AbstractModeling and observations have long demonstrated that Martian dust storms strongly interfere with global circulation patterns and change the diurnal and semidiurnal pressure variability as well as oscillations with periods greater than one sol associated with planetary waves. As of early 2022, five Mars years of pressure data have been collected by the Curiosity Rover in Gale crater with the Rover Environmental Monitoring Station (REMS). A combination of signal filtering techniques is used to search for pressure signatures that might warn large‐scale dust storms reaching Gale. The analysis combines an exploration of changes in both baroclinic waves and thermal tides for the first time to our knowledge. Focusing on the periods preceding local opacity increases as detected by Curiosity's Mastcam observations, the pressure analysis shows changes in the coupling between the diurnal pressure tide and quasi‐diurnal Kelvin wave, as well as in the temporal evolution of baroclinic waves that are harbingers of the larger dust storms. Changes in the phasing between Kelvin waves and diurnal tides are found to be precursors for the growth phase of periods Z (defined here as Ls ∼ 120°–160°), A (Ls ∼ 190°–240°), and C (Ls ∼ 300°–335°) dust storms. Changes in multi‐sol pressure oscillations also help predict the occurrence of A, B (Ls ∼ 245°–295°), and C storms. The specific pressure oscillations preceding each storm period are likely to be signatures of the large‐scale circulation patterns that enable the growth and propagation of the storm fronts.