A multidecade debate about the relationship between CMEs and flares has revealed that these phenomena are related to magnetic reconnection but are not causally related to each other. Nonetheless, there is a close association between energetic flares and CMEs. Flare-CME relationships have been studied by Kahler , Gosling , Harrison , Zhang et al. , Yashiro et al. , Chen and Zong , Yashiro and Gopalswamy , Jain et al. , Chen and Kunkel , Bak-Steslicka et al. , Bhatt et al. , and many others.
 Our work, based on the study of 259 flare/Dst pairs during high, declining, and rising solar cycle activity, and covering more than 18,000 observation hours totaling more than two years, enabled us to take the more general flare-CME relationship and move it into an operational paradigm. During the intervals that we studied at the suggestion of our customer (15 January to 15 July 2001; 1 March to 28 September 2005; and 1 December 2011 to 30 November 2012), nearly every energetic flare event above a certain irradiance threshold, described below, was deterministically related to a Dst event. This surprising relationship allowed us to create an algorithm with sufficient robustness to be incorporated into an operational forecasting routine that eventually forecasts neutral densities in the thermosphere, i.e., JB2008. A summary of the operational basis of Anemomilos and its relationship to physical processes is useful as a short introduction. The forecasting considerations are size, speed, and location for a magnetic eruptive event to intercept Earth.
4.4 X-ray Flux as Proxy for Magnitude of Dst Response
 Solar flares are identified in the GOES XRS 0.1–0.8 nm band, available with 1 min time resolution (Figure 3). NASA's SDO EUV Variability Experiment (EVE) produces an XRS surrogate in the event that the GOES XRS data stream is offline. In an operational (automated) setting, we find that it is important to distinguish between the X-ray irradiance background and the flare event. During very active times, emissions from individual flares are convolved with the emissions from nonflaring bright active regions in X-ray data time series. Thus, a magnitude X-class flare on the NOAA scale may actually be from a region producing a smaller M-class flare if the flare occurs in addition to an ensemble of emission background from across the solar disk or from active limb emission. In other words, many nonflare bright regions within the GOES field of view can contribute to the flare signal.
 To alleviate this problem, and to isolate the unique magnitude of each flaring event, SET developed the unitless daily X-ray background (Xb10) (Figure 6 lower panel) and hourly Xhf (Figure 6 upper panel) indices [Tobiska and Bouwer, 2006]. The Xb10 index is used to establish an irradiance baseline. The remaining Xhf index with the baseline removed is an indicator of the past hour's flare values and is updated every 5 min. We employ the hourly Xhf to quantify, then relate, solar flare activity to assumed solar charged particle ejecta and ultimately to Dst disturbances. There is a threshold, Xhf = 40, below which we do not forecast Dst events. Above this threshold, we scale a statistical Dst template to small, medium, and large sizes based on the Dst value during the main phase; the scaling has been empirically determined based on our study of the 2001 and 2005 data located in Appendix A. Figure 6 shows the Xhf and Xb10 time series for early 2012. The large flare events in March 2012 were associated with Xb10 values of ~375 and Xhf values of ~250. Figure 5 shows all occurrences of Xhf events in intervals of 2001, 2005, and 2012 used in this study. The magnitude of Xhf is represented by the dot color ranging from blue (Xhf = 40) to red (Xhf >210).
 The information in Figures 4-6 is empirically encapsulated in the Anemomilos algorithm as the basis for forecasting small, medium, or large Dst events at Earth. Anemomilos uses a statistical Dst storm profile that derives from a composite template for Dst events observed by the USGS during solar cycle 23 [Gannon, 2012]. The USGS composite Dst storm profile contains initial, main, and recovery phases; an example is shown in Figure 7 as the blue line. Anemomilos uses a scaled USGS template for Dst sizes of small, medium, and large events based on the Xhf index and location, described above, and the integrated irradiance hour flare index, Xhf, that is related to speed and described below.
