Search

The July 23, 2012 CME was an extremely fast backside event, reaching ∼1 AU (STEREO-A) within 20 h as compared to ∼3–6 days for typical CME events. Here, we present results from a simulation study of the CME and its driven shock using a combined kinematic and magnetohydrodynamic (MHD) simulation model, H3DMHD. In general, the model results match well with in situ measurements in the arrival time of the CME-driven shock and the total magnetic field strength, assuming an initial CME speed of 3100 km/s. Based on extrapolation of an empirical model, the fast CME and its large magnetic field (| B |∼120 nT) are capable of producing an extremely large geomagnetic storm ( Dst ∼−545 nT), comparable to the well-known Halloween storm in 2003, if the CME had made a direct impact to the Earth. We investigated the effect of the adiabatic index ( γ ). It is found that the shock tends to arrive slightly later for a smaller γ value, and γ =5/3 provides the best agreement for the shock arrival time. We also demonstrate that the strength (the Mach number) of the CME-driven fast-mode shock is not the largest at the “nose” of the CME. This is mainly due to the manifestation of fast-mode wave speed upstream of the shock.

Images observed by the twin spacecraft Solar TErrestrial RElations Observatory (STEREO) A and B appear as complex structures for two coronal mass ejections (CMEs) on 1 August 2010. Therefore, a series of sky maps of Thomson-scattered white light by interplanetary coronal mass ejections (ICMEs) on 1 August 2010 are simulated using the Hakamada–Akasofu–Fry (HAF) three-dimensional solar-wind model. A comparison between the simulated images and observations of STEREO-A and -B clarifies the structure and evolution of ICMEs (including shocks) in the observed images. The results demonstrate that the simulated images from the HAF model are very useful in the interpretation of the observed images when the ICMEs overlap within the fields of view of the instruments onboard STEREO-A and -B.

The goal of the Battlespace Environments Institute (BEI) is to integrate Earth and space modeling capabilities into a seamless, whole-Earth common modeling infrastructure that facilitates interservice development of multiple, mission-specific environmental simulations and supports battlefield decisions, improves interoperability, and reduces operating costs.

We are investigating the geometric and kinematic characteristics of interplanetary coronal mass ejections (ICMEs) using data obtained by the LASCO coronagraphs, the Solar Mass Ejection Imager (SMEI), and the SECCHI imaging experiments on the STEREO spacecraft. The early evolution of CMEs can be tracked by the LASCO C2 and C3 and SECCHI COR1 and COR2 coronagraphs, and the HI and SMEI instruments can track their ICME counterparts through the inner heliosphere. The HI fields of view (4 – 90°) overlap with the SMEI field of view (> 20° to all sky) and, thus, both instrument sets can observe the same ICME. In this paper we present results for ICMEs observed on 24 – 29 January 2007, when the STEREO spacecraft were still near Earth so that both the SMEI and STEREO views of large ICMEs in the inner heliosphere coincided. These results include measurements of the structural and kinematic evolution of two ICMEs and comparisons with drive/drag kinematic, 3D tomographic reconstruction, the HAFv2 kinematic, and the ENLIL MHD models. We find it encouraging that the four model runs generally were in agreement on both the kinematic evolution and appearance of the events. Because it is essential to understand the effects of projection across large distances, that are not generally crucial for events observed closer to the Sun, we discuss our analysis procedure in some detail.

In recent years remarkable advances have been made in the development of physics based models of various parts of the solar-terrestrial system (see JASTP special issues, October, November 2004; February 2007). In this paper, we focus our discussions in a specific region of the Sun to the Earth’s environment (i.e. 1 AU). It is well-known that geomagnetic storms are caused by solar eruptions. The consequences of these storms include particle acceleration, solar wind impact on the Earth’s magnetosphere and ionosphere, UV-EUV radiation effects on the lower atmosphere, etc. One of the main challenges is to predict the arrival time at 1 AU of the solar disturbance. The prospects look good for an accurate, real-time forecast scheme built on the acquisition of solar, heliosphere and the near-Earth data and large-scale models. However, the accuracy of these models still needs improvement. We will discuss the present status of the models and challenges to improve the simulation models.

