A surface pressure tendency equation incorporating hydrometeors and its preliminary application in tropical cyclones

Abstract The surface pressure tendency equation (SPTE) is an effective diagnostic tool for understanding processes governing the development of weather systems. Since the total‐mass‐conserving framework of SPTEs has limitations in heavily precipitating systems, dry‐mass‐conserving SPTEs that account for water mass changes were proposed in previous literature by adding a surface precipitation term to the SPTEs. This study derives a new dry‐mass‐conserving SPTE that explicitly incorporates water vapor, hydrometeors and surface precipitation. Results based on idealized tropical cyclone (TC) simulations reveal that the new SPTE shows improvement in reproducing TC intensity compared to the total‐mass‐conserving SPTE, especially in the eyewall region where there are active clouds and rainfall. The accumulated 360‐h bias of azimuthal mean surface pressure diagnosis from the new SPTE is less than 2 hPa, while the bias from the total‐mass‐conserving SPTE reaches approx. 5 hPa. The weight of the hydrometeors plays a secondary role in modulating surface pressure change during TC intensification, but acts to partly offset the contribution from the diabatic heating. The ice hydrometeors contribute more than liquid hydrometeors to surface pressure change. The phase changes of water condensates are shown to be dominant in the contribution of hydrometeors. From the SPTE proposed in this study, the underlying surface does not accurately “feel” the precipitation as the raindrops' gravity, but with a deviation at scales of 10%. Furthermore, the surface precipitation sink affects surface pressure via modulating liquid and ice water mixing ratio in the atmosphere column, and is suggested to be unimportant for storm intensification.