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HomeMy WebLinkAboutItem 6.1.k - 11. Public Correspondence1 Amy Million To:Martha Battaglia Subject:FW: VCC RedDot-Green Dot From: Norm <norm.lewandowski@att.net>   Sent: Friday, September 21, 2018 3:51 PM  To: David Haubert <David.Haubert@dublin.ca.gov>; Melissa Hernandez <Melissa.Hernandez@dublin.ca.gov>; Abe  Gupta <Abe.Gupta@dublin.ca.gov>; Arun Goel <Arun.Goel@dublin.ca.gov>; Janine Thalblum  <Janine.Thalblum@dublin.ca.gov>  Cc: Luke Sims <Luke.Sims@dublin.ca.gov>; Amy Million <Amy.Million@dublin.ca.gov>; Chris Foss  <Chris.Foss@dublin.ca.gov>  Subject: Fwd: VCC RedDot‐Green Dot      Dear Mayor and City Council Members, What do Red Dots / Green Dots have to do with Valley Christian Proposal ? Attached are 2 visual calendar year charts showing the scope of activities that are planned and documented in the Valley Christian Center (VCC) Supplemental EIR Report as well as Environmental Noise assessment report. RED DOTS: Amplified Sound or option for Amplified Sound - Athletic Stadium 50 events, Amphitheater 58 events. Total 108 GREEN DOTS: No plans for sound but does not state clearly that amplified sound cannot be used – 142 practice games, 100 lectures. Total 242 The data shown in the Supplemental EIR is very specific on the months, days and times for all the sports activities including games & practice as well as the amphitheater events and whether their will be amplified sound. The number of possible activities are very alarming. From school lectures during day to bible study lectures in evenings to church sermons on Sunday to theatrical plays in summer and to all the sports practices and actual games accounts for an unbelievable amount of activities. The noise will be heard from morning to evening almost every day of the year. This is a far cry from Valley Christian’s presentation to the Planning Commission and the neighborhood having 6-9 football games and some soccer and track games. We can literally hear people talking on top of VCC property from 500 -1000 feet away when the wind carries it our way. How are we supposed to live with this much activity with amplified sound or not…we will hear it loud and clear….morning, afternoon, evening and weekends. What we don’t want is VCC building a stadium right over our roof tops and everyone expect that this is going to be ok with us. Why not build it towards the back of the property where the athletic fields already exist and farther away from the neighborhood. 2 There is hardly any protection for the neighborhood in this Supplemental EIR Document. It is mostly left up to self monitoring by VCC. Without a valid noise study for this specific location taking into consideration wind, atmospheres and topography….no one has any idea of the noise impact on the neighborhood. HELP ! PLEASE HELP ! Distressed Resident of Dublin, Norm Lewandowski   3 September 25, 2018 VIA E-MAIL: council@dublin.ca.gov Dublin City Council 100 Civic Plaza Dublin, CA 94568 RE: Valley Christian Center Planned Development Zoning Amendment and Site Development Review Permit (PLPA-2014-00052) for the Project site located at 7500 Inspiration Drive. Dear City Council Members: I have a bachelor’s in science, Business Administration, emphasis in Finance and Real Estate Management, furthermore I am a Realtor and member of Bay East Association of Realtors for the past 12 years and I am in excellent standing. In addition, my primary residence is located just bellow Valley Christian Center, approximately 300 feet away. I am writing to you regarding my concerns over the Valley Christian Center’s (VCC) plans to develop a stadium. The increased of noise levels will have a negative impact in the value of my neighborhood as follows: Location, Location, Location: Hacienda Height’s Neighborhood will no longer be the Location of choice in West Dublin once this stadium is built. We, the sellers will have to Disclose all the negative aspects and material facts that will impact the value of our properties which will include noise, light, and traffic. Disclosures should be given if approved, beginning today, during, and after the stadium is built. The disclosures for the seller include: Seller Property Questionnaire: - Material Facts or defect affecting the property not otherwise disclosed to buyer. - Problems with pests on or in the property – rats due to construction - Neighborhood: Neighborhood noises, nuisance or other problems from sources such as, but not limited to the following: Neighbors, traffic, schools, sporting events, construction. - Other: Any past or present known material facts or other significant items affecting the value or desirability of the property not otherwise disclosed to buyer. Real Estate Transfer Disclosure Statement: - Are you (Seller) aware of any of the following: - Neighborhood noise problems or other nuisances – If yes: explain. You can attach or provide a link. Disclosure Information Advisory: - Consider all issues, condition or problems that impact your property, even those that are not necessarily on your property but are related to a neighbor’s property or exist in the neighborhood (such as noise, smells, disputes with neighbors, or other nuisances). Exempt Seller Disclosure: - Seller who are not legally required to complete a Transfer Disclosure Statement can use this form to make other required disclosures. Including the disclosure of material facts affecting the property not otherwise disclosure to buyers of which they are aware. After disclosing all the material facts that are required to be given to Buyers, the Buyer will select another neighborhood away from this location and our properties will no longer be the location of choice. It will take longer time to sell, thus causing financial hardship on us – especially, if we are buying another property on a contingency basis. Furthermore, once a neighbor sells at a lower price than the comparable homes due to the noise issues from the proposed sport stadium all our homes will immediately lose value. Please note: our neighborhood consists of 80% of homeowners over 55 years of age and close to retirement with no minors living at home and 20% homeowners with small children living at home. Which means that we spend more time enjoying our peaceful and quiet neighborhood. Once our property values decrease, we will have less buying power to relocate. Per my experience, whenever few people gather on the hill above our home (edge of parking lot of Valley Christian Center) to enjoy the view of Dublin, smoke cigarettes, listening to music, etc. we can see these young people from our living room, hear clear conversations and laughter. I can imagine all the noise that people will make before, during, and after the planned sport events till 10pm weekdays and weekends. In conclusion, I am asking for the City Council to not approve the project as submitted based upon potential loss of property values due to material facts affecting our properties. The Sporting events will be too noisy, we will no longer enjoy our peaceful and quiet neighborhood. Sincerely, Luz Marina Cablas, Realtor® BRE # 01763534 7437 Las Palmas Way Dublin, CA 94568 Cc: Martha Battaglia, via email: martha.battaglia@dublin.ca.gov Chris Foss, via email: chris.foss@dublin.ca.gov Luke Sims, via email: luke.sims@dublin.ca.gov Caroline P. Soto, via email: caroline.soto@dublin.ca.gov September 26, 2018 VIA EMAIL and HAND DELIVERY Mayor and City Council Members City of Dublin 100 Civic Plaza Dublin, CA 94568 Email: david.haubert@dublin.ca.gov; melissa.hernandez@dublin.ca.gov; abe.gupta@dublin.ca.gov; arun.goel@dublin.ca.gov; janine.thalblum@dublin.ca.gov Martha Battaglia Associate Planner City of Dublin 100 Civic Plaza Dublin, CA 94569 Email: martha.battaglia@dublin.ca.gov RE: Valley Christian Center Planned Development Zoning Amendment and Site Development Review Permit (PLPA-2014-00052) for the Project site located at 7500 Inspiration Drive (“Project”) – CEQA Compliance Dear Mayor Haubert, Honorable Members of the City Council and Ms. Battaglia: These comments are submitted on behalf of the Concerned Citizens of West Dublin regarding the above referenced Project. We are concerned about the environmental impacts of the proposed Project, particularly those associated with noise pollution. We object to Project on the grounds that the Initial Study/Supplemental Mitigated Negative Declaration (“IS/Supplemental MND”) fails to meet the minimum legal requirements as set forth in the California Environmental Quality Act (“CEQA”), Public Resources Code, Section 21000 et. seq. We reviewed the IS/Supplemental MND, City’s Staff Report and other plans with the help of our technical consultants, including Saxelby Acoustics which we engaged for an initial expert opinion. Their attached technical comments are submitted in addition to the comments in this letter. We have identified a number of significant deficiencies in Illingworth & Rodkin, Inc.’s (“I&R”) environmental noise assessment report (“I&R Report”) prepared on behalf of the City of Dublin (“City”), as well as additional, more severe impacts that were neglected or otherwise not identified, included and/or assessed in the IS/Supplemental MND. Therefore, the City lacks substantial evidence to support the conclusions in the IS/Supplemental MND and an EIR is required. I. The IS/Supplemental MND Fails to Adequately Analyze and Mitigate Noise Impact As case law has shown, compliance with applicable regulations does not automatically obviate the need for further analysis of impacts at this pre-approval stage of the Project. In Keep our Mountains Quiet v. County of Santa Clara, (2015) 236 Cal.App.4th 714, neighbors of a wedding venue sued over the County’s City of Dublin September 26, 2018 Page 2 failure to prepare an EIR due to significant noise impacts. The court concluded that “a fair argument [exists] that the Project may have a significant environmental noise impact” and reasoned that although the noise levels would likely comply with local noise standards, “compliance with the ordinance does not foreclose the possibility of significant noise impacts.” The court ordered the County to prepare an EIR. The ruling demonstrates the possibility that a project may be in compliance with an applicable regulation and still have a significant impact. In Communities for a Better Env’t v. California Res. Agency, (2002) 126 Cal.Rprt.2d 441, 453, the court struck down a CEQA Guideline because it “impermissibly allow[ed] an agency to find a cumulative effect insignificant based on a project's compliance with some generalized plan rather than on the project's actual environmental impacts.” The court concluded that “[i]f there is substantial evidence that the possible effects of a particular project are still cumulatively considerable notwithstanding that the project complies with the specified plan or mitigation program addressing the cumulative problem, an EIR must be prepared for the project.” Thus, the ruling supports the notion that despite assured compliance with applicable standard outside of the CEQA process, a lead agency still has an obligation to consider substantial evidence and analyze and mitigate potentially significant impacts. In Leonoff v. Monterey County Bd. of Supervisors, (1990) 222 Cal.App.3d 1337, 1355, the court held that conditions requiring compliance with regulations are proper “where the public agency had meaningful information reasonably justifying an expectation of mitigation of environmental effects.” The ruling suggests that an