Context. Large solar energetic particle events are able to enhance the radiation intensity present in interplanetary space by several orders of magnitude. Therefore the study, modeling and prediction of these events is a key factor to understand our space environment and to protect manned space missions from hazardous radiation. Aims. We model an intense solar energetic particle event observed simultaneously on the 6 of March 1989 by the near-Earth orbiting spacecraft IMP-8 and by the Phobos-2 spacecraft in orbit around Mars (located 72° to the East of the Earth and at 1.58 AU from the Sun). This particle event was associated with the second largest X-ray flare in solar cycle 22. The site of this long-duration X15/3B solar flare was N35E69 (as seen from the Earth) and the onset of the 1-8 A X-ray emission occurred at 1350 UT on 6 March 1989. A traveling interplanetary shock accompanied with

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.

This study performs simulations of interplanetary coronal mass ejection (ICME) propagation in a realistic three-dimensional (3D) solar wind structure from the Sun to the Earth by using the newly developed hybrid code, HAFv.2+3DMHD. This model combines two simulation codes, Hakamada–Akasofu–Fry code version 2 (HAFv.2) and a fully 3D, time-dependent MHD simulation code. The solar wind structure is simulated out to 0.08 AU (18 Rs) from source surface maps using the HAFv.2 code. The outputs at 0.08 AU are then used to provide inputs for the lower boundary, at that location, of the 3D MHD code to calculate solar wind and its evolution to 1 AU and beyond. A dynamic disturbance, mimicking a particular flare’s energy output, is delivered to this non-uniform structure to model the evolution and interplanetary propagation of ICMEs (including their shocks). We then show the interaction between two ICMEs and the dynamic process during the overtaking of one shock by the other. The results show that both CMEs and heliosphere current sheet/plasma sheet were deformed by interacting with each other. � 2007 Published by Elsevier Ltd on behalf of COSPAR.

We report the results of 15 hr of Chandra observations of comet 2P/Encke 2003 on November 24. X-ray emission from comet Encke was resolved on scales of 500-40,000 km, with unusual morphology due to the presence of a low-density, collisionally thin (to charge exchange) coma. A light curve with peak-to-peak amplitude of 20% consistent with a nucleus rotational period of 11.1 hr was found, further evidence for a collisionally thin coma. We confirm emission lines due to oxygen and neon in the 800-1000 eV range but find very unusual oxygen and carbon line ratios in the 200-700 eV range, evidence for low-density, high effective temperature solar wind composition. We compare the X-ray spectral observation results to contemporaneous measurements of the coma and solar wind made by other means and find good evidence for the dominance of a postshock bubble of expanding solar wind plasma, moving at 600 km/s with charge state composition between that of the "fast" and "slow" solar winds.

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.

The ionospheric total electron content (TEC) in the equatorial anomaly region is studied by analyzing dual-frequency signals from the global position system (GPS) acquired from a meridional chain of 9 observational sites clustered around Taiwan (21.9°–26.2°N, 118.4°–121.6°). This relatively dense GPS chain provides a powerful tool for studying ionospheric TEC in the northern hemispheric equatorial anomaly region with an unprecedented spatial resolution. Specifically, we studied seasonal and geomagnetic effects on the equatorial ionospheric anomaly during the solar minimum period between September 1996 and August 1997. We found that the surveyed data indicated semiannual variations in the magnitude of TEC, Ic, at the anomaly, with maxima in the equinoxes, similar to the semiannual variation of geomagnetic activity. The values of Ic were found to maximize in April, 1997 and minimize in July, 1997. Statistical studies indicate that the monthly values of Ic do not correlate with the planetary Kp magnetic index (r=0.41) but correlate well with the Dst geomagnetic activity index (r=0.72). This suggests that variations of TEC are mainly driven by a low-latitude forcing for the surveyed period. The most likely time for Ic to occur was 1400 local time (∼30%) at 20°N geographic latitude (∼37%).

