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How the solar wind influences the magnetospheres of the outer planets is a fundamentally important question, but is difficult to answer in the absence of consistent, simultaneous monitoring of the upstream solar wind and the large-scale dynamics internal to the magnetosphere. To compensate for the relative lack of in-situ data, propagation models are often used to estimate the ambient solar wind conditions at the outer planets for comparison to remote observations or in-situ measurements. This introduces another complication: the propagation of near-Earth solar wind measurements introduces difficult-to-assess uncertainties. Here, we present the Multi-Model Ensemble System for the outer Heliosphere (MMESH) to begin to address these issues, along with the resultant multi-model ensemble (MME) of the solar wind conditions near Jupiter. MMESH accepts as input any number of solar wind models together with contemporaneous in-situ spacecraft data. From these, the system characterizes typical uncertainties in model timing, quantifies how these uncertainties vary under different conditions, attempts to correct for systematic biases in the input model timing, and composes a MME with uncertainties from the results. For the case of the Jupiter-MME presented here, three solar wind propagation models were compared to in-situ measurements from the near-Jupiter spacecraft Ulysses and Juno which span diverse geometries and phases of the solar cycle, amounting to more than 14,000 hours of data over 2.5 decades. The MME gives the most-probable near-Jupiter solar wind conditions for times within the tested epoch, outperforming the input models and returning quantified estimates of uncertainty., Comment: 31 pages, 10 figures

Solar radio bursts (SRBs), are emitted by electrons propagating through the corona and interplanetary space. Tracking such bursts is key to understanding the properties of accelerated electrons and radio wave propagation as well as the local plasma environment that they propagate through. Here, we present a novel multilateration algorithm called BayEsian LocaLisation Algorithm (BELLA). In addition, apparent SRB positions from BELLA are compared with comparable localisation methods and the predictions of solar wind models. BELLA uses Bayesian inference to create probabilistic distributions of source positions and their uncertainties. This facilitates the estimation of algorithmic, instrumental, and physical uncertainties in a quantitative manner. We validated BELLA using simulations and a Type III SRB observed by STEREO A/B and Wind. BELLA tracked the Type III source from $\sim$ 10--150 $R_{sun}$ (2-0.15 MHz) along a spiral trajectory. This allowed for an estimate of an apparent solar wind speed of $v_{sw} \sim$ 400 km s$^{-1}$ and a source longitude of $\phi_0 \sim$ 30deg. We compared these results with well-established methods of positioning: Goniopolarimetric (GP), analytical time-difference-of-arrival (TDOA), and Solar radio burst Electron Motion Tracker (SEMP). We found them to be in agreement with the results obtained by BELLA. Additionally, the results aligned with solar wind properties assimilated by the Heliospheric Upwind Extrapolation with time dependence (HUXt) model. We have validated BELLA and used it to identify apparent source positions as well as velocities and densities of the solar wind. Furthermore, we identified higher than expected electron densities, suggesting that the true emission sources were at lower altitudes than those identified by BELLA, an effect that may be due to appreciable scattering of electromagnetic waves by electrons in interplanetary space., Comment: 13 pages, 12 figures, in press, accepted by Astronomy and Astrophysics for publication

The ISWAT clusters H1+H2 have a focus on interplanetary space and its characteristics, especially on the large-scale co-rotating and transient structures impacting Earth. SIRs, generated by the interaction between high-speed solar wind originating in large-scale open coronal magnetic fields and slower solar wind from closed magnetic fields, are regions of compressed plasma and magnetic field followed by high-speed streams that recur at the ca. 27 day solar rotation period. Short-term reconfigurations of the lower coronal magnetic field generate flare emissions and provide the energy to accelerate enormous amounts of magnetised plasma and particles in the form of CMEs into interplanetary space. The dynamic interplay between these phenomena changes the configuration of interplanetary space on various temporal and spatial scales which in turn influences the propagation of individual structures. While considerable efforts have been made to model the solar wind, we outline the limitations arising from the rather large uncertainties in parameters inferred from observations that make reliable predictions of the structures impacting Earth difficult. Moreover, the increased complexity of interplanetary space as solar activity rises in cycle 25 is likely to pose a challenge to these models. Combining observational and modeling expertise will extend our knowledge of the relationship between these different phenomena and the underlying physical processes, leading to improved models and scientific understanding and more-reliable space-weather forecasting. The current paper summarizes the efforts and progress achieved in recent years, identifies open questions, and gives an outlook for the next 5-10 years. It acts as basis for updating the existing COSPAR roadmap by Schrijver+ (2015), as well as providing a useful and practical guide for peer-users and the next generation of space weather scientists., Comment: Accepted for publication in Advances in Space Research

