Variations of the zero degrees isotherm and environmental lapse rate recorded with ADSB and Mode S EHS messages

Abstract

This study focuses on analyzing the altitude of the zero degrees isotherm and variations in the environmental lapse rate (ELR) using the publicly available data collected from Automatic Dependent Surveillance–Broadcast (ADS-B) and Mode S Enhanced Surveillance (EHS) messages emitted by airplanes over a five-month period in 2021. The data was gathered using a professional receiver stationed in Bucharest (Romania). The aviation messages were decoded and the air temperature and pressure were determined, at the location of the airplane. The method has the advantage of the continuous messages that are emitted by the aircrafts during flight that allow instantaneous determination of the meteorological parameters at no additional costs. It can also be extended to permit almost real time maps of the ELR. When data was analyzed and a standard ELR value of 6.5 K/km is employed it was observed that the mean altitude of the 0 degrees isotherm exhibits a seasonal increase during the summer months, with an average altitude of 2874.2 m. The highest recorded altitude of the 0 degrees isotherm was found to be 5346.8 m, near Alexandria city (Romania), on 22.07.2021. Using a standard Least Mean Square algorithm alongside the International Standard Atmosphere pressure formula, the ELR values were calculated from pressure measurements data. The resulting mean ELR for the five-month period was determined to be 5.1331 K/km, slightly lower than the standard value.

Introduction

Weather and climate impact numerous ecological processes¹. A key observation is that near-surface air temperature and precipitation are particularly important variables, as they greatly impact the development of surface and subsurface conditions, including vegetation and groundwater². The investigation of the zero degree isotherm has been the focus of numerous research articles³.

The temperature near the surface varies with altitude in accordance with the environmental lapse rate (ELR)⁴. Employing a linear lapse rate for adjusting temperature with altitude has been a common practice⁵, with its subsequent implications on the accuracy of results. An important factor to consider is that the uncertainties linked to the lapse rate can at times overshadow the effects of climate change in specific modeling scenarios⁶.

Characterizing the ELR has diverse applications, particularly in refining global or regional numerical weather predictions, and climate projections⁷. The lapse rate is also crucial for meteorologists in predicting specific types of cloud formations, the occurrence of thunderstorms, and the severity of atmospheric turbulence⁸. The ELR holds particular significance in regions characterized by complex terrain, as well as in the spatial modeling of biological phenomena like species distributions, phenology, and growing seasons⁹. The temperature gradient near the surface predominantly governs spatial temperature variations in mountainous areas, thereby impacting snowfall, snowmelt patterns, glacier mass balance, and species distribution⁶. Additionally, lapse rates play a critical role in hydrological modeling and in the downscaling of global climate models¹⁰. The spatial distribution of temperature is also crucial for other applications, including hydrology¹¹, ecology¹², agriculture¹³and surface energy balance models¹⁴.

The troposphere typically experiences a decrease in temperature with increasing altitude, at a rate of approximately 6.5^oC per kilometer⁶. However, multiple observational cues suggest that the environmental lapse rate varies both temporally and spatially, suggesting that the widely accepted constant value of 6.5^oC/km may be too high^11,15. Variations in the height of the zero degree isotherm were also spotted¹⁶.

The observed trends in radio occultation data obtained with Global Navigation Satellite System reflect well-documented responses to global warming, notably the widespread warming of the troposphere^17,18. In recent years, the rise of the zero-degree isotherm has been accelerating, primarily due to human-induced climate warming¹⁹.

The same increase trend has been observed in central Chile using radiosondes measurements²⁰. There are other studies that suggest a general correlation between the spatial distribution of the height of the zero degrees Celsius isotherm and geographical latitude²¹.

This highlights the desirability of spatially continuous yet finely detailed weather data for ecological research and predictions, such as the environmental lapse rate, which is essential for determining temperature distribution. Unfortunately, weather stations that measure precipitation or air temperature are often sparse, especially in mountainous regions (such as the Carpathians in Romania), at high elevations or in uninhabited areas. Consequently, obtaining precise climatic maps is challenging. This paper provides a method to estimate in real time the environmental lapse rate, for remote areas, without special instrumentation thus with no associated costs. The implications are tremendous.

