A Review and Practical Guide to In-Flight Calibration for Aircraft Turbulence Sensors

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CLEMENS DRU¨ E AND GU¨ NTHER HEINEMANN Department of Environmental Meteorology, University of Trier, Trier, Germany

(Manuscript received 2 May 2012, in ﬁnal form 5 June 2013)

ABSTRACT

A large number of quantities have to be measured and processed to determine the atmospheric-state variables, which are the actual measurands, from aircraft-based measurements. A great part of the de- pendencies between these quantities depends on the aerodynamic state of the aircraft. Aircraft-based meteorological measurements, hence, require in-flight calibration. Most operators of research aircraft perform some kind of calibration, but the schemes used and the degree they are documented greatly vary. The flight maneuvers and calculation methods required, however, are published in a number of partly overlapping and partly contradictory publications. Some methods are only presented as a minor issue in publications mainly focused on atmospheric processes and are therefore hard to find. For an aircraft user, it is hence challenging to either perform or verify a calibration because of missing comprehensive guidance. This lack was stated on occasion of the in-flight calibration of the German research aircraft Polar5 carried out for the field experiment Investigation of Katabatic Winds and Polynyas during Summer (IKAPOS). In the present paper, a comprehensive review of the existing literature on this field and a practical guide to the wind calibration of a research aircraft to be used for turbulent flux measurements are given.

1. Introduction the corrections needed due to flow distortion by the aircraft body require an in-flight calibration of each in- a. Motivation strumented aircraft (e.g., Lenschow 1976; Brown 1988; Aircraft-based in situ measurements are among the Tjernstrom€ and Friehe 1991; Bange and Roth 1999; most valuable tools for the investigation of physical Williams and Marcotte 2000). processes in the atmosphere. Although aircraft have Most aircraft available for atmospheric research are always been used as meteorological sensor platforms operated by instrumentation engineers and scientists (Moninger et al. 2003), and the equations to calculate who have great expertise in airborne measurements. wind vector and other quantities are well known (e.g., Hence, usually the operators ensure a proper calibration Tjernstrom€ and Friehe 1991; Lenschow 1986), obtaining (Lenschow et al. 2007). However, in some cases the re- good atmospheric measurements is still a complex and quired expertise is not present—for example, leased challenging task. Typically, 15 individual quantities have commercial aircraft or multipurpose aircraft that are to be measured to obtain the three-dimensional (3D) only occasionally instrumented—and a satisfying in- wind vector (e.g., Metzger et al. 2011). flight calibration may be left to the user. Planning and The design of the sensing probes is a science of its own performance of such a calibration, however, exceed the (for examples, see Spyers-Duran and Baumgardner expertise of many users. 1983; Crawford and Dobosy 1992; Haman et al. 2001; Lenschow (1986) gives a comprehensive recommen- Spiess et al. 2007; Wang and Geerts 2009), integrating dation for suitable calibration methods. But this book sensors requires engineering skills (e.g., AEEC 2001), was written before the public availability of the Navi- and is subject to strict regulations (FAA 1968, 1995). gation Satellite Timing and Ranging (NAVSTAR) sys- While the actual sensors can be calibrated in a laboratory, tem (Parkinson and Gilbert 1983)—often referred to as ‘‘the’’ global positioning system (GPS)—and fully digi- € € tal data acquisition. Hence, later advances (such as, e.g., Corresponding author address: Clemens Drue, Universitat Trier, € Umweltmeteorologie, FB VI, Behringstraße. 21, D-54286 Trier, Crawford et al. 1993; Tjernstrom and Samuelsson 1995; Germany. Matejka and Lewis 1997; Khelif et al. 1999; Kalogiros E-mail: [email protected] and Wang 2002) are not incorporated.

DOI: 10.1175/JTECH-D-12-00103.1

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All sensing elements delivering analog output as well as the analog-to-digital converters (ADCs) had been calibrated prior to the experiment. For sensors with calibrations expected to be stable, manufacturer-supplied calibration coefﬁcients are used, such as for the inertial navigation system (INS), GPS, and the altimeters. Default data output of the Polar5 data acquisition system contains temperature values only with a resolution of about 0.025 K. This turned out to be too coarse, for example, to investigate the sensor inertia (section 2f). Extracting analog-to-digital converter readings from a backup of the onboard database, however, allows calculation of calibrated sensor readings with almost ﬁve

FIG. 1. Polar5 fitted with the nose boom carrying the turbulence significant digits. sensors. (inset) Detail of the nose boom: the tip to the left is the five- As known from Polar5’s predecessor, Polar2, the data hole probe, the housed sensors are (top to bottom) Lyman-a hy- acquisition system tends to record occasional spikes. grometer, inlet for dewpoint mirror through a deicable Rosemount It appears that they are caused by uncorrected data com- housing, slow temperature sensor (TE) in deicable Rosemount munication errors, since spikes even occur in fully digitally housing, and fast temperature sensor (TRvF) in non-deicable Rosemount housing (see section 2f for details). recorded quantities such as INS position (Th. Garbrecht 2002, personal communication). Although it was com- The intention of the present paper is, hence, to give monly believed that these were caused by very high aircraft data users a practical guide to a state-of-the art frequency (VHF) radio, the spikes persisted after the in-flight calibration. The recommendations given are use of VHF was discontinued. To identify spikes, a developed for the German research aircraft Polar5 on simple method is used that removes all values that deviate occasion of the experiment Investigation of Katabatic more than a threshold value from high-pass-filtered Winds and Polynyas during Summer (IKAPOS; time series. To determine the threshold, the normal- Heinemann et al. 2011), but they can be easily trans- ized probability density distribution of each high-pass- ferred to any other aircraft of similar weight, ranging filtered measurement time series is compared to a from single-engine light aircraft (e.g., Crawford and Gaussian error function (Drue€ 2001). For IKAPOS, a Dobosy 1992) over twin-engine aircraft (e.g., Kalogiros value of 3.5 standard deviations was determined as and Wang 2002) to quad-engine utility aircraft (e.g., a suitable threshold. Khelif et al. 1999) and twin-engine business jet Upon delivery, the manufacturer of the nose boom, (Tjernstrom€ and Friehe 1991). MessWERK GmbH, performed an extensive verification of wind measurements (Cremer 2008). This report, b. IKAPOS however, gives the empirical relationships determined IKAPOS was performed in June 2010, using the using formulations that differ from the equations German polar aircraft ‘‘Polar5’’ of the Alfred Wegener commonly used (e.g., by Lenschow 1986; Bogel€ and Institute (AWI), which was based at Qaanaaq (north- Baumann 1991; Khelif et al. 1999; Strunin and Hiyama west Greenland). The investigations comprised studies 2004) or by Vorsmann€ et al. (1989), which is a somewhat of the summertime katabatic wind system in the expanded version of Vorsmann€ (1990). Hence, the re- coastal area of north and northwest Greenland, and of sults are difficult to compare to these other calibration atmosphere/sea ice/ocean exchange processes over the methods. Furthermore, the local angle-of-attack cor- North Water (NOW) polynya (see Heinemann et al. rections are determined by quasi-static maneuvers that 2011). Polar5 is a Basler BT-67 (Fig. 1) that consists of a do not allow for time shifts between the time series modified Douglas DC-3 airframe retrofitted with tur- (Bogel€ and Baumann 1991), which might be not optimal boprop engines (Herber et al. 2008). The main modi- for turbulence measurements. fications comprise a slight stretching of the fuselage, reinforced structure, and redesigned outer wing lead- 2. In-flight calibration ing edge and wing tip. Polar5 has a permanent ‘‘basic’’ meteorological in- In general, ‘‘calibration’’ denotes setting up a conver- strumentation and was carrying its optional nose boom and sion between the sensor reading (measured quantity) various radiation sensors during IKAPOS. The sensors and the sought quantity (the measurand; JCGM 2012), involved in calculating energy fluxes are listed in Table 1. but most authors use in-flight calibrations to yield

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TABLE 1. Polar5 turbulence instrumentation.