Many scientists use coronal hole (CH) detections to infer open magnetic flux. Detection techniques differ in the areas that they assign as open, and may obtain different values for the open magnetic flux. We characterize the uncertainties of these methods, by applying six different detection methods to deduce the area and open flux of a near-disk center CH observed on 9/19/2010, and applying a single method to five different EUV filtergrams for this CH. Open flux was calculated using five different magnetic maps. The standard deviation (interpreted as the uncertainty) in the open flux estimate for this CH was about 26%. However, including the variability of different magnetic data sources, this uncertainty almost doubles to 45%. We use two of the methods to characterize the area and open flux for all CHs in this time period. We find that the open flux is greatly underestimated compared to values inferred from in-situ measurements (by 2.2-4 times). We also test our detection techniques on simulated emission images from a thermodynamic MHD model of the solar corona. We find that the methods overestimate the area and open flux in the simulated CH, but the average error in the flux is only about 7%. The full-Sun detections on the simulated corona underestimate the model open flux, but by factors well below what is needed to account for the missing flux in the observations. Under-detection of open flux in coronal holes likely contributes to the recognized deficit in solar open flux, but is unlikely to resolve it., Comment: 28 pages, 10 figures, submitted to ApJ

The recent launches of Parker Solar Probe (PSP), Solar Orbiter (SO) and BepiColombo, along with several older spacecraft, have provided the opportunity to study the solar wind at multiple latitudes and distances from the Sun simultaneously. We take advantage of this unique spacecraft constellation, along with low solar activity across two solar rotations between May and July 2020, to investigate how the solar wind structure, including the Heliospheric Current Sheet (HCS), varies with latitude. We visualise the sector structure of the inner heliosphere by ballistically mapping the polarity and solar wind speed from several spacecraft onto the Sun's source surface. We then assess the HCS morphology and orientation with the in situ data and compare with a predicted HCS shape. We resolve ripples in the HCS on scales of a few degrees in longitude and latitude, finding that the local orientation of sector boundaries were broadly consistent with the shape of the HCS but were steepened with respect to a modelled HCS at the Sun. We investigate how several CIRs varied with latitude, finding evidence for the compression region affecting slow solar wind outside the latitude extent of the faster stream. We also identified several transient structures associated with HCS crossings, and speculate that one such transient may have disrupted the local HCS orientation up to five days after its passage. We have shown that the solar wind structure varies significantly with latitude, with this constellation providing context for solar wind measurements that would not be possible with a single spacecraft. These measurements provide an accurate representation of the solar wind within $\pm 10^{\circ}$ latitude, which could be used as a more rigorous constraint on solar wind models and space weather predictions. In the future, this range of latitudes will increase as SO's orbit becomes more inclined., Comment: Accepted version

