Investigations of Environmental Effects on Freeway Acoustics Final Report 605(1) Prepared by: H.J.S. Fernando Center for Environmental Fluid Dynamics, Arizona State University, Tempe, AZ 85287-9809 N.C. Ovenden Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K. S.R. Shaffer Center for Environmental Fluid Dynamics, Arizona State University, Tempe, AZ85287-9809 March 2010 Prepared for: Arizona Department of Transportation in cooperation with U.S. Department of Transportation Federal Highway Administration The contents of this report reflect the views of the authors who are responsible for the facts and the accuracy of the data presented herein. The contents do not necessarily reflect the official views or policies of the Arizona Department of Transportation or the Federal Highway Administration. This report does not constitute a standard, specification, or regulation. Trade or manufacturers’ names which may appear herein are cited only because they are considered essential to the objectives of the report. The U.S. Government and the State of Arizona do not endorse products or manufacturers. Research Center reports are available on the Arizona Department of Transportation’s internet site. Technical Report Documentation Page 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. FHWA-AZ-10-605(1) 4. Title and Subtitle 5. Report Date Investigations of Environmental Effects on Freeway Acoustics 6. Performing Organization Code 7. Author 8. Performing Organization Report No. March 2010 H.J.S. Fernando, N. Ovenden, S. Shaffer 9. Performing Organization Name and Address 10. Work Unit No. Arizona State University Office for Research & Sponsored Projects Administration P.O. Box 873503 Tempe, AZ 85287-3503 11. Contract or Grant No. SPR-PL-1(69)ITEM 605 12. Sponsoring Agency Name and Address 13.Type of Report & Period Covered Arizona Department of Transportation 206 S. 17th Avenue Phoenix, Arizona 85007 Final Report 05/04/2006 to 06/02/2008 14. Sponsoring Agency Code 15. Supplementary Notes Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration 16. Abstract The study reported here was designed to examine the impact of background meteorological conditions on the propagation of noise from urban freeways in the Phoenix area. The aim was to understand and predict how sound waves emanating from highways respond to the vertical profiles of atmospheric temperature gradients and velocity shear, so that sound measurements can be interpreted with regard to the environmental variability. Over the course of four days in late 2006 and two days in early 2007, field experiments were carried out at two freeway sites, where meteorological data and sound levels were measured and recorded from early morning until the middle of the day. Such periods span the stable, morning transitional and convective periods of the atmosphere. From the data collected, three test cases of varying atmospheric density stratification and wind shear are presented and discussed. These cases represent all measurement periods and were analyzed in detail. A parabolic equation model coupled to a Green’s function model close to the source field was developed and used to compute the refracted sound field for experimental cases up to half a mile from the freeway, permitting computations of noise exposure of residential areas nearby. The model demonstrates that atmospheric effects are able to raise sound levels by 10dB–20dB at significant distances from the highway, which at times led to exceeding acceptable limits imposed by Federal Highway Administration for residential areas. Mitigation strategies such as barriers and asphalt rubber friction course (ARFC) are also briefly discussed. 17. Key Words 18. Distribution Statement Noise propagation, meteorological effects, acoustic modeling, field studies, noise exposure, mitigation strategies, freeway noise Document is available to the U.S. public through the National Technical Information Service, Springfield, Virginia, 22161 19. Security Classification 21. No. of Pages Unclassified 20. Security Classification Unclassified 50 22. Price 23. Registrant's Seal inches feet yards miles in ft yd mi 3 milliliters liters cubic meters cubic meters 28.35 0.454 0.907 MASS grams kilograms megagrams (or “metric ton”) foot candles foot-Lamberts fc fl 10.76 3.426 ILLUMINATION 5(F-32)/9 or (F-32)/1.8 lux candela/m2 Celsius temperature 4.45 6.89 newtons kilopascals 2 C N kPa lx cd/m2 º g kg mg (or “t”) mL L m3 m3 mm m2 m2 ha km2 m m km mm Symbol C 2 N kPa lx cd/m2 º g kg mg mL L m3 m3 mm m2 m2 ha km2 m m km mm Symbol 0.035 2.205 1.102 MASS 0.034 0.264 35.315 1.308 VOLUME 0.0016 10.764 1.195 2.47 0.386 AREA 3.28 1.09 0.621 0.039 LENGTH Multiply By ounces pounds short tons (2000lb) fluid ounces gallons cubic feet cubic yards 0.0929 0.2919 ILLUMINATION 1.8C + 