The turning winds with height thermal advection rainfall diagnostic: Why does it work in the tropics?

For decades forecasters in the Queensland Regional Forecast Office of the Australian Bureau of Meteorology have been using winds that turn with height as a rainfall diagnostic, with good success in the subtropics and tropics. The diagnostic is based on the relationship between thermal advection (with its implied isentropic ascent or descent) and geostrophic winds that turn with height. This paper demonstrates that the above relationship also holds for gradient winds that turn with height, which suggests the relationship should be true for any slowly evolving pressure anomalies. Furthermore, it explains why the diagnostic is successful at low latitudes for most heavy rain bearing mesoscale and larger systems, including tropical depressions, tropical lows, monsoon depressions, tropical cyclones, and hybrid tropical/baroclinic storms such as the often destructive East Coast Low that forms off the eastern coast of Australia. Equations are derived to demonstrate the relationship between thermal advection and turning gradient winds with height, and the implications of each term are discussed. As with the geostrophic relationship the sign of the thermal advection is determined by the rotation direction, with anticyclonic (cyclonic) turning with height representing warm (cold) air advection and isentropic ascent (descent). In the geostrophic wind relationship the thermal advection magnitude is proportional to the Coriolis acceleration, whereas in the gradient wind relationship the thermal advection magnitude is proportional to the sum of the Coriolis and centrifugal acceleration terms. Alternative forms of the diagnostic are proposed that incorporate the additional centrifugal acceleration.