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In the PV inversion method, another robust strength is the piecewise PV inversion, i.e. when the flow field is divided into the mean and perturbation components, the above equation can be rederived (Davis, 1992) to obtain the balanced fields associated with each individual PV perturbation. By taking the perturbation field as '' = ' - $' = $ - $, and q' = q - q, the piecewise PV inversion is to calculate the balanced flow and mass fields associated with each PV perturbation. Such a method describes how the different PV features, the environment perturbations, affect the TC's track (Wu and Emanuel, 1995a,b; Shapiro, 1996; Shapiro and Franklin, 1999; Wu and Kurihara, 1996; Wu et al., 2003, 2004).

(3) Defining AT: the normalized steering effect associated with each PV perturbation in the along-track direction

In order to evaluate the steering flow due to various PV perturbations, the time series of the deep-layer-mean (DLM) flow associated with the total PV perturbation [Vsdlm (q')] and each PV perturbation [VSDLM(q„)] is defined. Note that q' = q'a + q'na while the subscript "a" represents some specific perturbation of interest and "na" stands for the remaining perturbation. The DLM (925-300-hPa-averaged) steering wind is defined as where

r300 hPa d J925 hPa dp

To realize the influence of the steering flow associated with each perturbation, the ratio of the steering flow associated with each perturbation to that associated with all perturbations has been calculated. Following Wu et al. (2003), this quantity is defined as

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