Dynamic Time Warping as a Means of Assessing Solar Wind Time Series

Abstract

Over 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 to assess the performance of those tools. Metrics are necessary to validate models, to compare different models, and to monitor the improvements to a certain model over time. In this work, we introduce dynamic time warping (DTW) as an alternative way of evaluating the performance of models and, in particular, of quantifying the differences between observed and modeled solar wind time series. We present the advantages and drawbacks of this method, as well as its application 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 for the evaluation of modeled solar wind time series in two ways. The first calculates the sequence similarity factor , a number that provides a quantification of how good the forecast is compared to an ideal and a nonideal prediction scenario. 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.