Meteorological data can be retrieved using several methods. One approach involves employing a numerical weather prediction model, which utilizes mathematical algorithms to predict weather patterns based on current data obtained from satellites, ground stations, weather balloons, and other sources²². These models generate forecasts by integrating data over time, starting from the present conditions.

The second method involves deploying radiosondes or weather balloons^20,21. Radiosondes are equipped with temperature and humidity sensors, while geopotential altitude is determined using a pressure sensor and/or GPS receiver.

The third method involves utilizing aircrafts. Aircraft Meteorological Data Relay (AMDAR) entails the transmission of meteorological data to ground stations through the Aircraft Communications Addressing and Reporting System (ACARS). However, this data is not publicly accessible. The frequency of AMDAR observations varies depending on the flight phase²³, resulting in an average resolution typically spanning a few tens of kilometers²⁴. During ascent/descent phases, AMDAR smoothes data from various aircraft sensors.

This smoothing process ensures consistency among observations from different sensors and onboard computer systems²³. Efforts have been made to employ drones for atmospheric monitoring²⁵.

The last method (employed in this paper) utilizes aircraft track and flight publicly available data to deduce meteorological conditions. This data is obtainable through Automatic Dependent Surveillance–Broadcast (ADS-B) transmissions, furnishing information such as position (e.g. latitude, longitude, and altitude), ground speed, track angle, and more. This provides an unique occasion to determine accurate the environmental lapse rate, with no additional costs, in real time, and for areas where no other meteorological equipment is available. An immediate application is connected to forecasts alerts for storms, as it will be detailed later.

The spatial distribution of aircraft population presents an opportunity to leverage aircraft as ‘atmospheric sensors,’ thereby enhancing and enriching the input data for tools dedicated to monitoring and predicting atmospheric conditions²⁶. The methodology highlighted in this research allows a real time estimate of the environmental lapse rate, even for remote areas, without the need of dedicated equipment. Furthermore, detailed precise climatic maps can be elaborated.

Aircraft compute local meteorological conditions using observations from onboard air data sensors. Readings from the sensors of the airplane are encoded and transmitted via ADS-B and Mode S messages (their decoding is described in Appendix A). The methodology employed for obtaining the meteorological parameters from the raw data is presented in Sect. 2 and the results obtained- in part 3. Section 4 provides comparison with other findings in the literature, together with their potential applications. The last part synthesizes the results.

Materials and methods

Sensors play a crucial role in the instrument systems aboard aircraft, covering flight, engine, and navigation instruments. Flight instruments, including altimeters, airspeed indicators, and vertical speed indicators, are essential components. Altimeters measure changes in static air pressure to determine the aircraft’s altitude. Airspeed indicators calculate true airspeed using pitot and static pressure, along with temperature data. Vertical speed indicators employ a solid-state pressure sensor, known as an aneroid, to measure changes in static air pressure.

Common elements of air data systems include total air temperature probes, angle of attack vanes and probes, Pitot probes, Pitot Static probes, multi-function probes, and outside air temperature probes²⁷. Every aircraft is equipped with a minimum of six fundamental instruments: airspeed indicator, attitude indicator, altimeter, turn coordinator, heading indicator, and vertical speed indicator. An Air Data Module (ADM) serves as a vital component of an aircraft’s avionics system, tasked with measuring and transmitting crucial data concerning the aircraft’s flight performance and environmental conditions²⁸.

The absence of detailed avionics information for the aircrafts²⁶ presented challenges in verifying the accuracy of the data collected by the sensors on board the airplanes involved in this study. The estimated temperature error was determined to be K²⁹. Nevertheless, conducting meteorological measurements aboard aircraft requires in-flight calibration. Consequently, most operators of research aircraft undertake some form of calibration³⁰, ensuring the quality of in-flight measurements.

