Evaluation of a reduced model for investigating hurricane formation from turbulence

Although hurricane formation has been studied for decades, it is not fully understood. Complex, cloud-system resolving models are commonly used to investigate the process, but are computationally expensive and often difficult to interpret. In principle, reduced models can be used to clarify the essential dynamics, and to efficiently discover new phenomena.

This study evaluates the adequacy of a reduced (3-layer) model for understanding hurricane formation from turbulent initial conditions. The evaluation is based on a direct comparison to tropical cyclogenesis in a cloud-system resolving model (RAMS-6.0) that uses single-moment, warm-rain microphysics. The reduced model has three alternative cumulus parameterizations. One parameterization is a variant of the classic convergence-based (CB) scheme of Ooyama 1969. Another regulates cumulus activity by enforcing boundary layer quasi-equilibrium (BLQ). The third resembles the CB parameterization, but provides a selective boost (SB) to convection in regions of exceptionally high instability.

Regardless of the cumulus parameterization, the reduced model produces hurricanes on the same time-scale as the cloud-system resolving model. Generally speaking, the hurricanes emerge from turbulence through the coalescence and convective intensification of cyclonic vorticity. Moreover, in both the reduced and cloud-system resolving models, the onset of rapid intensification follows pronounced local growth of the η-variable of Ooyama 1969, which is a combined measure of deep convective instability and middle tropospheric moisture. Eliminating the surface flux of moist entropy or surface friction in either model prevents or severely inhibits hurricane formation; however, hurricanes eventually form without surface friction in the BLQ or SB versions of the reduced model.

An analytical approximation is derived for steady-state hurricane intensity in the context of the reduced model. As in the more realistic but involved theory of Emanuel 1986, the square of the maximum wind speed is roughly proportional to the ratio of entropy to momentum exchange coefficients, times a measure of the ambient thermal disequilibrium between the sea-surface and the upper troposphere (not to be confused with CAPE). The analytical approximation compares favorably to a set of 3-layer numerical simulations that covers a broad range of parameter space. Limitations of the analysis are briefly addressed, and a supergradient wind correction is estimated.

Despite some measure of success, the reduced model has notable deficiencies that are apparent during the intermediate stage of genesis. Compared to the cloud-system resolving model, rotational storms are less sporadic and their winds are less severe. In the small-to-intermediate mesoscale, the horizontal kinetic energy spectrum is relatively steep, and horizontal divergence is relatively weak. Furthermore, the Lagrangian autocorrelation time of vertical vorticity is relatively long. These discrepancies indicate a simplified (quasi two-dimensional) form of rotational convective turbulence. The simplified turbulence has comparatively robust mesoscale cyclones, and tends to produce more hurricanes than its analogue generates in the cloud-system resolving model.

The behavior of the simplified turbulence is interesting in its own right. In some parameter regimes, the time required for tropical cyclogenesis varies dramatically with subtle changes to the initial conditions. Moreover, hurricanes do not always form. In a sufficiently large domain, the turbulence can evolve into a state with several hurricanes amid numerous vorticity filaments. Occasionally, hurricanes develop outer eye walls by entraining nearby filaments, and isolated filaments spawn new hurricanes.

This work is supported by NSF grant ATM-0750660.