Scope and limitations of ad hoc neural network reconstructions of solar wind parameters
Authors: Hecht Maximilian , Heidrich-Meisner Verena , Berger Lars , Wimmer-Schweingruber Robert F. 
Published: August 2023

Context.Solar wind properties are determined by the conditions of their solar source region and transport history. Solar wind parameters, such as proton speed, proton density, proton temperature, magnetic field strength, and the charge state composition of oxygen, are used as proxies to investigate the solar source region of the solar wind. The solar source region of the solar wind is relevant to both the interaction of this latter with the Earth’s magnetosphere and to our understanding of the underlying plasma processes, but the effect of the transport history of the wind is also important. The transport and conditions in the solar source region affect several solar wind parameters simultaneously. Therefore, the typically considered solar wind properties (e.g., proton density and oxygen charge-state composition) carry redundant information. Here, we are interested in exploring this redundancy.Aims.The observed redundancy could be caused by a set of hidden variables that determine the solar wind properties. We test this assumption by determining how well a (arbitrary, non-linear) function of four of the selected solar wind parameters can model the fifth solar wind parameter. If such a function provided a perfect model, then this solar wind parameter would be uniquely determined from hidden variables of the other four parameters and would therefore be redundant. If no reconstruction were possible, this parameter would be likely to contain information unique to the parameters evaluated here. In addition, isolating redundant or unique information contained in these properties guides requirements for in situ measurements and development of computer models. Sufficiently accurate measurements are necessary to understand the solar wind and its origin, to meaningfully classify solar wind types, and to predict space weather effects.Methods.We employed a neural network as a function approximator to model unknown, arbitrary, non-linear relations between the considered solar wind parameters. This approach is not designed to reconstruct the temporal structure of the observations. Instead a time-stable model is assumed and each point of measurement is treated separately. This approach is applied to solar wind data from the Advanced Composition Explorer (ACE). The neural network reconstructions are evaluated in comparison to observations, and the resulting reconstruction accuracies for each reconstructed solar wind parameter are compared while differentiating between different solar wind conditions (i.e., different solar wind types) and between different phases in the solar activity cycle. Therein, solar wind types are identified according to two solar-wind classification schemes based on proton plasma properties.Results.Within the limits defined by the measurement uncertainties, the proton density and proton temperature can be reconstructed well. Each parameter was evaluated with multiple criteria. Overall proton speed was the parameter with the most accurate reconstruction, while the oxygen charge-state ratio and magnetic field strength were most difficult to recover. We also analysed the results for different solar wind types separately and found that the reconstruction is most difficult for solar wind streams preceding and following stream interfaces.Conclusions.For all considered solar wind parameters, but in particular the proton density, proton temperature, and the oxygen charge-state ratio, parameter reconstruction is hindered by measurement uncertainties. The proton speed, while being one of the easiest to measure, also seems to carry the highest degree of redundancy with the combination of the four other solar wind parameters. Nevertheless, the reconstruction accuracy for the proton speed is limited by the large measurement uncertainties on the respective input parameters. The reconstruction accuracy of sector reversal plasma is noticeably lower than that of streamer belt or coronal hole plasma. We suspect that this is a result of the effect of stream interaction regions, which strongly influence the proton plasma properties and are typically assigned to sector reversal plasma. The fact that the oxygen charge-state ratio –a non-transport-affected property– is difficult to reconstruct may imply that recovering source-specific information from the transport-affected proton plasma properties is challenging. This underlines the importance of measuring the heavy ion charge-state composition.