The role of empirical space-weather models (in a world of physics-based numerical simulations)

Advanced forecasting of space weather requires prediction of near-Earth solar-wind conditions on the basis of remote solar observations. This is typically achieved using numerical magnetohydrodynamic models initiated by photospheric magnetic field observations. The accuracy of such forecasts is being continually improved through better numerics, better determination of the boundary conditions and better representation of the underlying physical processes. Thus it is not unreasonable to conclude that simple, empirical solar-wind forecasts have been rendered obsolete. However, empirical models arguably have more to contribute now than ever before. In addition to providing quick, cheap, independent forecasts, simple empirical models aid in numerical model validation and verification, and add value to numerical model forecasts through parameterization, uncertainty estimation and ‘downscaling’ of sub-grid processes

Time-window approaches to space-weather forecast metrics: a solar wind case study

Metrics are an objective, quantitative assessment of forecast (or model) agreement with observations. They are essential for assessing forecast accuracy and reliability, and consequently act as a diagnostic for forecast development. Partly as a result of limited spatial sampling of observations, much of space‐weather forecasting is focused on the time domain, rather than inherent spatial variability. Thus metrics are primarily “point‐by‐point” approaches, in which observed conditions at time t are compared directly (and only) with the forecast conditions at time t. Such metrics are undoubtedly useful. But in lacking an explicit consideration of timing uncertainties, they have limitations as diagnostic tools and can, under certain conditions, be misleading. Using a near‐Earth solar wind speed forecast as an illustrative example, this study briefly reviews the most commonly‐used point‐by‐point metrics and advocates for complementary “time window” approaches. In particular, a scale‐selective approach, originally developed in numerical weather prediction for validation of spatially patchy rainfall forecasts, is adapted to the time domain for space‐weather purposes. This simple approach readily determines the time scales over which a forecast is and isn’t valuable, allowing the results of point‐by‐point metrics to be put in greater context

Magnetic cloud distortion resulting from propagation through a structured solar wind: Models and observations

Numerical simulations of magnetic clouds (MCs) propagating through a structured solar wind suggest that MC-associated magnetic flux ropes are highly distorted by inhomogeneities in the ambient medium. In particular, a solar wind configuration of fast wind from high latitudes and slow wind at low latitudes, common at periods close to solar minimum, should distort the cross section of magnetic clouds into concave-outward structures. This phenomenon has been reported in observations of shock front orientations, but not in the body of magnetic clouds. In this study an analytical magnetic cloud model based upon a kinematically distorted flux rope is modified to simulate propagation through a structured medium. This new model is then used to identify specific time series signatures of the resulting concave-outward flux ropes. In situ observations of three well studied magnetic clouds are examined with comparison to the model, but the expected concave-outward signatures are not present. Indeed, the observations are better described by the convex-outward flux rope model. This may be due to a sharp latitudinal transition from fast to slow wind, resulting in a globally concave-outward flux rope, but with convex-outward signatures on a local scale

Quantifying the latitudinal representivity of in situ solar wind observations

Advanced space-weather forecasting relies on the ability to accurately predict near-Earth solar wind conditions. For this purpose, physics-based, global numerical models of the solar wind are initialized with photospheric magnetic field and coronagraph observations, but no further observation constraints are imposed between the upper corona and Earth orbit. Data assimilation (DA) of the available in situ solar wind observations into the models could potentially provide additional constraints, improving solar wind reconstructions, and forecasts. However, in order to effectively combine the model and observations, it is necessary to quantify the error introduced by assuming point measurements are representative of the model state. In particular, the range of heliographic latitudes over which in situ solar wind speed measurements are representative is of primary importance, but particularly difficult to assess from observations alone. In this study we use 40+ years of observation-driven solar wind model results to assess two related properties: the latitudinal representivity error introduced by assuming the solar wind speed measured at a given latitude is the same as that at the heliographic equator, and the range of latitudes over which a solar wind measurement should influence the model state, referred to as the observational localisation. These values are quantified for future use in solar wind DA schemes as a function of solar cycle phase, measurement latitude, and error tolerance. In general, we find that in situ solar wind speed measurements near the ecliptic plane at solar minimum are extremely localised, being similar over only 1° or 2° of latitude. In the uniform polar fast wind above approximately 40° latitude at solar minimum, the latitudinal representivity error drops. At solar maximum, the increased variability of the solar wind speed at high latitudes means that the latitudinal representivity error increases at the poles, though becomes greater in the ecliptic, as long as moderate speed errors can be tolerated. The heliospheric magnetic field and solar wind density and temperature show very similar behaviour