Quantity Sampling (Hz) Sensor Type Position 1 GPS Trimble 4000SSi Attitude and acceleration 50 INS Honeywell Laseref V family Height 100 Radar altimeter Honeywell KRA 405B Static pressure 20 Rosemount 1201F2A1B1A 3D wind 100 Five-hole probe Rosemount 858AJ Air temperature 100 Housed Pt100 Rosemount 102E4AL 100 Housed Pt100 Rosemount 102E Air humidity 100 Lyman-a Buck Research 100 Humicap Vaisala HMT333 100 Chilled mirror General Eastern 1011B Radiation ﬂuxes 20 Pyranometer Eppley Precision Spectral Pyranometer (PSP) Pyrgeometer Eppley Precision Infrared Radiometer (PIR)

correction functions for preexisting sensor calibrations Vorsmann€ 1990; Bogel€ and Baumann 1991; Drue€ 2001). determined in a wind tunnel or by the sensor manufac- We chose to use the last method because it can be difficult turer (Vorsmann€ 1990; Crawford et al. 1993; Bange and for a mere user of an aircraft to gather all the information Roth 1999; Kalogiros and Wang 2002; Metzger et al. to calculate proper propagation of uncertainty for all 2011). The usual exception are studies that describe the sensors and because extra flight maneuvers are usually development of new probes (e.g., Crawford and Dobosy expensive for the user. 1992; Haman et al. 2001) or use the aircraft radome as a. Time lags a flow-angle sensor (e.g., Brown et al. 1983; Tjernstrom€ and Friehe 1991; Khelif et al. 1999). Different processing speeds of the individual sensor The measurements usually calibrated in flight are systems can cause time lags between the recorded time angle of attack (a), sideslip angle (b), static pressure (ps) series. Analog measurements are associated with a time offset and defect (also called position error; Brown stamp upon A/D conversion. Digital data receive a time 1988), airspeed, and temperature probe recovery factor stamp when being sent—directly or via the Aeronautical (Williams and Marcotte 2000; Drue€ 2001; Kalogiros and Radio Incorporated (ARINC) bus (AEEC 2001)—to the Wang 2002). If sensors are mounted only occasionally, it data acquisition system. Both kinds of processing require has also turned out to be essential to determine the a certain processing time. current sensor alignment for each single experiment Internal lags of navigation data may arise from the (Vorsmann€ 1990; Freese and Kottmeier 1998; Drue€ 2001). internal data processing: INS integrates acceleration-to- In case the sensors have to be removed for transfer yield speed and position, while GPS derives position-to- flights or if the schedule for the aircraft is rather tight, an yield speed. Since both calculations are done at finite in-flight calibration under favorable atmospheric condi- time intervals using backward differences, the results tions in the area of the experiment is required. At the may be shifted in time too. beginning of the IKAPOS experiment, a calibration flight These time shifts are usually on the order of or below was performed on 12 June 2010, west of Qaanaaq (Fig. 2). 1 s. Such lags seem irrelevant for navigation purposes The basic idea of all maneuvers used for in-flight and are hence often neglected in aircraft sensor de- calibration is to vary only one quantity in a way such that velopment (de Mendonça et al. 2007). In the case of the variation can be measured at least in two ways, of scientific data collection, however, they may lead to er- which one does not need calibration. The uncertainty of roneous application of fast-varying corrections (Bogel€ the calibration coefficients or of the calibrated measured and Baumann 1991) or inhibit accurate calculation of values (see Axford 1968) may be assessed in a number of turbulent fluxes (Kristensen et al. 1997). ways: many authors use propagation of sensor uncer- For the present study, the lags of all measurements of tainties (e.g., Tjernstrom€ and Friehe 1991; Crawford and the same quantity were determined. To assess the lags Dobosy 1992; Garman et al. 2006), and the analysis of between measurements of different quantities, the lags specific flight maneuvers (e.g., Tjernstrom€ and Friehe of measurements from the same group (i.e., from the 1991; Williams and Marcotte 2000; Kalogiros and Wang same A/D converter or generated by one digital system) 2002), but also the spread of multiple calibrations can are assumed to be identical. The relative lag between be used (e.g., Spyers-Duran and Baumgardner 1983; each pair of groups was then determined by choosing

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FIG. 3. Example: RMS difference (m) and (cross) correlation vs time shift, for radar height (HradMPm) and barometric altitude FIG. 2. Flight path of the calibration flight performed for (HICAOmMP) for a series of ascents and descents. The maximum IKAPOS on 12 Jun 2010. The black line represents the 3D view, and covariance (and hence maximum correlation) is found at a shift of the gray line is its projection to the surface. The white square marks 0.29 s. Note how well the maximum and minimum are defined. Qaanaaq airport. Elevation data are taken from the Geoscience Laser Altimeter System (GLAS) dataset (Greenland above 788N; exhibit unsteady internal lags, but such variations were DiMarzio et al. 2007) and the Global Land One-Kilometer Base Elevation (GLOBE) database (elsewhere; Hastings et al. 1999). not observed in the course of the repeated local flow- angle calibrations (see section 2d). a pair of quantities, one from each group, for which b. Static pressure highly correlated values are expected—for example, radar height and static pressure (over water or suffi- The measurement of the static pressure ps on an air- ciently flat terrain). To determine the relative lag be- craft may be influenced by instrument deficits and by tween the measurements of two quantities, a flight distortion of the flow field. Static pressure for navigation segment was chosen, on which both are expected to is usually measured at ports on each side of the fuselage. cover a sufficiently wide range of values. Mean differ- The deviation of the indicated (i.e., actually measured) ence and covariance of both are calculated for a rea- pressure psi from the actual static pressure ps mainly sonable range of time lags (see Fig. 3 for an example). depends on the location of the static pressure ports and Depending on the physical relation, the time lag corre- the airspeed (Gracey 1958). This difference is usually sponding to the minimum difference, the minimum co- referred to as static (pressure) defect (Khelif et al. 1999) variance, or the maximum covariance was chosen (Drue€ or position error (Brown 1988). The only way to obtain 2001); see Table 2. a complete correction of the static defect is by compar- The internal lags between GPS and INS outputs can ison to an undisturbed pressure measurement taken on be determined by comparing derived position change, a trailing cone towed behind the aircraft (Brown 1988). integrated accelerations, and ground speed in the same Since altitude information used for navigation is de- way (Tjernstrom€ and Samuelsson 1995). Unfortunately, duced from the measured static pressure, strict airworthi- it turned out that the resolution of the position data as ness regulations—that is, Society of Automotive Engineers recorded by Polar5 was too coarse for this procedure (SAE) standard AS942A—ensure that the uncertainty and steplike structures dominate the time series, even altitude is, at least for modern passenger aircraft types after applying a low-pass filter. However, internal lags of (ICAO 2002), less than 15 m, requiring the uncertainty the INS could be determined in the course of the local of static pressure to be less than 0.4 hPa. This tolerance flow-angle calibration (see section 2d) and are included requires that the correction of the position error has to in Table 2. be included in the altimeter calibration inside the air Since all lags are relative, the choice of a time data computer (ADC; FAA 1988). Researchers using reference—that is, zero lag—is arbitrary. We chose to the static pressure from the aircraft altimeter, hence, give the lags in Table 2 relative to INS vertical accelera- usually can use the absolute value without corrections tion because in our experience, this measurement is most (e.g., Lenschow 1986; Bogel€ and Baumann 1991). Any crucial for retrieving the vertical wind variation. Some modification of the aircraft body, however, especially readers might argue that some INS systems tend to in places ahead of the static pressure ports (nose boom,