On 2020 April 19 a coronal mass ejection (CME) was detected in situ by Solar Orbiter at a heliocentric distance of about 0.8 AU. The CME was later observed in situ on April 20th by the Wind and BepiColombo spacecraft whilst BepiColombo was located very close to Earth. This CME presents a good opportunity for a triple radial alignment study, as the spacecraft were separated by less than 5$^\circ$ in longitude. The source of the CME, which was launched on April 15th, was an almost entirely isolated streamer blowout. STEREO-A observed the event remotely from -75.1$^\circ$ longitude, which is an exceptionally well suited viewpoint for heliospheric imaging of an Earth directed CME. The configuration of the four spacecraft has provided an exceptionally clean link between remote imaging and in situ observations of the CME. We have used the in situ observations of the CME at Solar Orbiter, Wind, and BepiColombo, and the remote observations of the CME at STEREO-A in combination with flux rope models to determine the global shape of the CME and its evolution as it propagated through the inner heliosphere. A clear flattening of the CME cross-section has been observed by STEREO-A, and further confirmed by comparing profiles of the flux rope models to the in situ data, where the distorted flux rope cross-section qualitatively agrees most with in situ observations of the magnetic field at Solar Orbiter. Comparing in situ observations of the magnetic field between spacecraft, we find that the dependence of the maximum (mean) magnetic field strength decreases with heliocentric distance as $r^{-1.24 \pm 0.50}$ ($r^{-1.12 \pm 0.14}$), in disagreement with previous studies. Further assessment of the axial and poloidal magnetic field strength dependencies suggests that the expansion of the CME is likely neither self-similar nor cylindrically symmetric.

Studying the ambient solar wind, a continuous pressure-driven plasma flow emanating from our Sun, is an important component of space weather research. The ambient solar wind flows in interplanetary space determine how solar storms evolve through the heliosphere before reaching Earth, and especially during solar minimum are themselves a driver of activity in the Earth's magnetic field. Accurately forecasting the ambient solar wind flow is therefore imperative to space weather awareness. Here we present a machine learning approach in which solutions from magnetic models of the solar corona are used to output the solar wind conditions near the Earth. The results are compared to observations and existing models in a comprehensive validation analysis, and the new model outperforms existing models in almost all measures. In addition, this approach offers a new perspective to discuss the role of different input data to ambient solar wind modeling, and what this tells us about the underlying physical processes. The final model discussed here represents an extremely fast, well-validated and open-source approach to the forecasting of ambient solar wind at Earth., Comment: 15 pages, 6 figures, 3 tables

The heliospheric magnetic field is of pivotal importance in solar and space physics. The field is rooted in the Sun's photosphere, where it has been observed for many years. Global maps of the solar magnetic field based on full disk magnetograms are commonly used as boundary conditions for coronal and solar wind models. Two primary observational constraints on the models are (1) the open field regions in the model should approximately correspond to coronal holes observed in emission, and (2) the magnitude of the open magnetic flux in the model should match that inferred from in situ spacecraft measurements. In this study, we calculate both MHD and PFSS solutions using fourteen different magnetic maps produced from five different types of observatory magnetograms, for the time period surrounding July, 2010. We have found that for all of the model/map combinations, models that have coronal hole areas close to observations underestimate the interplanetary magnetic flux, or, conversely, for models to match the interplanetary flux, the modeled open field regions are larger than coronal holes observed in EUV emission. In an alternative approach, we estimate the open magnetic flux entirely from solar observations by combining automatically detected coronal holes for Carrington rotation 2098 with observatory synoptic magnetic maps. This approach also underestimates the interplanetary magnetic flux. Our results imply that either typical observatory maps underestimate the Sun's magnetic flux, or a significant portion of the open magnetic flux is not rooted in regions that are obviously dark in EUV and X-ray emission.

More than 70 years ago it was recognised that ionospheric F2-layer critical frequencies $foF2$ had a strong relationship to sunspot number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of $foF2$ to sunspot numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17 - 21. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the sunspot number - $foF2$ relationship. Over the interval studied here, the ISN, $R$, the backbone group number $Rbb$, and the corrected number $Rc$ largely differ in their allowance for the 'Waldmeier discontinuity' around 1945 (the correction factor for which for $R$, $Rbb$ and $Rc$ is, respectively, zero, effectively over 20%, and explicitly 11.6%). It is shown that for Solar Cycles 18 - 21, all three sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for $Rbb$. We here use $foF2$ for those UTs for which $R$, $Rbb$, and $Rc$ all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes $R$ to underestimate the fitted values based on the $foF2$ data for 1932 - 1945 but $Rbb$ overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in $Rbb$ is too large by a factor of two. Fit residuals are smallest and most uniform for $Rc$ and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) sunspot group data for the same interval., Comment: 35 pages, 11 figures

