Estimating Vertical Velocity in Convective Updrafts from Temperature, Pressure, and Latent Heating

TL;DR

Estimating convective cloud vertical velocity $w_c$ is crucial for moisture transport and Earth's energy budget but has lacked global, long-term retrievals. The authors derive and test analytical relationships between $w_c$ and condensation rate $\dot{q}_{vc}$ using one-dimensional plume models under steady-state and non-steady-state assumptions, plus a supersaturation-based formulation, enabling $w_c$ estimates from satellite-capable quantities like latent heating. Validation against tropical and mid-latitude convection simulations (WRF and GCE) shows tropical $w_c$ can be retrieved to within about 1 m s$^{-1}$ using non-steady or KPM24 formulations, while mid-latitude estimates are more uncertain, particularly at higher altitudes or lower temperatures. The results suggest a viable path to generating long-term, satellite-derived records of convective updrafts, with clear avenues for improvement by incorporating entrainment, ice-phase processes, and radiative effects.

Abstract

The vertical velocity in convective clouds ($w_c$) mediates convective anvil development and global moisture transport, influencing Earth's energy budget, but has yet to be estimated globally over long periods due to the absence of spaceborne retrievals. Here, a method for estimating $w_c$ given vertical profiles of in-cloud temperature, pressure, and latent heating rate is presented and assessed. The method relies on analytical models for the approximately linear relationship between $w_c$ and condensation rate ($\dot{q}_{vc}$) in convective clouds, which we derive from steady-state and non-steady-state plume models. We include in our analysis a version of $\dot{q}_{vc}/w_c$ derived from the supersaturation rate in convective clouds, recently presented in Kukulies et al. (2024). We assess the accuracy of $w_c$ estimates against convective cloud simulations run with different model cores and spatial resolutions in both tropical and mid-latitude environments. Increased errors mid-latitude environments suggest that this approach for estimating $w_c$ leads to higher uncertainties in the mid-latitudes. Despite assumptions in the analytical expressions that theoretically restrict them to liquid water clouds, $w_c$ is estimated to within $\approx1$ m/s for most samples in the tropics. Potential applications, validation against future satellite mission observables, and future approaches for improving the estimation are discussed.

Figures (9)

• Figure 1: Temperature anomalies along cross sections of selected simulations domain overlayed with contours of vertical velocity of 1 m s$^{-1}$ (dashed), 5 m s$^{-1}$ (solid green), and 10 m s$^{-1}$ (solid black). All data has been coarsened to 4 km horizontal grid spacing.
• Figure 2: As in Fig. \ref{['fig:t_anomalies']}, but for water vapor instead of temperature. The same cross sections are used here. The dashed curves mark latent heating rates of 432 K/day, while the solid ones mark 2160 K/day.
• Figure 3: Vertical profiles of the mean vertical velocity in convective cores estimated using the $\alpha_p^{steady}$, $\alpha_p$, and $\alpha_{KPM}$ models and the mean simulated velocity profiles. The upper end of the shaded regions marks velocities predicted with an in-cloud temperature 5 K less than the mean core temperature, while the lower end of the shaded regions marks velocities predicted with $T_c$ 5 K higher than the in-core temperature.
• Figure 4: Two-dimensional histograms of estimated versus true vertical velocities given by each version of $\alpha$ for the tropical simulations. In each figure, the orange line delineates the most probable vertical velocity estimate for each true vertical velocity value. The green and red lines show the most probable estimated vertical velocities when the in-cloud temperature increases or decreases by 5 K, respectively. The red and green backgrounds show two-dimensional histograms of estimated vs. true vertical velocities for in-cloud temperatures shifted by 5 K. The velocity bin size is 0.5 m/s.
• Figure 5: As in Fig. \ref{['fig:pred_vs_true_a']}, but for the three mid-latitude simulations.