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TABLE 2. Lags of all sensor groups relative to INS (vertical) ac- additional laser altimeter, for example, for flux mea- celeration. surements near the ground (e.g., Drue€ and Heinemann Lag (s) Group contains 2007; van den Kroonenberg et al. 2012). 0.1 Nose boom turbulence c. True airspeed 0.15 Basic meteorological sensors 1.25 GPS speed/position As for the static port, the pressure at the side holes of a 1.30 ADC flow-angle sensor—such as Rosemount 858 (Rosemount 0.1 Radiation sensors 1988) or the best aircraft turbulence (BAT) probe 0.26 INS speed/position (Garman et al. 2006)—is not equal to the static pressure, 0.33 Radar altimeter since the airflow is partly decelerated or the pressure field is distorted by the aircraft body and propulsion. probes, inlets, and similar) can affect a previous cali- The static defect is generally regarded as a function of bration of the static pressure and may require new the dynamic pressure that might be defined as a poly- trailing cone flights. nomial (Brown 1988), but it is mostly approximated by

To verify the calibration of ps (or in case trailing cone a linear function (Williams and Marcotte 2000; Cremer flights are not possible), some authors use tower flyby 2008). If the indicated pressure values are already cor- maneuvers (Sethuraman et al. 1979; Tjernstrom€ and rected for their instrument offset, then the difference may Friehe 1991; Metzger et al. 2011), which is also the be expressed as an empirical factor (Lenschow 1972). preferred method for certification of small aircraft It has been called ‘‘pressure coefficient’’ (by Nacass (FAA 2011). Other authors use a missed approach 1992), but we call it ‘‘pressure partitioning factor’’ E (aircraft descends to a runway but does not touch down; (after Vorsmann€ 1990). It relates indicated pressures to Williams and Marcotte 2000), takeoff runs (aircraft ac- the undisturbed values via celerates, rolling on a runway until lift is generated but does not take off; Crawford and Dobosy 1992; Kalogiros 5 2 ps psi qciE (1) and Wang 2002), or a low pass (aircraft flies a few meters 5 1 at a constant height over the full length of a runway; qc qci qciE, (2) Vorsmann€ 1990) maneuver. Takeoff runs do have the disadvantage of possible disturbances by the ground where ps is static pressure, qc is dynamic pressure, and an effect (Stengel 2004), while a low pass allows for i appended to the subscript denotes indicated values. In checking the vertical wind offset, an additional benefit. our case, psi and qci were already corrected for their If the static pressure is measured on a five-hole probe instrument offset, which was determined in a laboratory such as the Rosemount 858 used on Polar5, then the on the ground. airspeed dependency of the static defect must be cali- If dynamic pressure (and flow angle) is not measured brated, either together with dynamic pressures qc,as on a nose boom but at the radome (i.e., the aircraft described in the next section (section 2c; Vorsmann€ nose), then impact pressure and static pressure correc- 1990; Bange and Roth 1999; Kalogiros and Wang 2002), tion have to be determined, including an additional de- or by a trailing cone flight in an accelerating or dependency on the flow angles a and b (Tjernstrom€ and celerating maneuver (Brown 1988). Friehe 1991), because an aircraft body is usually much In the case of Polar5, the barometric altitude calculated less rotationally symmetric than a nose boom. from the ps nose boom five-hole probe was within 615 m The usual procedure to determine E is to perform around the ADC altitude, and the difference between a straight flight at constant (pressure) altitude with in- ps measured at touchdown and the surface pressure was creasing airspeed from close to stall speed to maximum below the surface pressure accuracy of 1 hPa. Hence, no measurement speed. If the wind field is uniform, then further offset correction was applied. linear regression of true airspeed (TAS) versus ground Note that the uncertainty in the height (vertical dis- speed yields E (Lenschow 1986). It should be noted that tance to the ground) calculated from altitude (vertical qc has to be calculated for a compressible flow (Lenschow distance to sea level) determined from ps and the terrain 1986; Kalogiros and Wang 2002). elevation is often of a similar order or even much larger Many authors just use the terms acceleration and de- than the uncertainty caused by the measurement of ps, celeration, but as Williams and Marcotte (2000) and because the horizontal variation of the surface pressure Vorsmann€ (1990) point out, it is important to change and the air temperature profile below the aircraft are speed gradually. The reason is that the process of changing usually not known. Hence, it is advisable to determine throttle or the blade angle of the propellers results in sig- height from the aircraft radar altimeter or from an nificant deviations in the pressure measurements (e.g.,

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FIG. 4. Schematic view of selected ﬂight maneuvers: (a) wind squares, (b) racetrack maneuver, (c) eights, and (d) procedure turn.

6 5 1 0.5 hPa in Kalogiros and Wang 2002). These variations qc K1,qqci K0,q , (5) decay with time and usually become insignificant after less than a minute (Vorsmann€ 1990). where K0,p, K1,p, K0,q, and K1,q are empirical co- Another popular method used for this purpose is the efficients. Both equations allow for an offset in the ‘‘racetrack’’ maneuver (Williams and Marcotte 2000; pressure measurements, in contrast to (1) and (2). But Metzger et al. 2011)—that is, two parallel flight tracks because the variation of TAS is only a few tens of connected by two 1808 turns (see Fig. 4b)—which is a percent, they do not allow a sufficiently precise ex- performed at a number of different constant (indicated) trapolation to zero. Although (4) and (5) might repre- airspeeds (Williams and Marcotte 2000; FAA 2008). sent better a nonlinear behavior of the sensors, we Since such a maneuver was not performed during prefer to determine the zero offsets on the ground and to IKAPOS, a more simple method (also used by Telford correct the sensor readings before calculating the pres- and Wagner 1974; Telford et al. 1977; Vorsmann€ 1990) sure values. had to be employed: in the course of the calibration flight, The actual representation in Cremer (2008) contains a b two full circles were flown at an altitude of 3000 m, well an additional term that is a function of , , and ps, above the boundary layer, where turbulence was mini- apparently because it is assumed that the measured TAS mal. From these data, the horizontal wind vector was value actually represents the component of the TAS calculated. Then E was varied until the amplitude in both vector along the probe axis. But as Lenschow (1986) the eastward and northward wind components are mini- points out, the usual assumption is that the measured y mized (Vorsmann€ et al. 1989); see Fig. 5. This procedure TAS value equals the magnitude TAS of the vector (see was performed separately for both circles, which yields also Stickney et al. 1994), which we use in our data processing scheme, too. Although the difference is E 5 0:1969 6 0:0058. (3) usually negligible (Williams and Marcotte 2000), both assumptions are equivalent if they are properly reflected The correction formula for pressure partitioning used in the wind calculation. by the manufacturer of the nose boom (Cremer 2008) is Comparing (4) to (1) yields equivalent to K E 52 0,p 2 K . (6) p 5 K q 1 K 1 p (4) 1,p s 1,p ci 0,p si qci

