-generated shock waves and their subsequent disturbances in interplanetary space between the Sun and the Earths magnetosphere. The ‘canonical’ or ansatz series of shock waves include initial velocities near the Sun over the range 500 to 3500 km s−1. The ambient solar wind, through which they propagate, is taken to be a steady-state homogeneous plasma (that is, independent of heliolongitude) with a representative set of plasma and magnetic field parameters. Complete sets of solar wind plasma and magnetic field parameters are presented and discussed.Particular attention is addressed to the MHD models ability to address fundamental operational questions vis-à-vis the long-range forecasting of geomagnetic disturbances. These questions are: (i) will a disturbance (such as the present canonical series of solar flare shock waves) produce a magnetospheric and ionospheric disturbance, and, if so, (ii) when will it start, (iii) how severe will it be, and (iv) how long will it last? The models output is used to compute various solar wind indices of current interest as a demonstration of the models potential for providing ‘answers’ to these questions.

Parametric study of loop‐like magnetic cloud propagation

Propagation and evolution of loop-like magnetic clouds in the ambient solar wind flow are studied self-consistently using ideal MHD equations in the 2½ dimensional approximation. Magnetic clouds, as ideal force-free objects (cylinders lying in the ecliptic plane), are ejected near the Sun and followed beyond the Earths orbit. We investigate the influence of various initial parameters, like the injection velocity or different steady states of the solar wind, on their propagation and evolution. Simulation results are compared with an analytical theory of magnetic cloud evolution (expansion) published by Osherovich et al. [1993a, b]; good agreement is found, although no need to use a polytropic index less than 1 (as in the analytical approach) is required.

Distortion of the heliospheric plasma sheet by interplanetary shocks

A 2½D MHD model is used to investigate mutual interactions between interplanetary shocks with the interplanetary magnetic field (IMF), An ambient solar wind is considered with a flat equatorial heliospheric current sheet (HCS) that is embedded within a finite thickness heliospheric plasma sheet (HPS). Two different velocity pulses are introduced with four different latitudinal positions at 0.1 AU. We found that large values of the meridional IMF originate when the shock interacts with the HPS. This is caused by field-line draping around the highly distorted shock driver and by deflection of the HCS in asymmetric situations.