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Predicting the occurrence of large geomagnetic storms more than an hour in advance is an important, yet difficult task. Energetic ion data show enhancements in flux that herald the approach of interplanetary shocks, usually for many hours before the shock arrival. We present a technique for predicting large geomagnetic storms (Kp ⩾ 7) following the arrival of interplanetary shocks at 1 AU, using low-energy energetic ions (47–65 keV) and solar wind data measured at the L1 libration point. It is based on a study of the relationship between energetic ion enhancements (EIEs) and large geomagnetic storms by Smith et al. [Smith, Z., Murtagh, W., Smithtro, C. Relationship between solar wind low-energy energetic ion enhancements and large geomagnetic storms. J. Geophys. Res. 109, A01110, 2004. doi:10.1029/ 2003JA010044] using data in the rise and maximum of solar cycle 23 (February 1998–December 2000). An excellent correlation was found between storms with Kp ⩾ 7 and the peak flux of large energetic ion enhancements that almost always (93% of time in our time period) accompany the arrival of interplanetary shocks at L1. However, as there are many more large EIEs than large geomagnetic storms, other characteristics were investigated to help determine which EIEs are likely to be followed by large storms. An additional parameter, the magnitude of the post-shock total magnetic field at the L1 Lagrangian point, is introduced here. This improves the identification of the EIEs that are likely to be followed by large storms. A forecasting technique is developed and tested on the time period of the original study (the training data set). The lead times, defined as the times from the arrival of the shock to the start of the 3-h interval of maximum Kp, are also presented. They range from minutes to more than a day; the average for large storms is 7 h. These times do not include the extra warning time given when the EI flux cross the high thresholds ahead of the shock. Because the data-stream used in the original study is no longer available, we extended the original study (1998–2000) to 2001, in order to: (a) investigate EIEs in 2001; (b) present a validation of the technique on an independent data set; (c) compare the results based on the original (P1) energy channel to those of the replacement (P1′) and (d), determine new EIE thresholds for forecasting geomagnetic storms using P1′ data. The verification of this P1′ training data set is also presented, together with lead times.

We use a one-dimensional, time-dependent adaptive grid MHD code to study the evolution of shocks (both slow and fast shocks) from the surface of the Sun through the heliosphere. In order to achieve the goal, we track a specific solar event's plasma and magnetic field output as it propagates into interplanetary space with a possible geoeffective consequence. We have chosen the famous event of the October/November (“Halloween 2003”) epoch which produced two of the largest geomagnetic storms during solar cycle 23, followed by the arrivals of the shocks at Earth. These two geomagnetic storms are associated with two of these flares (X17/4B and X10/2B). Accordingly, four separate pressure pulses, at the appropriate times and with different strengths and duration, determined via a trial and error procedure, are introduced on the Sun to mimic the four flares. The results show that the simulated solar wind velocity temporal profiles successfully matched the observations at L1. The propagation speed of shock waves near the Sun also matched with the CME observations of SOHO/LASCO. The major objective, to demonstrate the detailed nature of interacting shocks and some of their products after origination from closely spaced solar events, is achieved. The evolution of both slow and fast shocks is also discussed in detail.

A user-friendly, real-time, observation-driven system for forecasting solar wind and interplanetary magnetic field conditions is described. The forecast system presently uses the Hakamada–Akasofu–Fry (version 2) kinematic solar wind model to predict, in real-time, solar wind conditions in the heliosphere, including at the location of Mars, and beyond. Properly characterizing and predicting this region of the space environment are essential steps towards improving the accuracy of “downstream” space weather models used to forecast the space radiation environment and geomagnetic activity. Representative modeling results are presented and the conclusion is made that uncertainty in determining the physical parameters needed for model inputs from real-time solar observations is the biggest factor limiting the accuracy of solar wind models used for space weather analysis and prediction. Future directions include extending the forecast system via a hybrid approach to include 3D MHD modeling.

Forecasting the arrival of solar-generated shocks and accelerated protons anywhere in the heliosphere presents an awesome challenge in the new field of space weather. Currently, observations of solar wind plasmas and interplanetary magnetic fields are made at the sun-Earth libration point, L1, about 0.01 astronomical units (∼245 Earth radii) sunward of our planet. An obvious analogy is the pilot tube that protrudes ahead of a supersonic vehicle. The Advanced Composition Explorer and Solar and Heliospheric Observatory spacecraft, currently performing this function, provide about -1 h advance notice of impending arrival of interplanetary disturbances. The signatures of these disturbances may be manifested as interplanetary shock waves and/or coronal mass ejecta. We describe a first-generation procedure, based on first-principles numerical modeling, that provides the key links required to increase the advance notice (or lead time) to days, or even weeks. This procedure, instituted at the start of the present solar cycle 23, involves three separate models, used in real time, to predict the arrival of solar-event-initiated interplanetary shock waves at the L1 location. We present statistical results, using L1 observations as ground truth for 380 events. We also briefly discuss how one of these models (Hakamada-Akasofu-Fry version 2) may be used with a model that predicts the flux and fluence of energetic particles, for energies up to 100 MeV, that are generated by these propagating interplanetary shock waves.

The purpose of this parametric study is to predict the arrival time at Earth of shocks due to disturbances observed on the Sun. A 3D magnetohydrodynamic (MHD) simulation code is used to simulate the evolution of these disturbances as they propagate out to 1 AU. The model in Han, Wu and Dryer (1988) uses solar data for input at 0.08 AU (18 solar radii). The initial shock speed (ISS) is assumed to be constant from the corona to 0.08 AU. We investigate how variations of this ISS affect the arrival times of the shock at Earth. This basic parametric study, however, does not consider inhomogeneous background solar wind structures such as corotating interaction regions and their precursor stream–stream interactions, nor interplanetary manifestations of complex coronal mass ejecta such as magnetic clouds. In the latter case, only their associated shocks are considered. Because the ambient (pre-existing background) solar wind speed is known to affect the shock arrival time at 1 AU, we also simulated events with various background solar wind speeds (BSWS) to investigate this effect. The results show that the shock arrival time at Earth depends on the BSWS, the speed of solar disturbances, their size, and their source location at the Sun. However, it is found that for a sufficiently large momentum input, the shock arrival time at Earth is not significantly affected by the pre-existing solar wind speed.