agency that merely provides a bare assertion that the project will be in compliance with applicable regulations, without further explanation or enforceability, may not fulfill the requirements of CEQA. In our case, the City failed to provide information explaining how compliance with the outside laws and regulations would reduce the risks posed to nearby residents from the elevated noise levels emanating from the Project’s proposed site. The City may not rely solely on compliance with regulations or laws as reducing impacts without a full analysis of impacts or enforceable mitigation. Furthermore, reliance on the Environmental Impact Report (“EIR”) dating back to 2003 is improper because the referenced EIR did not include substantial changes made to the proposed development plan, substantial changes in circumstances, and/or new information, any of which would have resulted in a new EIR. CEQA requires that the City describe all components of the Project that may have a significant impact, and adequately analyze and require mitigation for all potentially significant impacts. Here, the City failed to do so in its IS/Supplemental MND. II. Fair Argument Standard CEQA requires that an agency prepare an EIR for any project that may have a significant effect on the environment. (Pub. Resources Code § 21151(a).) An agency must prepare an EIR whenever substantial evidence in the record supports a fair argument that a project may have a significant effect on the environment. (Pub. Resources Code, §§ 21080(a); 21151(a); see Laurel Heights Improvement Ass’n v. Regents of the Univ. of Cal. (1993) 6 Cal.4th 1112, 1123.) “In reviewing an agency’s decision to adopt a negative declaration, a trial court applies the ‘fair argument’ test.” (City of Redlands v. County of San Bernardino (2002) 96 Cal.App.4th 398, 405.) The fair argument test requires that an agency “prepare an EIR whenever substantial evidence in the record supports a fair argument that a proposed project may City of Dublin September 26, 2018 Page 3 have a significant effect on the environment.” (City of Redlands, supra, 96 Cal.App.4th at p. 405: quoting Gentry v. City of Murrieta (1995) 36 Cal.App.4th at pp. 1399-1400.) If such evidence exists, the court must set aside the agency’s decision to adopt a negative declaration as an abuse of discretion in failing to proceed in a manner as required by law. (City of Redlands, supra, 36 Cal. App.4th at p. 406). The ‘fair argument’ standard is “a low threshold requirement for preparation of an EIR.” (No Oil, Inc. v. City of Los Angeles (1975) 13 Cal.3d 68, 84.) The fair argument standard reflects CEQA’s “preference for resolving doubt in favor of environmental review.” (Sierra Club v. County of Sonoma (1992) 6 Cal.App.4th 1307, 1316-1317.) Thus, an EIR must be prepared “whenever it can be fairly argued on the basis of substantial evidence that the project may have significant environmental impact” (No Oil, Inc. v. City of Los Angeles, supra, 13 Cal.3d at p. 75). CEQA defines “environment” as “the physical conditions which exist within the area which will be affected by a proposed project, including land, air, water, …noise….” (Pub. Resources Code § 21060.5.). “Significant effect upon the environment” is described as “a substantial or potentially substantial adverse change in the environment.” (Pub. Resources Code § 21068; CEQA Guidelines § 15382.) A project may have a significant effect on the environment if there is a reasonable probability that it will result in a significant impact. (No Oil, Inc. v. City of Los Angeles, supra, 13 Cal.3d at p.83.) Even if the overall effect of the project is beneficial, the lead agency must prepare an EIR if any part of the project “either individually or cumulatively, may cause a significant effect on the environment.” (CEQA Guidelines § 15063(b)(1).) III. Substantial Evidence Supports a “Fair Argument” that the City Must Prepare an EIR CEQA and the CEQA Guidelines provide assistance in evaluating what constitutes substantial evidence to support a ‘fair argument.’ (See CEQA Guidelines § 15384(a) (“’substantial evidence’ means enough relevant information and reasonable inferences … that a fair argument can be made to support a conclusion, even though other conclusions might also be reached.”).) Substantial evidence consists of “fact, a reasonable assumption predicated upon fact, or expert opinion supported by fact.” (Pub. Resources Code § 21080(e)(1); CEQA Guidelines § 15384(b).) Comments that present evidence of facts and reasonable assumptions from those facts may constitute substantial evidence to support fair argument that the project may have a significant effect on the environment. (City of Redlands, supra, 96 Cal.App.4th at p. 590; Stanislaus Audubon Society, Inc. v. County of Stanislaus, (1995) 33 Cal.App.4th 144, 152-153.) The individual members of the Concerned Citizens of West Dublin live, work, and raise their families in the City of Dublin and most of them live in very close proximity to the Project’s proposed site. They will therefore be first in line to be exposed to any noise impact created on the Project site and would be directly affected by the Project’s various impacts. As area residents, their relevant personal observations on nontechnical subjects may qualify as substantial evidence for a fair argument. (See Ocean View Estates Homeowner’s Assn., Inc. v. Montecito Water District (2004) 116 Cal.App.4th 396, 402.) As for the relevant personal observations of area residents, see the attached letters. Concerned Citizens of West Dublin submitted comments to the City on the Project and by declaration and letter. Their statements on noise impact constitute substantial evidence supporting a fair argument in numerous areas. The City must review and consider all such comments as “relevant personal City of Dublin September 26, 2018 Page 4 observations of area residents on nontechnical subjects may qualify as substantial evidence.” (Pocket Protectors v. City of Sacramento (2004) 124 Cal.App.4th 903, 928.) The I&R Report is faulty or otherwise inadequate as previously asserted by two PhD Physicists Dr. Rongfu Xiao (who has written 50 U.S. patents, one of which is about sound insulation) and Dr. Bruce Remington (who is a Senior Scientist and Distinguished Member of the Technical Staff at the Lawrence Livermore National Laboratory, a Fellow of the American Physical Society, and author/coauthor of over 400 papers published in the scientific literature) in their letters to the City, dated September 5, 2018 and September 3, 2018, respectively. The attached report prepared by Saxelby Acoustics dated September 17, 2018 (“Saxelby Report”) states that “Project-related noise levels are likely to be more than twice as loud as that concluded in the I&R Report.” Based on the I&R Report, it appears that I&R performed a noise monitoring survey during a six (6) day period in May 2015. The I&R Report fails to take into consideration numerous material acoustical factors or completely ignores them as follows: 1) The strength of the wind in May (low wind season) is very different than the strength of the wind in September, October and November (strong and steady westerly winds blowing from the Project site towards neighboring areas), which are the months when the Project site will be heavily utilized with sound amplification. Hence if I&R were to do the noise assessment test during strong westerly wind season, the results would be substantially different. 2) The sound reaching the neighborhoods on the eastern side of the Project site will be enhanced by (a) the westerly winds, (b) refraction which bends the sound waves back towards the ground, and (c) reflections off the homes that bound the streets, the pavement, and the sidewalks, all of which could create a wind tunnel like effect directing the sound down the streets, as opposed to dispersing in all directions. The I&R Report accounts for sound attenuation due to distance and topography, based on measurements done on a flat, open, grassy field, [which is quite the opposite of the conditions in the affected neighborhoods) and concludes that the increased noise level from the project would be up to 1 dB. This analysis fails to consider the effects of wind, refraction, pavement (vs grassy field) and streets bounded by homes, which could result in sound traveling much further into the surrounding neighborhoods than was considered in the I&R Report. Neither a realistic analysis of these effects nor appropriate and representative measurements in the neighborhoods were made by I&R. Our initial estimates, based on the relevant published scientific literature (copies of which are attached to the aforementioned Remington letter), suggest that the noise level increase on the downwind side could be up to ~10 dB or more due only to the westerly winds. The aforementioned “wind tunnel effects” could increase this estimate even more. This could enhance by a factor of 10 or more the 1 dB noise estimate given in the I&R Report. 3) The noise test was done in a blind-spot chosen by I&R so that such blind-spot would fit the data into I&R’s model. The IS/Supplemental MND states “LT-1 represented the existing noise environment near the location of the proposed multi-purpose recreation field" and LT2 "represented the noise-sensitive receptors." In other words, LT1 represents the noise source during a future football game and LT2 represents the noise level that would be heard in the surrounding neighborhood. Dr. Xiao recently made his own sound measurements near the Project City of Dublin September 26, 2018 Page 5 site and observed that some of the measurements done by I&R were in locations that corresponded to sound “blind spots,” meaning that the sound levels were unrepresentatively low. He subsequently re-did the measurements in neighborhood driveways and found an average baseline noise level of about 60 dB, which is higher than the 40-42 dB given in Table 7 in the I&R Report. Hence, I&R provided non-representative data to the City by putting (either intentionally or through lack of due diligence) a sound sensor in a quiet spot (i.e., “blind spot”) so that it can pass the City’s noise standard. 