## Abstract

Recently work has been conducted in using routine air traffic management (ATM) data from aircraft to derive meteorological observations (de Haan; de Haan and Stoffelen). The paper at hand introduces and provides an initial analysis for a method of finding layer temperatures from aircraft broadcast messages. The method is analyzed using error analysis and is shown capable of producing mean layer temperatures with below ±1-K error with a layer thickness of 2000 m. Observed aircraft data have been compared to the expected errors from the analysis and have shown to be consistent to within 0.01 K. An initial comparison using four Aircraft Meteorological Data Relay (AMDAR) flights is also provided. The new layer temperature, existing Mode-S enhanced surveillance (EHS)-derived temperature, and an average Mode-S EHS-derived temperature are all compared to the AMDAR temperatures. The averaged Mode-S EHS-derived layer temperature is shown to have the lowest spread (mean standard deviation K), followed by the layer temperature introduced by this paper (mean standard deviation K), and then the unaveraged Mode-S EHS-derived temperature (mean standard deviation K). The layer temperature method has the advantage that no requested data are required from the aircraft, as all of the required parameters are part of the routine broadcast messages, making the method ideal in areas with a limited air traffic management infrastructure where the existing methods would not work.

## 1. Introduction

At the Met Office, currently there are two main sources of aircraft observations: aircraft reports (AIREPS) [mostly manually and some automated reports made via air traffic management (ATM)] and Aircraft Meteorological Data Relay (AMDAR) (fully automated reporting via ground and satellite communication networks). The AMDAR reports make up the majority of the data and are considered to be of better quality. AMDAR uses an aircraft’s normal avionics and sensors with additional software to enable the observations to be sent to the ground using the aircraft’s onboard communications systems. Only a small fraction of aircraft on a subset of airlines carry the software required to create AMDAR reports.

Mode-Selective (Mode-S) is an aircraft messaging standard developed for use by the ATM community that requires aircraft to carry specific transponders that respond to ATM requests. In the enhanced surveillance (Mode-S EHS) regime, a large number of aircraft parameters are requested by ATM secondary surveillance radar (SSR) and transmitted by aircraft. In the United Kingdom, most of the mainland area is covered by SSR requesting the Mode-S EHS parameters.

Automatic Dependent Surveillance Broadcast (ADS-B) is an automated system where aircraft parameters are regularly broadcast via a transponder on the aircraft; the equipment is currently mandated in some airspace (e.g., Australian airspace above 30 000 ft), and there are plans for mandates in other areas (e.g., U.S. airspace and European airspace by 2020 and 2017, respectively). A significant proportion of commercial aircraft already carry the equipment. ADS-B and Mode-S are designed to work together on the same frequency band (1090 MHz) to allow SSR to gather a full picture of the aircraft state and intention. Automated Dependent Surveillance Contract (ADS-C) is an agreed datalink between an aircraft and ATM using a communication link different from that of Mode-S and ADS-B but capable of providing much of the same information.

Recently there has been increased interest in gathering observations from aircraft using unconventional methods (de Haan 2011; de Haan and Stoffelen 2012; Strajnar 2012; de Haan et al. 2013) deriving observations from ATM aircraft reports and getting observations reported directly through ATM organizations. The previous work has shown that the Mode-S EHS-derived wind observations are of similar quality to those reported by AMDAR aircraft with the Mode-S EHS-derived temperature data being of poorer quality (de Haan 2011). It has also been shown that this data type has a positive impact on numerical weather prediction models (de Haan and Stoffelen 2012). Mode-S does provide for meteorological observations to be requested and transmitted directly from aircraft, although very few ATM organizations request this and few aircraft are capable of returning the parameters (Strajnar 2012). Observations transmitted via ADS-C have also been investigated by de Haan et al. (2013). Both of these direct reporting methods provide data of a similar quality to AMDAR, which is to be expected, as the measurements all use the same source on board the aircraft. Further methods of deriving meteorological observations from aircraft messages have been developed by de Leege et al. (2013); for temperature, observations of pressure and altitude are fitted to a polynomial that allows a temperature to be extracted.

In an attempt to improve the quality and to extend the availability of the temperature data, this paper presents a different approach to extracting information from ATM data. The new approach is similar but distinct from that introduced by de Leege et al. (2013). An error analysis is performed that is then verified by comparison to the variability of real observations. The approach introduced here, unlike that used by de Haan (2011), does not require any ATM infrastructure, which allows for a significant increase in potential coverage, although it is limited to around airports.

