Prediction of Aircraft Noise Impact with Application to Hong Kong International Airport

As part of a collective research effort towards greener aviation, the present study focuses on the noise impact of aircraft operations around major airports. To this end, an aircraft noise prediction platform is developed, which relies on state-of-the-art functionalities as well as more specific, innovative features. Originally built upon the Aircraft Noise and Performance (ANP) database and its Noise–Power–Distance (NPD) table, the method is further refined to alleviate most of their inherent limitations (e.g., standardized and simplified aircraft noise scenarios). The resulting aircraft noise prediction platform is validated against benchmark cases of increasing complexity, being then applied to real-life situations involving actual aircraft operations around Hong Kong International Airport (HKIA). Specific comparative analyses are conducted, which allow highlighting the variability of the noise impact by aircraft, depending on their type (A330, B777) and/or operational conditions (power settings, meteorological conditions, routes, banks, etc.). The study delivers insightful outcomes, whether phenomenological (aircraft noise impact) or methodological (aircraft noise prediction). As a by-product, it illustrates how noise prediction methods/platforms such as the present one may help in guiding the further expansion of airport operations and/or infrastructures (as is currently the case with HKIA).


Introduction
The development of low-noise technologies and the establishment of more stringent regulations have led to a continuous decrease in the noise impact by air traffic over recent decades [1]. However, the environmental noise pollution caused by civil aviation is still a major societal concern, because of the many adverse effects it entails (annoyances, sleep disturbances, health issues, educational achievements, etc.) [2][3][4]. This makes aircraft noise a show-stopper for airports expansion [5], which may question the sustainable development of the aviation market [6][7][8] whose annual growth is about 5% [9]. Therefore, mitigating the noise impact of civil aviation is of utmost importance for all major countries, especially those which possess large aviation hubs located nearby highly dense cities, such as China [10,11]. Indeed, not only China is the most populous country in the world, but it also ranks second in the world in terms of passenger air traffic and it has now replaced the United States as the world's largest aviation market [12]. In particular, Hong Kong, which is the world's sixth most densely populated city, is also the busiest airport in terms of cargo volume, worldwide. To cope with the growing demand for air transportation, the Hong Kong International Airport (HKIA) is now expanding its capacity, through the deployment of a third runway [13]. This obviously raises legitimate concerns about how the noise impact by aircraft operations will affect the many residential areas surrounding HKIA.
Aircraft noise has been a matter of intense research over the past 50 years. Essentially, two main approaches exist to mitigate aircraft noise, namely at the aircraft level by reducing its sources [14] and at the operation level by reducing its perceived impact on the or add convection effects due to winds. Whereas the former effect can be incorporated in a rather straightforward manner, the latter raises more challenges in terms of practical implementations and CPU cost efficiency. Figure 1 sketches the overall methodology, both summarizing the baseline approach [49] and highlighting the specific addendums brought to it in the present work. Yet, not all of these effects can be incorporated in the approach, which would be too complex and costly otherwise. For instance, one can here remind that the sound refraction originates from the atmospheric heterogeneities, which either affect the sound speed (and thus the acoustic impedance) through the pressure and temperature variations, or add convection effects due to winds. Whereas the former effect can be incorporated in a rather straightforward manner, the latter raises more challenges in terms of practical implementations and CPU cost efficiency. Figure 1 sketches the overall methodology, both summarizing the baseline approach [49] and highlighting the specific addendums brought to it in the present work.  [49] (in black) whereas incorporating specific addendums (in red).

Baseline Approach
This section gives a brief overview of the baseline approach, whose detail can be found in [49]. Recommended by the International Civil Aviation Organization (ICAO), this approach is widely adopted by airports and legislation authorities for assessing the noise impact of aircraft operations (at least for commercial aircraft) [55].
As detailed in ref [53], this methodology relies on the fragmentation of the flightpath into specific segments, each one being allotted the aircraft corresponding characteristics (position, power settings, airspeed, etc.). Those characteristics are then translated into suitable inputs (power settings, aircraft-to-ground distance) for the NPD-based noise prediction tool to assess the aircraft noise impact on the ground. More precisely, the 3D flightpath is decomposed into the so-called ground track (i.e., the vertical projection of the flightpath on the ground) and flight profile (i.e., the altitude changes of the aircraft along the ground track), both of which are made of a finite number of continuous straight-line segments. The detail of these flight segments (endpoints) and associated aircraft characteristics (operational data) can be inferred from the flightpath records (either radar or Flight Data Recorder, FDR), or estimated using specific formulas [49]. Using this, the aircraft power settings and aircraft-to-ground distance can be obtained, thereby allowing the  [49] (in black) whereas incorporating specific addendums (in red).

Baseline Approach
This section gives a brief overview of the baseline approach, whose detail can be found in [49]. Recommended by the International Civil Aviation Organization (ICAO), this approach is widely adopted by airports and legislation authorities for assessing the noise impact of aircraft operations (at least for commercial aircraft) [55].
As detailed in ref [53], this methodology relies on the fragmentation of the flightpath into specific segments, each one being allotted the aircraft corresponding characteristics (position, power settings, airspeed, etc.). Those characteristics are then translated into suitable inputs (power settings, aircraft-to-ground distance) for the NPD-based noise prediction tool to assess the aircraft noise impact on the ground. More precisely, the 3D flightpath is decomposed into the so-called ground track (i.e., the vertical projection of the flightpath on the ground) and flight profile (i.e., the altitude changes of the aircraft along the ground track), both of which are made of a finite number of continuous straightline segments. The detail of these flight segments (endpoints) and associated aircraft characteristics (operational data) can be inferred from the flightpath records (either radar or Flight Data Recorder, FDR), or estimated using specific formulas [49]. Using this, the aircraft power settings and aircraft-to-ground distance can be obtained, thereby allowing the aircraft noise impact to be assessed through proper (linear and logarithmic) interpolations of the NPD database. As was said, however, the NPD database is built upon an ideal scenario following which the ground observer would be located right below the aircraft, with the latter flying at a constant speed and power settings along an infinite horizontal flightpath and under specific atmospheric conditions. For the method can be applied to more realistic scenarios, it is thus needed to enhance it with several correction terms, namely, start-of-roll directivity, engine installation, finite segment, duration, acoustic impedance, and lateral attenuation adjustments. The start-of-roll directivity correction reflects the highly directive radiation pattern of the engine noise during the take-off roll. The engine installation correction accounts for the modification of the aircraft noise source directivity due to the integration of the engines within the airframe (e.g., scattering by the wings, refraction effects in the nearfield, etc.). The finite segment correction translates the fact that, different from the NPD assumption, the flightpath is made of finite segments. The duration correction accounts for the difference between the actual aircraft speed and that from the NPD standard (160 knots), such disparity in speed translating into shorter or longer sound exposures. The acoustic impedance adjustment accounts for the difference between the local atmospheric conditions (taken at the airport level [49]) and that from the NPD standard. The lateral attenuation translates all the noise interferences induced by the reflection (and, to a lesser extent, by the refraction) effects inherited from the ground presence. Here it is worth noticing that these refraction effects are incurred by either the temperature and/or wind gradients induced by the ground, depending on its characteristics (e.g., roughness, heat transfer). All these correction terms enable the NPD-based noise prediction tool to assess more accurately the noise impact of aircraft in different scenarios. As an illustration, Appendix B exemplifies how these various correction terms weigh on the prediction of the noise impact by a typical aircraft at take-off.

Specific Improvements Brought to the Methodology
The ANP database is built on a standardized scenario of aircraft operations (flight profile, power settings, airspeed, etc.). However, in reality, the actual operations often deviate from these standard cases, due to various factors (terrain, wind speed and direction, noise abatement flight procedure, etc.). For the overall methodology to be closer to reality, the NPD-based noise prediction must therefore be enhanced with various refinementswhich was carried out here and is summarized hereafter.

Refinement of the Aircraft Noise Emission (Intensity), through the Incorporation of the Actual Power Settings
Ideally, the aircraft operational data should be inferred directly from actual records (either radar or Flight Data Recorder, FDR). Whereas FDR data offer the most comprehensive and accurate information, their proprietary nature makes them difficult to access. Conversely, radar data are open source and therefore readily available but they offer less detailed information. For instance, the flightpath characteristics of any aircraft can be easily accessed through their radar data, which can be accessed via public domain websites (e.g., FlightAware, Flightradar24, OpenSky Network, etc.). These data, however, do not provide any insights about the aircraft power settings, which makes them less straightforward to use in the present context. To overcome this issue, the present approach incorporates a functionality that offers assessing the aircraft power settings directly from the flightpath characteristics (flight profile and airspeed). To this end, we derive a simplified model for the thrust to be delivered by the engines when the aircraft is in dynamic equilibrium, whether it is considered at roll or aloft. By developing the corresponding equations of motion (cf. Appendix A), one can express the aircraft thrust via the following integrated formula (which is valid whether the flight segment is, i.e., either ground roll or aloft): In the above, T indicates the thrust (in lbf), L is the lift force, C D /C L is the drag-to-lift ratio, m is the aircraft mass (in lbm), a is the aircraft inertial acceleration (in average), g is the gravitational acceleration. Besides, γ and φ, respectively, stand for the flightpath and bank angles (which are zero when the aircraft is on its ground roll). On the other hand, µ F is the friction coefficient [56], which accounts for the additional drag effect due to the runway (and is zero when the aircraft is aloft). From there, two scenarios can be distinguished: When the aircraft is aloft (µ F = 0), Equation (1) can be re-expressed as (cf. Appendix A) Oppositely, when the aircraft is on the ground roll (γ = φ = 0), and by introducing a lift model [57], one can show that (cf. Appendix A) where V TAS and V LOF stand for the aircraft true airspeed (TAS) and its value at lift-off, respectively. All parameters appearing in the above Equations (2) and (3) are readily available from the flight data and/or ANP database, for each aircraft type and flight setting. One can thus get the actual thrust directly from the aircraft and flight parameters, in all flight phases (whether the aircraft is aloft or on its ground roll). For being readily exploitable, however, the actual thrust must be scaled back to the standardized value upon which the NPD database is built upon, namely the corrected net thrust at sea level. To do so, the actual thrust is then adjusted through a gross-to-net thrust factor, which translates the fact that the thrust delivered at a given altitude deviates from its sea-level counterpart. This factor can be expressed through δ, the ratio of the ambient air pressure around the aircraft to the standard air pressure at mean sea level [23]. Once scaled by the number of engines, N, one finally gets the corrected net thrust per engine, to be used as input for the NPD database. The way the engines are mounted within the airframe affects the directivity of the aircraft noise source. These so-called acoustic installation effects can be partially incorporated through the aircraft bank angle [49], which relates to the depression angle (ϕ) that is directly linked to the engine installation (see Figure 2 below, as well as Figure A1 in Appendix A). Indeed, when installed on an aircraft, engines see their noise directivity importantly altered because of the multiple scattering effects induced by the airframe elements (e.g., wings) [23]. This directivity, which is measured through the depression angle, mostly depends on the way the engines are positioned within the airframe (e.g., wing-mounted, fuselage-mounted). From a ground observer perspective, the noise intensity is thus to be driven by the combination of the depression and bank angles. radius (which is determined from the circumradius of the triangle formed with its two neighboring points). From there, using the aircraft airspeed along with the gravitational acceleration, the bank angle is derived [49]. Once filtered out from all possible irregularities coming from the flight characteristics inaccuracies (especially the aircraft position and airspeed), the bank angle values are interpolated back to the original ground track. Section 4.3.1 and Appendix C illustrate the sensitivity of the noise prediction towards these bank effects. By definition, the departure flight sequence begins when the aircraft initiates its ground roll and terminates once it has climbed up to an altitude of 10,000 ft. Oppositely, the approach flight sequence starts when the aircraft has descended down to an altitude of 6000 ft and finishes at the end of the landing ground-roll [37]. Because of this somehow arbitrary definition of the departure and approach procedures, any flightpath segment that would be beyond their altitude ranges is usually discarded in the aircraft noise assessment process. This may lead to underestimating the noise levels on the ground, whose discarded flight segments may still contribute to, depending on the situation (e.g., aircraft settings/flightpath  ground observer relationship). In order to correct such a potential bias in the noise estimation, some authors proposed to automatically enhance the default flight sequences with an extra flight segment, of arbitrary length [49]. Given its arbitrary nature, however, this fix may be partially conclusive (e.g., extra flight segment of insufficient length). Therefore, we here propose to rather incorporate all the flightpath segments that actually contribute to the noise impact on the ground, on a case-by-case basis. To do so, the flight sequence is extended in a dynamic fashion, being automatically added all the flight segments that are beyond its standard altitude range-this being carried out until their contribution to the aircraft noise impact is negligible, i.e., the noise levels on the ground are converged. More detail about this process is provided in Section 4.3.2.

Dynamic Specification of Ground Observers
Classically, the aircraft noise impact is characterized using a set of ground observer locations, over which the noise contribution by the various flight segments is summed up over time-all this leading to integrated noise contour maps. The overall efficiency (i.e., accuracy and rapidity) of the noise prediction is directly driven by the number and distribution of these prediction points. Therefore, past researches focused on how to optimize the latter, for instance using irregular grids [58,59]. Different from the baseline methodology, the present method incorporates an advanced dynamic grid refinement functionality [37], which allows increasing locally the density of observers wherever and whenever needed. This dynamic, local grid refinement process is conducted automatically during In the absence of any specific formulas provided in Ref [49], the aircraft bank angle is here estimated through the flightpath turn radius, using a geometrical approach [37]. To do so, the ground track is first approximated (using cubic spline interpolation) as a succession of evenly spaced points, each one being then inferred its corresponding turn radius (which is determined from the circumradius of the triangle formed with its two neighboring points). From there, using the aircraft airspeed along with the gravitational acceleration, the bank angle is derived [49]. Once filtered out from all possible irregularities coming from the flight characteristics inaccuracies (especially the aircraft position and airspeed), the bank angle values are interpolated back to the original ground track. Section 4.3.1 and Appendix C illustrate the sensitivity of the noise prediction towards these bank effects.

Refinement of the Aircraft Noise Propagation (Distance), through the Dynamic Specification of the Ground Track and Observers Dynamic Extension on the Ground Track
By definition, the departure flight sequence begins when the aircraft initiates its ground roll and terminates once it has climbed up to an altitude of 10,000 ft. Oppositely, the approach flight sequence starts when the aircraft has descended down to an altitude of 6000 ft and finishes at the end of the landing ground-roll [37]. Because of this somehow arbitrary definition of the departure and approach procedures, any flightpath segment that would be beyond their altitude ranges is usually discarded in the aircraft noise assessment process. This may lead to underestimating the noise levels on the ground, whose discarded flight segments may still contribute to, depending on the situation (e.g., aircraft settings/flightpath ⇔ ground observer relationship). In order to correct such a potential bias in the noise estimation, some authors proposed to automatically enhance the default flight sequences with an extra flight segment, of arbitrary length [49]. Given its arbitrary nature, however, this fix may be partially conclusive (e.g., extra flight segment of insufficient length). Therefore, we here propose to rather incorporate all the flightpath segments that actually contribute to the noise impact on the ground, on a case-by-case basis. To do so, the flight sequence is extended in a dynamic fashion, being automatically added all the flight segments that are beyond its standard altitude range-this being carried out until their contribution to the aircraft noise impact is negligible, i.e., the noise levels on the ground are converged. More detail about this process is provided in Section 4.3.2.

