Sound seed rofile structure and variability measured over flat terrain Bradley, SG, Waddington, DC and Von Hunerbein, S Title Authors Tye URL Published Date 6 Sound seed rofile structure and variability measured over flat terrain Bradley, SG, Waddington, DC and Von Hunerbein, S Conference or Worksho Item This version is available at: htt://usir.salford.ac.uk/9593/ USIR is a digital collection of the research outut of the University of Salford. Where coyright ermits, full text material held in the reository is made freely available online and can be read, downloaded and coied for non commercial rivate study or research uroses. Please check the manuscrit for any further coyright restrictions. For more information, including our olicy and submission rocedure, lease contact the Reository Team at: usir@salford.ac.uk.
SOUND SPEED PROFILE STRUCTURE AND VARIABILITY MEASURED OVER FLAT TERRAIN Stuart Bradley 1, Sabine von Hünerbein, and David Waddington 1 Physics Deartment, University of Auckland Private bag 919, Auckland, New Zealand Research Institute for the Built and Human Environment, University of Salford The Crescent, Salford M5 4WT, Greater Manchester, UK s.bradley@auckland.ac.n Abstract This aer describes a fundamental data base and data-variability guide for outdoor sound roagation models requiring sound seed rofiles. The vertical sound seed rofile has been measured directly over an extended eriod at a flat terrain site and to a height of 15m using a RASS (radio-acoustic sounding instrument). Additionally, vector wind rofiles were available at 1m height intervals from a SODAR (an acoustic radar), and carefully calibrated wind and temerature data recorded at a number of fixed sites on a 1m mast. Combinations of these data sources are used to evaluate a number of influences, which include: alicability of the log-linear aroximation; vertical variability of sound seed; change of wind direction with height; vector sound seed variability; effects of averaging intervals; short-term gust effects; longer-term diurnal effects; and fetch. These results demonstrate how variations in temerature, wind seed, and wind direction roagate through to sound seed rofile changes, and into fitted arameter changes, thereby roviding guidance on interretation of comarisons between model outut and roagation measurements. INTRODUCTION Sound roagation models are used extensively for urban lanning, traffic installations, and industry imact evaluations. These models tyically take source data which is estimated or known from rior measurements and redict the sound intensity field under various meteorological conditions. The main imact on roagation models by the meteorology is the rofile of sound seed with height. Since this rofile is unlikely to be measured throughout the model domain, or even above a single location, it must be estimated from meteorology either measured at the ground or redicted from a local-area meteorological model. Eds.: J. Eberhardsteiner, H.A. Mang, H. Waubke
Stuart Bradley, Sabine von Hünerbein, and David Waddington The function of the resent on-going work is to rovide guidance as to the quality of simle sound seed rofiles which are based on conventional, and limited, meteorological observations or exectations. In this aer we describe some initial results. The sound seed, c, deends on both (absolute) temerature, T, and wind seed U. For roagation in a direction making an angle φ with the direction the wind is flowing toward, c = ca + U cosφ (1) since most roagation aths of interest are at shallow angles to the ground [1]. The adiabatic sound seed, c a, is given by c a R = γ T () M where T is the absolute temerature of the air, R is the universal gas constant, γ is the ratio of secific heats for the air, and M is the molecular weight of the air. There is a very small influence on both γ and M due to water vaour. The question is: How well can T and U be estimated as a function of height based on simle observations or classifications of the weather? EXPECTED PROFILES OF SOUND SPEED Very near the surface, turbulent rocesses are most likely friction-dominated and further from the surface turbulent rocesses are more likely to be buoyancydominated. A useful length scale which is an estimator of the transition between these regimes is the Obhukov length 3 u Tρc L = (3) κgh where ρ is the air density, c is the secific heat of air at constant ressure, H is the sensible heat flux at the surface, T is the air temerature near the surface, u is called the frictional velocity, κ =.4 is von Karman s constant, and g is the acceleration due to gravity. For a stable atmoshere (in which air dislaced vertically returns to its original osition), L>, and L< for an unstable atmoshere. The Monin-Obukhov similarity theory ostulates that the shaes of the rofiles of U and otential temerature Θ are functions only of the dimensionless buoyancy arameter /L. The Businger-Dyer relations are emirical rofiles based on a large body of meteorological data. A modification of these rofiles gives = u U ln + 5 for κ L L (4a)