4) The I&R Report lacks consideration of the “hilltop effect” on sound propagation due to the source (i.e., the Project site) being on the top of the hill, overlooking the surrounding neighborhoods. The sound propagates further when it is less dissipated by interactions with the ground. Established scientific theory substantiates this ground dissipation effect. I&R made a noise level projection for the Project site by choosing Santa Teresa High School (“STH”) for its calibration measurement, which is located on flat land. I&R’s choice of a flat grassy venue to conduct a noise assessment test for a venue located on a hilltop overlooking the neighborhood is very non-representative, as the Project site (sitting 100-200 feet above the surrounding areas, enhancing the distance that noise produced at the Project site could propagate into such areas with the wind tunnel effect) has a very different micro-climate as compared with the STH (with still-air, and flat grassy field). There is a possibility that the noise increase generated by the utilization of the Project site will exceed the City’s noise impact threshold of significance, hence it is entirely possible that a significant adverse noise impact could result from the Project, as set forth in the Saxelby Report. I&R’s failure to utilize an industry standard acoustic analysis which would take into consideration of the points listed above (among other factors) and instead choosing to do manual calculations for an environmental noise assessment test would inevitably produce flawed analysis. Alternatively, a thorough and complete set of experimental measurements in the affected neighborhoods should have been taken. The aforementioned measurements taken by Dr. Xaio experimentally show the level to which the results provided by I&R are flawed and deficient. The Saxelby Report, Xiao and Remington comments, and other attached letters based on relevant personal observations of area residents, provide a reasonable basis to challenge the adequacy of the IS/Supplemental MND and include substantial evidence that supports a fair argument that the Project may result in a significant adverse noise impact. As discussed in the Saxelby Report, and in other comment letters submitted to the City, the IS/Supplemental MND fails to provide an adequate analysis of the Project’s noise impacts. To the extent that the IS/Supplemental MND discussed the Project’s noise impacts, the Saxelby Report, Xiao and Remington comments, and other nontechnical comment letters, constitute substantial evidence supporting a fair argument that the Project has significant adverse environmental impacts that have not been mitigated. Thus, CEQA mandates that the City prepare and certify a legally adequate EIR that addresses and mitigates the Project’s noise impacts. IV. Conclusion Substantial evidence overwhelmingly supports a fair argument that the Project will have a significant impact on the environment. If there is substantial evidence that a project may result in such an impact, contrary evidence is not adequate to support a decision to dispense with an EIR (Arviv Enterprises, Inc. v. South Valley Area Planning Com. (2002) 101 Cal.App4th 1333, 1346). Indeed, if there is a disagreement City of Dublin September 26, 2018 Page 6 among experts over the significance of an effect, the agency is to treat the effect as significant and prepare an EIR. The ‘fair argument’ standard creates a low threshold requirement for preparation of an EIR and reflects a preference for resolving doubts in favor of environmental review. Thus, under the low threshold requirement of the ‘fair argument’ standard, CEQA mandates that the City prepare and certify a focused EIR prior to approving the Project that includes description and analysis of a reasonable range of Project alternatives pursuant to CEQA Guidelines § 15126.6 (including without limitation, alternative locations for the football stadium, or at a minimum, an alternative with a different orientation/size of the stadium facilities and thus directions/projection of the primary noise producing elements like the amplified speakers, a sound wall high and thick enough to prevent noise traveling beyond the football stadium). Accordingly, we hereby demand the City Council direct the City’s Planning Department to prepare an EIR covering the impacts identified in the IS/Supplemental MND as requiring supplemental environmental review and analyzing Project alternatives that avoid or reduce the Project’s potentially significant noise impacts. The failure to prepare a legally adequate EIR would violate CEQA and constitute a prejudicial abuse of discretion. Very truly yours, Gigi Remington Gigi Remington, Esq. On behalf of the Concerned Citizens of West Dublin cc: Chris Foss, City Manager, City of Dublin, via email chris.foss@dublin.ca.gov Luke Sims, Community Development Director, via email luke.sims@dublin.ca.gov Caroline P. Soto, City Clerk, City of Dublin, via email caroline.soto@dublin.ca.gov Encl: Saxelby Acoustics Report, dated September 17, 2018 Remington Letter, dated September 5, 2018 (with attachments: Rasmussen_J.Sound.Vibration_1986, Pridmore-Brown_J.Acoustical.Soc.America_1962, and Wind Effect Slides) Xiao Letter, dated September 25, 2018 Letters from Concerned Citizens of West Dublin: Fisher; Jung; N. Lewandowski; Lee; Zhang & To; Kantorov; J. Smith; L. Cablas; A. Cablas; Malvania; T. Smith; Jayaraman Sound Propagation in a Temperature- and Wind-Stratified Medium David C. Pridmore-Brown Citation: The Journal of the Acoustical Society of America 34, 438 (1962); doi: 10.1121/1.1918146 View online: https://doi.org/10.1121/1.1918146 View Table of Contents: http://asa.scitation.org/toc/jas/34/4 Published by the Acoustical Society of America Articles you may be interested in A Review of the Influence of Meteorological Conditions on Sound Propagation The Journal of the Acoustical Society of America 25, 405 (1953); 10.1121/1.1907055 Tutorial on sound propagation outdoors The Journal of the Acoustical Society of America 100, 31 (1996); 10.1121/1.415879 Analytical solutions for outdoor sound propagation in the presence of wind The Journal of the Acoustical Society of America 102, 2040 (1997); 10.1121/1.419692 THE JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA VOLUME 34. NUMBER 4 APRIL, 1962 Sound Propagation in a Temperature- and Wind-Stratified Medium DAVID C. PRIDMORE-BROWN Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge 39, Massachusetts (Received October 3, 1961) The general linearized equations governing the propagation of sound in a dissipationless temperature- and wind-stratified medium are derived. A formal integral expression is given for the field of a point source located in such a medium, when it is bounded by an absorbing plane under conditions which lead to the formation of a shadow zone. This integral yields the following approximate (high-frequency) expression for the decay rate within the shadow [pl2= (B/r) exp•- (n/c)fi(-c'--U' cos•)lr-]. Here p is the acoustic pressure, r is radial distance from the source, B is independent of r, f is frequency in cps, ½ is sound speed, c' and U' are sound- and wind-speed gradients at the ground surface, q• is the angle between the wind direction and the direction of sound propagation, and n is equal to 5.93 for a pressure re- lease boundary and to 2.58 for a hard boundary. INTRODUCTION HE influence of temperature inhomogeneities on sound propagation has been the subject of num- erous theoretical studies, particularly in connection with underwater acoustics. A classical paper in this field is that of •e•.•e[is•,• who determined the sound field from a point source in a temperature-stratified semi- infinite medium bounded by a pressure release surface. He computed the decay rate of the sound field in the shadow zone, which results from the combined effect of the curvature of the rays and the boundary, and thus explained, at least in principle, a frequency ob- served sound-propagation anomaly in the sea. In the corresponding problem of sound propagation in the atmosphere studied in this paper, one finds that• wind gradients play as important a role as temperature gradients, as has been demonstrated in numerous ex- ZONE WIND SOURCE perimental investigations. TM The presence of a wind gradient makes the medium not only inhomogeneous but also is•c, and, as illustrated in Fig. 1, the sound field around a point source over a boundary is no longer symmetrical about the source as it is in a thermal gradient. Rays from the source are bent up- wards on the upwind side and downwards on the down- wind side. •he D[esence of a negative temperature gradient (lapse rate) tends to accentuate the bending of the.rays upwind and to reduce it downwind, whil• a positive tem,12•ature gradient (inversion) has the op- posite effectS: T. his behavior is well known from ray studies of sound propagation in which it is found that as far as the curvature of the sound rays is concerned, a wind gradient (dU/dz) is equivalent to a temperature gradient (dT/dz)= (2T/c) cos½(dU/dz), where ½ is the angie between the direction of sound propagation and the wind direction, and c is the speed of sound. ii 'is clear that the • shields the rays off from a•'•ihadow zone which lies within a sector on the upwind side of the source. This sector subtends an angie at the source which is greater than 180 ø in a negative temperature gradient and less than this value in a positive gradient. In the present analysis, it is found that the equivalence between temperature and wind gradients referred to above applies also to the rate of decay of the sound field within the shadow zone, and that the decay rates produced by temperature and wind gradients are additive. This analysis refers to the idealized situation of a point source of sound located above a flat boundary whose acoustic properties are described ,b_•..•,.•..•. normal !.mpedance. The atmosphere is steady and vertically stratified, that is, the temperature and wind velocity vary monotonically with the height above the plane. Since we assume the atmosphere to be steady, this Fro. 1. Illustrating the formation of a shadow zone due to the combined effect of a wind gradient and a temperature inversion (•s/&>0, •r/&>0). • C. L. Pekeris, J. Acoust. Soc. Am. 18, 295 (1946). •' U. Ingard, Proc. 4th Annual Nat. Noise Abatement Symp. 4, 11 (1953). , • F. M. Wiener and D. N. Keast, J. Acoust. Soc. Am. 31, 724 .•, (1959). 438 PROPAGATION IN A STRATIFIED MEDIUM 439 means, of course, that effects due to turbulence are not included. The diffracted field deep within the shadow is very small, and only a minute perturbation of the medium may noticeably influence the shadow field. •For this reason we have been careful to start from the servation equations including the effect •'(•f gravity and by so doing hay_•e been •d to retain terms' that have •ii•ll'•- b&7i ignored. EQUATIONS OF MOTION IN A STRATIFIED IN- HOMOGENEOUS MOVING MEDIUM IN THE PRESENCE OF A GRAVITATIONAL FIELD We assume the atmosphere to be a perfect gas which is horizontally stratified, that is, its undisturbed prop- erties are functions only of height z and its motion consists of a steady velocity U(z) which we take to lie in the x direction. If we neglect all dissipative ef- fects, then the propagation of small (acoustic) disturb- ances will be governed by the linearized equations ex- pressing the conservation of mass, momentum, and convected entropy. In order to carry out the lineariza- tion we shall write the total pressure p= P(z)+p as the sum of the undisturbed (barometric) pressure P(z) and the acoustic pressure flgctuations p(x,y,z,t), and s^imilarly for the density fi---•R(z)q-p and the velocity v= Es(z)+u; v; The conservation of mass equation (0 •/at) 4- div (•) = 0, then yields to first order in the acoustic variables Op Op /Ou Ov Ow\ --+U•+wR'+R|•+--+•J=O, (•) at Ox \Ox Oy Oz / where the prime denotes the z derivative. The effect of gravity is to introduce a force per unit volume in the medium with the components (0; 0; -- •g), so that the equation for the conservation of momentum becomes fi(O•/Ot)•+ fl. gradv+ gradp- fig=0. Linearization of this equation leads to the following three equations' Ou Ou 1 Op (2) Ot Ox R Ox Ov Ov 1 Op --+$--+----=0, (3) Ot Ox ROy Ow Ow 1 Op P' •-[- U•d p= 0. (4) Ot Ox R Oz R 2 Neglect of dissipation requires that the convected entropy be conserved (d•/dt)---- (O•/Ot)q- rv. grad•= 0. If we use the relation $= $o+C• ln[(p/po)/ (•/•o)•, which holds for the entropy of a perfect gas, then this requirement is equivalent to (0 •/ Ot) 4- •' grad• = g2[- (0 p/Ot) 4- • ' gradp-], where g2='•p/•, and '•=c•,/c,. Linearization of this equation then leads to Op (Op •+ uOP+ p'w= c • . Ox / Equations (1)-(5) are five first-order partial dif- ferential equations in the dependent variables p, p, u, v, w which are functions of x, y, z, and t. Owing to the assumption of vertical stratification, their coef- ficients are functions only of z. Thus if we assume har- monic time dependence, e -i•t and replace each de- pendent variable fi(x,y,z,t) by its corresponding Fourier transform Fi(afi,z) where these are connected by fi=e-i','tff then this set of partial differential equations will be replaced by a set of ordinary differential equations in the F's. We introduce the symbols II, A, t•, •, •2 to represent the Fourier transforms, respectively, of p, p, u, v, w. Then, taking the Fourier transforms of Eqs. (1)-(5), we obtain ,zXq-R'f•q-R(iatzq-i•v+•')=O, (la) vu+ U'f•+R-1/alI = 0, (2a) r/v+R-1i•1I = 0, (3a) wf•q-gR-•zXq-R-qI'=O, (4a) Rg= (5a) In these equations/9, has been eliminated by using the zeroth order contribution from the momentum equation, viz., P'.