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 unusually long-extended solar minimum between cycles 23 and 24 (from 2007 to 2008) yielded a number of anomalies with regard to solar/heliospheric phenomena wherein the solar wind magnetic field is 36% weaker than that for the previous solar cycle minimum (from 1996 to 1997) at 1 AU, the solar wind dynamic pressure is the lowest observed since the beginning of the space age, the unusually high tilted angle of the solar dipole, and the absence of a classical quiescent equatorial streamer belt. To understand the cause of the anomalies, we perform numerical simulation of a realistic inner heliosphere using a global three-dimensional, time-dependent, numerical model with observed solar inputs. It is suggested that these solar extremes are associated with (1) an inflated heliospheric current/plasma sheet (HCS/HPS) and (2) a decrease in the integrated fluxes of mass and magnetic field ejected from the Sun, which was manipulated by some unknown internal solar dynamics.

[1] Several coronal mass ejections (CMEs) were observed during 1–4 August 2010. At ∼17:12 UT on 3 August 2010, the Wind spacecraft detected an interplanetary shock followed by two magnetic cloud-like (MCL) structures that induced geomagnetic activity. The geomagnetic index, Dst, dropped to −65 nT while one of the MCLs passed through the magnetosphere. A global, three-dimensional magnetohydrodynamic (MHD) numerical model and a kinematic model (HAFv.2), with inputs based on actual solar observations, were used to simulate the response of the three-dimensional heliosphere. HAFv.2 and MHD models were used to simulate regions from 2.5 to 18 solar radii (Rs) and 18 to 285 Rs, respectively. A velocity pulse was used to simulate the major CME on 1 August 2010. The solar disturbances were injected into the lower boundary at 2.5 Rs. It is found that the background solar wind plays an important role in the evolution of this CME on its way to Earth. We compared the derived solar wind parameters (density, velocity, magnetic field, and temperature) with in situ observations from Wind near Earth. The simulation demonstrates a useful tool to link the general case of ICME at 1 AU to their solar sources. Simulation results also show that adiabatic value of γ = 5/3 seems to be appropriate for ideal MHD simulation studies of solar wind at 1 AU.

[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.

[1] Interplanetary coronal mass ejections (ICMEs) are the primary cause of severe space weather at Earth because they drive shocks and trigger geomagnetic storms that can damage spacecraft and ground-based systems. The Solar Mass Ejection Imager (SMEI) is a U. S. Air Force experiment with the ability to track ICMEs in white light from near the Sun to Earth and beyond, thus providing an extended observational range for forecasting storms. We summarize several studies of SMEI's detection and tracking capability, especially of the ICMEs associated with the intense (peak Dst ≤ −100 nT) geomagnetic storms that were the focus of the NASA Living With a Star Geostorm Coordinated Data Analysis Workshop. We describe the SMEI observations and analyses for the 18 intense storms observed from May 2003–2007 with adequate SMEI coverage and identified solar and interplanetary source regions. SMEI observed the associated ICMEs for 89% of these intense storms. For each event we extracted the time differences between these sets of times at 1 AU for shock arrival time, predicted ICME arrival time, onset of high-altitude aurora observed by SMEI, and storm onset. The mean intervals between successive pairs of these data were found to each be ∼4 hours. On average, SMEI first detected the geoeffective ICME about 1 day in advance, yielding a prediction lead time of ∼18 hours. Finally, the RMS values for the ICME-shock and storm-ICME time differences were determined, and provide at least a 1-hour improvement compared to similar observational and model-dependent studies.