It is well known that while flare-associated coronal mass ejections (CMEs) show higher speeds and little acceleration in the corona, filament-associated CMEs have lower speeds and large accelerations. In this paper, we examine three flare-associated CMEs with relatively large accelerations as counterexamples of the former tendency. The estimated accelerations are all larger than 45 m s-2 below 15 R☉. By analyzing SOHO EIT, SOHO LASCO, and GOES data, we attempt to find out what kind of physical characteristics control such strong accelerations. The first event is the 1999 July 9 event associated with a C1.1 flare. Considering the fact that its CME appearance, seen in the LASCO running difference imagery, is quite similar to the shape of a helmet streamer, we speculate that its eruption is related to the destabilization of a helmet streamer, which may induce the weak X-ray flare. The second event is the 1999 August 17 event associated with a C2.6 flare. The CME speed abruptly increased from 232 to 909 km s-1 for 1 hr, and the strong acceleration is coincident with the occurrence of a subsequent flare/CME. The third event is the 2000 November 24 event associated with a C4.1 flare. The CME speed first decreased and then constantly accelerated for 3 hr. The start of such an acceleration is also coincident with a subsequent CME/flare event. For the last two CME events, the Lorentz forces acting on the subsequent events may play an important role in accelerating CMEs. Our results show that large accelerations of flare-associated CMEs, as counterexamples of the two classes of CMEs, seem to be caused by other solar activities, such as helmet streamer disruptions or subsequent CMEs/flares.

We present the design, implementation, present status, and preliminary use of an operational forecaster-friendly solar wind prediction system. We have tested this architecture in our real-time "fearless forecast" prediction study of interplanetary shock arrival time (SAT) at Earth. This study has progressed on a continuous basis since 1997, near the rise of Solar Cycle 23. Comparisons of predicted SAT with observed SAT provide a measure of model forecast skill. We present our kinematic model's forecast skill statistics as compared with several other SAT models and propose important reference metrics for evaluating this and any other interplanetary modeling system. Our prediction system is presently being extended, via a hybrid approach, to include a three-dimensional magnetohydrodynamic (MHD) model. This procedure will accommodate proxy inputs for simulating interplanetary disturbances that are associated with various forms of solar activity (flares, disappearing filaments, coronal mass ejection imagery, shocks). The objective is to provide a capability in the near term to predict, shortly after the launch of large-scale structures at the Sun, the time-dependent interplanetary magnetic field vector (including the north-south component, Bz) at Earth. This is a key requirement for predicting geomagnetic storms.

The ability to predict the arrival of interplanetary shocks near earth is of great interest in space weather because of their relationship to sudden impulses and geomagnetic storms. A number of models have been developed for this purpose. For models to be used in forecasting, it is important to provide verification in the operational environment using standard statistical techniques because this enables the intercomparison of different models. A verification method is described here, comparing the prediction capabilities of four models that use solar observations for input. Three of the models are based on metric Type II radio burst observations, and one uses halo/partial-halo coronal mass ejections. A method of associating solar events with interplanetary shocks is described. The predictions are compared to associated shocks observed at L1 by the Advanced Composition Explorer (ACE) spacecraft. The time period of this study is January 2002-May 2002. Although the data sample is small, the statistical intercomparison of the results of these models is presented as a demonstration of the verification method.

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.

Prediction of solar-generated disturbances and their three-dimensional propagation through interplanetary space continues to present a vitally important operational space weather forecasting objective. This paper presents the first successful real-time prediction of a series of major heliospheric shock waves at Earth, including the one from the 14 July 2000 (`Bastille Day') flare. An ensemble of three models and their predictions were distributed to a world-wide group of interested scientists as part of an informal Internet space weather forecast research program. Two of the models, STOA (Shock Time of Arrival) and ISPM (Interplanetary Shock Propagation Model), presently in operation by the US Air Force Weather Agency, provided predictions of shock arrival time (SAT) that were, respectively, 0.5 hours after and 3.7 hours before the observed arrival. The third model, HAFv.2 (Hakamada–Akasofu–Fry version 2.0) predicted a time 0.3 hours after the observed shock arrival time (14:37 UT, 15 July 2000). Of primary interest to this study is the third model, firstly in terms of its capability of propagating shocks through non-uniform solar wind conditions, and secondly, in terms of its ability to integrate multiple solar events and display them graphically along with the background solar wind. This latter capability was brought to bear on ten real-time-reported flares, some with CMEs (coronal mass ejections) that took place as companions to the Bastille flare during the period 7–15 July 2000. Some limited statistics are given regarding the three models' shock arrival prediction capability at Earth, as an extension of our earlier studies with this three model ensemble in the prediction of SAT. HAFv.2, however, was able to describe not only the ten events and their interaction as measured at Earth, but also at the spacecraft NEAR (orbiting the asteroid, Eros, at 1.8 AU), and CASSINI (en route, at 4.0 AU, to Saturn). Several important points are noted: (1) this epoch represents a small statistical sample that should be expanded; and (2) the three models, based on theory, empiricism, and simulations represent the state of the art that should presage a similar community process. This paper was presented earlier as an Invited Talk at the American Geophysical Union Fall Meeting, December 14–19, 2000, in San Francisco, CA, U.S.A.toward space weather objectives in the Sun-Earth domain.

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.