Readings from sensors are encoded and transmitted as ADSB messages. The messages are captured using a Radarcape ADS-B Receiver from Jet Vision³¹. This device ensures unparalleled precision in capturing Mode-A/C, Mode-S, and ADS-B raw data. It achieves this through the integration of a GPS synchronous clock, enabling time stamps with a precision of up to 50 nanoseconds. Equipped with advanced high-frequency circuits, the ADS-B receiver guarantees sensitivity down to -93 dBm input level and detects signals from distances of up to 450 km³¹ .

The Radarcape’s antenna was mounted on top of the CAMPUS building in University of National Sciences and Technology Politehnica of Bucharest (approximately 45 m above ground), latitude 44.434796 ^oN, longitude 26.045906^oE and ground altitude of 106 m.

The data was acquired daily in the period 6th May − 22nd October 2021, each day at 8 o’clock in the morning. The recording time was limited to timeframes of 10 min. The abundance of received messages hindered continuous recording. All messages received as raw data were saved as text in the hex format and special codes written in Matlab R2015a were developed for decoding and data processing.

A detailed methodology for decoding of the ADSB messages is presented in the Appendix. Regarding the correctness of the received raw data, ADS-B uses cyclic redundancy check (CRC) to validate the correctness of the message³². This was used and the CRC checksum (supposed to be zero for correct messages) was calculated. Only correct messages were used in the subsequent analysis.

In the initial stage of the decoding algorithm, ADS-B messages are refined, and latitude, longitude, and altitude are obtained for each aircraft. Subsequently, Mach numbers, true airspeeds, ground airspeeds, and pressures are calculated for each aircraft, utilizing Mode-S EHS messages (as described in the following). As multiple messages may originate from the same aircraft, multiple values are acquired for each variable. The ultimate values are determined as the arithmetic means of the figures extracted from the data. Smoothing is necessary because of the resolution limitations of the reported Mach number and airspeed (Appendix A). The resulting data comprises a list of parameters (e.g. longitude, latitude, altitude, Mach number, true airspeed, and pressure) for each aircraft, counted once.

The temperature derived from Mode-S EHS represents a near-instantaneous temperature at the aircraft’s location. Its determination requires knowledge of both the Mach number and the true airspeed.

The Mach number is defined as the ratio between true airspeed and the speed of sound, making it a function of air temperature ³³:

1

The true airspeed specific heat constant is a conversion factor incorporating the ratio of specific heats and converting from knots to meters per second. In Eq. 1 the parameter is expressed in knots. The standard deviation when determining the temperature is approximately 0.8^oC, primarily due to the methodology used to derive it (for the Mach number the ADSB resolution is 0.004 M, while for the air speed 2 kts as detailed in Appendix A).

To compute pressure, the International Standard Atmosphere (ISA) serves as a reference standard for aircraft design calculations. It enables comparison of test results across various aircraft and components under standardized conditions. Furthermore, ISA is recommended for processing data from geophysical and meteorological observations³⁴. Pressure can be calculated using the following formula:

2

In Eq. (2) represents the altitude of the aircraft, and the constants are defined as follows: , 0 for the troposphere, , and the ideal gas constant ³⁵. The variable ELR denotes the temperature gradient . Please note that Eq. (2) can also be applied in reverse: by using the pressure decoded from Mode-S EHS messages (detailed in the Appendix A), the ELR can be determined.

Upon examining the raw data, it was determined that the messages were transmitted by airplanes flying within the latitude interval [40^oN, 47^oN] and longitude [21^oE, 30^oE]. The altitude of the planes ranged from 81.41 to 11,494 km. The resolution of ADSB messages for the altitude is 7.62 m and for latitude and longitude deg. (Appendix A).

The final numbers of processed information messages (i.e. longitude, latitude, altitude, Mach number, true airspeed, and pressure) were as follows: 62 in month 5, 105 in month 6, 97 in month 7, 122 in month 8, 112 in month 9, and 24 in month 10, totaling 522 messages.

Results

The first results in this paper targeted determination of the zero degrees isotherm . The zero-degree isotherm influences vegetation, the snowfall limit, and the water cycle, significantly impacting the habitats of humans, animals, and plants³⁶. During the last years the rise of the zero-degree isotherm has been accelerating, primarily due to human-induced climate warming¹⁹.

