Data-based modelling of the Earth's dynamic magnetosphere: a review

This paper reviews the main advances in the area of data-based modelling of the Earth's distant magnetic field achieved during the last two decades. The essence and the principal goal of the approach is to extract maximum information from available data, using physically realistic and flexible mathematical structures, parameterized by the most relevant and routinely accessible observables. Accordingly, the paper concentrates on three aspects of the modelling: (i) mathematical methods to develop a computational "skeleton" of a model, (ii) spacecraft databases, and (iii) parameterization of the magnetospheric models by the solar wind drivers and/or ground-based indices. The review is followed by a discussion of the main issues concerning further progress in the area, in particular, methods to assess the models' performance and the accuracy of the field line mapping. The material presented in the paper is organized along the lines of the author Julius-Bartels' Medal Lecture during the General Assembly 2013 of the European Geosciences Union

Improving Empirical Magnetic Field Models by Fitting to In Situ Data Using an Optimized Parameter Approach

A method for comparing and optimizing the accuracy of empirical magnetic field models using in situ magnetic field measurements is presented. The optimization method minimizes a cost function-tau-that explicitly includes both a magnitude and an angular term. A time span of 21 days, including periods of mild and intense geomagnetic activity, was used for this analysis. A comparison between five magnetic field models (T96, T01S, T02, TS04, and TS07) widely used by the community demonstrated that the T02 model was, on average, the most accurate when driven by the standard model input parameters. The optimization procedure, performed in all models except TS07, generally improved the results when compared to unoptimized versions of the models. Additionally, using more satellites in the optimization procedure produces more accurate results. This procedure reduces the number of large errors in the model, that is, it reduces the number of outliers in the error distribution. The TS04 model shows the most accurate results after the optimization in terms of both the magnitude and direction, when using at least six satellites in the fitting. It gave a smaller error than its unoptimized counterpart 57.3% of the time and outperformed the best unoptimized model (T02) 56.2% of the time. Its median percentage error in vertical bar B vertical bar was reduced from 4.54% to 3.84%. The difference among the models analyzed, when compared in terms of the median of the error distributions, is not very large. However, the unoptimized models can have very large errors, which are much reduced after the optimization. Plain Language Summary We present a method for comparing and optimizing the accuracy of commonly used empirical models that reproduce the Earth's magnetic field for altitudes ranging from a thousand to hundreds of thousands of kilometers. This method uses magnetic field data from satellites orbiting the planet to create a "penalty function" and uses an optimization algorithm to minimize this function and find the model input parameters that produce the best results for a given date and time. Our results show that these models can be improved by the use of satellite data. The model known as TS04 produced the best results after the optimization procedure generating a smaller error in 57.3% of the points in our data set when compared to the standard (unoptimized) inputs. The optimized TS04 also outperformed the best unoptimized model by 56.2%. The differences among all the models analyzed are usually not very large; however, the unoptimized models can have very large errors, which are much reduced by the optimization.Peer reviewe

A quantitative assessment of empirical magnetic field models at geosynchronous orbit during magnetic storms

[1] We evaluate the performance of recent empirical magnetic field models (Tsyganenko, 1996, 2002a, 2002b; Tsyganenko and Sitnov, 2005, hereafter referred to as T96, T02 and TS05, respectively) during magnetic storm times including both pre- and post-storm intervals. The model outputs are compared with GOES observations of the magnetic field at geosynchronous orbit. In the case of a major magnetic storm, the T96 and T02 models predict anomalously strong negative Bz at geostationary orbit on the nightside due to input values exceeding the model limits, whereas a comprehensive magnetic field data survey using GOES does not support that prediction. On the basis of additional comparisons using 52 storm events, we discuss the strengths and limitations of each model. Furthermore, we quantify the performance of individual models at predicting geostationary magnetic fields as a function of local time, Dst, and storm phase. Compared to the earlier models (T96 and T02), the most recent storm-time model (TS05) has the best overall performance across the entire range of local times, storm levels, and storm phases at geostationary orbit. The field residuals between TS05 and GOES are small (≤3 nT) compared to the intrinsic short time-scale magnetic variability of the geostationary environment even during non-storm conditions (∼24 nT). Finally, we demonstrate how field model errors may affect radiation belt studies when estimating electron phase space density