We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups $R_B$ above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of $R_B$ are then re-scaled to the observed RGO group number $R_A$ using a variety of regression techniques. It is found that a very high correlation between $R_A$ and $R_B$ ($r_{AB}$ > 0.98) does not prevent large errors in the intercalibration (e.g. sunspot maximum values can be over 30% too large even for such levels of $r_{AB}$). In generating the backbone sunspot number, Svalgaard and Schatten [2015] force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (Q-Q) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data., Comment: 14 pages, 1 Table, 11 figures

We investigate a CME propagating towards Earth on 29 March 2011. This event is specifically chosen for its predominately northward directed magnetic field, so that the influence from the momentum flux onto Earth can be isolated. We focus our study on understanding how a small Earth-directed segment propagates. Mass images are created from the white-light cameras onboard STEREO which are also converted into mass height-time maps (mass J-maps). The mass tracks on these J-maps correspond to the sheath region between the CME and its associated shock front as detected by in situ measurements at L1. A time-series of mass measurements from the STEREO COR-2A instrument are made along the Earth propagation direction. Qualitatively, this mass time-series shows a remarkable resemblance to the L1 in situ density series. The in situ measurements are used as inputs into a 3D magnetospheric space weather simulation from CCMC. These simulations display a sudden compression of the magnetosphere from the large momentum flux at the leading edge of the CME and predictions are made for the time-derivative of the magnetic field (dB/dt) on the ground. The predicted dB/dt were then compared with observations from specific equatorially-located ground stations and show notable similarity. This study of the momentum of a CME from the Sun down to its influence on magnetic ground stations on Earth is presented as preliminary proof of concept, such that future attempts may try to use remote sensing to create density and velocity time-series as inputs to magnetospheric simulations., Comment: Accepted for publication 8th March 2013. Submitted 18th Dec 2012. 19 Pages, 10 figures, 2 Appendices

Stereoscopic white-light imaging of a large portion of the inner heliosphere has been used to track interplanetary coronal mass ejections. At large elongations from the Sun, the white-light brightness depends on both the local electron density and the efficiency of the Thomson-scattering process. To quantify the effects of the Thomson-scattering geometry, we study an interplanetary shock using forward magnetohydrodynamic simulation and synthetic white-light imaging. Identifiable as an inclined streak of enhanced brightness in a time-elongation map, the travelling shock can be readily imaged by an observer located within a wide range of longitudes in the ecliptic. Different parts of the shock front contribute to the imaged brightness pattern viewed by observers at different longitudes. Moreover, even for an observer located at a fixed longitude, a different part of the shock front will contribute to the imaged brightness at any given time. The observed brightness within each imaging pixel results from a weighted integral along its corresponding ray-path. It is possible to infer the longitudinal location of the shock from the brightness pattern in an optical sky map, based on the east-west asymmetry in its brightness and degree of polarization. Therefore, measurement of the interplanetary polarized brightness could significantly reduce the ambiguity in performing three-dimensional reconstruction of local electron density from white-light imaging., Comment: 27 pages, 8 figures, 4 tables, Solar Physics

Recent coordinated observations of interplanetary scintillation (IPS) and stereoscopic heliospheric imagers (HIs) are significant to continuously track the propagation and evolution of solar eruptions throughout interplanetary space. In order to obtain a better understanding of the observational signatures in these two remote-sensing techniques, the magnetohydrodynamics of the macro-scale interplanetary disturbance and the radio-wave scattering of the micro-scale electron-density fluctuation are coupled and investigated using a newly-constructed multi-scale numerical model. This model is then applied to a case of an interplanetary shock propagation within the ecliptic plane. The shock could be nearly invisible to an HI, once entering the Thomson-scattering sphere of the HI. The asymmetry in the optical images between the western and eastern HIs suggests the shock propagation off the Sun-Earth line. Meanwhile, an IPS signal, strongly dependent on the local electron density, is insensitive to the density cavity far downstream of the shock front. When this cavity (or the shock nose) is cut through by an IPS ray-path, a single speed component at the flank (or the nose) of the shock can be recorded; when an IPS ray-path penetrates the sheath between the shock nose and this cavity, two speed components at the sheath and flank can be detected. Moreover, once a shock front touches an IPS ray-path, the derived position and speed at the irregularity source of this IPS signal, together with an assumption of a radial and constant propagation of the shock, can be used to estimate the later appearance of the shock front in the elongation of the HI field of view. The results of synthetic measurements from forward modelling are helpful in inferring the in-situ properties of coronal mass ejection from real observational data via an inverse approach., Comment: 31 pages, 8 figures, Journal of Atmospheric and Solar-Terrestrial Physics, accepted