A study of the interaction of interplanetary shock waves with the heliospheric current sheet/heliospheric plasma sheet (HCS/HPS) and the disturbed flow behind them is made with a 2.5 dimensional MHD code that uses improved computational techniques. The aim is to determine if such interactions for typical shocks can produce sufficiently large changes in the interplanetary plasma and field to be geoeffective. The mutual interaction of the shock waves with the HCS/HPS is examined for several angles between the shock normal and the HCS/HPS. We separate the effects of the HCS from those due to angular distance of observer from the initial shock center. The shocks are initiated at 0.1 AU by a finite-duration increase in initial radial velocity. We examine the transit times of the resultant shocks to 1-AU and their strengths along their peripheries. We also examine the 1-AU signatures of the polar component of the magnetic field, Bθ, in the interplanetary disturbance at and following the leading fast mode MHD shock. Note that Bθ = −Bz. We show the differences that result from the presence of the HCS, both qualitatively and quantitatively. The largest effects occur in Bθ, which reaches its largest excursions within 10° of the edge of the HPS. For the moderate shocks simulated in this study, deflections of the field lines produce values of Bθ between 4 and 5 nT in the presence of a HCS. These values are at the lower end of the range considered necessary for interplanetary events to initiate moderate geomagnetic storms. Further study is required to investigate the nature of input pulses and HCS that would give larger Bθ variations.

The first X-class flare in four years occurred on 9 July 1996. This X2.6/1B flare reached its maximum at 09:11 UT and was located in active region 7978 (S10° W30°) which was an old-cycle sunspot polarity group. We report the SOHO LASCO/EIT/MDI and SOONSPOT observations before and after this event together with Yohkoh SXT images of the flare, radio observations of the type II shock, and GOES disk-integrated soft X-ray flux during an extended period that included energy build-up in this active region. The LASCO coronagraphs measured a significant coronal mass ejection (CME) on the solar west limb beginning on 8 July at about 09:53 UT. The GOES 8 soft X-ray flux (0.1–0.8 nm) had started to increase on the previous day from below the A-level background (10-8 W m-2). At the start time of the CME, it was at the mid-B level and continued to climb. This CME is similar to many events which have been seen by LASCO and which are being interpreted as disruption of existing streamers by emerging flux ropes. LASCO and EIT were not collecting data at the time of the X-flare due to a temporary software outage. A larger CME was in progress when the first LASCO images were taken after the flare. Since the first image of the 'big' CME was obtained after the flare's start time, we cannot clearly demonstrate the physical connection of the CME to the flare. However, the LASCO CME data are consistent with an association of the flare and the CME. No eruptive filaments were observed during this event. We used the flare evidence noted above to employ in real time a simplified Shock-Time-of-Arrival (STOA) algorithm to estimate the arrival of a weak shock at the WIND spacecraft. We compare this prediction with the plasma and IMF data from WIND and plasma data from the SOHO/CELIAS instrument and suggest that the flare - and possibly the interplanetary consequences of the 'big' CME - was the progenitor of the mild, high-latitude, geomagnetic storm (daily sum of Kp=16+, Ap=8) on 12 July 1996. We speculate that the shock was attenuated enroute to Earth as a result of interaction with the heliospheric current/plasma sheet.

A series of our papers in the Journal of Geophysical Research, 1995-1996, was devoted to simulations of propagation of cylindrical magnetic clouds (flux ropes) having different orientation of their axes to the ecliptic plane and initial parameters. In this paper we supplement our study with the case of detached spherical plasmoids. By varying the velocity, density, temperature, and the magnetic field strength inside clouds, we simulate a number of plasmoid scenarios that can be compared with observations and with existing models and simulations of flux ropes. Initially, the spherical clouds have a poloidal magnetic field configuration within a sphere. During the propagation they evolve into toroids (i.e., closed flux ropes). Radial profiles of magnetic field and plasma quantities in these toroids are similar to cylindrical magnetic clouds. However, they are different in the central (now external) part of the cloud, where the poloidal axis was originally situated, that is, in the toroid's hole. Here the magnetic field is greatly enhanced but does not rotate, and the temperature decrease is absent. The deceleration and transit time to 1 AU is comparable between spherical and cylindrical clouds. The shock wave ahead of a spherical cloud is about 2 times closer than for a corresponding cylindrical cloud.

It is necessary to identify signatures of solar sources in order to improve predictions of solar-caused geomagnetic activity. This is not a straightforward task as the relationship is not well understood. We apply an algorithm, derived from numerical simulations to identify the solar source of an interplanetary event that was observed by the WIND spacecraft on October 18, 1995 and was followed by a geomagnetic storm. No specific geomagnetic activity had been predicted at Space Weather Operations (SWO) in Boulder, CO, on the basis of earlier solar observations. The algorithm is used to estimate the time and location of the expected solar source of this interplanetary event. A review of solar observations prior to the WIND observations showed that solar activity precursors could be identified. A long-duration-event was seen by GOES in soft X-rays at the same time as a type IV burst was observed in metric radio wavelengths, and a rearrangement of fields was observed by the soft X-ray telescope on the Yohkoh satellite. This suggests that the algorithm is useful for post facto identification of solar sources, and that such combinations of solar activity should be further investigated for use in geomagnetic forecasting.

Propagation of magnetic clouds as flux ropes or spheromaks is studied with use of a self-consistent MHD numerical approach. Flux ropes are approximated by cylinders in a 2.5-D treatment, while spheromaks (plasmoids) described initially as spherical clouds are treated in 3-D. We deal with the reliability of 2.5-D solutions, comparing results of different codes, different mesh resolutions and different conditions for the cloud's injection. Despite this variety, we find that the results of the cloud's propagation are very similar and consistent. Indeed, we find that the results are independent of code mesh size and the numerical technique used. Cylindrical clouds are deflected from straight, radial propagation to the side where the inner and outer magnetic fields have the opposite sense. The magnitude of the deflection depends on the magnetic field strength and the gradient of the ambient magnetic field near the cloud's boundary. Spherical clouds with a poloidal field and axes aligned along the background magnetic field are not deflected. But they evolve into toroids, closed flux ropes. These results were obtained using a unipolar background magnetic field, that is, we do not consider interactions with the heliospheric current sheet.

