Diagnostic Equations for the Stable Boundary Layer Height: Evaluation and Dimensional Analysis

Abstract

The performance of diagnostic equations for the stable boundary layer height h is evaluated with four observational datasets that represent a broad range of latitudes, land use, and surface roughness. In addition, large-eddy simulation results are used. Special care is given to data-quality selection. The diagnostic equations evaluated are so-called multilimit equations as derived by Zilitinkevich and coworkers in a number of papers. It appears that these equations show a serious negative bias, especially for h Ͻ 100 m, and it was found that the parameters involved could not be determined uniquely with calibration. As an alternative, dimensional analysis is used here to derive a formulation for h that is more robust. The formulation depends on the surface friction velocity u * , surface buoyancy flux B s , Coriolis parameter, and the free-flow stability N. The relevance of the Coriolis parameter for the boundary layer height estimation in practice is also discussed. If the Coriolis parameter is ignored, two major regimes are found: h ϳ u * /N for weakly stable conditions and h ϳ (|B s | /N 3 ) 1/2 for moderate to very stable conditions.

Wind-Tunnel Simulation of the Wake of a Large Wind Turbine in a Stable Boundary Layer. Part 1: The Boundary-Layer Simulation

“…At full scale, assuming a wind speed of, say, 10 m s -1 rather than the !1.5 m s -1 of these experiments, Eq. 9 gives this as equivalent to 4.9#10 -4 #20 K m -1 = 0.01 K m -1 , comparable to levels given, for example, by Mahrt et al (1979) and André and Mahrt (1982), and with more recent data given by Steeneveld et al (2007). …”

Measurements and Parametrizations of the Atmospheric Boundary-Layer Height at Dome C, Antarctica

“…The values found with the two methods range between 10 and 150 m; the correlation coefficient is 0.8. The Richardson number method generally gives lower values with respect to the visual observation method; the mean difference is 12 m. On the other hand, no correlation and a systematic overestimation were found between the stable layer height determined from experimental data and the values estimated using the parametrizations for the stable boundary layer given in Table 1 and the formulation proposed by Steenelveld et al (2007). A better correlation is obtained with the formulation proposed by Zilitinkevich (2002) for the LLSL.…”

“…The parametrizations summarized in Table 1 and the formulation proposed by Steenelveld et al (2007) show, however, a correlation with the height corresponding to the surface temperature inversion that does not necessarily correspond to the stable boundary-layer height.…”

“…The height h SL has also been calculated using the formulation proposed by Steenelveld et al (2007), obtained by arranging the relevant parameters in the development of the stable layer, that is: Table 1 and Eqs. 2 and 3 is shown in the scatter plots in Figs.…”

Continuous monitoring of the boundary-layer top with lidar

“…Thus, only the equilibrium BL top can be provided rather than the actual BL height (Zilitinkevich and Baklanov, 2002). The limits of the Richardsonnumber approach are further discussed by Vogelezang and Holtslag (1996) and Steeneveld et al (2007) and alternative approaches to predict the boundary layer are suggested.…”