Dynamic Specification of Ground Observers
Classically, the aircraft noise impact is characterized using a set of ground observer locations, over which the noise contribution by the various flight segments is summed up over time-all this leading to integrated noise contour maps. The overall efficiency (i.e., accuracy and rapidity) of the noise prediction is directly driven by the number and distribution of these prediction points. Therefore, past researches focused on how to optimize the latter, for instance using irregular grids [58,59]. Different from the baseline methodology, the present method incorporates an advanced dynamic grid refinement functionality [37], which allows increasing locally the density of observers wherever and whenever needed. This dynamic, local grid refinement process is conducted automatically during the noise prediction, which can be seen as a multi-stage calculation. More precisely, the noise prediction is first conducted on a coarse mesh, being then bi-linearly interpolated on a twice finer grid. The interpolated result is then compared to that of the direct calculation, which is repeated for each new grid point created. Whenever the two results fall within a certain threshold, the calculation is considered converged, and the local grid refinement stops. Should this not be the case, the process is repeated, until a local convergence is reached. Besides the tolerance (i.e., interpolation accuracy threshold), the degree of refinement is controlled through two other criteria, namely, the maximum refinement level allowed (with respect to the initial, coarse grid), and some pre-defined extrema of noise levels. Thanks to such a dynamic grid refinement functionality, the calculation process is optimal, offering the best trade-off in terms of accuracy and cost.

Refinement of the Aircraft Noise Propagation (Attenuation), through the Incorporation of Meteorological Effects
Aside from its emission characteristics (intensity, directivity), the aircraft noise is also driven by the properties of the atmospheric medium through which it propagates to the ground. It is not rare, however, that the actual atmospheric conditions deviate from the standard values upon which the NPD database is built. In this case, the noise prediction must be corrected from the specific biases induced by these offsets in atmospheric properties [55]. This can be achieved through two correction terms, namely, the acoustic impedance adjustment and the atmospheric absorption adjustment. The former correction accounts for the offset in the sound speed (which is driven by the atmospheric pressure and temperature values) whereas the latter accounts for the offset in the noise absorption effect (which is primarily driven by the temperature and relative humidity).
Deviation of the Sound Speed Characteristics (Acoustic Impedance Adjustment) Acoustic impedance adjustment accounts for the deviation of the medium sound speed with respect to its NPD standard value. This correction term [49] is classically built as a function of the atmospheric pressure and temperature (e.g. using Equation (4)(5)(6) and Equation (4-7) from Ref. [49]), both of which have a monotonic effect on the propagation. As exemplified in Figure 3, a rise in pressure (resp. temperature) shall result in a higher (resp. lower) correction required. The latter corrections, however, are usually moderate, with a variability that remains in the order of a decibel (dB). For instance, a pressure increase of 50 kPa entails a difference of +2.3 dB (regardless of the temperature), whereas a temperature increase of 40 • C induces an effect of −0.3 dB, regardless of the pressure. the noise prediction, which can be seen as a multi-stage calculation. More precisely, the noise prediction is first conducted on a coarse mesh, being then bi-linearly interpolated on a twice finer grid. The interpolated result is then compared to that of the direct calculation, which is repeated for each new grid point created. Whenever the two results fall within a certain threshold, the calculation is considered converged, and the local grid refinement stops. Should this not be the case, the process is repeated, until a local convergence is reached. Besides the tolerance (i.e., interpolation accuracy threshold), the degree of refinement is controlled through two other criteria, namely, the maximum refinement level allowed (with respect to the initial, coarse grid), and some pre-defined extrema of noise levels. Thanks to such a dynamic grid refinement functionality, the calculation process is optimal, offering the best trade-off in terms of accuracy and cost.

Refinement of the Aircraft Noise Propagation (Attenuation), through the Incorporation of Meteorological Effects
Aside from its emission characteristics (intensity, directivity), the aircraft noise is also driven by the properties of the atmospheric medium through which it propagates to the ground. It is not rare, however, that the actual atmospheric conditions deviate from the standard values upon which the NPD database is built. In this case, the noise prediction must be corrected from the specific biases induced by these offsets in atmospheric properties [55]. This can be achieved through two correction terms, namely, the acoustic impedance adjustment and the atmospheric absorption adjustment. The former correction accounts for the offset in the sound speed (which is driven by the atmospheric pressure and temperature values) whereas the latter accounts for the offset in the noise absorption effect (which is primarily driven by the temperature and relative humidity).
Deviation of the Sound Speed Characteristics (Acoustic Impedance Adjustment) Acoustic impedance adjustment accounts for the deviation of the medium sound speed with respect to its NPD standard value. This correction term [49] is classically built as a function of the atmospheric pressure and temperature (e.g. using Equation (4)(5)(6) and Equation (4-7) from Ref. [49]), both of which have a monotonic effect on the propagation. As exemplified in Figure 3, a rise in pressure (resp. temperature) shall result in a higher (resp. lower) correction required. The latter corrections, however, are usually moderate, with a variability that remains in the order of a decibel (dB). For instance, a pressure increase of 50 kPa entails a difference of +2.3 dB (regardless of the temperature), whereas a temperature increase of 40 °C induces an effect of −0.3 dB, regardless of the pressure. The atmospheric absorption relates to the energy dissipation that sound waves experience when interacting with air molecules. It is mostly driven by the temperature and relative humidity, upon which the atmospheric absorption adjustment is thus usually built [60]. As an illustration, Figure 4 depicts the difference in the noise levels that are The atmospheric absorption relates to the energy dissipation that sound waves experience when interacting with air molecules. It is mostly driven by the temperature and relative humidity, upon which the atmospheric absorption adjustment is thus usu- ally built [60]. As an illustration, Figure 4 depicts the difference in the noise levels that are radiated on the ground by a given sound source located at an altitude of 25,000 ft, depending on if the propagation medium corresponds to a standard or a non-standard atmosphere. As can be seen, these differences are nonlinear and non-monotonic, which makes it uneasy to predict how a given deviation in temperature and/or relative humidity shall impact the noise prediction. Notably, these effects may cancel out each other-as highlighted in Figure 4 by the red line, which depicts those atmospheric conditions for which the difference is nil. In the present approach, the atmospheric absorption adjustment not only incorporates the deviations in temperature and/or relative humidity (as classically carried out [60]), but it also includes those in atmospheric pressure. Relying on the so-called Volpe method [61], this correction is thus expected to yield still more accurate results, especially for what concerns long-distance propagation. For more detail about this correction term, the interested reader is referred to Ref. [49] (Equations (D-1) to (D-4)) and Ref. [61] (Equations (1) to (6), Equations (16) and (17)). These atmospheric absorption effects are further discussed in Section 4.2.
R PEER REVIEW 9 of 40 radiated on the ground by a given sound source located at an altitude of 25,000 ft, depending on if the propagation medium corresponds to a standard or a non-standard atmosphere. As can be seen, these differences are nonlinear and non-monotonic, which makes it uneasy to predict how a given deviation in temperature and/or relative humidity shall impact the noise prediction. Notably, these effects may cancel out each other-as highlighted in Figure 4 by the red line, which depicts those atmospheric conditions for which the difference is nil. In the present approach, the atmospheric absorption adjustment not only incorporates the deviations in temperature and/or relative humidity (as classically carried out [60]), but it also includes those in atmospheric pressure. Relying on the socalled Volpe method [61], this correction is thus expected to yield still more accurate results, especially for what concerns long-distance propagation. For more detail about this correction term, the interested reader is referred to Ref. [49] (Equations (D-1) to (D-4)) and Ref. [61] (Equations (1) to (6), Equation (16) and Equation (17)). These atmospheric absorption effects are further discussed in Section 4.2.

Validation of the Methodology Using Standardized Cases
In this section, the present noise prediction approach is validated using benchmark cases, which correspond to either virtual standard scenarios or to real-life but well-known situations (noise certification tests).

Standardized Scenarios
Here, we consider a total of 12 standardized scenarios, which were previously documented in [62]. These cases describe the noise impact induced by an aircraft, depending on its type and/or flightpath. More precisely, we here consider three different types of aircraft, namely, a jet-powered aircraft with either fuselage-mounted (JETF) or wingmounted (JETW) engines, as well as a propeller-powered aircraft (PROP). Each aircraft is taken under either a departure (D) or an approach (A) flight, which both follow either a straight (S) or a curved (C) route. Please, see Ref. [62] for a detailed description of these benchmark cases, some aspects of which are nevertheless further documented in Appendix B (e.g., aircraft routes, observers locations). Figures 5 and 6, respectively, depict the noise contour maps associated with all three aircraft at departure and approach (only the curved routes are considered, for the sake of conciseness). Of note, the noise metric used here is Sound Exposure Level (SEL). For each case, the differences between the present prediction and the reference one [62] are quantified using error maps (obtained by subtracting the reference values from the calculated results). As one can see, the agreement is good, with absolute error levels that are typically less than 0.01 dB. Notably, compared to some of the past works [23], the present calculations rely on a coarser distribution of ground observers, whereas delivering more accurate results (compare for instance the error map of JETFDC case with its counterpart from Ref. [23] whose visual rendering was here duplicated on purpose.).

Validation of the Methodology Using Standardized Cases
In this section, the present noise prediction approach is validated using benchmark cases, which correspond to either virtual standard scenarios or to real-life but well-known situations (noise certification tests).

Standardized Scenarios
Here, we consider a total of 12 standardized scenarios, which were previously documented in [62]. These cases describe the noise impact induced by an aircraft, depending on its type and/or flightpath. More precisely, we here consider three different types of aircraft, namely, a jet-powered aircraft with either fuselage-mounted (JETF) or wing-mounted (JETW) engines, as well as a propeller-powered aircraft (PROP). Each aircraft is taken under either a departure (D) or an approach (A) flight, which both follow either a straight (S) or a curved (C) route. Please, see Ref. [62] for a detailed description of these benchmark cases, some aspects of which are nevertheless further documented in Appendix B (e.g., aircraft routes, observers locations). Figures 5 and 6, respectively, depict the noise contour maps associated with all three aircraft at departure and approach (only the curved routes are considered, for the sake of conciseness). Of note, the noise metric used here is Sound Exposure Level (SEL). For each case, the differences between the present prediction and the reference one [62] are quantified using error maps (obtained by subtracting the reference values from the calculated results). As one can see, the agreement is good, with absolute error levels that are typically less than 0.01 dB. Notably, compared to some of the past works [23], the present calculations rely on a coarser distribution of ground observers, whereas delivering more accurate results (compare for instance the error map of JETFDC case with its counterpart from Ref. [23] whose visual rendering was here duplicated on purpose.).

PROPDC
0.0200 0.00423 PROPDS 0.0124 0.00159 All in all, these benchmark cases provide a validation of the present noise prediction platform and underlying methodology. Appendix B provides a further illustration (along with a more incremental validation) of the overall prediction process, exemplifying each calculation step in the particular JETWDS case.

Noise Certification Cases
To further assess the accuracy of the methodology as well as to lean towards real-life situations, the present section focuses on actual flight scenarios whose characteristics are however close enough from the ANP standard ones. To this end, we consider several noise certification flight tests, for which field measurements were made available by the European Union Aviation Safety Agency (EASA) [63]. These flights tests were performed for two different aircraft (B737-800 and A320-211), delivering for each the Effective Perceived Noise Level (EPNL) over a set of certification points. Indeed, aircraft noise certification tests follow a very specific protocol [64], which consists in flying the airplane along its standard approach and take-off flightpaths whereas measuring the resulting noise at three ground locations, namely the approach, lateral full-power and flyover reference points [64] (see. Figure 7). Notably, these ground measurements are performed such that the ground reflections are minimized at best (e.g., displaying the microphones over a flat terrain of known impedance, with no surrounding buildings, etc.). The two considered certification flights were here virtually duplicated using the noise prediction platform, thereby delivering the EPNL results provided in Table 2. This good agreement is verified for all 12 benchmark cases, as shown in Table 1, which quantifies the mismatches between the present predictions and the reference values. For each case, this mismatch is characterized via both the maximum absolute error (δ max ) and the average (root-mean-square) error δ RMS , as recorded throughout the ground observers. Notably, for all cases, the average error, δ RMS , is much less than the threshold of 0.01 dB, which is the indicator of a reliable prediction [62]. Moreover, this accuracy level appears to be higher than the one reached by previous similar studies which focused on the same benchmark [23]. All in all, these benchmark cases provide a validation of the present noise prediction platform and underlying methodology. Appendix B provides a further illustration (along with a more incremental validation) of the overall prediction process, exemplifying each calculation step in the particular JETWDS case.

Noise Certification Cases
To further assess the accuracy of the methodology as well as to lean towards real-life situations, the present section focuses on actual flight scenarios whose characteristics are however close enough from the ANP standard ones. To this end, we consider several noise certification flight tests, for which field measurements were made available by the European Union Aviation Safety Agency (EASA) [63]. These flights tests were performed for two different aircraft (B737-800 and A320-211), delivering for each the Effective Perceived Noise Level (EPNL) over a set of certification points. Indeed, aircraft noise certification tests follow a very specific protocol [64], which consists in flying the airplane along its standard approach and take-off flightpaths whereas measuring the resulting noise at three ground locations, namely the approach, lateral full-power and flyover reference points [64] (see Figure 7). Notably, these ground measurements are performed such that the ground reflections are minimized at best (e.g., displaying the microphones over a flat terrain of known impedance, with no surrounding buildings, etc.). The two considered certification flights were here virtually duplicated using the noise prediction platform, thereby delivering the EPNL results provided in Table 2.

