The Dynamic Time Warping as a Means to Assess Solar Wind Time Series

During the last decades, international attempts have been made to develop realistic space weather prediction tools aiming to forecast the conditions on the Sun and in the interplanetary environment. These efforts have led to the development of appropriate metrics in order to assess the performance of those tools. Metrics are necessary to validate models, compare different models and monitor improvements of a certain model over time. In this work, we introduce the Dynamic Time Warping (DTW) as an alternative way to evaluate the performance of models and, in particular, to quantify differences between observed and modeled solar wind time series. We present the advantages and drawbacks of this method as well as applications to WIND observations and EUHFORIA predictions at Earth. We show that DTW can warp sequences in time, aiming to align them with the minimum cost by using dynamic programming. It can be applied in two ways for the evaluation of modeled solar wind time series. The first, calculates the sequence similarity factor (SSF), a number that provides a quantification of how good the forecast is, compared to an ideal and a non-ideal prediction scenarios. The second way quantifies the time and amplitude differences between the points that are best matched between the two sequences. As a result, DTW can serve as a hybrid metric between continuous measurements (e.g., the correlation coefficient), and point-by-point comparisons. It is a promising technique for the assessment of solar wind profiles providing at once the most complete evaluation portrait of a model.