Dynamical response of the magnetotail to changes of the solar wind direction: an MHD modeling perspective

We performed global MHD simulations to investigate the magnetotail response to the solar wind directional changes (<I>V<sub>z</sub></I>-variations). These changes, although small, cause significant variations of the neutral sheet shape and location even in the near and middle tail regions. They display a complicated temporal response, in which ~60 to 80% of the final shift of the neutral sheet in <I>Z</I> direction occurs within first 10–15 min (less for faster solar wind), whereas a much longer time (exceeding half hour) is required to reach a new equilibrium. The asymptotic equilibrium shape of the simulated neutral sheet is consistent with predictions of Tsyganenko-Fairfield (2004) empirical model. To visualize a physical origin of the north-south tail motion we compared the values of the total pressure in the northern and southern tail lobes and found a considerable difference (10–15% for only 6° change of the solar wind direction used in the simulation). That difference builds up during the passage of the solar wind directional discontinuity and is responsible for the vertical shift of the neutral sheet, although some pressure difference remains in the near tail even near the new equilibrium. Surprisingly, at a given tailward distance, the response was found to be first initiated in the tail center (the "leader effect"), rather than near the flanks, which can be explained by the wave propagation in the tail, and which may have interesting implications for the substorm triggering studies. The present results have serious implications for the data-based modeling, as they place constraints on the accuracy of tail magnetic configurations to be derived for specific events using data of multi-spacecraft missions, e.g. such as THEMIS

Pro‐ L * ‐ A probabilistic L * mapping tool for ground observations

Both ground and space observations are used extensively in the modeling of space weather processes within the Earth's magnetosphere. In radiation belt physics modeling, one of the key phase‐space coordinates is L*, which indicates the location of the drift paths of energetic electrons. Global magnetic field models allow a subset of locations on the ground (mainly sub‐auroral) to be mapped along field lines to a location in space and transformed into L*, provided that the initial ground location maps to a closed drift path. This allows observations from ground, or low‐altitude space‐based platforms to be mapped into space in order to inform radiation belt modeling. Many data‐based magnetic field models exist; however these models can significantly disagree on mapped L* values for a single point on the ground, during both quiet times and storms. We present a state of the art probabilistic L* mapping tool, Pro‐L*, which produces probability distributions for L* corresponding to a given ground location. Pro‐L* has been calculated for a high resolution magnetic latitude by magnetic local time (MLT) grid in the Earth's northern hemisphere. We have developed the probabilistic model using 11 years of L* calculations for 7 widely used magnetic field models. Usage of the tool is highlighted for both event studies and statistical models, and we demonstrate a number of potential applications

Statistics of a parallel Poynting vector in the auroral zone as a function of altitude using Polar EFI and MFE data and Astrid-2 EMMA data

We study the wave-related (AC) and static (DC) parallel Poynting vector (Poynting energy flux) as a function of altitude in auroral field lines using Polar EFI and MFE data. The study is statistical and contains 5 years of data in the altitude range 5000–30000 km. We verify the low altitude part of the results by comparison with earlier Astrid-2 EMMA Poynting vector statistics at 1000 km altitude. The EMMA data are also used to statistically compensate the Polar results for the missing zonal electric field component. We compare the Poynting vector with previous statistical DMSP satellite data concerning the electron precipitation power. We find that the AC Poynting vector (Alfvén-wave related Poynting vector) is statistically not sufficient to power auroral electron precipitation, although it may, for <i>K<sub>p</sub></i>>2, power 25–50% of it. The statistical AC Poynting vector also has a stepwise transition at <i>R</i>=4 <i>R<sub>E</sub></i>, so that its amplitude increases with increasing altitude. We suggest that this corresponds to Alfvén waves being in Landau resonance with electrons, so that wave-induced electron acceleration takes place at this altitude range, which was earlier named the Alfvén Resonosphere (ARS). The DC Poynting vector is ~3 times larger than electron precipitation and corresponds mainly to ionospheric Joule heating. In the morning sector (02:00–06:00 MLT) we find that the DC Poynting vector has a nontrivial altitude profile such that it decreases by a factor of ~2 when moving upward from 3 to 4 <i>R<sub>E</sub></i> radial distance. In other nightside MLT sectors the altitude profile is more uniform. The morning sector nontrivial altitude profile may be due to divergence of the perpendicular Poynting vector field at <i>R</i>=3–4 <i>R<sub>E</sub></i>. <p><b>Keywords.</b> Magnetospheric physics (Auroral phenomena; Magnetosphere-ionosphere interactions) – Space plasma physics (Wave-particle interactions

