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1. Evaluating the Conservation of Energy Variables in Simulations of Deep Moist Convection

   https://doi.org/10.1175/JAS-D-20-0351.1  

   Peters, John M.; Chavas, Daniel R. (October 2021, Journal of the Atmospheric Sciences)

   Abstract It is often assumed in parcel theory calculations, numerical models, and cumulus parameterizations that moist static energy (MSE) is adiabatically conserved. However, the adiabatic conservation of MSE is only approximate because of the assumption of hydrostatic balance. Two alternative variables are evaluated here: MSE − IB and MSE + KE, wherein IB is the path integral of buoyancy ( B ) and KE is kinetic energy. Both of these variables relax the hydrostatic assumption and are more precisely conserved than MSE. This article quantifies the errors that result from assuming that the aforementioned variables are conserved in large-eddy simulations (LES) of both disorganized and organized deep convection. Results show that both MSE − IB and MSE + KE better predict quantities along trajectories than MSE alone. MSE − IB is better conserved in isolated deep convection, whereas MSE − IB and MSE + KE perform comparably in squall-line simulations. These results are explained by differences between the pressure perturbation behavior of squall lines and isolated convection. Errors in updraft B diagnoses are universally minimized when MSE − IB is assumed to be adiabatically conserved, but only when moisture dependencies of heat capacity and temperature dependency of latent heating are accounted for. When less accurate latent heat and heat capacity formulae were used, MSE − IB yielded poorer B predictions than MSE due to compensating errors. Our results suggest that various applications would benefit from using either MSE − IB or MSE + KE instead of MSE with properly formulated heat capacities and latent heats. 

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2. An analytic formula for entraining CAPE in mid-latitude storm environments

   https://doi.org/10.1175/JAS-D-23-0003.1  

   Peters, John M.; Chavas, Daniel R.; Su, Chun-Yian; Morrison, Hugh; Coffer, Brice E. (June 2023, Journal of the Atmospheric Sciences)

   Abstract This article introduces an analytic formula for entraining convective available potential energy (ECAPE) with an entrainment rate that is determined directly from an environmental sounding, rather than prescribed by the formula user. Entrainment is connected to the background environment using an eddy diffusivity approximation for lateral mixing, updraft geometry assumptions, and mass continuity. These approximations result in a direct correspondence between the storm relative flow and the updraft radius and an inverse scaling between the updraft radius squared and entrainment rate. The aforementioned concepts, combined with the assumption of adiabatic conservation of moist static energy, yield an explicit analytic equation for ECAPE that depends entirely on state variables in an atmospheric profile and a few constant parameters with values that are established in past literature. Using a simplified Bernoulli-like equation, the ECAPE formula is modified to account for updraft enhancement via kinetic energy extracted from the cloud’s background environment. CAPE and ECAPE can be viewed as predictors of the maximum vertical velocity w max in an updraft. Hence, these formulas are evaluated using w max from past numerical modeling studies. Both of the new formulas improve predictions of w max substantially over commonly used diagnostic parameters, including undiluted CAPE and ECAPE with a constant prescribed entrainment rate. The formula that incorporates environmental kinetic energy contribution to the updraft correctly predicts instances of exceedance of by w max , and provides a conceptual explanation for why such exceedance is rare among past simulations. These formulas are potentially useful in nowcasting and forecasting thunderstorms and as thunderstorm proxies in climate change studies. 

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3. Time-dependent freezing rate parcel model

   https://doi.org/10.5194/acp-15-2071-2015  

   Vali, G.; Snider, J. R. (January 2015, Atmospheric Chemistry and Physics)

   The time-dependent freezing rate (TDFR) model here described represents the formation of ice particles by immersion freezing within an air parcel. The air parcel trajectory follows an adiabatic ascent and includes a period in time when the parcel remains stationary at the top of its ascent. The description of the ice nucleating particles (INPs) in the air parcel is taken from laboratory experiments with cloud and precipitation samples and is assumed to represent the INP content of the cloud droplets in the parcel. Time dependence is included to account for variations in updraft velocity and for the continued formation of ice particles under isothermal conditions. The magnitudes of these factors are assessed on the basis of laboratory measurements. Results show that both factors give rise to three-fold variations in ice concentration for a realistic range of the input parameters. Refinements of the parameters specifying time dependence and INP concentrations are needed to make the results more specific to different atmospheric aerosol types. The simple model framework described in this paper can be adapted to more elaborate cloud models. The results here presented can help guide decisions on whether to include a time-dependent ice nucleation scheme or a simpler singular description in models. 