•Rg=O. Also, for brevity we have used v = -iw+iaU. W4"now successively eliminate t•, v, •2, and zX from these equations to obtain a second-order differential equation for II II"- -- ln[-r?R (1-- gp)'] II', dz •2 •q-(1-gQ)(a2q-• •) q_g d ln[-r?c •(1 gQ)'] } II O. c • dz (6) 440 DAVID C. PRIDMORE-BROWN Here Q=•-2(g/cS-qdR•'•/•R_.•nd, as before, primes denote deri've/ti'V'es •'it•h•'t•-•'• 't to z. It is interesting to study the behavior of Eq. (6) in the absence of wind. In an di•tlImsphere where P/Po = -••'nd no wind it reduces to the simple form where and II" q- (g/cS) II' q- [-kS-- Ksq- (3'-- 1)g¾cC]II= O, d= co• (1- z/tt) , tt= (eo/og), •=a•+• •. In an isothermal atmosphere with no wind the equation becomes II" q- ('rg/d') II' q- { k s- •[ 1 - ('• - 1) (g/coc)•} II = O, which has the solution II= exp(-'rgz/2d) exp{ 4-i[k•- •2(1 - •) - ('rg/2d)•'•z} , studied by Lamb. • Here •= (-},--1)(g/coc) •' and c is of course constant. If one neglects the barometric pressure variation, as Pekeris did, by setting g-0 in Eq. (6), one obtains II"+2(c'/c)1I'+ (k•- •)II= 0, which differs from the corresponding equation of Pekeris by the presence of the first-derivative term. This is due to the fact that Pekeris assumed the relation p=pc s instead of Op/Ot=d'Op/Ot+R'w which follows from Eq. (5) in the absence of wind and gravity. Since this first- derivative term goes roughly as 1/X (X is wavelength) whereas the other terms in the equation go as 1/X •, it can be expected to be important only at low frequencies. Thus it does not affect the final high-frequency approxi- mation given by Pekeris. In the more general case with wind Eq. (6) can be simplified if one is willing to neglect terms of the order gQ with respect to unity. In fact, for a •91ytropic g.t•9• • for which P/Po = (R/Ro)" we readily find that gp= (g/coc)s.r/n - 1)(1-aU/co)% where zt= )3(eo/og) is the "height" of the polytropic atmosphere, P0 and R0 being the pressure and density at the ground z-0. Thus for wind speeds smaller than the sonic speed gQ i,•[.tllg order of (g/coc) •which at 100 cps is about 10 -ø. If then we consistently neglect terms of this order of magnitude compared to one, Eq. (6) simplifies to ii,,_ ( 2¾ R'•ii,_ (•+as+•.)ii = 0, •H. Lamb, ttydrodynamics (Cambridge University Press, Cambridge,•England, 1940), 6th ed., pp. ,541-543. which can be cast in the form II" ( k'--aM' ?g -- \2 •_-• 7)11' where k=co/c, M= U/c. (7) FIELD OF A POINT SOURCE OVER A PLANE WITH IMPEDANCE-BOUNDARY CONDITIONS In order to study the sound field from a point source it is convenient to introduce polar coordinates by putting x = r cosqb• c•---- • cos0, y = r sin•, /•= • sin0. With this substitution, the equation connecting p and its Fourier transform II becomes exp[&r cos(0-q•)3II(g,0; z)Kd•dO, (8) and there is an ,exac.tly similar relation between w and 9. Equation (7) takes the form ( k• •M' cosO Vghli, H •-- 2' • •M cos0 c • / -J-[(k-- gM cos0) s- •s3II= 0. (9) We now turn to the task of writing the function II appearing in the integrand in Eq. (8) in such a form that the integral shall represent the pressure field around a point source of sound which •s at a, height h above ground and is in the presence of the tem•r•i•k•' and wind gradients described by c(z) and U(z). We adopt a cylindrical coordinate system with the grou•n_.d. at z--0 and the source at r=0, z=h.)The boundary •ond•hon at the ground sdr•ce •s specified by assigning •o the ground a normal impedance Z, which is assumed independent of the angle of incidence, i.e., the grou•.od.•..• !is lo__c_a.l__l¾• r.e•cting.• The condition at'the s0ur•c•'e - is ob- obtained by S•oecifying the mass outflow across a small surface enclosing it. The condition at infinity (the outgoing radiation condition) is imposed in that sector on the upwind side of the source within which the sound rays are concave upwards. We shall call this the shadow sector. These conditions can be conveniently expressed in terms of the two independent solutions of Eq. (9), which we denote by II•(z) and II•.(z), where II•(z) is chosen such that it represents upgoing radiation at large heights in the shadow sector (in conjunction with the time factor e-g•t). Clearly, below the source we shall have both a downgoing wave and a reflected up- going wave, whereas above the source, we shall have only the one represented by the function II•. Accord- ingly we can write PROPAGATION IN A STRATIFIED MEDIUM of Eq. (13) leads to •" 441 II=AII•(z), above the source (z>h), (10) 1 f•f2• =-- •(r)e-iKr oos(O-•)drdc) =BIIx(z)+ClI2(z), below the source (z<h), •2(h+)-•2(h-) *r 2 J o • o where A, B, and C are constants to be determined. The functions II•(z) and II2(z) cannot, of course, be deter- = 1/r. (14) mined until M(z) and k(z) are specified in Eq. (9). If, for example, M=0, g-0 and k-constant everywhere, . The relation between ft and II can be got by eliminating then, clearly, ,-• •xfrom Eqs. (4a) and (5a). This gives II•=e 'k"*, II2=e -'•"*, r/Rft+II'= (g/d')II. (15) where where k?= k•'--K •'. In the general case of varying sound and wind speeds one must usually have recourse to approximate solutions. Convenient high-frequency ap- proximations can always be obtained by the method of Langer, 5 according to which one can write the in- dependent solutions to Eq. (9•ha.•the following form II•= (k-KM cosO).(l•"7gz/2co•')s}q-'•H«('•)(s), (11) m= 1 or 2, q (k- •M cosO)" s = q•dz. 1 Here zx is a zero of q which is assumed to be of first order [so that q(zx)/(z--zx)•O• and the phase of s is taken to be zero when s is real. If s is large and posi- tive, the function Hx becomes asymptotically Hx• (2/r)•(k--•M cos0)(1--7gz/2coS)Cie •(•-•/•), (12) which is obtained in the WKB approximation. We shall see later that the radiation requirement is satisfied with this form for The requirement that the vertical component of the particle velocity be continuous across the plane of the source, except right at the source, leads to Thus in terms of II and IV Eq. (14) becomes [ (g/c •') H-- II']n -•+= •R (h)/,r, where the left-hand side is the jump in (g/d)II-II' across the plane of the source. Reference to Eq. (10) then leads us to write this equation explicitly in the form (A -- B) ['IIx' (h)-- (g/c•)IIx(h)• --C[-II.o'(h)-- (g/c•')II•(h)•= --•R(h)/r. (16) Another relation between the constants A, B, C is given by the requirement that the pressure be continu- ous across the plane of the source, z= h, A II • (h) = BII • (h) +ClI2 (h). (17) Finally, a third relation is provided by the normal impedance boundary condition at the ground surface. Since the wind velocity is assumed to be zero at the ground, this condition takes the usual form p/w = -- Z = const at z = 0. Using Eq. (!5), this becomes g - . c0 z The three relations (16), (17), and (18) determine A, B, and C as follows' w(h+)--w(h-)= (4/r)•(r). (13) Here, •(r) is the delta function having the property that •(r)=0 for r•0 and 2 fo •(r)dr= 1. If this relation is integrated over a "pillbox" enclosing the source, it is seen to be equivalent to the requirement fv.dS=4,r, i.e., that the total outflow from the source be equal to 4•r. Taking the inverse Fourier transforms of both sides where A = B + II:(h)/W, II:' (0)+ (iooRo/Z-- g/co•)II:(O) IIx (h) •- • --• (o) + (ino/Z- g/o n, (o) C= II(h)/W, w W = , k- •M cos0 /•=• involves the Wronskian of II• and 112 Thus, above the source we obtain [ = (O)+ (ioRo/Z_ g/co.)Ih (O) * R. Langer, Trans. Am. Math. Soc. 33, 29 (1931). See also M. J. Lighthill, Quart. J. Mech. Appl. Math. 3, 311 (1950). (20) 442 DAVID C. PRIDMORE-BROWN Interchanging z and h in this expression gives the form which holds below the source. This'is then the explicit form of the function which appears in the integrand of Eq. (8). Note that approximate expressions for II• and II•. have been given in Eq. (11). Approximate Evaluation of the Field In the presence of a temperature gradient only and no wind [so that k= k (z) but M(z) = 0-] the dependence on 0 drops out of Eq. (9) and hence out of II(•,O,z) which becomes simply II(g,z). The integration over 0 can then be carried out directly in Eq. (8) with the result that p(r,•)= 2•e-iøøt fo Jo(•r)II(•,z)•d•. (21) This is the case of a variable index of refraction in a quiescent medium which has been treated extensively in the literature. •,ø,7 In the more general case the integration over 0 can still be approximately carried out, for large •r, by the saddle-point method. It is clear that the integration range for 0 passes through two points of stationary phase of the exponential term exp[-i•r cos(0-qO)-] in Eq. (8), namely 0=qO and 0=qOq-•r (for Saddle-point integration through these two points yields fo©/2,r\• p(r,ck,z)=e -i"'t -- ei('r-•/4)II(• ß qO,z) •+ XI1 .... lgdg 8gr Jo \gf/ ß 8•r where II is given in Eq. (20). (22) The result is that the integrals appearing in Eq. (22) can be evaluated, at least asymptotically (for high frequencies), as a sum of residues of a contour integral. Within the shadow sector the various terms of this series decay at such a rate that far enough from the source the pressure field is adequately represented by the first term alone. Under these conditions the square of the pressure takes the form I ply,= (B/r) expE-n(f/co)'¾r, where B is independent of r, f=w/2r is the frequency, and•'y=-(Co'/co+Uo ' cosqO/c0) is positive within the shad5"w•s-•-5•i•;5'r •nd can' be •egarded as an equivalent sound speed gradient. Notice that it depends only on the values of the gradients at the ground surface. The quantity n is a function of the ground impedance. For a very "hard" ground (specifically for Z/Roco=i213f where f is frequency in cps) n is easily evaluated as 2.58, whereas for a pressure-release boundary (Z= 0), n=5.93 in agreement with the results of a previous paper 7 for the case of no wind. ACKNOWLEDGMENT The author is indebted to U. Ingard for some valuable discussion of this problem. APPENDIX The normal mode representation is obtained formally by replacing the integration paths in Eq. (22) by con- tours such that the first integral is taken over a path enclosing the first quadrant of the complex • plane in an anticlockwise sense while the second is taken over a path enclosing the fourth quadrant in a clockwise sense. In general, the presence of branch points will necessitate the introduction of cuts •hich these contours must skirt if they are to close upon themselves. These contour integrals will then differ from the original integrals (22) by the values of the integrations along the infinite arcs, along the imaginary axes, and around the branch cuts. Now Pekeris has shown that although these con- In this way the double integral (8) for the pressure field is reduced to the sum of two single integrals