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This paper defines a parametric threat model for tropospheric duct anomalies based on ten years of tropospheric data. It is shown that tropospheric ducts can produce differential ranging errors on the order of 10 cm. Furthermore, the probability of occurrence of tropospheric duct anomalies (up to 90% in certain locations) is much higher than the integrity and continuity risk requirements used in aviation applications. Because tropospheric ducts are not particularly rare and can cause non-negligible ranging errors, they are potential threats to navigation integrity for high accuracy and integrity applications. The impact of tropospheric duct anomalies on the integrity risk and accuracy are quantified and evaluated on an example carrier phase differential navigation system. In doing so, dynamic error modeling and probabilistic bounding approaches are used to evaluate the integrity risk resulting from the developed threat model. The troposphere is the lower part of the earth’s atmosphere, extending from earth surface to about 16 km altitude. It is made of electrically neutral gases that are not uniform in composition, including water vapor and dry gases. Refraction in the troposphere delays the transmission of satellite signals. The tropospheric delay consists of a largely predictable dry component, and of a wet component that varies with latitude, altitude, season, and weather condition but represents a much smaller fraction of the error. Therefore, the majority of the tropospheric delay can be removed by troposphere modeling (e.g., using a Modified Hopfield Model). Several models exist that describe the tropospheric delay under nominal conditions. Although some of these models exploit regularly updated weather parameters, they do not account for anomalous conditions. Recent work acknowledged that a tropospheric threat model must be defined and means for bounding the potential errors be derived [3]. In that work, a preliminary analysis with the aim of evaluating the impact of anomalous troposphere on GBAS was presented. Two types of tropospheric anomalies impact high accuracy navigation systems: severe weather fronts and tropospheric ducts. A weather front is characterized by an abrupt change in refractivity (measured by variations in temperature, pressure, and relative humidity) over short horizontal distances. Published research reports experimental observations of tropospheric delays of up to 40 cm over a 5-km distance [1]. Further published work, with application to ground based augmentation systems (GBAS), assumed a ‘weather-wall’ model to investigate the impact of high stationary fronts on differential ranging measurements (between a user and a local reference station) [2]. This paper focuses on tropospheric duct anomalies. Under nominal conditions, pressure drops exponentially with height, and temperature decreases with altitude at an approximate rate of 1K/100m (over the first few kilometers above sea level). As a result, the computed refractivity gradient with respect to altitude is approximately -40 /km. However, this standard behavior does not apply under anomalous atmospheric conditions, and tropospheric ducts can be generated. Ducts tend to form when either temperature is increasing, or water vapor concentration is decreasing with height (due to climatologic mechanisms such as temperature inversion, evaporation ducts, air subsidence and air advection). Published literature shows that ducts appear at varying altitudes with likelihood of occurrence depending on location. Severe refractivity gradients (up to two orders of magnitude larger than nominal) were observed in localized layers of the troposphere at various altitudes and with different thicknesses. In a previous work [4], as a preliminary study on tropospheric ducts, duct thickness, altitude and refractivity gradient statistics were quantified and their probability of occurrence was established for a worldwide grid of 1 degree resolution. However, it was shown that a threat model using the worst case value of each of these parameters was overly conservative. In this work, ten years of data from the European Center for Medium-range Weather Forecasts (ECMWF) was analyzed. Since tight integrity and accuracy requirements are usually required during final approach and landing phases and the differential measurements are influenced by portions of the tropospheric duct located between the aircraft altitude and the reference receiver antenna height, the ECMWF data is screened for ducts occurring at altitudes lower than 200 m and 500 m (below the aircraft decision height). Each time there was a duct incident reported with a height of less than 200m (or 500m), the tropospheric zenith error due to duct was computed by subtracting the integrated delay introduced due to the duct from the nominal tropospheric model. This zenith duct error is then quantified with respect to the probability of occurrence for a worldwide grid of 1 degree resolution. Using this data, a distribution of the zenith duct error is established that can be used to provide a stochastic bound. This stochastic bound is then used to quantify the impact of ducts on differential ranging measurements for a benchmark aviation application using various methods such as inflating the measurement error standard deviation, deriving a robust dynamic model of the duct error profile (to be incorporated in the position estimation process), and bounding the positioning error in protection level and integrity risk computation. References: [1] Huang, Jidong, van Graas, Frank, Cohenour, Curtis, "Characterization of Tropospheric Spatial Decorrelation Errors Over a 5-km Baseline", NAVIGATION, Vol. 55, No. 1, Spring 2008, pp. 39-53. [2] van Graas, F., Zhu, Z., "Tropospheric Delay Threats for the Ground Based Augmentation System," Proceedings of the 2011 International Technical Meeting of The Institute of Navigation, San Diego, CA, January 2011, pp. 959-964. [3] Guilbert, A., "Non-Nominal Troposphere Reassessment for Meeting CAT II/III with MC/MF GBAS," Proceedings of the 28th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+ 2015), Tampa, Florida, September 2015, pp. 1526-1537. [4] Khanafseh, S., Joerger, M., Pervan, B., Von Engeln, A., "Accounting for Tropospheric Anomalies in High Integrity and High Accuracy Positioning Applications," Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, September 2011, pp. 513-522. |