4.5 Integrated Irradiance X-ray Flare Index, Xhf, as a Proxy Ejecta Speed
 The Earth arrival timing for the ejected solar plasma is critical if one is to obtain an accurate Dst magnitude change and morphology. We empirically derived a radial velocity (line-of-sight speed) for events within 45° radially of the solar disk center. It is based on the integrated flare magnitude, i.e., the integrated value of the Xhf flare index, and is consistent with previous theoretical work [Chen and Kunkel, 2010]. We find that a temporal integration of the Xhf value provides a good proxy for the speed of the ejecta in its transit from the Sun to Earth. Thus, the integral of Xhf (IX) provides crucial information regarding the start of a Dst event initial phase.
 Mass leaving the Sun during eruptive events is generally associated with flux rope ejections. The ejecta are often modeled as force-free erupting flux ropes (EFRs) that undergo dramatic expansion and changes in acceleration within a small number of solar radii posteruption [Chen, 1996]. The EFRs have been described by many authors [e.g., Chen, 1996; Shimojo and Shibata, 2000; Reames, 2002; Török and Kliem, 2005; NASA/TM—2006–214137, 2006, and Chen and Kunkel, 2010] and are acted upon by a combination of forces, e.g., Lorentz, gravity, and drag.
 Chen and Kunkel  investigated a range of flare/CME events and found a temporal and physical connection between coronal mass ejections and flares. They treated flares and CMEs as separate manifestations of the same energetic process whereby poloidal magnetic flux was injected into the toroidal flux ropes. They found that flare brightness, due to accelerating particles, was proportional to the strength of the electrodynamics of the magnetic flux injection into the flux rope. They considered the XUV GOES light curves for B-, C-, and M-class limb flares and their associated CME trajectories determined from SOHO LASCO and STEREO/SECCHI images. Their study established a relationship between the theoretical rate of injection of magnetic flux, dϕp(t)/dt, into an erupting flux rope, the integrated GOES XUV emission, and the acceleration, a, of the flux rope out of the corona and into the interplanetary medium. This relationship is expressed in equation (1) as
 For one GOES B-class flare event in 2008, they were able to follow the subsequent deceleration in the interplanetary medium. The peak speed of the ejecta was 1400 km s−1 near the Sun and over the course of 24 h the ejecta decelerated to a speed just above 500 km s−1.
 Our study independently found a similar relationship between the integrated GOES XRS 0.1–0.8 nm light curve from eruptive events on the solar disk (not limb) and Dst events. Below, we describe a relationship between an empirically derived line-of-sight ejecta speed and GOES XRS integrated measurements; later we show how the ensemble of these observations can be used operationally to create a forecast of Dst geoeffectiveness for events within 45° radially of the solar disk center.
 The speed of the ejecta was first calculated for our 2001 test period by identifying flaring events and their locations in SOHO Extreme ultraviolet Imaging Telescope (EIT) images, associating them with Xhf index values at the same epoch, then finding the most probable Dst perturbation created by each event. SOHO EIT images were often not available during a specific event; as a result, we used only those eruptive events where we could unambiguously determine the flare location and Xhf-Dst pair association for a Dst occurrence of any size. We also selected events that were close to the solar equator in order to maximize ecliptic plane effectiveness as well as restricted events to 45° radial from the disk center to ensure the validity of a line-of-sight velocity approximation. The combination of these restrictions resulted in a small sampling but it still allowed us to calculate a rough time-of-flight for each ejecta event from the Sun to Earth.
 These constraints resulted in a reduced set of 35 events that are shown in Figure 8; a subset (11 events in 2001) from these is shown in Table 1. Their speed was considered a total average speed for liftoff from the Sun, transit through the IPM, and arrival at Earth. The ensemble of these identified events provided a means to derive velocity from integrated Xhf; they are shown as the points closest to the linear regression blue line in Figure 8. Other points close to the regression line were not part of the 2001 derivation set. There are also several data points considerably off the line and these are events that had slower or faster velocities than those calculated from the 2005 and 2012 time periods. Error in estimating velocity can occur from unknown geometry of flux ropes, ejecta source regions being on the edge of IMF lines connected to the Earth, unresolved accelerations at ejecta liftoff, or unknown causes for velocities changes (e.g., shock interactions) while the material is in transit to Earth.
