Elucidating Atmospheric Turbulence Across Scales in Numerical Models: Land-Atmosphere Interaction Controls of Moist Processes


This research aims to understand the development of the atmospheric energy spectrum and energy transfer mechanisms across scales. A clear understanding of energy spectrum development and transfer mechanisms is necessary for improving the representation of multiscale processes in the atmosphere, modeling turbulence in the boundary layer, and understanding the limits of atmospheric predictability. This work consists of three parts.

The first part investigates the Navier Stokes Equations (NSE) behavior under idealized conditions relevant to large-scale atmospheric turbulence. This study uses a series of direct numerical simulations (DNS) of two-dimensional (2D) with forcing applied at different scales to investigate energy transfer between the synoptic scale and the mesoscale. The DNS results, forced by a single kinetic energy source at large scales, show that the energy spectra slopes of the direct enstrophy cascade are steeper than the theoretically predicted -3 slope. Next, the presence of two inertial ranges in 2D turbulence at intermediate scales is investigated by introducing a second energy source in the meso-a-scale range. The energy spectra for the simulations with two kinetic energy sources exhibit flatter slopes closer to -5/3, consistent with the observed kinetic energy spectra of horizontal winds in the atmosphere at synoptic scales. Further, the results are independent of model resolution and scale separation between the two energy sources, with a robust transition region between the lower synoptic and the upper meso-a scales in agreement with classical observations in the upper troposphere. These results suggest the existence of mesoscale feedback on synoptic-scale predictability that emerges from the concurrence of the direct (downscale) enstrophy transfer in the synoptic scales and the inverse (upscale) kinetic energy transfer from the mesoscale to the synoptic-scale in the troposphere.

The second part of this research is devoted to the characterization of atmospheric energy spectra over mountainous terrain under various environmental conditions using the Weather and Research Forecasting (WRF) model. First, a comprehensive analysis of climatology and mesoscale structure of cold air intrusions (CAIs) over the Andes shows that the events are responsible for localized heavy rainfall events (200 mm, less than 6 hours) in the mid-elevations (~1,500) Peruvian Andes. The climatology analysis uses European Center Medium-Range Weather Forecasts (ECMWF) reanalysis, Tropical Rainfall Measurement Mission (TRMM) data products, and rain-gauge observations. This analysis emphasized characterizing year-round CAI frequency, CAI interactions with Andes topography, and their impact on orographic precipitation climatology. The results show a robust enhancement of the diurnal cycle of precipitation during CAI events in all seasons, particularly in the increase in surface rainfall rate during early morning at intermediate elevations (~ 1,500m), the eastern Andes orographic maximum. This link between CAI frequency and rainfall suggests that they play an essential role in maintaining the Andes to Amazon year-round terrestrial connectivity through runoff production and transport by the river networks. Second, the next step examines the transient behavior of horizontal scaling in the vertical during the evolution of extreme orographic precipitation storms. Furthermore, a mechanistic framework to examine the implications of ongoing deforestation in the western Amazon on orographic precipitation in the tropical Andes through land-atmosphere interactions is provided. Understanding the interplay between large-scale dynamics and land-atmosphere interactions is critical to developing an effective boundary layer processes parameterizations for future numerical weather prediction models. The study includes a case over the Appalachians as middle mountains in comparison to high mountains (Andes) highlighting terrain and weather contrasts. Previous work showed that atmospheric model simulations exhibit different scaling behavior of vertically averaged horizontal wind (u, v) and moisture (q) in the mesoscales for convective (spectral slopes β~−5/3) and non-convective (β~−11/5) conditions. Here, the results show that β exhibits a strong diurnal cycle switching between convective and non-convective behavior following the space‐time evolution of atmospheric stability in the lower troposphere (below 700 hPa) depending on latitude, topography, landform, and the synoptic environment. Anomalous flattening of the wind and moisture spectra (i.e., spectral saturation, ∣β ∣ < 5/3) at high wavenumbers and up to 200 hPa is tied to convective activity, where and when strong vertical motions develop, corresponding to an abrupt directional switch from horizontal energy transfer to vertical energy transfer including latent heating release and parameterized microphysical processes. In the small mesoscales (<50 km), β~ − 5/3 at all times up to 200 hPa with nighttime steepening (β~−11/5) below the orographic envelope where cold air pools form at low elevations and vertical motion weakens in the Appalachians. In the Andes, at a high elevation, the scaling behavior exhibits a stronger diurnal cycle at low levels (below 700 hPa) with significant shoaling between tropical and high latitudes. Furthermore, blocking and strong modification of regional circulations result in nighttime anisotropy at midlevels on the altitudinal profile along the North‐South topographic divide.

The third part focuses on modeling turbulent fluxes near the surface, which is essential for an accurate representation of the heterogeneous surface boundary layer. Second-moment turbulent models have been widely used in numerical weather prediction models for parameterizing the planetary boundary layer (PBL). The most commonly used schemes are based on the Mellor and Yamada (1982) model, which are currently implemented to only account for the contribution of the vertical divergences of the vertical turbulent fluxes in the WRF model. Horizontal tendencies are parameterized separately based on a Smagorinsky scheme. Although this approach may be successful in coarse grid models (e.g., dx~12-2 km), the influence of horizontal gradients becomes more important when the grid spacing is smaller (less than 1 km). Recently, a full 3D PBL scheme (3DPBL) has been implemented in WRF to reconcile the representation of the vertical and horizontal turbulent mixing. The model integrates 3DPBL parameterization with a diagnostic model of the three-dimensional second-order turbulent properties of the flow in the surface layer. A set of modifications introduced to the surface parameters provides a better diagnosis of the surface layer covering different flow regimes based on anisotropy and stability conditions. The near-surface diagnostic variables are analyzed and compared with the data from the Weather Forecast Improvement Project II (WFIPII).

Finally, the dissertation discusses and recommends potential directions for future research focusing on boundary layer processes.





Eghdami, Masih (2020). Elucidating Atmospheric Turbulence Across Scales in Numerical Models: Land-Atmosphere Interaction Controls of Moist Processes. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/21525.


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