Noise Certification Cases
To further assess the accuracy of the methodology as well as to lean towards real-life situations, the present section focuses on actual flight scenarios whose characteristics are however close enough from the ANP standard ones. To this end, we consider several noise certification flight tests, for which field measurements were made available by the European Union Aviation Safety Agency (EASA) [63]. These flights tests were performed for two different aircraft (B737-800 and A320-211), delivering for each the Effective Perceived Noise Level (EPNL) over a set of certification points. Indeed, aircraft noise certification tests follow a very specific protocol [64], which consists in flying the airplane along its standard approach and take-off flightpaths whereas measuring the resulting noise at three ground locations, namely the approach, lateral full-power and flyover reference points [64] (see. Figure 7). Notably, these ground measurements are performed such that the ground reflections are minimized at best (e.g., displaying the microphones over a flat terrain of known impedance, with no surrounding buildings, etc.). The two considered certification flights were here virtually duplicated using the noise prediction platform, thereby delivering the EPNL results provided in Table 2.    For what concerns the approach procedure, the noise levels predicted at the approach reference point compare favorably with their flight test counterpart, entailing an error of 0.229% and 1.558% for the A320-211 and B737-800 aircraft, respectively. Besides modeling aspects, these slight discrepancies between the predicted and measured results may be attributed to the multiple uncertainties coming from the field test (e.g., slight deviations in the aircraft trajectory, variations in the atmospheric conditions, variable impedance effects by the ground, etc.). For what concerns the departure procedure, the EPNL perceived on the lateral full-power reference point is first considered. Here too, the prediction matches well the flight tests, with an error of less than 1% between the predicted and measured noise levels. Notably, this good agreement also holds when the two aircraft are considered under different atmospheric conditions (as proven by successfully retrieving the prediction results from Ref. [65], which are not reproduced here for the sake of conciseness). The assessment is then conducted for the flyover reference point (see Figure 7), leading to an agreement that is less favorable. Indeed, whatever the aircraft is, the predicted noise levels are about 8% higher than their measured counterpart. Such discrepancies are likely to be due to the mismatches between the flight procedure used in the prediction (ANP database standard scenario) and that adopted in the certification (flight test scenario). Indeed, compared to the former, the latter comes with an earlier reduction in the power settings (thrust is decreased before the flyover reference point [64]), thereby leading to lower noise levels, overall. Rather than questioning the validity of the noise prediction approach (which was demonstrated through all previous cases), these discrepancies rather advocate for basing it on actual flightpaths rather than on standard ANP-based ones-as usually carried out. This point is discussed in the following section.

Further Illustration of the Methodology Using Realistic Scenarios
The present section further illustrates the capacity of the aircraft noise prediction methodology to tackle real-life situations by considering actual flight scenarios coming from one of the major international airports, worldwide.

Context
Hong Kong International Airport (HKIA) is among the busiest airports in the world, ranking 1st and 13th in terms of cargo and passenger traffic, respectively. On the other hand, Hong Kong is the 6th densest city worldwide, and many of its highly populated residential areas are prone to be impacted by air traffic pollution, whether chemical or acoustical. Since HKIA's current two-runway system has almost reached its maximum operational capacity, a third runway is now being developed so as to cope with the expected growth of air traffic (of about 5% per year). This makes it critical to accurately assess the noise impact by aircraft take-off and landing operations at HKIA on local communities. Such an assessment must account properly for the specificities that characterize the local Hong Kong aviation scene, whether these concern aircraft operations (power settings, flight trajectories) or meteorological conditions. Indeed, because of both the complicated airspace (crowded air traffic, topography, densely populated areas, available routes) and the adoption of specific procedures (e.g., continuous descent approach, CDA [66]), the flight trajectories around HKIA are pretty diverse, and definitely non-standard. In addition, due to its unique geographical location, Hong Kong undergoes important seasonal changes over the year (namely, the summer is hot and very humid, whereas the winter is rather cool and dry.).
To further illustrate the ability of the present approach to tackle real-life scenarios, the present section assesses the noise impact entailed by actual aircraft flying in and out from HKIA, a special focus being put on those Hong Kong's densely populated areas that are likely to be more exposed to it. The left side of Figure 8 plots the spatial distribution of Hong Kong's population in 2020 (as provided by the Hong Kong Census and Statistics Department) whereas its center side depicts some typical flightpaths of representative aircraft flying to/from Taipei in 2020 (as provided by the major airline in Hong Kong, Cathay Pacific). The areas depicted in black (namely, D1-D7) are densely populated districts with many aircraft flying over, which the focus is put on here. In that regard, a representative set of aircraft and flightpaths are selected, their noise footprint on the ground being then simulated using the noise prediction platform. Department) whereas its center side depicts some typical flightpaths of representative aircraft flying to/from Taipei in 2020 (as provided by the major airline in Hong Kong, Cathay Pacific). The areas depicted in black (namely, D1-D7) are densely populated districts with many aircraft flying over, which the focus is put on here. In that regard, a representative set of aircraft and flightpaths are selected, their noise footprint on the ground being then simulated using the noise prediction platform. A quick analysis of the air traffic around HKIA in 2021 reveals that the most frequently used aircraft types are A330-343, B787-9 and B777-3ER. We thus here consider both A330-343 and B777-3ER aircraft flying in/out HKIA from/to Taipei (the B787-9 being discarded since its characteristics are not yet incorporated in the ANP database and are rather close to those of A330-343). For each aircraft considered, the operational characteristics and associated flightpaths are excerpted from actual data provided by the airline (Cathay Pacific). Among all available possibilities, specific flights are selected, and their noise impact (SEL) on Hong Kong residential areas is predicted using the present approach. The latter incorporates most features, e.g., it accounts for the atmospheric properties (humidity, temperature, pressure), the installation effects (bank angle), the dynamic grid functionality. On some occasions, additional methodological ingredients are used, e.g., the ground track extension (cf. Section 4.3.2), the thrust approximation (cf. Section 4.3.3). Unless stated otherwise (e.g., Section 4.2.2), the atmospheric conditions correspond to the so-called ISA+10 atmosphere, which is classically used (including for noise certification tests) and is rather close to the yearly averaged meteorological data recorded in Hong Kong. Finally, for helping the reader identifying more easily the various scenarios considered hereafter, each flight is labeled using a specific nomenclature, namely, XYn, where X refers to the aircraft type ("A" for A330-343, "B" for B777-3ER) whereas Y relates to the flight type ("A" for approach, "D" for departure) and n is the subsequent scenario index (1, 2, etc.).
Regarding the aircraft noise exposure in Hong Kong, the solely available data are the official records from HKCAD. The latter come as averaged ground noise levels, which are recorded annually over a few specific locations and integrated over time (irrespective of aircraft movements). In the absence of suitable validation means coming from field tests, all the noise predictions presented hereafter are thus used for illustration purpose. They however deliver insightful information, whether the latter relates to phenomenological aspects (see section 4.2) or to methodological considerations (see section 4.3). More precisely, here, we assess the noise impact sensitivity towards various key factors, namely the flight characteristics (flightpath, power settings), the meteorological effects (atmos- A quick analysis of the air traffic around HKIA in 2021 reveals that the most frequently used aircraft types are A330-343, B787-9 and B777-3ER. We thus here consider both A330-343 and B777-3ER aircraft flying in/out HKIA from/to Taipei (the B787-9 being discarded since its characteristics are not yet incorporated in the ANP database and are rather close to those of A330-343). For each aircraft considered, the operational characteristics and associated flightpaths are excerpted from actual data provided by the airline (Cathay Pacific). Among all available possibilities, specific flights are selected, and their noise impact (SEL) on Hong Kong residential areas is predicted using the present approach. The latter incorporates most features, e.g., it accounts for the atmospheric properties (humidity, temperature, pressure), the installation effects (bank angle), the dynamic grid functionality. On some occasions, additional methodological ingredients are used, e.g., the ground track extension (cf. Section 4.3.2), the thrust approximation (cf. Section 4.3.3). Unless stated otherwise (e.g., Section 4.2.2), the atmospheric conditions correspond to the so-called ISA+10 atmosphere, which is classically used (including for noise certification tests) and is rather close to the yearly averaged meteorological data recorded in Hong Kong. Finally, for helping the reader identifying more easily the various scenarios considered hereafter, each flight is labeled using a specific nomenclature, namely, XYn, where X refers to the aircraft type ("A" for A330-343, "B" for B777-3ER) whereas Y relates to the flight type ("A" for approach, "D" for departure) and n is the subsequent scenario index (1, 2, etc.).
Regarding the aircraft noise exposure in Hong Kong, the solely available data are the official records from HKCAD. The latter come as averaged ground noise levels, which are recorded annually over a few specific locations and integrated over time (irrespective of aircraft movements). In the absence of suitable validation means coming from field tests, all the noise predictions presented hereafter are thus used for illustration purpose. They however deliver insightful information, whether the latter relates to phenomenological aspects (see Section 4.2) or to methodological considerations (see Section 4.3). More precisely, here, we assess the noise impact sensitivity towards various key factors, namely the flight characteristics (flightpath, power settings), the meteorological effects (atmospheric absorption, acoustic impedance), the aircraft type, but also the way to infer them better (flightpath extension, trajectory and/or thrust approximation), etc. Of note, these predictions incorporate the ground effects regardless of the specificities coming from the actual terrain (e.g., landscape, buildings, vegetation, or water), which would be too cumbersome to account for. These specificities are nevertheless expected to be of secondary importance compared to the effects that are primarily sought after, here.

Noise Impact Variability upon the Flight Scenarios
Aircraft operations around HKIA rarely comply with standardized flightpaths, being rather characterized by scattered flight profiles. In that regard, the present section illustrates the variability of aircraft noise impact towards the diversity in flight routes.

Departure Scenarios
We consider those departure routes followed by A330-343 aircraft flying from Hong Kong to Taipei, focusing on those Hong Kong densely populated areas that are located underneath flight corridors (namely, D1, D5, D6, and D7 in Figure 8). Among all corresponding flights available from the database, two specific A330-343 departure flights are chosen upon the high disparity between their characteristics. Indeed, the first aircraft (flight AD1) flies over D1 and D7 districts following a standard route, while the second aircraft (AD2) rather flies over D5 district with a much lower rate of climb (ROC). The left and center sides of Figure 9, respectively, depict the ground track and flight profile of the corresponding routes, which are here plotted up to the nominal maximum altitude of 10,000 ft [37]. The right side of Figure 9 plots the observer grid, as generated using the dynamic meshing technique (cf. Section 2.3.3). actual terrain (e.g., landscape, buildings, vegetation, or water), which would be too cumbersome to account for. These specificities are nevertheless expected to be of secondary importance compared to the effects that are primarily sought after, here.

Noise Impact Variability upon the Flight Scenarios
Aircraft operations around HKIA rarely comply with standardized flightpaths, being rather characterized by scattered flight profiles. In that regard, the present section illustrates the variability of aircraft noise impact towards the diversity in flight routes.

Departure Scenarios
We consider those departure routes followed by A330-343 aircraft flying from Hong Kong to Taipei, focusing on those Hong Kong densely populated areas that are located underneath flight corridors (namely, D1, D5, D6, and D7 in Figure 8). Among all corresponding flights available from the database, two specific A330-343 departure flights are chosen upon the high disparity between their characteristics. Indeed, the first aircraft (flight AD1) flies over D1 and D7 districts following a standard route, while the second aircraft (AD2) rather flies over D5 district with a much lower rate of climb (ROC). The left and center sides of Figure 9, respectively, depict the ground track and flight profile of the corresponding routes, which are here plotted up to the nominal maximum altitude of 10,000 ft [37]. The right side of Figure 9 plots the observer grid, as generated using the dynamic meshing technique (cf. Section 2.3.3). The left and right sides of Figure 10 depict the SEL contours generated by flights AD1 and AD2, respectively. As can be seen, each flight exhibits a rather specific noise signature on the ground, thereby impacting Hong Kong in its own way. This disparity between both flights' impacts is quantified on the Figure 11, which depicts the differences between the two noise maps (obtained here by subtracting the former from the latter).  The left and right sides of Figure 10 depict the SEL contours generated by flights AD1 and AD2, respectively. As can be seen, each flight exhibits a rather specific noise signature on the ground, thereby impacting Hong Kong in its own way. This disparity between both flights' impacts is quantified on the Figure 11, which depicts the differences between the two noise maps (obtained here by subtracting the former from the latter). The left and right sides of Figure 10 depict the SEL contours gen and AD2, respectively. As can be seen, each flight exhibits a rather sp on the ground, thereby impacting Hong Kong in its own way. This d flights' impacts is quantified on the Figure 11, which depicts the di two noise maps (obtained here by subtracting the former from the l  Compared to flight AD1 (standard route, higher ROC), flight AD2 (deviated route, lower ROC) has a much higher impact on some of the populated areas, namely districts D1, D5 and D6 (see the right side of Figure 11). More precisely, the excess in SEL raises up to 5dB in districts D1 and D5, whereas it can reach up to 15dB in district D6, which is the most densely populated area in Hong Kong. On the other hand, the opposite holds for other city areas-such as district D7, where the impact of flight AD1 is about 10dB higher than that of flight AD2. At this stage, it is worth noting that the higher altitude of flight AD1 does not necessarily translate into a lower noise impact on the ground areas it flies over, compared to what happens for flight AD2. For instance, the noise impact by flight AD1 on the D7 district is comparatively higher than that of flight AD2 on the D5 district, although the latter flight travels at an altitude that is half of the former. This can be explained by the difference in the power settings adopted by both aircraft along their respective routes. Indeed, the power settings associated with both flights are depicted in Figure 12, which delineates (in dash-dotted lines) the particular flight phase during which both aircraft pass nearby districts D1 and D5. During this phase, flight AD1 exhibits an engine power that is more than twice that of flight AD2 (whose ROC is suddenly and drastically reduced at that time). This excess of propulsive power translates into a more important noise emission, whose effect cannot be completely mitigated by the longer propagation distance entailed from flight AD1 higher altitude. Independently of the engines power (i.e., noise source amplitude), the flightpath angle (i.e., noise source directivity) may also explain such a comparatively higher noise impact by flight AD1. Indeed, during this flight phase, flight AD2 adopts a lower climb angle than that of flight AD1, as revealed by the flight profiles on the center side of Figure 9. Considering the highly directive patterns of jet noise (whose maximum radiation is aligned with the aircraft axis), this lower flightpath angle by flight AD2 is likely to induce a lower noise impact on the ground. This being said, these more favorable characteristics of flight AD2 (less power, reduced climb angle) do not prevent it to generate a quite substantial noise impact on these areas it flies over rather closely, such as districts D1 and D5. Compared to flight AD1 (standard route, higher ROC), flight AD2 (deviated route, lower ROC) has a much higher impact on some of the populated areas, namely districts D1, D5 and D6 (see the right side of Figure 11). More precisely, the excess in SEL raises up to 5dB in districts D1 and D5, whereas it can reach up to 15dB in district D6, which is the most densely populated area in Hong Kong. On the other hand, the opposite holds for other city areas-such as district D7, where the impact of flight AD1 is about 10dB higher than that of flight AD2.
At this stage, it is worth noting that the higher altitude of flight AD1 does not necessarily translate into a lower noise impact on the ground areas it flies over, compared to what happens for flight AD2. For instance, the noise impact by flight AD1 on the D7 district is comparatively higher than that of flight AD2 on the D5 district, although the latter flight travels at an altitude that is half of the former. This can be explained by the difference in the power settings adopted by both aircraft along their respective routes. Indeed, the power settings associated with both flights are depicted in Figure 12, which delineates (in dash-dotted lines) the particular flight phase during which both aircraft pass nearby districts D1 and D5. During this phase, flight AD1 exhibits an engine power that is more than twice that of flight AD2 (whose ROC is suddenly and drastically reduced at that time). This excess of propulsive power translates into a more important noise emission, whose effect cannot be completely mitigated by the longer propagation distance entailed from flight AD1 higher altitude. Independently of the engines power (i.e., noise source amplitude), the flightpath angle (i.e., noise source directivity) may also explain such a comparatively higher noise impact by flight AD1. Indeed, during this flight phase, flight AD2 adopts a lower climb angle than that of flight AD1, as revealed by the flight profiles on the center side of Figure 9. Considering the highly directive patterns of jet noise (whose maximum radiation is aligned with the aircraft axis), this lower flightpath angle by flight AD2 is likely to induce a lower noise impact on the ground. This being said, these more favorable characteristics of flight AD2 (less power, reduced climb angle) do not prevent it to generate a quite substantial noise impact on these areas it flies over rather closely, such as districts D1 and D5. A similar analysis was conducted for B777-3ER aircraft flying along both the standard and an alternative deviated route, leading to the same observations (see Appendix C).
All the above illustrate well how the variability in departure procedures around HKIA may have a quite large impact on specific, highly densely populated areas of Hong Kong city. From a methodological viewpoint, this underlines the necessity to account as accurately as possible for all flight characteristics when assessing the noise impact by air traffic operations.

