Melting-Level Detrainment

First uploaded on 2023/04/04
Last updated on 2023/10/09
Copyright(C)2022-2023 jos <jos@kaleidoscheme.com> All rights reserved.

RDC can be derived theoretically as we showed in the main article. However, some of you may still suspect that RDC relies on our own models, DCM extracting RDC and KCM confirming the transport capacity of RDC. Our third paper on RDC using a completely different cloud-resolving atmospheric model (Iwasa et al. 2012) should dispel such doubts.

After establishing RDC theory, we were given a project to run a cloud-resolving model, RAMS (which had already been modified in many parts, including radiative processes), on the newly built Earth Simulator. Initially, we intended to compare the results of two scenarios: a standard atmosphere and a CO₂-doubled atmosphere. However, shortly after submitting a job for the warming scenario to the queue of the heavily-used system, we found that we would not be able to start the calculations before the end of the year. Our plans were shattered. We had to produce a report from calculations of the atmosphere under a standard condition only.

In the course of examining model atmospheric physics, longitude-averaged horizontal mass flux data showed that at melting altitudes (corresponding to 0 degrees Celsius), there is an outflow from the low-latitude cumulus zone to the cloud-free subtropical zone. As is well known, such outflow also occurs near the tropopause, but the mass outflow at the melting altitude was of the same magnitude. Furthermore, when the water vapor transport is compared, the outflow at lower melting heights is by far larger. However, there is no special dynamical property at the melting height that affects convective motion. Since the condensation heat released when water vapor changes to water is very large at L= 2.442 x 10⁶ J kg^-1, condensation is responsible for raising the air temperature and driving the convective motion of the cumulus. On the other hand, the amount that changes between water and ice is small, and the freezing heat that is released during freezing and absorbed during melting is small at L= 3.30 x 10⁵ J kg^-1, so that the phase change between water and ice at this altitude has little effect on the buoyancy motion of the atmosphere. Why is the dynamically improbable outflow occurring at this melting altitude?

The clue was that this outflow could only be clearly recognized when longitude averaged. If the atmospheric motion is assumed to be ergodic (ergodic theorem: time and space averages are equal to each other), the longitude-averaged physical quantity can be considered to correspond to the time-averaged physical quantity in a vertical two-dimensional atmosphere consisting of latitude and altitude. The phase change of water at the melting altitude cannot have a significant effect dynamically, but the changes between liquid and solid (ice, snow, hail, etc.) can have a very large effect on radiation processes such as absorption and scattering. The difference in the morphology of the water causes a strong radiative cooling near the melting altitude. In the real atmosphere, this corresponds to strong radiative cooling at the top of the water cloud. In DCM and KCM, the radiative cooling rate in the atmosphere is homogeneous in the vertical direction, but in RAMS, this strong radiative cooling layer suddenly appears in the middle troposphere. When RDC theory was applied to such an atmosphere, it was able to explain the mid-level outflow in the model in a consistent manner.

The fact that RDC theory can be applied to the results of a cloud-resolving model, other than our own models DCM/KCM, proves the generality and universality of RDC.