## 2. Derived temperature methods

ADS-B routinely broadcasts data containing aircraft type, an aircraft unique identifier, pressure altitude , the difference between the Global Navigation Satellite System (GNSS) altitude and the pressure altitude (*a*), ground speed , and the position of the aircraft. In addition to this information, ATM can request a large number of other values from the aircraft using the Mode-S system. The most commonly requested information includes maneuvering information, true airspeed , Mach number (*M*), and magnetic heading.

Aircraft have a range of instruments for measuring their environment and further parameters are derived. Most aircraft measure a true heading with a GNSS providing a true altitude and location. Instruments measure the pressure, temperature, and indicated airspeed, which are used on board to derive pressure altitude, Mach number, and true airspeed.

As the Mach number is derived on board, an aircraft using the true airspeed and temperature and the Mach number and true airspeed are downlinked from the aircraft, the equation used by aircraft can be rearranged such that

where *T* is the temperature in kelvins, is the true airspeed in knots (kt; 1 kt = 0.51 m s^{−1}), and 38.975 kt K^{−1/2} is a conversion factor incorporating the ratio of specific heats and converting from knots to meters per second. This temperature (i.e., Mode-S EHS-derived temperature) is a near-instantaneous temperature at the location of the aircraft. The error in the temperature (*T*) is estimated to be K (de Haan 2011).

The hypsometric equation relates the layer temperature in kelvins to the pressure change of a layer of air in the atmosphere with a thickness in meters by

where *g* is the acceleration due to gravity (m s^{−2}), and are the pressure at the bottom and top of the air layer (hPa), respectively; and *R* is the specific air gas constant (McIntosh and Thom 1983). It is important to note that this will change with altitude and humidity. These effects have been ignored below, and the dry air value for *R* has been J (kg K)^{−1}. Equation (2) can be rearranged in the form

such that if an aircraft changes GNSS altitude and the pressure change is also known, then the mean layer temperature can be found. Where this is found using the parameters from ADS-B messages, it will be referred to as the ADS-B-derived layer temperature (ADLayer temperature).

The pressure (*p*, hPa) can be related to the pressure altitude in meters by referencing the international standard atmosphere with equation (ICAO 1993)

where is the assumed surface pressure (1013.25 hPa), and is the assumed surface temperature (288.15 K). Aircraft report their GNSS altitude as a difference (*a*) from their pressure altitude (ICAO 2012); therefore, the difference in true altitude between two aircraft reports can be found by

The two pairs of two variables in Eq. (6), the pressure altitude and the correction of the pressure altitude, are reported by aircraft as part of the ADS-B messages. Therefore, no ATM-requested data are required for the calculation.

### Error analysis of the ADLayer temperature

The following is an error analysis approach to analyzing Eq. (3). The analysis is split into separate numerator and denominator sections, as applying the generic error propagation equation to Eq. (6) yields a large equation that is difficult to interpret and manipulate. The two errors are then combined to create a single error equation that can be interrogated.

Throughout this assessment it has been assumed that the errors due to reporting precision dominate over the instrument errors. Aircraft can report their pressure altitude with two different accuracies (100 or 25 ft) but of 2.5 million observations, only 33 were made using the lower accuracy; therefore, a reporting resolution of 25 ft has been assumed (a maximum error of 12.5 ft; the root-mean-square error will be less than this) (ICAO 2012). The reporting resolution of the difference between the GNSS altitude and pressure altitude is also 25 ft; therefore, ft m. The discrepancy of the GNSS altitude with the true altitude is of the order 10 m, but it is relatively consistent over time periods less than 2 h; therefore, as the difference between two GNSS altitudes is the parameter of interest, the accuracy is thought to be below the reporting resolution (ICAO 2013; Fisher 2014). The reporting resolution is set and limited by international standards (ICAO 2012).

As and are defined as constants, the error in pressure depends only on the error in pressure altitude . Therefore, has been estimated to be

From Eq. (3) the denominator is

From the general error propagation equation (Taylor 1997), the error associated with the denominator is

Substituting for the differentials yields

From Eq. (3) the numerator is

with an associated error of

As ,

Thus, the error in the GNSS altitude must be known. The GNSS altitude *z* is found by applying an altitude correction (*a*) to the pressure altitude :

For additions such as this, a simplified error propagation equation can be applied (Taylor 1997),