Approach Scenarios
Whereas the previous section focused on A330 aircraft departing from HKIA (with their B777 counterpart being documented in Appendix C), this section rather focuses on B777-3ER aircraft at approach. More precisely, we consider the two approach routes to HKIA (namely 25R and 25L), which both pass through three densely populated districts (namely D2, D3, and D4 in Figure 8). Among all B777-3ER aircraft flying from Taipei to Hong Kong in 2020, two specific flights are selected for their high disparity in terms of characteristics (see Figure 13). Whereas the first one (flight BA1) approaches the 25L runway at a higher altitude, the second one (flight BA2) follows the route 25R at a lower altitude. As can be seen, these flight characteristics differences are more prominent at the beginning of the flight sequence, since both aircraft adopt similar trajectories as they get closer to HKIA, to comply with the noise abatement procedures enforced in Hong Kong, namely the Continuous Descent Approach. The left and right sides of Figure 14 depict the SEL contours generated by these two flights BA1 and BA2, respectively. As for what could be observed with the departure scenarios (cf. Section 4.2.1), each flight impacts differently Hong Kong residential areas. This disparity between their respective noise impact is quantified on the Figure 15, which depicts the differences between the two noise maps (obtained here by subtracting the former from the latter). A similar analysis was conducted for B777-3ER aircraft flying along both the standard and an alternative deviated route, leading to the same observations (see Appendix C).
All the above illustrate well how the variability in departure procedures around HKIA may have a quite large impact on specific, highly densely populated areas of Hong Kong city. From a methodological viewpoint, this underlines the necessity to account as accurately as possible for all flight characteristics when assessing the noise impact by air traffic operations.

Approach Scenarios
Whereas the previous section focused on A330 aircraft departing from HKIA (with their B777 counterpart being documented in Appendix C), this section rather focuses on B777-3ER aircraft at approach. More precisely, we consider the two approach routes to HKIA (namely 25R and 25L), which both pass through three densely populated districts (namely D2, D3, and D4 in Figure 8). Among all B777-3ER aircraft flying from Taipei to Hong Kong in 2020, two specific flights are selected for their high disparity in terms of characteristics (see Figure 13). Whereas the first one (flight BA1) approaches the 25L runway at a higher altitude, the second one (flight BA2) follows the route 25R at a lower altitude. As can be seen, these flight characteristics differences are more prominent at the beginning of the flight sequence, since both aircraft adopt similar trajectories as they get closer to HKIA, to comply with the noise abatement procedures enforced in Hong Kong, namely the Continuous Descent Approach. A similar analysis was conducted for B777-3ER aircraft flying along both the standard and an alternative deviated route, leading to the same observations (see Appendix C).
All the above illustrate well how the variability in departure procedures around HKIA may have a quite large impact on specific, highly densely populated areas of Hong Kong city. From a methodological viewpoint, this underlines the necessity to account as accurately as possible for all flight characteristics when assessing the noise impact by air traffic operations.

Approach Scenarios
Whereas the previous section focused on A330 aircraft departing from HKIA (with their B777 counterpart being documented in Appendix C), this section rather focuses on B777-3ER aircraft at approach. More precisely, we consider the two approach routes to HKIA (namely 25R and 25L), which both pass through three densely populated districts (namely D2, D3, and D4 in Figure 8). Among all B777-3ER aircraft flying from Taipei to Hong Kong in 2020, two specific flights are selected for their high disparity in terms of characteristics (see Figure 13). Whereas the first one (flight BA1) approaches the 25L runway at a higher altitude, the second one (flight BA2) follows the route 25R at a lower altitude. As can be seen, these flight characteristics differences are more prominent at the beginning of the flight sequence, since both aircraft adopt similar trajectories as they get closer to HKIA, to comply with the noise abatement procedures enforced in Hong Kong, namely the Continuous Descent Approach. The left and right sides of Figure 14 depict the SEL contours generated by these two flights BA1 and BA2, respectively. As for what could be observed with the departure scenarios (cf. Section 4.2.1), each flight impacts differently Hong Kong residential areas. This disparity between their respective noise impact is quantified on the Figure 15, which depicts the differences between the two noise maps (obtained here by subtracting the former The left and right sides of Figure 14 depict the SEL contours generated by these two flights BA1 and BA2, respectively. As for what could be observed with the departure scenarios (cf. Section 4.2.1), each flight impacts differently Hong Kong residential areas. This disparity between their respective noise impact is quantified on the Figure 15, which depicts the differences between the two noise maps (obtained here by subtracting the former from the latter). Being sandwiched between 25L and 25R routes, the populated D3 district sees northwestern part impacted more by flight BA2 than by flight BA1 (with a difference SEL of up to 7.6dB), whereas the opposite occurs on D3 southern part (where flight B impact exceeds that of flight BA2 by up to 7.3dB in SEL)-see the right side of Figure 1  Considering that most of D3 residents are concentrated in its central and southe areas, flight BA1 thus appears to be less environmentally friendly for this district. T same observation holds for the D2 district, whose population concentration is four tim higher than that of its D3 counterpart. Being located right underneath 25L route, this d trict is impacted more by flight BA1, with an excess in SEL of up to 9dB (compared to t of flight BA2). On the other hand, the D4 district appears to be equally exposed to bo flights, each inducing an excess of 5-7 dB compared to the other for those observers t are located underneath their respective flightpath. All in all, it appears that these dens populated districts are more exposed to flight BA1, overall. Therefore, the 25R approa route should be privileged whenever the conditions permit (operational, meteorologic etc.).
A similar analysis was conducted for an A330-343 aircraft flying along these two a proach routes, leading to the same observations (see Appendix C).
As for the departure scenarios (cf. Section 4.2.1), the above results illustrate furth how the approach procedures around HKIA may impact very differently those high densely populated areas of Hong Kong city.

Noise Impact Variability upon the Meteorological Conditions
As said, because Hong Kong usually undergoes important seasonal changes, the Being sandwiched between 25L and 25R routes, the populated D3 district sees its northwestern part impacted more by flight BA2 than by flight BA1 (with a difference in SEL of up to 7.6dB), whereas the opposite occurs on D3 southern part (where flight BA1 impact exceeds that of flight BA2 by up to 7.3dB in SEL)-see the right side of Figure 15. Considering that most of D3 residents are concentrated in its central and southern areas, flight BA1 thus appears to be less environmentally friendly for this district. The same observation holds for the D2 district, whose population concentration is four times higher than that of its D3 counterpart. Being located right underneath 25L route, this district is impacted more by flight BA1, with an excess in SEL of up to 9dB (compared to that of flight BA2). On the other hand, the D4 district appears to be equally exposed to both flights, each inducing an excess of 5-7 dB compared to the other for those observers that are located underneath their respective flightpath. All in all, it appears that these densely populated districts are more exposed to flight BA1, overall. Therefore, the 25R approach route should be privileged whenever the conditions permit (operational, meteorological, etc.).
A similar analysis was conducted for an A330-343 aircraft flying along these two approach routes, leading to the same observations (see Appendix C).
As for the departure scenarios (cf. Section 4.2.1), the above results illustrate further how the approach procedures around HKIA may impact very differently those highly densely populated areas of Hong Kong city.

Noise Impact Variability upon the Meteorological Conditions
As said, because Hong Kong usually undergoes important seasonal changes, the local atmospheric conditions may present large deviations compared to the standard ones. For instance, according to the meteorological data records acquired over the past decade by the Hong Kong Observatory and Iowa State University, Hong Kong is characterized Being sandwiched between 25L and 25R routes, the populated D3 district sees its northwestern part impacted more by flight BA2 than by flight BA1 (with a difference in SEL of up to 7.6 dB), whereas the opposite occurs on D3 southern part (where flight BA1 impact exceeds that of flight BA2 by up to 7.3 dB in SEL)-see the right side of Figure 15.
Considering that most of D3 residents are concentrated in its central and southern areas, flight BA1 thus appears to be less environmentally friendly for this district. The same observation holds for the D2 district, whose population concentration is four times higher than that of its D3 counterpart. Being located right underneath 25L route, this district is impacted more by flight BA1, with an excess in SEL of up to 9dB (compared to that of flight BA2). On the other hand, the D4 district appears to be equally exposed to both flights, each inducing an excess of 5-7 dB compared to the other for those observers that are located underneath their respective flightpath. All in all, it appears that these densely populated districts are more exposed to flight BA1, overall. Therefore, the 25R approach route should be privileged whenever the conditions permit (operational, meteorological, etc.).
A similar analysis was conducted for an A330-343 aircraft flying along these two approach routes, leading to the same observations (see Appendix C).
As for the departure scenarios (cf. Section 4.2.1), the above results illustrate further how the approach procedures around HKIA may impact very differently those highly densely populated areas of Hong Kong city.

Noise Impact Variability upon the Meteorological Conditions
As said, because Hong Kong usually undergoes important seasonal changes, the local atmospheric conditions may present large deviations compared to the standard ones. For instance, according to the meteorological data records acquired over the past decade by the Hong Kong Observatory and Iowa State University, Hong Kong is characterized by large yearly variations in temperature and relative humidity (which can range from 3 • C to 37 • C and 6.91% to 100% throughout the year, respectively). Moreover, these fluctuations may be important on a much shorter timescale, with large deviations occurring throughout a single day.
The present section illustrates how such a meteorological variability may affect the aircraft noise impact on the ground, for instance, because of the deviations in the atmospheric absorption (which focus is put on, here). To do so, we consider the particular case of an A330-343 aircraft flying from Hong Kong to Taipei along a standard departure route, this flight being successively operated under four specific meteorological scenarios, which reproduce the extrema in temperature or relative humidity one can get in Hong Kong, yearly (see Table 3). For each one of the four scenarios (respectively labeled as AD3, AD4, AD5, AD6), Figure 16 depicts the corresponding SEL on the ground, whose differences are quantified and discussed in the next subsections. by large yearly variations in temperature and relative humidity (which can range from 3 °C to 37 °C and 6.91% to 100% throughout the year, respectively). Moreover, these fluctuations may be important on a much shorter timescale, with large deviations occurring throughout a single day. The present section illustrates how such a meteorological variability may affect the aircraft noise impact on the ground, for instance, because of the deviations in the atmospheric absorption (which focus is put on, here). To do so, we consider the particular case of an A330-343 aircraft flying from Hong Kong to Taipei along a standard departure route, this flight being successively operated under four specific meteorological scenarios, which reproduce the extrema in temperature or relative humidity one can get in Hong Kong, yearly (see Table 3). For each one of the four scenarios (respectively labeled as AD3, AD4, AD5, AD6), Figure 16 depicts the corresponding SEL on the ground, whose differences are quantified and discussed in the next subsections.

Effect of Temperature
By comparing either cases AD3 and AD4 or cases AD5 and AD6, we first highlight how the noise impact may be altered by variations in temperature (alone), for a given relative humidity. For each pair of cases, Figure 17 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 (resp. AD5) from that of case AD4 (resp. AD6). As can be seen, such a 28 °C rise in temperature noticeably impacts the ground noise levels, whatever the relative humidity is. This effect on the noise impact appears to be driven by both the observer location and the actual level of relative humidity. When the latter is low (13%), the noise impact is seen to increase (resp. decrease) for those observers that are located close to (resp. away from) the ground track (cf. left side of Figure 17). Oppositely, when the relative humidity is high (100%), a lower (resp. higher) noise impact is recorded for those observers that are positioned close to (resp. away from) the ground track (cf. right side of Figure 17).

Effect of Temperature
By comparing either cases AD3 and AD4 or cases AD5 and AD6, we first highlight how the noise impact may be altered by variations in temperature (alone), for a given relative humidity. For each pair of cases, Figure 17 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 (resp. AD5) from that of case AD4 (resp. AD6). As can be seen, such a 28 • C rise in temperature noticeably impacts the ground noise levels, whatever the relative humidity is. This effect on the noise impact appears to be driven by both the observer location and the actual level of relative humidity. When the latter is low (13%), the noise impact is seen to increase (resp. decrease) for those observers that are located close to (resp. away from) the ground track (cf. left side of Figure 17). Oppositely, when the relative humidity is high (100%), a lower (resp. higher) noise impact is recorded for those observers that are positioned close to (resp. away from) the ground track (cf. right side of Figure 17).

Effect of Relative Humidity
Similarly, by comparing either cases AD3 and AD5 or cases AD4 and AD6, we highlight how the noise impact may be altered by the variations in relative humidity (alone), for a given temperature. Figure 18 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 (resp. AD4) from that of case AD5 (resp. AD6). Whatever the temperature is, such an 87% variation in relative humidity significantly alters the ground noise levels, which now increase everywhere. Again, this effect on the noise impact appears to depend on both the observer location and the actual temperature. When the latter is low (7 °C), the impact is seen to be more important for those observers that are located close to the ground track (cf. left side of Figure 18). Oppositely, under a high temperature (35 °C), the impact is higher for those observers that are positioned further away from the ground track (cf. right side of Figure 18).

Combined Effect of Both Temperature and Relative Humidity
Finally, by comparing cases AD3 and AD6, we illustrate the combined effect of temperature and relative humidity on the noise impact. Figure 19 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 from that of case AD6. As can be seen, when both temperature and relative humidity increase, the ground noise impact goes higher. For instance, a variation of +9.6dB is recorded for that observer located at the left/bottom corner of the grid. Notably, this difference represents the arithmetic sum of the ones recorded separately for a variation in temperature alone (−9.1dB, cf. left side of Figure 17/AD3 → AD4) and in relative humidity alone (+18.7dB, cf. right side of Figure 18/AD4 → AD6). This illustrates well the dual dependency of the noise impact onto both the temperature and humidity, whose respective effects are cumulative (and may mitigate each other, depending on the situation, cf. Section 2.3.4).

