Measuring the 3-D wind vector with a weight-shift microlight aircraft

successive calibration steps. For our aircraft the horizontal wind components receive their greatest single amendment (14%, relative to the initial uncertainty) from the correction of flow distortion magnitude in the dynamic pressure computation. Conversely the vertical wind component is most of all improved (31%) by subsequent steps considering the 3-D flow distortion distribution in the flow angle computations. Therein the 10

Here airborne measurements are capable of supplementing and extrapolating ground based information (e.g., Lenschow, 1986;Desjardins et al., 1997;Mauder et al., 2008).However, to date manned platforms, such as fixed-wing aircraft (FWA, see Appendix C for a summary of all notation) and helicopters, are expensive to operate.Furthermore, their application is often not possible in settings such as remote areas beyond the range of an airfield.Here small size unmanned aerial vehicles are of use.These allow the measurement of a limited range of variables, such as temperature, humidity and wind vector (e.g., Egger et al., 2002;Hobbs et al., 2002;van den Kroonenberg et al., 2008).However due to payload constraints, they do not allow a comprehensive sensor package.A weight-shift microlight aircraft (WSMA) may provide a low-cost and easily transportable alternative, which also places a minimal demand on infrastructure in the measurement location.After successfully applying a WSMA to aerosol and radiation transfer studies (e.g., Junkermann, 2001Junkermann, , 2005)), the possibility of 3-D wind vector measurement from WSMA shall be explored.The underlying motivation is to work towards eddy-covariance (EC) flux measurements in the atmospheric boundary layer (ABL).
The determination of the 3-D wind vector from an airborne, i.e. moving platform, requires a high degree of sophistication.Specially designed probes enable the measurement of the 3-D turbulent wind field with respect to the aircraft (e.g., Brown et al., 1983;Crawford and Dobosy, 1992).At the same time the aircraft's movement with respect to the earth must be captured (e.g., Lenschow, 1986;Kalogiros and Wang, 2002a).A total of 15 measured quantities are involved in the computation of the 3-D wind vector (Appendix A), and consequently a similar number of potential uncertainty sources need to be considered.Furthermore, flow distortion by the aircraft itself can affect the measurement (e.g., Crawford et al., 1996;Kalogiros and Wang, 2002b;Garman et al., 2008).This complexity led to a number of quantitative uncertainty assessments of the wind measurement from aircraft, of which a few shall be mentioned here.While the carriers are commonly FWA, they cover a wide range, from single-engined light aircraft (e.g., Crawford and Dobosy, 1992) to twin-engined business jet (e.g., Tjernstr öm and Friehe, 1991) and quad-engined utility aircraft (e.g., Khelif et al., 1999).A similar variety of methodologies is used for the individual proof-of-concept.Widespread are uncertainty propagation of sensor uncertainties (e.g., Tjernstr öm and Friehe, 1991;Crawford and Dobosy, 1992;Garman et al., 2006) and the analysis of specific flight manoeuvres (e.g., Tjernstr öm and Friehe, 1991;Williams and Marcotte, 2000;Kalogiros and Wang, 2002a).Probably due to the higher infrastructural demand, wind tunnel studies (e.g., Garman et al., 2006), comparison to ground based measurements (e.g., Tjernstr öm and Friehe, 1991) and aircraft inter-comparisons (e.g., Khelif et al., 1999) are less common.Often statistical measures are used to express uncertainty, such as repeatability (e.g.0.03 m s −1 , Garman et al., 2006), deviation range (e.g.0.4-0.6 m s −1 , Williams and Marcotte, 2000), median differences (e.g.0.1 ± 0.4 m s −1 , Khelif et al., 1999), or root mean square deviation (e.g.≥ 0.1 m s −1 at ≤ 2 m s −1 deviation range, Kalogiros and Wang, 2002a).
The EC technique (e.g., Kaimal and Finnigan, 1994) relies upon the precise measurement of atmospheric fluctuations, including the fluctuations of the vertical wind.Measured from aircraft, the determination of the wind vector requires a sequence of thermodynamic and trigonometric equations (Appendix A).These ultimately define the wind component's frame of reference.Yet, owing to its flexible wing-and aircraft architecture, the dynamics and flow distortion of the WSMA are likely more complex than those of FWA.Therefore the use of well established wind vector algorithms for FWA requires adaptation and correction.Consequently this study first and foremost investigates the feasibility and reliability of the wind measurement from WSMA.Based on these findings the measurement precision will be addressed in a successive study.The WSMA's overall measurement uncertainty was quantified by one standard deviation (σ) for sensor uncertainties provided by the manufacturers (combined effects of temperature dependence, gain error, non-linearity), and one root mean square deviation (RMSD, Appendix B2) for uncertainties from comparison experiments (including the uncertainty of the external reference, where applicable).Due to their analogous role in variance statistics, σ and RMSD are both referred to with one σ for convenience.
After introducing the WSMA and outlining its physical properties, the sensor package for this study is presented.Following the analysis of the aircraft's dynamics, a toolbox is derived for the calibration of the 3-D wind vector measurement and assessment of its uncertainty.It consists of a wind tunnel study, uncertainty propagation and in-flight manoeuvres.The toolbox is used to customize a wind vector algorithm for use with the WSMA.To evaluate this procedure, the final calibration is applied to measurements in the ABL.Wind measurements from the WSMA are compared to simultaneous ground based measurements from sonic detection and ranging (SODAR) and tall tower sonicand cup anemometer and vane measurements.Based on three independent lines of analysis the overall uncertainty of the WSMA wind measurement is determined.