Therefore,

The numerator and denominator errors can be combined using another standard error analysis equation (Taylor 1997)—if

then the associated error in *k* from *x* and *y* is

therefore,

## 3. Analysis

In this section the error equation derived above will be tested against real data. A further comparison of the ADLayer temperatures, Mode-S EHS-derived temperatures, and an averaged Mode-S EHS-derived temperatures to AMDAR temperatures will be made. To provide a benchmark, the World Meteorological Organization (WMO) Observing Systems Capability Analysis and Review Tool (OSCAR) requirements database provides the necessary uncertainties in observations before they are useful (“breakthrough”), when they show a marked improvement in usefulness (“threshold”), and the uncertainty past which further improvements will offer little improvement (“goal”). For troposphere temperatures for use in “aeronautical meteorology,” these are 5 K (threshold), 3 K (breakthrough), and 2 K (goal). The errors in AMDAR and radiosonde temperatures have been estimated to be and K, respectively (Painting 2003; Drüe et al. 2008; Corner et al. 1999).

### a. Initial analysis of the error equation

From Eq. (19) it is evident that depends on the input pressure and layer thickness. To provide some indicative error values, realistic pressure and GNSS altitudes are required to be substituted into Eq. (19). The values used are found from the international standard atmosphere (ISA) (ICAO 1993). The ISA differs from a real atmosphere in that it is stable in time and space with no dust, moisture, or water vapor. It provides ideal values with which to test the error equation; some confidence in these results can be found by the close comparison to real data described below.

Figure 1 shows the errors from Eq. (19) for an aircraft flying through the ISA, where m and , the altitude difference (layer thickness), is changing and shown on the *x* axis. From this it can be seen that the absolute error drops below 1 K (chosen as being well below the OSCAR aeronautical meteorology goal uncertainty) at a layer thickness of m. Assuming no overall bias and random errors, an average of 25 individual Mode-S EHS temperatures derived from the Mach number would be required to have a similar uncertainty. Whether this can be achieved in the same altitude depth as the ADLayer temperature depends on both the flight characteristics and the interrogation regime of the ATM SSR, whereas the ADLayer temperature observations do not require any interrogation from SSR (they rely only on the ADS-B transmissions).

The error also depends on the altitude of the aircraft, which is investigated using values from the ISA. Figure 2 again shows results using the ISA values substituted into Eq. (19). Here with changing and , and the midpoint is changing and shown on the *x* axis (the line continuing below 1000 m is shown for completeness). As can be seen over the general flying altitudes of aircraft (up to m), the error decreases with altitude but does not vary significantly, changing by less than 0.15 K over the whole range shown.

To test the validity of the assumed constant static gas constant, different values can be used in Eq. (19). For water vapor, J (kg K)^{−1}; 2000 m, with a midpoint altitude of 3500 m; 0.6 K; and for dry air [ J (kg K)^{−1} as used throughout] 1.0 K. In a real atmosphere, it is likely that the errors would be lower than those predicted here due to water vapor in the air. Changing the assumption of constant gravity to a realistic value based on altitude changes the error calculations by less than five significant figures over normal aircraft altitudes.

### b. Comparison of ADLayer temperature observations to error analysis

Observations using the ADLayer temperature method have been made. Data have been collected over the southwest of the United Kingdom on August 2013. All of the mean ADLayer temperatures from a single aircraft ascent on 11 August 2013 are shown in Fig. 3. The stratification is caused by the reporting resolution. The fine detail is caused by the pressure reports changing. The large jumps are where the GNSS difference to pressure altitude has changed from one value to the next, causing the value to jump; this is a direct result of the reporting resolution.

The reporting frequency of ADS-B messages is so high that within a small time window (1 s), multiple sets of pressure altitude and GNSS correction values can be collected for a single aircraft. It is therefore possible to create a pair of ADLayer temperatures from the same aircraft for a nearly identical atmosphere. Over a period of 3 h on 11 August 2013, 1367 pairs of ADLayer temperatures can be identified. The difference in ADLayer temperatures between the pair of observations is then calculated. The largest difference between these values should be close to that predicted by the error in Eq. (19), assuming that the error is dominated by the reporting resolution. The layer thickness used for calculating the ADLayer temperatures ranged from 1500 to 2500 m depending on aircraft and time. Using the smallest layer thickness in Eq. (19) with the ISA provides an expected maximum discrepancy between the pairs of 1.46 K. The maximum discrepancy between a pair of observations was found to be 1.47 K. The 0.01-K difference can be explained by small changes in the atmospheric conditions around the aircraft and the lack of the inclusion of instrument error above; the observations and equation are consistent. The inset of Fig. 1 shows the differences between the pairs of observations as symbols plotted along with the results from the ISA using Eq. (19). The curve of the maximum discrepancy between the pairs of observations closely follows that produced by the equation. Some difference is expected between the maximum data points and the lines, as the average GNSS altitude for the aircraft varies. For the single aircraft data shown in Fig. 3, the calculated maximum error from Eq. (19) given the aircraft altitude and layer thickness for each ADLayer temperature is K, and the maximum calculated difference for matched pairs for this aircraft is K; these two values are again consistent. This provides some confidence in using the ISA and the assumptions used to find Eq. (19).

