Basics of meteorology for outdoor sound propagation and related modelling issues

2.1 Atmospheric stability

Actual everyday conditions of the atmosphere rarely resemble those of the Standard Atmosphere, and this is especially true for the lower layers of air masses, where sound propagation occurs. The ABL is the bottom layer from the ground to the altitude between 0.2 and 4 km of the troposphere (Figure 1), varying in thickness over space and time. ABL is often turbulent and is affected by solar radiation, winds (surface drag), humidity, and temperature (heat fluxes) near the Earth’s surface.

Figure 1

ABL (shaded). The Standard Atmosphere is dotted, along with typical temperature profiles during the day (black line) and night (blue line). Adapted from the study by Stull [9].

In terms of sound propagation, the main feature of the ABL is atmospheric stability, which refers to the ability of the atmosphere to be turbulent, which, in turn, can be determined from vertical profiles (soundings) of temperature, wind, and humidity. Stability varies with time and place because of the corresponding variation of the thermodynamic state of the air.

Formally, fluid-flow stability is a characteristic of how the system reacts to little disturbances: if these are damped, the system is stable; if they are amplified, the system is unstable. Roughly, three main atmospheric classes can be distinguished:

1. Unstable: air is turbulent (i.e. gusty, stormy);

2. Stable: air is laminar (i.e. non-turbulent, smooth);

3. Neutral: air shows no tendency to change (disturbances are neither amplified nor dampened).

Many processes concur to determine flow stability: in the first place, buoyancy (air parcels’ tendency to rise or sink) and wind shear (change of wind speed or direction with altitude); secondarily, inertia and rotation. If we consider buoyancy alone, we refer to static stability; when wind shear is also accounted for, we refer to dynamic stability.

An air parcel (an imaginary volume of air, dimensions of a city block, to which may be assigned any or all of the basic dynamic and thermodynamic properties of atmospheric air) undergoing an adiabatic process is characterised by a vertical temperature gradient Γ _d = 9.8 K/km (9.8°C/km), called the dry adiabatic lapse rate.

It can be proved, refer to the study by Stull [9] for more details, that if an unsaturated air parcel is slightly displaced adiabatically upward or downward in the Standard Atmosphere, its temperature will respectively be cooler or warmer than the corresponding environment. Thus, it will be pushed back to its original position either way. In short, the Standard Atmosphere is statically stable because its environmental lapse rate γ (6.5°C/km) is smaller than the dry adiabatic lapse rate Γ _d (9.8°C/km).

The above outcome also applies to any other environmental lapse rate (e.g. actual temperature profile) and both dry (unsaturated, Γ _d) and moist (saturated, Γ _s) air parcels.

As mentioned, dynamic stability is controlled by buoyancy and wind shear. The main physical quantities in a laminar flow becoming turbulent are temperature sounding (vertical profile) and variation (vertical profile) of the square of the horizontal components of wind speed U (east–west) and V (north–south), that is (ΔU)² and (ΔV)², their sum representing the kinetic energy available to cause turbulence.

2.2 The ABL

Air masses closer to the Earth’s surface are often turbulent, which causes mixing and homogenising of the lower layers of the Standard Atmosphere.

Static stability via buoyant forces determines and controls the formation and structure of the ABL, which is variable with location and time. It extends from ground to altitude between 0.2 and 4 km of the troposphere, and because turbulent transport causes the ABL to undergo the direct effects of the Earth’s surface, it exhibits substantial diurnal and seasonal variations in terms of wind, temperature, and moist conditions. These, in turn, determine strong effects on sound propagation.

Figure 2 shows the fair weather ABL daily cycle by season at mid and high latitudes; the ABL components are a statically unstable mixed layer (ML), a stable boundary layer, and a statically neutral residual layer (RL). The entrainment zone (EZ), separating the ML from the upper atmosphere, is strongly stable and characterised by intermittent turbulence; in the late afternoon in winter and at the beginning of the night in summer, turbulence ceases, leaving a strongly statically stable layer called the capping inversion (CI).

Figure 2

Components of the ABL during fair weather over land and daily cycle by season (at mid and high latitudes). White stands for statically unstable air, light blue for neutral stability, and darker blue for stronger static stability. Adapted from the study by Stull [9].