[1] A practical database method for predicting the interplanetary shock arrival time at L1 point is presented here. First, a shock transit time database (hereinafter called Database-I) based on HAFv.1 (version 1 of the Hakamada-Akasofu-Fry model) is preliminarily established with hypothetical solar events. Then, on the basis of the prediction test results of 130 observed solar events during the period from February 1997 to August 2002, Database-I is modified to create a practical database method, named Database-II, organized on a multidimensional grid of source location, initial coronal shock speed, and the year of occurrence of the hypothetical solar event. The arrival time at L1 for any given solar event occurring in the 23rd solar cycle can be predicted by looking up in the grid of Database-II according to source location, the initial coronal shock speed, and the year of occurrence in cycle 23. Within the hit window of ±12 h, the success rate of the Database-II method for 130 solar events is 44%. This could be practically equivalent to the shock time of arrival (STOA) model, the interplanetary shock propagation model (ISPM), and the HAFv.2 model. To explore the capability of this method, it is tested on new data sets. These tests give reasonable results. In particular, this method's performance for a set of events in other cycles is as good as that of the STOA and ISPM models. This gives us confidence in its application to other cycles. From the viewpoint of long-term periodicity for solar activity, it is expected that the Database-II method can be applicable to the next solar cycle 24.

This is an investigation of the effects of corotating interaction regions (CIRs) in the heliosphere (< 1 AU) on geomagnetic disturbances during solar cycle 23 (1996-2005). Three kinds of interplanetary structures, "pure'' CIR, interaction of CIR with ICME, and "pure'' ICME by transient events, are identified by using the Hakamada-Akasofu-Fry (HAF) solar wind model. Yearly occurrence of 157 "pure'' CIRs has a minimum value in 2001 and a peak value in 2003 at the declining phase during the 23rd solar cycle. The maximum correlation coefficient of the daily sum of Kp indices between consecutive Carrington Rotations indicates that recurrent geomagnetic disturbances are dominant during the declining phase near solar minimum. Eighty percent of storms that are related to "pure'' CIRs belong to weak and moderate storms. The statistical analysis shows that about 50% of CIRs produce classical interplanetary shocks during the descending phase and 89% of the CIR-related shocks are followed by geomagnetic storms. These results demonstrate that CIR-related shock is not a necessary condition for generating a magnetic storm, but most CIR-related shocks are related to a storm. The Dst index that corresponds to CIR-related storms has a better linear relationship with IMF Bz, Ey, and the coupling function (epsilon) when the Dst indices are higher than -100 nT. Finally, the geoeffectiveness of CIRs appears clearly to have a seasonal variation.

[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.

[1] A newly developed hybrid code, HAFv.2+3DMHD, that combines two simulation codes, Hakamada-Akasofu-Fry code version 2 (HAFv.2) and a fully three-dimensional (3-D), time-dependent MHD simulation code, is used to study the global interplanetary coronal mass ejection (ICME) from the 12 May 1997 solar event. The solar wind structure is first simulated from the photosphere (1 solar radius, Rs) out to 2.5 Rs. The first step is derived from daily solar magnetograms. The HAFv.2 code is then used from 2.5 Rs to provide input at 18 Rs (0.08 AU) for the three-dimensional MHD code that calculates the evolution of solar wind plasma and interplanetary magnetic field beyond this distance into the heliosphere. A dynamic disturbance, mimicking the flare's energy output from the 12 May 1997 solar event, is then delivered to this quiescent nonuniform heliospheric structure to model the evolution and interplanetary propagation of the ICME (including its shock). We compare the derived ICME velocity and number density with the Wind spacecraft observations near Earth. We integrate the line-of-sight density in the plane of sky to compare with the white light brightness data observed by the Large-Angle Spectrometric Coronograph (LASCO) instrument on SOHO. This simulation will provide a tool to link the general cases of ICME at 1 AU to their solar sources, as well as to identify the possible origins of shock formation due to CMEs and CME/corotating interaction region interactions. In the case of complex or interacting ejecta, model interpretation is often required to accurately determine the solar sources of the ejecta at 1 AU. Because this newly developed model is performed using 3-D MHD, its results can be extended to simulate coronal and heliospheric observations, including the ambient medium's nonuniformity provided by the HAFv.2 model, from the recently launched Solar Terrestrial Relations Observatory (STEREO) mission.