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Either vanes are used as a flow-angle sensor (e.g., Axford 1968; Grant and Hignett 1998) or pressure differences on a forward-facing hemispheric structure are converted to the flow angle (e.g., Bange and Roth 1999; Lenschow et al. 2007). In the case of a five-hole probe— like Rosemount 858 or the BAT probe—the local flow angles are determined from the measured pressure differences using the manufacturer-supplied (Rosemount 1988) wind tunnel calibration (Bennett 1975; Crawford and Dobosy 1992; Garman et al. 2006; Metzger et al. 2011), or by a calibration device integrated into a wing- mounted five-hole probe (which allows for tilting the probe while maintaining a and b; Wood et al. 1997). Should pressure ports at a radome be used, the results of FIG. 5. Dependence of the amplitude of the eastward wind component during a full circle on the pressure partitioning factor E theoretical calculations (Nacass 1992) or indicated [see (1) and (2)]. pressure differences (Brown et al. 1983; Tjernstrom€ and Friehe 1991) are used.

1) ANGLE OF ATTACK Although this expression depends on airspeed, the var- 2 iation of E is only of the order of 10 5 (or 0.01% relative The most usual procedure to determine the conver- change) over the full speed performance range of typical sion between aL and the (vertical) angle of attack a is propeller-driven aircraft. The values K0,p 5 0.27 hPa and a straight and level flight with a stepwise increase of TAS € K1,p 5 1.063 supplied by the manufacturer hence cor- (Lenschow 1986; Tjernstrom and Friehe 1991; Crawford respond to E 5 0.08, which is quite different from our and Dobosy 1992; Williams and Marcotte 2000; value (E 5 0.1969). In turn, if applied to the full-circle Kalogiros and Wang 2002). Fewer authors use racetrack maneuvers from IKAPOS, then the manufacturer value maneuvers (Williams and Marcotte 2000), starlike pat- yields a variation of the horizontal wind components terns (Garman et al. 2006; van den Kroonenberg et al. that is clearly larger than the variation obtained by using 2008), or wind squares—that is, box patterns at a con- our value. This demonstrates the need for a new cali- stant altitude with four 908 turns and short straights in bration before every experiment. between—flown at a range of airspeeds kept constant Since the differences correspond to a change in the throughout the pattern (Fig. 4a; Cremer 2008; French et al. static pressure offset of only 0.25 hPa, a replacement of 2007; Metzger et al. 2011). Although the latter maneuvers the pilot’s altimeter or wear of its static port (Brown favor the assumption of constant horizontal wind, the need 1988) in the meantime could explain the change in E. to wait at least 30 s after each turn for the aerodynamic state to settle (Bogel€ and Baumann 1991) causes a much d. Flow angles longer overall trajectory, generating higher costs. Similar to the measurement of TAS, pressure field Since the angle of attack a can be assumed to equal deformation around the aircraft causes the local flow the aircraft pitch angle u in steady flight and zero vertical angles aL and bL at the tip of the flow-angle sensor to be wind (Williams and Marcotte 2000), a linear regression different from the flow angles a and b of the general between the local angle of attack aL and the free stream airflow around the aircraft (Lenschow 1986). The cor- angle of attack a 5 u then yields the coefficients of the rection needs to be determined in flight because it depends linear equation on the flight dynamic state of the aircraft, in particular airspeed, throttle, and aerodynamic configuration (setting a 5 a 1 a Ca L 0 . (7) of flaps, rudder, elevator, etc.; Garman et al. 2008). How- ever, measurements are usually made in clean configura- Some authors only determine the offset of a from tion (retracted flaps, gear, etc.; see Stengel 2004); hence, these maneuvers and prefer to perform slow oscillations such influences (Drue€ 2011) may be neglected. of the pitch angle, also called (slow) pitching maneuver, Several authors introduce an interdependence term in to determine sensitivity Ca in (7) (Brown et al. 1983; the calibrations of a and b. In our and other authors’ Vorsmann€ 1990; Bogel€ and Baumann 1991) or to check experience (Kalogiros and Wang 2002), however, such the robustness of the calibration of a against vertical interdependences are small as long as a and b remain speed or acceleration (Lenschow 1986; Williams and small. Marcotte 2000).

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Another common approach is to calculate the vertical wind throughout a pitching maneuver and to minimize the vertical wind variance by variation of coefficients a0 and Ca (e.g., French et al. 2007; Petersen and Renfrew 2009). For IKAPOS, we use a modified form of the approach presented by Bogel€ and Baumann (1991). For this method, the aircraft has to perform a series of fast pitch angle variations of 6108 in an area where zero vertical wind can be expected. The usual assumption is that the vertical wind is zero well above the atmospheric boundary layer (ABL) in calm synoptic conditions (e.g., Lenschow 1986; Bogel€ and Baumann 1991). This condition has been found to be not satisfied in areas above or in the lee of mountain ridges or islands (Corby 1954), near deep convection (Stull 1976), or above areas from which katabatic wind systems originate (Klein and Heinemann 2002). An- other approach used by van den Kroonenberg et al. FIG. 6. Example of a fast pitching maneuver: Vertical wind (right (2008) and Metzger et al. (2011), because of insufficient axis) before (dashed, using manufacturer coefficients) and after calibration (solid) vs time of flight. Pitch angle (left axis) is shown ceiling (highest altitude at which it can sustain level as dashed–dotted line. flight) of their aerial vehicles, are horizontal flight segments (‘‘ABL runs’’) at constant height in the lower ABL over flat terrain. Although the variance of the The nose boom manufacturer calibration of a (Cremer s vertical wind w is large, its mean w is zero, if the flight 2008) uses segment is long enough. 5 q With w 0, the vertical component of the TAS vector a 5 a 1 K0,a , (11) (wTAS) equals the vertical speed of the aircraft wac. qciK1,a Recalling the approximation wTAS ’ yTAS sin(u 2 a) illustrates well that a pure pitching oscillation causes with K0,a 521.158 and K1,a 5 0.087. periodic variations in both vertical speeds (Bogel€ and Other literature (e.g., Lenschow 1986) uses a formu- Baumann 1991). Aircraft speed wac is calculated pri- lation equivalent to our (7): marily from the INS vertical acceleration, as described € q C in Drue (2001), following the method of Matejka and a 5 a a 1 a 0 , (12) Lewis (1997). To allow for internal lags of data pro- qci K1 cessing, a time shift dtINS of the INS vertical acceleration is introduced. Finally, Powell’s method (Press et al. where K1 5 0.079 is a manufacturer-supplied value from 1986) is used to minimize the RMS of the difference wind tunnel calibration of the Rosemount 858’s five- 21 (wac 2 wTAS) by synchronous variation of a0, Ca,and hole probe, valid for around 130 kt (1 kt 5 0.51 m s ; € dtINS. However, as Tjernstrom and Friehe (1991) and typical measurement speed). Bogel€ and Baumann (1991) point out, it is important to The values determined by Cremer (2008) hence cor- 21 use the full wind calculation, including all corrections, respond to Ca 5 0.9088 hPa , which differs by about 21 21 in this optimization. 5% from our value (Ca 5 0.9608 hPa 6 0.0218 hPa ). During IKAPOS, four series of oscillations were The smaller value of Cremer (2008) presumably reflects performed, which yield the neglected influence of time shift between INS and the pressure sensors. a 52 : 86 : 8 52 8 0 2 068 0 193 , (8) The value K0,a 1.15 differs significantly from our value (a0 522.068). A difference of almost 18 seems 21 21 Ca 5 0:9608 hPa 6 0:0218 hPa , and (9) surprising at first glance, since the nose boom mounting is rather solid, which makes it an unlikely source of 18 5 : 6 : dtINS (0 103 0 005) s. (10) misalignment. However, it has to be considered that such offset includes mechanical tolerances in the nose The vertical wind before and after application of the boom and in the INS mounting, as well as pressure calibration according to (8)–(10) is shown in Fig. 6. sensor temporal behavior and aging.

