Turbulence characteristics of a stable boundary layer over sloping terrain D. Cava *, U. Giostra *, F. Trombetti * & M. Tagliazucca * *Istituto ISIAtA-CNR, s.p. per Monteroni km 7.2,1-70300 Lecce, Italy Email: umberto@elettra.isiata.le.cnr.it *htituto FISBAT-CNR, via Gobetti 707,7-40729 Bologna, Italy Email: m.tagliazucca@fisbat.bo.cnr.it Abstract During the austral summer 1993-94 turbulence data have been taken in a coastal region of Antarctica over a gently sloping surface. The objective of this study is to determine how the turbulent structure of the stable boundary layer is perturbed by slope and waves. Spectral analysis of wind velocity components evidences the production of energy, prevalently in the mid frequency subrange, by local orographic forcing. The power contribute of waves is highly variable as single or multiple waves of different amplitudes are observed. A criterion, based on the shear stress correlation coefficient, to distinguish turbulent flows from the ones affected also by waves activity is suggested. This procedure should give an estimate of the relative entity of wavy and turbulent contributes to velocity standard deviations. 1 Introduction The thermal stratification of the atmospheric boundary layer is often stable. A stable boundary layer (SBL) develops almost every night over land as consequence of the radiative cooling of surface or during advection of warm air over a colder ground as observed in warm fronts and in proximity of coastal areas. The SBL undergoes a slow evolution driven by turbulent and radiative processes and in most of the cases it does not reach the equilibrium, i.e. quasistationary conditions. This is a consequence of the low turbulence intensity due to buoyancy forces acting to suppress mechanical production combined with decreasing SBL depth and increasing height and strength of the temperature
92 Air Pollution Modelling, Monitoring and Management inversion layer. The turbulent structure of the SBL is sensitive to many factors: the slope of terrain, even moderate, favours the development of drainage flows; the propagation of gravity waves which non-linearly interact with turbulence; the development of a low level jet when light winds near the ground are accelerated at higher levels to supergeostrophic velocities. Waves are generated by the interaction of the flow with orography, by inhomogeneity of surface fluxes (e.g. in coastal areas) or by discontinuities of flow characteristics (e.g. fronts). In strong stable conditions, above the surface layer, turbulence is uncoupled from surface forcings and is governed by the local value of stability and shears; sometimes turbulence becomes intermittent and displays alternating turbulent and laminar flow characteristics. Therefore, the determination of the turbulent structure of the SBL is a difficult task, differently from the convective boundary layer where quasi-stationary condition occurs, waves propagation is not supported and slope effects are not so important. Here we deal with spectral analysis of wind velocity components to highlight the energy contribute of sloping surface as well of waves. Moreover, we present an analysis of the standard deviation of wind velocity components as a function of stability. The analysis has been done on data taken in Antarctica during the austral summer where a stable stratification persist frequently over periods largely exceeding the daily cycle. 2 The measurement site and data acquisition Turbulence measurements have been performed on the Nansen Ice Sheet (NIS), a permanently frozen branch of Ross sea throughout the period 20 November 1993-12 February 1994. The micrometeorological tower was located at 74 4T58" S and 163 30'50" E, in the middle of a homogeneous snowy area of 50x30 km^ gently sloping («0.4%) along the north-south axis. The area is surrounded from SW to NE by mountains rapidlyrisingtowards the Antarctic plateau, on E and SE by hills 600 m high, whereas on the S is bordered by the open sea. In this area converge from the N, along a narrow gently sloping valley, the Priestley glacier and from the NW, along a wide and steep valley, the Reeves glacier. Through these glaciers flow katabatic winds which strongly influence the local climatology. But we recorded sporadic events of katabatic wind only in the mid of the observing period. Turbulence measurements have been performed at the height of 2, 4.5, and 10 m by symmetric 3-axis ultrasonic anemometers, model Research, of Gill Inst. Ltd. Wind velocity components and sonic temperature 7, have been sampled at the frequency of 20.8 Hz. 3 Preliminary data analysis The evaluation of turbulence quantities requires a preliminary handling of raw data in order to avoid errors due to misalignment of ultrasonic anemometers
