How do cold pools influence the size of tropical cyclone embryos?

Abstract

The size of tropical cyclone (TC) embryos is an essential predictor of TC genesis. Recent studies have identified cold pools and planetary rotation as factors that increase and decrease TC embryo size. While the planetary rotation effect has been depicted using a quasi-geostrophic (QG) model, the cold pool effect still lacks a theoretical model. This paper presents a cloud chain model to derive the length scale regarding the influence of cold pools on the TC embryo vortex. Within the model, the amount of rain evaporation during a single convective event determines the wind speed and humidity at the cold pool edge, influencing the amount of sub-cloud moisture convergence for the next-generation convection and, therefore, the intensity of the next-generation cold pool. A perturbation analysis shows that cold pools exhibit a nonlocal dependence on air-column humidity, with the influence range determined by the cold pool size and a convective memory weight. The memory weight relies on the sum of the contributions of mechanical lifting and thermodynamic forcing to convective initiation. A crucial parameter is the ratio of rain evaporation to surface evaporation in a cold pool. By coupling the cloud chain model with the QG equation, an analytical expression for the TC embryo size is obtained. The theory captures the trend but overestimates the TC embryo size in cloud-permitting simulations. The deviation might be due to the oversimplification in estimating the fractional contribution of cold pools to convective initiation.

Figures (13)

• Figure 1: A schematic diagram for the diffusion of convective activity induced by cold pools. Suppose there is an array of clouds. The mean radius of cold pools is ${R}$. The upper panel shows an equilibrium state where the PW and convective activity are horizontally homogeneous. The lower panel shows a non-equilibrium state in which the overturning circulation of a TC embryo produces a locally moist air column, denoted as the blue shading. Water vapor is transported laterally by cold pools, influenced by entrainment and surface evaporation, affecting neighboring convection. This influencing chain is marked with yellow arrows. This paper studies the influencing length scale of a humid air column on the distant convective/cold pool activity, ${l}$, which depends on $R$ and a "convective memory weight" $\mathcal{W}$.
• Figure 2: Zoom-in plots of the 1080 km $\times$ 1080 km simulations to the 300 km $\times$ 300 km southwest corner region. The three columns show the $\mathrm{E_v}=0.2$, 1, and 2.5 experiments, respectively. All use $f=10^{-4}$ s$^{-1}$. The first row shows the horizontal anomaly of column precipitable water $\mathrm{PW}'$. The second row shows the horizontal anomaly of near-surface ($z=25$ m) water vapor mixing ratio $q'_s$. The third row shows the horizontal anomaly of the near-surface ($z=25$ m) potential temperature anomaly. The 100 km $\times$ 100 km red boxes highlight a moist patch in the $\mathrm{E_v}=1$ simulation. All plots use the data at the time $t=2.5$ days. A movie can be downloaded from: https://doi.org/10.5281/zenodo.17668821.
• Figure 3: A further zoom-in plot of the 100 km $\times$ 100 km red box region in Fig. \ref{['fig:pcolor']} for the $\mathrm{E_v}=1$ reference simulation. (a)-(c) show the horizontal anomaly of column precipitable water, near-surface water vapor mixing ratio, and near-surface potential temperature.
• Figure 4: The modulus of the Fourier spectrum of (a) near-surface ($z=25$ m) water vapor mixing ratio $q_s$ and (b) column-precipitable water PW, averaged with 13 time snapshots between $t=2.5$ days$\pm$0.25 days. The first row shows experiments with varying $\mathrm{E_v}$, with the line color progressing from dark to bright indicating increasing $\mathrm{E_v}$. The second row shows experiments with varying $f$, with the line color progressing from dark to bright indicating increasing $f$. The dashed black lines in (a) and (c) show the 18 km wavelength as a reference.
• Figure 5: A schematic diagram of the 1-D cloud chain model, with the abscissa denoting the spatial dimension $x$ and the ordinate denoting time $t$. The blue shading shows the gust fronts' trajectories. The ${R}$ is the mean cold pool radius, which corresponds to the cold pool's propagation distance. The $\Delta t$ is the cold pool's propagation time. The slot between the two dashed lines denotes the $n^{th}$ lifecycle. The $Q^{n+1}_{\uparrow,j}$ denotes the latent heat transported to the updraft by sub-cloud moisture convergence at $x_j = j {R}$, and $Q^{n+1}_{\downarrow,j}$ denotes the sub-cloud latent heat absorption in the follow-up downdraft.