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 - 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, 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, i.e. 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 6 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.