Optimum Solar Wind Monitor Locations Based on Dst Predictability

G. M. Lindsay, J. G. Luhmann and C. T. Russell
Institute of Geophysics and Planetary Physics
University of California, Los Angeles

Abstract

The formula of Burton et al. (1975) provides a quick and simple means by which the strength of the ring current and the Dst index can be calculated based solely on upstream solar wind density, velocity, and north/south component of the magnetic field. Solar wind data from ISEE-3, Pioneer Venus Orbiter, and Helios-A are used to show how well Dst predictions based on the Burton et al. formula applied to data from upstream monitors at various heliospheric distances match Dst observations. The prediction capability is found to depend upon the nature of the large-scale disturbances observed at the monitor as well as the position of the monitor with respect to Earth. As the distance in front of the Earth increases, the lead time of the prediction increases, but the accuracy of the prediction decreases. It is shown that a solar wind monitor that provides a substantial geomagnetic forecast lead time, with reliable predictions of the characteristics of the solar wind can be stationed ~0.7 AU if it is near the ecliptic plane and within 10 East of the Earth-Sun line.

Introduction

Burton et al, (1975) provided a relatively simple formula that allowed the accurate prediction of ring current strength and the Dst index based on upstream solar wind conditions near 1 AU. This formula is shown in

Figure 1. The assumed sources of change in the strength of the ring current are the amount of injection (F(E)=d(Ey-0.5), where d = -1.5x10- nT((mV/m)s)-1 Ey is the y GSM component of the interplanetary electric field) and the amount of decay which is proportional to the strength of the ring current. In their formula, dDsto/dt = F(E)-aDsto, where F(E) is non-zero only for southward solar wind magnetic fields (the half-wave rectifier assumption), and "a" is an empirically derived constant representing the fractional loss of ring current per unit time (3.6x10-5 s-1). When the IMF is southward and the solar wind convective electric field (VBz) is sufficiently strong such that F(E) exceeds aDsto, the ring current is energized. When the IMF turns northward, F(E) is zero and the ring current is no longer energized, decaying and becoming weaker. Dst is the perturbation of the horizontal component of the Earth's magnetic field as measured by mid-latitude ground stations in nanoteslas. It is the sum of the ring current and the magnetopause currents and equals zero when the magnetopause currents and ring currents have their quiet day values. Burton et al. (1975) obtained their ring current value by subtracting from Dst the correction term b(rV2)1/2-c. The constants "b" and "c," also empirically derived, represent the response to dynamic pressure changes in the solar wind (15.8 nT(nPa)-1/2) and the quiet day currents (20 nT), respectively. Large, negative Dst characteristic of geomagnetic storms occurs when the ring current is strong (i.e., during periods of large, duskward Ey). Positive Dst occurs when the magnetopause currents are strong and the ring current is weak (i.e., during periods of strong solar wind dynamic pressure and northward Bz).

By virtue of the Burton et al. formula, forecasting Dst is essentially a matter of predicting the solar wind conditions at the front of the magnetosphere. The best way to forecast interplanetary conditions at the Earth is to have a solar wind monitor on the streamline that intersects the Earth, well inside 1.0 AU, but not so close to the sun that the solar wind and the IMF are still evolving significantly. Here, the formula of Burton et al. is applied to solar wind observations from ISEE-3, Pioneer Venus Orbiter (PVO), and Helios-A, to evaluate possible locations for an upstream monitor. It is found that good daily average Dst prediction capability with 24-hour forecast lead times can be achieved with an upstream solar wind monitor as far inside 1.0 AU as 0.7 AU, but that the accuracy of the prediction is less accurate for more distant monitors closer to the sun.