Effect of Relative Humidity
Similarly, by comparing either cases AD3 and AD5 or cases AD4 and AD6, we highlight how the noise impact may be altered by the variations in relative humidity (alone), for a given temperature. Figure 18 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 (resp. AD4) from that of case AD5 (resp. AD6). Whatever the temperature is, such an 87% variation in relative humidity significantly alters the ground noise levels, which now increase everywhere. Again, this effect on the noise impact appears to depend on both the observer location and the actual temperature. When the latter is low (7 • C), the impact is seen to be more important for those observers that are located close to the ground track (cf. left side of Figure 18). Oppositely, under a high temperature (35 • C), the impact is higher for those observers that are positioned further away from the ground track (cf. right side of Figure 18).

Effect of Relative Humidity
Similarly, by comparing either cases AD3 and AD5 or cases AD4 and AD6, we highlight how the noise impact may be altered by the variations in relative humidity (alone), for a given temperature. Figure 18 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 (resp. AD4) from that of case AD5 (resp. AD6). Whatever the temperature is, such an 87% variation in relative humidity significantly alters the ground noise levels, which now increase everywhere. Again, this effect on the noise impact appears to depend on both the observer location and the actual temperature. When the latter is low (7 °C), the impact is seen to be more important for those observers that are located close to the ground track (cf. left side of Figure 18). Oppositely, under a high temperature (35 °C), the impact is higher for those observers that are positioned further away from the ground track (cf. right side of Figure 18).

Combined Effect of Both Temperature and Relative Humidity
Finally, by comparing cases AD3 and AD6, we illustrate the combined effect of temperature and relative humidity on the noise impact. Figure 19 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 from that of case AD6. As can be seen, when both temperature and relative humidity increase, the ground noise impact goes higher. For instance, a variation of +9.6dB is recorded for that observer located at the left/bottom corner of the grid. Notably, this difference represents the arithmetic sum of the ones recorded separately for a variation in temperature alone (−9.1dB, cf. left side of Figure 17/AD3 → AD4) and in relative humidity alone (+18.7dB, cf. right side of Figure 18/AD4 → AD6). This illustrates well the dual dependency of the noise impact onto both the temperature and humidity, whose respective effects are cumulative (and may mitigate each other, depending on the situation, cf. Section 2.3.4).

Combined Effect of Both Temperature and Relative Humidity
Finally, by comparing cases AD3 and AD6, we illustrate the combined effect of temperature and relative humidity on the noise impact. Figure 19 depicts the differences in ground noise levels, as obtained by subtracting the SEL map associated with case AD3 from that of case AD6. As can be seen, when both temperature and relative humidity increase, the ground noise impact goes higher. For instance, a variation of +9.6 dB is recorded for that observer located at the left/bottom corner of the grid. Notably, this difference represents the arithmetic sum of the ones recorded separately for a variation in temperature alone (−9.1 dB, cf. left side of Figure 17/AD3 → AD4) and in relative humidity alone (+18.7 dB, cf. right side of Figure 18/AD4 → AD6). This illustrates well the dual dependency of the noise impact onto both the temperature and humidity, whose respective effects are cumulative (and may mitigate each other, depending on the situation, cf. Section 2.3.4). At this stage, it is worth observing that the above results (both trends and numbers) are specific to the present HKIA-based scenario and should not be extrapolated readily to other situations. They however highlight well how important the atmospheric properties may alter the noise impact by air traffic operations, from a phenomenological viewpoint. From a methodological perspective, they underline the crude necessity of accounting properly for the local atmospheric conditions when assessing the noise impact of air traffic operations, especially in those regions that are known to undergo important seasonal variations, such as Hong Kong.

Noise Impact Variability upon the Aircraft Type
The previous sections highlighted how far a given aircraft may see its noise impact varying, depending on its operational conditions (flight route and power settings, meteorological conditions, etc.). Here, we rather explore how, for identical operational conditions, two distinct aircraft may entail different noise impacts. To do so, we consider two of the previous flights, whereas allotting them with a different aircraft type than previously carried out.
Focusing first on departure scenario (cf. Section 4.2.1), we repeat the noise prediction associated with flight AD2 (deviated route, lower ROC), the previous aircraft (A330-343) being now replaced with a (virtual) B777-3ER. Of note, it was checked that such a virtual scenario is realistic, e.g., the B777 engines can deliver the power required by the corresponding A330 flight settings. Figure 20 depicts the SEL maps induced by both cases (respectively labeled AD2 and BD1), along with their difference. As can be seen, B777-3ER aircraft impacts Hong Kong less than its A330-343 counterpart, with noise levels that are lower by about 3dB over most residential areas. This trend is however inverted further away from the ground track, with an excess noise by the B777 of up to 5dB recorded over some more remote locations (which are nevertheless sparsely populated). At this stage, it is worth observing that the above results (both trends and numbers) are specific to the present HKIA-based scenario and should not be extrapolated readily to other situations. They however highlight well how important the atmospheric properties may alter the noise impact by air traffic operations, from a phenomenological viewpoint. From a methodological perspective, they underline the crude necessity of accounting properly for the local atmospheric conditions when assessing the noise impact of air traffic operations, especially in those regions that are known to undergo important seasonal variations, such as Hong Kong.

Noise Impact Variability upon the Aircraft Type
The previous sections highlighted how far a given aircraft may see its noise impact varying, depending on its operational conditions (flight route and power settings, meteorological conditions, etc.). Here, we rather explore how, for identical operational conditions, two distinct aircraft may entail different noise impacts. To do so, we consider two of the previous flights, whereas allotting them with a different aircraft type than previously carried out.
Focusing first on departure scenario (cf. Section 4.2.1), we repeat the noise prediction associated with flight AD2 (deviated route, lower ROC), the previous aircraft (A330-343) being now replaced with a (virtual) B777-3ER. Of note, it was checked that such a virtual scenario is realistic, e.g., the B777 engines can deliver the power required by the corresponding A330 flight settings. Figure 20 depicts the SEL maps induced by both cases (respectively labeled AD2 and BD1), along with their difference. As can be seen, B777-3ER aircraft impacts Hong Kong less than its A330-343 counterpart, with noise levels that are lower by about 3 dB over most residential areas. This trend is however inverted further away from the ground track, with an excess noise by the B777 of up to 5 dB recorded over some more remote locations (which are nevertheless sparsely populated). At this stage, it is worth observing that the above results (both trends and numbers) are specific to the present HKIA-based scenario and should not be extrapolated readily to other situations. They however highlight well how important the atmospheric properties may alter the noise impact by air traffic operations, from a phenomenological viewpoint. From a methodological perspective, they underline the crude necessity of accounting properly for the local atmospheric conditions when assessing the noise impact of air traffic operations, especially in those regions that are known to undergo important seasonal variations, such as Hong Kong.

Noise Impact Variability upon the Aircraft Type
The previous sections highlighted how far a given aircraft may see its noise impact varying, depending on its operational conditions (flight route and power settings, meteorological conditions, etc.). Here, we rather explore how, for identical operational conditions, two distinct aircraft may entail different noise impacts. To do so, we consider two of the previous flights, whereas allotting them with a different aircraft type than previously carried out.
Focusing first on departure scenario (cf. Section 4.2.1), we repeat the noise prediction associated with flight AD2 (deviated route, lower ROC), the previous aircraft (A330-343) being now replaced with a (virtual) B777-3ER. Of note, it was checked that such a virtual scenario is realistic, e.g., the B777 engines can deliver the power required by the corresponding A330 flight settings. Figure 20 depicts the SEL maps induced by both cases (respectively labeled AD2 and BD1), along with their difference. As can be seen, B777-3ER aircraft impacts Hong Kong less than its A330-343 counterpart, with noise levels that are lower by about 3dB over most residential areas. This trend is however inverted further away from the ground track, with an excess noise by the B777 of up to 5dB recorded over some more remote locations (which are nevertheless sparsely populated). At this stage, one could wonder about the exact reason for such an inverted trend, in terms of noise impact by both aircraft with respect to the distance to the ground track. Indeed, both AD2 and BD1 scenarios differ only by the aircraft type (i.e., noise source), all other parameters being strictly identical (flightpath, power settings, atmospheric absorption, etc.). However, as can be inferred from the NPD database (see Figure 21), both aircraft see their noise levels varying (i.e., decreasing) differently along the propagation distance. In particular, although they are less than the A330 ones at short distances, the B777 noise levels emerge more further away. This can be related to the atmospheric attenuation effects, which are to impact differently both noise signatures depending on their respective spectral content.
Indeed, both AD2 and BD1 scenarios differ only by the aircraft type (i.e., noise source), all other parameters being strictly identical (flightpath, power settings, atmospheric absorption, etc.). However, as can be inferred from the NPD database (see Figure 21), both aircraft see their noise levels varying (i.e., decreasing) differently along the propagation distance. In particular, although they are less than the A330 ones at short distances, the B777 noise levels emerge more further away. This can be related to the atmospheric attenuation effects, which are to impact differently both noise signatures depending on their respective spectral content.
Focusing now on approach scenarios (cf. Section 4.2.1), we repeat the noise prediction associated with flight BA1 (25L runway, lower altitude), the previous aircraft (B777-3ER) being now replaced with a (virtual) A330-343 counterpart. Notably, here too, it was checked that such a virtual scenario is realistic, e.g., the A330 engines can deliver the power required by the corresponding B777 flight settings. Figure 22 depicts the SEL maps induced by both flights (respectively labeled BA1 and AA1), along with their difference. As can be seen, compared to its B777-3ER counterpart, A330-343 aircraft impacts Hong Kong less, with noise levels that are systematically lower-wherever the observer location is. In particular, the populated D6 district sees its noise impact reduced by as much as 5dB when flown over by an A330 instead of a B777.  The above results illustrate how aircraft noise prediction methods such as the one presented here constitute not only a useful diagnostic tool but also a powerful predictive means. Indeed, beyond simply allowing to measure the noise impact by existing aircraft operations around major airports, such kind of tool can also help better planning them. Focusing now on approach scenarios (cf. Section 4.2.1), we repeat the noise prediction associated with flight BA1 (25L runway, lower altitude), the previous aircraft (B777-3ER) being now replaced with a (virtual) A330-343 counterpart. Notably, here too, it was checked that such a virtual scenario is realistic, e.g., the A330 engines can deliver the power required by the corresponding B777 flight settings. Figure 22 depicts the SEL maps induced by both flights (respectively labeled BA1 and AA1), along with their difference. As can be seen, compared to its B777-3ER counterpart, A330-343 aircraft impacts Hong Kong less, with noise levels that are systematically lower-wherever the observer location is. In particular, the populated D6 district sees its noise impact reduced by as much as 5 dB when flown over by an A330 instead of a B777. At this stage, one could wonder about the exact reason for such an inverted trend, in terms of noise impact by both aircraft with respect to the distance to the ground track. Indeed, both AD2 and BD1 scenarios differ only by the aircraft type (i.e., noise source), all other parameters being strictly identical (flightpath, power settings, atmospheric absorption, etc.). However, as can be inferred from the NPD database (see Figure 21), both aircraft see their noise levels varying (i.e., decreasing) differently along the propagation distance. In particular, although they are less than the A330 ones at short distances, the B777 noise levels emerge more further away. This can be related to the atmospheric attenuation effects, which are to impact differently both noise signatures depending on their respective spectral content.
Focusing now on approach scenarios (cf. Section 4.2.1), we repeat the noise prediction associated with flight BA1 (25L runway, lower altitude), the previous aircraft (B777-3ER) being now replaced with a (virtual) A330-343 counterpart. Notably, here too, it was checked that such a virtual scenario is realistic, e.g., the A330 engines can deliver the power required by the corresponding B777 flight settings. Figure 22 depicts the SEL maps induced by both flights (respectively labeled BA1 and AA1), along with their difference. As can be seen, compared to its B777-3ER counterpart, A330-343 aircraft impacts Hong Kong less, with noise levels that are systematically lower-wherever the observer location is. In particular, the populated D6 district sees its noise impact reduced by as much as 5dB when flown over by an A330 instead of a B777.  The above results illustrate how aircraft noise prediction methods such as the one presented here constitute not only a useful diagnostic tool but also a powerful predictive means. Indeed, beyond simply allowing to measure the noise impact by existing aircraft operations around major airports, such kind of tool can also help better planning them. The above results illustrate how aircraft noise prediction methods such as the one presented here constitute not only a useful diagnostic tool but also a powerful predictive means. Indeed, beyond simply allowing to measure the noise impact by existing aircraft operations around major airports, such kind of tool can also help better planning them. This is of critical importance when new airport developments are on their way, as is currently the case with HKIA.

Methodological Aspects
Whereas the previous sections primarily focused on phenomenological aspects of aircraft noise impact, we here discuss the prediction process under a more methodological angle.

Accounting for the Bank Angle
In the previous sections, all noise predictions accounted for the engine installation effects (cf. Section 2.3.2), which were incorporated through the bank angle. One can however wonder about how big their influence on the noise impact is, that is, how critical it is to integrate them in the calculation process. To do so, we repeat the noise prediction of flight AD2 (which undergoes more banked turns than flight AD1), the bank angle effect being either incorporated or neglected in the calculation. Figure 23 compares the SEL maps obtained with (left) and without (center) the bank angle effect, along with their difference (right). This is of critical importance when new airport developments are on their way, as is currently the case with HKIA.

Methodological Aspects
Whereas the previous sections primarily focused on phenomenological aspects of aircraft noise impact, we here discuss the prediction process under a more methodological angle.

Accounting for the Bank Angle
In the previous sections, all noise predictions accounted for the engine installation effects (cf. Section 2.3.2), which were incorporated through the bank angle. One can however wonder about how big their influence on the noise impact is, that is, how critical it is to integrate them in the calculation process. To do so, we repeat the noise prediction of flight AD2 (which undergoes more banked turns than flight AD1), the bank angle effect being either incorporated or neglected in the calculation. Figure 23 compares the SEL maps obtained with (left) and without (center) the bank angle effect, along with their difference (right). As can be seen, when the aircraft is engaged into a banked turn, most of the observers that are located on the same (resp. opposite) side of the turn are exposed to lower (resp. higher) noise levels (see what happens on the right side of Figure 23, for instance). This trend, however, is inverted for the small fraction of observers that are located very close to the ground track. All this can be easily explained upon the respective way each observer perceives the relative depression angle, which is either increased or decreased because of the bank (see Figure 2, wing-mounted engines polar). From another hand, this effect of the bank angle appears to be rather modest, with noise differences of less than 0.3dB overall. This number appears to be even lower for flight AD1, whose straighter flightpath naturally leads to a less important effect of the bank angle (cf. Appendix C).
A similar analysis was conducted for B777-3ER aircraft flying along different departure routes, leading to the same trends (see Appendix C).
On one hand, the above results confirm that the noise impact by an aircraft does not vary much during a banked turn, which explains why this aspect is often neglected in the prediction [62]. On the other hand, however, these results illustrate how one can further refine the accuracy of the noise prediction by incorporating still more additional effects, even though they are of secondary importance.