The weight-shift microlight aircraft
According to Joint Aviation Authorities, microlight aircraft are defined as aircraft with a maximum stall speed of 65 km h −1 and a take-off mass of no more than 450 kg.
Figure 1 shows the weight-shift microlight research aircraft D-MIFU.It consists of two distinct parts, the wing and the trike (the unit hung below the wing, containing pilot, engine and the majority of the scientific equipment).The weight-shift control system is enabled by the pilot's direct application of pitching or rolling moments to the wing via the basebar.Counterbalance is provided by the mass of the trike unit suspended below the wing.Simple procedures for certification of installations on an open aircraft allow a wide spectrum of applications as well as flexible installation of scientific equipment.At an operational airspeed of ≈ 100 km h −1 D-MIFU can carry a maximum of 80 kg scientific payload from 15 m above ground (a.g.l.) to 4000 m above sea level (a.s.l.).The full performance characteristics can be found in Junkermann (2001).D-MIFU consists of a KISS 450 cambered wing by Air Creation, France, and the ENDURO-1150 trike manufactured by Ultraleichtflug Schmidtler, Germany.Owing to its aeroelasticity, the tailless delta wing is termed a flex-wing, contributing ≈ 15% to the aircraft weight.The primary parts of the wing structure are the leading edges joined at the nose to the keel tube, which runs the root length of the wing (Fig. 1).Stretched over upper and lower surface is a high strength polyester sail.At a span of 9.8 m and keel length of 2.1 m, the wing provides a surface (S) of 15.1 m 2 .It is put under considerable internal loads during rigging, it's form and rigidity being ensured by cross-tubes, rods and a wiring system.The basebar in front of the pilot seat is linked to the keel via two uprights and tensioned flying wires.It provides transmission of pitch and roll forces and is the primary flight control (Gratton, 2001).In the hangpoint on the wing keel the trike is attached to the wing.Since the trike is free to rotate in pitch and roll without hindrance, there is no pendular stability.In this regard the relationship of trike to wing is similar to the relationship of a trailing bomb to its carrier (e.g.HELIPOD, Bange et al., 1999).However trike and wing are fixed in their longitudinal axis, i.e. in the heading direction.The trike does not contribute significantly to the WSMA's lift, but represents a large portion of weight (≈ 85%), drag, and provides all thrust through a 73 kW pusher engine-propeller combination.Flight stability in three axes is based on the offset of torques appearing at different locations on the wing (Cook, 1994).Torques result from wing aerodynamical effects, which sum nearest to neutral (slight nose-down torque for cambered wings) in one point along the wing's chord line, termed the wing's centre of pressure (Fig. 3).The centre of gravity, as far as the wing is concerned, is located in the hangpoint.The net aerodynamical torque is offset by an longitudinal lever arm between the centres of pressure and -gravity, determining the aircraft's trim speed (the airspeed at which the aircraft will fly steadily without pilot input).Moreover increasing airspeed will result in an aeroelastical flattening of the wing, which is in contrast to FWA.This in turn can alter the balance of torsional loads and with it the circulation about the wing (Cook and Spottiswoode, 2006).

Physical properties
The need to adapt wind calibration procedures designed for fixed-wing aircraft is mainly caused by two structural features of the WSMA.The trike, i.e. the turbulence measurement platform, is mobile for pitching and rolling movements below the wing.Therefore the trike-based flow-and attitude angles must be measured with high resolution, precision and accuracy.Moreover, wing aerodynamics depends on its aeroelasticity with airspeed, and varying flow distortion in front of the wing must be considered.The effects of these WSMA features are not necessarily independent of each other, and may have a different impact on the wind measurement depending on the aircraft dynamics at a particular time.Therefore the WSMA was equipped with motion sensors.On the trike these were placed in the fuselage (Inertial Navigation System, INS) and the wind measuring pressure probe (3-D acceleration), extending ≈ 0.7 m and ≈ 3.5 m forward from fuselage and aft-mounted propeller, respectively (Figs. 1 and 3).Further, the wing was equipped with motion sensors in the hangpoint (3-D acceleration) and atop the wing (3-D attitude).The INS is the most reliable motion sensor (Table 2), since it integrates the complementary characteristics of global positioning system (unbiased) and inertial measurement (precise).Position and velocity are calculated from inertial measurements of 3-D acceleration and 3-D angular rate, and matched with data from two global positioning units using a Kalman filter.The INS outputs 3-D vectors of position, attitude, velocity, angular rates and acceleration.
Airborne wind measurements are susceptible to distortion, since the aircraft itself is (a) a flow barrier and (b) must produce lift to remain airborne (Wyngaard, 1981;Cooper and Rogers, 1991).The aircraft's propeller, fuselage, and wing can be sources of flow distortion.Since the pressure probe is aligned on the longitudinal axis of fuselage and propeller, only little distortion from trike structural features is expected transverse to the pressure probe.Longitudinal and vertical distortions can be expected to carry continuously through the pressure probe location, since the probe is rigidly fixed to the trike.This however is not the case for distortion from the WSMA wing.While the wind measurement encounters lift-induced upwash from the wing (Crawford et al., 1996;Garman et al., 2008), the trike, and with it the pressure probe, has rotational freedom in pitch and roll towards the WSMA wing.In the following we will outline the dependences of upwash generation.The amount of lift (L) generated by the wing with the aircraft mass (m) and the vertical acceleration (a g,z ) in the geodetic coordinate system (GCS, superscript g, positive northward, eastward and downward) at the wing's centre of gravity (measured at, or dislocated to the hangpoint).During level, unaccelerated flight, lift essentially equals the aircraft's weight force, but is opposite in sign.The loading factor (LF ) during vertically accelerated flight is then LF = L mg , the ratio of liftto weight force with g = 9.81 m s −2 .Normalizing L for the airstream's dynamic pressure (p q ) and the wing's surface area (S) yields the unit-free lift coefficient (CL): with wing loading ( L S ).Moreover p q in Eq. ( 2) can be substituted by air density (ρ) and true airspeed (v tas ).In CL the wing's ability to generate lift is determined to be approximately linear with wing pitch.As a consequence of lift generation air rises in front of the wing, which is defined as upwash.Crawford et al. (1996) provide the following parametrization to calculate the upwash velocity (v w up ) for FWA: Here v w up is defined as the tangent on a circle with normalized radius n.Thereby n is the separation distance from the wing's centre of pressure to the position of the pressure probe, normalized by the effective wing chord (Fig. 3).The upwash attack angle ξ is then enclosed by n and the trike body axis X b .Since the wing is free to rotate in pitch and roll, v w up carries the orientation of the wing coordinate system (WCS, superscript w, positive forward, starboard, and downward).In Eq. (3) v w up varies inversely with n.Furthermore v w up can be expressed either directly proportional to v tas and CL, or directly proportional to relative airspeed ( ) and L S .Based on these relations a treatment for the wind measurement from WSMA is derived in Sect.4.1.

