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Heavy rain is especially enhanced when enhanced low-level inflow interacts with coastal fronts and/or terrain.
This slide shows the basic model for heavy inland rains across the northeast U.S. associated with tropical cyclones. Warm, upper-level outflow builds the upper level heights north of the cyclone, increasing the height gradient and upper-level wind speed in that area. The strengthening upper-level jet is associated with an enhanced area of upper-level divergence over portions of the northeast. The upper-level divergence induces an enhanced low-level southerly / southeasterly jet across the area. Rainfall can be particularly heavy when the low-level jet interacts with a coastal front or terrain.