Hunting for “Windows of Opportunity” in Forecasts Across Timescales? Cross it
Authors: Muñoz Ángel G. , Doblas-Reyes Francisco , DiSera Laurel , Donat Markus , González-Reviriego Nube , Soret Albert , Terrado Marta , Torralba Verónica 
Published: February 2023

Stakeholders in all socio-economic sectors require reliable forecasts at multiple timescales as part of their decision-making processes. Although basing decisions mostly on a particular timescale (e.g., weather, subseasonal, seasonal) is the present status quo, this approach tends to lead to missing opportunities for more comprehensive risk-management systems (Goddard et al. 2014).&#160;While today a variety of forecasts are produced targeting distinct timescales in a routine way, these products are generally presented to the users in different websites and bulletins, often without an assessment of how consistent the predictions are across timescales. Since different models and strategies are used at different timescales by both national and international seasonal and subseasonal forecasting centers (Kirtman et al. 2014, Kirtman et al. 2017, Vitart et al. 2017), and skill is different at those timescales, it is key to guarantee that a physically consistent &#8220;bridging&#8221; between the forecasts exists, and that the cross-timescale predictions are overall skilful and actionable, so decision makers can conduct their work.&#160;Here, we propose and explore a new methodology &#8211;that we call the Xit (&#8220;cross-it&#8221;) operator&#8211; based on the Liang-Kleeman information flow (e.g., Tawia Hagan et al. 2019) and wavelet spectra and entropy (e.g., Zunino et al. 2007), to &#8220;bridge&#8221; forecasts at different timescales in a smooth and physically-consistent manner.&#160;In summary, the Xit&#160;operator (1) conducts a wavelet spectral analysis (e.g., Ng and Chan 2013, Zunino et al. 2007) and (2) a non-stationary time-frequency causality analysis (e.g., Tawia Hagan et al. 2019, Liang 2015) on forecasts at different timescales to assess cross-timescale coherence and physical consistency in terms of various sources of predictability. In principle, the approach permits to identify which &#8220;intrinsic&#8221; periods/scales (i) in the timescale continuum (t) are more suitable for the bridging to occur, and/or which ones can produce more skillful forecasts, by pointing to particular target times&#8212;i.e., potential windows of opportunity (Mariotti et al. 2020)&#8212;in the forecast period where wavelet entropy (uncertainty) is lower.&#160;While the first component of the Xit&#160;operator, i.e., the wavelet spectral and entropy analysis (Zunino et al. 2007), is designed to identify the optimal time-frequency bands for cross-timescale bridging, the fact that two forecast systems (e.g., a subseasonal and a seasonal) exhibit significant wavelet coherence does not imply that bridging those systems will provide physically-consistent predictions. The second component of the Xit operator, i.e., the non-stationary causality analysis (Tawia Hagan et al. 2019), is thus designed to assess physical consistency of the bridging by analyzing the causal link between different climate drivers (acting at different timescales) and the forecast variable of interest.