Extending the Flightpath Cut-Off Limit
In the previous sections, all noise predictions relied on the classical approach of incorporating only those flightpath segments that would fall under an (arbitrary) reference altitude of 10,000 ft. As discussed previously (see Section 2.3), this is likely to induce a bias in the noise prediction because some of the contributing flight segments would then be As can be seen, when the aircraft is engaged into a banked turn, most of the observers that are located on the same (resp. opposite) side of the turn are exposed to lower (resp. higher) noise levels (see what happens on the right side of Figure 23, for instance). This trend, however, is inverted for the small fraction of observers that are located very close to the ground track. All this can be easily explained upon the respective way each observer perceives the relative depression angle, which is either increased or decreased because of the bank (see Figure 2, wing-mounted engines polar). From another hand, this effect of the bank angle appears to be rather modest, with noise differences of less than 0.3 dB overall. This number appears to be even lower for flight AD1, whose straighter flightpath naturally leads to a less important effect of the bank angle (cf. Appendix C).
A similar analysis was conducted for B777-3ER aircraft flying along different departure routes, leading to the same trends (see Appendix C).
On one hand, the above results confirm that the noise impact by an aircraft does not vary much during a banked turn, which explains why this aspect is often neglected in the prediction [62]. On the other hand, however, these results illustrate how one can further refine the accuracy of the noise prediction by incorporating still more additional effects, even though they are of secondary importance.

Extending the Flightpath Cut-off Limit
In the previous sections, all noise predictions relied on the classical approach of incorporating only those flightpath segments that would fall under an (arbitrary) reference altitude of 10,000 ft. As discussed previously (see Section 2.3), this is likely to induce a bias in the noise prediction because some of the contributing flight segments would then be ignored. In Section 4.2.1, for instance, flight AD1 (standard route, higher ROC) reaches the limit altitude much earlier than flight AD2 (deviated route, lower ROC), which may translate into a predicted noise impact that becomes less than the actual one. To illustrate this point, the noise prediction of flight AD1 is here refined, being now conducted using the automatic flightpath extension proposed in Section 2.3.3 (i.e., all contributing flight segments are incorporated in the prediction). As revealed by Figure 24, the noise impact by such an extended flight (labeled hereafter AD1-ext) goes on increasing beyond its former (10,000 ft limited) value until it reaches a plateau (around an altitude that is almost twice, i.e., 18,670 ft). This leads to a ground SEL that is higher, with differences of up to 30 dB at some locations (see right side of Figure 24). ignored. In Section 4.2.1, for instance, flight AD1 (standard route, higher ROC) reaches the limit altitude much earlier than flight AD2 (deviated route, lower ROC), which may translate into a predicted noise impact that becomes less than the actual one. To illustrate this point, the noise prediction of flight AD1 is here refined, being now conducted using the automatic flightpath extension proposed in Section 2.3.3 (i.e., all contributing flight segments are incorporated in the prediction). As revealed by Figure 24, the noise impact by such an extended flight (labeled hereafter AD1-ext) goes on increasing beyond its former (10,000 ft limited) value until it reaches a plateau (around an altitude that is almost twice, i.e., 18,670 ft). This leads to a ground SEL that is higher, with differences of up to 30 dB at some locations (see right side of Figure 24). The above result illustrates well how aircraft noise predictions can be biased by the arbitrary limitation of the route beyond a given reference altitude. In turn, it shows how to avoid such a bias by using a dynamic flightpath extension, such as the one proposed here.

Approximating the Flightpath and/or Power Settings
As said, aircraft operations around HKIA rarely comply with standardized flightpaths, being rather characterized by scattered flight profiles (cf. Figure 25). In the absence of any FDR (Flight Data Recorder) inputs, modeling these flights requires using radar information and inferring power settings, for instance using the model proposed in Section 2.3.1. Radar data, however, are of limited accuracy [67,68], and it is not rare that they noticeably differ from the actual (FDR) ones. These discrepancies may question the validity of either the thrust estimation (which requires knowing accurately both the acceleration and attitude of the aircraft, cf. Section 2.3.1) or of the noise prediction (which relies on the correct knowledge of the aircraft-to-ground distance, i.e., flight trajectory). Assessing this point is the matter of the present section. The above result illustrates well how aircraft noise predictions can be biased by the arbitrary limitation of the route beyond a given reference altitude. In turn, it shows how to avoid such a bias by using a dynamic flightpath extension, such as the one proposed here.

Approximating the Flightpath and/or Power Settings
As said, aircraft operations around HKIA rarely comply with standardized flightpaths, being rather characterized by scattered flight profiles (cf. Figure 25). In the absence of any FDR (Flight Data Recorder) inputs, modeling these flights requires using radar information and inferring power settings, for instance using the model proposed in Section 2.3.1. Radar data, however, are of limited accuracy [67,68], and it is not rare that they noticeably differ from the actual (FDR) ones. These discrepancies may question the validity of either the thrust estimation (which requires knowing accurately both the acceleration and attitude of the aircraft, cf. Section 2.3.1) or of the noise prediction (which relies on the correct knowledge of the aircraft-to-ground distance, i.e., flight trajectory). Assessing this point is the matter of the present section.
We here consider two pairs of specific flights, each relating to an identical aircraft and mission (B777-3ER or A330-343 aircraft flying from Hong Kong to Taipei) whereas presenting rather different characteristics in terms of flight profile (cf. Figure 25) and/or engine power evolution (cf. top right of Figures 26-29). Here, we solely consider departure scenarios since those are primarily concerned with pure propulsive noise, for which a correct estimation of the thrust is vital. We first assess the validity of the thrust estimation alone, this being performed by applying Equations (2)-(4) to accurate trajectory inputs coming from FDR data. The latter are then replaced with their (less accurate) radar data counterparts, which are extracted from FlightRadar24 website (business version). The objective is to assess how far the radar data inaccuracies may impact the thrust estimation, and ultimately, the noise prediction. Of note, since the present radar data solely provide the aircraft ground speed, we infer its airspeed counterpart by adding to it a headwind component (whose value is arbitrarily taken as 8 kt [49], for a lack of better information on wind profiles). Besides, here, the atmosphere characteristics are based on the average values recorded in Hong Kong for 2020. We here consider two pairs of specific flights, each relating to an identical and mission (B777-3ER or A330-343 aircraft flying from Hong Kong to Taipei) presenting rather different characteristics in terms of flight profile (cf. Figure 25 engine power evolution (cf. top right of Figures 26-29). Here, we solely consider de scenarios since those are primarily concerned with pure propulsive noise, for whi rect estimation of the thrust is vital. We first assess the validity of the thrust est alone, this being performed by applying Equations (2)-(4) to accurate trajectory coming from FDR data. The latter are then replaced with their (less accurate) rad counterparts, which are extracted from FlightRadar24 website (business version). jective is to assess how far the radar data inaccuracies may impact the thrust est and ultimately, the noise prediction. Of note, since the present radar data solely the aircraft ground speed, we infer its airspeed counterpart by adding to it a he component (whose value is arbitrarily taken as 8kt [49], for a lack of better inform wind profiles). Besides, here, the atmosphere characteristics are based on the aver ues recorded in Hong Kong for 2020.
For both pairs of flights (hereafter labeled as BD2, BD3 and AD7, AD8), th evolution is first estimated using the actual (FDR) data, its averaged value (lab "smoothed thrust") being then compared with its actual counterpart (labeled as thrust"). As can be seen on the top right of Figures 26-29, the agreement is fair whatever the scenario is. In particular, for both B777 flights (BD2, BD3), the estim very satisfactory, with an estimated thrust that matches the actual one almost p (compare black and red curves on the top right of Figures 26 and 27, respective good match slightly degrades for both A330 flights (AD7, AD8), whose actual a dicted thrust differ in some places (compare again the black and red curves on right of Figures 28 and 29, respectively). These discrepancies come from the m monotonic character of the flight (and, thus, power) settings, whose important va make the thrust estimation more challenging. Despite such a fussy timeline of th settings (which turned out to be the more complicated ones, among all the con cases), the thrust estimation is still very favorable, delivering trends that are quite    , airspeed (center), calculated and actual thrust (right) inferred from the FDR and radar data. Bottom: Noise contour map, as obtained using FDR data and actual thrust (left). Error entailed by an approximation of the thrust (center: smooth calculated thrust) plus the trajectory estimation (right: radar data, calculated thrust).    , airspeed (center), calculated and actual thrust (right) inferred from the FDR and radar data. Bottom: Noise contour map, as obtained using FDR data and actual thrust (left). Error entailed by an approximation of the thrust (center: smooth calculated thrust) plus the trajectory estimation (right: radar data, calculated thrust).

Conclusions and Perspectives
The present study focuses on the noise impact by aircraft operations around major airports. To this end, an aircraft noise prediction platform was developed, which relies on state-of-the-art functionalities as well as more specific, innovative features. More precisely, the method classically relies on the Aircraft Noise and Performance (ANP) database and its Noise-Power-Distance (NPD) table. The latter, however, are known to suffer from For both pairs of flights (hereafter labeled as BD2, BD3 and AD7, AD8), the thrust evolution is first estimated using the actual (FDR) data, its averaged value (labeled as "smoothed thrust") being then compared with its actual counterpart (labeled as "actual thrust"). As can be seen on the top right of Figures 26-29, the agreement is fairly good, whatever the scenario is. In particular, for both B777 flights (BD2, BD3), the estimation is very satisfactory, with an estimated thrust that matches the actual one almost perfectly (compare black and red curves on the top right of Figures 26 and 27, respectively). This good match slightly degrades for both A330 flights (AD7, AD8), whose actual and predicted thrust differ in some places (compare again the black and red curves on the top right of Figures 28 and 29, respectively). These discrepancies come from the much less monotonic character of the flight (and, thus, power) settings, whose important variations make the thrust estimation more challenging. Despite such a fussy timeline of the power settings (which turned out to be the more complicated ones, among all the considered cases), the thrust estimation is still very favorable, delivering trends that are quite close to the actual result. This fair character of the thrust estimation naturally translates into a fair prediction of the aircraft noise impact, as shown on the bottom of Figures 26-29: whereas the left image plots the actual SEL map (predicted using the actual thrust), its center counterpart depicts the error incurred by the thrust estimation (obtained by subtracting the former SEL map from the one predicted using the estimated thrust). Whatever the considered flight is, this error on the SEL prediction (∆SEL) is mostly in the range of ± 1dB: whereas it can reach up to ±2.5 dB at the beginning (start-of-roll) and/or the end of the flight sequence (standard limit altitude of 10,000 ft), the ∆SEL never exceeds ± 1dB in the rest of the flight sequence. Such discrepancies, which primarily reflect the accuracy limitations of FDR data (e.g., lack of discretization, absence of information on flap settings, etc.), are deemed to be acceptable for such low-order modeling of the thrust.
Independent of the thrust model itself, the uncertainties that weigh on the flight settings (trajectory, airspeed) provided by the radar data may however entail additional errors. To illustrate this point, we here re-assess the thrust estimation, its FDR-originated inputs being now replaced with their radar data counterpart. The latter may indeed importantly differ from the former, whether this concerns the flight profile (cf. top/left images of  or the airspeed (cf. top/center images of Figures 26-29). Notably, only the actual ground track appeared to be accurately reproduced by the radar data, across all cases. For each flight, the cumulative effect of all these discrepancies onto the aircraft noise is again quantified in terms of ∆SEL maps (see bottom right image of Figures 26-29). The latter are obtained by subtracting the actual ground noise levels (predicted using the FDR inputs, among which is the actual thrust) from their approximated counterpart (predicted using the radar-originated inputs and subsequently estimated thrust). Overall, the fidelity of the noise prediction appears to be driven by the radar data accuracy. Considering for instance the BD2 flight, one can see that the radar-originated flight profile, airspeed and thrust do not devoid much from their actual counterparts (the early take-off excepted). The resulting bias on the noise prediction is fairly low (cf. bottom right of Figure 26), with deviations of less than 0.5 dB for most of the flight sequences (except at the take-off start, where radar uncertainties entail noise discrepancies of about 15 dB). For BD3 flight, the radar-estimated altitude is higher than its actual value throughout the entire flight sequence (so much that the 10,000 ft limit altitude is reached earlier), which results in slightly higher error levels on the noise prediction (∆SEL~1 dB, overall). Notably, the radar-based estimated thrust still agrees well with both its actual and its FDR-estimated counterparts (compare the blue, red and black curves on the top right of Figure 27). Only at the start and at the end of the flight sequence, this agreement on both the thrust estimation and the noise impact appears to be less satisfactory. This may tend to indicate that, here, the radar data inaccuracies primarily weigh on the thrust prediction, more than on the propagation aspects (e.g., the aircraft-to-ground distance). Notably, because their respective discretization levels differ, FDR and radar data exhibit slightly different start-of-roll point, lift-off point and endpoint. Similar trends are observed for the AD7 flight, whose radar-originated airspeed appears to be less accurate than its flight profile counterpart (cf. left and center images on top of Figure 28, respectively). Combined with the fuzzy evolution of the power settings, these radar data inaccuracies challenges still more the thrust estimation (compare the blue, red and black curves on the top right of Figure 28). Besides, such a variability of the radar data airspeed is very likely to incur a different exposure duration to the noise associated with each flight segment, thereby further affecting the entire prediction, ultimately. Despite all these discrepancies, however, the noise impact is predicted rather accurately, with error levels that fall in the range of [−2; 0] dB (except again near the start-of-roll point, where differences reach 40 dB). Finally, AD8 flight reveals how radar data may resemble their actual counterparts (cf. left and center images on top of Figure 29) whereas entailing still more bias on the thrust estimation (compare the blue, red and black curves on the top right of Figure 29). At this stage, however, it is believed that the lesser discretization of the radar data (compared to their FDR counterpart) might explain such discrepancies on the thrust, whose estimation might then be still more challenged by the fuzzy timeline of the power settings. Whatever the reason for such biases on the thrust estimation, the overall impact on the noise prediction is still acceptable, with ∆SEL that never goes under −3 dB (cf. bottom right of Figure 29).
All in all, the above results illustrate the ability of the noise prediction method (and its underlying thrust model) to solely rely on radar data, thereby allowing to handle flightpaths that differ from standard ones whenever FDR information is unavailable.

