Studies on calculating convective energy with different moist adiabatic processes

Convections, especially deep convections are always connected with moist adiabatic processes. Convective energy parameters calculation, which are closely related to the moist adiabatic processes and in which reflect the gravitational effects of condensed liquid water, are reintroduced or defined, including MCAPE (Modified CAPE), DCAPE and MDCAPE (Modified DCAPE). Four moist adiabatic methods, which based on static energy conservation, pseudo equivalent potential temperature conservation, the strict pseudo adiabatic equation, and the reversible moist adiabatic process, respectively, are studied as well. Several sets of moist adiabatic lines are drawn to find the similarities and differences between each moist adiabatic process. Static energy conservation is nearly the same process as the pseudo-equivalent potential temperature conservation, and their calculated results are very similar. The specific heat of water vapor is considered in the strict pseudo-adiabatic equation. So the lapse rate of strict pseudo-adiabatic process is slightly smaller than static energy conservation and pseudo-equivalent potential temperature conservation. Liquid water and ice are not considered in these three moist adiabatic processes, therefore, they are not reversible. Sensible heat of liquid water and specific heat of water vapor are both considered in reversible moist adiabatic process. There are little differences between each other of these four methods when the initial temperatures of lifted air parcels are low. With respect to high initial lifted temperatures, the differences are not very obvious in lower levels of the atmosphere. When they are lifted to high levels, the reversible moist adiabatic lines are distinguished by relative smaller lapse rates of temperature due to the total sensible heats of the accumulated liquid water. When considering the heat of solidification of the large quantity of liquid water, the lapse rate is slower even more and the convective energy becomes larger correspondingly. This might be one of the reasons why the hailstorm can develop very strong. With the consideration of liquid water, the reversible moist adiabatic process is therefore a relatively reasonable choice sometimes. Real case analyses with special attention given to condensed liquid water and ice shows that the selection of moist adiabatic process does affect the calculated results of CAPE, and the gravitational effects of condensed liquid water and ice are not negligible in severe storms, especially in hailstorm. DCAPE is a measurement that reflects the maximum potential intensity of downdraft flow. MDCAPE is a modified form of DCAPE with the gravitational effect of liquid water and ice.