If the wind moves ABL air over ground (or water) surfaces of different temperatures, the ABL structure can evolve in space rather than time. The crucial factor is always the temperature difference between the Earth’s surface and the air: a warmer ground (or water) surface will determine a ML, whereas colder surfaces will generate stable layers. So, an unstable layer occurs whenever colder air blows over a warm surface, day or night; thermals of warm air rise from the surface to an altitude of 0.2–4 km, and turbulence is vigorous. On the other hand, a stable layer will form whenever warmer air blows over a cold surface, regardless of the time of the day; so-formed layers are usually shallow (20–500 m). Finally, neutral conditions occur during overcast, typically associated with bad weather; winds will be moderate to strong. As shown in Figure 2, stable conditions favourable to long-distance sound propagation occur more frequently at night than during the daytime and in winter rather than summer.

2.3 Typical temperature and wind speed profiles

The ABL bottom (from 0 to 20/200 m), called the surface layer (SL), undergoes the most substantial variations in temperature, wind speed, and humidity with altitude, regardless of the time of day. During the daytime, the SL is extremely unstable; warm blobs of air (thermals) rise from it through the ML (where the environmental lapse rate γ is nearly adiabatic) to the EZ. A typical temperature profile at 3 p.m. is outlined in Figure 3 left, and Figure 3 right sketches a zoom of the SL temperature profile.

Figure 3

Typical boundary-layer (left) and surface-layer (right) temperature profiles during fair weather over land at 3 p.m.; the dry adiabatic lapse rate Γ _d is dashed; altitudes are illustrative. Adapted from the study by Stull [9].

At night (around 3 a.m.), the ground is typically colder than at other times of the day, and the bottom part of the ML reduces its temperature too. Thus, the SL and this portion of ABL are stable. On the other hand, the upper part of the ABL (i.e. the residual layer, RL) has not undergone cooling from the ground and maintains the nearly adiabatic environmental lapse rate of the previous day. Then, high up, there is the non-turbulent CI.

A typical temperature profile at 3 a.m. is outlined in Figure 4 left, and Figure 4 right sketches a zoom of the SL temperature profile, where thermal inversions usually occur at night.

Figure 4

Typical boundary-layer (left) and surface-layer (right) temperature profiles during fair weather over land at 3 a.m.; the dry adiabatic lapse rate Γ _d is dashed; the heights are illustrative. Adapted from the study by Stull [9].

The wind profile is no less important than the temperature profile. Like temperature, winds typically experience a diurnal cycle over land in fair weather. At 9 a.m., for instance, a shallow near-surface ML is expected, say 300 m thick, as shown in Figure 5. Within this unstable layer, subgeostrophic winds (where “sub” means the wind speed is less than the geostrophic) are uniform with altitude, except near the surface where wind speed approaches zero. Later in the day, say at 3 p.m., the ML has developed, and the layer of uniform subgeostrophic winds deepens accordingly, leaving moderate winds near Earth’s surface. After sunset (e.g. at 9 p.m.), turbulence intensity diminishes, causing two opposite effects: (1) the winds at the ground level get slower because the surface drag effect is not balanced anymore by the mixing with faster upper winds, and (2) the air in the mid-ABL decouples from the slower near-surface winds and begins to move faster. At night (e.g. at 3 a.m.), winds can be supergeostrophic (where “super” means the wind speed is greater than the geostrophic) a few hundred meters above ground and calm at the Earth’s surface due to the combination of a minimum of turbulence and a maximum of surface drag; the low-altitude region of supergeostrophic winds is called a nocturnal jet. After sunrise, turbulence begins again, together with a new daily cycle.

Figure 5

Typical ABL wind profiles; G is the geostrophic wind speed, M _BL is the average ABL wind speed, and z _i is the average ML depth at 3 pm. Adapted from the study by Stull [9].

As for the wind speed evolution with altitude, up to roughly 50 m of altitude, winds are calm at night and get stronger during the daytime; the opposite occurs above 100 m, where winds are slower during the day because of the turbulent mixing and faster at night when turbulence ceases.

In terms of friction velocity u* (ranging from 0 m/s for calm winds to 1 m/s for strong winds and being about 0.5 m/s for moderate winds) and roughness length z ₀ (whose typical values range from 0.0002 at sea to 2 or more inside large cities), wind profiles in neutral and stable atmosphere can be described.