which ,•xtributions will not in general vanish, they do vanish can be treated by methods which have already been •asymptotically if one uses the high-frequency solutions used in studying the integral (21) corresponding to the ' of Langer given in Eq. (11). Thus in this limit the tw6 temperature problem. Thus we can represent these integrals in Eq. (22) become expressible as two contour integrals as an infinite series of normal modes whose convergence is rapid in the shadow zone or, alternatively, we can evaluate them approximately by performing an additional saddle-point integration through the station- ary phase points in the g plane; this last procedure then yields a ray-acoustics representation which is adequate in the normal region. Since both of these methods are discussed by Pekeris, 1,ø we merely summarize the first one in the Appendix, showing how it applies to the pres- ent formulation. o-•C. L. Pekeris, J. Appl. Phys. 18, 667 (1947). /"•'% D.C. Pridmore-Brown and U. Ingard, J. Acoust. Soc. Am. 27, 36 (1955). integrals encircling the first and fourth quadrants of the g plane in the manner described. It is worth remarking that the restriction to high frequencies is not usually stringent in practice since it is roughly equivalent to the requirement that fractional changes in the tempera- ture and velocity of the medium over the distance of a wavelength be small. Having the two integrals in (22) expressed as contour integrals, we evaluate them as a sum of residues taken at the poles of the respective integrands. Now, on physi- cal grounds we should expect the fourth quadrant to be free of poles so as to give no contribution from the sec- ond integral, which has the form of a sum of waves PROPAGATION IN A STRATIFIED MEDIUM 443 converging on the source. That this is the case can again be readily verified with the help of the Langer solutions. For simplicity we shall restrict ourselves for the moment to extreme values of the ground impedance. For a very "hard" ground for which Z/Roco=iooco/g the poles in Eq. (20) will occur at the zeros of II/(0). According to Eq. (11) these are asymptotically equivalent to the zeros of H_•(•)(So), which occur at so=A•e -• where A•=0.686, A2=3.90, ...,A• --• (n--3/4)•r (as n --• oo). Conversely we can consider a pressure-release boundary (Z-0) corresponding to which the poles occur at the zeros of II•(0) which are asymptotically the zeros of H• (•) (So). These are given by So= A •e -i•, where A • = 2.38, A2= 5.51, ß ß., A • --• (n- 1/4)•r. The quantity so is given by the integral /o foqoq-•dq (A1) so= (q)•dz= dq/dz' 1 where the subscript zero denotes the value of the quan- tity at z=0, and q(z•)=0. If we expand q and dq/dz in Taylor series about z=0 we obtain q= qo+ qo' z q- «qo" Z2+ ' . ., (A2) dq/dz= qo' q-qo"Z-½ ' ß ', where primes denote differentiation with respect to z. If we now eliminate z from the second series by substi- tuting for it the reversion of the first series we obtain dq qo" qo'"qo'-qo "• d-•= qo' + •.--7(q-- qo) + (q-- qo)2+ ' " . qo 2qo 'a In terms of this series the integral for So yields 2qøTl+2_qø"qø 1 so= . +.-. , (A3) • q0'L 5 q0 '• which must be set equal to A ne -i•, the A n being real and positive. It is dear that within the range of integration .,• the series expansion for dq/dz converges rapidly at high ",frequencies, since• q0 must he p•0p9 rtiønal to co• whereas qo', qo", etc., are all proportional to ,o • as w-• oo. Thus, if we take the first term only, we obtain qo= (•qo'Ae-i•) Since q0 = k0 •- •', this leads to t•,•=ko['l--«(•[qo'lko-aA,•)le-2i•/a-], (m4) for qo'= qo' and •= ko•l--«(•lq0'lk0--aAn)r], (A5) for qo'=--Iqo'l. Thus the poles g• will lie in the first quadrant of the complex • plane if q0' is positive and on the real axis if qo' is negative. In either case we can take •the integration paths in Eq. (22) just below the real axis so that when the contours are completed, the second integral, encircling the fourth quadrant, will vanish since this quadrant will then be free of poles. Thus the pressure field is given by the first contour integral only and takes the form p(r,qb,z)=e -i•øt ei(•r--•r/4)II(t½j q•,z)gd•. (A6) Here II is given by Eq. (20) and the contour encloses the first quadrant in an anticlockwise sense and in- cludes any poles that may exist on the real axis. Expressing this integral as a sum of residues at the poles we obtain formally p(r,qb,z) = -- 2•'ie -iø't • e ir•nr-•'/4) n•:l \ ,,,,[ n,.'+ (ioo•/Z-g/c•)n• w a/o•[n•'+ (iooR/Z-g/c•)n• z=0 n• (h)n• (z)+O(•/•r)•. (^7) If qo' <0 and the poles lie along the real axis the convergence of this series will be slow, and the integral (A6) is probably better evaluated by the saddle-point method. On the other hand if q0>0 and the g• lie in the first quadrant so that Im(g•r)>0, then the terms of the series decay rapidly with r so that at sufficient distances from the source the pressure may be adequately represented by the first term alone. The radial dependence of the pressure squared due to the first term is I pl 2= (B/r)e -2•m•xr, (AS) where B is independent of r. Now 2Im• «VJk0 a •- , , = (•qo,ko•A •)• where q0'= (O/Oz)[(k-- •M cos½) •-- •']•=0, = -- 2ko•(Co'/Co+ go' cos•/½0). Combining these terms leads us to write 2 Img•= n(f/co)«T •, (A9) where n=3.32A 1 •, f=oo/2•r and •= - (co'/co+ So' cosO/co). Journal of Sound and Vibration (1986) M(2), 321-335 OUTDOOR SOUND PROPAGATION UNDER THE INFLUENCE OF WIND AND TEMPERATURE GRADIENTS K. B. RASMUSSEN~ Danish Acoustical Institute, c/o Technical University of Denmark DK-2800 Lyngby, Denmark (Received 27 October 1984, and in revised form 26 February 1985) The situation investigated is sound propagation from a monopole point source located over an impedance surface. The sound propagation is assumed to be influenced by wind and temperature gradients. A very accurate calculation method for taking into account the effect of wind and temperature gradients on sound propagation oufdoors is presented and used for verification of a new approximate calculation model. This comparison shows that the approximate model is accurate. A series of loudspeaker measurements has been carried out over a grass-covered ground for distances up to 80 m. The measurements were carried out for a wind speed of 2-2.5 m/s measured 10 m above the ground. The measured data agree very well with the calculated results. Furthermore the results from the approxi- mate calculation model agree with results from previous investigations [ 1,2]. Hence, the main conclusion is that a simple and powerful approximate model for sound propagation under the influence of wind and temperature gradients has been developed. However, the influence of turbulence is not taken into account in this paper, and the wind and temperature gradients are assumed to be constant as functions of height. 1. INTRODUCTION In recent years a substantial effort has been made in order to develop theoretical models for sound propagation outdoors. The starting point is usually a monopole point source over a locally reacting impedance plane. Appropriate models for the description of the acoustic ground impedance exist and are still being developed [3-61. Efficient and accurate approximate solutions for a monopole point source over an impedance plane have been developed, too. Hence, the calculation of sound propagation over plane ground represents no major problem so long as atmospheric effects may be ignored. A number of efficient calculation models for taking the effect of terrain profile into account have also been developed [7,8]. Thus one of the remaining problems is to take the influence of atmos- pheric effects into account. These effects are atmospheric absorption, the influence of wind and temperature gradients, and of turbulence in the atmosphere. Atmospheric absorption is today considered to be well known as a function of relative humidity and temperature. It may be considered as an extra contribution to attenuation versus distance apart from the basic spherical spreading. The atmospheric absorption is, however, frequency-dependent. The influence of atmospheric turbulence on sound propagation outdoors has not been investigated to very large extent, but some preliminary investigations have been performed [9]. As regards the influence of wind and temperature gradients most of the previously developed calculation models are very crude and inaccurate [lo]. In the following sections a new and powerful calculation model will be introduced. Comparisons are made with tedious, but precise, calculations as well as measured data t Presently with Bdegaard & Danneskiold-Sams#e, Kroghsgade 1, DK-2100 Copenhagen 8, Denmark. 321 0022-460X/86/020321 + 15 $03.00/O @ 1986 Academic Press Inc. (London) Limited 322 K. B. RASMUSSEN from outdoor measurements using a loudspeaker as source. The influence of turbulence is ignored in this paper. 2. THEORY 2.1. PRECISE THEORY The analysis given in this section follows those of Pridmore-Brown [ 1 l] and Pierce [ 121. In a still and homogeneous atmosphere one may write for the sound pressure p emitted from a monopole point source at (x, y, z) = (0, 0, zO) v*p + k2p = -47r 6(x) 6(y) 6(z - zo), (1) where 6 is the Dirac delta function, and k is the wavenumber. If one assumes that a vertical temperature gradient is present in the atmosphere, the sound speed will vary with height. One can still apply equation (l), but now k varies with height since k(z) = w/c(z). (2) Assuming that the field is cylindrically symmetric around the z-axis, one may introduce a Hankel transform p=- * I 2J,,(~d)P(z, K)K dK, (3) 0 where P denotes the transform of p, and d is the horizontal distance between source and observation point. If p satisfies equation (1) then P must satisfy the transformed equation ~2P/~Z2+[W2/C2(Z)-K2]P=~(Z-ZO). (4) Thus equation (4) may be solved, with appropriate boundary conditions, in order to find solutions for sound propagation under the influence of temperature gradients. It should be noted that the vertical density variation in the air has been ignored in equation (4). The boundary conditions which are to be used together with equation (4) are the Sommerfeld radiation condition (for z + CO) and an impedance boundary condition for z =O. Two solutions, (1, and 4, of the homogeneous equivalent to equation (4) are considered. $ is assumed to satisfy the condition at infinity while 4 is taken to satisfy the impedance condition for z = 0, a4/az+ik(O)/%$ = 0, (5) where p is the specific normalized admittance of the surface. For the inhomogeneous equation (4) the solution may be defined as P=AIC, forz>zo, P=&#J forz<z,. (6) The constants a and b may be determined from the fact that the sound pressure p is continuous for z = z,, and that the vertical component of the particle velocity is also continuous for z = z. except right at the source. Continuity in sound pressure across the plane z = z. leads to continuity in the transformed sound pressure P. Considering the vertical particle velocity component leads to aP(Z,+&, K)/aZ-aP(ZO-E, K)/dZ= 1 (7) for E small and positive. Equation (7) is obtained by integration of equation (4) with respect to z. Hence equation (6) may be written as P(z, K) = Ijl(z~, K)+(zw K)/[(a+/az)+ -(@/az)+]z=+, (8) where zL is the larger of z and z. and zs is the smaller. The denominator in equation (8) OUTDOOR SOUND PROPAGATION 323 is the Wronskian of 4 and 4. In order to find explicit expressions for II, and 4 it is necessary to specify how the sound speed varies with height. Here a linear variation c(z) = c(O)(l+ yz), (9) is assumed, where y is a constant. Inserting this in the homogeneous equivalent of equation (4) one obtains, for yzcc 1, a~P/az*+[k*(o)-K~-2yzk*(o)]P=o. (10) The restriction to small sound speed gradients which is inherent in equation (10) is likely to be unimportant as far as outdoor sound propagation is concerned. Solutions to this equation may be expressed as Airy functions [ 12,131. For y < 0 one chooses $(z, K) = W(T_Y), (11) where w(x)= ~JYi e' ~' ~~i ( x ei2m' 3 ) and ~=[~*-k~(0)]1*, y=z/Z, l=[]y12k2(0)]P”‘. Ai denotes the Airy function as defined by Pierce [12]. $ may be shown to satisfy the Sommerfeld radiation condition. The +-function satisfying the impedance condition is then given by (for y<O) (12) where V(X) =&Ai(x) and q = ik(O)@ This choice of $ and C#I leads to a Wronskian of -1 in equation (8). Hence one obtains p(z, K) = -“‘(T-Y&#‘(zs, K)i, (13) where yL = zL/ 1. For y > 0 one chooses +(z, K) = ‘J(T+Y), and consequently (14) o(T+Y), (15) and hence one obtains, instead of equation (13), p(Z, K) = -u(T+Y~b#'(zs, K)i. (16) Tedious but very accurate calculations of the influence from sound speed gradients may be carried out by implementing equation (3) with either equation (13) or equation (16) inserted for P This has been done by means of numerical methods given in the Appendix. The formulas above have been derived for a sound speed gradient only. This sound speed gradient may be caused by a temperature gradient or a wind speed gradient. The speed of sound is proportional to the square root of the absolute temperature, and it is therefore easy to interpret a temperature gradient as a sound speed gradient. In the case of a wind speed gradient the cylindrical symmetry which has been assumed around the z-axis is no longer present, since downwind propagation is equivalent to propagation in a positive sound speed gradient, whereas upwind propagation is similar to propagation in a negative sound speed gradient. Hence, the angle between the wind speed vector and the vector pointing from source to receiver is essential. Another difficulty is to quantify the sound speed gradient which is equivalent to a given vector wind. In ray tracing calculations it is found that the curvature of the rays due to a wind speed gradient of 324 K. B. RASMUSSEN dV/dz is the same as the curvature due to a temperature gradient dT/dz if dT/dz = [2T,/c(O)](dV/dz) cos 8, (17) where 0 is the angle between the direction of propagation and the wind direction. T is the absolute temperature and To is the absolute temperature at the ground. The relation between y in equation (9) and dT/dz is y =;T-“2T;1’2 dT/dz = (dT/dz)/(2T,). (18) Hence equation (18) specifies y in equation (9) for a temperature gradient. In the case of a wind gradient equation (18) is used with equation (17) inserted. If both wind and temperature gradients are present, y is determined as the sum of the y’s due to each type of gradient. In practice, however, y is usually dominated by the effect of the wind speed gradient. Figure 1 shows typical y-values as a function of wind and temperature gradients. dT/dz(OK/m) V (m/s) Figure 1. y versus wind speed 10 m above the ground and versus temperature gradient. 2.2. APPROXIMATE THEORY An approximate theory for the calculation of sound propagation under the influence of wind- and temperature gradients has been developed. It would seem logical to develop such an approximate theory on the basis of the precise theory presented in the previous section. Attempts in this direction were, however, not quite satisfactory [lo]. Instead an approach based upon the Rayleigh integral has been employed. The approach is by no means mathematically rigorous, but, as will become clear in the following, the resulting expressions are efficient as well as accurate. As a starting point the Rayleigh integral will be derived. Figure 2 shows the source and receiver geometry and a screen halfway between source and receiver. x Figure 2. Geometry of source and receiver and screen. Source is located at (xs, 0, zs) and receiver at (xR, 0, zR). OUTDOOR SOUND PROPAGATION 325 From Green’s theorem one obtains for the sound pressure in a homogeneous and still atmosphere [ 141 d, denotes the normal derivative, and pL is the solution for a point source over an impedance plane [5,15], pL = (eikR1/R1) + Q( R,, 0) eikh/ RZ, (20) where RI is the direct ray path and R, is the reflected ray path (see also Figure 3). Q is the spherical wave reflection coefficient given by the relations Q(&, e)=R(e)+[l-R(B)lE(P,), R(B)=(cos t’-/?)/(cos e+p), E(P,) = 1 +iJGP, eCPe2erfc (-iP,), P, = J$kR,(j3 + cos 0). (21) Recewer J / /I’ , Figure 3. Point source over impedance plane. 8 is the angle of incidence, also shown in Figure 3. Erfc is the complementary error function [15]. Equation (21) is a very good approximation to point source propagation over an impedance plane. For equation (19), the integration is to be carried out over the screen surface. An explicit expression for p is obtained from equation (19) by making reasonable assumptions regarding the field on the screen. Assuming the screen to be hard one can make use of the Rayleigh assumption that p=2p, and a,,p=o (22) on the illuminated side, and p=O and a,p=O (23) on the shadowed side. Inserting equations (22) and (23) in equation (19) one obtains P=Pr& 2PL anPL dS, where S, is the illuminated side of the screen. If the screen is extended to infinity, p is zero provided that source and receiver are separated by the screen. Hence, from these considerations, one obtains the Rayleigh integral for pL, 1 PL=g PL anPL dS (25) 326 K. B. RASMUSSEN or, from equation (20), ik% ikRa >xR+QZ> xR 3 4 1 dy dz, (26) where R,, RZ, R3 and R4 are shown in Figure 4. Q, is calculated on the basis of R2 and Q2 is calculated on the basis of Rd. Equation (26) is valid only if Q varies slowly as a Figure 4. Ray paths used in connection with the Rayleigh integral. function of horizontal distance. This assumption is justified by numerical investigation of equation (21) [14]. Furthermore, this assumption makes it possible to use the method of stationary phase as an approximation to the integral over y. Hence one obtains, for k-a, eik(R,+%) ik(%+R,) +Q1 [R,R:(R,+ R,)]“‘+ Q1Q2 [R2R;(R2+ R4),l12 1 dz’ (27) In equation (27) RI to R4 denote ray paths located in the vertical plane containing source and receiver (the plane containing the stationary points). So far it has been assumed that the atmosphere is still and homogeneous. If a wind gradient or a temperature gradient is present, one may replace k by k(z) = m/c(z), (28) so that, with c(z) as defined in equation (9), k(z)=[w/c(O)](l-yz)= k(O)(l-yz). (29) In equation (27) the sound field is calculated on the basis of a vertical column of secondary sources. For each secondary source k is regarded as constant along the ray paths R, to R4, but k is calculated on the basis of half the height of the secondary source. In this way the average wind (or temperature gradient) is taken into account for each secondary source. Formally equation (27) leads to pL = -xR[2rk(0)]1/2 g eik(zlZ)(R,+R,) ik(zlZ)(R,+R,) [RIR;(R,+ R,)]‘/‘+ Q2 [RI&R,+ R4)]l12 eiWz/2)(R,+R,) eik(z/2)(R,+R,) +Q1[R2R~(R2+R3),1/2+Q1Q2[R2R:(R2+R4)]”2 dz9 1 (30) where k(z) is given by equation (29). However, equation (30) does not take curvature of the rays into account-and curvature must arise when sound is propagating through a gradient. Instead equation (30) introduces a phase change at each secondary source. Lindblad [16] has suggested simulating sound propagation in gradients by curving the ground. In equation (30) the introduction of a phase change as a function of height may be regarded as equivalent to curving the ground. Physical intuition suggests that the OUTDOOR SOUND PROPAGATION 327 aperture (x = 0) should be located something like halfway between source and receiver. Numerical investigations have confirmed that this is a reasonable choice, hence in the following xs = -xR (see Figure 1). Numerical integration of equation (30) was performed with N points where N = Max (L/IX, 25) + 25. DL is the spacing between points, which is l/5 wavelength, and L is a distance which is determined from L = Max {[0.5 Min (x,, -xR) + Max (zs, zR) + 1.0],24}. The contributions from the last 25 points were reduced by a window-function in order to reduce spurious end-point contribu- tions. The CPU-time necessary for such a numerical integration is approximately 5 s for l/3 octave calculations between 100 Hz and 2 kHz for a 120 m distance between source and receiver. In Figures 5 and 6 a comparison is shown of results from equations (3), (12) and (15) (the precise theory) and results from equation (30) (the approximate theory). The com- parison is based upon a typical impedance for grass-covered ground. Hence the impedance versus frequency is assumed to follow the Delany-Bazley flow resistance model [3] with a flow resistance of 200 x lo3 Nsme4 inserted. From the figures one can see that for downwind propagation the sound pressure level is generally increased with increasing wind speed. This is to be expected since, according to traditional ray tracing, this situation may allow multiply reflected rays to reach the receiver. In the upwind situation, on the other hand, the rays are bent upwards, and if the wind speed is sufficiently high, no rays will reach the receiver. Hence a shadow zone is created according to ray theory. And indeed the sound pressure level does decrease for increasing wind speed in Figure 6. A comparison between Figures 5 (a) and (b) and 6(a) and (b) shows that the approximate theory is in general very accurate, but that it underestimates the influence of wind (and temperature) gradients for higher wind speeds. These trends are found for other source-receiver geometries also [lo], but, as will become -25 (b) I I , 1 125 250 500 1000 2000 Frequency (Hz) Figure 5. Sound pressure level relative to free field for downwind propagation over typical grassy field. Horizontal distance 120 m; source height 1.8 m; receiver height 2.0 m. Flow resistance, a, is 200 x kd Nsm-“. Wind speed -, 0 m/s; - - -, 1 m/s; -. -, 3 m/s; . . ‘, 5 m/s. Calculated from (a) equation (3); (b) equation (30). 328 K. B. RASMUSSEN -15 - _.,... -20 - -25 - (b) I 1 I I 125 250 500 1000 2000 Frequency (Hz) Figure 6. Key as in Figure 5, but for upwind propagation. clear in the next section, the effect of gradients increases with horizontal distance. In the next section only the approximate model will be used since it requires only less than one-tenth of the computation time needed for the calculation of the precise model. 