Instrumentation and data processing
Wind measurement by airborne systems is challenging.High resolution sensors are needed to determine the attitude, position, and velocity of the aircraft relative to the earth, as well as the airflow in front of the fuselage.The instrumentation involved in the wind measurement and data acquisition, including the respective manufacturers, is summarized in Table 1.A more detailed description of sensor characteristics and uncertainties is provided in Table 2, while respective locations are displayed in Figs. 1  and 2.
The principle is to resolve the meteorological wind vector from the vector difference of the aircraft's inertial velocity (recorded by the inertial navigation system) and the wind vector relative to the aircraft.To determine the latter, the aircraft was outfitted with a specially designed lightweight five hole half sphere pressure probe (5HP, e.g., Crawford and Dobosy, 1992;Leise and Masters, 1993).The 5HP provides ports of 1.5 mm diameter to directly measure dynamic pressure, static pressure, as well as the vertical and horizontal differential pressures (Fig. 2).To connect these ports to their respective pressure transducers polyetherketone tubings of ≤ 80 mm length and 1 mm inner diameter are used.At a typical true airspeed of 28 m s −1 only about 30% and 15% of the dynamic-and differential pressure transducer's range is exploited, respectively.This however enables the 5HP to be used also on faster aircraft such as motorized gliders, e.g. for inter-comparison measurements.100 Hz temperature and pressure signals pass through hardware (analogue) fourpole Butterworth filters with 20 Hz cut-off frequency to filter high-frequency noise.Filter slope and frequency were chosen to allow miniaturization and comply with the system's 15 Hz bottleneck filter frequency of the infra-red gas analyser for EC flux calculation (not used in this study).The filter leads to a phase shift in the signal of ≈ 20 ms, and the amplitude of a 10 Hz sine signal is reduced by < 1%.The INS data are stored in a standalone system at a rate of 100 s −1 .Remaining data streams for the wind computation are stored centrally at a rate of 10 s −1 by an in-house developed data acquisition system (embedded Institute for Meteorology and Climate Research data acquisition system, EIDAS).EIDAS is based on a ruggedized industrial computer and a real-time UNIX-like operating system.5 V analogue signals at ≥ 10 Hz pass through a multiplexer and A/D converter at a resolution of 16 bits.For oversampled variables (100 Hz) the resulting signal is block averaged. The

Wind vector
Approaches to compute the wind vector from fixed-wing aircraft are often similar in principle, though differ considerably in detail (e.g., Tjernstr öm and Friehe, 1991;Williams and Marcotte, 2000;van den Kroonenberg et al., 2008).Therefore, Appendix A details the specific implementation that was found suitable for the wind measurement with our weight-shift microlight aircraft.The system's calibration was arranged bottom-up, i.e. from single instrument to collective application.The procedure starts with the laboratory calibration of the individual sensors, continues with the characterization of flow around the 5HP, and concludes with the treatment of WSMA specific effects on the wind measurement.Finally three independent lines of analysis are used to quantify the overall system uncertainty: (a) uncertainty propagation through respective equations, (b) in-flight testing and (c) comparison of the measured wind vector with ground based measurements.

Calibration and evaluation layout
Prior 0.7% or σ = 0.03 hPa dynamic pressure.The airflow angles were varied by a calibration robot, the uncertainty in the wind tunnel angles was σ α, β < 0.1 • (equal to the alignment repeatability between 5HP and INS).The wind tunnel angles α, β are flight mechanical angles, defined with respect to the wind tunnel X axis.In contrast the 5HP measured airflow angles α and β are defined with respect to the aerodynamical X a axis (Appendix A).In order to allow comparison, the wind tunnel angles must be converted (Boiffier, 1998): The wind vector calculated from airborne measurements is very sensitive to uncertainties in its input variables.Calibration in laboratory and assessment in wind tunnel yield the basic sensor setup.However the effect of sensor and alignment uncertainties on the wind vector is not straightforward, and involves numerous trigonometric functions (Appendix A).To make the influence of individual measured quantities on the wind vector transparent, linear uncertainty propagation models were used (Appendix B1).The

Lake Starnberg, Germany
The first flight campaign took place from 19 June to 11 July 2008 over Lake Starnberg (47.9 • N, 11.3 • E).The lake is located in the foreland of the German Alps, that is a slightly rolling landscape (600-800 m a.s.l.) and mainly consists of grassland with patches of forest.The campaign focused on early morning soundings in the free atmosphere above Lake Starnberg.