A three-dimensional, time-dependent, MHD model of solar-disturbance-caused storms (Wu, 1993; Wu et al., 1996a) is used to predict the turning direction of the interplanetary magnetic field (IMF) at Earth. More explicitly, we examine the polarity of Bz caused by solar disturbances on the Sun. Three manifestations of solar disturbances, as studied by previous workers, are examined. Firstly, twenty-nine kilometric Type II events, associated (Cane, 1985) with geomagnetic storms, are studied within the context of our three-dimensional model. Then, an additional eleven long-duration X-ray events (LDEs) with radio fluxes greater than 100 solar flux units were examined; these events were not associated with interplanetary Type II events but were also associated (Cane, 1985) with geomagnetic storms. Finally, in situ interplanetary phenomena that caused ten large (Dst < −100 nT, the intensification of the storm) geomagnetic storm episodes (Tsurutani et al., 1988) near solar maximum are also studied via the Bz predictions of our 3D MHD model. The accuracy of these Bz turning-direction-predictions is found to be as follows: (1) for the kilometric Type II events, the model's prediction was successful for 26 of the 29 events studied; (2) 10/11 for the LDE events; and (3) 7/9 for the major geomagnetic storm events. The overall prediction accuracy of these three independent data sets is 43/49. Thus, consideration of these three independent data sets strongly suggests that the recipe proposed by the basic 3D MHD model may be valid for a zero-th order prediction scheme.

MHD simulations of the propagation of magnetic clouds in the interplanetary medium show that interplanetary magnetic field (IMF) lines, draping around the cloud, are often bent in a complicated way. The magnetic field along these field lines (even on nonbent sections) is not smoothly decreasing with increasing distance from the Sun but usually exhibits several extreme values (minima and maxima). Depressions in the IMF strength may trap energetic particles with suitable energies and pitch angles. These particles may remain trapped (in the expanding region) until the IMF configuration changes. Possible locations of magnetic traps are shown in this paper.

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.

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 front's dimple did not form in our simulation.

A spectacular change in the lower corona on the south-west limb has been found in solar images taken by the Yohkoh soft X-ray telescope. The event is characterized by a large topological change in magnetic field and a large intensity decrease observed after the X1. 1/1B flare on 9 November, 1991. A coronal mass ejection (CME) was observed by the Mark III K-coronameter (MK3) at the HAO/Mauna Loa Observatory. Both the MK3 (white-light) and soft X-ray observations showed that one leg of this CME was located above the flare site. An interplanetary shock associated with this event was observed by Pioneer Venus Orbiter, and, possibly, by IMP-8.

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 Earth's 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.

This paper continues studies of the cylindrical magnetic clouds' propagation in the interplanetary medium. In our first paper devoted to this topic (Vandas et al., 1995) we dealt with the cloud with the axis perpendicular to the ecliptic plane and derived time dependencies of its velocity, field magnitude, and temperature as well as its shape for different initial conditions. Here, analogously, we present simulations for the cloud with the axis parallel to the ecliptic plane and show that the propagation of these clouds practically does not depend on the inclination of their axes to the ecliptic plane. We made a new conclusion concerning the helicity of the magnetic field inside the cloud. Because of the magnetic interaction with the background field, the cloud is shifted to the side where it meets with the external interplanetary magnetic field (IMF) polarity that is opposite to that within the cloud. The net effect of the time dependent Lorentz, inertial, and pressure gradient forces probably causes the complementary deformation of the whole cloud.

The propagation of radially expanding magnetic clouds from 18 solar radii to the Earth and their interaction with the solar wind plasma is simulated self-consistently using both 2 1 2- D and 3-D MHD codes. The cloud is assumed to be a cylinder with its axis perpendicular to or lying in the ecliptic plane. Our results show that there are no significant differences in the clouds' kinematics or cross-section evolutionary changes between the two axis orientations. Calculated time profiles of magnetic field and plasma parameters (velocity, temperature, density, beta) as would be measured by a hypothetical spacecraft passing through the center of the cloud are qualitatively in general agreement with spacecraft observations. We also find that the IMF magnitude distribution along externally-draped field lines suggests the possibility of trapped and/or mirroring of particles… even outside the cloud itself.

We have quantified the injection rate of low-energy particles (90-1000 keV) at the front of three interplanetary shocks detected by ISEE-3 spacecraft. We have used a MHD code to simulate the shock propagation and the focused-diffusion equation for particle propagation. This allows us to quantify the injection rate of particles, Q, at the shock by fitting the observed flux and anisotropy at different energies. We relate the variations of the efficiency of the particle acceleration with the interplanetary magnetic field and plasma conditions in the shock front region magnetically connected with the observer. Particularly, with the MHD strength of the shock, the interplanetary magnetic field-shock normal angle, the extent of the shock, and the heliolongitude of the parent solar activity that generates the shock.

[1] Predictions of interplanetary shock arrivals at Earth are important to space weather because they are often followed by geomagnetic disturbances that disrupt human technologies. The success of numerical simulation predictions depends on the codes and on the inputs obtained from solar observations. The inputs are usually divided into the more slowly varying background solar wind, onto which short-duration solar transient events are superposed. This paper examines the dependence of the prediction success on the range of values of the solar transient inputs. These input parameters are common to many 3-D MHD codes. The predictions of the Hakamada-Akasofu-Fry version 2 (HAFv2) model were used because its predictions of shock arrivals were tested, informally in the operational environment, from 1997 to 2006. The events list and HAFv2's performance were published in a series of three papers. The third event set is used to investigate the success and accuracy of the predictions in terms of the input parameter ranges (considered individually). By defining three thresholds for the input speed, duration, and X-ray class, it is possible to categorize the prediction outcomes by these input ranges. The X-ray class gives the most successful classification. Above the highest threshold, 89% of the predictions were successful while below the lowest threshold, only 40% were successful. The accuracy, measured in terms of the time differences between the observed and predicted shock arrivals, also shows largest improvement for the X-ray class. Guidelines are presented for space weather forecasters using the HAFv2 or other interplanetary simulation models.