Air Pollution Modelling, Monitoring and Management 93 with the mean streamline of the flow and to discard time series affected by flow distortion induced by tower shadowing. Therefore, the measured wind components have been rotated twice to obtain the longitudinal wind component U. A third rotation in the plane normal to the longitudinal wind vector has been performed to align the vertical axis to the turbulent flux of momentum w'w', so that v'v/ = 0 (McMillen*). The resulting mean wind vector is U = (U + w',v',w), where u\ V and w are fluctuations in the rotated reference system. Turbulent fluxes have been estimated using the eddy correlation technique. In the framework of Monin-Obukhov (M-O) similarity theory, in a surface layer over a horizontally homogeneous and flat ground, the scaling parameter of any turbulent quantity is = z/l, where z is the measuring height and L = -^us /(kg(w'$[\) the M-O length,^ (=?T = ^) the mean virtual potential temperature, w» the friction velocity, k the von Karman constant, g the gravity acceleration and (w'd^ the nearly constant turbulent heat flux. In the 1/2 present case we adopt the local scaling, i.e. u^ = w'v/ and w'$' instead of w, and (w'$')o so that the local M-O length becomes L^ = -OyW'w' /(kgw'$[). This choice is suggested by the fact that we consider flows over a sloping surface where turbulent quantities and the scaling parameters assume different values for up- and down-slope flows, as results from the model of Brost & Wyngaard. Moreover the low value of the roughness length (ZQ =4-l(T*m) and the high value of albedo for snow give rise to low turbulent exchanges and the SBL depth is often very shallow. One way to evaluate the incidence of waves and local or remote orographic forcings is to perform the spectral analysis of wind velocity components by means of Fast Fourier Transforms. To do this a low-frequency cut-off to the data is necessary to eliminate low-frequency oscillations and trends that usually affect time series of meteorological data. A spectral filter (Jenkins & Watts^) has been applied to cut frequencies lower than the threshold value set at about one hour. The analysis has been performed only on data relative to winds blowing from the mountains or the sea along the fall line of the slope. 4 Spectra of wind velocity components The power spectral densities S,( i), where / = u, v, w and k^ is the one dimensional turbulence wavenumber along the mean flow direction, satisfy the condition,(*,)^=a (1) where a. are the standard deviations of velocity components.
94 Air Pollution Modelling, Monitoring and Management The Kolmogorov form of one-dimensional velocity spectra in the inertial subrange is -5/3 (2) where a, are the Kolmogorov constants for velocity components and e is the dissipation rate of turbulent kinetic energy (TKE) into heat at small scales. We have assumed a,, =0.55 and a^ =0.41. Taylor's frozen turbulence hypothesis ^ = 2nf /U is applied to express Eq. (2) in terms of normalised frequency spectra ^ a/ -2/3 (3) where / (in s"*) is the frequency, U the longitudinal wind velocity at the measurement height and n=-fz!u the reduced frequency. Over homogeneous and flat terrain in quasi stationary conditions the turbulence in the inertial subrange is three-dimensional and isotropic, the normalised power spectra collapse, regardless of stability, on an unique curve proportional to n~^. In the low frequency part, power spectra are spread as a function of stability into different curves proportional to n. 1.6 1.2 o.a 0.4 n n 4/3 -Q-A--B--0-- A * & a 5 7 " a % o v o -. 9 o 0 0,? n=fz/u n A V o 0-0.7 P 0.7 - OJ 6 OJ - 0.3 6 0.5-1.0 5 Figure 1: Ratio of vertical to longitudinal velocity spectra for different stability ranges. N is the number of cases. In our case the spectra of wind velocity components, plotted as a function of H, display an inertial subrange. In fact, as required by isotropy of turbulence, the ratio (/)/ (/) = 4/3 is reached for n > 2 (Fig. 1). As consequence the TKE dissipation rate e can be derived from the inertial subrange of spectra themselves. The normalised spectra of Eq. (3), regardless of any orographic effect, are forced to collapse in the inertial subrange (Andreas*) and they overlap the reference spectra measured by Kaimal et al/ over uniform and flat ground. In fact small scale turbulence rapidly responds to slope forcing and to
Air Pollution Modelling, Monitoring and Management 95 orographic effects (Panofsky et al. *). On the contrary, in the mid or low frequency subranges different spectral shapes are observed according to the production of energy by the local orographic forcing, by waves of various amplitudes or by the low level jet The slope forcing generates an increment of energy, mainly in the midfrequency subrange, as consequence the spectra of horizontal components display a turbulence maximum shifted towards lower frequencies (Fig. 2). In the w-spectrum the increment of power is generally lower because fluctuations are limited by SBL depth and most of energy is contained in relatively high frequency modes. 2 0.1 I I I 25 30 35 40 45 50 55 60 Time (min) Figure 2: Normalised u- and w-spectra N(/) = /S.(/)/(ez)^ vs reduced frequency n (a) and time record of u and w velocity components (b) measured in the period 18-19 29 January 1994. Vertical bars represent the standard deviation of the mean; curves are reference spectra at = 0.01 (Kaimal et al/). Waves are generated at different frequencies as a function of local stability and are shifted towards higher (lower) frequencies as stability increases (decreases). They interact non-linearly with turbulence and are progressively spread over a range of frequencies. Therefore waves are observed in a variety of frequencies and amplitudes that allows only a phenomenological description of single events.