Conclusions and Perspectives
The present study focuses on the noise impact by aircraft operations around major airports. To this end, an aircraft noise prediction platform was developed, which relies on state-of-the-art functionalities as well as more specific, innovative features. More precisely, the method classically relies on the Aircraft Noise and Performance (ANP) database and its Noise-Power-Distance (NPD) table. The latter, however, are known to suffer from restrictive assumptions which limit their application to simplified situations. For instance, the ANP database is built upon standardized scenarios of aircraft operations (aircraft types, flightpaths, power settings, atmospheric conditions, etc.). Besides, its NPD component relies on the simplistic scenario of a punctual noise source radiating within a homogeneous free field. Last but not least, the ground observer is assumed to be located right underneath the aircraft, with the latter flying with a constant speed and power settings along an infinite horizontal flightpath. To alleviate all these limitations, the present method incorporates several functionalities, some of which are specific to the present study. These features aim at (i) refining the noise emission stage (e.g., source intensity and directivity) as well as (ii) improving the propagation phase. Regarding for instance the refinement of the aircraft noise source, an innovative method is proposed, which allows inferring the engine power solely from the aircraft flightpath characteristics (whose access is much easier than that of Flight Data Recorder). Besides this, a functionality is introduced which allows extending automatically and dynamically the flightpath, thereby avoiding an arbitrary truncation of the aircraft noise emission as well as ensuring an accurate representation of its subsequent propagation. The latter propagation is also refined through the proper incorporation of the noise attenuation effects induced by any realistic, non-standard atmosphere. Other specific features are incorporated into the method, which aim at improving its efficiency (accuracy and execution speed). For instance, a recursive, dynamic grid refinement technique offers to optimize the number and distribution of ground observers, thereby maximizing the results accuracy whereas minimizing the prediction time.
The noise prediction method and subsequent computational platform are successfully validated using several benchmark cases of increasing representativeness. They are then applied to several realistic scenarios coming from actual aircraft operations around Hong Kong International Airport (HKIA). Specific comparative analyses are conducted, which allow highlighting the variability of the noise impact by aircraft, depending on their type (A330, B777) and/or operational conditions (power settings, meteorological conditions, routes, banks, etc.). From a phenomenological viewpoint, results allow discriminating the more prominent drivers, namely, the aircraft flightpath characteristics, the engine power settings, etc. It is also shown how important the meteorological conditions can be, because of the specific atmospheric attenuation effects they entail. Oppositely, the engine installation effects (assessed through the aircraft bank effects) appear to be of secondary importance. From a methodological perspective, the results showcase the capacity of the present approach to handling real-life situations, including when the latter greatly differ from the standardized scenarios underlying the ANP database. They also illustrate how noise prediction methods/platforms such as the present one may help in guiding the further expansion of airport operations and/or infrastructures (as is currently the case with HKIA).
With this end in view, it is planned to further improve the present approach, whether it is by refining still more its noise emission stage (e.g., assessing better the aircraft power settings using the Base of Aircraft Data database, BADA [69][70][71]), or by strengthening further its propagation phase (e.g., incorporating variable atmospheric conditions such as wind effects [72][73][74]). Last but not least, it is envisioned to extend the tool's capacities from an aircraft to a fleet level [75] so as to allow better optimizing air traffic operations. Figure A1. Forces exerted on the aircraft, as depicted in its longitudinal (left) or lateral (right) planes. Angles associated with the projection in the Earth (x, y, z) and aircraft stability (x', y', z') reference frames: Angle-of-attack ( ), flightpath ( ) and bank ( angles, along with the elevation ( ) and depression ( ) angles.
In the above equations, and W, respectively, stand for the mass and weight of the aircraft, whose (average) acceleration is . On the other hand, , and stand for the aircraft's angle of attack, flightpath and bank angles, respectively. Of note, the bank angle refers to the angle between the Earth reference frame's horizontal axis (y) and that of the aircraft's stability reference frame (y'), whose angle with the aircraft-to-observer noise propagation path corresponds to the depression angle ( ). Aside from that, , and are the propulsive (thrust) and aerodynamic (lift and drag) forces. and are the two components of the runway reaction, namely the vertical reaction and the roll resistance, which are related through the friction coefficient characterizing the runway, Figure A1. Forces exerted on the aircraft, as depicted in its longitudinal (left) or lateral (right) planes. Angles associated with the projection in the Earth (x, y, z) and aircraft stability (x', y', z') reference frames: Angle-of-attack (α), flightpath (γ) and bank (φ) angles, along with the elevation (β) and depression (ϕ) angles.
In the above equations, m and W, respectively, stand for the mass and weight of the aircraft, whose (average) acceleration is a. On the other hand, α, γ and φ stand for the aircraft's angle of attack, flightpath and bank angles, respectively. Of note, the bank angle refers to the angle between the Earth reference frame's horizontal axis (y) and that of the aircraft's stability reference frame (y'), whose angle with the aircraft-to-observer noise propagation path corresponds to the depression angle (ϕ). Aside from that, T, L and D are the propulsive (thrust) and aerodynamic (lift and drag) forces. R and F R are the two components of the runway reaction, namely the vertical reaction and the roll resistance, which are related through the friction coefficient characterizing the runway, µ F As a reminder, a typical value for this friction factor is 0.02 (resp. 0.4) for a dry concrete runway without (resp. with) brakes applied.
By combining Equations (A3) and (A2), one can express the ground vertical reaction as When introducing the lift and drag coefficient (C L , C D ), one can then express the drag in terms of the lift alone One can legitimately assume that the aircraft's angle of attack is small (that is cosα ∼ 1 and sinα ∼ 0), which further simplifies the above relationships. After a few developments, the thrust can be expressed as

. Particular Case of in-Flight Segments
When the aircraft is aloft, the ground reaction is nil (µ F = 0), and Equation (A6) becomes Considering that the lift equals the weight corrected from the simultaneous projection of flightpath and bank angles Of note, all parameters appearing in the above equation are readily available from the flight data and/or ANP database.

Appendix A.3. Particular Case of Ground-Roll Segments
On the other hand, when the aircraft is on the ground roll (γ = φ = 0), Equation (A6) becomes Expressing the lift force in these conditions is less straightforward, and requires developing an alternative lift model [57]. To do so, we start from the definition of lift where ρ is the air density, V TAS indicates the true airspeed of the aircraft, S is the wing area and C L is the lift coefficient. Assuming that the wing can be considered as a thin airfoil, the lift coefficient can be classically related to the angle of attack, α (which is supposed to be small enough).
where C L,0 stands for the zero-lift coefficient and C L,α is the lift coefficient slope. Assuming that the aerodynamic settings (α, S) and the atmospheric conditions (ρ) do not vary during the ground roll (i.e., C = 1 2 ρSC L = const), Equation (A11) turns into a parabolic equation of the aircraft speed (alone) At the lift-off point, the ground reaction vanishes and the lift strictly equals the aircraft weight, where V LOF is the lift-off speed of the aircraft. By neglecting any variation of the aircraft weight during the ground roll, one can thus re-express the lift force as All in all, Equation (A6) then becomes Here too, all parameters appearing in the above equation are readily available from the flight data and/or ANP database.

Appendix B. Further Illustration of the Noise Prediction Process and of Its Validation against Reference Cases
This section further illustrates the validation cases provided in Section 3.1, one of which is selected and documented more thoroughly. Figure A2 depicts the routes (departure and approach, either straight or curved) as well as the set of observers (namely R1-R17) used for all cases [62]. For more details about the other parameters (flightpath, meteorological conditions, power settings, airspeed, etc.), the reader is referred to Ref. [62]. Among the various cases listed, we here specifically focus on the JETWDS configuration (i.e., a wing-mounted jet engines aircraft flying along a straight departure route), whose relevant observers as those labeled R1-R5. Figure A3 depicts the time trace of various key quantities, as recorded for each observer along the flight evolution, which is broken down in terms of flight segments, either ground-roll (1-9) or airborne (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29). These key quantities constitute the main ingredients of the noise prediction process, namely the baseline noise level perceived by each observer ( Figure A3a) and its further adjustment through the cumulative corrections introduced in Section 2.2 ( Figure A3b-g). The final result is provided in Figure A3h, which also quantifies the error made with the reference solution [62]. This breakdown of the noise prediction process is summarized hereafter, for illustration and validation purposes.
At the lift-off point, the ground reaction vanishes and the lift strictly craft weight, is the lift-off speed of the aircraft. By neglecting any variation weight during the ground roll, one can thus re-express the lift force as

= •
All in all, Equation (A6) then becomes Here too, all parameters appearing in the above equation are readily the flight data and/or ANP database.

Appendix B. Further Illustration of the Noise Prediction Process and of I against Reference Cases
This section further illustrates the validation cases provided in Sect which is selected and documented more thoroughly. Figure A2 depicts the routes (departure and approach, either straigh well as the set of observers (namely R1-R17) used for all cases [62]. For mor the other parameters (flightpath, meteorological conditions, power setti etc.), the reader is referred to Ref. [62]. Among the various cases listed, we h focus on the JETWDS configuration (i.e., a wing-mounted jet engines aircra a straight departure route), whose relevant observers as those labeled R1depicts the time trace of various key quantities, as recorded for each obse flight evolution, which is broken down in terms of flight segments, either g 9) or airborne (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29). These key quantities constitute the main ingredien prediction process, namely the baseline noise level perceived by each ob A3a) and its further adjustment through the cumulative corrections introdu 2.2 ( Figure A3b-g). The final result is provided in Figure A3h, which also error made with the reference solution [62]. This breakdown of the noise p cess is summarized hereafter, for illustration and validation purposes. Figure A2. Departure and approach routes for reference cases, with the associated Figure A2. Departure and approach routes for reference cases, with the associated observers.

•
Baseline noise level (cf. Figure A3a): Originated from the NPD database, this quantity represents the noise that would be perceived by each selected observer if the aircraft was flying according to a standard scenario (cf. Section 2.2). It was checked that the associate prediction results agree well with the reference values [62], the maximum errors being less than 10 −5 %. Since the JETWDS case corresponds to a non-standard flight, these baseline noise levels must be refined through successive correction terms (see below). • Start-of-roll directivity adjustment (cf. Figure A3b): This correction accounts for the highly directive pattern of the jet noise at take-off, which impacts more especially those observers that are located upstream the ground roll segments (cf. Section 2.2). Logically, the effect is nil for these observers that are located downstream (i.e., R1 and R5). Here too, the predicted results match well the reference values, with a maximum error of less than 10 −5 %. • Engine installation correction (cf. Figure A3c): This correction accounts for the lateral directivity patterns induced by the engine installation effects, which depend on the relative depression angle seen by each observer (cf. Section 2.3.2). Logically, the effect is nil for those observers that are located right underneath the airborne segment (e.g., R1). Again, the predicted values compare favorably against their reference counterparts, with an error of less than 10 −9 %. • Finite segment correction (cf. Figure A3d): This correction accounts for both (i) the finite nature of each concerned flight segment and (ii) its relative position with respect to the observers. The effect is more important for those observers that are located away from the flight segment, whose perceived noise is then corrected from the loss incurred by the respective propagation distance. Here too, the calculation results are in good agreement with the reference ones, leading to a maximum error of less than 1%. • Duration correction (cf. Figure A3e): This correction translates the variation in the noise exposure duration, which logically varies with the fly-over time and, thus, the aircraft speed. In the present case where the aircraft continuously accelerates (from 0kt at the start-of-roll point) and eventually exceeds the standard value of 160kt (for which the correction is nil), this effect decreases monotonically. Here too, the prediction result is very close to the reference one, with errors in the range of 10 −12 %-10 −2 %. • Acoustic Impedance adjustment (cf. Figure A3f): This correction translates the impact of atmospheric effects (cf. Section 2.3.4), which are solely driven by the local meteorological conditions, thereby affecting all observers equally. Here, no error is recorded. • Lateral attenuation (cf. Figure A3g): This correction accounts for the lateral attenuation induced by the ground presence (cf. Section 2.2). Logically, this effect does not impact those observers that are located right beneath the flightpath (here, R1 and R3 for airborne segments [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The other observers are impacted differently, depending on their respective (lateral) distance to the aircraft, as well as on the nature of the flight segment considered (airborne or ground roll [49], e.g., R2-R4 for segments 9 and 10, respectively). Again, the predicted values match the reference ones, with maximum errors of less than 10 −1 %.

•
Single event noise level (cf. Figure A3h): This quantity represents the cumulative noise level perceived by each observer, once the contributions coming from all segments are summed up into a single noise event. As can be seen, the prediction is very close to the reference, with errors in the order of zero (except for the R1 observer, for which an error of about 0.011% is recorded).

Appendix C. Further Illustration of the Noise Impact Dependency towards Real-Life Operations
This section first focuses on the noise impact incurred by a B777-3ER (resp. an A330-343) aircraft departing from (resp. approaching) HKIA, thereby mirroring the discussion of Section 4.2.1. In a second time, the effect of banked turn is assessed on these various flights.

Appendix C.1. Noise Impact Incurred by B777-3ER Aircraft Flying along Two Departure Routes
Regarding the departure scenario, we select two specific B777-3ER flights with very distinct characteristics, and we assess their respective noise impact on three densely populated districts (namely D1, D5, and D7) that they both fly over. Whereas the first flight (labeled BD4) flies over districts D1 and D7 along a standard route with a high rate of climb (ROC), the second one (BD5) passes over district D1 at a lower altitude (see Figure  A4).  Figure A5 depicts the SEL contours generated by flights BD4 (left) and BD5 (center) along with their difference, which is obtained by subtracting the former from the latter (right).

Appendix C. Further Illustration of the Noise Impact Dependency towards Real-Life Operations
This section first focuses on the noise impact incurred by a B777-3ER (resp. an A330-343) aircraft departing from (resp. approaching) HKIA, thereby mirroring the discussion of Section 4.2.1. In a second time, the effect of banked turn is assessed on these various flights.
Appendix C.1. Noise Impact Incurred by B777-3ER Aircraft Flying along Two Departure Routes Regarding the departure scenario, we select two specific B777-3ER flights with very distinct characteristics, and we assess their respective noise impact on three densely populated districts (namely D1, D5, and D7) that they both fly over. Whereas the first flight (labeled BD4) flies over districts D1 and D7 along a standard route with a high rate of climb (ROC), the second one (BD5) passes over district D1 at a lower altitude (see Figure A4).

Appendix C. Further Illustration of the Noise Impact Dependency towards Real-Life Operations
This section first focuses on the noise impact incurred by a B777-3ER (resp. an A330-343) aircraft departing from (resp. approaching) HKIA, thereby mirroring the discussion of Section 4.2.1. In a second time, the effect of banked turn is assessed on these various flights.