We perform a numerical study of the evolution of a Coronal Mass Ejection (CME) and its interaction with the coronal magnetic field based on the May 12, 1997, CME event using a global MagnetoHydroDynamic (MHD) model for the solar corona. The ambient solar wind steady-state solution is driven by photospheric magnetic field data, while the solar eruption is obtained by superimposing an unstable flux rope onto the steady-state solution. During the initial stage of CME expansion, the core flux rope reconnects with the neighboring field, which facilitates lateral expansion of the CME footprint in the low corona. The flux rope field also reconnects with the oppositely orientated overlying magnetic field in the manner of the breakout model. During this stage of the eruption, the simulated CME rotates counter-clockwise to achieve an orientation that is in agreement with the interplanetary flux rope observed at 1 AU. A significant component of the CME that expands into interplanetary space comprises one of the side lobes created mainly as a result of reconnection with the overlying field. Within 3 hours, reconnection effectively modifies the CME connectivity from the initial condition where both footpoints are rooted in the active region to a situation where one footpoint is displaced into the quiet Sun, at a significant distance ($\approx 1R_\odot$) from the original source region. The expansion and rotation due to interaction with the overlying magnetic field stops when the CME reaches the outer edge of the helmet streamer belt, where the field is organized on a global scale. The simulation thus offers a new view of the role reconnection plays in rotating a CME flux rope and transporting its footpoints while preserving its core structure., Comment: Accepted to JGR Space Physics, 15 pages, 8 figures

An update of Owens et al. (2008) shows that the relationship between the coronal mass ejection (CME) rate and the heliospheric magnetic field strength predicts a field floor of less than 4 nT at 1 AU. This implies that the record low values measured during this solar minimum do not necessarily contradict the idea that open flux is conserved. The results are consistent with the hypothesis that CMEs add flux to the heliosphere and interchange reconnection between open flux and closed CME loops subtracts flux. An existing model embracing this hypothesis, however, overestimates flux during the current minimum, even though the CME rate has been low. The discrepancy calls for reasonable changes in model assumptions., Comment: in press, ASP Conference Series, SOHO-23: Understanding a Peculiar Solar Minimum, edited by S. Cranmer, T. Hoeksema, and J. Kohl

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude lambda(|B|) increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field lambda(Bxyz) and of the velocity lambda(Vyz) do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4 x 10^6 km. We conclude that a linear relation between lambda(|B|), VB^2 and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geo-effective structures which is in turn proportional to VB^2. By looking at the distribution of daily correlation lengths we show that the solar minimum values of lambda(|B|) correspond to the turbulent outer scale. A tail of larger lambda(|B|) values is present at solar maximum, causing the increase in mean value., Comment: 10 pages, 4 figures, in press in Solar Physics

A fraction of the total photospheric magnetic flux opens to the heliosphere to form the interplanetary magnetic field carried by the solar wind. While this open flux is critical to our understanding of the generation and evolution of the solar magnetic field, direct measurements are generally limited to single-point measurements taken in situ by heliospheric spacecraft. An observed latitude invariance in the radial component of the magnetic field suggests that extrapolation from such single-point measurements to total heliospheric magnetic flux is possible. In this study we test this assumption using estimates of total heliospheric flux from well-separated heliospheric spacecraft and conclude that single-point measurements are indeed adequate proxies for the total heliospheric magnetic flux, though care must be taken when comparing flux estimates from data collected at different heliocentric distances.