The interaction between transpolar arcs and cusp spots

Transpolar arcs and cusp spots are both auroral phenomena which occur when the interplanetary magnetic field is northward. Transpolar arcs are associated with magnetic reconnection in the magnetotail, which closes magnetic flux and results in a "wedge" of closed flux which remains trapped, embedded in the magnetotail lobe. The cusp spot is an indicator of lobe reconnection at the high-latitude magnetopause; in its simplest case, lobe reconnection redistributes open flux without resulting in any net change in the open flux content of the magnetosphere. We present observations of the two phenomena interacting--i.e., a transpolar arc intersecting a cusp spot during part of its lifetime. The significance of this observation is that lobe reconnection can have the effect of opening closed magnetotail flux. We argue that such events should not be rare

Do we know the actual magnetopause position for typical solar wind conditions?

We compare predicted magnetopause positions at the subsolar point and four reference points in the terminator plane obtained from several empirical and numerical MHD models. Empirical models using various sets of magnetopause crossings and making different assumptions about the magnetopause shape predict significantly different magnetopause positions (with a scatter >1 RE) even at the subsolar point. Axisymmetric magnetopause models cannot reproduce the cusp indentations or the changes related to the dipole tilt effect, and most of them predict the magnetopause closer to the Earth than nonaxisymmetric models for typical solar wind conditions and zero tilt angle. Predictions of two global nonaxisymmetric models do not match each other, and the models need additional verification. MHD models often predict the magnetopause closer to the Earth than the nonaxisymmetric empirical models, but the predictions of MHD simulations may need corrections for the ring current effect and decreases of the solar wind pressure that occur in the foreshock. Comparing MHD models in which the ring current magnetic field is taken into account with the empirical Lin et al. model, we find that the differences in the reference point positions predicted by these models are relatively small for Bz=0. Therefore, we assume that these predictions indicate the actual magnetopause position, but future investigations are still needed.Key PointsEmpirical models predict significantly different magnetopause positions even at the subsolar pointAxisymmetric empirical models predict the magnetopause closer to the Earth than nonaxisymmetric empirical models for zero tilt angleResults of MHD models with the ring current magnetic field lie close to results of the nonaxisymmetric Lin et al. modelPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/134087/1/jgra52758_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/134087/2/jgra52758.pd

Prompt energization of relativistic and highly relativistic electrons during a substorm interval: Van Allen Probes observations

Abstract On 17 March 2013, a large magnetic storm significantly depleted the multi-MeV radiation belt. We present multi-instrument observations from the Van Allen Probes spacecraft Radiation Belt Storm Probe A and Radiation Belt Storm Probe B at ~6 Re in the midnight sector magnetosphere and from ground-based ionospheric sensors during a substorm dipolarization followed by rapid reenergization of multi-MeV electrons. A 50% increase in magnetic field magnitude occurred simultaneously with dramatic increases in 100 keV electron fluxes and a 100 times increase in VLF wave intensity. The 100 keV electrons and intense VLF waves provide a seed population and energy source for subsequent radiation belt enhancements. Highly relativistic (\u3e2 MeV) electron fluxes increased immediately at L* ~ 4.5 and 4.5 MeV flux increased \u3e90 times at L* = 4 over 5 h. Although plasmasphere expansion brings the enhanced radiation belt multi-MeV fluxes inside the plasmasphere several hours postsubstorm, we localize their prompt reenergization during the event to regions outside the plasmasphere. Key Points Substorm dynamics are important for highly relativistic electron energization Cold plasma preconditioning is significant for rapid relativistic energization Relativistic / highly relativistic electron energization can occur in \u3c 5 hrs