Lindenberg, Germany
In a second campaign from 14-21 October 2008 comparison flights were carried out at the boundary layer measurement field of the German Meteorological Service, Richard-Aßmann-Observatory, near Lindenberg (52.2 • N, 14.1 • E).The area lies in the flat North German Plain (40-100 m a.s.l.), where land-use in the vicinity is dominated by an equal amount of agriculture and forests, interspersed by lakes.Flights in the atmospheric boundary layer were conducted under near-neutral stratification (stability parameter 2).However due to the WSMA's low wing loading the wind measurement might be especially susceptible to the influence of thermal turbulence.

Xilinhot, China
To extend the operational range, an additional dataset under conditions approaching free convection ( z L −0.2) was included in this study: From 23 June to 4 August 2009 an eddy-covariance flux campaign was performed over the steppe of the Mongolian Plateau.The hilly investigation area south of the provincial capital Xilinhot, Inner Mongolia, China (43.6 • N, 116.7 • E, 1000-1400 m a.s.l.) is covered by semi-arid grassland, intersected by a dune belt.
A summary of all flights as well as an overview of the synoptic weather conditions is provided in Table 3 them serve to isolate independent parameters for the flow distortion correction, while the last one is used to compare aircraft to ground based measurements.The patterns are used for the actual calibration and evaluation of the wind measurement in Sect. 4.

Racetrack pattern
The first type of flight pattern consists of two legs parallel to the mean wind direction at constant altitude (one pair), one upstream leg (subscript +) and one downstream leg (subscript −).For any racetrack pair flown at constant true airspeed (v tas ), the (assumed homogeneous and stationary) mean wind (v m ) cancels out (Leise and Masters, 1993;Williams and Marcotte, 2000): (5) In this way the INS measured ground speed (|v m gs |) can be used to minimize the difference ||v m gs | − v tas | by iteratively adjusting dynamic pressure in Eq. (A8).This yields an inverse reference for dynamic pressure, which is solely based on INS data.Since the temperature and static pressure sensitivities of Eq. (A8) are two orders of magnitude lower than that of the dynamic pressure (Table 5), the inverse reference can now be used to adjust the 5HP measured dynamic pressure to in-flight conditions.A total of 14 racetrack pairs at airspeeds ranging from 21 to 32 m s −1 were conducted in the calm and steady atmosphere above the ABL (Table 3).

Wind square pattern
The second type of flight pattern consists of four legs flown at constant altitude and constant v tas in the cardinal directions (north (N), east (E), south (S), west (W)).Assuming that the flights were carried out in a homogeneous and stationary wind field, the measured horizontal wind components (v m u , v m v ) should be independent of aircraft heading, i.e. constant at each side of the wind square.With it a potential offset in β can be determined: The offset in β is changed iteratively, until the standard deviation of v m u and v m v throughout a wind square is minimized.For flights above the ABL, in addition the vertical wind component can be expected to be negligible.A potential offset in α can be determined in a similar fashion to β, however, under the constraint of minimizing the absolute value of the vertical wind component (v m w ).The wind square pattern further allows to estimate the uncertainties of v tas and β: Since the flight legs are aligned in the cardinal directions, along-track wind components (v are predominantly sensitive to errors in v tas .Cross-track wind components (v m v (N, S), v m u (E, W)) are predominantly sensitive to errors in the β.Thus, errors in v tas and β can be estimated as: Six wind squares were flown above the ABL at airspeeds from 23 to 29 m s −1 (Table 3).

Variance optimization pattern
The third type of flight pattern is a straight and level ABL sounding, intended for EC flux measurement.
The assumption made here is that errors in the flow angles increase the wind variance.In contrast to the previous two patterns, this method does not imply homogeneity or stationarity.It can therefore be applied even in the presence of thermal turbulence, i.e. in the convective ABL (Tjernstr öm and Friehe, 1991;Khelif et al., 1999;Kalogiros and Wang, 2002a). of the mean vertical wind.Here it is expected that, for a sufficiently high number of datasets above approximately level terrain, v m w approaches zero.12 straight and level ABL soundings (or 360 km of flight data, Table 3) at airspeeds from 24 to 28 m s −1 between 50 and 160 m above ground were used for this variance optimization.

Vertical wind specific patterns
The fourth type of flight pattern specifically addresses errors in v m w , the wind component crucial for EC flux applications.Based on Lenschow (1986) straight-flight calibration patterns were performed above the ABL.These are intended to assess and minimize the possible influence of aircraft (in our case WSMA) trim and dynamics on v m w .At airspeeds ranging from 21 to 32 m s −1 a total of five vertical wind (VW) specific flights, divided into three sub-patterns, were utilized in this study (Table 3): VW1 (Level acceleration -deceleration): Whilst the engine's power setting was gradually varied, the wing pitch (and with it lift coefficient) was adjusted to maintain flight altitude.With this pattern the influence of aircraft trim on v m w can be determined.
VW2 (Smooth oscillation): Starting from level flight the power setting was slowly varied, while the wing pitch was adjusted to maintain constant v tas .In consequence, the aircraft ascended and descended about the mean height, while CL remained approximately unchanged.VW2 was used to assess the influence of wing pitch and aircraft vertical velocity on v m w .
VW3 (Forced oscillation): Starting from level flight the wing pitch was forcibly alternated.The aircraft ascended and descended around the mean height, while power setting remained unchanged.In response aircraft accelerations and velocities, and with it the airflow around the aircraft, changed.VW3 was used to assess the integral influence of vertically accelerated flight on v m w , for flights in the ABL e.g.provoked by thermal turbulence.