3. MEASUREMENTS Outdoor sound propagation measurements were carried out with a loudspeaker as source. Wide band noise was emitted by the loudspeaker and received by Briiel & Kjaer 4165 microphones fitted with wind screens. The signal was recorded on Nagra IV SJ tape recorders for later one-third octave analysis in the laboratory. During the propagation measurements the direction and speed of the wind were measured and the temperature gradient was measured. The meteorological measuring system consisted of a wind vane and cut anemometer mounted on top of a mast, 10 m high, and of two temperature probes in double radiation shields. The temperature probes were located at O-5 m above the ground and on top of the mast, respectively. The central unit of the equipment printed the mean vector wind and the average temperature gradient once every minute. The measurements were carried out on 14 August 1984, in the afternoon, on a grass- covered plane. The atmospheric conditions were very stable during the measurements. The wind speed was 2-2.5 m/s, the temperature gradient less than O.O3”K/m, and the relative humidity was 70%. (The humidity value was obtained from a nearby meteorologi- cal centre.) Measurements were made for source-receiver distances of 40 m and 80 m. The source height was 1.45 m in all cases and for each horizontal distance recordings were made for a receiver height of 0.5 m as well as 1.5 m. Recordings were made with two different loudspeakers, one at a time. Hence, a Briiel & Kjaer 4205 sound power source was used as well as a loudspeaker developed at the OUTDOOR SOUND PROPAGATION 329 Acoustics Laboratory, Technical University of Denmark, consisting of 20 units in a spherical arrangement. The former loudspeaker is a reasonable approximation to a point source at higher frequencies (the approximate directional characteristic has been given in reference [S]) whereas the latter has a high output and is omnidirectional within 1 dB up to 1 kHz. Hence, the Briiel & Kjaer loudspeaker could be employed over the entire frequency range from 100 Hz to 5 kHz except when the signal-to-noise ratio became too low because of acoustic background noise. The 20 unit loudspeaker was used in order to obtain a better signal-to-noise ratio at lower frequencies. Thus the results presented in the following are from the Briiel & Kjaer loudspeaker for frequencies above 1250 Hz and from the 20 unit loudspeaker for lower frequencies. The measured data are the results obtained after an integration time of 31 s. Repeated measurements gave only very slight differences, and no influence of the loudspeaker source used could be found. The measured sound pressure levels were related to the free field level obtained for the same distance. The free field levels from the loudspeakers were measured in an anechoic room at a distance of 5 m and this result was then extrapolated to the distance in question, with spherical spreading being assumed. The measured values in Figures 7,8, 10 and 11 have all been corrected for atmospheric absorption according to ANSI [17] for 70% r.h. and 20°C. In Figures 7 and 8 the results for 40 m are shown for downwind and upwind propagation. One can see that calculated results (equation (30)) agree very well with the measured data. The calculated results are based upon a flow resistance value of 200 x lo3 Nsmm4 in the Delany-Bazley flow resistance model for the ground impedance. This flow resistance value gives a very good agreement between theory and measurement, and also for a horizontal separation of 20 m where the influence of atmospheric effects may be ignored. These results are not shown here, but may be found in reference [lo]. From Figure 9 it is clear that the theoretical influence of the atmospheric effects is not very strong at the (a) i -15 - -20 - -25 - (b) I 1 1 1 1 125 250 500 1000 2000 4000 Frequency (Hz) Figure 7. Sound pressure level relative to free field for downwind propagation over grass-covered ground. Horizontal distance 40 III; source height 1.45 m; receiver height: (a) 1.5 m; (h) 0.5 m. Wind speed 2.5 m/s. -, measured; - - -, equation (30) for v = 200 x lo3 Nsmm4. 330 K. B. RASMUSSEN -10 - -15 - -20 - -25 - (b) - I 1 125 250 500 1000 2000 4000 Frequency (Hz) Figure 8. Key as in Figure 7, but for upwind propagation. Wind speed 2 m/s. -lO- -15- -20 - is -25 - 0 (0) i -25 (b) 1 I I I 125 250 500 1000 2000 4000 Frequency (Hz) Figure 9. Sound pressure level relative to free field for propagation over grass-covered ground. Horizontal distance 40 m; source height 1.45 m; receiver height: (a) 1.5 m; (b) 0.5 m. Flow resistance, o, is 200x ld Nsmm4. Wind speed -, 0 m/s; - - -, 2.5 m/s; -. -, -2.0 m/s. Calculated from equation (30). 40 m distance. However, the measured difference is slightly larger than the calculated difference. Figures 10 and 11 show the results for 80 m for downwind and upwind propagation. Again the agreement between theory and measurement is very satisfactory. The theoretical OUTDOOR SOUND PROPAGATION 331 z - 25 Z (0) 5 b J - 25 (b) I , 1 I 125 250 500 1000 2000 4000 Frequency (Hz) Figure 10. Key as in Figure 7, but horizontal distance is 80 m. -15- -2o- 73 -25- 9 (0) u i?l J -15- -2o- - 25 (b) I I 1 I 125 250 500 1000 2000 4000 Frequency (Hz) Figure 11. Key as in Figure 7, but for horizontal distance 80 m and upwind propagation. Wind speed 2 m/s. curves in Figure 12 show that the difference between downwind and upwind propagation is much greater than for the 40 m distance. A marked discrepancy is, however, present in Figure 11 between theoretical and measured data in the high frequency region. This is not surprising since it has been assumed that the influence of turbulence is marginal 332 K. B. RASMUSSEN ii? -25 3 (a) -25 (b) 1 I I , I 125 250 500 1000 2000 4000 Frequency (Hz) Figure 12. Key as in Figure 9, but horizontal distance is 80 m. -I 5- ‘\ -15- ‘\ /’ c,“\. ,A. ‘\ ‘.“./ ‘. -2o- ‘\._. 1’ _.X’ -25 (b) h I I 0 1 125 250 500 loo0 2000 Freqa-cy (Hz) Figure 13. Sound pressure level relative to free field for propagation over grass-covered ground. Horizontal distance 110 m; source height 1.8 m; receiver height 1.6 m. Wind speed -, 0 m/s; - - -, 5 m/s; - . -, -5 m/s. Temperature gradient; neutral. (a) Measured [l]; (b) equation (30) for v = 200x IO3 Nsm-4. Also see text. and that the gradients are constant as functions of height. Both assumptions are reasonable except for high frequencies and long distances. Figure 13 shows a comparison of measured data reported by Parkin and Scholes [l] and calculated data. The distance is 110 m. Both measurements and calculations are made OUTDOOR SOUND PROPAGATION 333 with reference to a point 20 m from the source (which was a jet engine). One can see that the agreement between theory and experiment is good although the combined effect of wind and ground is somewhat greater in theory than in practice in this case. Calculations were made for a flow resistance of 200 x lo3 Nsme4 [ 18 1. It should also be mentioned that long distance downwind propagation measurements from the Netherlands [2] confirm the trends observed in Figures 7 and 10 for downwind propagation. These measurements were carried out for distances of several hundred metres. The wind speed and temperature gradient are, however, not specified in reference PI . 4. DISCUSSION The results from the previous section show that the calculation procedure proposed in equation (30) for sound propagation under the influence of wind and temperature gradients is very accurate. The results from equation (30) are confirmed by calculations made on a far more rigorous basis, equations (3), (13) and (16), as well as by experimental data. Two basic restrictions are, however, present in ail the calculations presented in this paper. Firstly the influence of turbulence in the atmosphere is ignored, and secondly the gradients are assumed to be constant versus height. The influence of turbulence increases with distance and frequency. The main effect of turbulence is that random phase fluctuations are introduced so that interference dips become less pronounced than they should be according to theory in which turbulence is ignored. Hence for distances exceeding, say, 500 m, the combined effect of wind and temperature gradients and the ground effect will usually be smaller than predicted when ignoring the turbulence. This difference between theory and measurement increases with the wind speed. This tendency may be found even in Figure 13 for a distance of 110 m and a wind speed of 5 m/s. Preliminary investigations of the influence of turbulence have been made by Daigle et al. [9]. The fact that the gradients are assumed to be constant is also bound to introduce some kind of error since the wind speed and temperature profiles are usually logarithmic in shape [ 191. What has been employed in this investigation is thus actually a sort of average gradient, since the wind speed has been measured 10 m above the ground and it is known to be zero at ground level. In this investigation a linear variation has been assumed between these two points, but in reality the variation is approximately logarithmic. Similarly, the air temperature has been measured at 10 m and close to the ground, and a linear variation assumed. These approximations introduce an error which increases with frequency since the wavelength compared to the shape of the actual gradient determines the size of the error. If the wavelength is sufficiently long, a constant gradient is a good approximation. The high frequency deviations in Figure 11 are probably due to the logarithmic shape of the wind speed profile. Most of the previously published calculation methods for propagation under the influence of wind and temperature gradients are based solely on ray tracing techniques, and as a consequence the accuracy has not always been satisfactory [ 10,201. Recently De Jong has developed a very advanced calculation method based upon extrapolation [18]. At present the results, however, do not agree well with experimental data. The reason for this is not known. Actually the theoretical results displayed in Figures 5 and 6 may be compared directly with calculated results in reference [18]. Apart from the inaccuracies inherent in the calculations for taking the influence of wind and temperature gradients into account, it should be mentioned that the flow 334 K. B. RASMUSSEN resistance ground model could also be responsible for some of the deviations between theory and measurement. One such example is the discrepancy in Figures 7(a) and (b) between the measured and calculated first dip. Finally, it should be pointed out that the influence of a wind component having a direction normal to the sound propagation direction is not taken into account in the present study. Such a side-wind component is, however, expected to have only limited influence on sound propagation from a point source. ACKNOWLEDGMENT The present work was sponsored by the Danish Technical Research Council. REFERENCES 1. P. H. PARKIN and W. E. SCHOLES 1965 Journal of Sound and Vibration 2, 353-374. The horizontal propagation of sound from a jet engine close to the ground, at Hatfield. 2. P. KOERS 1983 Technisch Physische Dienst tno-th, Delft. A calculation method for the propaga- tion of outdoor sound over several kinds of barriers on an inhomogeneous ground. 3. M. E. DELANY and E. N. BAZLEY 1970 Applied Acoustics 3, 105-116. Acoustical properties of fibrous absorbent materials. 4. S.-I. THOMASSON 1977 Journal of the Acoustical Society of America 61, 659-674. Sound propagation over a layer with a large refraction index. 5. K. B. RASMUSSEN 1981 Journal of Sound and Vibration 78, 247-255. Sound propagation over grass covered ground. 6. K. ATTENBOROUGH 1983 Journal of the Acoustical Society of America 73,785-799. Acoustical characteristics of rigid fibrous absorbents and granular materials. 7. T. KAWAI 1981 Journal of Sound and Vibration 79,229-242. Sound diffraction by a many-sided barrier or pillar. 8. K. B. RASMUSSEN 1984 Journal of Sound and Vibration 98, 35-44. On the effect of terrain profile on sound propagation outdoors. 9. G. A. DAIGLE, J. E. PIERCY and T. F. W. EMBLETON 1983 Journal of the Acoustical Society of America 74, 1505-1513. Line-of-sight propagation through atmospheric turbulence near the ground. 10. K. B. RASMUSSEN 1985 Danish Acoustical Institute Report. The effect of wind and temperature gradients on sound propagation outdoors. 