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.