Figure 8. Derived speed from integrated Xhf (IX). Eleven points close to the regression line are the 2001 values used to derive the relationship.
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Table 1. Dst-Related Events Used in Integrated Xhf-Speed Derivation
 We note that a solution to the problem of velocity uncertainty is to incorporate observations of this material during its inner heliosphere passage and the Interplanetary Scintillation (IPS) methodology holds promise for providing that type of observation to correct the in-transit velocities. IPS observations are line-of-sight-integrated observations through the solar wind to distant galactic radio sources that may contain smearing in the data, i.e., an ambiguity in determining where, along a line of sight, the observed signal originates. Researchers use a tomographic technique to disentangle this line-of-sight smearing where both solar rotation and outward motion of structures in the solar wind over time provide views from different perspectives that are required for a tomographic analysis [Jackson et al., 1998].
 The linear regression equation used in this work to create an average ejecta velocity is described below and is reprinted in Figure 8. In Figure 8, “IX” refers to the Integrated Xhf. The blue line is the relationship derived from the 11 events in the 2001 data period and those regression coefficients are now used operationally.
 We tested our derived velocities against all available data. There were a total of 259 flare eruption/Dst associated pair events and these are identified in Appendix A. The listing in Appendix A of the Xhf-Dst paired events provides the UT time (YYYYMMDDhhmm), Xhf value, a magnitude class for Xhf (similar, but not identical, NOAA X-ray flare classes), speed (km s−1), solar flare event location (heliocentric latitude and longitude), obliquity angle corrected latitude Lat*, radius, and azimuth from solar sub-Earth point where Az is N = 0, W = 90, S = 180 or −180, E = −90, and Dst size. Eleven derivation and four example events are listed as the shaded rows in Appendix A. The entire data set has a range from 194 to 3000 km s−1, a median ejecta transit speed of 750 km s−1, and a mean of 779 km s−1.
 For operations, Anemomilos uses two methods for estimating speed. First, when there is no other ability to obtain speed, e.g., the existence of an ambiguity in, or undetermined, Xhf start/stop times, then 750 km s−1 (the median speed in our data set) is used as the default value for estimating the ejecta time-of-arrival at Earth. Second, if all operational information is available at the given epoch, that is, if the SDO EVE Solar Aspect Monitor (SAM) location data matches the GOES XRS Xhf timing within a few minutes to declare an event has been observed, then a derived speed can be calculated based on the Xhf integrated time. The Xhf integrated time is the start-to-end of the flare event. The event start is defined as the beginning of the GOES XRS 0.1–0.8 nm light curve rise above background and the event end is defined as the time where the irradiance values are one half the flare peak value compared to the background at the start of the event.
 The empirically derived speed-integrated Xhf relationship is
where V is the ejecta's line-of-sight velocity [km/s], Xhf is the dimensionless flare index, 0 and 1 are start and stop times of the flare event, and dt is the length of the time for the event in seconds. This linear regression was based on the subset of 11 events that occurred in 2001 and shown in Table 1 and Figure 8.
 In support of our methodology that relates flare brightness to speed from solar disk observations, we note that Zhang et al.  found a limb CME-speed relationship with integrated GOES soft X-ray flux measurements. Their study predated, but was similar to, the conclusions of Chen and Kunkel  and they also indicated that flare-induced thermal pressure was not the cause of the CMEs but that flares and CMEs were two manifestations of the same magnetic process.