11. D. C. PRIDMORE-BROWN 1962 Journal of the Acoustical Society of America 34,438-443. Sound propagation in a temperature and wind-stratified medium. 12. A. D. PIERCE 1981 Acoustics: An Introduction to its Physical Principles and Applications. New York: McGraw-Hill. 13. V. A. FOCK 1965 Electromagnetic Diffraction andPropagation Problems. Oxford: Pergamon Press. 14. K. B. RASMUSSEN 1982 Danish Acoustical Institute, Report 35 Sound propagation over non-flat terrain. 15. C. F. CHIEN and W. W. SOROKA 1980 Journal of Sound and Vibration 69, 340-343. A note on the calculation of sound propagation along an impedance surface. 16. S. LINDBLAD 1979 Personal communication. 17. American National Standard S1.26-1978. Method for the calculation of the absorption of sound by the atmosphere. 18. B. A. DE JONG 1983 Ph.D. Thesis, Devt Chtiuersity Press. The influence of wind and temperature gradients on outdoor sound propagation. 19. R. E. MUNN 1966 Descriptioe Micrometeorology. London: Academic Press. 20. C. LARSSON and S. ISRAELSSON 1981 Uppsala University, Report. The influence from meteoro- logical parameters on sound propagation from a point source, Part 1, Atmospheric refraction (in Swedish). 21. M. ABRAMOWITZ and I. A. STEGUN 1965 Handbook of Mathematical Functions. Washington D.C.: National Bureau of Standards, Applied Mathematics, Series 55. OUTDOOR SOUND PROPAGATION 335 APPENDIX: NOTES ON THE CALCULATION OF THE PRECISE THEORY The numerical integration of equation (3) with either equation (13) or equation (16) inserted is far from simple. First, appropriate expressions for the u and w functions must be found. Both functions are closely related to the Airy function Ai [12,13]: u(t) = r”2Ai( t), w(t)=2?r l/2 ei”/6Ai( t ei2r/3). (AI, A2) Series representations for Ai may be found in the book by Abramowitz and Stegun [21]. For t much larger than one the following approximations were used: v(t) = 0.5t-“4 eex, w(t) = tC”4 ex, v’(t) = -0.5t”4 epx, w’(t) = t1’4 ex, (A3) where x = (2/3) t 3’2 For large negative arguments similar expressions could be obtained: . u(-r) E r-‘/4 sin (x+ g/4), w(-t)= t -l/4 ei(*+rr/4) 3 v’(-t)--tt”4COS(X+7r/4), wl(_t) ~ _it1/4 ei(x+r/4)s (A4) Whenever the argument was large enough, v and w were calculated by means of equations (A3) and (A4) in order to save computer time. The Bessel function in equation (3) was calculated from rational approximations [21]. The actual numerical integration was performed by repeated use of Simpson’s rule [21]. It was discovered that for upwind propagation it was suitable to integrate from 0 to 2 k(O), with 2000 points used in the numerical integration. For frequencies between 1 kHz and 2 kHz it was, however, sufficient to integrate from 0 to 1.5 k(O). For downwind propagation the phase of the integrand varies rapidly for K close to zero. In this case it was found suitable to integrate only in a small interval around k(0). The integration was performed over the K-interval [(-4k(0)/12+ k’(O))“‘, (4k(0)/12+ k’(O))“‘], (A5) where 1 is defined in connection with equation (10). The number of points was 600. If the above interval was increased, the number of points had to be increased very much, but the results were virtually unchanged. September 3, 2018 VIA EMAIL: council@dublin.ca.gov Dublin City Council 100 Civic Plaza Dublin, CA 94568 RE: Valley Christian Center Planned Development Zoning Amendment and Site Development Review Permit (PLPA-2014-00052) for the Project site located at 7500 Inspiration Drive Dear City Council Members: I have a PhD in nuclear physics and am the Discovery Science Program Manager, a senior scientist and Distinguished Member of the Technical Staff at Lawrence Livermore National Laboratory (LLNL). I am also a fellow of the American Physical Society (APS), recipient of the APS Excellence in Plasma Physics award (Dawson award), recipient of the American Nuclear Society Excellence in High Energy Density Physics award (Teller award), and author/coauthor of over 400 in the scientific literature on nuclear physics, plasma physics, high pressure materials science, and laboratory astrophysics. I am writing to you regarding my concerns over the Valley Christian Center’s (VCC) plans to develop a stadium, which will be situated about 500 feet away from our property. The increased noise levels projected to result from this development have not been adequately assessed or analyzed. Three points need to be raised as follows: 1. In their report, VCC say that they accounted for sound attenuation due to distance and topography, and conclude that the increased noise level from the project would be up to 1 dB. They do not mention the effects of wind and temperature gradients. For noise from VCC traveling downwind, the effect of wind can cause refraction (or bending) of the sound waves downwards towards the ground, enhancing the sound strength that reaches the surrounding neighborhoods. Our initial estimates, based on published scientific literature suggest, depending on frequency, that the noise level increase due to wind on the downwind side could be up to ~10 dB, compared to the case of no wind. This wind effect could enhance significantly the 1 dB noise level estimate given in the VCC reports to 10 dB. The two relevant scientific papers are attached. 2. There is potential sound amplification due to a “wind tunnel effect” from the surrounding roads, bounded on either side by houses which act like the walls of a wind tunnel. Consequently, sound may be able to travel much further into the surrounding neighborhoods than one might otherwise assume, which is an effect not taken into consideration in the VCC reports. 3. The VCC calibration measurements of noise level vs distance were done on flat land near San Jose, whereas VCC sits 100-200 ft above the affected neighborhoods in west Dublin in hilly land, enhancing the distance that noise produced at VCC above us can propagate into our neighborhoods. Based on my initial review of various related reports posted on the City’s website, I believe that further substantive study and analysis of this development project relating to the effects on noise propagation of wind, temperature, and the “wind tunnel effect” is essential prior to final approval. Therefore, I request that City Council postpone making a decision during its September 4th meeting and send the matter back 2 to the Planning Commission for further review and analysis, based on the scientific deficiencies in the noise analysis of this project. Sincerely, /Bruce A. Remington/ Bruce A. Remington 11221 Las Palmas Ct. Dublin, CA 94568 cc: Chris Foss, City Manager, City of Dublin, via email chris.foss@dublin.ca.gov Caroline P. Soto, City Clerk, City of Dublin, via email caroline.soto@dublin.ca.gov Encl: David C. Pridmore-Brown, Sound Propagation in a Temperature- and Wind-Stratified Medium; The Journal of the Acoustical Society of America 34, 438 (1962) K.B. Rasmussen, Outdoor Sound Propagation Under the Influence of Wind and Temperature Gradients; Journal Sound and Vibration M(2), 321-335 (1986) Three (3) viewgraphs on Sound Effects Due to Wind remington_VCC_3.pptx;1 “Sound propagation in a temperature-and wind-stratified medium,” David C. Pridmore-Brown, MIT, The Journal of the Acoustical Society of America, Vol. 34, No. 4 pp. 438-443 (April 1962). The effects of sound propagation traveling with the wind could increase the sound levels by up to 10-15 dB, based on theory, simulations, and reference experiments. The effects of sound propagation traveling with the wind could increase the sound levels by up to 10-15 dB, based on theory, simulations, and experiments, described in published scientific papers. The VCC report, which does not mention wind effects, estimates the increased noise level would be 1 dB.Our (very preliminary) estimates, based on published scientific literature, is a factor of 10 higher. “Outdoor sound propagation under the influence of wind and temperature gradients,” K.B. Rasmussen, Danish Acoustical Institute, Technical University of Denmark, Journal of Sound and Vibration 104 (2), 321-335 (1986). 0 m/s 5 m/s 3 1 Wind level: 0 m/s 5 m/s 3 1 Wind level: (1 m/s ~ 2 mph) (1 m/s ~ 2 mph) <http://www.hkphy.org/iq/sound_wind/sound_wind_e.html> remington_VCC_3.pptx;2 <http://www.hk-phy.org /iq/sound_wind/sound_wind_e.html> <https://weatherspark.com/y/1074/Average-Weather-in-Dublin-California-United-States-Year-Round#Sections-Wind> remington_VCC_3.pptx;3 Sound wave travels faster in the air when it is with the wind. Generally speaking,wind speed is lower near the ground because of the presence of blockages, and so it increases with height (Fig. 1). Therefore, when traveling with the wind,sound wave farther from the ground travels faster. <http://www.hkphy.org /iq/sound_wind/sound_wind_e.html> Dear Mayor and Councilmembers, September 25, 2018 My name is Rongfu Xiao and my house is located at Las Palmas court, less than 400 feet from the VCC property line.Here I would like to make some comments about VCC’s early noise assessment for their multipurpose sport field. Although I am not a sound expert, I do have a PhD in Physics and I do have scientific knowledge about sound propagation. Actually I have written about 50 US patents and one of which is about sound insulation. We know sound travel very dependent on wind direction: we hear very loudly if we are downstream, but weakly in the upstream from the source. In west Dublin, we are in 580 freeway corridor with strong winds from the east Bay. Unfortunately our neighborhood is directly down steam from VCC. In the early report it said in May 2015 the sound contractor Illingworth &Rodkin (I&R)did long term noise tests in two spots to project the future noise impact to its neighborhood:One spot (LT1)near the future stadium to represent the source of noise environment and another spot (LT2)in Las Palmas neighborhood to represent the noise-receptor,and claimed that the noises from the future football field will not exceed city noise standard in its neighborhood.But if you go to that test spot LT 2,you will realize that it is a noise blind-spot about 50 feet right below the flat area where the football field is to be built.As an experimental physicist,I did some noise measurement in our neighborhood last week myself.Here is my finding:The noise level at VCC test spot (LT2)was indeed between 35-50dB,while the noise level elsewhere in our neighborhood is between 45-75dB depending on the time and wind speed,a 15-20dB higher noise level than at LT 2.The chief engineer from the sound contractor also admitted that they intentionally chose such a quite spot as their reference.Were they trying to avoid the actual noise condition in VCC’s neighborhood so that it can pass the city required noise standard? In the report,I&R used an existing noise level of football games from Santa Teresa High School in San Jose as an analogy to their future football noise here.This is totally an UNACCEPTABLE COMPARISON.Here we have a very different micro-climate as compared with Santa Teresa (hill-top here versus valley over there,wind tunnel here versus still-air over there). At this time,we neither believe I&R’s noise assessment study is adequate &convincing and nor the game noise analogy is appropriate.Here I strongly request City planning committee to re-consider VCC application and make sure it truly meets city's noise standard before approving this project. Valley Christian Center Supplemental Mitigated Negative Declaration / Initial Study (Test spots of noise assessment by I&R (see P. 65 of report in PLPA-2014-00052)