[1] This is the third in a series of papers showing the performance of the Hakamada-Akasofu-Fry version 2 (HAFv2) model in predicting, in the operational environment, the arrival of interplanetary shocks at Earth. The first and second studies covered the time of the rise and maximum of Solar Cycle 23. This study covers the declining phase, through December 2006. The prediction of shock arrivals is important in space weather applications because these events are often followed by geomagnetic disturbances that disrupt human technologies. The HAFv2 uses, for input, a continuously updating background solar wind onto which transient events (interplanetary shocks) are superimposed whenever near-real-time observations are reported of a metric type II radio burst and/or a halo or partial halo coronal mass ejection (CME). Supporting inputs are obtained from GOES 1–8 A X-ray data and solar images. We present the performance of the model in standard meteorological forecast metrics and compare the accuracy of the three phases of Solar Cycle 23. We find that the accuracy of the model is consistent between the three periods. For this third phase, we show the added confidence in model predictions provided by the presence of halo/partial halo observations. Halo/partial halo CMEs were found to accompany approximately one half of the events. The predictions of this subset of events have a higher level of confidence and success. Thus the observation of a large CME should not be a requirement for a forecast but rather an indication that when one is observed, the confidence in the prediction is greatly increased.

A large Energetic Storm Particle event was observed by ISEE-3 between 23 and 25 April 1979. This event was associated with an interplanetary shock which was generated by a solar disappearing filament. Flux and anisotropy profiles in the upstream region of the event have been reproduced by means of a particle propagation model which includes particle injection both at the Sun and at the shock front. Injection at the front takes into account the fact that the IMF connection between the shock and the spacecraft is disrupted by the shock itself. The model, coupled to a 2D MHD time-dependent model, makes it possible for us to study the parameters for the interplanetary propagation of the particles, the injection rates both at the Sun and at the shock front, from near the Sun out to 1 AU.

Large disturbances in the interplanetary medium were observed by several spacecraft during a period of enhanced solar activity in early February 1986. The locations of six solar flares and the spacecraft considered here encompassed more than 100 deg of heliolongitude. These flares during the minimum of cycle 21 set the stage for an extensive multispacecraft comparison performed with a two-dimensional, MHD numerical experiment. The plasma instruments on the Giotto spacecraft, on its way to encounter Comet Halley in March 1986, made measurements of the solar wind for up to 8 hours/day during February. Solar wind measurements from the Johnstone Plasma Analyzer experiment on Giotto are compared with the MHD simulation of the interplanetary medium throughout these events. Using plasma data obtained by the IMP-8 satellite in addition, it appears that an extended period of high solar wind speed is required as well as the simulated flares to represent the interplanetary medium in this case. The plasma and magnetometer data from Vega-1 is compared with the MHD simulation. This comparison tends to support an interpretation that the major solar wind changes at both Giotto and Vega-1 on February 8, 1986 were due to a shock from a W 05 deg solar flare on February 6, 1986 (06:25 UT). The numerical experiment is considered, qualitatively, to resemble the observations at the former spacecraft, but it has less success at the latter one.

A parametric study of the evolution within, and signatures at, 1 AU of high-speed streams is performed with the use of a MHD two-and-a-half-dimensional time-dependent model. This study is an extension of an earlier one by Smith and Dryer (1990) who examined the ecliptic plane consequences of relatively short-duration, energetic solar disturbances. The present study examines both the erupting and corotating parts of long-duration, high-speed streams characteristic of coronal hole flows. By examining the variation of the simulated plasma velocity, density, temperature, and magnetic field at 1 AU, as well as the location of the solar coronal hole sources relative to the observer at 1 AU, it was possible to provide some insight into the identification of the solar sources of interplanetary disturbances. Two definitions for angle locating the solar source of interplanetary disturbances at 1 AU are presented and discussed. The results are applied to the suggestion by Hewish (1988) that low-latitude coronal holes are suitably positioned to be the sources of major geomagnetic storms when the holes are in the eastern half of the solar hemisphere at the time of the commencement of the storm. The results indicate that, for these cases, the streams emanating from within the hole must be very fast, greater than 1000 km/s, or very wide, greater than 60 deg, at the inner boundary of 18 solar radii.

[1] A 3-D, kinematic, solar wind model (Hakamada-Akasofu-Fry version 2 (HAFv.2)) is used to predict interplanetary shock arrivals at Venus, Earth, and Mars during a sequence of significant solar events that occurred in the interval 5–14 December 2006. Mars and Venus were on the opposite side of the Sun from Earth during this period. The shocks from the first two east limb events (5 and 6 December) were predicted to interact to form a single disturbance before reaching Earth and Venus. A single shock was indeed recorded at Earth only about 3 h earlier than had been predicted. The composite shock was predicted by HAFv.2 to arrive at Venus on 8 December at ∼0500 UT. Solar energetic particles (SEPs) were detected in Venus Express Analyzer of Space Plasmas and Energetic Atoms-4 data for some 3 d (from

[1] The 12 May 1997 solar event is used to demonstrate the improvements that have been made in recent years in the accuracy of predicting, in the operational environment, the time of arrival at Earth of solar-caused interplanetary shocks. This event provides a simple test case because it was both well isolated in time from other events and well documented, with the observation of a large flare (in optical and X-ray), a large halo CME, metric type-II radio burst and near-Earth solar wind and interplanetary magnetic field data. The Hakamada-Akasofu-Fry model (version 2: HAFv2) near-real-time prediction gave an error of 31 h. Because the accuracy of predicted Sun-to-Earth transit times of such shocks depends both on the model and our ability to determine the proper inputs from available observations, we reexamined the predictions made for the 12 May event using inputs that could have been available in near-real-time, both with HAFv2 and a second, ensemble-partnered solar wind prediction model, the 3-D MHD Hybrid Heliospheric Model System (HHMS). We use updated methods of estimating the initial shock velocity (from Smith et al., 2005b) and examine the influence of the background solar wind. This reexamination reduced the error from the original 31 h to less than 4 h. Achieving near-real-time accuracies to this level would greatly enhance operations of technologies such as electrical power grids, satellite systems, and polar flight communications.