 The Xhf value is an excellent indicator of the flare magnitude and its integration over time serves as a proxy for acceleration. This is similar to the electromotive force associated with the flux injection that destabilizes and ejects the flux rope as described by Chen and Kunkel . Thus, the kinematic acceleration of the ejecta through an interval of time results in a velocity; the relationship is only strictly valid for line-of-sight velocity (speed) of events observed near disk center but in operations we use this for all events. In practice, most of the geoeffective events only occur near the disk center and are not limb events. If we assume that there is a constant velocity offset, c1 (km s−1), to correct for unknown total deceleration in the IMF and an acceleration multiplier, c2 (km s−2), that incorporates all the Chen and Kunkel  main and residual ejecta liftoff acceleration terms, then equation (3) helps us understand the gross kinematics of equation (1) and the empirical relationship of equation (2)
 Here, the observationally determined linear regression constants for the Dst-effective Xhf events occurring near the center of solar disk are c1 = −2191 km s−1 and c2 = 4.74 km s−2 where v1 is the average velocity at the Earth, a is the average acceleration between the Sun and Earth, and t1 is the arrival time at Earth.
 For every hour of the 12 months of December 2011 through November 2012, we observed the Xhf, derived a velocity, found an integrated Xhf, determined an event location, and estimated a Dst event timing and magnitude. This 2012 period was used for operationally testing of our 2001 and 2005 development parameters and, based on this test period, we established the deterministic geoeffectiveness of flaring events as observed in Dst.
 Figure 4 shows all the paired events in traditional heliocentric Mercator coordinates with the center-of-disk marked by a circle/cross. Figure 5 shows all the paired events in polar plot coordinates; both plots have the solar obliquity angle corrected as discussed below. The Figure 5 radial angle from the disk center is used in Anemomilos as a discriminator to test whether or not an event has the potential for geoeffectivity based on location. The Dst relative event size of small (−34 < Dst ≤ 0 nT), medium (−159 < Dst ≤ −34 nT), or large (Dst ≤ −159 nT) is graphically represented by the size of the dot. The magnitude of Xhf is represented by the dot color ranging from blue (Xhf = 40) to red (Xhf >210).
4.7 Southward Bz and Other Issues
 The Anemomilos algorithm does not contain an explicit IMF relationship. It is challenging to understand the performance of our simplified approach to geomagnetic storm forecasting as we were struck by the overall success of Anemomilos without using an observed Bz. We believe that there are two aspects of the method and its application that are important. The first is related to the likelihood of southward IMF during the passage of any given ejecta from the Sun to the Earth; the second is the relative role of southward IMF during storm processes.
 Most ejecta have intervals of southward IMF. Mulligan et al.  discussed two types of idealized magnetic flux ropes that could pass Earth, i.e., magnetic flux ropes in the ecliptic that produce bipolar magnetic clouds and those tipped 90° with respect to the ecliptic that produce unipolar magnetic clouds. Magnetic flux ropes lying in the ecliptic have southward IMF either at the leading or trailing edge. Half of the highly inclined magnetic flux ropes should have southward IMF in their axial field. Thus, for idealized magnetic clouds at least 75% should contain intervals of southward IMF. Only about one third of all ejecta are magnetic clouds. The remaining two thirds of ejecta have “rougher” magnetic profiles that usually have at least some short intervals of southward IMF. Further, fast CMEs often drive shocks with enhanced IMF, which may point southward and thus initiate geospace storm processes even before the main body of the CME arrives. We suspect that our simplified forecasting approach is simply taking advantage of the likelihood that southward IMF is present in fast solar wind transients that pass Earth.
 The importance of southward IMF cannot be denied, but it is not the only factor in geomagnetic storm strength. Since Dungey's  groundbreaking work on solar wind interaction with the Earth's magnetosphere, numerous studies have shown that southward IMF is the dominant factor in controlling energy input to geospace. The role of southward IMF was captured in the relationship known as the Akasofu epsilon coupling function that relates the solar wind IMF to the convective electric field [Perreault and Akasofu, 1978]. Newell et al.  reviewed solar wind coupling processes and produced a new “universal coupling function,” which places a strong emphasis on solar wind speed.