Despite its significance, there remains a research gap worldwide concerning the spatial variability of the zero-degree isotherm, its long-term changes, and its sensitivity to regional climate change³⁷. Rising near-surface air temperatures are expected to increase surface precipitation¹⁹. The combination of heavy precipitation and an elevated zero-degree isotherm creates extremely hazardous conditions, potentially leading to extensive flooding and localized flash floods³⁸.

The zero-degree isotherm was calculated following the altitude of the plane and the recorded temperature obtained from Eq. (1). A standard ELR of 6.5^oC/km was adopted. Figure 1show results, that are consistent with other observations in the literature which show large variability of lapse rates geographically in California³⁹, central Asia⁴⁰, Canada⁴¹etc. The summer months show overall higher figures. The same increase trend was determined for the Carpathians region⁴².

Fig. 1.

Altitude [km] of the 0 degrees isotherm for May-October 2021.

The observed variations in the altitude of zero-degree isotherm may be due to spatial and temporal shifts in precipitation phase, or changes in the mass of air, with a moving hot or cold fronts. This alters the isotherm gradually, over tens of kilometers for a cold front and hundreds of kilometers for a warm front.

Local levels can be affected by wind, sunlight reflection, and humidity, causing rapid changes over several kilometers. Additionally, atmospheric subsidence and ascent can contribute to variations in the zero degree isotherm level. For a full interpretation of the results combination with other types of meteorological measurements are necessary.

The highest determined altitude of the zero degrees isotherm was found to be 5346.8 m, observed at the location 44.19^oN, 25.02^oE, near Alexandria city in Romania, on 22.07.2021. The ground temperature was recorded at 18.88 deg. C, with a pressure of 754.634 mmHg and humidity at 78%⁴³. This measurement is comparable to the value obtained using weather balloons in Payerne, western Switzerland, which recorded a height of 5298 m⁴⁴. Additionally, records obtained with radiosondes in South America have also shown similarly high altitudes⁴⁵.

In August, the highest altitude of the zero degrees isotherm was recorded at 4404.1 m, observed near Plovdiv (Bulgaria) at the coordinates 42.19^oN, 23.94^oE, on 30.08.2021. The ground temperature was measured at 20^oC, with a pressure of 742.188 mmHg and humidity at 64%⁴⁶. Other recorded values for the highest altitude of the zero degrees isotherm include: 4175.5 m in May, 4255 m in June, 3920 m in September, and 5052.5 m in October.

Figure 2 illustrates the average altitude and standard deviation of the 0 degrees isotherm recorded from all aircraft for each month. The standard environmental lapse rate of 6.5^oC/km was employed in the simulations. It is evident that the mean altitude of the 0 degrees isotherm tends to rise during the summer months. The level of the zero degrees isotherm may be an indicator of precipitation level, as for days with intense precipitation, a lowering of the isotherm has been recorded⁴⁷. For Romania, in the analyzed time interval, August is the month with the lowest precipitation level⁴⁸. An overall average of the 0 degrees isotherm of 2874.2 m is observed.

Fig. 2.

Mean altitude of the 0 degrees isotherm when a ELR of 6.5^oC/km was adopted.

In the subsequent analysis, the measured pressure data will be utilized. Through Eq. (2), a standard Least Mean Square (LMS) algorithm will be applied to ascertain the values for ELR. The outcomes are depicted in Fig. 3.

Fig. 3.

ELR obtained from the measured pressure.

The environmental lapse rate is contingent upon the characteristics of the overlying air masses, the broader-scale atmospheric conditions, and local influences⁴⁹. It is also influenced by factors such as radiation, convection, and condensation⁵⁰, and is highly variable.

