Dominant Role of Initial Error in Weather Predictability Through the Study on Saturation Value

Weather predictability is a significant topic that measures the time limit for accurate weather forecasts. Pioneer studies defined predictability as the time interval for the initial error to reach a prechosen level. Saturation value (SA) and the average difference between two randomly chosen atmospheric states (ADRA) are often chosen as the thresholds. To reveal factors influencing weather predictability, this study examines the difference between SA and ADRA using a two-dimensional quasi-geostrophic (QG) model. Results show that (1) SA is consistently smaller than ADRA, confirming its significance as a predictability metric; (2) identical initial errors yield different SAs in different background fields, yet with similar saturation times. This indicates distinct error growth rates but comparable predictability, suggesting predictability depends more on initial error magnitude than error growth rate; (3) within a single background flow, smaller initial errors lead to smaller SAs and longer saturation times. SA correlates monotonically with initial error magnitude within a certain range, implying that forecast improvement is possible by reducing initial errors. Beyond this range, further initial error reduction contributes negligibly to forecast quality. Growth rates are also found to depend on initial error size. Collectively, these findings demonstrate that initial error magnitude is the primary determinant of predictability.