96 Air Pollution Modelling, Monitoring and Management 10 C=0.24 2 0.1 b- 5 10' n-2 10* n =fz/u 10" Iff 70 5 2 'bjfil*^ b) - -3 0 5 70 75 20 25 30 35 40 45 50 55 60 Time (min) Figure 3: As in Fig.2, but for the period 09-10 23 December 1993. 0 S 5-2 0.7 *-3 10 10 10 n=fz/u 10' \",tyrt****«^^ 0 ^i^f^^,,,, i,,,. i,,., i..,. i.... i.... i,... i.... i,... i..,. i.,,, i,,,." 0 5 70 75 20 25 30 35 40 45 50 55 60 Time (min) Figure 4: As in Fig.2, but for the period 03-04 29 January 1994.
Air Pollution Modelling, Monitoring and Management 97 When gravity waves are excited at only one frequency, u- and v-spectra clearly display the different turbulent and wavy contribute (Nai-Ping & al/; Caughey *). In the w-spectrum, shown in Fig. 3, the wave subrange is apparent, although the depth of the gap between turbulence and wave is partially filled-up by power supplied by slope. In the wave-subrange eddies are quasi twodimensional and, as consequence, the power increment in the w-spectrum is usually low (Fig. 3). More frequently u- and v-spectra exhibit broad single or multiple secondary power peaks. In Fig. 4 the w-spectrum displays three peaks of energy with periods of about 20, 3 and 1 minutes, respectively. Oscillations with these periods are apparent also in the time record of longitudinal wind velocity, they could be interpreted in terms of waves spread to higher and lower frequencies by the interaction with turbulence. In some events, horizontal spectra display a well defined gap between the wave and turbulent energy maxima. These features seem to be forced by a low level jet that inhibits the inactive turbulence (Smedman et al/). As a matter of fact in the study case presented in Fig. 5 the wind velocity at 10 m was 4 m s~* and the time record of longitudinal velocity does not display any remarkable wave activity, whereas the sodar recorded a maximum speed of 20 m s~* at the height of about 150 m. But in our case the shear correlation coefficient (see next section) R^, = 0.35 differs from the value close to 0.5 reported by Smedman et ala It indicates that the momentum flux is not so strong as expected in such situations. 10 "5" 8 5 s 0 b) -1 3 0 1 1 1 1 1 1 1 1 1 1 1 0 5 10 15 20 25 30 35 40 45 50 55 60 Time (min) Figure 5: As in Fig.2, but for the period 01-02 30 January 1994.
98 Air Pollution Modelling, Monitoring and Management 5 Standard deviation of wind velocity components The measured longitudinal and lateral standard deviations of wind velocity, scaled by u^ and plotted as a function of, display largely spread distributions with sharply defined lower limits at 2.0 and 1.75, respectively. These limits do not change with in the range 0.001 < < 5. a / u^ behaves differently, the data are less scattered and distribute asymmetrically around a mean value increasing with stability. The lower limit of a /u^ distribution as well the mean value of a^/w^do not significatively change at the three measuring levels or for up- or down-slope flows. This behaviour means that the standard deviations, in the limit of flows not perturbed by the propagation of waves, vary according to u^ also on sloping terrain. This finding is in good agreement with wind tunnel data measured in neutral conditions over gently sloping hills (Khurshudyanetal.'O). 75 70». Jk ^. «_^ * &!L_ I I I I I 1 1 1 I I I I I I I 10* 2 10* 2 Z/Lr 10 0 Figure 6: Normalised standard deviation of longitudinal and vertical components vs stability. Bars represent the standard deviations of the mean for -R^ > 0.25 (o) and for -R^ < 0.25 ( + ). Dashed lines represent the constant mean values reported in Eq. (4). When the flow is affected by the propagation of waves, fluctuations associated to them contribute to increase both the horizontal and, to a lower extent, the vertical standard deviations, but they leave unaffected the turbulent
Air Pollution Modelling, Monitoring and Management 99 flux of momentum. These characteristics of flow are evidenced by considering the shear stress correlation coefficient -R^, = w'w'/cj^a^which, over a homogeneous andflatsurface when the SBL is not affected by waves, assumes values between 0.3-0.4 in a large stability range, according to results obtained in neutral conditions. -R^, is equal to about 0.5 when a low level jet is present and decreases down to very low values when the SBL is affected by the propagation of strong waves. On the base of these considerations, assuming as a threshold value -R^ = 0.25, measured standard deviations have been divided in two groups. Figure 6 displays the different