### c. Comparison of ADLayer and Mode-S EHS-derived temperatures to AMDAR temperatures

In addition to the error calculations given above, a comparison of the two temperature methods to AMDAR data can be made. Three types of temperatures will be compared to the AMDAR temperature data for four AMDAR ascents between 0500 and 1830 UTC 20 August 2013: the ADLayer temperature derived in this paper , Mode-S EHS-derived temperatures found using Eq. (1) (*T*), and an average layer temperature created using the Mode-S EHS-derived temperatures . A mean Mode-S EHS-derived layer temperature is calculated for each ADLayer temperature by averaging all of the Mode-S EHS-derived temperatures within the layer. For a fair comparison, where averaged layer temperatures are used (ADLayer and Mode-S EHS-derived layer temperature), an averaged AMDAR layer temperature is used; this is described further below.

The four ascents were observed from Bristol airport flying south over Exeter, United Kingdom, using a Mode-S/ADS-B receiver at the Met Office headquarters in Exeter. Ascents have been chosen because of the increased frequency available of AMDAR observations. For the ascent between the surface and 10 000 m, 28 AMDAR observations were recorded in the region in which Mode-S data are received. A local polynomial regression fitting method (Cleveland et al. 1992) is used to fit the temperature–pressure altitude relationship for each AMDAR ascent. The comparison to the Mode-S EHS-derived temperatures uses a value extracted from the fitted AMDAR polynomial at the observation altitude. For the layer temperatures, 100 temperatures are extracted from the fit and averaged. The extracted temperatures are evenly spaced in altitude between the lower and upper altitudes of the layer with which they are to be compared. A negative difference indicates an AMDAR temperature below the derived temperature. It is known that AMDAR temperatures have a warm bias of 0.5 K for the aircraft types used here (Ballish and Kumar 2008; Cardinali et al. 2003); therefore, small negative differences would be expected for an observation that is better than AMDAR. On average, no difference would be expected for the Mode-S EHS-derived temperatures, as the same sensors are used as for AMDAR reports. The number of temperature observations, the mean difference, and the standard deviation (SD) of the differences for each of the four ascents are provided in Table 1.

To provide an idea of the distribution and the altitude dependence Fig. 4 shows the AMDAR temperatures against pressure altitude as the line with box plots with a bin width of 250 m of the derived temperatures, where Fig. 4a shows the ADLayer temperatures and Fig. 4b shows the Mode-S EHS-derived temperatures; the circles show the outliers in the data used for the box plots. These plots are produced from AMDAR flight 2, and the numbers represent the number of derived temperatures used for each box-and-whisker level. The narrower distribution for the ADLayer temperatures can be seen throughout the altitude range shown. On average the standard deviation is 0.94 K for the ADLayer temperatures compared to 1.85 K for the Mode-S EHS-derived temperatures. Not plotted, the Mode-S EHS layer temperature has an even smaller SD of 0.72 K. No consistent correlation to altitude has been observed. The change in temperature gradient between 3000 and 4500 m in the AMDAR data is not observed for the ADLayer temperatures, but it is observed for the point-derived temperatures; it is unclear from these data as to whether this is a real feature.

More work is required to further understand the data, although from this small sample some initial comments can be made based on the statistics shown in Table 1. An average of the four flights shows that the mean difference to the AMDAR data is smaller for the Mode-S EHS-derived temperatures (0.04-K average mean difference compared to −1.43 K for the ADLayer temperatures). The mean Mode-S EHS-derived temperature difference is less consistent between the four flights than that for the ADLayer temperature difference mean with a variation of 0.2 K compared to 3.7 K for the Mode-S EHS-derived temperatures. These figures are skewed by flight 4, but even when this flight is disregarded, similar conclusions can be made: Mode-S EHS values are closer to the AMDAR temperatures, but the ADLayer temperature statistics are more consistent. For the mean difference, the averaged Mode-S EHS layer temperatures perform similarly to the Mode-S EHS-derived temperatures; the results are again skewed by flight 4. The origin of the consistent -K mean bias in the ADLayer temperature is not well understood. It is potentially caused by avionics standards, where corrections, rounding, and truncations are performed.