32 foot-candles foot-Lamberts Fahrenheit temperature newtons kilopascals 0.225 0.145 poundforce poundforce per square inch FORCE AND PRESSURE OR STRESS lux candela/m2 Celsius temperature feet yards miles inches To Find square inches square feet square yards acres square miles TEMPERATURE (exact) grams kilograms megagrams (or “metric ton”) milliliters liters Cubic meters Cubic meters Square millimeters Square meters Square meters hectares Square kilometers meters meters kilometers millimeters When You Know APPROXIMATE CONVERSIONS FROM SI UNITS SI is the symbol for the International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380 poundforce poundforce per square inch FORCE AND PRESSURE OR STRESS Fahrenheit temperature lbf lbf/in2 29.57 3.785 0.028 0.765 VOLUME meters meters kilometers millimeters To Find square millimeters square meters square meters hectares square kilometers TEMPERATURE (exact) ounces pounds short tons (2000lb) F º oz lb T fluid ounces gallons cubic feet cubic yards fl oz gal ft3 yd3 645.2 0.093 0.836 0.405 2.59 AREA 0.305 0.914 1.61 25.4 LENGTH Multiply By NOTE: Volumes greater than 1000L shall be shown in m . square inches square feet square yards acres square miles in ft2 yd2 ac mi2 2 When You Know Symbol APPROXIMATE CONVERSIONS TO SI UNITS SI* (MODERN METRIC) CONVERSION FACTORS F lbf lbf/in2 fc fl º oz lb T fl oz gal ft3 yd3 in2 ft2 yd2 ac mi2 ft yd mi in Symbol TABLE OF CONTENTS EXECUTIVE SUMMARY .................................................................................................1 I. INTRODUCTION ...........................................................................................................3 II. EXPERIMENTS ............................................................................................................7 III. MODELLING .............................................................................................................15 IV. CHOSEN TEST CASES AND MODELLING PARAMETERS ..............................19 Case A: Nov 7th 2006 (Rt 202) 11am .........................................................................20 Case B: Nov 7th 2006 (Rt 202) 8am ...........................................................................21 Case C: Nov 8th 2006 (Rt 202) 8am ...........................................................................22 V. ANALYSIS OF TRAFFIC SPECTRA TAKEN BY NOISE METERS .....................23 VI. CONSTRUCTION OF LEQ PLOTS ...........................................................................27 VII. CONCLUSIONS/FURTHER COMMENTS ............................................................37 REFERENCES ..................................................................................................................41 BIBLIOGRAPHY ..............................................................................................................44 LIST OF FIGURES FIGURE 1. MAP OF SITES 3D AND 3E ON THE METROPOLITAN PHOENIX FREEWAY SYSTEM ...............................................................8 FIGURE 2. LOCATION MAPS .........................................................................................9 FIGURE 3. LOCATION CROSS SECTIONS AND EXPERIMENTAL SETUP 202 ...10 FIGURE 4. LOCATION CROSS SECTIONS AND EXPERIMENTAL SETUP 101 ...11 FIGURE 5. INSTRUMENT IMAGES: SONICS, SODAR-RASS ..................................12 FIGURE 6. INSTRUMENT IMAGES: BALLOON-TETHERSONDE ..........................13 FIGURE 7. SCHEMATIC OF COMPUTATIONAL DOMAIN .....................................16 FIGURE 8. METEOROLOGICAL PROFILES: CASE A ..............................................20 FIGURE 9. METEOROLOGICAL PROFILES: CASE B ...............................................21 FIGURE 10. METEOROLOGICAL PROFILES: CASE C .............................................22 FIGURE 11. TIME DEPENDENCE OF LEQ DIFFERENCE 50 FT–100 FT .................23 FIGURE 12. MODELING SCHEMATIC: LINE SOURCE CONFIGURATION ..........24 FIGURE 13. MODELING SCHEMATIC: SOURCE HEIGHT CALCULATION ........25 FIGURE 14. CALCULATED SOURCE HEIGHT EXAMPLE ......................................25 FIGURE 15. CALCULATED SOURCE STRENGTH EXAMPLE ................................26 FIGURE 16. CASE A LEQ CONTOUR PLOT .................................................................28 FIGURE 17. CASE A LEQRANGE PLOT .......................................................................29 FIGURE 18. CASE A LEQRANGE VS FREQUENCY CONTOUR PLOT ....................30 FIGURE 19. CASE B LEQ CONTOUR PLOT .................................................................31 FIGURE 20. CASE B LEQRANGE PLOT .......................................................................32 FIGURE 21. CASE B LEQRANGE VS FREQUENCY CONTOUR PLOT ....................33 FIGURE 22. CASE C LEQ CONTOUR PLOT .................................................................34 FIGURE 23. CASE C LEQRANGE PLOT .......................................................................35 FIGURE 24. CASE C LEQRANGE VS FREQUENCY CONTOUR PLOT ....................36 FIGURE 25. EXAMPLE OF FLOW DISTORTION OVER BARRIERS ......................38 ACKNOWLEDGMENTS We are extremely grateful to Arizona Department of Transportation (ADOT), Arizona State University (ASU), and University College London (UCL) for their support of this ongoing collaborative research. In particular, we thank Christ Dimitroplos, Fred Garcia, and Lisa Anderson at ADOT for their interest and encouragement. The consultant Illingworth & Rodkin’s assistance in the project in measuring and processing the sound data is also gratefully acknowledged and we also thank Dragan Zajic, Leonard Montenegro, and Adam Christman for their help with the field experiments and subsequent data analysis. EXECUTIVE SUMMARY The study reported here was designed to examine the impact of background meteorological conditions on the propagation of noise from urban freeways in the Phoenix area. The aim was to understand and predict how sound waves emanating from highways respond to the vertical profiles of atmospheric temperature gradients and velocity shear, so that sound measurements can be interpreted with regard to the environmental variability. Over the course of four days in late 2006 and two days in early 2007, field experiments were carried out at two freeway sites, where meteorological data and sound levels were measured and recorded from early morning until the middle of the day. Such periods span the stable, morning transitional and convective periods of the atmosphere. From the data collected, three test cases of varying atmospheric density stratification and wind shear are presented and discussed. These cases represent all measurement periods and were analyzed in detail. A parabolic equation model coupled to a Green’s function model close to the source field was developed and used to compute the refracted sound field for experimental cases up to half a mile from the freeway, permitting computations of noise exposure of residential areas nearby. The model demonstrates that atmospheric effects are able to raise sound levels by 10dB–20dB at significant distances from the highway, which at times led to exceeding acceptable limits imposed by the Federal Highway Administration (FHWA) for residential areas. Mitigation strategies such as barriers and asphalt rubber friction courses (ARFC) are also briefly discussed. 1 2 I. INTRODUCTION Noise pollution is a serious and worsening environmental concern in urban areas. Not only does it diminish the quality of human life,1,2,3 but it also alters wildlife habitats.4 Highway traffic, airports, heavy industry, railways, and even leisure activities located close to builtup areas all contribute to the noise menace, and thus urban planners and managers pay close attention to mitigate it. This report concerns a study on a significant contributor to noise pollution in urban areas — freeway traffic noise — which varies considerably. The noise level depends upon a myriad of factors, such as ground conditions; terrain and the presence of sound barriers; temporal variations in traffic speed, volume, and vehicle types; and also spatiotemporal variation of meteorological variables such as temperature, wind velocity, and turbulence.5,6 While some of these factors are accounted for in operational sound prediction models, available operational models do not take all salient factors into account.7,8 For example, the latest version of the Federal Highway Administration's (FHWA) Traffic Noise Model (TNM)9 (Version 2.5 released in 2004) does not account for the effects of temperature and wind variability: uniform, isothermal atmospheric conditions are assumed in the calculations. The latter is a reasonable assumption for shorter (less than 650 ft (198 m) distances from the sound source, but errors can be substantial when predicting intermediate and far field noise. This drawback is of particular importance when refraction of sound due to temperature and wind causes anomalous intensity variations of sound at distance from the source. For example, noise measurements and analysis conducted in Scottsdale, Arizona, following complaints by residents living more than ¼ mile (about 400 m) from the eastern portion of Loop 101, suggest that ground-level inversions (surface stable temperature stratification) can increase the sound level by as much as 10 decibels to 15 decibels (dB).10 While the noise level under neutral atmospheric conditions is well within the Federal Highway Administration (FHWA) noise abatement criterion (NAC), an inversion can cause decibel levels to violate the standard. FHWA-NAC recommends implementing