 Recent studies have shown that there is more to the coupling processes than can be explained by a single coupling function. Borovsky and Denton  suggested that cold dense plasma, in the form of plasmaspheric drainage plumes from the inner magnetosphere, could be set into motion when the convective electric field increases abruptly. If this circulating plasma comes in contact the dayside reconnection site, the efficiency of solar wind-magnetospheric coupling is observed to decrease. Thus, processes other than direct solar wind interaction may be at work during storm time. In global simulations with a southward IMF, Lopez et al.  showed that for large enough IMF strengths, the geoeffectiveness is not proportional to the field because the field convects around the magnetosphere instead of being reconnected. Additionally Knipp et al. [2011 and references therein] and Li et al.  report that the east-west interplanetary field (IMF By) can dominate energy input to the dayside ionosphere-thermosphere system.
 We have not solved the issue of IMF orientation but hopefully these types of studies can offer more insight. Other questions were also raised in this regard: (a) perhaps BZ is important for larger CME events but not for smaller ones; (b) we note that the superposition of multiple small events can create moderately large Dst activity, which may have been interpreted as a southward Bz effect in some cases; (c) perhaps if there is a By component of any significance, it may provide coupling paths to the magnetosphere in almost all cases except where Bz is almost entirely northward; (d) the coupling between speed, size, and Bz is an avenue for future study outside this empirical algorithm; and (e) the dominant orientation of the IMF may have a solar cycle dependency as noted by Mulligan et al.  and our Anemomilos derivation with solar cycle 23 data may not be entirely accurate for solar cycle 24.
 Additionally, Anemomilos does not take into account corotating interaction regions (CIRs) or HSS. CIRs, while not eruptive events, are sourced in the open field lines emanating from coronal holes and can induce Dst disturbances on the order of a small substorm for a prolonged period of time. We anticipate improving the algorithm with CIRs and HSS in the future.
 We have seen cases in our event list where very large solar limb events or greatly elongated moderate-sized midlongitude events may discharge a fraction of their plasma onto IMF lines that intersect the Earth even though the bulk of the material is not Earth directed. The algorithm does not distinguish the extent of the plasma on and off Earth-directed field lines or the geometry of EFRs; thus, some events may be missed while others are overstated in magnitude.
 Finally, knowledge of the speed of the ejecta is critical to accurately estimate superposition of events and their timing; we believe our calculation of speed can be refined. If plasma is not ejected with most of the velocity component based on the line-of-sight assumption, the algorithm may overestimate the impact of the event; fortunately, smaller events that are geoeffective are also relatively close to the center of the solar disk and this maintains the validity of the assumption.
 Improvements to Anemomilos are anticipated and will focus on: (i) an IMF B specification to obtain better Dst magnitudes, e.g., perhaps through IPS observations; (ii) the effects of CIRs and HSS; (iii) asymmetric plasma discharges onto Earth-directed and non-Earth-directed IMF lines and EFR geometry; and (iv) refined knowledge of ejecta speeds.
4.8 An Anemomilos Example
 An example of the Anemomilos forecast using the operational observables (flare magnitude, integrated flare irradiance, and location) is shown for 2012 in Figures 15a–15j. This is a period in late January 2012 when a series of medium-sized solar flare events occurred starting on 19 January around 1500 UT and centered at N34E27. While this was a particularly clear example, nearly all the events we studied had a similar forecast evolution and we show Figures 15a–15j that are representative of the Anemomilos capability. A movie example for the entire 2001 study period is available on YouTube at http://youtu.be/snxgoQ_s0o0.
Figure 15. (a) The first Xhf event (AX166) resulting in Dst event (AD-49). (b) The second Xhf event (BX179) resulting in Dst event (BD-49). (c) Event AX166 arrival as AD-49. (d) Event BX179 arrival as BD-49. (e) Combined enroute events. (f) Dst event BD-49 SSC arrival. (g) Storm main phase minimum. (h) The third Xhf event (CM200) resulting in Dst event (CD-34). (i) Dst event CD-34 SSC arrival. (j) End Dst recovery—all events.
