Data-driven equation discovery of the maximum vertical velocity in idealized deep convection

The maximum vertical velocity within deep convective updrafts (w_max) is a key control on precipitation intensity and lightning, yet the physical processes that set its magnitude remain unclear. Here we use data-driven equation discovery to identify the dominant controls on w_max in idealized deep convection. We analyze a set of radiative-convective equilibrium simulations spanning a wide range of sea surface temperatures (290-310 K) and imposed radiative cooling rates (0.75-3 K/day), tracking individual clouds and diagnosing their pre-storm environment and in-cloud properties. Treating the pre-storm environment and in-cloud processes separately, for each we identify  a small number of predictors from a broad set of physically motivated variables that robustly explain variations in w_max across simulation regimes. Interpretable equations derived via symbolic regression from the in-cloud variables indicate that latent heating provides the primary acceleration of updrafts, while pressure perturbations act as a leading-order decelerating mechanism that limits peak velocities. Pre-storm predictors such as CAPE and triggering strength constrain the range of possible w_max values, whereas in-cloud condensate loading and pressure effects determine the realized extremes. This work provides a physically interpretable framework for understanding convective updraft intensity, using data-driven analysis informed by existing physical knowledge.