abatement procedures such as noise walls or modified pavement types (quiet pavements) when the energy averaged or equivalent sound level (Leq) approaches a value of 67 Aweighted decibels (dBA). (A-weighting is used to account for typical human sensitivity to various frequencies of absolute pressure fluctuations following ISO standard IEC 651 (1993-09) by applying a band-pass filter. Note that when referring to a difference in sound pressure levels, dB are interchangeable with dBA.) Such levels can be observed at some distance around certain Arizona freeways merely as a result of inversions and wind shear. The influence of atmospheric factors becomes particularly critical when noise mitigation is realized via a combination of techniques, for example, noise walls and quiet pavements. The Arizona Department of Transportation (ADOT) has received approval from the FHWA for the Quiet Pavement Pilot Program (QPPP) to investigate the usefulness of pavement-surface type as a noise mitigation strategy, subject to the condition that Arizona would be a pilot program with specific research objectives and requirements.40 This research is intended to validate the efficacy of asphalt rubber friction courses (ARFC) as a noise mitigation method. Over several years ADOT will overlay Portland cement concrete 3 pavement (PCCP) in metropolitan Phoenix with a 1-inch–thick ARFC surface. Where the ARFC is placed and noise walls are required, the walls may be reduced in height in view of the extra mitigation offered by ARFC surfacing.40 Sound barrier walls, also known as sound walls, are designed to protect the public and particularly the nearby residents against noise pollution, which is adverse sound level exposure that can lead to hearing loss, sleep disturbance, stress, and increased blood pressure. To decrease noise pollution effects, regulations have been instituted by governments. Such statutes in the United States include the U.S. National Environmental Policy Act, the Federal-Aid Highway Act, and the Noise Control Act of 1972. These acts have promoted decreased noise pollution, quantitative noise analyses, use of sound barrier walls, and city noise planning. A well-designed noise wall diffracts and reflects sound waves to optimize the attenuation of far field sound. To determine if sound barrier walls are effective, the sound is allowed to pass through or over the wall and the transmitted noise levels are gauged. When a 9dB reduction is reached, a sound barrier wall is considered adequate. Nine decibels lower in sound is equal to approximately a 90 percent drop in sound waves traveling past the wall. Beginning in 2003, ADOT has been monitoring six sites across the Phoenix metropolitan area for traffic-generated noise over a 10-year period to evaluate the effectiveness of ARFC. While measurements show that ARFC has reduced freeway noise appreciably (8dB–10dB) at close-in and community locations, sound refraction due to environmental conditions can defeat the noise abatement approaches (e.g., the use of walls) at some distances away. In such instances, noise walls would be of little help as a mitigation tool and, as noise walls are expensive, the merits of their installation should be carefully evaluated a priori. ARFC pavements, sound walls, and environmental factors become dominant only at certain intrinsic frequency ranges. The relationships between these variables and Aweighted noise levels in the field thus are intricate and can be delineated only via models that properly quantify fundamental relationships and their complex interactions. It is therefore important to develop scientific knowledge and tools to predict atmospheric effects on freeway noise that help evaluate alternative design options. Such tools will also help with interpretation of measurements taken at different positions and/or times and in placing results on a unified scientific basis (i.e., in terms of a certain base or standard state). The only viable method for predicting sound in complex field situations is the use of a numerical model that incorporates all governing factors, the straightforward (yet onerous) method in this context being nesting of an acoustic model with an environmental forecasting model. Such a modeling system is prohibitively computer intensive and so can be invoked only under very special circumstances. A simpler method is to use available representative atmospheric data from the area to feed the acoustic model, assuming local smaller scale variations are unimportant. The research reported here is of this type and includes a meteorological measurement component. This study’s aim was to examine how different meteorological conditions, especially ground-based inversions, can affect freeway noise under high-pressure, low-synoptic flow conditions prevalent in