[1] The three-dimensional Hakamada-Akasofu-Fry (HAFv.2) kinematic solar wind model can be extended to predict what the Solar Terrestrial Relations Observatory (STEREO) spacecraft might expect in observing large-scale plasma clouds ejected from the Sun. In order to demonstrate this capability, the HAFv.2 model was used to simulate the first observations of a halo coronal mass ejection (CME) from the Solar Mass Ejection Imager (SMEI) instrument on the Coriolis spacecraft, acquired after the solar events of 27–29 May 2003. Projections of the Thomson-scattered white light intensity on the plane of sky, as observed by the SMEI cameras, were calculated from the three-dimensional simulations. These simulations of the background solar wind and two shock fronts compare favorably with the white light observations of plasma clouds by the SMEI instrument. The method thus developed is then applied to hypothetical locations of the STEREO spacecraft in a later phase of the STEREO mission. It is shown that the model can be a valuable aid and guide in the identification of multiple shock-induced variations of the solar wind.

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 shock's 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.

An attempt is made to reconcile the different power laws obtained when relating, on the one hand, interplanetary scintillation (IPS) to solar-wind density and, on the other, density turbulence to density. A numerical experiment was performed using a 2-D magnetohydrodynamical (MHD) model to simulate the solar wind in the ecliptic plane and then generating IPS g values by line-of-sight integration through the model solar wind. This simulation showed that any breakdown of the assumptions implicit in comparing a line-of-sight integral with a time average made near Earth was insufficient to account for the difference.

[1] The arrival times at Earth of 166 flare-related shocks identified exiting the Sun (using metric radio drift data) during the maximum phase of Solar Cycle 23, were forecast in near-real time using the Shock Time of Arrival Model (STOA), the Interplanetary Shock Propagation Model (ISPM) and the Hakamada-Akasofu-Fry Model (version 2, HAFv.2). These predictions are compared with the arrival at L1 of shocks recorded in plasma and magnetic data aboard the ACE spacecraft. The resulting correspondences are graded following standard statistical methods. Among other parameters, a representative reference metric defined by {(“hits” + “correct nulls”) × 100}/(total number of predictions) is used to describe the success rates of the predictions relative to the measurements. Resulting values for STOA, ISPM, and HAFv.2 were 50%, 57%, and 51%, respectively, for a hit window of ±24 hours. On increasing the statistical sample by 173 events recorded during the rise phase of the same cycle, corresponding success rates of 54%, 60%, and 52%, respectively, were obtained. A χ2 test shows these results to be statistically significant at better than the 0.05 level. The effect of decreasing/increasing the size of the hit window is explored and the practical utility of shock predictions considered. Circumstances under which the models perform well/poorly are investigated through the formation, and statistical analysis, of various event subsets, within which the constituent shocks display common characteristics. The results thereby obtained are discussed in detail in the context of the limitations that affect some aspects of the data utilized in the models.

[1] We describe a Sun-to-Earth system of coupled models. Our main goal is to create a real-time, three-dimensional (3-D), MHD-based system to aid in the operational forecasting of geomagnetic activity, but we expect the system to have other uses. We give here our initial survey of the system's characteristics. The Hybrid Heliospheric Modeling System (HHMS) is composed of two physics-based models, combined with two simple empirical models. The physics-based models are a source surface (potential field) current sheet model for the corona and a time-dependent 3-D MHD solar wind model. The system is driven by a sequence of photospheric magnetic maps composed from daily magnetograms. An empirical relationship between magnetic flux tube expansion factor and solar wind speed at 0.1 AU is a key element of the system. The solar wind model gives a predicted time series of MHD parameters at the location of Earth in the model grid; this is verified against Omni, Wind, or ACE satellite data, depending on the time period. The predicted solar wind at Earth is used as input to the second, data-based, empirical model to predict the geomagnetic Ap index. We compare test results for simulated 1 day ahead Ap forecasts for the years 1993 through 2002 with forecast skill of the official Ap forecasts that were issued by the NOAA Space Environment Center in that time interval. Results show the HHMS would have been useful to forecasters in some years. Simulations of transient events such as coronal mass ejections and interplanetary shocks with the HHMS will be reported on later.

[1] The October/November 2003 (“Halloween 2003”) epoch of intense solar flares provided an opportunity to test the results of earlier parametric 1.5 MHD studies of interacting interplanetary shock waves. These preliminary studies used an adaptive numerical grid that made it possible to identify products of these interactions. During 28 October to 2 November 2003, three shocks generated by four solar flares were observed at the L1 libration point by ACE/SWEPAM/SWICS/MAG. Two very distinct geomagnetic storms, associated with two of these flares (X17/4B and X10/2B), rank as two of the largest storms of solar cycle 23. The purpose of this paper is to present the use of an adaptive grid 1.5-dimensional MHD model that is initiated at the solar surface to study in detail the three shocks observed at L1 that were generated by the four solar flares. Accordingly, four separate pressure pulses, at the appropriate times and with different strengths and duration, determined via a trial and error procedure, are introduced on the Sun to mimic the four flares. The results show that the simulated solar wind velocity temporal profiles successfully matched the observations at L1. The major objective, to demonstrate the detailed nature of interacting shocks and some of their products after origination from closely spaced solar events, is achieved. In addition, the MHD model is able to suggest the solar sources that are associated with specific geomagnetic storms at Earth.

