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

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.

💡 Research Summary

This paper presents and evaluates a novel method for estimating the vertical velocity within convective cloud updrafts (w_c), a critical but historically unobserved variable, using satellite-retrievable parameters: in-cloud temperature (T_c), pressure (p), and latent heating rate (proportional to condensation rate, ¤q_vc). The core of the method leverages the approximately linear relationship between w_c and ¤q_vc observed in high-resolution simulations. The authors derive analytical models for the proportionality constant (α = -¤q_vc L_v / (w_c g)) from first principles using two main theoretical frameworks and include a third model from recent literature for comparison.

The first theoretical derivation is based on a steady-state, one-dimensional entraining plume model. By combining conservation equations for water vapor and moist static energy with mass continuity, the authors derive an expression (α_steady_p) that relates w_c to the local temperature lapse rate and the entrainment-driven temperature difference between the cloud and its environment. This derivation reveals that w_c is linearly related to the total diabatic heating rate, suggesting potential applicability even in ice-phase processes. The second derivation relaxes the steady-state assumption, formulating a non-steady-state plume model that includes time dependence. Using the material derivative and assuming the cloud remains saturated, a more comprehensive expression (α_p) is derived, though it relies on simplifications of the Clausius-Clapeyron equation and hydrostatic balance. The third model, labeled α_KPM, is adopted from Kukulies et al. (2024), which is based on setting the supersaturation tendency to zero within a rising parcel.

The performance of these α models is rigorously assessed against benchmark data from high-fidelity convective cloud simulations. These simulations span both tropical and mid-latitude environments and are run with different model cores and spatial resolutions to test robustness. The analysis focuses on identified convective core regions. Key findings indicate that in the tropics, despite theoretical assumptions tailored for liquid-water clouds, the methods estimate w_c to within approximately 1 m/s for most samples across altitudes, demonstrating high accuracy. However, in mid-latitude environments, the estimation errors increase significantly for all models. This is attributed to the more complex dynamics of mid-latitude convection, which often involves stronger environmental wind shear, more prominent ice-phase microphysics, and potentially more heterogeneous entrainment—factors not fully captured by the simplified analytical models.

The study discusses the significant implications of this work. By requiring only vertical profiles of T_c, p, and latent heating (the latter available from missions like TRMM, GPM, and geostationary satellites), the method opens the door to generating the first long-term, global observational records of convective vertical velocity. Such datasets would be invaluable for validating and improving convective parameterizations in climate models, studying trends in convective dynamics, and serving as a benchmark for future high-resolution satellite missions. The paper concludes by acknowledging limitations, particularly the reduced skill in mid-latitudes, and suggests future directions for improvement, such as incorporating environmental shear corrections and better accounting for mixed-phase microphysics. Overall, this research provides a practical and observationally grounded framework to quantify a fundamental driver of the climate system.