the desert Southwest.11,12 The study was particularly motivated by the Quiet Pavement Pilot 4 Program, where the noise reduction capabilities of the rubber friction course are being measured over a decade. To put results into a consistent framework, the meteorological effects need to be included in presenting the noise results. Although physical mechanisms underlying atmospheric sound propagation are well understood, the lack of both sufficiently detailed atmospheric data and computer models capable of incorporating them into an integrated formulation have hampered progress on modeling the impact of environmental effects on sound propagation. A review of literature suggests that: for downwind propagation, the magnitude of sound fluctuations increases with the frequency of the signal and with distance; for upwind propagation, the fluctuations are greatest near the shadow boundary; in a stable atmosphere (clear night, weak winds) the range of fluctuations is typically about 5dB, mainly due to the gravity waves and turbulence, but sound levels can be enhanced due to refraction at distances beyond ¼ mile (400 m); in an unstable atmosphere (clear sunny day, strong winds) the range of fluctuation is typically 15dB–20dB; the spectrum of fluctuations measured over open ground encompasses a range of frequencies that humans can hear from 50 Hz to above 3 kHz; and sound propagation from hilltop to hilltop and from air to ground is frequently characterized by large low-frequency fluctuations. A suite of computational approaches is being used for atmospheric sound propagation studies,5 which include: Gaussian beam methods — this is a variant of the classical ray tracing technique by solving the wave equation in the neighborhood of the conventional rays and associating a Gaussian amplitude profile normal to each ray. An approximate overall solution can then be constructed as a superposition of these so-called beams. Fast Field Program Models (FFP) — a semi-analytical method involving computation of the sound field in a horizontally layered homogeneous atmosphere in horizontal wave number domain, which is then inverted to the spatial domain using an inverse Fourier transform. Parabolic Equation (PE) models — a marching solution based on splitting the governing wave equations into left- and right-traveling components, originating at the source and capable of being ―perturbed‖ en route to account for topography, barriers, and turbulence. Ray theories, although robust for indoor acoustics, rapidly become highly cumbersome to compute in downward refracting media where many rays are needed and caustics are problematic. Additional complications, such as diffraction by obstacles, turbulence, and prediction of acoustic shadow regions, further urge the use of alternative methods. The key to PE models is the use of an effective sound speed based upon temperature and wind speed of the actual mean flow field, both of which modify the isotropic adiabatic sound speed.13,14 5 When assuming a line (or axisymmetric) source, the two-dimensional wave operator is factored into left- and right-traveling components transverse to the source. The pressure field due to a source can then be resolved in the domain by marching the solution numerically away from the source, while discounting any waves that propagate towards the source. Major disadvantages of this method are that it becomes inaccurate at high elevation angles and cannot directly account for back scatter unless the more difficult task of handling propagation in both directions is addressed. It has many advantages, however, including the ease of incorporating atmospheric absorption and varying boundary conditions and geometries, along with actual spatially varying meteorological profiles. Extensions that incorporate turbulence and flow details, such as over a barrier or rough terrain (e.g., large eddy simulations) have also begun to be incorporated into the scheme. For these reasons, methodologies based on the PE equation prove highly popular.15-21 The FFPs typically have a faster run time than their PE counterparts and can handle realistically complicated vertical atmospheric profiles. They can also account for the vectorial nature of the mean flow without requiring an ―effective‖ sound speed and are accurate at high elevation angles. However, the required Fourier transformation in the horizontal direction means that the model is restricted to homogeneous ground surfaces, with a flat topography containing at most a single and relatively simple topographical feature.22-27 It is common to use hybrids—models that combine several methods—to address aspects of the problem at hand in an attempt to circumvent potential drawbacks of any individual method.5, 28-32 In order to understand and quantify the effects of atmospheric