Development of a High-Latitude Convection Model by Application of Machine Learning to SuperDARN observations

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Climatological convection modeling has been carried out for decades by binning various localized mea-22 surements of the ionospheric plasma velocity or electric field collected over the high-latitude regions 23 versus some set of parameters, most often the interplanetary magnetic field (IMF) components. Such 24 models often are used to drive circulation models such as the Thermospere Ionosphere Electrodynamic 25 General Circulation Model (TIEGCM) (Roble & Ridley, 1994) and the Global Ionosphere-Thermosphere 26 Model (GITM) (Ridley et al., 2006). They are also used to constrain the data driven convection pat-27 terns produced from SuperDARN data (Ruohoniemi & Baker, 1998). The measurements have been col-28 lected using a variety of instruments such as satellite based drift meters (e.g. Heelis et al., 1982) or elec-29 tric field booms (e.g. Heppner & Maynard, 1987), incoherent-scatter radar (Foster, 1983), ground-based 30 magnetometers (e.g. Papitashvili et al., 1994), and coherent-scatter radars (e.g. Ruohoniemi & Green-31 wald, 1996). Construction of the models typically has involved grouping observations based upon pre-32 vailing IMF conditions and perhaps some other parameter such as the planetary K-index (k p ) (Heppner 33 & Maynard, 1987), or the geomagnetic Auroral Electrojet Index (A e ) (Weimer, 2005), or the dipole 34 -2-manuscript submitted to Space Weather tilt angle (Thomas & Shepherd, 2018), and then using the binned observations to constrain an expan-35 sion of the electrostatic potential in a set of orthogonal functions. 36 The underlying assumption of such a binning is that when repeated, a given set of driving conditions 37 will on average produce the same unique convection pattern. In a general sense, physical reasoning and 38 observations show this to be true. For example, when the IMF is southward, there is magnetic merg-39 ing on the dayside magnetopause and the near-noon field lines connecting from the ionosphere out to 40 the magnetopause are directly influenced by the electric field across the merging region. Those field 41 lines are convected anti-sunward across the polar cap from noon to midnight where they eventually re-42 connect to the field lines from the opposite hemisphere. Once reconnected, the demand for magnetic 43 flux on the dayside causes the field lines to return, following a path through the magnetosphere that   C. Maynard, provides an excellent summary of the patterns that have been observed and how the IMF 53 influences them. In particular, they highlighted the influence of the sign of the IMF y-component on 54 the location and direction of the flow in the dayside throat. Their study contrasts with most others in 55 that rather than binning the observations on a grid and then constraining a functional expansion of the 56 potential with the binned observations, they examined individual satellite passes and categorized them 57 as signatures or "quasi-signatures" and then sorted them based on the IMF. Their result was a set of 58 three basic patterns that covered the majority of southward IMF situations. Those patterns illustrated 59 sharper features (Harang Discontinuity, dayside throat) than are evident in most other models. In ad-60 dition, they examined the influence of k p and A e , but only by comparing the average total cross po-61 lar cap potential drop for ranges of the parameters. between the dayside and nightside merging rates (Siscoe & Huang, 1985). That nightside merging rate 69 is highly variable and depends on the internal state of the magnetosphere. In the growth phase of a 70 substorm the nightside merging rate may be substantially lower than the dayside rate, leading to an 71 expanding polar cap and expanding convection pattern. During a substorm expansion phase the op-72 posite is true and rapid night-side merging can lead to a contracting polar cap and convection pattern. 73 Further, features like the enhancement of the Harang Discontinuity during growth phase (Bristow & 74 Jensen, 2007) change the shape of the pattern in addition to its diameter.

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To account for some of the dependence on conditions beyond the solar wind and IMF, a new convec-76 tion model was constructed using parameters that provide some indication of the state of the magne-  (Schulz, 1997). These indicies are readily available for use from the NASA OMNI database 82 (King & Papitashvili, 2005), which also provides the solar wind and IMF parameters aligned in time 83 to reflect solar wind propagation delays from the point of observation to the Earth's bow shock. In-84 cluding the magnetospheric parameters increases the dimension of the parameter space to seven, which 85 is fairly large for traditional method of binning the observations. In addition, as will be demonstrated 86 the dependence of the convection velocities on some of the parameters is nonlinear. Because of these 87 two factors, machine learning (ML) was used to form the model.  Figure 1b shows the potential contours predicted by the TS18 model for the con-

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-5-manuscript submitted to Space Weather ditions observed at the time from the observed IMF conditions. There are several subtle differences be-107 tween observed pattern and that predicted by the model. First, the total cross-cap potential drop is 108 significantly lower in the observations. The drop is only 30 kV, while the predicted value was 58 kV. The 109 observed pattern is shifted toward midnight and rotated slightly toward dusk. That is, the flow across

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To test each algorithm, the data base was processed with each model in a ten-cell subset of the grid  The need for accurate forecasting of space weather increases on a nearly daily basis. There isn't a bet-276 ter example of this than the requirement for accurate orbit prediction that becomes more critical with 277 the launch of every new low-Earth-orbit satellite. Orbit prediction is based on thermospheric density, 278 which can be predicted using global circulation models driven by convection models such as described 279 in this study. Hence, it is imperative that we have models of convection that accurately capture the  observations. Those velocities were separated into north-south, and east-west components and sorted 346 into a magnetic local time -magnetic latitude grid that ran from 55°to the magnetic pole with a bin 347 size of 2°, and MLT bins of 1-hour.

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In each MLT-MLAT bin, the two velocity components were used separately to train a ML model us-

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RMSE values for the model were compared to those from the TS18 model in each bin of the grid. The

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ML model exhibited smaller errors than TS18 at all locations. In particular, errors in the ML showed 361 the largest improvement over TS18 in bins that are near the average latitude of the convection rever-362 sal boundary. It is likely that the improvement was due to the ML model's ability to expand and con-363 tract in latitude in response to changes of A l and A u .

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The software for generating the model is free and available for download from the scikit-learn web site. Data Facility's OMNIWeb service, and OMNI data.