As expected the SD for the ADLayer temperatures is smaller than that of the Mode-S EHS-derived temperatures, implying a more consistent dataset (an average SD of 1.0 K for ADLayer temperatures compared to 1.95 K for the Mode-S EHS-derived temperatures). The average Mode-S EHS layer temperature perform the best with an average SD of 0.76 K. The apparently worse SD for the Mode-S EHS-derived temperatures may be partially due to the variability in the atmosphere, as well as the limited resolution of the reported true airspeed and Mach number. The improved SD for the mean Mode-S temperature is due to a reduction in noise from the averaging.

Flights 1–3 are all A319-111 aircraft, whereas flight 4 is an A320-214, which could explain the notably different results in Mode-S EHS-derived temperature statistics for this flight shown in Table 1. It is known that temperature biases depend on airframe (Ballish and Kumar 2008), and it is difficult to routinely find the airframe type for ADS-B data (due to the large number of aircraft and no single complete database); therefore, having a temperature source (ADLayer temperature) that is more consistent between airframes may be of some advantage in operational quality control. This analysis is limited in scope and further work is required for comparing the data to more aircraft (and aircraft types) over different prevailing weather conditions and including descent data. The layer thickness over which the ADLayer temperatures are calculated again varies between 1500 and 2500 m. The SD is therefore within the expected range found from Eq. (19).

In the region flown through by three of the aircraft, there was enough requested Mode-S EHS data to produce an averaged Mode-S EHS-derived temperature per layer with a better SD and mean bias than the other methods, which can be seen in Table 1. Flight 4 is again very different from the others, and it is possible that this is due to a poorly responding instrument. The observations are all between 0700 and 1900 UTC, and flight 4 was the second to take off. No fronts moved through the area during the day. It is therefore unlikely that the increased uncertainly is due to atmospheric changes.

## 4. Conclusions

This paper reported on an approach for finding a layer temperature (ADLayer temperature) of air through which an aircraft has flown using broadcast aircraft parameters that were not intended for this purpose. An error analysis approach was applied to the ADLayer temperature method, indicating that the error characteristics are an improvement on the existing Mode-S EHS-derived temperature method (of the order 1 K for a layer thickness of 2000 m compared to 3–5 K). ADLayer temperatures have been calculated from real data where the discrepancy between the stratified derived layer temperatures agrees with the calculated expected error to within 0.01 K. While the error analysis has been unable to explain all of the factors, the results compare favorably to real observations; the other results can therefore be used with some confidence.

An initial comparison to AMDAR data has been made. This comparison shows a larger bias for the ADLayer temperature (−1.4 K) than the Mode-S EHS-derived temperature method ( 0.04) but a smaller SD. Using an averaged Mode-S EHS-derived temperature provided the best agreement with AMDAR data (Table 1 provides a summary of the statistics for four AMDAR/ADS-B/Mode-S EHS flights). The ADLayer temperature method reported above has a significant advantage over the Mode-S EHS-derived temperature method in that the messages from aircraft are routinely broadcast; no ATM infrastructure is required, only a means of receiving the messages. The Mode-S EHS-derived temperature measures an instantaneous point temperature; therefore, more variability may be expected in observations when compared to the ADLayer temperatures, which are averaged over time, and vertical and horizontal space.

Because of the large number of overlapping layer samples, it may be possible to deconvolute the ADLayer temperature observations and find point temperatures; this may be of more use for numerical weather prediction models, which are rarely set up to assimilate ADLayer temperatures. ADLayer temperatures may prove useful to forecasters in areas with little ATM infrastructure. Further work is required for looking at the consistency of the observation source between airframe types and for better understanding the origins of the biases found in this paper. There may also be some value in investigating ADLayer temperatures using pressure altitude and GNSS altitude from separate aircraft flying en route at different altitudes yet with a small horizontal separation. Using different aircraft to find a single ADLayer temperature would increase the number of observations available when not near airports and remove the temporal and horizontal averaging effects of using single aircraft ascents or descents, although it would rely on the pressure sensor calibration of the aircraft being consistent.

The results presented here indicate that the data source is worth further investigation to provide data where Mode-S EHS data are not available. The data may also be exploited as an additional quality control measure for the existing temperature derivation methods.

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