Systematic multiscale models for deep convection on mesoscales
Systematic multiscale models for deep convection on mesoscales
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DOI：
10.1007/s00162-006-0027-9
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发表时间：
2006-08
影响因子：
3.4
通讯作者：
R. Klein;A. Majda
中科院分区：
文献类型：
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作者：
R. Klein;A. Majda
本文建立在最近发展的一个统一的渐近方法气象建模[ZAMM，80：765-777，2000，SIAM Proc. App. Math. 116，227-289，2004]，这是成功地用于热带Majda和Klein [J. Atmosph. Sci. 60：393-408，2003]和Majda和Biello [PNAS，101：4736-4741，2004]。Biello和Majda [J. Atmosph. Sci. 62：1694-1720，2005]。在这里，我们占在这个框架内的湿过程的典型的散装微物理参数化。的关键步骤是仔细无量纲化的散装微观物理方程和选择适当的区别限制出现的各种无量纲小参数。然后，我们就可以研究大气中涉及潮湿物理的尺度相互作用。我们证明了这一点，通过开发两个系统的多尺度模型，我们的兴趣在中尺度有组织的对流的动机。这里的重点是多个长度尺度，但共同的时间尺度。其中第一个模型描述了细长的、深对流热塔的短时演化，水平尺度约为1 km，在长度和时间尺度（10 km/3 min）上与线性动量平衡相互作用。我们希望这个模型来描述如何对流抑制可能被克服表面附近，如何发生的深对流触发对流尺度重力波，它也将产生新的见解，这些局部对流事件如何可能合谋创造更大规模的强风暴。第二个模型解决了下一个更大的范围内的长度和时间尺度（10公里，100公里，20分钟），并表现出强烈的数学特征，让人想起中尺度有组织的对流。在这两种情况下，渐近分析揭示了冷凝/蒸发过程的刚度如何引起高度非线性动力学。除了提供新的理论见解，派生的模型也可以作为一个理论设备，用于分析和解释复杂的潮湿过程模式模拟的结果，他们可能会刺激新的，理论上接地子网格尺度参数化的发展。
This paper builds on recent developments of a unified asymptotic approach to meteorological modeling [ZAMM, 80: 765–777, 2000, SIAM Proc. App. Math. 116, 227–289, 2004], which was used successfully in the development ofSystematic multiscale models for the tropicsin Majda and Klein [J. Atmosph. Sci. 60: 393–408, 2003] and Majda and Biello [PNAS, 101: 4736–4741, 2004]. Biello and Majda [J. Atmosph. Sci. 62: 1694–1720, 2005]. Here we account for typical bulk microphysics parameterizations of moist processes within this framework. The key steps are careful nondimensionalization of the bulk microphysics equations and the choice of appropriate distinguished limits for the various nondimensional small parameters that appear. We are then in a position to study scale interactions in the atmosphere involving moist physics. We demonstrate this by developing two systematic multiscale models that are motivated by our interest in mesoscale organized convection. The emphasis here is on multiple length scales but common time scales. The first of these models describes the short-time evolution of slender, deep convectivehot towerswith horizontal scale ~ 1 km interacting with the linearized momentum balance on length and time scales of (10 km/3 min). We expect this model to describe how convective inhibition may be overcome near the surface, how the onset of deep convection triggers convective-scale gravity waves, and that it will also yield new insight into how such local convective events may conspire to create larger-scale strong storms. The second model addresses the next larger range of length and time scales (10 km, 100 km, and 20 min) and exhibits mathematical features that are strongly reminiscent of mesoscale organized convection. In both cases, the asymptotic analysis reveals how the stiffness of condensation/evaporation processes induces highly nonlinear dynamics. Besides providing new theoretical insights, the derived models may also serve as a theoretical devices for analyzing and interpreting the results of complex moist process model simulations, and they may stimulate the development of new, theoretically grounded sub-grid-scale parameterizations.