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The nose boom sensor head has a mounting base of 210 mm and the tolerance for a regular 4-mm washer is 0.2 mm (ISO 4759, class A); the resulting reproducibility of the nose boom orientation is on the order of 0.28. The same applies to the INS inertial reference system from the Honeywell Laseref V family, which has an outside dimension of 6.5 in. (16 cm), allowing a mean orientation tolerance of 0.18 (Honeywell 2004). The pressure transducer offsets were determined in a laboratory calibration by the manufacturer of the nose boom and turned out to be on the order of 0.05 hPa (at least more than 40 min after powering them on). Assuming a differential pressure of 5 hPa, this uncertainty roughly equals 0.58. Hence, the sum of all such uncertainties may sum up to a mission-to-mission change of the offset of a on the order of almost 18.

2) SIDESLIP

In the literature, three main procedures to determine FIG. 7. Horizontal wind measured on a horizontal box pattern the conversion between the horizontal pressure difference flown during of the calibration flight over Smith Sound (Fig. 2). at the tip of the five-hole probe into the horizontal flow Land surfaces are shaded gray. Note the inhomogeneity of the wind angle b are found, which all assume a linear relationship, field. Each straight segment is about 45 km long (12-min flight).

b 5 b 1 b Cb L 0 . (13) and ground speed (Bogel€ and Baumann 1991), however, Most authors use a reverse-heading maneuver (also allows for a time shift between pressure and attitude known as go-and-return maneuver) on a straight tra- measurements and drift during the maneuver (Williams jectory at constant altitude (e.g., Lenschow 1986; Wood and Marcotte 2000). et al. 1997; Williams and Marcotte 2000). As Lenschow During the IKAPOS calibration flight, the wind field (1986) points out, it is important to perform a procedure in the area turned out to be rather inhomogeneous turn (Fig. 4d; FAA 2008) in between to stay in the same (Fig. 7). Hence, none of the above-mentioned tech- air volume. The difference between the two heading niques could be applied and a split technique was Cb dt angles in each direction then corresponds to twice the used: The sensitivity and time shift INS were de- offset of b (Tjernstrom€ and Friehe 1991). termined from fast yawing maneuvers. For this pro- b Other authors use full circles (Lenschow 1986; cedure, both prescribing offset 0 as zero and including b Lenschow et al. 1999) or wind squares (Cremer 2008) 0 in the variation process yielded almost the same results (Fig. 8). and adjust the coefficients b and Cb by minimizing the 0 b variance of the horizontal wind. According to Bogel€ and Offset 0 is determined from two perpendicular Baumann (1991), calculations are facilitated by flying reverse-heading maneuvers; see Fig. 9. To check the close to one of the four cardinal headings (0, 90, 180, or plausibility of this result, the same procedure was ap- 270) because deviations are visible as variations of one plied to the corners of the box pattern shown in Fig. 7, b 5 wind component at a time, while other authors recom- which yielded a similar result ( 0 0.97) but with much mend flying boxes with two sides parallel to the mean greater uncertainty, because the inhomogeneity of the wind direction to minimize the influence of the drift wind field can make the actual wind direction vary be- angle variations (Vorsmann€ 1990). tween the box sides much more than during a reverse- The third approach is to perform one or more slow heading maneuver. yawing oscillations (also called sideslip maneuver). If To summarize, the split technique yields they are carried out slowly with a period of 10 s or more, 21 21 then the procedure is similar to that used for a Cb 520:8988 hPa 6 0:0358 hPa (14) (Lenschow 1986; Tjernstrom€ and Friehe 1991; Williams b 52 : 86 : 8 and Marcotte 2000; Kalogiros and Wang 2002; Garman 0 0 957 0 013 (15) et al. 2006). Applying fast yawing oscillations and min- ’ : imizing the difference between the indicated airspeed dtINS 0 10 s. (16)

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FIG. 8. Horizontal wind (right axis) assuming zero offset (thin FIG. 9. Horizontal wind components during a reverse-heading line) and after offset calibration (thick line). The eastward com- maneuver. Representation as in Fig. 8, but true heading (left axis), ponent is plotted as solid lines, and the northward component is which is shown as plus signs. plotted as dashed lines. Yaw angle (left axis) is shown by crosses.

possible reason is that this correlation did not allow for Analogous to the previous section, the nose boom time shifts between nose boom and INS measurements. manufacturer (Cremer 2008) used A distance of 5 m between the mounting position of the INS inertial reference system and the five-hole probe q b 5 b 1 1 provides a large cantilever (Brown et al. 1983). There- K0,b K2,bqci , (17) qciK1,b fore, any rotation of the aircraft body causes quite a large movement of the flow-angle probe. Some authors whereas most authors prefer Lenschow (e.g., Lenschow argue that this contribution to the sensor motion is 1986), who used negligible, for example, because typical angular rates cause rather small speeds of the nose boom tip. But qb Cb when looking at the distribution of angular rates, we b 5 1 b . (18) 0 found that the contribution from rotations of the body qci K1 should not be omitted. Assuming a typical measurement speed of 130 kt, the During the calibration flight the pitching rate 21 21 values K0,b 520.68, K1,b 5 0.0888, and K2,b 5 0.0258 exceeded 0.548 s , corresponding to about 0.05 m s reported by Cremer (2008) correspond to b0 520.158 vertical speed of the probe in 10% of the time. Values and Cb 5 0.8988. for the other axes are similar. In consequence, for 10%