The findings are in line with other results from literature^11,15, indicating a smaller value than the standard one. The overall mean ELR for the six months is calculated to be 5.1331^oC/km. This revised figure will be employed for another simulation involving data averaging to eliminate the local effects. The latitude and longitude intervals are divided into four bins, and mean values for the 0 degrees isotherm are computed within each of these intervals. The 2D Freedman-Diaconis modeling approach was utilized to determine an appropriate bin width⁵¹. Results are presented in Fig. 4, obtained for all data recorded in the 5 months. The values of the 0 degrees isotherm exhibit variations with both latitude and longitude, consistent with other observations²¹. The region where the highest values recorded is in the Gavanu-Burdea Plain. The precipitation level was low for the analysed period (below 10 mm in September, while the highest recorded values were in the 51. 75 mm interval in May, June and October^52–57and the temperature higher than surrounding regions^52–57.

Fig. 4.

Altitude [km] of the 0 degrees isotherm.

Such a detailed map meets the need for spatially continuous yet highly detailed weather data for refining global/regional numerical weather predictions, reanalysis efforts, and climate projections.

Discussion

In this work the average ELR over the 6-month period was determined to be 5.1331^oC/km, slightly lower than the standard value. This finding is consistent with previous research^11,15. Yearly lapse rates ranging from 5.4 to 5.8^oC/km were obtained for studies in Italy⁵⁸. Measurements in the USA indicate an ELR of 4.5^oC/km⁴. Regional variations have been identified, such as in Chile, where values range from 5.8 to 6.2^oC/km in the western subtropical Andes³⁸ and 6.5^oC/km in the coastal mountains⁵⁹. In the Himalayan basins, the mean annual ELR is 6.0^oC/km⁶⁰ and values of 5^oC/km were recorded in New Zealand⁶¹.

Although only a few months of data are available, existing literature provides some insight into the seasonal variations of the ELR: a bimodal pattern was observed in the monthly variations of the ELR, with steeper lapse rates occurring in spring and autumn, and shallower lapse rates in summer and winter. Similar patterns have been previously reported in the Iberian Peninsula⁶², the Ecuadorian Andes⁶³, Bhutan⁶⁴, the central Himalayas⁶⁵, and Morocco⁶⁶.

Results indicating that the altitude of the 0 degrees isotherm varies significantly with both latitude and longitude are consistent with findings from previous studies²¹. The highest altitude of reached 5346.8 m. This figure aligns closely with observations from weather balloons in Payerne, Switzerland, which recorded a height of 5298 m⁴⁴, and with measurements obtained using radiosondes in South America⁴⁵.

Regarding the accuracy of the results, the standard deviation when determining the temperature is approximately 0.8^oC, primarily due to the methodology used to derive it. The resolution in altitude is given by the resolution of the ADSB messages, that is 7.62 m. For the latitude and longitude the resolution is of deg. (Appendix A).

The lack of detailed avionics information for the aircraft made it difficult to verify the accuracy of the data collected by the onboard sensors used in this study. The estimated temperature error was determined to be K²⁹. Other work⁶⁷applied smoothing methods and found temperature variance between altitudes of 3,000 and 1,000 m of 1–2 K, while below 1,000 m, to increases to 2–4 K. The mean error for the altitude was calculated⁶⁸to be 173.43 m, while for the pressure, it was determined to be ±0.1 hPa. Taking into account error propagation⁶⁹the uncertainty in the Environmental Lapse Rate was found to be 1.92 °C/km. Please note that the obtained value of uncertainty for the pressure aligns with the specifications set forth by ICAO’s Operational Uncertainty Requirements⁷⁰. The high error of the temperature can be explained by the fact that pressure-based altitude measurements rely on a standard pressure and are not adjusted for the local pressure at the aircraft’s flying altitude. The geometric altitude is more accurate (as it is based on GNSS systems), but it does not update as frequently.

Regarding the immediate implications for the findings, for meteorologists, determination of the lapse rate provides a reliable indicator of atmospheric stability. A real time estimation of ELR would impact the meteorological forecasts and alerts. The dry adiabatic lapse rate (DALR) is defined as the negative temperature gradient that occurs when dry air expands adiabatically while ascending, and has a value of 9.8 K/km⁵⁰. Atmospheric instability arises when an air parcel (DALR) cools more slowly than the surrounding atmosphere (ELR), which cools more quickly. This can lead to the formation of cumulonimbus clouds, resulting in heavy thunderstorms with frequent lightning. High wind speeds may occur, and tornadoes might even form⁵⁰.