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 In these figures, the blue dots are the 1 h predicted Dst from Anemomilos and the black dots are the 1 h Kyoto Dst reported values (y axis scale); the red dots are the 1 h Xhf value (arbitrarily scaled for viewing and not related to the y axis). All three are shown on the same UT time x axis with the time and date plus the day-of-year reported. The vertical dotted line is the current epoch, which is listed in the first set of figure title items as UT hours plus year and day-of-year.
 The second set of figure title items includes two pieces of information (superscript FORECAST) related to the predicted state for the most severe Dst based on all the combined future conditions, postcurrent epoch. The first two-character set describes the predicted size of the Dst event and is labeled as AC (All Clear), SE (Small Event), ME (Medium Event), or LE (Large Event) for Dst. The second two-character set is the NOAA G-scale prediction. Other plotted information that may exist in the real-time figures includes NOAA reported M5 – X10 flare class (labeled along a gold vertical bar above the Xhf values) and the NOAA reported Type II radio burst velocities (labeled along a purple vertical bar above the 0 nT line). The two red and/or green vertical bars above 60 nT are the daily solar flare probabilities (top bar, SP) and geomagnetic activity probabilities (bottom bar, GP) for the next 24 h. These are reported from the NOAA daily Report of Solar Geophysical Activity (RSGA) and plotted. SP green indicates an M5-class flare probability and red indicates an X1-class flare probability where the length of the colored bar is the relative probability on a 1% – 99% scale. GP green indicates a minor storm (Kp = 5) probability and red indicates a major storm (Kp ≥ 6) probability where the length of the colored bar is the relative probability on a 1% – 99% scale. All NOAA information is provided for informational purposes only and is not used in the Anemomilos Dst forecast.
 The third set of the figure title items contains six pieces of information (superscript NOW) related to the current state of the Dst at that specific epoch. Included are the Dst event size (none, small, medium, or large with thresholds previously defined), its probability of occurrence (1% – 99% scale), source of the forecast (NN = NoNe, SO = Solar Observed event, SP = Solar daily Probability estimate from NOAA, and GP = Geomagnetic daily Probability estimate from NOAA), Xhf flare class and value (C, M, X with the Xhf value appended as a superscript), location of the eruptive event on the solar disk in heliocentric latitude and latitude (N, S and W, E), and speed of the ejecta (km s−1).
 Figures 15a and 15b show the Dst effect from two EFRs arising out of two closely spaced erupting events starting at 19 January 2012 centered around 1500 UT. The first Xhf event (AX166) during the 1 h (operationally constrained) interval 19 January 2012 1400 UT (reported the next hour in the 1500 UT time frame) with a location of N34E27 (45° radius from sub-Earth at −30° azimuth) produced an EFR with a calculated velocity of 568 km s−1 resulting in a medium size Dst event (AD-49). The second Xhf event (BX179) during 19 January 2012 1500 UT (reported in the 1600 UT time frame) with a location of N34E27 (45° radius from sub-Earth at −30° azimuth) was a continuation of the first event but had grown larger; the event produced an EFR with a calculated velocity of 623 km s−1 resulting in a medium size Dst event (BD-49).
 Figures 15c and 15d show the 12 h time step predictions of the first and second events. The graphical location of the erupting event on the Earth-visible solar hemisphere from a North pole perspective is a solid-filled dot if the event occurs in the northern hemisphere. If it occurs in the southern hemisphere, it is an open circle. The dot is sized according to its Xhf value with a redundant Xhf magnitude color coding using the size/color scheme of Figure 4. The EFR arc length is notionally sized according to Xhf class ID where “C” is shortest, “M” is medium, and “X” is longest length. The EFR is color coded by Dst size (blue = none, green = small, orange = medium, and red = large) and the dot size is redundantly set by the size scheme in Figure 4.