For a statically neutral atmosphere (say overcast and windy) over a uniform surface, wind speed M is zero at an altitude equal to the aerodynamic roughness length z ₀; speed increases then approximately logarithmically with altitude in the SL, according to the equation:

with the von Karman constant k equal to 0.4. Thus, knowing wind speed M ₁ at height z ₁, wind speed M ₂ at any other height z ₂ is calculated by the equation:

When the atmosphere is statically stable, wind speed is slower near the ground and faster higher up than would result from a logarithmic profile. Under such conditions, a formula giving the SL wind profile is a log-linear one, i.e. with both a logarithmic and a linear term in z, as follows:

with the known meaning of the symbols M, k and z ₀. The L parameter is the Obukhov length (m), conceivable as the height in the stable surface layer below which, notwithstanding buoyant forces, some turbulence mechanically generated by wind shear is present. As pointed out in the study by Sathe et al. [10], atmospheric stability classification based on Monin–Obukhov length is possible.

During statically unstable ABLs, strong convective thermals are generated, making wind speed uniform with altitude a short distance above the Earth. Between this uniform wind-speed layer and the ground is the radix layer (RxL); in the bottom of RxL, wind speed increases more rapidly with altitude than would be expected from a logarithmic profile, like that of a neutral surface layer; it then approaches the uniform wind speed M _BL in the mid-mixed layer.

A summary of the above about wind profiles is shown in Figure 6.

Figure 6

Typical surface layer wind speed profiles for different static stabilities; z _RxL and z _SL give order-of-magnitude depths for the radix layer and SL. Adapted from the study by Stull [9].

2.4 Effective speed of sound

The literature on this topic [1,11–14] shows that sound propagation is affected by the atmosphere state via refraction, scattering, and absorption phenomena. Vertical wind speed and temperature gradients govern refraction, the most decisive factor of all.

The wind speed component in the direction of sound propagation controls the strength of wind-induced refraction, and the angle between the horizontal wind direction and the source-receiver path determines upwind, downwind, or crosswind propagation. Wind speed also controls scattering by shear-induced turbulence. As for the temperature, a negative vertical gradient (i.e. a positive lapse rate) refracts sound upward and enhances scattering because of the generation of buoyancy-induced turbulence, whereas temperature inversion refracts sound downward and extinguishes scattering because turbulence is damped. Lastly, and less importantly, temperature and relative humidity determine the degree of air absorption (more effective at the highest sound frequencies), and relative humidity hardly influences the vertical speed of sound.

It is worth noting that the refraction of sound in the atmosphere can be described by a single parameter representing the effective sound speed c _eff(z), the sum of the adiabatic (in dry air) sound speed c(z) and the horizontal wind speed component u(z) in the source-receiver direction, as per the formula (simplified via Taylor expansion):

with κ = c _p/c _v = 1.4 (ratio of the specific heat capacities at constant pressure and constant volume, respectively), R = 287 J/kg/K (the gas constant of dry air), T representing the temperature (K), and T ₀ the surface temperature.

Thus, the effective sound speed c _eff(z) now shows a linear dependence with both temperature T(z) and wind speed u(z), and the goal is to classify vertical profiles of c _eff with respect to an appropriate number of parameters. According to Heimann and Salomons [13], a suitable (logarithmic-linear) relationship that accomplishes the task is the expression:

This relationship was tested using the meteorological tower measurements at Garching (near Munich) over 1 year [13]. First, c _eff(z) was determined from the measured values at the sensor heights (0.2–50 m) via Eq. (4). Then, the logarithmic-linear profile function parameters were determined by applying a curve-fitting algorithm. In the second stage of the analyses, acoustic simulations based on the Crank–Nicholson Parabolic Equation were performed, taking into account the different meteorological situations (grouped in classes) that occurred at Garching during the one-year measurements period. Two ground types were taken into consideration, namely rigid and absorbing; point-source and receiver heights were set at 0.5 and 4 m, respectively; calculations were performed at three different source-receiver distances: 20, 200, and 1,000 m. The findings of the study performed by Heimann and Salomons [13] can be summarised as follows:

