The Impact of Spray-Mediated Enhanced Enthalpy and Reduced Drag Coefficients in the Modelling of Tropical Cyclones

Abstract

The impact of new parametrizations for drag and air–sea enthalpy exchange on modelling the intensity of tropical cyclones with a numerical weather prediction (NWP) model is examined. These parametrizations follow from a model for the marine atmospheric boundary layer for high wind-speed conditions in the presence of spray droplets that originate from breaking wave crests. This model accounts for the direct impact of these droplets on the air–sea momentum flux through action of a spray force, which originates from the interaction of the ‘rain’ of spray droplets with the vertical wind shear and is expressed in terms of the spray generation function (SGF). The SGF is cubic in the wind speed up to 50 m s$^{-1}$ beyond which its value increases less strongly. The drag coefficient ($C_\mathrm{D}$) decreases from a wind speed of approximately 30 m s$^{-1}$, in agreement with the available measurements in these conditions. The enthalpy exchange coefficient ($C_k$) increases with increasing wind speed and slowly decreases beyond a wind speed of about 40 m s$^{-1}$ due to the strong decrease in $C_\mathrm{D}$. The value for $C_k/C_\mathrm{D}$ is in agreement with observational data for wind speeds up to 30 m s$^{-1}$; for higher wind speeds the value is in the range 1.2–1.5 in agreement with a well-established theory. The parametrization is tested in an NWP model. The tropical cyclones Ivan (2004) and Katrina (2005) in the Gulf of Mexico are simulated. To the sea surface temperatures (SSTs) from the European Centre archive that were prescribed to the NWP model, a parametrized cooling (based on estimations from theoretical studies and measurements) was applied during the model forecasts, as the NWP model does not resolve locally rather strong induced reductions in SSTs. The simulations show that realistic tropical cyclone wind speeds and central pressure can be obtained with the proposed drag and enthalpy parametrizations. The results indicate that the value for $C_k/C_\mathrm{D}$ at very high wind speeds is in the correct range. Moreover, the results motivate the application of the parametrizations in atmosphere–ocean coupled models.