Comparison to ground based reference measurements
The fifth and last type of flight pattern is a series of comparison measurements between WSMA and ground based measurements.These were carried out at the boundary layer measurement field of the German Meteorological Service, Richard-Aßmann-Observatory, near Lindenberg.The lower part of the ABL was probed by a 99-m tower and a SODAR with their base at 73 m a.s.l.The 99-m tower provided cup measurements (10 min averages) of wind speed at four levels (40, 60, 80, and 98 m a.g.l.), the wind direction was measured with vanes at heights of 40 and 98 m a.g.l.(10 min averages).Sonic anemometers mounted at the tower provided turbulent wind vector measurements at 50 and 90 m a.g.l.The SODAR wind vector profiles (15 min averages) reached, at increments of 20 m, from 40 to 240 m a.g.l.In addition a reference for static pressure was provided at 1 m a.g.l.17 cross-shaped patterns (van den Kroonenberg et al., 2008), with flight legs of 3 km centred between tower and SODAR, were performed at 24 and 27 m s −1 airspeed (Table 3).The flights were carried out at the approximate sounding levels of tower and SODAR (50, 100, 150, 200 and 250 m a.g.l.).
This allows a direct comparison of WSMA and ground based measured wind components.Aircraft and sonic wind measurements were filtered using the stationarity test for wind measurements by Foken and Wichura (1996).SODAR, cup and vane data were stratified for the best quality rating assigned by the German Meteorological Service.Simultaneous wind data of WSMA and ground based measurements were accepted for comparison only if they agreed to within ±20 m height above ground (which equals ≈ 2σ of variations in WSMA altitude).This data screening resulted in a total of 20 data couples (between WSMA and cups/vanes, sonics and SODAR) for v m uv , and 19 data couples for v m w .Compared to cups/vanes, sonics and SODAR, the WSMA soundings were on average higher above ground by 0.1 ± 5.5, 8.7 ± 5.6, and 0.5 ± 5.

Application to weight-shift microlight aircraft
To understand operational requirements for setup and calibration of the wind vector measurement, aircraft attitude and dynamics were assessed for a straight and level boundary layer flight (Table 3, variance optimization flight on 31 July 2009).Variations in true airspeed and aircraft vertical movement (Fig. 4) were mainly resulting from thermal turbulence (labile stratification, stability parameter z L ≈ −0.9).Attitude angles (Θ b , Φ b ) indicate constant upward pitching and anti-clockwise roll of the trike, respectively.Pitching as well as rolling increase in magnitude with v tas , i.e. power setting of the engine.The pitching moment can be understood as a result of imbalanced increase of aerodynamic resistance of wing (high) and trike (low) with v tas .This is confirmed by an estimate of the attack angle (α), which shows fewer variation due to alignment with the streamlines, though alike Θ b increases with v tas (≈ 0.4 ).The rolling moment can be understood as counter-balance of the clockwise rotating propeller torque.In addition side-slipping of the trike over its port side was detected from an estimate of the sideslip angle (β), increasing at a rate of ≈ −0.6 • per m s −1 with v tas .The operational range in α and β estimates were found ≈ |15 • |, averaging to 6.0±1.8 • and −5.5±3.2 • , respectively (Fig. 4).Following the lift Eq. ( 2), wing pitch decreases with v tas .That is, with increasing v tas the noses of wing and trike approach each other.Wing roll does not display dependence on v tas , i.e. no counter reaction on propeller torque or trike roll.The wing loading factor (LF ) was found to vary within a range of σ ≈ 0.1 g (Fig. 4), from which the upwash variation in front of the wing can be assessed.
Using five hole probe measured v tas in Eq. ( 3) the upwash velocity (v w up ) at 5HP location was determined to 1.52 ± 0.19 m s −1 .D-MIFU is travelling at low airspeed and has a small relative separation (n) between wing and 5HP.Both factors lead to an increase in v w up .Various research aircraft have been assessed with regard to upwash generation (Crawford et al., 1996), compared to which D-MIFU ranges mid-table.This can be ascribed to the low wing loading, which is a fraction of those of fixed-wing aircraft, and decreases v w up .Wing loading, and with it v w up , are directly proportional to vertical acceleration and aircraft mass in Eq. ( 1).Hence σ ≈ 10% variation in LF (Fig. 4) accounts for most of the variance in v w up .In addition aircraft mass can vary during the flight due to fuel consumption (±4%) and among measurements due to weight differences of pilots (±2%).Due to the trike's rotational freedom, upwash about the wing's centre of pressure can partially translate into along-and sidewash (longitudinal and transverse to the trike body, respectively) at the 5HP location in the trike body coordinate system (BCS).Mean aerodynamic chord theory yields the centre of pressure's position of the wing within 0.2 m or < 10% chord length of the centre of gravity.Assuming the centres of pressure and gravity to coincide, the pitch difference between wing and trike can be neglected, and v w up is easily transformed into the BCS: The transformation Eq. (A13) was carried out about zero heading difference, the upwash attack angle (ξ = −41.9± 0.3 • ), and the roll difference between wing and trike.Wing upwash net effect at the 5HP location was then directed forward, right and upward with 1.01 ± 0.13 m s −1 , 0.12 ± 0.13 m s −1 , and −1.12 ± 0.14 m s −1 in trike body coordinates (Fig. 5).