 The arrival of the first event AX166 was predicted to arrive with the Dst event initiation at 22 January 2012 1700 UT having a minimum Dst peak of −46 nT (NOAA G3) 10 h later at 23 January 2012 0300 UT. The second event was predicted to overtake the first event, arriving earlier at 22 January 2012 1100 UT with a minimum (combined with the first event) Dst peak of −75 nT (NOAA G3) 16 h later also at 23 January 2012 0300 UT. Thus, the second event overtakes the first event, arriving about 6 h earlier but combining to form a larger Dst event of −75 nT. The algorithm saves the separate time series vectors of each separate event then sums them with any previous results to arrive at a new Dst profile. Figure 15e shows the combined superposition of both events after the two EFRs have left the Sun and are enroute to Earth. Figure 15f shows the Dst combined event at the arrival positive phase peak SSC of event BD-49 at 22 January 2012 0600 UT (reported 1 h later), which is about 5 h earlier than predicted. We do not yet attempt to refine the arrival time using ACE solar wind information.
 The storm proceeds to develop into its main phase, reaching its minimum at 23 January 2012 0300 UT (Figure 15g) just as predicted and based on the superposition of both events. Serendipitously, but unrelated, another eruptive event occurs on the Sun at the time of the Dst minimum (Figure 15h) and creates a third Dst prediction. This event was the smallest of the three and the Xhf event (CM200) during 23 January 2012 0300 UT (reported in the 0400 UT time frame) at a location of N29W22 (39° radius from sub-Earth at 29° azimuth) produced an EFR with a calculated velocity of 1128 km s−1 resulting in a small size Dst event (CD-34). Figure 15i shows the arrival positive phase peak SSC of third event CD-34 at 24 January 2012 1500 UT (reported 1 h later) during the recovery phases of the combined events AD-49 and BD-49. Figure 15j shows the end of the recovery period for all three events.
 The Anemomilos forecast Dst has been correlated against the actual Dst values for the 2001 and 2005 hourly predictions out to +72 h. Tables 2 and 3 show the results of the forecast compared with the actual Dst using hour-by-hour values in a linear regression correlation. This technique compares initial arrival, main, and recovery phases equally. In both tables are listed the UT hour (HR), mean value percent difference for the Nowcast timeframe (−24 to 0 h, NowMean), the 1-sigma standard deviation (1-σ) for the Nowcast (NowSTD), the current epoch mean value percent difference (0DyMean), 1-σ for the current epoch (0DySTD), 1 day forecast mean value percent difference (+24 h, 1DyMean), 1-σ for the 1 day forecast (1DySTD), 2 day forecast mean value percent difference (+48 h, 2DyMean), 1-σ for the 2 day forecast (2DySTD), and 3 day forecast mean value percent difference (+72 h, 3DyMean), and 1-σ for the 3 day forecast (3DySTD). In each hour epoch example, the mean value, e.g., NowMean, is the simple arithmetic mean (total of the data for all hours in the 2001 or 2005 test period at that hour epoch divided by the number of nonzero elements). The standard deviation is calculated on the mean values so that the 1-σ results can be reported as ratios.
Table 2. Dst Forecast to Actual Comparisons for Jan–Jul 2001
Table 3. Dst Forecast to Actual Comparisons for Mar–Sep 2005
 For high solar activity in 2001, the mean of the 1 day predictions for the entire data set are 99% of the actual Dst values, the 2 day predictions are 90%, and the 3 day predictions are 60%. The reason that the 3 day predictions deteriorate is that if there are large Dst events, they tend to arrive earlier than 3 days and these are not predicted; thus, the prime source of error at 3 days is in the magnitude of the events. For low solar activity in 2005, the values are slightly worse for each of the 3 days although the forecast-to-actual ratios of the 1-σ standard deviations are better than in 2001, i.e., less scatter. It is unclear why this difference occurs and is an area of study.
 Figures 16a and 16b as well as Figures 17a and 17b show the Tables 2 and 3 mean value and 1-σ differences for the 00 UT nowcast, current epoch, 1 day, 2 day, and 3 day forecast comparisons in 2001 and 2005. The 12 UT hour plots were similar and are not shown. The blue line is the relevant comparison while the red lines were from reference comparisons not directly related to this discussion.