Another fact connected to the atmospheric processes is that turbulence and mixing play a crucial role in air pollution dispersion modeling. An unstable atmosphere enhances turbulence and mixing, improving the dispersion of air pollutants, while a stable atmosphere inhibits turbulence, resulting in poor dispersion of pollutants⁷¹. Again, detailed maps of ELR would enhance modeling of pollution and its impact.

Increased spatial resolution is also gaining importance in climate change research, as evidenced by examples such as the Coordinated Regional Climate Downscaling Experiment⁷². More, due to the fact that the phase of precipitation is influenced by conditions at its formation site and ground conditions, relying solely on typical dry temperature interpolation for flood forecasting models can result in significantly inaccurate information if lapse rates are assumed to remain constant over time⁷³.

Another implication of the ELR is its use in the Water Balance Model (WBM)⁷⁴that simulates both vertical water exchange between the atmosphere and the land surface and horizontal water transport, including land surface runoff and river network flow. This was studied⁶⁰, where the economic consequences of climate-induced alterations in river flow within two drainage basins were investigated.

As mentioned, the height of the 0 degrees isotherm is useful for various applications, including evaluation of the optimal performance of Earth-space satellite communication links. The signal attenuation values may be overestimated by system designers if constant values as the ones recommended by the International Telecommunications Union (ITU) are used¹⁶, thus maps with the spatial variability would be immensely helpful.

Conclusions

This article investigates the altitude of the zero degrees isotherm and variations in the environmental lapse rate (ELR) using ADS-B and Mode S EHS messages collected over five months in 2021 with a receiver stationed in Bucharest. The aim is to improve the accuracy of environmental models through enhancements in lapse rate estimates.

In this study it was noted that the average altitude of the 0 degrees isotherm exhibits an upward trend during the summer months, with an overall mean of 2874.2 m (assuming an ELR value of 6.5^o/km). The highest altitude of reached 5346.8 m, near Alexandria (Romania), on 22.07.2021.

By employing a standard LMS algorithm and the International Standard Atmosphere pressure formula, the ELR values were computed. The average ELR over the 6-month period was determined to be 5.1331^oC/km, slightly lower than the standard value.

Subsequently, the updated ELR value was utilized to assess variations in the 0 degrees isotherm with respect to latitude and longitude. Latitude and longitude intervals were divided into four bins, and mean values for the 0 degrees isotherm were calculated within each interval (see Fig. 4).

Due to the complexity of the variation of the ELR, it is recognized that more detailed regional-scale research is necessary, especially through combining the results with other types of meteorological measurements: e.g. wind speed (that can be determined using avionic messages), cloud cover measurements^85,86(ground-based or satellite), humidity⁶⁶ etc. Longer monitoring periods would also be beneficial.

Regarding the humidity, as previously mentioned, Mode-S technology includes the Mode-S Meteorological Routine Air Report (MRAR), which allows for direct measurement of wind speed, direction, and temperature. Although the register is designed to transmit data on turbulence and humidity, these parameters are typically not relayed because most aircraft lack the required sensors. Moreover, Mode-S MRAR is not mandatory, and fewer than 5% of aircraft fill this register, usually only with wind speed and direction data⁸⁷. Future advancements in aircraft capabilities, along with updated regulations, could enhance the type and quality of meteorological data derived from aircraft.

Quality indicators for aircraft position, velocity, and related data are usually derived from the onboard GNSS system. Inertial sensors alone do not yet provide the necessary accuracy or integrity data, though future advancements are expected to resolve this issue. However, some modern aircraft installations now use an integrated GNSS and inertial navigate-on system, which delivers position, velocity, and quality indicators for ADS-B transmissions⁸⁸. The uncertainty of Mode-S EHS observations increases at lower altitudes due to the low resolution of airspeed (2 knots) and Mach number, which becomes more pronounced at lower speeds, and consequently, at lower altitudes⁸⁹.

Future regulatory updates, combined with advancements in aircraft capabilities, will enhance our understanding of how these observed changes impact the environment and economic activities.

