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Convective available potential energy (CAPE), a metric associated with severe weather, is expected to increase with warming. Under the most widely-accepted theory, developed for strongly convective regimes, mean CAPE should rise following…
Atmospheric moist available potential energy (MAPE) has been traditionally defined as the potential energy of a moist atmosphere relative to that of the adiabatically sorted reference state defining a global potential energy minimum.…
We extend the local theory of available potential energy (APE) to a general multicomponent compressible stratified fluid, accounting for the effects of diabatic sinks and sources. As for simple compressible fluids, the total potential…
This note is a companion of Marquet and Geleyn (2013, {arXiv:1401.2379 [ao-ph]}), where adiabatic lapse rates $\Gamma_{ns}$ and $\Gamma_{sw}$ are derived for non-saturated ($\Gamma_{ns}$) or saturated ($\Gamma_{sw}$) parcel of moist-air.…
The aim of this note is to derive the mixed-phase version of the moist-air entropy potential temperature $\theta_s$ derived in Marquet (2011). This mixed-phase version is suitable to describe parcels where liquid water and ice are allowed…
Column-integrated moist static energy (MSE) budgets underpin theories of tropical convection and circulation, yet in reanalyses and climate models the budget rarely closes; residuals routinely match the leading terms and mask physical…
The specific thermal enthalpy of a moist-air parcel is defined analytically following a method in which specific moist entropy is derived from the Third Law of thermodynamics. Specific thermal enthalpy is computed by integrating specific…
Exact analytical expressions for available potential energy density (APE) and available potential vorticity (APV) are derived from first principles. These APE and APV expressions align with previously known quantities found using…
Available Potential Energy (APE) dissipation plays a central role in the description of mixing in turbulent stratified fluids. The dominant paradigm is that it converts APE into background gravitational potential energy ${\rm GPE}_r$, and…
A new potential vorticity is derived by using a specific entropy formulation expressed in terms of a moist-air entropy potential temperature. The new formulation is compared with Ertel's version and with others based on virtual and…
This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from the storm environment. Extending previous formulas derived in Peters et al.…
Some existing approaches to modeling the thermodynamics of moist air make approximations that break $\textit{thermodynamic consistency}$, such that the resulting thermodynamics do not obey the 1st and 2nd laws or have other inconsistencies.…
How phase transitions affect the motion of moist atmospheric air remains controversial. In the early 2000s two distinct differential equations of motion were proposed. Besides their contrasting formulations for the acceleration of…
Idealized convection-permitting simulations of radiative-convective equilibrium (RCE) have become a popular tool for understanding the physical processes leading to horizontal variability of tropical water vapor and rainfall. However, the…
A moist entropy potential temperature -- denoted by ${\theta}_{s}$ -- is defined analytically in terms of the specific entropy for moist air. The expression for ${\theta}_{s}$ is valid for a general mixing of dry air, water vapour and…
To elucidate how land surface state and soil moisture dynamics regulate moist convection, and how convective rainfall subsequently reshapes surface and root-zone hydrology, we develop a stochastic dynamical model that couples soil moisture,…
Potential vorticity (PV) is one of the most important quantities in atmospheric science. The PV of each fluid parcel is known to be conserved in the case of a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase…
This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from…
We consider the compressible Euler equations with potential temperature transport, a system widely used in atmospheric modelling to describe adiabatic, inviscid flows. In the low Mach number regime, the equations become stiff and pose…
The upwind conservation element and solution element (CESE) scheme is an alternative discontinuity-capturing numerical approach to solving hyperbolic conservation laws. To evaluate the numerical properties of this spatiotemporal coupled…