Impact of stationarity criteria on surface layer similarity functions in complex terrain

Monin-Obukhov similarity theory (MOST) is the most widely accepted and used theoretical framework for the investigation of turbulent processes in the atmospheric boundary layer. MOST has been extensively studied over various locations including flat, homogeneous terrains, urban and adjacent rural areas, and coastal regions. However, there is a lack of investigations detailing the applicability of similarity theory and the validity of its basic assumptions in complex mountainous terrain. One of these basic assumptions is stationarity. The aim of the current study is to investigate the impact of stationarity criteria on surface layer similarity functions.

We use data obtained in a three-month period during the Terrain-induced Rotor Experiment (T-REX). Three 30-m towers were positioned along the Owens Valley in California, one of the deepest valleys in the contiguous United States. Two of the towers were located on the valley's central axis, while the third tower was positioned on the east facing slope of the Sierra Nevada mountain. Each tower was equipped with CSAT3 ultrasonic anemometers on six levels (5, 10, 15, 20, 25 and 30 m), capturing 3D wind speed and sonic temperature with a sampling frequency of 60 Hz. A main feature of the data preprocessing was the application of five stationarity criteria, providing us with differently defined stationary data, which are necessary in order to properly apply MOST.

Since MOST applies in the inertial sublayer, also sometimes refered to as the constant flux layer, we first assess the degree of vertical divergence of kinematic momentum and heat fluxes. We find that there is substantial vertical divergence of the fluxes and conclude that local similarity scaling rather than the usual Monin-Obukhov similarity should be used. We calculate the non-dimensional standard deviations of wind velocity components and potential temperature as a function of local stability and calculate the best fit through the data points for unstable and stable situations. Our results show that the use of data selected using the five different stationarity criteria has a large impact on the form of the similarity functions. Data selected using the various certain stationary criteria also has an large impact on the scatter. With a reduction of the scatter, the fitting parameters in the local similarity functions converge to values that are different from values typically found for flat terrain. The fitting parameters appear to depend on location in the valley and on height in the surface layer for both stable and unstable situations. We will discuss how our results can be used to improve the parameterization of surface layer turbulence in complex terrain.