Composite hodographs and inertial oscillations in the nocturnal boundary layer

Abstract

In this work the dynamic behaviour of the wind in the nocturnal boundary layer is studied, with a particular focus on systematic behaviour of the near-surface wind. Recently, an extension of the well-known Blackadar model for frictionless inertial oscillations above the nocturnal boundary layer was proposed by Van de Wiel et al., which accounts for frictional effects within the nocturnal boundary layer. It appears that the nocturnal wind velocity profile tends to perform an inertial oscillation around an equilibrium wind profile, rather than around the geostrophic wind vector (as in the Blackadar model).In the present study we propose the concept of 'composite hodographs' to evaluate the ideas and assumptions of the aforementioned analytical model. Composite hodographs are constructed based on a large observational dataset from the Cabauw observatory. For comparison and deeper analysis, this method is also applied to single-column model simulations that represent the same dataset. From this, it is shown that winds in the middle and upper part of the nocturnal boundary layer closely follow the dynamics predicted by the model by Van de Wiel et al. In contrast, the near-surface wind shows more complex behaviour that can be described by two different stages: (1) a decelerating phase where the wind decreases rapidly in magnitude due to enlarged stress divergence in the transition period near sunset (an aspect not included in the analytical model), and (2) a regular type of inertial oscillation, but with relatively small amplitude as compared to the oscillations in the middle and upper parts of the nocturnal boundary layer.

An Analytical Solution of Nocturnal Low Level Jets

“…Their results are at least qualitatively well reproduced (see Fig. 4 in Baas et al 2012) although they attributed the rapid damping to the evening transition.…”

“…2 in Shapiro and Fedorovich 2010). Baas et al (2012) presented the numerically simulated hodographs of nighttime wind velocity based on their composite data. To reproduce their result, we take f = 1 × 10 -4 s -1 , K = 0.88 m 2 s -1 , K = 0.22 m 2 s -1 , α = 15, and H = 1000 m in the solution (27), and show the hodographs of the nigttime wind velocity U N (z, t) in Fig.…”

“…As is well-known, the angle between the Ekman solution and the geostrophic wind velocity at the ground is 45°, which is rather large compared with that in some observations and numerical simulations (e.g., Grisogono 2011; Holtslag et al 2013). In addition, usually the daytime equilibrium wind profile is vertically more uniform than the Ekman solution (e.g., Baas et al 2012). Not only Shapiro and Fedorovich (2010) but also several other analytical studies on LLJs usually assume the diffusion for the turbulent friction (e.g., Sheih 1972).…”

“…In addition, by the replacement of the turbulent friction with the equilibrium counterpart, the temporal evolution of nighttime wind velocity becomes an undamped inertial oscillation, instead of a damped inertial oscillation, which may be regarded as a usual case. For example, the numerical simulation based on composite data in Baas et al (2012) shows a damped inertial oscillation. The damping of oscillation becomes conspicuous as the level decreases, although therein the rapid damping at the lowermost level is explained to be caused by the evening transition.…”

“…The nighttime equilibrium wind velocity is the Ekman solution with a reduced diffusion coefficient. By appropriately selecting the values of the parameters, the solution can represent several characteristic features of the LLJ, for example, backward inertial oscillations in addition to the well-known forward inertial oscillations (e.g., Baas et al 2012). Approximately, the solution of forward inertial oscillation evolves toward the geostrophic wind velocity.…”