Dynamic Time Warping (DTW) as a Means of Assessing Solar Wind Time Series

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, compare different models, and monitor the improvements of a certain model over time. In this work, we present the dynamic time warping (DTW) technique as an alternative way of evaluating solar wind predictions in the heliosphere. Even though this technique was introduced many decades ago and has been used extensively in other scientific fields, we show, for the first time, how it can be applied to the evaluation of solar wind time series, for the better understanding of modelled solar wind profiles and their comparisons with measurements. DTW can warp sequences in time, aiming to align them with the minimum cost by using dynamic programming. It is a powerful tool that combines the qualities of both point-by-point and time window metrics for a more complete assessment of the relation between predictions and observations. Besides its clear benefits, we also discuss its restrictions and show applications between solar wind observations and predictions made by the EUHFORIA model. We eventually conclude that DTW overcomes problems that other famous metrics do not and show that it can be used as a more objective quantification measure for model evaluation.