Energy Decompositions for Moist Boussinesq and Anelastic Equations with Phase Changes
Energy Decompositions for Moist Boussinesq and Anelastic Equations with Phase Changes
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DOI：
10.1175/jas-d-19-0080.1
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发表时间：
2019-11
影响因子：
3.1
通讯作者：
David H. Marsico;L. Smith;S. Stechmann
中科院分区：
文献类型：
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作者：
David H. Marsico;L. Smith;S. Stechmann
为了定义一个有水相变化的大气的守恒能量（如蒸汽和液体），过去的动机来自于对干能量的概括，特别是来自于引力势能ρgz。这里引入了湿能的一个新定义，它推广了另一种形式的干势能，与θ2成正比，这是有价值的，因为它是明显的二次和正定的。这里的湿势能是分段二次的，并且可以分解成三个部分，与bu 2Hu、bs 2Hs和M2 Hu成比例，这三个部分分别表示浮力能和在相变时释放的湿势能。赫维赛德函数Hu和Hs分别表示不饱和相和饱和相。M2能量也与一个额外的本征模有关，该本征模在潮湿的大气中出现，但在干燥的大气中不出现。这两个Boussinesq和滞弹性方程进行检查，并显示在这两种情况下，类似的能量分解，虽然滞弹性能量不是二次的。还讨论了包括云微物理学在内的扩展，如凯斯勒暖雨方案。作为应用，考虑了经验正交函数（EOF）分析，与标准L2能量相比，使用分段二次湿能量作为加权能量。通过将有关相变的信息纳入能量中，领先的模式变得根本不同，并捕获云层的变化，而不是干燥的云下层。
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.