The Limit of Tropical Cyclone Track Predictabilities in the Northwest Pacific and Atlantic Oceans

Due to the chaotic nature of the atmosphere, even with a perfect model, the lead time range of skillful weather forecasts (i.e., predictability) is limited and controlled by the level of initial (analysis) error. In several recent BAMS articles, the TC track forecast error is found to grow exponentially within 5 days lead time, thus an exponential growth of error development is assumed, based on this assumption, the tropical cyclone track forecasts are expected to be extended by one day per decade in Atlantic Ocean (ATL) while two days per 15 years in Western North Pacific Ocean (WNP). Now another question is raised: since there is no bound for an exponential growth, will the error grow unbounded? If not, what will the errors behave outside 5 days? Furthermore, what are the bound of the lead time ranges? Will the improvement be unbounded?

Due to the limitation of the linear assumption, the previous studies cannot reach the bounds. Here, building on those BAMS articles, namely, using the same data set, we re-estimate the error amplification rate and the initial error reduction rate in a nonlinear way by introducing a logistical function. Results for short lead times are found to be consistent with those found by the linear method, confirm the nonlinear method is adoptable. Then the limit of forecast improvement as well as the limit of forecast lead times can be estimated.

Take a 5 days’ forecast error that had been reached in 2021 in WNP as the largest acceptable TC track error, and supposing the initial position error will go down to 1km, the limit of forecast lead times will be 13.7 days in WNP and 15.5 days in ATL. While the limit of forecast improvement will be about 60km for a lead time of 1 day, and 150km for a lead time of 3 days, and 260km for a lead time of 5 days. These are hopefully to be achieved in 80 years for WNP while 100 years for ATL with current speed of technological progress.