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Abstract Large‐scale integral constraints on cloud behaviors can guide their more precise representation in present and future climates. We show theoretically that the mean moist static energy at cloud edge is nearly equivalent to the mean saturated static energy of the entire atmospheric domain, whether for a given level or for the cloudy troposphere as a whole. A numerical model simulation of a deep‐convective cloud field shows this equivalence holds over a 10 K range in sea surface temperature. The constraint offers a simple method for estimating the mean level of convective neutral buoyancy, one that rises linearly with the energy of sea surface air. The simulations suggest an interesting second constraint, that the maximum deviation of the saturated static energy profile from its tropospheric mean value is equivalent to the tropospheric mean energy of the saturation deficit.
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This content will become publicly available on October 1, 2026
Can Second‐Order Numerical Accuracy Be Achieved for Moist Atmospheric Dynamics With Non‐Smoothness at Cloud Edge?
Non‐smoothness arises at cloud edge because, in moist thermodynamics, the thermodynamic properties of the atmosphere are different inside a cloud versus in clear air. In particular, inside a cloud, the vapor pressure of water is constrained by the saturation vapor pressure, which acts as a threshold. Due to this threshold, while the water vapor mixing ratio may vary continuously across cloud edge, its derivatives are not necessarily continuous at cloud edge. Similarly, non‐smoothness also arises for buoyancy and other variables. Consequently, this non‐smoothness in buoyancy and other variables can cause a degraded accuracy in computational simulations. Here we consider special treatment of numerical methods for the interface that arises from phase changes and cloud edges, in order to enhance the accuracy and potentially achieve second‐order accuracy. Numerical solutions are computed for the moist non‐precipitating Boussinesq equations as an idealized cloud‐resolving model with phase changes of water, that is, with cloud formation. Convergence tests, both spatial and temporal, are conducted to measure the numerical error as the grid spacing and time step are refined. While approximately second‐order accuracy is seen in root‐mean‐square (L2) error, the accuracy is degraded in the maximum (Linfinity) error. Discussion is also included on theoretical issues and potential implications for numerical simulations.
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- Award ID(s):
- 2326631
- PAR ID:
- 10656878
- Publisher / Repository:
- Wiley
- Date Published:
- Journal Name:
- Journal of Advances in Modeling Earth Systems
- Volume:
- 17
- Issue:
- 10
- ISSN:
- 1942-2466
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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