[1] Solar wind speed plays an important role in the study of space weather prediction. Some workers have used it for measuring the arrival time of solar disturbances at 1 AU. The purpose of this work is to extend our previous study (Wu et al., 2005c) of some Halloween 2003 events by presenting additional physical effects of multiple shock interactions on the solar wind profile during a complex compound event. In order to achieve this goal, we track a group of specific solar events' plasma and magnetic field output as they propagate into interplanetary space. A one-dimensional, time-dependent adaptive grid MHD code is used to study the evolution and interaction of shocks from Sun through the heliosphere. The MHD simulation results demonstrate that the solar wind speed might increase about ≈25% after two shocks collide with each other. This kind of interaction can affect the accuracy of the identification of the solar source that causes the interplanetary event (e.g., magnetic cloud, coronal mass ejection, interplanetary shock, or some other interplanetary discontinuity.) In this study we further simulate part of the famous Halloween 2003 events that contain at least four major solar events (flares) during 28 October to 1 November 2003. These major events, simulated by pressure pulses, generated shocks that matched well with ACE (Advanced Composition Explorer) observations as reported by Wu et al. (2005c) in our previous study. The present work presents new details concerning the interplay (such as sunward and antisunward traveling compression and rarefaction waves) between fast forward and fast reverse interplanetary shocks.

[1] The Solar Mass Ejection Imager (SMEI) on the Coriolis spacecraft has been obtaining white light images of nearly the full sky every 102 minutes for three years. We present statistical results of analysis of the SMEI observations of coronal mass ejections (CMEs) traveling through the inner heliosphere; 139 CMEs were observed during the first 1.5 years of operations. At least 30 of these CMEs were observed by SMEI to propagate out to 1 AU and beyond and were associated with major geomagnetic storms at Earth. Most of these were observed as frontside halo events by the SOHO LASCO coronagraphs.

[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.

We compare 3D results from the 3D HAFv2 forecasting kinematic model, the 3D MHD HHMS model, and in‐situ observations. These comparisons provide insights on the 3D effects of interplanetary shocks. There is good agreement between results from our 3D models and spacecraft data. Voyager 1 and Voyager 2 continue to observe the effects of solar — induced shocks.

[1] We use the space weather validated 3-D HAFv2 model to help us study the interplanetary propagation of the October/November 2003 solar eruptions from the Sun to >90 AU and over a wide range of heliolongitudes and heliolatitudes. The HAFv2 model predictions at ACE (1 AU), Ulysses (5.23 AU), Cassini (8.67 AU), Voyager 2 (73 AU), and Voyager 1 (93 AU) are compared with available data. These comparisons indicate the importance of asymmetric interplanetary propagation both in heliolongitude and heliolatitude. We recommend that these effects explicitly be taken into account. The HAFv2 results appear to be useful for interpreting the Voyager 2 and Voyager 1 energetic particle data in the outer heliosphere. They are consistent with the effects of the Halloween solar events observed in the energetic particle data at both spacecraft. The HAFv2 results also may be helpful for predicting the plasma wave 2–3 kHz radio emission previously associated with large shocks and their interaction with the heliopause. Our study indicates that the Halloween events may give rise to 2–3 kHz radio emission in early 2005, assuming that the shocks which propagated beyond Voyager 1 will be strong enough.

[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 intense level of solar activity recorded from 19 October to 12 November 2003 led to unusually high energetic particle intensities observed throughout the heliosphere. The fleet of spacecraft distributed in the inner and outer heliosphere offers us the opportunity to study both the effects of these events in different regions of the heliosphere and the evolution of the energetic particle intensities measured at different heliocentric radial distances. Observations at 1 AU by the ACE and GOES-11 spacecraft show multiple particle intensity enhancements associated with individual injections of solar energetic particles (SEPs) and with the arrival of shocks driven by coronal mass ejections (CMEs), resulting in a long time interval (∼40 days) of elevated low-energy (

