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Integral length scales in atmospheric surface boundary layers

In many NWP and climate models with prognostic turbulence kinetic energy (TKE) equation, one can find that the TKE dissipation rate is parameterized via suitable ratio of TKE and some kind of a length scale. This length scale is often referred to as the integral length scale, l, and, in this case, a constant of proportionality, C, is introduced in the parameterization equation (PE). Estimation of C from real datasets will therefore be sensitive to the choice of l, and this can lead to inconsistencies in parameterization of ε in NWP and climate models. Regarding l, one can find a variety of different formulations in the literature. Most frequently used are integral scales derived from autocorrelation functions (so called 1/e and zero crossing scales) and scales at which a normalized Fourier spectra achieve their maximum values. Therefore, it appears that there is no consensus in the scientific community on the unique definition of l. This work was initiated with the goal to estimate l and, after that, C for bora flows. For the analysis of bora flows, we used data obtained in the town of Senj settled at the north-eastern Adriatic coast (44.99°N, 14.90°E, 2 m above MSL). In the period from March 2004 to June 2006, WindMaster ultrasonic anemometer (Gill Instruments) mounted 13 m above the ground (at the very coast in Senj) recorded 294 bora events with cumulative duration of almost 7000 h. Possessing such a large dataset gives us an opportunity to estimate l, as well as C, and test the PE for bora’s surface layer flows. Prior to this analysis, we used certain reference data to test different formulations of l mentioned above and choose the one that is most suitable for bora flows. These reference data include well known CASES99 dataset (which is considered as the reference data for a flat, homogeneous terrain) and T-REX dataset (which is considered as the reference data for a complex, mountainous terrain). Our results suggest that 1/e scale performs best as the integral scale for bora flows.

turbulence ; integral scales ; TKE parameterization

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