behaviour of the mean value of (? /%» &nd o^/w* for the two groups (the lateral component, not shown here, behaves similarly to the longitudinal one). When -R^ > 0.25, the mean values of normalised standard deviations are nearly constant for any. It results that o,/w^=2.7 oju^=2.2 c*/w^=1.2 (4) These estimates are in good agreement with the ones, reported in literature, relative to near neutral conditions over homogeneous and flat surfaces. For -R^ < 0.25 the increasing a^*, /u^ with evidence the growing contribute by waves to standard deviations as stronger stable stratification is approached. In the horizontal plane waves can reach very large amplitudes and the amount of low frequency energy causes the grow of a / u.^ to arbitrarily large values (King**). In the vertical the increment of the standard deviation is lower becausefluctuationsare limited by the SBL depth. 6 Conclusions Even a gently sloping surface perturbs the turbulent structure of the SBL supplying energy, prevalently in the mid-frequency subrange, that shifts the turbulence power maximum towards lower frequencies. Although spectral analysis is useful to determine how and at what scales waves contribute to power spectrum, nevertheless it is not useful to separate wavy and turbulence amounts in the wind velocity standard deviations as the energy supplied by the slope forcingfillsup the gap between the two power maxima. Anyway the analysis of averaged quantities and the observation that, in the limit of no wave activity, normalised standard deviations vary according to momentum turbulent flux also on sloping terrain, allow to define a critical value of the shear stress correlation coefficient to separate wave and turbulent effects. We have set this value on the base of both empirical and theoretical arguments at 0.25. When flows are not affected by waves, a *, /u^ assume constant values, regardless of stability; otherwise they increase with stability as consequence of the growing waves. The knowledge of the mean profile of velocity standard deviations as a function of stability could be interesting for modelling pollutants dispersion in
100 Air Pollution Modelling, Monitoring and Management the SBL both as regards meandering of plumes and diffusion which seems to be affected by wave activity. This study should be extended to SBL over a variety of slopes and larger scale orographic features to get a more exhaustive quantification of their effects on the turbulence structure. We conclude recommending that slopes and larger scale boundary conditions, which trigger waves, should be taken into account in models formulation to explicitly represent their effect on surface layer characteristic parameters as well on the wind velocity standard deviations. Acknowledgements This study has been sponsored by PNRA (Italian Program for Antarctic Researches) and data analysis has been supported by the CNR Strategic Project MAP (Mesoscale Alpine Programme). References 1. McMillen, R.T. An eddy correlation technique with extended applicability to non-simple terrain, Boundary-Layer MeteoroL, 1988, 43, 231-245. 2. Brost, R.A. & Wyngaard, J.C. A model study of the stably stratified planetary boundary layer, /. Atmos. Sci., 1978, 35, 1427-1440. 3. Jenkins, G.M. & Watts, D.G. Spectral Analysis and its Applications, Holden-Day, Oackland, 1968 4. Andreas, E.L. Spectral measurements in a disturbed boundary layer over snow, /. Atmos. ScL, 1987, 44, 1912-1939. 5. Kaimal, J.C., Wyngaard, J.C., Izumi, Y. & Cote, O.R. Spectral characteristics of surface layer turbulence, Quart. J. R. Met. Soc., 1972, 98, 563-589. 6. Panofsky, H.A., Larko, D., Lipschutz, R., Stone, G., Bradley, E.F., Bowen, A.J. & Hojstrup, J. Spectra of velocity components over complex terrain, Quart. J. R. Met. Soc., 1982,108, 215-230. 7. Nai-Ping, L., Neff, W.D. & Kaimal, J.C. Wave and turbulence structure in a disturbed nocturnal inversion. Boundary-Layer MeteoroL, 1983, 26, 141-155. 8. Caughey, S.J. Boundary layer turbulence spectra in stable conditions, Boundary-Layer MeteoroL, 1977,11, 3-14. 9. Smedman, A.S., Bergstrom, H & Hogstrom, U. Spectra, variances and length scales in a marine stable boundary layer dominated by a low level jet, Boundary-Layer MeteoroL, 1995, 76, 211-232. 10. Khurshudyan, L.H., Snyder, W.H. & Nekrasov, I.V. Flow and Dispersion of Pollutants over Two-Dimensional Hills, US-EPA Report N EPA- 600/4/81/067, Research Triangle Park., NC, 1981. 11. King, J.C. Some measurements of turbulence over an antarctic ice shelf, Quart. J. R. Met. Soc., 1990,116, 379-400.