[1] The speed of a shock that precedes ejecta from a solar energetic eruption is one of the key parameters used for input by many numerical models that predict the arrival of interplanetary shocks at Earth. These shocks are likely to be followed by significant geomagnetic activity. Near-real-time “fearless forecasts” of shock arrival times at the L1 libration point have been made for more than 6 years with several models. Initially, these models used, for input speeds near the Sun, speeds obtained from observations of metric type II radio bursts that are signatures of shocks propagating out through the solar corona. More recently, speeds of halo/partial halo coronal mass ejections (CMEs) were also considered in these models as another measure of shock speeds close to the Sun. During the period of high solar activity in October–November 2003, the data required for input into the models were often available in near real time from a number of observing stations. Therefore the fearless forecasts were issued in some cases with alternative inputs. These forecasts provided a basis on which to compare the success of the predictions (in terms of how close each prediction of the shock arrival time was to the observed time). The results of the analysis of this data set provide guidelines for selecting the input speed for shock propagation models. Both CME and metric type II radio burst measurements are shown to be useful and complementary. In general, the highest speed gave the best predictions. This demonstrates the desirability of having coronagraph data available for operational use.

[1] The “Halloween” epoch from 19 October to 20 November 2003 was marked by 19 major solar flares that were accompanied by metric type II radio bursts. Several of these flares were followed by major geomagnetic storms. The radio bursts were used in real time because they imply coronal and interplanetary transport. Most of these events were also associated with halo (or partial halo) coronal mass ejections (CMEs). A continuing, widely distributed, real-time research project called “fearless forecasts,” using an ensemble of four physics-based models, has been made of the ensuing shock arrival times since 1997 at the L1 libration point. Model inputs include consideration of the type II shock speed estimates above the flare sites as well as preliminary CME leading edge speeds in the plane of sky. Thus the model ensemble used inputs that were guided by both speed estimates. The rationale for using CME speeds includes the assumption that their high speeds represented the shocks themselves in addition to an assumption concerning their quasi-sphericity as they left the Sun. We compare the shock arrival predictions to those observed by the solar wind and magnetic field monitors on the Advanced Composition Explorer (ACE) and the solar wind monitor on the Solar and Heliospheric Observatory (SOHO) satellite. Success rates of the models are provided as a metric for this kind of active epoch. These success rates are 79% for one of the considered models using a “hit” window of ±24 hours and 74% when ±15 hours was used. This model demonstrates the importance of simulating both nonhomogeneous background environments and complex shock interactions.

[1] It is well established that energetic ion enhancements (an energetic ion enhancement will hereafter be referred to as an EIE) are partly due to acceleration by interplanetary shocks as the shocks propagate towards Earth and that arrivals of these shocks at Earth are well associated with geomagnetic storms. The observation of EIEs at satellites located at L1 is a potential tool for predicting the arrival of interplanetary shocks hours before they arrive at L1. Following an earlier study using WIND satellite data [Smith and Zwickl, 1999], we evaluate the potential of EIEs for forecasting geomagnetic storms during the period of February 1998 through December 2000. Since there are many more EIEs than large geomagnetic storms, additional associations that might improve the identification of precursors of large storms were investigated. These included probable solar sources, accompanying interplanetary shocks, and the shocks' interplanetary drivers. Solar images and data from the Advanced Composition Explorer (ACE) and WIND satellites were used. The Potsdam Kp was used to specify geomagnetic storm severity. Almost all large geomagnetic storms (Kp ≥ 7) in this time period were preceded by EIEs that were associated with shocks driven by transient interplanetary disturbances. The converse is not true. Although most transient-associated EIEs were followed by some geomagnetic activity, there is a large span in the response. Most (95%) of EIEs with maximum flux ≥1.105 pfu were followed by activity with Kp > 4 and 80% by storms with Kp ≥ 5. For a threshold of 3.105 pfu, 67% of the large storms would be identified, 89% of the EIEs were followed by storms with Kp ≥ 5, and 53% by large storms (Kp ≥ 7). Using the additional information on the interplanetary drivers results in an increase in the correctly predicted events from 53% to 61%. For a threshold of 1.106 pfu, all (100%) EIEs were followed by storms with Kp ≥ 5, 76% of the events were correctly predicted but 16 of the 30 large storms were missed. Most of the EIEs were followed by significant periods of southward Bz and in close to 70% of the EIEs, the Bz following the EIE was first northward before turning southward. We also investigated the relationship of the EIEs to halo or partial-halo coronal mass ejections (CMEs), and found that EIE events associated with halo CMEs are more likely to be followed by a large geomagnetic storm, but a lack of halo or partial-halo CME association does not preclude the occurrence of a large geomagnetic storm.

[1] We present simulated plane-of-sky maps of the shock waves in interplanetary space from several representative solar events by using the Hakamada-Akasofu-Fry solar wind model (HAFv.2). This kinematic model uses a three-dimensional approach to construct plane-of-sky maps of interplanetary shock waves initiated by solar flares and CMEs. The simulated plane-of-sky maps are in a form that can be directly compared with assimilated optical observations of shock waves from Earth-orbiting and interplanetary satellites. Combining these simulations with observations would provide a new tool for monitoring the propagation of interplanetary shocks in interplanetary space and for predicting the arrival of shock waves at Earth.