Wind measurement calibration
The sensitivity of the wind model description was analysed by linear uncertainty propagation models (Appendix B1).The first model in Eq. (B1) permits to express the sensitivity of the wind computation as a function of attitude angles, flow angles and true airspeed.It was carried out for two reference flight states at v tas = 27 m s −1 .In State 1 attitude and flow angles were assumed small (1 • ), as it would be typical for calm atmospheric conditions.In State 2 attitude (10 • ) and flow angles (−15 • ) were approximately increased to their 95% confidence interval extremes during soundings in the convective ABL (Fig. 4).Uncertainties of 1 • and 0.5 m s −1 were assumed for angular-and v tas measurements, respectively.From State 1 it can be seen that the major uncertainty in the horizontal wind components (v m uv ) originates from v tas , sideslip angle (β) and heading angle (Ψ), where β and Ψ carry similar sign and sensitivity (Table 6).On the contrary, the vertical wind component (v m w ) is similarly sensitive to 1321 was assumed as reference state, parametrized as 3.7 hPa dynamic pressure (p q ), 21 • C static temperature, 850 hPa static pressure, and 9.5 hPa water vapour pressure.Derived sensitivities indicate a dominant dependence of α and β on their respective differential pressure measurement, as well as on p q (Table 5).In case of v tas sensitivity on the p q measurement clearly prevails.This procedure allows to separate, and consequently further concentrate on, the variables most sensitive to the wind vector calculation.For v m w , the central wind component in the eddy-covariance flux technique, the variables to focus calibration effort on are α, Θ and p q .Likewise correct readings of β, p q and Ψ are of greatest importance for the calculation of v m uv .Due to the same adiabatic heating effect (ram rise) as in Eq. (A9), the temperature measured by the thermocouple might be slightly higher than the static temperature intrinsic to the air.At the same time the measured temperature is smaller than the total temperature at the stagnation point on the tip of the 5HP, since the air at the thermocouple is not brought to rest.Even at peak v tas = 30 m s −1 of the WSMA the ram rise of 0.4 K does not surpass the overall uncertainty of the thermocouple (Table 2).As a practical advantage of the slow flying WSMA therefore no fractional "recovery factor" correction as known from faster fixed-wing aircraft needs to be introduced (Trenkle and Reinhardt, 1973).Using above sensitivity analysis the associated uncertainty amounts to 0.02 m s −1 in v tas .According to the parametrizations ( 5) and ( 7) in Foken (1979) the error caused by solar radiation intermittently incident at the unshielded thermocouple was estimated to be < 0.05 K. Since no radiation shielding was applied, both temperature errors were included in the uncertainty propagation (Table 5).The actual calibration sequence was organized in seven steps.To reduce scatter and computation time, 10 Hz aircraft data were block averaged to 1 Hz for steps D-G: Step A -Laboratory: Initial calibration of all A/D devices.
Step B -Wind tunnel: Assessment of attack-(α) and sideslip angle (β) and first correction of dynamic pressure (p q ).
Step C -Tower fly-bys: Adjustment of static pressure (p s ).
Step D -Racetracks: Second p q correction.
Step E -Wind squares: First estimate of α and β correction.
Step F -Variance optimization: Second estimate of α and β correction.
Step G -Vertical wind treatment: Relation of measured upwash to lift coefficient, iterative optimization with step E-F.
Step A -Laboratory Calibration coefficients from laboratory and all successive steps are summarized in Table 4. Residuals are propagated together with sensor uncertainties as provided by the manufacturers.The resulting uncertainties are summarized in Table 5.

Step B -Wind tunnel
Since the wind tunnel was too small for the complete aircraft, the setup was reduced to the five hole probe and the aircraft's nose-cap.Therefore the actual flow distortion during flight was not included in this step.For angles of attack (α) and sideslip (β) within ±17.5 • the first-order approximations Eqs. with a Pearson Coefficient of determination R 2 > 0.99.Residuals did not scale with true airspeed, but resulted from incomplete removal of α and β cross dependence (Fig. 6).Yet the probe design was working less reliably with the exact solutions for flow angle determination (e.g.Eq. ( 7) in Crawford and Dobosy, 1992).On the other hand use of a calibration polynomial as suggested by Bohn and Simon (1975) has the advantage that it does not assume rotational symmetry.A fit of the calibration polynomial yielded high precision, however did not prove robust for in-flight use and was discarded.For dynamic pressure (p q,A , subscript upper-case letters A-G indicating calibration stage), offset (0.22 hPa) and slope (1.05) were corrected from zero working angle measurements.Applying the pressure drop correction Eq. (A7) thereafter reduced the scatter significantly, in particular for elevated working angles (Fig. 6).Below 20 • working angle (≈ 15 • flow angle) p q,B was slightly overestimated, above this a loss of only ≈ −0.1 hPa remained.RMSD and BIAS amounted to 0.042 and 0.012 hPa, respectively, with R 2 = 0.999.

Step C -Tower fly-bys
A wing induces lift by generating lower pressure atop and higher pressure below the airfoil.Since the five hole probe is measuring at a position being located below the wing, the static pressure (p s ) measurement is potentially biased.Though sensitivity of the wind computation on p s is low (Table 5), correct air densities are required for EC computations.An offset adjustment was estimated to −2.26 ± 0.43 hPa from comparison with tower based measurements (Table 3).No dependence of the adjustment on true airspeed or lift coefficient could be detected.This can most probably be attributed to the small v tas range of the WSMA.

Step D -Racetracks
For racetrack and wind square flights, inhomogeneous flight legs were discarded using the stationarity test for wind measurements by Foken and Wichura (1996).Respective optimality criteria Eqs. ( 5)-( 6) were applied to 1 Hz block averages of the remaining legs.The dynamic pressure inverse reference from racetracks suggests an offset (0.213 hPa) and slope (1.085) correction.Without considering additional dependences, the fit for different power settings is well determined with 0.115 hPa residual standard deviation and R 2 = 0.974.We have seen that the upwash (v w up ) in front of the wing of the WSMA is effective forward, right and upward at the 5HP location in body coordinate system (Fig. 5).That is, the magnitude of dynamic pressure (p q,B ) measured at the 5HP tip, and with it the calculated true airspeed, is reduced by v w up .Therefore the slope correction from racetracks was used to account for the loss in p q,B magnitude due to upwash in front of the wing.The suggested offset was considered as inversion residue of atmospheric inhomogeneities during the racetrack manoeuvres, and consequently discarded.