temperature and velocity profiles on sound propagation, refraction, and diffraction, we have combined a field measurement campaign with modeling efforts. The field measurements are to provide realistic vertical profiles of temperature and cross wind velocities to the model and were performed over six days at two freeway sites in Scottsdale, Arizona, and Mesa, Arizona, where meteorological and sound data were taken and recorded over roughly a six-hour period between 6am and 12pm. For the modeling, the sound data is entered into a Green’s function model to evaluate the near source field generated from the freeway traffic. This source field, along with the meteorological data, is then input into a parabolic equation (PE) model to compute the refracted sound field out to a distance of 1968 ft (600 m). The results are compared to neutral atmospheric conditions; the effect of stratification and wind shear are separated and quantified in three 20-minute time-averaged cases selected from the field data. The outline of this report is as follows. The field experiments and equipment used are described in detail in Section II. Section III briefly outlines the acoustic propagation model. The selection of the three test cases to be entered into the model is presented in Section IV. The procedure of using sound measurements to construct a near-source field using a Green’s function model and calculated ground impedance is given in Section V. The evolution of the noise frequency spectra with range and the construction of overall Leq plots are then presented in Section VI. Finally, conclusions, recommendations to ADOT, and plans for future work are described in Section VII. 6 II. EXPERIMENTS To study the influence of meteorological conditions on noise propagation from Phoenix highways, the Center for Environmental Fluid Dynamics at Arizona State University (EFD-ASU) conducted a joint field campaign with ADOT and Illingworth & Rodkin, Inc. The EFD-ASU team provided detailed measurements of atmospheric meteorological conditions, while Illingworth & Rodkin, Inc. provided sound measurements. ADOT staff videotaped the traffic and recorded its speed. Field measurements were taken at two different sites along highways in the Phoenix metropolitan area. The sites are standard designated sites for ADOT, and the details of these sites are outlined in Saurenman et al.10 The first series of measurements was taken on October 10 and 11, 2006, on the west side of Loop 101 at milepost 47 (ADOT location site 3E). The second series was carried out on November 7 and 8, 2006, on the north side of Loop 202 (ADOT location 3D). The third series was on March 20 and 21, 2007, again at the Phoenix Loop 202 site. Figure 1 shows the location of the sites on the metropolitan Phoenix freeway system. Figure 2 shows maps of both locations with red dots indicating the approximate measurement sites. Both sites have a relatively flat homogeneous terrain (see cross-sectional profiles in Figures 3 and 4) with hard sandy soil and sparse bushes. However, away from the sites is complex topography that may alter the meteorological variables. Measurements were taken from 7am to 11am, and beginning at 6am for the two days in March, in order to better understand how noise levels change with atmospheric conditions. The earliest time for the start of the experiment was determined by the logistical constraints of the contractor. The goal was to obtain data during periods of temperature inversion, typical daytime adiabatic lapse conditions, and morning transition, covering representative periods of the months concerned. It is interesting to note that the temperature conditions near the surface were found to be unstable even in the early morning hours, and this is believed to be due to turbulent mixing and heat retention of the freeway surface. Further work is necessary to investigate such features. A number of instruments were employed, which included three-dimensional sonic anemometers, a meteorological balloon with tethersonde system, and a SODAR (SOund Detection And Ranging) with RASS (Radio Acoustic Sounding System) attachment. Sound measurement instruments were located at distances of 50 ft and 100 ft from the center of the nearest lane of the highway at the 3E site and 50 ft, 100 ft, and 250 ft (15.24 m, 30.48 m, and 76.2 m) from the center of the nearest lane at the 3D site. The sonic anemometers were located on towers at the same distance from the highway as the sound measurement instruments. Tethersonde and SODAR/RASS systems were located slightly further away to avoid contamination of sound-level measurements. Schematics of the cross-sectional area of the sites are given in Figures 3 and 4. Figure 5 has photographs of the instruments employed. 