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Abstract
Seamless prediction means bridging discrete short-term weather forecasts valid at a specific time and time-averaged 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. Time-averaged 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.
Abstract
Seamless prediction means bridging discrete short-term weather forecasts valid at a specific time and time-averaged 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. Time-averaged 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.
Abstract
This paper investigates empirical strategies for correcting the bias of a coupled land–atmosphere model and tests the hypothesis that a bias correction can improve the skill of such models. The correction strategies investigated include 1) relaxation methods, 2) nudging based on long-term biases, and 3) nudging based on tendency errors. The last method involves estimating the tendency errors of prognostic variables based on short forecasts—say lead times of 24 h or less—and then subtracting the climatological mean value of the tendency errors at every time step. By almost any measure, the best correction strategy is found to be nudging based on tendency errors. This method significantly reduces biases in the long-term forecasts of temperature and soil moisture, and preserves the variance of the forecast field, unlike relaxation methods. Tendency errors estimated from ten 1-day forecasts produced just as effective corrections as tendency errors estimated from all days in a month, implying that the method is trivial to implement by modern standards. Disappointingly, none of the methods investigated consistently improved the random error variance of the model, although this finding may be model dependent. Nevertheless, the empirical correction method is argued to be worthwhile even if it improves only the bias, because the method has only marginal impacts on the numerical speed and represents forecast error in the form of a tendency error that can be compared directly to other terms in the tendency equations, which in turn provides clues as to the source of the forecast error.
Abstract
This paper investigates empirical strategies for correcting the bias of a coupled land–atmosphere model and tests the hypothesis that a bias correction can improve the skill of such models. The correction strategies investigated include 1) relaxation methods, 2) nudging based on long-term biases, and 3) nudging based on tendency errors. The last method involves estimating the tendency errors of prognostic variables based on short forecasts—say lead times of 24 h or less—and then subtracting the climatological mean value of the tendency errors at every time step. By almost any measure, the best correction strategy is found to be nudging based on tendency errors. This method significantly reduces biases in the long-term forecasts of temperature and soil moisture, and preserves the variance of the forecast field, unlike relaxation methods. Tendency errors estimated from ten 1-day forecasts produced just as effective corrections as tendency errors estimated from all days in a month, implying that the method is trivial to implement by modern standards. Disappointingly, none of the methods investigated consistently improved the random error variance of the model, although this finding may be model dependent. Nevertheless, the empirical correction method is argued to be worthwhile even if it improves only the bias, because the method has only marginal impacts on the numerical speed and represents forecast error in the form of a tendency error that can be compared directly to other terms in the tendency equations, which in turn provides clues as to the source of the forecast error.