Figure 2. This figure shows a 540 day comparison between Dst predicted from the Burton et al formula (red trace) using ISEE-3 solar wind data near 1.0 AU when the plasma analyzer was functioning (1 September, 1978 to 23 February, 1980) and that observed (black trace) by midlatitude ground stations. The observed Dst (obtained from the NSSDC data base) has a 1-hr resolution while the ISEE-3 predicted Dst has a 5-minute resolution. ISEE-3 provides about a 45-minute lead time between Dst prediction and Dst observation at 1.0 AU. The predicted Dst shown in Figure 2 has not been delayed by the expected solar wind convection time between ISEE-3 and 1.0 AU. We have not attempted to predict this delay because the convection time depends on the location of ISEE-3 perpendicular to the streamline of the solar wind passing through the stagnation point and the orientation of the structure convected past ISEE-3. This orientation will be different for coronal mass ejections (CMEs) and stream interaction regions. To highlight any recurrent features, the length of each data strip is 27 days (approximately one solar rotation). At this resolution, Dst predicted by the Burton et al. formula is in excellent agreement with the actual Dst observations. For most of the time, the predicted and observed Dst values differ only slightly (an average amount of only ~5 nT). However, there are isolated periods where the agreement in magnitude differs by an average of ~50 nT (29-30 September, 1978; 21-24 February, 1979; 24-28 April, 1979; 3-9 July, 1979).

Figure 3. Here, 27 days extracted from Figure 2 are shown (February 10 - March 9, 1979). During this time, interplanetary shocks are noted by the filled arrows, CMEs are noted by the unfilled arrows, and stream interactions are noted by the filled circles. In this case, predicted Dst (red trace) is greater than observed Dst (black trace) on February 21-23, indicating that more ring current energization occurred than predicted. Examination of hourly resolution data during this time indicates that other factors in the solar wind may alter the efficiency of reconnection expected in the Burton et al. formula. High beta values in the magnetosheath have been found to reduce the rate of reconnection [Paschmann et al., 1986; Scurry and Russell, 1991; Scurry et al., 1994]. However, during this period the solar wind was characterized by extremely low solar wind beta (beta<0.4) as is associated with the passage of a CME [Klein and Burlaga, 1982]. Dynamic pressure has been found to enhance geomagnetic activity and by inference, the rate of reconnection [Scurry and Russell, 1991]. In the case shown here, more ring current energization was observed than predicted, perhaps as a result of the much higher than average solar wind dynamic pressure associated with large IMF during this period.

Figure 4. This figure shows a 27 day comparison between predicted Dst (red trace) using 10 minute resolution solar wind data measured at 0.7 AU with Pioneer Venus Orbiter (PVO) and observed Dst (black trace) at 1.0 AU from 1-28 June, 1980. During this period, PVO is within 10 of the Earth-Sun line, and the Venus orbital and ecliptic planes were practically coincident. It is assumed that solar wind velocity does not vary appreciably between 0.7 AU and 1.0 AU and that the values of r and Bz vary as r-2 and r-1, respectively. In this case, the solar wind monitor is 0.3 AU inside 1.0 AU so that there is ~1 day lead time between Dst prediction and Dst observation at 1.0 AU. No allowance for the solar wind convection time between 0.7 and 1.0 AU has been incorporated here. So, the predicted trace is shown ~1 day in advance of the observed Dst at 1.0 AU. The agreement in the variation and magnitude of predicted and observed Dst is quite good. Interplanetary shocks, CMEs, and stream interactions are noted as in Figure 2.