Appendix A. ADS-B message decoding

Modern technologies facilitate the transmission of meteorological data from aircraft through two primary methods: the Aircraft Communications Addressing and Reporting System and Selective Interrogation via Mode S technology.

In Mode S interrogation, aircraft respond to an uplink frequency of 1030 MHz, while their transponder replies are transmitted on the 1090 MHz downlink frequency.

Within Mode S, the signal commences with a preamble comprising four pulses, each lasting 0.5 microseconds, distributed over an 8-microsecond period. Following the preamble, a data block is appended, consisting of either 56 bits (56 microseconds) or 112 bits (112 microseconds) in duration.

Aircraft states and intention data can be accessed through 25 distinct Downlink formats (DF), i.e. the first 5 bits of the message. Notable examples include DF17 and DF18, which utilize Extended squitter (ADS-B), DF20 featuring Comm-B with altitude reply, and DF21 also incorporating Comm-B with identity reply⁷⁵.

DF20 and DF21 enable the transmission of Mode S Enhanced Surveillance (EHS) data, including Meteorological Routine Air Report registers (MRAR). In Mode S Enhanced Surveillance (EHS) messages associated with DF20 or DF21, the ICAO address is contained within the final 24 bits, and subsequent decoding follows protocols outlined in other work^32,75–77. The only distinction between DF20 and DF21 lies in bits 20 to 32, representing either the altitude code or identity, respectively.

BDS registers are denoted by two-digit hexadecimal numbers, with commonly encountered ones: BDS 2,0: Aircraft identification (call sign); BDS 2,1: Aircraft and airline registration markings; BDS 3,0: ACAS active resolution advisory; BDS 4,0: Selected vertical intention (EHS); BDS 4,4: Meteorological routine air report (MRAR); BDS 4,5: Meteorological hazard report; BDS 5,0: Track and turn report (EHS); BDS 5,3: Air-referenced state vector; BDS 6,0: Heading and speed report (EHS). Of interest in this work are BDS 4,0, 5,0 and 6,0.

In reference to BDS 4,4 MRAR, it encompasses direct meteorological data without requiring any derivations^24,78–80. Nonetheless, as MRAR is not mandatory in Mode S registers, only a limited number of aircraft transmit MRAR messages^24,78.

Furthermore, it’s worth noting that aircraft manufactured by Airbus and Boeing either do not transmit MRAR information or do so infrequently. Conversely, other commercial passenger aircraft are more inclined to transmit MRAR data^24,78–80.

In Comm-B messages BDS codes may not always be included. Each message type is identified by an 8-bit Comm-B Data Selector code, which is transmitted exclusively in the uplink message and is not embedded in the downlink message.

In this context, the first four BDS codes (1,0, 1,7, 2,0, 3,0) correspond to the Elementary Surveillance Service (ELS), followed by the next three (4,0, 5,0, 6,0) which are linked to Enhanced Surveillance Services (EHS), while the last two codes (4,4, 4,5) convey meteorological information.

It’s important to note that despite ADS-B messages being part of Mode S extended squitter, they are still assigned BDS codes. The list of BDS codes for these ADS-B messages includes: BDS 0,5 (Extended squitter airborne position), BDS 0,6 (Extended squitter surface position), BDS 0,7 (Extended squitter status), BDS 0,8 (Extended squitter identification and category), and BDS 0,9 (Extended squitter airborne velocity information).

BDS registers 5,0 and 6,0 are transmitted by a specific aircraft within a ten-second timeframe. The update frequency for BDS registers adheres to a minimum interval outlined⁸¹ .

The Mode S transponder is capable of storing and retrieving information from 255 distinct 56-bit wide Comm-B Data Selector (BDS) registers⁸². These registers correspond to the hexabits 9 to 22 in the original message. In the case of BDS 5,0, the true airspeed is represented by bits 47–56 and falls within the interval [0, 2046] kts with a resolution of 2 kts. The message also includes the ground speed (bits 25–34), which similarly lies within the same interval and resolution.

The Mach number M is conveyed in BDS 6,0 messages, occupying bits 25–34, resulting in a range of [0, 4.092] M with a resolution of 0.004 M.