1. the instantaneous sound levels vary due to different meteorological conditions by up to 2 dB @20 m, 18 dB @200 m, and 42 dB @1,000 m;

2. as a consequence of the specific meteorological conditions, the annual average night-time level exceeds the annual average day-time level by up to 5 dB;

3. ignoring meteorological effects, namely taking c _eff(z) as independent of z, in the determination of annual A-weighted average sound levels would cause errors of up to 9 dB @1,000 m for the geometry investigated;

4. even considering a small number of meteorological classes reduces the error substantially: nine logarithmic-linear classes are necessary to reduce the risk to less than 20% that the annual average sound level @1,000 m in an arbitrary climate is estimated with an error of more than 2 dB;

5. given the number of classes, the expected errors in the annual-average sound level estimates are larger for absorbing ground than for a rigid one;

6. purely linear profile classes perform better than purely logarithmic classes, but in both cases, they are worse than mixed logarithmic-linear classes.

3.1 The scenario

The main features of the basic scenario (and sub-scenarios) setup for the calculations are as follows:

1. straight road 1 km long, no longitudinal and lateral slope, newly paved with non-porous asphalt;

2. Average Annual Daily Traffic: 16,500 vehicles (about 6 million vehicles per year), 95% light and 5% heavy vehicles, steady traffic flow, average speed of 90 km/h for both light and heavy vehicles;

3. flat terrain;

4. no obstacles, such as buildings, trees, or other objects (free field sound propagation);

5. two alternative ground absorption values, namely hard G = 0.2 and soft ground G = 0.8;

6. three receivers, all 4 m above the ground, and at three different perpendicular distances from the road edge, namely R1 = 15 m, R2 = 200 m, and R3 = 500 m.

The SoundPLAN software (ver. 8.2) was used to set up the acoustical–geometrical model and to perform the calculations according to the chosen numerical models, all implemented in the software.

3.2 The calculation methods

The chosen calculation methods were the NMPB-Routes 1996 (from 2002 to 2019, the interim European method required by Directive 2002/49/EC of the European Parliament [16] for road traffic noise), CNOSSOS-EU (since 2019, the new common European method required by Directive 2002/49/EC of the European Parliament [16] for all types of sources) and NORD2000 (a calculation method having a detailed approach for meteorological factors).

The models use different frequency ranges at both the lower and upper ends; however, this is not a concern, given the A-weighting in the lower part and the absence of traffic sound energy in the upper part.

3.3 The meteorological conditions and settings used for the calculations

The parameters common to all methods and selected for the computation were as follows:

1. max search radius: 2,000 m;

2. max reflection distance – receiver (R): 200 m;

3. max reflection distance – source (S): 50 m;

4. reflection order: 1;

5. ground absorption G = 0.2 and G = 0.8; in NORD2000, the terrain characteristics were specified via the effective flow resistivity, σ (kN sm⁻⁴), and the roughness class (m); the chosen values were σ = 5,000 (hard soil), roughness = 0.25 (nil) corresponding to G = 0.2, and σ = 31.5 (soft forest floor), roughness = 1 (medium) corresponding to G = 0.8. Hereinafter, the terrain is labelled with the coefficients G = 0.2 or G = 0.8 for all the calculation methods.

Settings for calculation of horizontal grid maps were as follows:

• – grid space (m): 2;

• – grid height (m): 4.

• Settings for calculation of vertical grid maps were as follows:

• – grid space (m): 1;

• – grid height (m): 20.

NMPB-Routes 1996 and CNOSSOS-EU manage weather-related issues the same way; two types of calculations were performed: 100% downwind conditions (sound waves bent to the ground) and 100% homogeneous conditions (sound propagating along straight lines). NORD2000 allows the simulation of both favourable and unfavourable conditions, and this can be done via the two different approaches, namely engineering-statistical and physical-parametric, described in Section 2.2. For the engineering-statistical approach, the settings selected for the calculations are given in Table 3.

For calculations via the physical-parametric approach, the selected parameters are reported in Table 4.

Since the focus of the article is not on the source module (emission database), the three methods have been fine-tuned (for favourable conditions scenarios) to deliver almost equal sound levels at the nearest receiver (R1), namely within a small span (1.1 dB); the process required minimal changes in sound power levels.