Figure 5. This figure shows a 54 day comparison (17 October-30 November, 1975) between Dst predicted from the Burton et al. formula (red trace) using 1-hour resolution solar wind data from Helios-A and observed Dst (black trace). During this period Helios-A is between ~10 to ~5 East of the Earth-Sun line, 9 to 3 North of the ecliptic, and varies in radial distance from ~0.6 to ~1.0 AU. The forecast lead time changes from ~2 days to ~1 hr during the period shown. As with the case in Figure 4, it is assumed that solar wind velocity does not vary appreciably between 0.7 AU and 1.0 AU and that the values of r and Bz vary as r-2 and r-1, respectively Because of the long time that Helios-A spends near the Earth-Sun line and the variation in radial and angular separation between Helios-A and the Earth, this pass provides an opportunity to evaluate the merits of various locations of an upstream solar wind monitor. When Helios-A is at radial distances between ~0.6 and ~0.7 AU (17-27 October), it is ~8 north of the ecliptic and ~10 East of the Earth-Sun line. The Dst predictions and observations agree in the level of activity, but the correspondence in predicted and observed variation is not clear. From 0.7 to 0.8 AU (28 October - 9 November), Helios-A is ~6 north of the ecliptic and ~7 east of the Earth-Sun line. The agreement between predicted and observed Dst, both variation and level of activity is not good. That the PVO predictions at 0.7 AU are quite good while the Helios-A predictions at ~0.7 AU are not can be attributed to the fact that PVO was very near the ecliptic during the period observed whereas Helios-A is ~6 north of the ecliptic. Since the average solar wind is not latitudinally uniform [Woo, 1988], it is possible that the solar wind conditions sampled by Helios-A are not observed at Earth. When Helios is between ~0.8-1.0 AU (10 November-30 November), it travels from ~6 north to ~3 north of the ecliptic. Helios-A is at its closest approach to the Earth-Sun line (~5 ) on 9-13 November. The agreement between prediction and observation is fairly good.

Conclusions

Figures 2 through 5 demonstrate that it is possible to make useful predictions of Dst based upon solar wind measurements made between ~0.7 and 1.0 AU. However, the accuracy of this extrapolation is dependent upon the position of the solar wind monitor with respect to Earth and the type of solar wind phenomena encountered. Obviously, the best prediction capability is provided by a solar wind monitor that samples solar wind conditions representative of those later seen at 1.0 AU. This means a monitor in the ecliptic plane and near the Earth-Sun line.

It is preferable to have a large forecast lead time. This can only be provided by a monitor as far inside 1.0 AU as possible. The inherent characteristics of the solar wind cause problems in stationing a monitor far from 1.0 AU. Inside ~0.5 AU, the solar wind exhibits many small scale features which are not observed at 1.0 AU [Schwenn et al., 1990]. These characteristics in the solar wind do not vary in the simple radially dependent manner assumed here. Thus, the known properties of the solar wind lead us to conclude that a solar wind monitor should be placed at least beyond 0.5 AU.

Forecast lead time is also dependent upon the type of large-scale solar wind phenomena being observed. When the solar wind monitor and Earth are in near-alignment, the time delay between observations of a CME at the two locations is just that determined by the velocity of the CME which is presumed to travel radially outward. Stream interactions are corotational solar wind features, so that the simple time delay between observations at the monitor and 1.0 AU will depend upon the radial separation as well as the east/west separation angle between the monitor and Earth. For example, when Venus is eastward of the Earth-Sun line, PVO will observe the stream interaction first. The stream interaction will then be observed at Earth at a time determined by the angular separation between Earth and Venus and the corotational speed and archimedean spiral angle of the interaction region. As PVO travels from east to west of the Earth-Sun line, the time between observation at 0.7 AU and 1.0 AU will decrease. When PVO is ~18 west of the Earth-Sun line, the stream interaction may be detected nearly simultaneously at 0.7 AU and 1.0 AU. So, a useful solar wind monitor should be deployed no further west of the Earth-Sun line than ~18 at 0.7 AU. To provide the largest forecast lead time for both CMEs and stream interaction passages, the monitor should be placed east of the Earth-Sun line but not so far east that the characteristics of the solar wind are uncorrelated with those that intersect the Earth.

Marubashi (1989) notes that the key to the establishment of space weather forecasting systems are: 1) the development of an efficient algorithm for predictions of critical solar and geophysical phenomena and 2) secure continuous streams of real-time data required for the prediction algorithm. In its current form, Burton et al. formula provides the first key. It is simple, fast, and based solely upon solar wind measurements it generally predicts Dst to within a few nanoteslas of the observed Dst. Thus, a magnetospheric storm can be readily predicted. Deployment of an upstream solar wind monitor that would remain substantially inside 1.0 AU (0.7 to 0.95 AU), near the ecliptic plane, and orbit about the sun synchronously with the Earth providing an ongoing capability to make these predictions would be the second key towards establishing a true space weather forecast system.

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Last modified: July 18, 1995