The difference of offset b0 between Cremer (2008) and of all data points, the error of the wind measurement this study is on the same order as for a0. The magnitude of caused by neglecting the rotation of the body exceeds 21 Cb is the same for Cremer (2008) and this study. The sign, 0.1 m s , which is quite significant compared to all however, is opposite, which is hard to explain by any other contributions. uncertainties. It appears more likely that during the last Allowing a time lag between INS and flow-angle mea- assembly of the nose boom sensor, the hoses connecting surements (see section 1) revealed a slight dependency— the left and right holes of the five-hole probe to the re- a correlation coefficient of 0.55—between the local angle spective pressure sensors were interchanged. of attack aL andtheINSpitchingrateinthepresent study. The vertical wind was hence corrected for the e. Angular rates vertical movement of the flow-angle sensor, calculated The calibration report by Cremer (2008) states that no from the INS angular rates and the three-dimensional significant correlation between (uncorrected) vertical cantilever between the INS and flow-angle sensor posi- wind and pitch rate could be found, although wind was tions (Vorsmann€ et al. 1989). It should be noted that this not corrected for the probe movement because of aircraft correction is already included in the full wind calculation body rotations. As the report states, this is surprising. A used in section 1.

Unauthenticated | Downloaded 09/26/21 02:56 AM UTC 2830 JOURNAL OF ATMOSPHERIC AND OCEANIC TECHNOLOGY VOLUME 30 f. Fast temperature sensor which does not conﬂict with the manufacturer value, but it does not add great value because of the large The nose boom of Polar5 carries two Rosemount 102 uncertainty. temperature sensors, one of them in a Rosemount 102 As Williams and Marcotte (2000) point out, this deiced housing (model 102-EJ2BB), called TE, and method requires assumptions about static and airspeed the other one in a Rosemount 102 nondeiced housing that are often fairly crude appropriations. They recom- (model 102-E4AL), called TRvF. The idea of both is to mend the method by Leise and Masters (1993), that is, to supplement measurements of a more robust sensor by pass a racetrack pattern twice with different airspeeds. a faster sensor. Then r can be calculated from indicated temperature 1) RECOVERY FACTOR and INS- or GPS-measured ground speed, which has much greater accuracy. Air passing the sensor location inside the housing is (incompletely) decelerated, which causes compres- 2) RESPONSE TIME sion of the air inside the housing and, in consequence, The inertia of a temperature sensor in a housing a rise in temperature by adiabatic heating dT .To i usually behaves like a so-called two-component system convert the measured (‘‘indicated’’) temperature into (Rodi and Spyers-Duran 1972). Such a system has two true (‘‘static’’) temperature, the recovery factor r of the response times [see Inverarity (2000) for a comprehen- sensor housing must be known. Then as in Lenschow sive review]. On a short time scale (e.g., ,1 s) it behaves (1986), like having a response time t2, while on a longer time . y 2 scale (e.g., 1 s) it behaves like having a response time 0 t dT 5 T 2 T 5 r , (19) 1. For the non-deicable Rosemount 102-E2AL housing i i s c 2 p (Stickney et al. 1994), Spyers-Duran and Baumgardner

(1983) found t1 5 0.17 s and t2 5 45 ms [values from where dTi is the temperature increase; Ti and Ts are other sources are listed in Inverarity (2000)]. indicated and static temperatures, respectively; y0 is the If these values are assumed valid for TRvF, then the mean speed of the airflow, and cp is the specific heat time constant of another sensor can be determined by capacity of air. It is often assumed that the flow speed fitting the phase spectrum of the two time series recor- at the sensor location is equal to the true airspeed, ded by both sensors. Figure 10 shows coherence, phase y0 5 yTAS. As a consequence it is possible to use the lag, and calculated response time difference versus fre- recovery factor as provided by the manufacturer or in quency. Below 1 Hz, the coherence is close to one and a wind tunnel (e.g., Vorsmann€ 1990; Crawford and the mean response time difference is 21.15 s. Assuming

Dobosy 1992). the above-mentioned value for t1 for TRvF yields In the case of Rosemount, the manufacturer supplies h t ’ : a recovery correction value that can be related to the 1(TE) 1 32 s (21) 5 2 h 1 y2 recovery factor r via r 1 (1 Ts2cp/ 0). For the 2 target airspeed of 65 m s 1 during measurements, we between about 2 and 20 Hz, the coherence drops to used hTE 5 0.000 30 or r(TE) 5 0.961 for sensor TE and values below 0.2 and the phase lag becomes poorly de- hTRvF 5 0.000 70 or r(TRvF) 5 0.908 for sensor TRvF fined. Above 20 Hz, however, coherence increases to 0.8 (for Mach 0.2, see Stickney et al. 1994). and the phase lag exhibits less scatter (see error bars in Since, the local flow velocity at the probe position is Fig. 10). Such behavior could be caused either by both likely to be slightly reduced relative to the overall air- sensors exhibiting identical inertia in this range or by craft airspeed (Williams and Marcotte 2000), it might be one senor being too slow to yield anything but random useful to determine the recovery factor for a particular noise (de Sa et al. 2002). Earlier experience with the TE combination of housing and mounting position. sensor, however, had shown that it has a faster response € Lenschow (1986) suggested varying the aircraft speed on time t2(TE) that is similar to t1(TRvF) (Drue 2001). a straight and level flight segment. A linear regression of As a consequence, TRvF can be used as the exclusive y2 ( 0)/(2cp) versus Ti then yields r as slope and Ts as in- temperature sensor with TE as a backup, for example, tercept. We performed two acceleration maneuvers at in case of icing. the beginning and end of two reverse-heading maneu- g. Pyranometer misalignment vers, which ensures that they are performed in the same air volume. Averaging the fitted slopes yields then As discussed with the flow-angle sensors in section 1, the alignment of the hemispheric radiation sensors mounted 5 : 6 : r(TRvF) 0 954 0 038, (20) on top and below the fuselage of Polar5 can change

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FIG. 10. (top) Coherence, (middle) phase difference, and (bottom) response time difference vs frequency for the temperature indicated by sensor TRvF vs sensor TE (see text). slightly with every installation.Hence,minimalangular artifacts, and other forms of inadequate data processing. changes are expected to occur from mission to mission. Finally, calculating uncertainties of the final atmospheric The misalignment for a mission can be determined by quantities such as temperature and wind components in-flight calibration, using the modified method of Freese allows for quantifying the success of the calibration. and Kottmeier (1998), as described by Drue€ (2001). This 1) ADDITIONAL MANEUVERS method applies a low-pass filter to the data and then de- termines global radiation Kdown by linear regression of the Several authors recommend simple maneuvers either indicated global radiation Kdowni versus the dimensionless to add some redundancy to the actual calibration ma- incidence coefficient c 5 cos(z)/cos(Q), where Q repre- neuvers or to enable an independent verification of sents the solar zenith angle and z is the angle between the calibration results. As a reasonable rule of thumb, pyranometer zenith and the sun. The mechanical offset French et al. (2007) state that none of the wind speed angles are then varied until the variance of the corrected components should vary more than 10% of the parallel

