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Leslie M. Smith and Samuel N. Stechmann

Abstract

Precipitating versions of the quasigeostrophic (QG) equations are derived systematically, starting from the equations of a cloud-resolving model. The presence of phase changes of water from vapor to liquid and vice versa leads to important differences from the dry QG case. The precipitating QG (PQG) equations, in their simplest form, have two variables to describe the full system: a potential vorticity (PV) variable and a variable M including moisture effects. A PV-and-M inversion allows the determination of all other variables, and it involves an elliptic partial differential equation (PDE) that is nonlinear because of phase changes between saturated and unsaturated regions. An example PV-and-M inversion is provided for an idealized cold-core cyclone with two vertical levels. A key point illustrated by this example is that the phase interface location is unknown a priori from PV and M, and it is discovered as part of the inversion process. Several choices of a moist PV variable are discussed, including subtleties that arise because of phase changes. Boussinesq and anelastic versions of the PQG equations are described, as well as moderate and asymptotically large rainfall speeds. An energy conservation principle suggests that the model has firm physical and mathematical underpinnings. Finally, an asymptotic analysis provides a systematic derivation of the PQG equations, which arise as the limiting dynamics of a moist atmosphere with phase changes, in the limit of rapid rotation and strong stratification in terms of both potential temperature and equivalent potential temperature.

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L. M. Leslie and R. K. Smith

Abstract

A recent numerical study of vortex growth in a flow configuration which models the principal characteristics of a tornado cyclone (Smith and Leslie, 1978) is extended to take account of vertical stability. It is shown that for a given strength of convection and rotation (in the model, the driving effect of a ‘supercell’ updraft is simulated by an imposed body force), the intensity of the mature vortex which forms in the presence of a typical vertical gradient of potential temperature is significantly lower than that which forms in an adiabatic atmosphere. We conclude that the effects of vertical stratification on tornadogenesis may often be important and may prevent some vortices, which might otherwise do so, from establishing ground contact.

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Gerardo Hernández-Dueñas, M.-Pascale Lelong, and Leslie M. Smith

Abstract

Submesoscale lateral transport of Lagrangian particles in pycnocline conditions is investigated by means of idealized numerical simulations with reduced-interaction models. Using a projection technique, the models are formulated in terms of wave-mode and vortical-mode nonlinear interactions, and they range in complexity from full Boussinesq to waves-only and vortical-modes-only (QG) models. We find that, on these scales, most of the dispersion is done by vortical motions, but waves cannot be discounted because they play an important, albeit indirect, role. In particular, we show that waves are instrumental in filling out the spectra of vortical-mode energy at smaller scales through nonresonant vortex–wave–wave triad interactions. We demonstrate that a richer spectrum of vortical modes in the presence of waves enhances the effective lateral diffusivity, relative to QG. Waves also transfer energy upscale to vertically sheared horizontal flows that are a key ingredient for internal-wave shear dispersion. In the waves-only model, the dispersion rate is an order of magnitude smaller and is attributed entirely to internal-wave shear dispersion.

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R. K. Smith, J. V. Mansbridge, and L. M. Leslie

Abstract

No abstract available.

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Gerardo Hernandez-Duenas, Leslie M. Smith, and Samuel N. Stechmann

Abstract

A linear stability analysis is presented for fluid dynamics with water vapor and precipitation, where the precipitation falls relative to the fluid at speed V T. The aim is to bridge two extreme cases by considering the full range of V T values: (i) V T = 0, (ii) finite V T, and (iii) infinitely fast V T. In each case, a saturated precipitating atmosphere is considered, and the sufficient conditions for stability and instability are identified. Furthermore, each condition is linked to a thermodynamic variable: either a variable θ s, which denotes the saturated potential temperature, or the equivalent potential temperature θ e. When V T is finite, separate sufficient conditions are identified for stability versus instability: e/dz > 0 versus s/dz < 0, respectively. When V T = 0, the criterion s/dz = 0 is the single boundary that separates the stable and unstable conditions; and when V T is infinitely fast, the criterion e/dz = 0 is the single boundary. Asymptotics are used to analytically characterize the infinitely fast V T case, in addition to numerical results. Also, the small-V T limit is identified as a singular limit; that is, the cases of V T = 0 and small V T are fundamentally different. An energy principle is also presented for each case of V T, and the form of the energy identifies the stability parameter: either s/dz or e/dz. Results for finite V T have some resemblance to the notion of conditional instability: separate sufficient conditions exist for stability versus instability, with an intermediate range of environmental states where stability or instability is not definitive.