7 8 Figure 1. Map of Sites 3D and 3E on the Metropolitan Phoenix Freeway System Figure 2. Location maps for Loop 101 (top; location site 3E) and Loop 202 (bottom; location site 3D). The red dot indicates the approximate location of the measurement sites. 9 Figure 3.Cross section for Loop 202 location expressed as the elevation above sea level (ASL) (in feet). Horizontal distance is shown measured in feet from the fence on the north side. Positions of instruments are shown as squares for microphones, triangles and stars for sonic anemometers in November (top) and March (bottom), respectively. Arrows indicate horizontal distances of 50 ft, 100 ft, and 250 ft from the center of the nearest travel lane on the westbound (WB) side. 10 Figure 4. Location cross section for Loop 101 expressed as the elevation above sea level. Horizontal distance is shown measured in feet from the fence on the west side. Positions of instruments are shown as squares for microphones and triangles for sonic anemometers in the October 2006 field campaign. Arrows indicate horizontal distances of 50 ft and 100 ft from the center of the nearest travel lane on the southbound (SB) side. 11 Figure 5. Photographs of instruments deployed in the experiment. Two sonic anemometers on a short tripod on right side, and two microphones on the tripod in the left side of the picture, at Loop 202 in November 2006 (top); and the SODAR-RASS system at Loop 101 in October (bottom). 12 Figure 6.Photograph of the balloon-tethersonde system used at the Loop 101 site in October 2006. The balloon and tethersonde system is an important tool in atmospheric boundary-layer studies since it provides detailed profiles of wind speed, wind direction, temperature, air pressure, and humidity in the lower atmosphere. During the two days of field experiments in October, the balloon system shown in Figure 6 was deployed with a single tethersonde, thus providing profiles of temperature, wind speed and direction, and atmospheric pressure, and the data could be obtained up to 164 ft (50 m) above ground level (agl). The allowable height of balloon flights was determined by the FAA air traffic permit. However, due to problems with a malfunctioning sonde on the second day, the balloontethersonde system was used only during these two days of measurements. Also, during the first day, there was a period of stronger winds when the balloon was not used due to safety reasons. Comparison of sonic anemometer data located on the tower with those obtained by the balloon system show a good agreement, and hence the data from the sonic anemometers were used for velocity calculations when the balloon system was inoperative. 13 The sonic anemometers were operated at a frequency 10 Hz, providing all three velocity components (one in each dimension Ux, Uy, Uz) and temperature. The large frequency of measurements provided an opportunity to obtain information on mean flow and temperature close to the surface, as well as properties of the turbulence. The latter was used to calculate turbulence statistics, such as the root mean square for velocities and temperature, as well as for turbulent momentum and heat fluxes. The sonic anemometer placement is discussed below. (i) October 10 and 11 — two sonic anemometers were located on a tripod 50 ft (15.24 m) and three on a meteorological tower 100 ft (30.48 m) from the center line of the closest travel lane. The heights of instruments on the tripod were 5.9 ft and 9.5 ft (1.8 m and 2.9 m) agl and the heights of those on the tower were 6.6 ft, 13.2 ft and 19.7 ft (2 m, 4 m and 6 m) agl. (ii) November 7 and 8 — an additional tripod was also located closest to the highway 50 ft (15.24 m) where the heights of sonic anemometers were 5.9 ft and 9.5 ft (1.8 m and 2.9 m) agl, while sonic anemometers at the tower were placed at levels 22.3 ft, 34.1 ft and 45.3 ft (6.8 m, 10.4 m and 13.8 m) agl. On November 8, one more sonic was placed on a tripod at a location 250 ft (76.20 m) from the center of the near lane at 7.2 ft (2.2 m) agl in order to measure atmospheric conditions close to the farthest sound measurement point. (iii) March 20 and 21 — two towers were set up at distances of 50 ft and 100 ft (15.24 m and 30.48 m) from the center of the near lane. Two sonic anemometers were positioned at heights of 10.8 ft and 21.6 ft (3.30 m and 6.60 m) agl on the tower closest to the roadway, while three sonic anemometers at 12.4 ft, 25.1 ft and 34.1 ft (3.78 m, 7.65 m and 10.39 m) agl were used on the farthest tower. In some cases, the sonic anemometers did not work properly, and data from these periods were not included in the data set and subsequent analysis. The SODAR/RASS system was utilized to measure wind speed and temperature profiles between roughly 65 ft to 1968 ft (20 m to 600 m) agl. This system was used in order to provide more