On the origin of otho-gardenhose heliospheric flux

Parker-spiral theory predicts that the heliospheric magnetic field (HMF) will have components of opposite polarity radially toward the Sun and tangentially antiparallel to the solar rotation direction (i.e., in Geocentric Solar Ecliptic (GSE) coordinates, with Bx/By 0 which is frequently observed. We here study the occurrence and structure of OGH flux, as seen in near-Earth space (heliocentric distance r = 1 AU) by the Wind and Advanced Composition Explorer (ACE) spacecraft (for 1995 – 2017, inclusive) and by the Helios-1 and -2 spacecraft at 0.29 AU < r ≤ 1 AU (for December 1974 to August 1981), in order to evaluate the contributions to OGH flux generation of the various mechanisms and factors that are not accounted for by Parker-spiral theory. We study the loss of OGH flux with increasing averaging timescale T between 16 seconds and 100 hours and so determine its spectrum of spatial/temporal scale sizes. OGH flux at Earth at sunspot minimum is shown to be more common than at sunspot maximum and caused by smaller-scale structure in the HMF (with a mode temporal scale at a fixed point of Tmp of about 10hours compared to Tmp of about 40hours for sunspot maximum, corresponding to about 5.5 and 22 degrees (respectively) of heliocentric angular width for co-rotational motion or 21 Rs and 84 Rs for radial solar-wind flow (where Rs is a mean solar radius). OGH generated by rotating the HMF through the radial direction is also shown to differ in its spectrum of scale sizes from that for OGH generated by rotating the HMF through the tangential direction – the former does not contribute to the “excess” open heliospheric flux at a given r but the latter does. We show that roughly half of the HMF deflection from the ideal Parker-spiral needed to give the observed occurrence of OGH at Earth occurs at r below 0.3 AU. By comparing the Helios and near-Earth data we highlight some questions that can be addressed by the Parker Solar Probe mission which will study the HMF down to r = 0.046 AU. We suggest that with decreasing heliocentric distance, Probe will detect decreased OGH field due to draping around transient ejecta, such as blobs and coronal mass ejections, but increasing structure in the radial field within traditional HMF sectors that are remnant Alfvénic disturbances in outflow regions from coronal reconnection sites

Coronal mass ejections and magnetic flux buildup in the heliosphere

To test for magnetic flux buildup in the heliosphere from coronal mass ejections (CMEs), we simulate heliospheric flux as a constant background open flux with a time-varying interplanetary CME (ICME) contribution. As flux carried by ejecta can only contribute to the heliospheric flux budget while it remains closed, the ICME flux opening rate is an important factor. Two separate forms for the ICME flux opening rate are considered: (1) constant and (2) exponentially decaying with time. Coronagraph observations are used to determine the CME occurrence rates, while in situ observations are used to estimate the magnetic flux content of a typical ICME. Both static equilibrium and dynamic simulations, using the constant and exponential ICME flux opening models, require flux opening timescales of ∼50 days in order to match the observed doubling in the magnetic field intensity at 1 AU over the solar cycle. Such timescales are equivalent to a change in the ICME closed flux of only ∼7–12% between 1 and 5 AU, consistent with CSE signatures; no flux buildup results. The dynamic simulation yields a solar cycle flux variation with high variability that matches the overall variability of the observed magnetic field intensity remarkably well, including the double peak forming the Gnevyshev gap

