On the possible role of condensation-related hydrostatic pressure adjustments in intensification and weakening of tropical cyclones

It is shown that condensation and precipitation do not disturb the hydrostatic equilibrium if the local pressure sink (condensation rate expressed in pressure units) is proportional to the local pressure, with a proportionality coefficient $k$ that is independent of altitude. In the real atmosphere, however, the condensation rate depends, among other factors, on the vertical velocity, which varies with height. As a result, condensation generally disturbs hydrostatic equilibrium and induces pressure adjustments through air-mass redistribution. We propose that a profile in which $k$ is maximized in the upper atmosphere leads to additional upward motion and cyclone intensification, whereas a maximum closer to the surface induces downward motion and cyclone weakening. The magnitude of both effects is expected to be set by the strength of the precipitation mass sink. Using observational data, we find that the median intensification and weakening rates – $12$ and $8$hPaday$^{-1}$, respectively, measured over six-hour intervals in Atlantic tropical cyclones – amount to about three quarters of the maximum concurrent precipitation rate (multiplied by gravity) in the core precipitation region. This implies intensification under conditions of positive vertically integrated air convergence, a regime impossible in modeled dry hurricanes, with the negative pressure tendency arising because precipitation exceeds the vertically integrated moisture convergence by absolute magnitude. The implications of these results for recent studies that evaluate tropical cyclone (de-)intensification using mass continuity equations that neglect the precipitation mass sink are discussed.

💡 Research Summary

The paper investigates how condensation‑related hydrostatic pressure adjustments, mediated by precipitation, influence the intensification and weakening of tropical cyclones (TCs). The authors first demonstrate analytically that if the local pressure sink associated with condensation (expressed in pressure units) is proportional to the local pressure, p, with a proportionality coefficient k that does not vary with height, then the hydrostatic balance is preserved despite mass loss. In the real atmosphere, however, the condensation rate depends on vertical velocity w and the vertical gradient of water‑vapour mixing ratio ∂γ/∂z, so k ≈ w ∂γ/∂z generally varies with altitude. When k is maximised aloft, the removal of mass in the upper troposphere produces an additional upward pressure gradient, encouraging extra ascent and thus intensifying the cyclone. Conversely, if k peaks near the surface, the mass loss is concentrated low, reducing the net inflow and leading to weakening.

To test these ideas, the authors analyse observational data from the EBTRK best‑track dataset (6‑hourly) and the TRMM 3‑hourly precipitation product for Atlantic TCs between 1998 and 2015. For each 6‑hour interval they compute an intensification rate I = ‑4(pₖ₊₁ ‑ pₖ) (hPa day⁻¹) based on the change in minimum central pressure, and they derive radial precipitation profiles Pₖ(r) from TRMM. The maximum precipitation value Pₘ and its radius r_P, as well as precipitation at the radius of maximum wind r_m, are recorded.

Statistical results show that for storms over land the median weakening rate is ‑16 hPa day⁻¹ (interquartile range ‑32 to ‑8) with a concurrent median maximum precipitation‑derived pressure tendency of 8 hPa day⁻¹ (4–14). For intensifying land storms the median intensification rate is ‑4 hPa day⁻¹ (4–8) and the median precipitation‑derived pressure tendency is 11 hPa day⁻¹ (5–14). Thus, the magnitude of the pressure tendency is roughly 30–50 % of the maximum precipitation term (g Pₘ). Similar relationships hold for oceanic storms, with errors of 120–130 % if the precipitation term is omitted.

These findings directly challenge recent studies (e.g., Sparks & Toumi 2022a,b) that model TC pressure tendency using a reduced form of the mass‑continuity equation that neglects the precipitation mass sink. The authors show that ignoring ‑g P in the pressure tendency equation leads to substantial quantitative errors: underestimation of pressure drops in weakening storms (≈ 50 % error) and overestimation in intensifying storms (≈ 275 % error). Moreover, the radius of maximum precipitation r_P is systematically larger than the radius of maximum wind r_m, indicating that the pressure adjustments associated with condensation occur outside the wind core assumed by Sparks & Toumi.

A key conceptual implication is that intensification can occur under conditions of positive vertically integrated air convergence, a regime impossible in dry, adiabatic models where a pressure fall must be accompanied by net mass outflow. In the observed storms, the precipitation term dominates the pressure tendency, and the sign of ∂p/∂t is set by the absolute magnitude of precipitation rather than by the sign of the convergence term. This demonstrates that condensation‑driven mass removal is a primary driver of central pressure changes.

The paper concludes that any realistic TC intensity theory or numerical model must explicitly include the precipitation mass sink in the continuity equation. Neglecting it not only misrepresents the physics of pressure adjustments but also leads to erroneous diagnostics of radial inflow/outflow and, consequently, of wind intensity. The authors suggest that future work should develop parameterisations for the vertical profile of k (related to w ∂γ/∂z) and incorporate the resulting pressure‑adjustment feedbacks into operational forecasting models.