Step E -Wind squares
Over all wind square flights the optimality criteria for horizontal and vertical wind components were averaged.Offsets for α (0.005 rad) and β (−0.012 rad) were iteratively adjusted to minimize this single measure (Table 3).

Step F -Variance optimization
From the variance optimization method a second set of offsets for α (0.017±0.003 rad) and β (−0.014 ± 0.001 rad) was found.The optimality criteria were applied to each leg individually and the offsets determined were averaged.The estimates differ from those for the wind squares by 0.6 • for α and by 0.1 • for β.While the deviation for β lies within the installation repeatability, the deviation for α corresponds to ≈ 0.3 m s −1 uncertainty in the vertical wind (Table 6).The wing's upwash in Eq. ( 3), and its variation due to different aircraft trim was considered as one possible reason for this deviation: While flying level with similar power setting, flights in denser air in the atmospheric boundary That is CL in Eq. ( 2) is inversely proportional to air density.For flights in the ABL, in particular thermal turbulence is likely to additionally alter the wing loading, and with it CL in Eq. ( 2).
Step G -Vertical wind treatment Among all the wind components the vertical wind measurement is of prevailing importance to reliably compute eddy-covariance fluxes.Correspondingly its assessment and treatment is the centrepiece of this calibration procedure.To disentangle the comprehensive sequence of assessment and treatment, Step G is further divided into five sub-steps: Step G1 -Net effect of aircraft trim and wing loading.
Step G2 -Reformulation of the upwash correction.
Step G3 -Parametrization of aircraft trim and wing loading effects.
Step G5 -Iterative treatment of cross dependences.

Step G1 -Net effect of aircraft trim and wing loading
The net effect of changing aircraft trim and wing loading was investigated with the likely approaching zero above the ABL, measured variations in v m w are referred to as "measured upwash".As opposed to the parametrization by Crawford et al. (1996) for fixed-wing aircraft, measured upwash at the five hole probe location is highest during fast flight at low CL.Yet, also in contrast to FWA, the WSMA's wing-tip and trike nose approach each other with increasing airspeed (Sect.4).The wing's centre of pressure is within < 10% chord length of the centre of gravity.Considering this distance, wing pitching by −5 • would result in a decrease of the normalized distance between centre of pressure and 5HP (n), by ≈ −1%.Though modelled upwash inversely varies with n in Eq. ( 3), the approach of wing and trike alone can not explain the upwash phase inversion.On the other hand, the wing flattens aeroelastically with true airspeed.That is, with increasing v tas the wing's cambering and with it the relative lift generation is attenuated.Therefore the wing upwash of a WSMA can neither be parametrized nor corrected with the Crawford et al. (1996) model alone.Garman et al. (2008) on the other hand proposed to correct for upwash by considering the actual wing loading factor (LF ), which carries information on the aircraft's vertical acceleration.In contrast to the study of Garman et al. (2008), WSMA weight, fuel level as well as dynamic pressure (p q ) are known.Therefore CL can be directly determined in Eq. ( 3) and used instead of LF.This has the advantage that additional information on the aircraft's trim is included: As formulated in Eq. ( 2), p q carries information on v tas at given air density.Over eight independent flights of patterns VW1, VW2 and VW3 measured upwash correlated with CL (−0.53±0.16),change in v tas (0.57±0.16), and wing pitch (−0.50±0.20).
Step G2 -Reformulation of the upwash correction Crawford et al. (1996); Kalogiros and Wang (2002b) have shown that the upwash Eq. ( 3) can be reformulated as a function of CL in the 5HP measured attack angle (α).
Yet, as opposed to FWA, the WSMA is defined in two different coordinate systems, those of the wing (upwash) and the trike (5HP measurement, Fig. 3).Therefore an 1327 upwash correction in α would not explicitly consider the mobility of the trike in the wing circulation.As shown above only minor uncertainty would be introduced for pitching movements, though rolling movements and their possible influence would be left out.Consequently wind measurements during horizontal manoeuvres would not be covered, which however are not the subject of this study.In return correcting the upwash in α yields several advantages compared to explicitly modelling and subsequently subtracting the upwash: one explanatory variable is sufficient to explain the upwash variability effectively incident at the 5HP.With it a potential phase shift between variables measured in the wing and the trike body coordinate systems, as well as additional coordinate transformations are omitted.Therefore the upwash variability was treated for straight and level flight (such as during EC soundings) using a linear model in α:

Discussion
with α ∞ the (desired) free air stream angle of attack, α A being the 5HP derived attack angle, and α upw an additive attack angle provoked by the upwash with α upw,off and α upw,slo being its constant part and sensitivity on CL, respectively.