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David H. Marsico, Leslie M. Smith, and Samuel N. Stechmann

Abstract

To define a conserved energy for an atmosphere with phase changes of water (such as vapor and liquid), motivation in the past has come from generalizations of dry energies—in particular, from gravitational potential energy ρgz. Here a new definition of moist energy is introduced, and it generalizes another form of dry potential energy, proportional to θ 2, which is valuable since it is manifestly quadratic and positive definite. The moist potential energy here is piecewise quadratic and can be decomposed into three parts, proportional to bu2Hu, bs2Hs, and M 2 H u, which represent, respectively, buoyant energies and a moist latent energy that is released upon a change of phase. The Heaviside functions H u and H s indicate the unsaturated and saturated phases, respectively. The M 2 energy is also associated with an additional eigenmode that arises for a moist atmosphere but not a dry atmosphere. Both the Boussinesq and anelastic equations are examined, and similar energy decompositions are shown in both cases, although the anelastic energy is not quadratic. Extensions that include cloud microphysics are also discussed, such as the Kessler warm-rain scheme. As an application, empirical orthogonal function (EOF) analysis is considered, using a piecewise quadratic moist energy as a weighted energy in contrast to the standard L 2 energy. By incorporating information about phase changes into the energy, the leading EOF modes become fundamentally different and capture the variability of the cloud layer rather than the dry subcloud layer.

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Alfredo N. Wetzel, Leslie M. Smith, Samuel N. Stechmann, Jonathan E. Martin, and Yeyu Zhang

Abstract

Atmospheric flows are often decomposed into balanced (low frequency) and unbalanced (high frequency) components. For a dry atmosphere, it is known that a single mode, the potential vorticity (PV), is enough to describe the balanced flow and determine its evolution. For a moist atmosphere with phase changes, on the other hand, balanced–unbalanced decompositions involve additional complexity. In this paper, we illustrate that additional balanced modes, beyond PV, arise from the moisture. To support and motivate the discussion, we consider balanced–unbalanced decompositions arising from a simplified Boussinesq numerical simulation and a hemispheric-sized channel simulation using the Weather Research and Forecasting (WRF) Model. One important role of the balanced moist modes is in the inversion principle that is used to recover the moist balanced flow: rather than traditional PV inversion that involves only the PV variable, it is PV-and-M inversion that is needed, involving M variables that describe the moist balanced modes. In examples of PV-and-M inversion, we show that one can decompose all significant atmospheric variables, including total water or water vapor, into balanced (vortical mode) and unbalanced (inertio-gravity wave) components. The moist inversion, thus, extends the traditional dry PV inversion to allow for moisture and phase changes. In addition, we illustrate that the moist balanced modes are essentially conserved quantities of the flow, and they act qualitatively as additional PV-like modes of the system that track balanced moisture.

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Randall M. Dole, J. Ryan Spackman, Matthew Newman, Gilbert P. Compo, Catherine A. Smith, Leslie M. Hartten, Joseph J. Barsugli, Robert S. Webb, Martin P. Hoerling, Robert Cifelli, Klaus Wolter, Christopher D. Barnet, Maria Gehne, Ronald Gelaro, George N. Kiladis, Scott Abbott, Elena Akish, John Albers, John M. Brown, Christopher J. Cox, Lisa Darby, Gijs de Boer, Barbara DeLuisi, Juliana Dias, Jason Dunion, Jon Eischeid, Christopher Fairall, Antonia Gambacorta, Brian K. Gorton, Andrew Hoell, Janet Intrieri, Darren Jackson, Paul E. Johnston, Richard Lataitis, Kelly M. Mahoney, Katherine McCaffrey, H. Alex McColl, Michael J. Mueller, Donald Murray, Paul J. Neiman, William Otto, Ola Persson, Xiao-Wei Quan, Imtiaz Rangwala, Andrea J. Ray, David Reynolds, Emily Riley Dellaripa, Karen Rosenlof, Naoko Sakaeda, Prashant D. Sardeshmukh, Laura C. Slivinski, Lesley Smith, Amy Solomon, Dustin Swales, Stefan Tulich, Allen White, Gary Wick, Matthew G. Winterkorn, Daniel E. Wolfe, and Robert Zamora

Abstract

Forecasts by mid-2015 for a strong El Niño during winter 2015/16 presented an exceptional scientific opportunity to accelerate advances in understanding and predictions of an extreme climate event and its impacts while the event was ongoing. Seizing this opportunity, the National Oceanic and Atmospheric Administration (NOAA) initiated an El Niño Rapid Response (ENRR), conducting the first field campaign to obtain intensive atmospheric observations over the tropical Pacific during El Niño.

The overarching ENRR goal was to determine the atmospheric response to El Niño and the implications for predicting extratropical storms and U.S. West Coast rainfall. The field campaign observations extended from the central tropical Pacific to the West Coast, with a primary focus on the initial tropical atmospheric response that links El Niño to its global impacts. NOAA deployed its Gulfstream-IV (G-IV) aircraft to obtain observations around organized tropical convection and poleward convective outflow near the heart of El Niño. Additional tropical Pacific observations were obtained by radiosondes launched from Kiritimati , Kiribati, and the NOAA ship Ronald H. Brown, and in the eastern North Pacific by the National Aeronautics and Space Administration (NASA) Global Hawk unmanned aerial system. These observations were all transmitted in real time for use in operational prediction models. An X-band radar installed in Santa Clara, California, helped characterize precipitation distributions. This suite supported an end-to-end capability extending from tropical Pacific processes to West Coast impacts. The ENRR observations were used during the event in operational predictions. They now provide an unprecedented dataset for further research to improve understanding and predictions of El Niño and its impacts.

Open access