[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] We examine a possibility that metric type II solar radio bursts are all caused by coronal mass ejection (CME) generated shocks. For this we consider 129 type II flare events from February 1997 to October 2000 and examine their associations with SOHO/LASCO CMEs according to their temporal and spatial closeness using SOHO/EIT and GOES data. We then carefully inspected 26 CME-less events to examine if there are CME-related features in LASCO and EIT images. In addition we examined 28 limb type II CME events to compare the kinematics of coronal shocks with those of the CME fronts. Under the assumption that the observed type IIs are all generated by CME-related shocks, we determine the formation heights of the CME-associated type IIs using LASCO CME speeds and type II onset times. From these studies, we have found (1) a large fraction (81%) of the type II bursts have temporal and spatial association with CMEs, and the association increases as their source position approaches to the limb; (2) most of the events without the association are related with weak flares and/or disk events; (3) most of the events are super-Alfvenic with a mean speed of 900 km s−1; (4) the front heights of all CMEs except for a few events are in the range of 1 to 3 solar radii, which are consistent with the type II formation heights; (4) the onset time difference (CME-type II) of all events are within about ±1 hour, mostly −30 min to 10 min; (5) the CME speeds have a possible correlation (r = 0.6) with coronal shock speeds, when two outliers are excluded. Considering a possibility that some outliers could result from some effects such as the coronal shock generation at CME flanks and CME accelerations, our results show that most of the type II bursts can be explained by the CME origin.

A first‐generation 3D kinematic, space weather forecasting solar wind model (HAFv2) has been used to show the importance of solar generated disturbances in Voyager 1 and Voyager 2 observations in the outer heliosphere. We extend this work by using a 3D MHD model (HHMS) that, like HAFv2, incorporates a global, pre‐event, inhomogeneous, background solar wind plasma and interplanetary magnetic field. Initial comparisons are made between the two models of the solar wind out to 6 AU and with in‐situ observations at the ACE spacecraft before and after the October/November 2003 solar events.

[1] Intense, prolonged solar flare activity during March 1989 was used to provide a retrospective scenario for predictions of associated interplanetary shocks and accompanying particle radiation at planet Mars. Shocks from five major flares were simulated to hit both the Earth and Mars during the interval 9–23 March 1989. The simulated scenario was provided by the Hakamada-Akasofu-Fry version 2 (HAFv.2) solar wind model. Since part of the generally required inputs for the model (specifically metric radio Type II coronal shock speeds) were not available, the shock speeds were iteratively determined via a “calibration” that uses limited IMP 8 particle and sudden storm commencement (SSC) data as proxies for shock arrival at the Earth. The shocks from four major solar flares were, thereby, found to arrive at Mars at times that are appropriate to explain solar energetic particle (SEP) and energetic storm particle (ESP) events recorded in situ by the particle radiation detector experiments Solar Low Energy Detector (SLED) and Low Energy Telescope (LET) aboard Phobos-2. Supporting measurements were provided by the magnetometer (MAGMA) and plasma spectrometer (TAUS) experiments. A gap in the spacecraft records occurred at the simulated time of arrival of the fifth flare-associated shock. There were some uncertainties attending the selection of certain of the events deemed to be “parent” flares. Such uncertainty can be expected in view of the incomplete set of energetic particle, plasma, and magnetic field measurements made at relevant times at both the Earth and Mars (the latter planet was then located at a distance of 1.6 AU, at about 78° east of the Sun-Earth line). Use of the HAFv.2 solar wind model affords a 4-day lead time between predicted and measured space weather events at Mars, with an error of approximately ±12 hours. Solar radiation events of the magnitude studied occur often enough to warrant consideration in the design of both manned and unmanned expeditions to Mars.

[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.