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4. Quantifying Energy Balance Regimes in the Modern Climate, Their Link to Lapse Rate Regimes, and Their Response to Warming

   https://doi.org/10.1175/JCLI-D-21-0440.1  

   Miyawaki, O. (February 2022, Journal of Climate)

   Abstract Energy balance and lapse rate regimes qualitatively characterize the low, middle, and high latitudes of Earth’s modern climate. Currently we do not have a complete quantitative understanding of the spatiotemporal structure of energy balance regimes [e.g., radiative convective equilibrium (RCE) and radiative advective equilibrium (RAE)] and their connection to lapse rate regimes (moist adiabat and surface inversion). Here we use the vertically integrated moist static energy budget to define a nondimensional number that quantifies where and when RCE and RAE are approximately satisfied in Earth’s modern climate. We find RCE exists year-round in the tropics and in the northern midlatitudes during summertime. RAE exists year-round over Antarctica and in the Arctic with the exception of early summer. We show that lapse rates in RCE and RAE are consistent with moist adiabatic and surface inversion lapse rates, respectively. We use idealized models (energy balance and aquaplanet) to test the following hypotheses: 1) RCE occurs during midlatitude summer for land-like (small heat capacity) surface conditions, and 2) sea ice is necessary for the existence of annual-mean RAE over a polar ocean, such as the Arctic. Consistent with point 1, an aquaplanet configured with a shallow mixed layer transitions to RCE in the midlatitudes during summertime whereas it does not for a deep mixed layer. Furthermore, we confirm point 2 using mechanism-denial aquaplanet experiments with and without thermodynamic sea ice. Finally, we show energy balance regimes of the modern climate provide a useful guide to the vertical structure of the warming response in the annual mean, and seasonally over the tropics and the southern high latitudes. 

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5. Evidence of deviations between experimental and empirical mixing lengths: Multi-discharge field tests in an arid river system

   https://doi.org/10.1016/j.watres.2024.121629  

   Khandelwal, Aashish; Castillo, Tzion; González-Pinzón, Ricardo (June 2024, Water Research)

   Despite advances in wastewater treatment plant (WWTP) efficiencies, multiple contaminants of concern, such as microplastics, pharmaceuticals, and per- and poly-fluoroalkyl substances (PFAS) remain largely untreated near discharge points and can be highly concentrated before they are fully mixed within the receiving river. Environmental agencies enforce mixing zone permits for the temporary exceedance of water quality parameters beyond targeted control levels under the assumption that contaminants are well-mixed and diluted downstream of mixing lengths, which are typically quantified using empirical equations derived from one-dimensional transport models. Most of these equations were developed in the 1970s and have been assumed to be standard practice since then. However, their development and validation lacked the technological advances required to test them in the field and under changing flow conditions. While new monitoring techniques such as remote sensing and infrared imaging have been employed to visualize mixing lengths and test the validity of empirical equations, those methods cannot be easily repeated due to high costs or flight restrictions. We investigated the application of Lagrangian and Eulerian monitoring approaches to experimentally quantify mixing lengths downstream of a WWTP discharging into the Rio Grande near Albuquerque, New Mexico (USA). Our data spans river to WWTP discharges ranging between 2-22x, thus providing a unique dataset to test long-standing empirical equations in the field. Our results consistently show empirical equations could not describe our experimental mixing lengths. Specifically, while our experimental data revealed “bell-shaped” mixing lengths as a function of increasing river discharges, all empirical equations predicted monotonically increasing mixing lengths. Those mismatches between experimental and empirical mixing lengths are likely due to the existence of threshold processes defining mixing at different flow regimes, i.e., jet diffusion at low flows, the Coanda effect at intermediate flows, and turbulent mixing at higher flows, which are unaccounted for by the one-dimensional empirical formulas. Our results call for a review of the use of empirical mixing lengths in streams and rivers to avoid widespread exposures to emerging contaminants. 

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