Appendix C.1. Noise Impact Incurred by B777-3ER Aircraft Flying along Two Departure Routes
Regarding the departure scenario, we select two specific B777-3ER flights with very distinct characteristics, and we assess their respective noise impact on three densely populated districts (namely D1, D5, and D7) that they both fly over. Whereas the first flight (labeled BD4) flies over districts D1 and D7 along a standard route with a high rate of climb (ROC), the second one (BD5) passes over district D1 at a lower altitude (see Figure  A4).  Figure A5 depicts the SEL contours generated by flights BD4 (left) and BD5 (center) along with their difference, which is obtained by subtracting the former from the latter (right).  Figure A5 depicts the SEL contours generated by flights BD4 (left) and BD5 (center) along with their difference, which is obtained by subtracting the former from the latter (right). Compared to flight BD4 (standard route, higher ROC), flight BD5 (deviated route, lower ROC) impacts less some of the populated areas, with noise levels that are lower by around 4 dB in D1 and D5 districts, and by about 7.5 dB in the western part of D7 district. The opposite trend is observed to occur in the eastern part of D7 district, where flight BD5′s impact exceeds that of BD4 by up to 13dB in SEL (see Figure A6).
As was observed in Section 4.2.1 for Airbus-related flights, the lower altitude of a given flight (here BD5) does not automatically entail a higher noise impact on the ground. For instance, even though flight BD5 passes over D1 district at a lower altitude than its BD4 counterpart, it results in a smaller noise footprint over this area. Here too, this is likely to be explained by the difference in the power settings (i.e., engine thrust) characterizing both aircraft along their respective routes. For instance, Figure A7 compares the time history of the thrust delivered by the two aircraft, with a focus put on that specific flight phase where they both pass nearby D1 and D6 districts (highlighted with vertical dashdotted lines). At that time, flight BD5 exhibits a propulsive power that is almost one-third of its BD4 counterpart. This is likely to incur a comparatively much lower noise emission for BD5 flight, whose lower noise attenuation (short propagation distance) is then favorably balanced. In addition, here again, the smaller ROC exhibited by flight BD5 is likely to diminish its noise footprint, compared to its BD4 counterpart whose higher flightpath angle somehow exacerbates its noise impact (jet noise directivity). All in all, these two features of flight BD5 (lower power setting, smaller ROC) suffice to offset the detrimental effect entailed by its lower altitude (reduced noise attenuation), when flying over D1 and D6 districts.  Compared to flight BD4 (standard route, higher ROC), flight BD5 (deviated route, lower ROC) impacts less some of the populated areas, with noise levels that are lower by around 4 dB in D1 and D5 districts, and by about 7.5 dB in the western part of D7 district. The opposite trend is observed to occur in the eastern part of D7 district, where flight BD5 s impact exceeds that of BD4 by up to 13 dB in SEL (see Figure A6).
As was observed in Section 4.2.1 for Airbus-related flights, the lower altitude of a given flight (here BD5) does not automatically entail a higher noise impact on the ground. For instance, even though flight BD5 passes over D1 district at a lower altitude than its BD4 counterpart, it results in a smaller noise footprint over this area. Here too, this is likely to be explained by the difference in the power settings (i.e., engine thrust) characterizing both aircraft along their respective routes. For instance, Figure A7 compares the time history of the thrust delivered by the two aircraft, with a focus put on that specific flight phase where they both pass nearby D1 and D6 districts (highlighted with vertical dash-dotted lines). At that time, flight BD5 exhibits a propulsive power that is almost one-third of its BD4 counterpart. This is likely to incur a comparatively much lower noise emission for BD5 flight, whose lower noise attenuation (short propagation distance) is then favorably balanced. In addition, here again, the smaller ROC exhibited by flight BD5 is likely to diminish its noise footprint, compared to its BD4 counterpart whose higher flightpath angle somehow exacerbates its noise impact (jet noise directivity). All in all, these two features of flight BD5 (lower power setting, smaller ROC) suffice to offset the detrimental effect entailed by its lower altitude (reduced noise attenuation), when flying over D1 and D6 districts. Compared to flight BD4 (standard route, higher ROC), flight BD5 (deviated route, lower ROC) impacts less some of the populated areas, with noise levels that are lower by around 4 dB in D1 and D5 districts, and by about 7.5 dB in the western part of D7 district. The opposite trend is observed to occur in the eastern part of D7 district, where flight BD5′s impact exceeds that of BD4 by up to 13dB in SEL (see Figure A6).
As was observed in Section 4.2.1 for Airbus-related flights, the lower altitude of a given flight (here BD5) does not automatically entail a higher noise impact on the ground. For instance, even though flight BD5 passes over D1 district at a lower altitude than its BD4 counterpart, it results in a smaller noise footprint over this area. Here too, this is likely to be explained by the difference in the power settings (i.e., engine thrust) characterizing both aircraft along their respective routes. For instance, Figure A7 compares the time history of the thrust delivered by the two aircraft, with a focus put on that specific flight phase where they both pass nearby D1 and D6 districts (highlighted with vertical dashdotted lines). At that time, flight BD5 exhibits a propulsive power that is almost one-third of its BD4 counterpart. This is likely to incur a comparatively much lower noise emission for BD5 flight, whose lower noise attenuation (short propagation distance) is then favorably balanced. In addition, here again, the smaller ROC exhibited by flight BD5 is likely to diminish its noise footprint, compared to its BD4 counterpart whose higher flightpath angle somehow exacerbates its noise impact (jet noise directivity). All in all, these two features of flight BD5 (lower power setting, smaller ROC) suffice to offset the detrimental effect entailed by its lower altitude (reduced noise attenuation), when flying over D1 and D6 districts.  As for what could be observed with the A330 aircraft (cf. Section 4.2.1), the above analysis further illustrates how HKIA departure procedures may impact very differently those highly densely populated areas of Hong Kong.

Appendix C.2. Noise Impact Incurred by A330-343 Aircraft Flying along Two Approach Routes
Mirroring Section 4.2.1, we here compare the noise impact induced by two A330-343 aircraft approaching HKIA, with a special focus on those densely populated areas (namely D2, D3, and D4) that are located beneath the flight corridors. The two flights are selected for their rather different flightpaths, so as to highlight how the latter may alter the noise footprint on the ground. More precisely, the first aircraft (flight AA2) approaches the 25L runway via a higher altitude route, while the second one (flight AA3) flies towards the 25R runway at a lower altitude. These differences hold to a certain point, after which both aircraft adopt a similar flightpath, following the Continuous Descent Approach protocol enforced in Hong Kong. Figure A8 depicts the ground track and flight profile of both flights. Figure A8. A330 aircraft approaching HKIA. Flights AA2 and AA3 respective routes (left: ground track, center: flight profile) and corresponding ground observers (dynamic grid, right). Figure A9 depicts the SEL contours incurred by both flight AA2 (left) and flight AA3 (center), along with their difference (right). The densely populated D3 district which is sandwiched between 25L and 25R routes sees its northwestern part impacted more importantly by flight AA3 (with noise levels exceeding AA2 ones by about 10.6 dB, see Figure A10), while the opposite occurs in the southeastern part (with an excess noise by flight AA2 of up to 7.8 dB). Given the distribution of residents in the D3 district (whose central and southern areas are more populated, see Figure 8), flight AA2 (lower altitude) appears to be less environmentally friendly than its AA3 counterpart (higher altitude). This observation also holds for the four times denser D2 district, which is flown over directly by flight AA2 whose noise impact exceeds the AA3 one by about 9.1 dB. Finally, both flights As for what could be observed with the A330 aircraft (cf. Section 4.2.1), the above analysis further illustrates how HKIA departure procedures may impact very differently those highly densely populated areas of Hong Kong.

Appendix C.2. Noise Impact Incurred by A330-343 Aircraft Flying along Two Approach Routes
Mirroring Section 4.2.1, we here compare the noise impact induced by two A330-343 aircraft approaching HKIA, with a special focus on those densely populated areas (namely D2, D3, and D4) that are located beneath the flight corridors. The two flights are selected for their rather different flightpaths, so as to highlight how the latter may alter the noise footprint on the ground. More precisely, the first aircraft (flight AA2) approaches the 25L runway via a higher altitude route, while the second one (flight AA3) flies towards the 25R runway at a lower altitude. These differences hold to a certain point, after which both aircraft adopt a similar flightpath, following the Continuous Descent Approach protocol enforced in Hong Kong. Figure A8 depicts the ground track and flight profile of both flights. As for what could be observed with the A330 aircraft (cf. Section 4.2.1), the above analysis further illustrates how HKIA departure procedures may impact very differently those highly densely populated areas of Hong Kong.

Appendix C.2. Noise Impact Incurred by A330-343 Aircraft Flying along Two Approach Routes
Mirroring Section 4.2.1, we here compare the noise impact induced by two A330-343 aircraft approaching HKIA, with a special focus on those densely populated areas (namely D2, D3, and D4) that are located beneath the flight corridors. The two flights are selected for their rather different flightpaths, so as to highlight how the latter may alter the noise footprint on the ground. More precisely, the first aircraft (flight AA2) approaches the 25L runway via a higher altitude route, while the second one (flight AA3) flies towards the 25R runway at a lower altitude. These differences hold to a certain point, after which both aircraft adopt a similar flightpath, following the Continuous Descent Approach protocol enforced in Hong Kong. Figure A8 depicts the ground track and flight profile of both flights. Figure A8. A330 aircraft approaching HKIA. Flights AA2 and AA3 respective routes (left: ground track, center: flight profile) and corresponding ground observers (dynamic grid, right). Figure A9 depicts the SEL contours incurred by both flight AA2 (left) and flight AA3 (center), along with their difference (right). The densely populated D3 district which is sandwiched between 25L and 25R routes sees its northwestern part impacted more importantly by flight AA3 (with noise levels exceeding AA2 ones by about 10.6 dB, see Figure A10), while the opposite occurs in the southeastern part (with an excess noise by flight AA2 of up to 7.8 dB). Given the distribution of residents in the D3 district (whose central and southern areas are more populated, see Figure 8), flight AA2 (lower altitude) appears to be less environmentally friendly than its AA3 counterpart (higher altitude). This observation also holds for the four times denser D2 district, which is flown over directly by flight AA2 whose noise impact exceeds the AA3 one by about 9.1 dB. Finally, both flights  Figure A9 depicts the SEL contours incurred by both flight AA2 (left) and flight AA3 (center), along with their difference (right). The densely populated D3 district which is sandwiched between 25L and 25R routes sees its northwestern part impacted more importantly by flight AA3 (with noise levels exceeding AA2 ones by about 10.6 dB, see Figure A10), while the opposite occurs in the southeastern part (with an excess noise by flight AA2 of up to 7.8 dB). Given the distribution of residents in the D3 district (whose central and southern areas are more populated, see Figure 8), flight AA2 (lower altitude) appears to be less environmentally friendly than its AA3 counterpart (higher altitude). This observation also holds for the four times denser D2 district, which is flown over directly by flight AA2 whose noise impact exceeds the AA3 one by about 9.1 dB. Finally, both flights impact equally the D4 district, each incurring a noise excess of 1-2 dB underneath its respective route. To sum up, flight AA2 appears to be less environmentally friendly for these densely populated districts, thereby revealing that the 25R approach route should be given priority whenever the conditions permit (operational, meteorological, etc.). Notably, all these observations are fully consistent with the ones recorded for Boeing aircraft (cf. Section 4.2.1). impact equally the D4 district, each incurring a noise excess of 1-2 dB underneath its respective route. To sum up, flight AA2 appears to be less environmentally friendly for these densely populated districts, thereby revealing that the 25R approach route should be given priority whenever the conditions permit (operational, meteorological, etc.). Notably, all these observations are fully consistent with the ones recorded for Boeing aircraft (cf. Section 4.2.1). Figure A9. A330 aircraft approaching HKIA. Noise impact (SEL) generated by flight AA2 (left) and AA3 (center) over Hong Kong city, along with difference (∆SEL) between both results (as obtained by subtracting the former from the latter, right).

Appendix C.3. Specific Effect of the Bank Angle on the Various Routes and Aircraft
This section further illustrates the sensitivity of the noise prediction towards the bank angle (i.e., engines installation) effect, thereby extending the investigation conducted in Section 4.3.1. Here, we perform the noise prediction for alternatives flights, with the bank angle being either incorporated or neglected in the SEL evaluation.
Focusing first on departure scenarios, we consider the flights AD1 (cf. Section 4.2.1), BD4, and BD5 (cf. Appendix C.1) departing from HKIA. Similar to what happened for flight AD2 (cf. Section 4.3.1), when the aircraft performs a banked turn, most of the observers located on the same (resp. opposite) side of the turn experience less (resp. more) noise impacts (see Figure A11). The opposite nevertheless holds for those observers that are located very close to the ground track. All the previous observations derive logically from the relative depression angle perceived by each observer (see Section 2.3.2). This being said, the bank effect on the SEL levels appears to be fairly subtle, with differences of less than 0.4 dB overall (see Figure A11). impact equally the D4 district, each incurring a noise excess of 1-2 dB underneath its respective route. To sum up, flight AA2 appears to be less environmentally friendly for these densely populated districts, thereby revealing that the 25R approach route should be given priority whenever the conditions permit (operational, meteorological, etc.). Notably, all these observations are fully consistent with the ones recorded for Boeing aircraft (cf. Section 4.2.1). Figure A9. A330 aircraft approaching HKIA. Noise impact (SEL) generated by flight AA2 (left) and AA3 (center) over Hong Kong city, along with difference (∆SEL) between both results (as obtained by subtracting the former from the latter, right).

Appendix C.3. Specific Effect of the Bank Angle on the Various Routes and Aircraft
This section further illustrates the sensitivity of the noise prediction towards the bank angle (i.e., engines installation) effect, thereby extending the investigation conducted in Section 4.3.1. Here, we perform the noise prediction for alternatives flights, with the bank angle being either incorporated or neglected in the SEL evaluation.
Focusing first on departure scenarios, we consider the flights AD1 (cf. Section 4.2.1), BD4, and BD5 (cf. Appendix C.1) departing from HKIA. Similar to what happened for flight AD2 (cf. Section 4.3.1), when the aircraft performs a banked turn, most of the observers located on the same (resp. opposite) side of the turn experience less (resp. more) noise impacts (see Figure A11). The opposite nevertheless holds for those observers that are located very close to the ground track. All the previous observations derive logically from the relative depression angle perceived by each observer (see Section 2.3.2). This being said, the bank effect on the SEL levels appears to be fairly subtle, with differences of less than 0.4 dB overall (see Figure A11).

Appendix C.3. Specific Effect of the Bank Angle on the Various Routes and Aircraft
This section further illustrates the sensitivity of the noise prediction towards the bank angle (i.e., engines installation) effect, thereby extending the investigation conducted in Section 4.3.1. Here, we perform the noise prediction for alternatives flights, with the bank angle being either incorporated or neglected in the SEL evaluation.
Focusing first on departure scenarios, we consider the flights AD1 (cf. Section 4.2.1), BD4, and BD5 (cf. Appendix C.1) departing from HKIA. Similar to what happened for flight AD2 (cf. Section 4.3.1), when the aircraft performs a banked turn, most of the observers located on the same (resp. opposite) side of the turn experience less (resp. more) noise impacts (see Figure A11). The opposite nevertheless holds for those observers that are located very close to the ground track. All the previous observations derive logically from the relative depression angle perceived by each observer (see Section 2.3.2). This being said, the bank effect on the SEL levels appears to be fairly subtle, with differences of less than 0.4 dB overall (see Figure A11).
Focusing then on approach scenarios, we repeat the noise prediction associated with flights AA3 (cf. Appendix C.2), BA1 and BA2 (cf. Section 4.2.1). Here too, the impact of the bank angle is rather modest, with no more than 0.5dB differences overall (see Figure A12). These differences are again positive or negative, depending on how each observer perceives the relative depression angle. Focusing then on approach scenarios, we repeat the noise prediction associated with flights AA3 (cf. Appendix C.2), BA1 and BA2 (cf. Section 4.2.1). Here too, the impact of the bank angle is rather modest, with no more than 0.5dB differences overall (see Figure  A12). These differences are again positive or negative, depending on how each observer perceives the relative depression angle.