[1] Forecasting the time of arrival at Earth of interplanetary shocks following solar metric type II activity is an important first step in the establishment of an operational space weather prediction system. The quality of the forecasts is of utmost importance. The performances of the shock time of arrival (STOA) and interplanetary shock propagation models (ISPM) were previously evaluated by Smith et al. [2000] for 36 solar events. Here we use 173 solar events between February 1997 and October 2000 to set thresholds for the Hakamada–Akasofu–Fry version 2 (HAFv.2) model and then present the results of a comparison of the performance of this model to the STOA and ISPM solar wind models. Each model predicts shock arrival time (SAT) at the Earth using real-time metric type II radio frequency drifts and coincident X-ray and optical data for input and L1 satellite observations for verification. Our evaluation of input parameters to the models showed that the accuracy of the solar metric type II radio burst observations as a measure of the initial shock velocity was compromised for those events at greater than 20° solar longitude from central meridian. The HAF model also calculates the interplanetary shock propagation imbedded in a realistic solar wind structure through which the shocks travel and interact. Standard meteorological forecast metrics are used. A variety of statistical comparisons among the three models show them to be practically equivalent in forecasting SAT. Although the HAF kinematic model performance compares favorably with ISPM and STOA, it appears to be no better at predicting SAT than ISPM or STOA. HAFv.2 takes the inhomogeneous, ambient solar wind structure into account and thereby provides a means of sorting event-driven shock arrivals from corotating interaction region (CIR) passage.

Over the past several years, our group has been conducting a study of the performance of several solar wind models for predicting, immediately following solar events, the propagation of interplanetary shocks from the Sun to the Earth. Our “fearless forecasts” are distributed in real-time to anyone interested. We are presently using three separate models to provide these predictions: the Interplanetary Shock Propagation Model (ISPM), the Shock Time of Arrival model (STOA), and the Hakamada-Akasofu-Fry (HAF) model. Each model is driven by the same set of solar observations and each predicts interplanetary shock arrival time (SAT) at the L1 spacecraft location. In addition, the HAF model predicts solar wind conditions at L1 and other locations in the heliosphere, and produces ecliptic-plane maps of IMF topology and solar wind conditions. We are also conducting a detailed study of the HAF model capabilities to provide quantitative forecasts of the geoeffectiveness of solar-driven space disturbances. The development of a space weather forecast scheme is a test of our physical understanding of solar-terrestrial relationships. It is also an engineering challenge. This talk presents the status of our forecasting efforts. The lessons we have learned should benefit others soon to join the real-time space weather prediction challenge.

It is well established that energetic particle enhancements are due, in part, to acceleration by interplanetary shocks as they propagate towards Earth. Thus the observation of these enhancements at satellites located at L1 can be considered a potential tool for forecasting the arrival of interplanetary shocks and the start of geomagnetic storms in Earth’s magnetosphere. The signatures of energetic particle enhancements observed by the WIND spacecraft during the time-period 1996–1998 are studied, together with the accompanying interplanetary shocks; their interplanetary drivers; their probable solar sources, and the ensuing geomagnetic storms. The results, based on 115–400 keV ion data, show that enhancements in ion intensity can be seen up to several days in advance of the arrival of the shock. Therefore monitoring the energetic particles will allow predictions/warnings of up to 3 days in advance.

Interplanetary shocks often propagate along the heliospheric plasma sheet (HPS) where the interplanetary magnetic field (IMF) changes its polarity. This problem is investigated by the time-dependent 2.5-D MHD numerical model in the meridional plane. An example of computation is shown in the figure using density (log) contours and IMF vectors. Values of plasma parameters along the HPS fluctuate in time due to the Kelvin-Helmholtz instability. The HPS with its decreased intensity of the IMF as well as with its increased mass density causes a dimple in the shock structure (relatively weak for the forward shock, significant for the reverse shock, and very large for the contact discontinuity). Beyond the forward shock, the HPS is slightly compressed due to the post-shock increase of the azimuthal IMF component. Then follows expansion of the HPS surrounded by the highly-deformed contact discontinuity. A significant draping of IMF lines occurs around this structure that increases the meridional component of the IMF. This can cause a favorable condition for initiation of a geomagnetic storm.

Propagation and evolution of magnetic clouds in the ambient solar wind flow are studied self-consistently using ideal MHD equations in three dimensions. Magnetic clouds as ideal force-free objects (cylinders or spheres) are ejected near the Sun and followed beyond the Earth’s orbit. We investigate the influence of various initial parameters like the injection velocity, magnetic helicity, orientation of the clouds’ axes, etc., on their propagation and evolution. We demonstrate that the injection velocity has a major influence on propagation. Simulation results are compared with an analytical theory of magnetic cloud evolution (aging) published by Osherovich et al. [1993a]; good agreement is found although no need to use a polytropic index less than one (as in the analytical approach) is required.

We present results from a parametric study of interplanetary shocks made using a 3D, time- dependent MHD numerical simulation code. The results are compared to those obtained from a 2 1/2D code and also to spacecraft data. The simulations model the propagation within 1 AU of interplanetary shocks that are produced by relatively short-duration and modest-width inputs at 18 R ˙ . The 3D results are qualitatively the same as those of the 2 1/2D study but quantitatively different. When simulations are compared to Prognoz spacecraft data it is seen that both cover the same range of parameters.

[1] We have examined a possibility for improvement of the STOA (Shock Time Of Arrival) model for interplanetary shock propagation. In the STOA model, the shock propagating velocity is given by Vs ∼ R−N with N = 0.5, where R is the heliocentric distance. Noting observational and numerical findings that the radial dependence of shock wave velocity depends on initial shock wave velocity, we suggest a simple modified STOA model (STOA-2) which has a linear relationship between initial coronal shock wave velocity (Vis) and its deceleration exponent(N), N = 0.05 + 4 × 10−4Vis, where Vis is a numeric value expressed in units of km s−1. Our results show that the STOA-2 model not only removes a systematic dependence of the transit time difference predicted by the previous STOA model on initial shock velocity, but also reduces the number of events with large transit time differences.