details on the structure of the atmospheric boundary layer at greater heights, but for the present study the most important were data near the lowest 328 ft (100 m) or so. 14 III. MODELING Based on sound data from field experiments provided by Illingworth & Rodkin, a twodimensional model can be constructed on acoustic propagation from a single monofrequency coherent line source in a vertically layered atmosphere. A rectangular xy coordinate system is used, with y measuring the vertical height and x measuring the horizontal range from the center line of the near lane of the highway. All lengths are nondimensionalized on a typical source height L0, velocities are non-dimensionalized on the sound speed measured at the ground level C0, density is non-dimensionalized on the density of air at 1 atmosphere (ρ0=1.2 kg m-3) and pressure p is non-dimensionalized on ρ0C02. For a given frequency f Hz, we define the Helmholtz number as ω=2π f L0/C0 and by writing the acoustic pressure perturbation as p(x,y,t)=pc(x,y)e-i ω t, the Helmholtz equation for a line source at x=x0 of strength S in a vertically layered atmosphere is obtained as 2 pc x2 c~ 2 ( y) pc 2 y c~ 2 ( y) y 2 2 pc c~ 2 ( y) S (x (1) x0 ). Here, is the non-dimensional effective sound speed, which includes the effects of both temperature and crosswind. Given a measured vertical temperature profile T(y) and crosswind speed profile U0(y), the effective sound speed is defined in a standard manner to be where γ is the ratio of specific heats and R is the ideal gas constant. The boundary conditions imposed are a far-field Sommerfield radiation condition as r becomes large, of the form x2 y2 (2) and an impedance boundary condition at the surface Throughout this report, the empirical impedance model of Delany and Bazley33 is used where, for a ground surface with flow resistivity σ [Pa s m-2], the impedance Z is given by (4) 15 Two models are used in tandem to compute the far-field sound propagation: (i) a near-field Green's function method assuming a homogeneous atmosphere and (ii) a parabolic equation approximation. Figure 7 shows the regions of the xy domain where each model is used. Figure 7. A schematic of the coupled models used to resolve the far-field propagation of traffic noise from a freeway corridor. The red dots represent monofrequency coherent effective line sources positioned above the center of the nearest lane of traffic. The near-field Green's function method34 is used to obtain the acoustic field in the vicinity of the line source where the refractive effects of atmospheric factors can be assumed to be negligible. In other words, the Green's function method assumes a constant %=1 and solves equations (1) to (3) with this assumption up to the effective sound speed c edge of the highway, at 22 ft (6.7 m), obtaining the sound field (5) where H0(1) is the zeroth order Hankel function of the first kind, and the term PZ(x,y;y0) represents the correction to the hard-wall solution for finite z. This correction is derived by Chandler-Wilde and Hothersall34 and is given in terms of 16 x 2 ( y y0 ) 2 , x 2 ( y y0 ) 2 ( y y0 ) / 1 a 1 Z Z 2 1/ 2 2 1/ 2 1 with the result PZ ( x, y; y 0 ) ei Z e s 1/ 2 e s g ( s / )ds 0 i (1 a ) 2 Z 2 erfc e i /4 a 1 where Z g(t)= 1 (1 it ) (t 2i )1/ 2 t 2 2i (1 / Z )t ( Z 1 )2 e i /4 a 2(1 Z 2 )1/ 2 (t ia ) The first integral expression is calculated using Gauss-Laguerre Quadrature and the second surface wave term (due to its strong exponential decay away from the ground) is evaluated using the formula given in Attenborough.35Assume over the near-field calculation, the ground impedance is typically of porous asphalt with σ = 3x107 Pa s m-2, which is given in Table 4.9 of Attenborough.6 The near-field Green's function model provides an acoustic field at the edge of the freeway pini(y)=pc(xedge,y), which is subsequently used as an initial condition for a twodimensional Cartesian variant of the standard axisymmetric parabolic equation (PE) model, first derived by Gilbert and White.13 The PE model used is the parabolic wide-angle approximation of (1) assuming a twodimensional line source. The pressure field is rewritten as pc(x,y)=ψ(x,y) eiωx and ψ(x,y) is obtained by solving the equation 1 x 4 2 i 2 2 1 ~2 c y x c~ 2 y 1 c~ 2 2 ~ c y 2 2 y 1 ~ c2 1 1 ~ c2 1 17 x . (6) The equation (6) and the impedance boundary condition (3) are finite-differenced and the solution is obtained by marching forward in the x direction. Sandy soil is taken to be the ground surface type beyond the freeway with σ = 4x105 Pa s m-2 and we assume the ground is completely flat to concentrate strictly on atmospheric effects in this study. The radiation condition (2) is dealt with numerically by a buffer zone14,36,37 occupying approximately the upper one third of the grid domain, yatt< y