In BDS 4,0 messages, the barometric pressure is encoded, encompassing bits 28–39. This range spans [0, 410] mb with a resolution of 0.1 mb. It’s essential to recognize that this value represents the actual pressure minus 800 mb⁸³.

Since the BDS codes are absent, identifying the type of received message requires certain criteria to be met. For BDS 5,0 messages, bits 40–47 are designated and should remain zero. If any of these bits are non-zero, it’s necessary to rule out the possibility of a particular BDS code.

Different fields within the messages display distinct physical ranges. For example, in BDS 6,0 messages, the Mach number should not exceed 1. In a BDS 5,0 message, examine the difference between ground speed and true airspeed. This disparity should not be significant. Typically, an empirical threshold of around 200 knots is used to accommodate potential wind speed variations.

Additional information is superimposed on the parity, encompassing the aircraft ICAO address, AA field information, or the interrogator code. Interrogator parity is exclusively utilized for DF11. DF20 and DF21 incorporate either address parity or data parity, while all other DFs employ address parity.

Cyclic polynomial techniques are employed to detect errors in the transmitted message, and in some cases, they can even correct transmission errors³². The parity is generated through a modulo-2 division of the message by the generator polynomial ³². The resulting remainder (parity) is then appended to the end of the signal along with the associated information.

In the case of address parity, the parity is combined with the ICAO address of the aircraft. Regarding data parity, the parity is added to a modified AA field. This modification involves performing a modulo-2 addition of the most significant 8 bits of the discrete address with the first two hexadecimal characters of the BDS register. The specifications for this modification are outlined by the Reply Request and Reply Request Subfield field in the uplink transmission from the interrogator.

ADS-B messages contain various data, including the aircraft’s position (latitude, longitude), pressure altitude, and geometric altitude. The aircraft airborne position message is utilized to broadcast the position and altitude of the aircraft, categorized by Type Codes ranging from 9 to 18 and 20 to 22. When the Type Code is from 9 to 18, the encoded altitude represents the barometric altitude of the aircraft. Conversely, Type Codes from 20 to 22 encode the GNSS altitude of the aircraft. Position information is encoded in a Compact Position Reporting (CPR) format, optimizing resolution with fewer bits.

The structure of a message transmitted through extended squitter DF17 includes the DF field containing the squitter’s name, represented by the binary number 17 (10001). The subsequent 3 bits, known as “Capacity” or “CA,” denote the subtype number of the ADS-B message used from a total of 8 possible types. Following this are 24 bits allocated for transmitting the ICAO address. Specific information regarding ADS-B signals is contained within a group of 56 bits, depending on the message type encoded in the CA section. The final 24 bits serve for error detection and are referred to as “parity bits” (Parity Information - PI). Encoded latitude is found in bits 55–71, encoded longitude in bits 72–88, and the encoded altitude of the aircraft is transmitted in bits 41–52. Additionally, bit 54 represents the CPR Format⁷⁵.

To decipher the altitude, the value of the 8th bit, counted from the most significant to the least significant bit, is examined, and a word is constructed with the remaining 11 bits, excluding this bit. If this bit has a value of 1, the number encoded by the remaining 11 bits is multiplied by 25, and 1000 (the value of barometric altitude) is subtracted from the result. Conversely, if the 8th bit is 0, the multiplier becomes 100. The outcome is presented in feet⁸⁴. The resolution for the altitude is 7.62 m.

In each position message, bit 54 determines whether it is an odd or even frame. A value of 0 indicates an even message, while 1 indicates an odd message. To obtain the aircraft’s latitude and longitude, it was necessary to decode two squitters occurring within a time difference of less than 10 s. The decoding process for latitude and longitude adheres to the guidelines provided in^75,84 and require determination first of the number of latitude zones and number of longitudes zones, latitude zone index and longitude index. The resolution of the latitude and longitude is deg.

Author contributions

A.M. B. has done the conception of the work; the acquisition, analysis, and interpretation of data. A.M.B. wrote and reviewed the manuscript.

Data availability

Data sets generated during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.