Kdown is minimized. aircraft speed component during such a check. Petersen This procedure was applied to two full circles per- and Renfrew (2009) even recommend repeating such formed during the calibration flight (see Fig. 11), which patterns several times during a longer experiment. yields The authors recommend reverse-heading maneuvers or L-shaped flight segments to verify TAS, sideslip pitch Du 521:228 and (22) (Lenschow 1986), and temperature sensor recovery factors (Lenschow and Pennell 1974). To check flow- Df 52 8 roll 0.918 . (23) angle offsets, full circles or eights (two opposite full circles, see Fig. 4c) at a range of roll angles (Lenschow h. Check of calibration 1986; Williams and Marcotte 2000), or ABL runs (van To determine if a new calibration is needed or to as- den Kroonenberg et al. 2008; Metzger et al. 2011; see sess the uncertainty of the coefficients, it is useful to check section 1) are recommended. a present calibration. This is usually done by performing Several authors use comparison flights using two or additional maneuvers. Analyzing power spectra of cal- more aircraft (Lenschow and Pennell 1974; Lilly et al. culated quantities allows for identifying remaining noise, 1982; Spiess et al. 2007) for the same purpose. Among

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FIG. 11. Solar radiation recorded during two full circles flown as part of the IKAPOS calibration flight. Uncorrected (dashed) and corrected (solid) (top) shortwave downward radiation flux and (bottom) solar zenith angle seen from the pyranometer (solid) and in the geodetic system (dashed). these Lilly et al. (1982) particularly recommend L-shaped because of high-frequency noise of the TAS raw data. formation flights. Such procedures are of special impor- Although the spectra are averaged over rather small tance, if measurements taken by different aircraft are (1/20 decade) bins, no spikes are visible at multiples of 50 composed to one dataset. For safety, however, the aircraft or 60, which would indicate a ripple in the power supply have to maintain a certain separation, which makes it hard or persisting timing issues in digital data transmission to distinguish between instrumental differences and at- (both found in Drue€ and Heinemann 2007). The flight mospheric gradients (Drue€ et al. 2010). was performed in a stable boundary layer, but the spectral density values are much higher than in a strongly stable 2) SPECTRA boundary layer (Drue€ and Heinemann 2007), because of 2 Figure 12 shows power spectra from a flight section of the rather high wind speed of 18 m s 1. Because of a typ- 2 a measurement flight carried out on 15 June 2010 in ical airspeed of around 70 m s 1, the scaled maximum in fairly stable conditions over ocean at approximately the along-wind spectrum is located at a scaled frequency

50-m height. The flight direction was to the west, almost (fz/Ua)ofaround1.0,whichisclosetothevaluesfoundby perpendicular to the average (northerly) wind direction. Kalogiros and Wang (2002). The spectra are smoothed over equal logarithmic in- 3) UNCERTAINTY OF THE MEASURED tervals of frequency and multiplied by frequency. Both ATMOSPHERIC QUANTITIES spectra show a reasonably defined inertial subrange with the expected 22/3 slope above 2 Hz. At lower frequen- The methods to estimate the uncertainty of the mea- cies, contamination by aircraft motions is visible. Such sured results that are used in the literature are repeated contamination often appears as a peak corresponding to measurements (e.g., Cremer 2008), propagation of un- one of the autopilot control loops. The small peak near certainty [also known as Gaussian error propagation 9 Hz in the vertical wind component, hence, most prob- (GEP); e.g., Drue€ (2001)], a differential error analysis ably corresponds to the autopilot vertical speed control (DEA; Tjernstrom€ and Friehe 1991), or a Monte Carlo loop. Above 15 Hz, the spectra deviate from the slope, simulation (Buzorius et al. 2006). Although theoretically because of excessive (vertical wind) or scarce (along identical, GEP and DEA differ in practice. Using GEP wind) antialiasing filtering. As also reported by Kalogiros usually means calculating uncertainties of each in- and Wang (2002), the spectrum of the along-wind com- termediate variable and propagating it to the next result ponent decreases less, or increases in the present case, of each individual formula, where it is used. DEA, in

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FIG. 12. Power spectra scaled by frequency [fS(f)] of (top) temperature, the horizontal wind components (second) parallel and (third) perpendicular to the flight direction, and (bottom) vertical wind at 50-m height above ocean. A dashed 22/3 slope is plotted for comparison. The data shown are high-pass filtered with a 600-s cutoff period. contrast, means evaluating the total differential of the with the manufacturer-supplied specifications. In our full equation describing a measurand. Because of the case, laboratory calibrations of the sensing elements complexity of the differentials involved, GEP is tempt- yielded the following precisions: temperature (TE, 2 ing to omit terms considered ‘‘minor’’ and DEA is rarely TRvF): 61 3 10 3 K, static pressure sensor: #0.1 hPa, found in literature, probably because it is practically differential pressure sensors: #0.001 hPa, INS pitch and impossible using pen and paper. roll angles: 0.18, and INS heading: 0.48. Since the exact Because of this complexity, one might argue that type of INS used in the Polar5 avionics is not known to omitting terms in most steps of GEP leads to a potential us, we assume the precisions of the attitude angles to be underestimation of the combined uncertainty. There- identical to the rather similar Honeywell avionics suite fore, we have additionally performed a DEA of the full on the Dassault Falcon research aircraft of Deutsches equations (not shown here because of excessive space Zentrum fur€ Luft- und Raumfahrt (DLR): pitch/roll: requirements) using the open-source computer algebra 0.18 and heading: 0.48. The precisions of the ADCs by system ‘‘Maxima’’ (Joyner 2006). The calculations are means of the standard uncertainty of the digitized value performed using typical values for a low-level straight are determined from the manufacturer’s specifications: flight (taken from a constant level flight over Baffin Bay 0.05 K, in the case of temperature; and 0.13% of the on 15 June 2010). As a result, Maxima yields the value of reading plus 60 ppm of the full (electric) range, in the each partial derivative to each individual input quantity. case of the pressure sensors. Using these values, we The contribution of each input quantity to the standard obtain the uncertainties given in Table 3. measurement uncertainty is this gradient times the un- The values for the standard uncertainty given in certainty of the input quantity. The standard uncertainty Table 3 are similar or lower than other precisions pre- of the measured value of each measurand is then calcu- sented in literature (e.g., Vorsmann€ 1990; Metzger et al. lated by the law of propagation (defined in JCGM 2008). 2011). Tjernstrom€ and Friehe (1991) report slightly All quantities not being natural constants are regar- smaller values for the uncertainty of wind components, ded as input quantities: measured quantities, calibration which is apparently caused by their attitude reference values of sensors and ADCs, and aircraft dimensions. system having errors of about 1/10 compared to the INS of The instrument precisions were determined from the Polar5. On the other hand, they estimate their calculated latest laboratory calibration of each sensor, alternatively temperature of having a greater uncertainty than ours,

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TABLE 3. Calculated standard measurement uncertainties (fourth column) of the atmospheric measurands (ﬁrst column). Values in parentheses in the fourth column represent values estimated by ‘‘manual’’ GEP. Second and third columns give contribution input quantities and their respective contributions. Note that third and fourth column contain absolute values in the respective units indicated in the ﬁrst column. For clarity, contributions of less than 10% of the total value are omitted. Sensing element calibration (SEC), pressure partitioning factor (PPF) E, differential pressure sensor (DPS), and static pressure sensor (SPS).

