Thermodynamic correction of particle concentrations measured by underwing probes on fast-flying aircraft

Abstract. Particle concentration measurements with underwing probes on aircraft are impacted by air compression upstream of the instrument body as a function of flight velocity. In particular, for fast-flying aircraft the necessity arises to account for compression of the air sample volume. Hence, a correction procedure is needed to invert measured particle number concentrations to ambient conditions that is commonly applicable to different instruments to gain comparable results. In the compression region where the detection of particles occurs (i.e. under factual measurement conditions), pressure and temperature of the air sample are increased compared to ambient (undisturbed) conditions in certain distance away from the aircraft. Conventional procedures for scaling the measured number densities to ambient conditions presume that the air volume probed per time interval is determined by the aircraft speed (true air speed, TAS). However, particle imaging instruments equipped with pitot tubes measuring the probe air speed (PAS) of each underwing probe reveal PAS values systematically below those of the TAS. We conclude that the deviation between PAS and TAS is mainly caused by the compression of the probed air sample. From measurements during two missions in 2014 with the German Gulfstream G-550 (HALO – High Altitude LOng range) research aircraft we develop a procedure to correct the measured particle concentration to ambient conditions using a thermodynamic approach. With the provided equation, the corresponding concentration correction factor ξ is applicable to the high-frequency measurements of the underwing probes, each of which is equipped with its own air speed sensor (e.g. a pitot tube). ξ values of 1 to 0.85 are calculated for air speeds (i.e. TAS) between 60 and 250 m s⁻¹. For different instruments at individual wing position the calculated ξ values exhibit strong consistency, which allows for a parameterisation of ξ as a function of TAS for the current HALO underwing probe configuration. The ability of cloud particles to adopt changes of air speed between ambient and measurement conditions depends on the cloud particles' inertia as a function of particle size (diameter D_p). The suggested inertia correction factor μ (D_p) for liquid cloud drops ranges between 1 (for D_p < 70 µm) and 0.8 (for 100 µm < D_p < 225 µm) but it needs to be applied carefully with respect to the particles' phase and nature. The correction of measured concentration by both factors, ξ and μ (D_p), yields higher ambient particle concentration by about 10–25 % compared to conventional procedures – an improvement which can be considered as significant for many research applications. The calculated ξ values are specifically related to the considered HALO underwing probe arrangement and may differ for other aircraft. Moreover, suggested corrections may not cover all impacts originating from high flight velocities and from interferences between the instruments and e.g. the aircraft wings and/or fuselage. Consequently, it is important that PAS (as a function of TAS) is individually measured by each probe deployed underneath the wings of a fast-flying aircraft.