A technique for seamless forecast construction and validation from weather to monthly time scales

Seamless prediction means bridging discrete short-term weather forecasts valid at a specific time and timeaveraged forecasts at longer periods. Subseasonal predictions span this time range and must contend with this transition. Seamless forecasts and seamless validation methods go hand-in-hand. Time-averaged forecasts often feature a verification window that widens in time with growing forecast leads. Ideally, a smooth transition across daily to monthly time scales would provide true seamlessness-a generalized approach is presented here to accomplish this. We discuss prior attempts to achieve this transition with individual weighting functions before presenting the two-parameter Hill equation as a general weighting function to blend discrete and time-averaged forecasts, achieving seamlessness. The Hill equation can be tuned to specify the lead time at which the discrete forecast loses dominance to time-averaged forecasts, as well as the swiftness of the transition with lead time. For this application, discrete forecasts are defined at any lead time using a Kronecker delta weighting, and any time-averaged weighting approach can be used at longer leads. Timeaveraged weighting functions whose averaging window widens with lead time are used. Example applications are shown for deterministic and ensemble forecasts and validation and a variety of validation metrics, along with sensitivities to parameter choices and a discussion of caveats. This technique aims to counterbalance the natural increase in uncertainty with forecast lead. It is not meant to construct forecasts with the highest skill, but to construct forecasts with the highest utility across time scales from weather to subseasonal in a single seamless product.