There are two models for the surface layer in the convective boundary layer (CBL). First is the standard Monin–Obukhov similarity theory, and second is the McNaughton–Laubach model (Laubach and McNaughton 2009, Boundary-Layer Meteorology 133:219–252; hereafter MNL model) developed based on the complex dynamical system approach to address characteristics of the unstable surface layer. The fundamental difference between the Monin–Obukhov similarity theory and the MNL model is the use of local and non-local parameters for analyzing surface-layer spectra in the CBL. However, there is a need to check applicability of this new model at various flow conditions before the model could be extensively used. Subsequently, applicability of the MNL model is tested in comparison to the standard model using CBL observations from three different regions with increasing terrain complexity (i.e. over flat-terrain, onslope, and ridge-top sites). The MNL model is tested by estimating and using the non-local scaling parameters to collapse the power spectra of velocity and temperature on the frequency–amplitude scale under the generalized hypothesis that convective surface layer depends on non-local outer variables. We find that the u and v spectra for all sites indicate run-to-run similarity of each spectra with MNL scaling irrespective of the height limiting role of local buoyancy on the shape of the spectra. Similarly, w spectra from all sites indicate transitions between the surface friction layer and the outer layer are governed by flow in the entire CBL. The temperature spectra collapse using $$(z \epsilon _o)^{2/3} H_0^{-2}$$ ( z ϵ o ) 2 / 3 H 0 - 2 as amplitude scaling and $$kz_i^{1/2}z^{1/2}$$ k z i 1 / 2 z 1 / 2 as wavenumber scaling, is a new observation within the surface friction layer, where the streamwise wavenumber is k , measurement height is z , CBL height is $$z_i$$ z i , the dissipation rate of turbulence energy in the outer CBL is $$\epsilon _o$$ ϵ o , and the surface heat flux is $$H_0$$ H 0 . These observations corroborate well with the MNL model conjecture that the convective temperature spectra do not depend only on local stability, and CBL parameters affect spectra when a subset of local factors remains constant.

中文翻译：

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对流边界层的新替代标度特性的评估：在速度和温度谱中的应用

对流边界层 (CBL) 中的表层有两种模型。首先是标准的 Monin-Obukhov 相似理论，其次是 McNaughton-Laubach 模型（Laubach 和 McNaughton 2009，Boundary-Layer Meteorology 133:219-252；此后称为 MNL 模型）基于复杂动力系统方法开发，以解决不稳定的表层。Monin-Obukhov 相似理论和 MNL 模型之间的根本区别是使用局部和非局部参数来分析 CBL 中的表层光谱。然而，在模型被广泛使用之前，需要检查这个新模型在各种流动条件下的适用性。随后，MNL 模型的适用性与标准模型进行了比较，该模型使用来自地形复杂性不断增加的三个不同区域（即平坦地形、斜坡和脊顶站点）的 CBL 观测。MNL 模型通过估计和使用非局部标度参数在对流表面层取决于非局部外部变量的广义假设下在频率 - 幅度标度上折叠速度和温度的功率谱来进行测试。我们发现所有站点的 u 和 v 光谱表明每个光谱与 MNL 缩放的运行之间的相似性，而与局部浮力对光谱形状的高度限制作用无关。类似地，来自所有位置的 w 光谱表明表面摩擦层和外层之间的过渡受整个 CBL 中的流动控制。使用 $$(z \epsilon _o)^{2/3} H_0^{-2}$$ ( z ϵ o ) 2 / 3 H 0 - 2 作为幅度缩放和 $$kz_i^{1/ 2}z^{1/2}$$ kzi 1 / 2 z 1 / 2 作为波数标度，是表面摩擦层内的新观测，其中流向波数为 k ，测量高度为 z ，CBL 高度为 $$ z_i$$ zi ，外层CBL的湍流能量耗散率为$$\epsilon _o$$ ϵ o ，表面热通量为$$H_0$$ H 0 。这些观察结果很好地证实了 MNL 模型的猜想，即对流温度谱不仅取决于局部稳定性，而且当局部因素的子集保持不变时，CBL 参数会影响光谱。