Solar-wind structure

The hot solar atmosphere continually expands out into space to form the solar wind, which drags with it the Sun’s magnetic field. This creates a cavity in the interstellar medium, extending far past the outer planets, within which the solar magnetic-field dominates. While the physical mechanisms by which the solar atmosphere is heated are still debated, the resulting solar wind can be readily understood in terms of the pressure difference between the hot, dense solar atmosphere and the cold, tenuous interstellar medium. This results in an accelerating solar-wind profile which becomes supersonic long before it reaches Earth orbit. The large-scale structure of the magnetic field carried by the solar wind is that of an Archimedean spiral, owing to the radial solar-wind flow away from the Sun and the rotation of the magnetic footpoints with the solar surface. Within this relatively simple picture, however, is a range of substructure, on all observable time and spatial scales. Solar-wind flows are largely bimodal in character. “Fast” wind comes from open magnetic-field regions, which have a single connection to the solar surface. “Slow” wind, on the other hand, appears to come from the vicinity of closed magnetic field regions, which have both ends connected to the Sun. Interaction of fast and slow wind leads to patterns of solar-wind compression and expansion which sweep past Earth. Within this relatively stable structure of flows, huge episodic eruptions of solar material further perturb conditions. At the smaller scales, turbulent eddies create unpredictable variations in solar-wind conditions. These solar-wind structures are of great interest as they give rise to space weather that can adversely affect space- and ground-based technologies, as well as pose a threat to humans in space

The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds

Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE's SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes

Tests of sunspot number sequences: 4. Discontinuities around 1946 in various sunspot number and sunspot group number reconstructions

We use five test data series to search for, and quantify, putative discontinuities around 1946 in five different annual-mean sunspot-number or sunspot-group number data sequences. The data series tested are: the original and new versions of the Wolf/Zurich/International sunspot number composite [RISNv1 and RISNv2] (respectively Clette et al., Adv. Space Res., 40, 919, 2007 and Clette et al., in “The Solar Activity Cycle”, 35, Springer, 2015); the corrected version of RISNv1 proposed by Lockwood, Owens, and Barnard (J. Geophys. Res. Space Physics, 119, 5193, 2014a) [RC]; the new “backbone” group number composite proposed by Svalgaard and Schatten (Solar Physics, 2016) [RBB]; and the new group-number composite derived by Usoskin et al. (Solar Physics, 2016) [RUEA]. The test data series used are: the group number [NG] and total sunspot area [AG] from the Royal Observatory, Greenwich / Royal Greenwich Observatory (RGO) photoheliographic data; the Ca K index from the recent re-analysis of Mount Wilson Observatory (MWO) spectroheliograms in the Calcium II K ion line; the sunspot-group number from the MWO sunspot drawings [NMWO]; and the dayside ionospheric F2-region critical frequencies measured by the Slough ionosonde [foF2]. These test data all vary in close association with sunspot numbers, in some cases non-linearly. The tests are carried out using both the “before-and-after” fit-residual comparison method and the correlation method of Lockwood, Owens, and Barnard, applied to annual mean data for intervals iterated to minimise errors and to eliminate uncertainties associated with the precise date of the putative discontinuity. It is not assumed that the correction required is by a constant factor, nor even linear in sunspot number. It is shown that a non-linear correction is required by RC, RBB, and RISNv1, but not by RISNv2 or RUEA. The five test datasets give very similar results in all cases. By multiplying the probability distribution functions together we obtain the optimum correction for each sunspot dataset that must be applied to pre-discontinuity data to make them consistent with the post-discontinuity data. It is shown that, on average, values for 1932 - 1943 are too small (relative to later values) by about 12.3 % for RISNv1 but are too large for RISNv2 and RBB by 3.8 % and 5.2 %, respectively. The correction that was applied to generate RC from RISNv1 reduces this average factor to 0.5 % but does not remove the non-linear variation with the test data, and other errors remain uncorrected. A valuable test of the procedures used is provided by RUEA, which is identical to the RGO NG values over the interval employed