ICSV13, July -6, 6, Vienna, Austria u 1 1 1 + x + x π U = ln ln + tan for < x (4b) κ L where x = 1 15 L 1 4 and is the roughness length which is related to the sie of the individual features rotruding from the surface. Excet above forest and urban canoies <.1 m. Although the unstable case has a more comlex deendence on, logarithmic rofiles of the form U = a + a + a ln( ) (5) 1 3 aly aroximately in all cases (see Fig. 1). For otential temerature θ Θ = Θ + ln + 5 for (6a) κ L L θ 1+ x Θ = Θ + ln ln for < (6b) κ L H where θ = and Θ is effectively the otential temerature at height. The ρc u temerature rofile is related to the rofile of the otential temerature through T = g c T Θ + Θ (7) but for sound rofiles near the surface T g c Θ +. (8) Therefore θ g T = T + ln 5 for + κ L c L (9a) θ 1+ x g T = T + ln ln for κ <. c L (9b) Again, both rofiles are closely aroximated by a rofile of the form c a = b + b + b ln( ). 1 3
Stuart Bradley, Sabine von Hünerbein, and David Waddington The combination of temerature variation and wind seed variation with height means that the sound seed rofile can be exected to vary in a log-linear form with height. This conclusion is based on emirical evidence from meteorological data collected in relatively unchanging conditions over level terrain at numerous sites. In ractice, the situation might be more comlicated because of temoral variations or because the surface conditions over which the wind is blowing are changing. This is the focus of the current work. 3..5 Scaled height. 1.5 1..5. 1 3 Scaled wind seed 4 Figure 1. Log-linear variation of scaled wind seed κu/u * with scaled height /L for =.5m. Unstable atmoshere (dots); log-lin fit (dashed line); stable atmoshere (solid line). In fact, even the similarity-based behaviour of the fitted coefficients b 1, b, and b 3 is quite comlex, as shown in Fig.. REMOTE ATMOSPHERIC PROFILING METHODOLOGY It is generally quite difficult to obtain rofiles of the actual sound seed for use in model validations. However, a combination of SODAR and RASS instruments rovides such a rofile. A RASS sends a ulse of sound vertically and uses a microwave transmitter and receiver to obtain reflections off the uward-roagating sound wave. Suitable design gives a real-time vertical rofile of c a : this is a direct measurement of how quickly the sound roagates uward. A SODAR sends a ulse of sound uward slightly off-vertical. Echo signals are received from scattering by turbulence and the Doler shift gives the radial wind seed comonent. By suitable choice of three acoustic beam directions, the three vector comonents of the wind can
ICSV13, July -6, 6, Vienna, Austria be obtained tyically every 1 m u to a height of more than 1 m. The combination of RASS and SODAR therefore gives c estimates every 1 m or so, but of course with measurement errors. Log-lin coefficients 5 4 3 1-1 - -3-4 -5-5 -4-3 - -1 1 3 4 5 1/L Figure. Predicted behaviour of log-lin coefficients as the atmoshere varies from unstable through neutral to stable conditions. Coefficients b 1 -c (dark line), b (dashed line), and b 3 (light line). During the WISE EU Project [], the Profiler Inter-comarison Exeriment (PIE) involved very careful measurements of wind seed made with Metek, AeroVironment, and Scintec SODARs in comarison with a 1 m instrumented tower at Hovsoere in Denmark. A Metek RASS was also used to record vertical rofiles of temerature, obtained through the relationshi between c a and T. Because of the careful validation of the remotely-sensed database, this exeriment rovides a articularly good source of sound seed data under a range of meteorological conditions over a flat terrain site. Here we concentrate on data recorded with the Metek PCS-64 SODAR with the Metek 19MH RASS. The test site is the National Danish Test Station for Large Wind Turbines situated in the northwest of Denmark close to the North Sea. The test site is flat, surrounded by grassland, with no major obstacles in the immediate neighbourhood and at a distance of 1.7 km from the west coast of Denmark. The revailing wind direction is from the west. Reliable measurements were recorded from 1/4/4 until /8/4.
