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

Abstract

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—τ—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 |B| 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.

Testing Efficiency of Empirical, Adaptive, and Global MHD Magnetospheric Models to Represent the Geomagnetic Field in a Variety of Conditions

“…Based on this table we also see that the hierarchy of the model scores does not differ drastically among the different score types, as well as between June (unshaded line) and March (grey‐shaded line) storm periods. As expected, in general, the magnetic field is best reproduced by the adaptive AM03 model, which removes most of outliers in the predictions, as previously noticed by Brito and Morley (). Whereas the older T96 model is on the last place in the row, the success of AM03 which uses the current system formulations from the T96 model obviously illustrates the effectiveness of data‐assimilation procedure.…”

“…It is important to mention that in the time of larger activity (hours 72–96) the error of SWMF simulation is notably (almost twice) smaller compared to any empirical model, and after that it remains in the same range as the error of TS05 and TA15 empirical models up to the end of the period. The T96 model shows the worst results during the whole recovery phase, as was also noticed by other researchers (e.g., Brito & Morley, ). At the same time the adaptive model, based on T96 functions (currents), shows a very good result, being the most accurate among all examined models if we consider the whole six‐day period.…”

Observations and Fokker‐Planck Simulations of the L‐Shell, Energy, and Pitch Angle Structure of Earth's Electron Radiation Belts During Quiet Times

“…Journal of Geophysical Research: Space Physics that is, overestimation and underestimation errors are equally graded (Morley, 2016;Brito & Morley, 2017). The median symmetric accuracy is ζ ¼ 100Â 10 Med log 10 Q dir=omni j j À 1 and the median log accuracy ratio is…”

Empirical Modeling of the Geomagnetosphere for SIR and CME‐Driven Magnetic Storms

“…To more quantitatively assess the model's performance, we also compared its output with independent data and with two empirical TA15 and TS05 models, chosen because the present model synthetically combines the TA15 modular structure and the TS05 parameterization, specially developed to represent storm time effects. Besides, as demonstrated in a number of papers (e.g., Huang et al, ; Kubyshkina et al, ), TS05 usually outperforms other empirical models during active periods and can be further improved by applying an additional optimization using in situ data fitting (the so‐called adaptive modeling) (Brito & Morley, ).…”