The asymmetric propagation through the solar wind of shocks from solar eruptions influences the dynamics of the outer heliosphere. In 2002, these effects — and not the crossing of the termination shock (TS) — may have been responsible for the differences in observations made by Voyager 1 (V1) at 85 AU, 34° North and Voyager 2 (V2) at ∼67 AU, 24° South. We suggest these observations stemmed from two series of solar eruptions that propagated asymmetrically in longitude and primarily to the south. At V1 this led to unusually weak magnetic fields and increased access to particles from two sources: the TS and particles accelerated at the shocks created by the second series of solar eruptions as they propagated outward, passing V2. Because V1 was farther out, these particles showed anisotropies from an interior source. We used the HAFv2 model to study the propagation of the solar events. It predicted: 1) the 1 August 2002 shock observed on V2; 2) the trends in the V2 plasma and magnetic field data in August 2002; and implied 3) an extended period of increased particle transport near V1 in 2002. We estimate that on August 1, 2002 the termination shock was at ∼ 121 AU.

[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.

[1] We have compared the prediction capability of two types of Sun-Earth connection models: (1) ensemble of physics-based shock propagation models (STOA, STOA-2, ISPM, and HAFv.2) and (2) empirical CME propagation (CME-ICME and CME-IP shock) models. For this purpose, we have selected 38 near-simultaneous pairs of coronal mass ejections (CMEs) and metric type II radio bursts. By applying the adopted models to these events, we have estimated the time difference between predicted and observed arrivals of interplanetary (IP) shocks and ICMEs at the Earth or L1. The mean absolute error of the shock arrival time (SAT) within an adopted window of ±24 hours is 9.8 hours for the ensemble of shock propagation models, 9.2 hours for the CME-IP shock model, and 11.6 hours for the CME-ICME model. It is also found that the success rate for all models is about 80% for the same window. The results imply that the adopted models are comparable in their prediction of the arrival times of IP shocks and interplanetary CMEs (ICMEs). The usefulness of these models is also discussed in terms of real-time forecasts, underlying physics, and identification of IP shocks and ICMEs at the Earth. INDEX TERMS: 2722 Magnetospheric Physics: Forecasting; 7519 Solar Physics, Astrophysics, and Astronomy: Flares; 7513 Solar Physics, Astrophysics, and Astronomy: Coronal mass ejections; 2139 Interplanetary Physics: Interplanetary shocks; 2111 Interplanetary Physics: Ejecta, driver gases, and magnetic clouds; KEYWORDS: space weather forecasting, solar flares, CMEs, interplanetary shocks

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.

[1] We compare simulation results of real time shock arrival time prediction with observations by the ACE satellite for a series of solar flares/coronal mass ejections which took place between 28 March and 18 April, 2001 on the basis of the Hakamada-Akasofu-Fry, version 2 (HAFv.2) model. It is found, via an ex post facto calculation, that the initial speed of shock waves as an input parameter of the modeling is crucial for the agreement between the observation and the simulation. The initial speed determined by metric Type II radio burst observations must be substantially reduced (30 percent in average) for most high-speed shock waves.

Three-dimensional structure of the heliospheric current sheet, HCS, out to 5 AU is constructed for actual observed source field configurations.

The two major disturbances in the heliosphere during the present sunspot cycle, the event of June to August, 1982, and the event of April to June, 1978, are simulated by the method developed by Hakamada and Akasofu (1982). Specifically, an attempt was made to simulate the effects of six major flares from three active regions in June and July, 1982, and April and May, 1978. A comparison of the results with the solar wind observations at Pioneer 12 (approximately 0.8 au), ISEE-3 (approximately 1 au), Pioneer 11 (approximately 7 to 13 au) and Pioneer 10 (approximately 16 to 28 au) suggests that some major flares occurred behind the disk of the sun during the two periods. The method provides qualitatively some information as to how such a series of intense solar flares can greatly disturb both the inner and outer heliospheres. A long lasting effect on cosmic rays is discussed in conjunction with the disturbed heliosphere.

The three-dimensional structure of the heliospheric current sheet is constructed for Carrington rotations 1647, 1654, 1661, 1667, 1693, 1699, and 1719. These rotations are chosen from different epochs during the sunspot cycle 21, so that geometrical changes of the current sheet during a sunspot cycle can be inferred. Only for relatively simple neutral lines on the source surface, do the structures of the current sheet approximate those envisaged by Svalgaard and Wilcox (1976) and Thomas and Smith (1981).