skip to main content


Title: Potential Vorticity and Balanced and Unbalanced Moisture
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.  more » « less
Award ID(s):
1907667 1443325
NSF-PAR ID:
10159122
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
Journal of the Atmospheric Sciences
Volume:
77
Issue:
6
ISSN:
0022-4928
Page Range / eLocation ID:
1913 to 1931
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    Potential vorticity (PV) is one of the most important quantities in atmospheric science. In the absence of dissipative processes, the PV of each fluid parcel is known to be conserved, for a dry atmosphere. However, a parcel's PV is not conserved if clouds or phase changes of water occur. Recently, PV conservation laws were derived for a cloudy atmosphere, where each parcel's PV is not conserved but parcel‐integrated PV is conserved, for integrals over certain volumes that move with the flow. Hence a variety of different statements are now possible for moist PV conservation and non‐conservation, and in comparison to the case of a dry atmosphere, the situation for moist PV is more complex. Here, in light of this complexity, several different definitions of moist PV are compared for a cloudy atmosphere. Numerical simulations are shown for a rising thermal, both before and after the formation of a cloud. These simulations include the first computational illustration of the parcel‐integrated, moist PV conservation laws. The comparisons, both theoretical and numerical, serve to clarify and highlight the different statements of conservation and non‐conservation that arise for different definitions of moist PV.

     
    more » « less
  2. Abstract. Although conventionally attributed to dry dynamics, increasing evidence points to a key role of moist dynamics in the formation and maintenance of blocking events. The source of moisture crucial for these processes, however, remains elusive. In this study, we identify the moisture sources responsible for latent heating associated with the wintertime Euro-Atlantic blocking events detected over 31 years (1979–2010). To this end, we track atmospheric particles backward in time from the blocking centres for a period of 10 d using an offline Lagrangian dispersion model applied to atmospheric reanalysis data. The analysis reveals that 28 %–55 % of particles gain heat and moisture from the ocean over the course of 10 d, with higher percentages for the lower altitudes from which particles are released. Via large-scale ascent, these moist particles transport low-potential-vorticity (PV) air of low-altitude, low-latitude origins into the upper troposphere, where the amplitude of blocking is the most prominent, in agreement with previous studies. The PV of these moist particles remains significantly lower compared to their dry counterparts throughout the course of 10 d, preferentially constituting blocking cores. Further analysis reveals that approximately two-thirds of the moist particles source their moisture locally from the Atlantic, while the remaining one-third of moist particles source it from the Pacific. There is also a small fraction of moist particles that take up moisture from both the Pacific and Atlantic basins, which undergo a large-scale uplift over the Atlantic using moisture picked up over both basins. The Gulf Stream and Kuroshio and their extensions as well as the eastern Pacific northeast of Hawaii not only provide heat and moisture to moist particles but also act as “springboards” for their large-scale, cross-isentropic ascent, where its extent strongly depends on the humidity content at the time of the ascent. While the particles of Atlantic origin swiftly ascend just before their arrival at blocking, those of Pacific origin begin their ascent a few days earlier, after which they carry low-PV air in the upper troposphere while undergoing radiative cooling just as dry particles. A previous study identified a blocking maintenance mechanism, whereby low-PV air is selectively absorbed into blocking systems to prolong blocking lifetime. As they used an isentropic trajectory analysis, this mechanism was regarded as a dry process. We found that these moist particles that are fuelled over the Pacific can also act to maintain blocks in the same manner, revealing that what appears to be a blocking maintenance mechanism governed by dry dynamics alone can, in fact, be of moist origin. 
    more » « less
  3. 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 θ2, 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 M2Hu, which represent, respectively, buoyant energies and a moist latent energy that is released upon a change of phase. The Heaviside functions Hu and Hs indicate the unsaturated and saturated phases, respectively. The M2 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 L2 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.

     
    more » « less
  4. Observations and theory of convectively coupled equatorial waves suggest that they can be categorized into two distinct groups. Moisture modes are waves whose thermodynamics are governed by moisture fluctuations. The thermodynamics of the gravity wave group, on the other hand, are rooted in buoyancy (temperature) fluctuations. On the basis of scale analysis, it is found that a simple nondimensional parameter—akin to the Rossby number—can explain the processes that lead to the existence of these two groups. This parameter, defined as N mode , indicates that moisture modes arise when anomalous convection lasts sufficiently long so that dry gravity waves eliminate the temperature anomalies in the convective region, satisfying weak temperature gradient (WTG) balance. This process causes moisture anomalies to dominate the distribution of moist enthalpy (or moist static energy), and hence the evolution of the wave. Conversely, convectively coupled gravity waves arise when anomalous convection eliminates the moisture anomalies more rapidly than dry gravity waves can adjust the troposphere toward WTG balance, causing temperature to govern the moist enthalpy distribution and evolution. Spectral analysis of reanalysis data indicates that slowly propagating waves ( c p ~ 3 m s −1 ) are likely to be moisture modes while fast waves ( c p ~ 30 m s −1 ) exhibit gravity wave behavior, with “mixed moisture–gravity” waves existing in between. While these findings are obtained from a highly idealized framework, it is hypothesized that they can be extended to understand simulations of convectively coupled waves in GCMs and the thermodynamics of more complex phenomena. 
    more » « less
  5. Abstract

    Many definitions of moist potential vorticity (PV) have been proposed to extend the dry theory of Ertel PV. None of the moist PV definitions seem to have all of the desirable properties of the dry Ertel PV. For instance, dry PV is not only a globally conserved quantity, but also a material invariant that is conserved along fluid parcel trajectories. Therefore, an open question remains: Is there a moist PV that is a material invariant, if clouds and phase changes of water are present? In prior studies, definitions of moist PV have been proposed based on physical and mathematical intuition. Here, a systematic approach is used. In particular, a particle relabeling symmetry is devised for a moist atmosphere and then Noether's theorem is employed to arrive at the associated conservation laws for a moist PV. A priori, it is not clear whether this systematic approach will be viable, since it relies on variational derivatives in Hamilton's principle, and phase changes introduce singularities that could potentially prevent derivatives at the cloud edge. However, it is shown that the energy and the Lagrangian density are sufficiently smooth to allow variational derivatives, in a moist Boussinesq system with reversible phase transitions between water vapor and liquid cloud water. From the particle relabeling symmetry, a moist Kelvin circulation theorem is found, along with a moist PV conservation law that applies not for each individual parcel but for parcel‐integrated PV, integrated over certain local volumes.

     
    more » « less