The study focused on the relationship between Condensation Rate (CR) and the upward/Plus Mass Flux (MFP) in a system of trade wind cumulus clouds simulated by an LES model. The model was initialized with data observed during the RICO field project, and simulated in a

In our previous study (Kogan, 2021) we showed that a nearly perfect
correlation exists between CR and MFP (correlation coefficient

The study results suggest that condensation rates, for a variety of cloud conditions, can be precisely estimated using the single variable–upward mass flux. Possible implications of the results for evaluating supersaturation and degree of non-adiabaticity in clouds are discussed.

In tropical shallow cumulus clouds latent heat released during water phase transition is an important source of energy driving formation and evolution of cumulus convection. The formulation of phase transition processes (condensation and evaporation) in computer models depends on grid resolution (LES/CRM/NWP) and the method chosen to describe the microphysics (explicit/bin or parameterized/bulk). Obviously, condensation is influenced by microphysics, including aerosols (Kogan and Martin, 1994). The latter effect is often referred to as “convection invigoration”. It is, therefore, important to formulate parameterizations for phase transition processes, especially applicable to cloud resolving (CRM) and NWP models.

In our previous study (Kogan, 2021) we found that a strong correlation exists
between integral cloud condensation rate (CR) and integral upward mass flux (MFP). At first sight this result should not be surprising, as mass flux has long been recognized as a major factor affecting cumulus convection (see
e.g., Arakawa and Schubert, 1974; Tiedtke, 1989; Suselj et al., 2019). It was
also well known that vertical velocity has a strong effect on supersaturation, and, therefore, cloud microphysics (see, e.g., Squires, 1952; Politovich and Cooper, 1988). Nevertheless, the exceptionally high
correlation (correlation coefficient

This study provides theoretical formulation of the CR–MFP relationship based on the cloud drop condensational growth equation and the concept of quasi-steady supersaturation.

Our LES model (SAMBM) employs the dynamical core of the System for Atmospheric Modeling (SAM; Khairoutdinov and Randall, 2003) and the Bulk Microphysics (BM; Kogan, 2013) fine-tuned for shallow Cu convection. The
observations from the RICO field campaign (vanZanten et al., 2011) were used
for initialization of the LES simulations conducted in a rather large

Over the course of the simulation from 8 to 32 h, we selected 2031 clouds by applying a threshold of liquid water path

The analysis of the LES dataset described in Kogan (2021) revealed a remarkably strong correlation between the condensation rate and the upward mass flux. The scatter plot in Fig. 1 shows the CR–MFP dependence for the whole dataset, e.g., for clouds of all sizes and all stages of their evolution.

Scatter plot of condensation rates (CR) as a function of upward mass flux (MFP) for clouds in all groups.

The data clearly shows a perfect linear relationship (

The coefficients

Scatter plots of condensation rates (CR) as a function of upward mass flux (MFP) for clouds in each of the four groups.

The SAMBM model used in our study is a so-called two and half moment model,
i.e., it employs three prognostic moments for cloud water variables (cloud
water content,

In order to solve Eq. (3), we first calculate changes in temperature

Substituting Eq. (6) into Eq. (3) and using Eq. (5), we can rewrite Eq. (3) as:

The vertical profile of

Vertical profile of the ratio of supersaturation to its quasi-steady value.

As Fig. 3 shows, in the early formed clouds at

While all these factors may qualitatively explain the increase of

Data from LES simulations of shallow cumulus clouds demonstrated a nearly perfect correlation between Condensation Rate (CR) and upward/Plus Mass Flux (MFP).

The strong correlation and the linear relationship between these variables, is explained using the condensation theory. The theory also shows that the linear CR–MFP dependence is due to the fact that cloud supersaturations, on average, are equal to their quasi-steady values.

In cloud regions where, because of entrainment and mixing, supersaturation differs from its quasi-steady value, the degree of non-adiabaticity may be evaluated by the

The strong dependence of condensation rates on vertical mass flux, and the simple linear functional relationship between these variables, may be useful in formulation of condensation process in simple conceptual models of cloud topped convective boundary layer.

Finally, we note that the theoretical formulation of the CR–MFP linear relationship was based on the cloud drop condensational growth equation, and, thus, applicable for local variables. As a result, it may be integrated over limited regions of the clouds, e.g., over horizontal cloud slices to obtain relationships for horizontally averaged variables. Expanding the CR–MFP relationship for horizontally averaged variables which vary in the vertical, may serve as a framework for sub-grid scale latent heat release parameterization.

The software code for data analysis was developed by the author and is available upon request.

Analysis data is available upon request from the author.

The author has declared that there are no competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “21st EMS Annual Meeting – virtual: European Conference for Applied Meteorology and Climatology 2021”.

This investigation was supported by ONR Grant N00014-20-1-2050. The author is grateful to the two reviewers for many constructive comments. The computing for this project was performed at the OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma.

This research has been supported by the Office of Naval Research (grant no. N00014-20-1-2050).

This paper was edited by Emily Gleeson and reviewed by two anonymous referees.