Measurand (Units) Input quantity Contribution Standard uncertainty Temperature r(TRvF) 0.09 0.13 (0.08) Ts (K) SEC TRvF 0.08 ADC #0.05 Horizontal wind INS heading 0.24 0.39 (0.6) –1 yh (m s ) INS ground speed 0.19 PPF 0.17 SEC DPS b 0.13 ADC DPS qci 0.05 ADC DPS b 0.05 Vertical wind a calibration 0.15 0.20 (0.26) w (m s–1) ADC DPS a 0.07 SEC DPS a 0.07 Static pressure ADC SPS psi 1.24 1.25 (&1) ps (hPa) PPF 0.14 probably because of a disadvantageous positioning of the unlimited flight time is available. Some maneuvers, temperature sensor in front of the windscreen. however, that may provide some more redundancy but In the last column of Table 3, the results of a typical are not essentially needed are marked as optional. ‘‘manual’’ GEP are shown for comparison. It is re- All sensors should be well calibrated in the laboratory markable that the GEP result is not always smaller than before the start of the experiment. Data acquisition the result of the full-scale DEA. It appears justified to should be set up to record data with sufficient resolution. use GEP at least as a quick method to get a reasonable Even if the accuracy of the absolute value recorded does estimation of the uncertainties. not require the finest possible resolution, the calibration procedures may benefit from the additional information on fluctuations of the measured values, for example, the 3. Conclusions calculations presented in section 2g. We summarize our results as a recommendation that To determine the static pressure offset, no dangerous allows for the determination of the best calibration, even maneuvers close to the ground—such as tower flybys— if we did not perform all maneuvers in the experiment are required, nowadays, if the aircraft altimeter complies IKAPOS, which is used to exemplify most procedures. with reduced vertical separation minimum (RVSM) re- Based on the procedures we performed, as described, quirements for pilot altimeters (6;1,5 hPa; ICAO 2002). and based on the review of all literature we could find, If the compliance is ensured even after doing all scientific the maneuvers recommended below have been shown to modifications to the aircraft body, then comparing the provide adequate in-flight calibration for turbulence aircraft altimeter to the scientific static pressure sensor measurements, at least for the type of investigations yields a sufficient estimation of the static pressure offset. performed by the Polar5 for the IKAPOS field cam- To double-check the offset, a low pass appears to be op- paign. Although investigators on other aircraft and/or timal, since it also allows for a check of the vertical wind different configurations may want to add or repeat cal- calibration. ibration maneuvers for further validation, we believe True airspeed (via the pressure partitioning) should that this set is the best choice for an economic state-of- be calibrated by straight and level flights at increasing the-art in-flight calibration, in many cases. and decreasing speeds. It is essential to change speed in The aim of the recommended set of maneuvers is to steps rather than continuously. Racetrack maneuvers yield a good calibration without any need to add pat- seem likewise adequate but require at least roughly terns for ‘‘better’’ values. Although we mentioned sev- twice the flight time. eral times the goal to minimize the calibration flight The (vertical) angle of attack is best calibrated by fast duration, we used this criterion only to make our se- pitching maneuvers, minimizing vertical wind variance lection among equally suited choices. We hence see no by variation of offset and sensitivity (a0, Ca) and the need to change the recommendations for the case that sensor time lags. Likewise, sideslip sensitivity Cb and

Unauthenticated | Downloaded 09/26/21 02:56 AM UTC € DECEMBER 2013 D R UE A N D H E I N E M A N N 2835 sensor time lags are calibrated by fast yawing maneu- Brown, E. N., 1988: Position error calibration of a pressure survey vers. For calibration of offset b , a reverse-heading aircraft using a trailing cone. NCAR Tech. Note NCAR/ 0 1 maneuver seems most adequate. TN-313 STR, 29 pp. [Available online at http://nldr.library. ucar.edu/repository/assets/technotes/TECH-NOTE-000-000- Ideally, full circles flown at two different roll angles 000-579.pdf.] are the best choice to determine the radiation sensor ——, C. A. Friehe, and D. H. Lenschow, 1983: The use of pressure misalignment. fluctuations on the nose of an aircraft for measuring air mo- Finally, a calibration flight should contain enough tion. J. Climate Appl. Meteor., 22, 171–180. redundancy to 1) make the results robust against failure Buzorius, G., J. Kalogiros, and V. Varutbangkul, 2006: Airborne aerosol flux measurements with eddy correlation above the of a single maneuver, 2) allow checking the results on ocean in a coastal environment. J. Aerosol Sci., 37, 1267–1286, independent data, and 3) yield an estimate of the un- doi:10.1016/j.jaerosci.2005.11.006. certainty of the results achieved. Corby, G. A., 1954: The airflow over mountains: A review of the Hence, we recommend the following flight program: state of current knowledge. Quart. J. Roy. Meteor. Soc., 80, 491–521, doi:10.1002/qj.49708034602. d speed steps: straight flight at constant altitude; in- Crawford, T. L., and R. J. Dobosy, 1992: A sensitive fast-response crease TAS in steps, approximately five steps around probe to measure turbulence and heat flux from any airplane. typical measurement speed; procedure turn; deceler- Bound.-Layer Meteor., 59, 257–278, doi:10.1007/BF00119816. ——, R. T. McMillen, and R. D. Dobosy, 1993: Correcting airborne ate TAS in steps again; flux measurements for aircraft speed variation. Bound.-Layer d square at 0, 90, 180, and 270 heading on each side; Meteor., 66, 237–245. d straight flight (3–5 min); Cremer, M., 2008: Kalibrierung der turbulenzmesssonde der Polar 5. d fast pitch, roll, and yaw oscillations (each 6108); MessWERK Doc. mW-AWI-P5-2008-06, 23 pp. de Mendonça, C. B., E. M. Hemerly, and L. C. S. Goes, 2007: d straight flight (1–3 min); Adaptive stochastic filtering for online aircraft flight path re- d eights (one left and one right circles) at 108 and 208 roll construction. J. Aircr., 44, 1546–1558, doi:10.2514/1.27625. angle; de Sa, A. M., A. Infantosi, and D. Simpson, 2002: Coherence be- d two (cross or L shaped) reverse-heading maneuvers; tween one random and one periodic signal for measuring the d (optional) acceleration maneuver: straight flight at strength of responses in the electro-encephalogram during constant altitude, decelerate to close to stall speed, sensory stimulation. Med. Biol. Eng. Comput., 40, 99–104, slowly accelerate to maximum cruise speed, slowly doi:10.1007/BF02347702. DiMarzio, J., A. Brenner, R. Schutz, C. A. Shuman, and H. J. decelerate, procedure turn, slowly accelerate to max- Zwally, 2007: GLAS/ICESat 1 km laser altimetry digital ele- imum cruise speed, slowly to close to stall speed; and vation model of Greenland. National Snow and Ice Data d (optional) low pass above a flat surface (runway). Center, Boulder, CO, digital media. [Available online at http://nsidc.org/data/nsidc-0305.html.] Acknowledgments. 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