Stuart Bradley, Sabine von Hünerbein, and David Waddington FITTING LOG-LINEAR PROFILES TO MEASURED DATA Central to the current work is the fitting of the arameters b 1, b, and b 3 to measured data and also considering the associated uncertainties in the fitted arameters. Since the log-lin rofile is linear in its arameters, conventional linear least-squares fitting can be used. SODAR measurement errors generally increase with height because of the sherical sreading of the signal and greater influence of the background acoustic noise in the Doler shift determination. However, for the low heights considered for most outdoor sound roagation, the quality of the Doler sectrum eak estimation is generally very good, so we will not consider weighted least-squares at this stage. The arameters are estimated in the usual least-squares manner, using basis functions of 1, /, and ln(/ ) for the model U = b1 + b + b3 ln( ). The errors in the arameters can also be estimated a riori by going through the least-squares methodology and aroximating the various sums by integrals over from to the uer measurement height m. This gives b 1 b b 3 4 N U 48 N 4 N U ln U m m 5ln m + 7 (1) where N is the number of heights at which U is measured, and U is the variance in U measurement. From this the variance in U can be estimated when a log-lin rofile is used. As an initial case study, 33 measured rofiles of U and T were fitted with the log-lin rofile model. Fig. 3 shows all rofiles. There is generally a maximum around 7m. This may be due to a static echo from the instrumented mast, which is at about this distance. On the other hand the rofiles are consistently monotonically increasing to this height and also decrease beyond this height. When least-squares fitting is erformed, the residuals shown in Fig. 4 are obtained. Here we have fitted both a log rofiles and a log-lin rofile for comarison. It can be seen that the log-lin residuals are smaller (closer to ero). Also shown are the standard deviations in residuals, which give a measure of measure and fitting variability. The errors in the sound seed gradient are found to be greatest near the ground: if weighted least-squares fitting is used, with weighting decreasing with height, this conclusion may change.
ICSV13, July -6, 6, Vienna, Austria 11 Comosite of all sound seed rofiles 1 9 8 Height [m] 7 6 5 4 3 336 338 34 34 344 346 348 Sound seed [m/s] 11 1 Figure 3. A comosite of all rofiles in the case study. Residuals for sound seed rofile fits [m/s] Residuals for log-lin fit Residuals for log fit 9 8 Height [m] 7 6 5 4 3-4 -3 - -1 1 3 4 5 (Sound seed)-(fitted seed) [m/s] Figure 4. Mean residuals in fitting sound seed rofiles, and variability in the residuals.
Stuart Bradley, Sabine von Hünerbein, and David Waddington 11 1 Rms error for sound seed gradient [1/s] log-lin fit log fit 9 8 Height [m] 7 6 5 4 3..4.6.8.1.1.14 Rms error in gradient of adiabatic sound seed [1/s] Figure 5. The rms error in the sound seed gradient, based on the errors in fitted sound seed rofile. SUMMARY In this work we are seeking to answer a number of questions: alicability of the loglinear aroximation; vertical variability of sound seed; change of wind direction with height; vector sound seed variability; effects of averaging intervals; short-term gust effects; longer-term diurnal effects; and influence of fetch. The material above gives a first introduction to the aroach taken, the data set available, and some early results on a very limited case study of 33 rofiles. Given that rofiles are obtained every few seconds, and data were recorded for over four months, there is a very large dataset available for addressing the questions listed above. REFERENCES [1] Ostashev, V. E. Acoustics in moving inhomogeneous media. (E & FN SPON, London, 1997). [] Bradley, S. G. (ed), Antoniou, I., von Hünerbein, S., Kindler, D., de Noord, M., H. E. Jorgensen. SODAR calibration for wind energy alications. WP3 Final Reort (EU WISE roject NNE5-1-97. 69, 5).