Step G3 -Parametrization of aircraft trim and wing loading effects
For vertical wind specific flights (VW) above the ABL, α in Eq. (A11) was changed iteratively until yielding a vertical wind (v m w ) of zero.Subtracting this inverse reference of α ∞ from α A gives us an estimate of α upw .To reduce scatter, α upw was averaged after binning over increments of 0.01 CL.From this binned and averaged data α upw,off and α upw,slo were obtained with a linear fit (Fig. 8).Scatter for the level acceleration-deceleration (VW1) flight and the forced oscillation ( VW3 the accelerating-and decelerating legs.Non-binned values of the VW3 flight are considerably more scattered than for VW1.This can be attributed to the rising and sinking process of the aircraft and changing flow regimes about the wing during load change at the turning points.Fitted coefficients differed slightly between the two flights.The analysis was continued with the coefficients of the better determined VW1 flight (R 2 = 0.85), which amount to α up,off = 0.031 rad and α upw,slo = −0.027rad.
That is α A would be overestimated by ≈ 1.7 • if the WSMA could fly at zero lift.The effect decreases with slower flight at a rate of ≈ −1.7 • per CL.The correction reduces the vertical wind fluctuations for systematic deviations resulting from varying wing trim (53%, relative to the bias-adjusted overall fluctuation) and wing loading (16%) for above named VW1 and VW3 flights, respectively.For the VW3 flight (Fig. 7) the decorrelation of v m w with v tas improves from 0.79 to −0.11, and the decorrelation with wing pitch improves from −0.78 to 0.17.Assuming zero vertical wind, RMSD and BIAS slightly improved from 0.17 and 0.15 m s −1 to 0.13 and −0.11 m s −1 , respectively.Lenschow (1986) proposed a 10% criteria for the effect of the aircraft's vertical velocity It is employed as an operational limit by the Research Aviation Facility of the US National Centre for Atmospheric Research (NCAR, Tjernstr öm and Friehe, 1991).Using the upwash correction this measure was improved from 3.8% to 2.7% (σ).A slight trend in v m w remains.The correction was also applied to two smooth oscillation (VW2) patterns.The flight on 24 June 2008 was conducted in less calm air and two different power settings were applied (Fig. 9).The correction changed overall RMSD and BIAS from 0.26 and 0.13 m s −1 to 0.25 and −0.13 m s −1 , respectively.That is the quality measures did not indicate significant improvement, but the vertical wind BIAS was inverted.However after correction the change in power settings (4800-5000 s slow, 5200-5400 s fast) did not alter the offset in v calm air (Fig. 9).Here our correction leads to a change in RMSD and BIAS from 0.22 and 0.20 m s −1 to 0.09 and −0.02 m s −1 .After correction the dependence on vertical aircraft movement increased slightly from 7.7% to 8.3% (σ), which still well agrees with the limit used by NCAR.

Step G4 -Parametrization of offsets
We learned from the VW3 pattern (Fig. 7), that calculation of v m w was improved for flights which include vertical accelerations.This is an important step, since due to its low wing loading the WSMA is more susceptible to e.g.convective gusts in the ABL than large FWA's.These gusts also transport the scalars to be investigated, i.e. vertical wind and scalar quantity are correlated in the gust.Not accounting for the negative correlation of measured v m w with CL would decrease the magnitude of fluctuations in v m w , such spuriously decreasing fluxes derived from the airborne measurements.From the VW2 pattern we have seen that the decorrelation of v m w with v tas was improved (Fig. 9).Also v m w was proven independent of slow aircraft rising and sinking manoeuvres, such as they are occurring in the ABL while following topographic features at constant altitude above ground.After applying the correction, BIAS in v m w was negative, ranging from −0.13 to −0.02 m s −1 . Assuming independence of v m w from v tas , the detected BIAS depends on α up,off in Eq. ( 7).Both, α up,off and α upw,slo were determined using the VW1 flight on 25 June 2008 during ambiguous cyclonality atop and below measurement altitude (Table 3).In Fig. 8 the determination of α upw,slo depends on the change of CL, while the offset α up,off depends on the ambient vertical wind.During the inverse reference procedure v m w was forced to zero while, e.g. in an anticyclone, subsidence occurs.In such a situation α up,off would be underestimated.During the VW flights on 24 and 25 June 2008, cyclonality and BIAS in v m w both changed.While α upw,slo is insensitive, no constant α up,off could be determined from the VW flights.At this point the variance optimization flights in the ABL are of importance.
Assuming constant ABL height (approximately fulfilled for noontime EC soundings) the second optimality criteria states that due to mass conservation v m w approaches zero for a sufficiently high number of datasets.With it α up,off was determined directly from ABL flights.Using the first variance optimization optimality criteria, i.e. the minimization of the wind variance, also α and β slopes were tested.

Step G5 -Iterative treatment of cross dependences
An approach similar to Eq. ( 7), the explanation of upwash in α, was used to explain sidewash in β: using the calibration criteria of the wind square flights for parametrization.Compared to the upwash parametrization, sidewash was found to be modest (β upw,off = −0.004rad) and less sensitive regarding CL (β upw,slo = −0.010rad, Table 4).This is in line with the first attempt to resolve the circulation around a FWA wing and trike movement independently (Fig. 5).Using Eq. ( A11) cross dependence occurs between the parametrizations in α and β.This problem was solved by iterating the optimality criteria for wind square, vertical wind, and variance optimization flights in sequence.The order of this sequence, i.e. first optimizing for the horizontal wind components (v m uv ), then for the vertical wind component (v m w ), was chosen due to their different order of magnitude and importance for EC application.Spurious contamination with v  4.

Wind measurement evaluation
After completing all calibration steps, the wind measurement with the WSMA was evaluated.The evaluation was carried out in three lines of analysis, (a) uncertainty propagation, (b) wind square flights, and (c) comparison to ground based wind measurements.For a true airspeed of 27 m s −1 the propagation of uncertainties in sensors (flow angle differential pressures, dynamic-and static pressures, static temperature, and water vapour pressure), their basic calibration and wind model description yield an uncertainty (σ) of 0.76 • , 0.76 • , and 0.34 m s −1 in attack angle (α), sideslip angle (β) and true airspeed, respectively (Table 5).Feeding the input uncertainty Eq. (B1) with these quantities extends the uncertainty propagation to the wind components (Table 6).The input error is formulated worst case, and parametrized at the extremes of the attitude and flow angle 95% confidence intervals.In addition the uncertainty of the inertial navigation system (0.02 m s −1 ) was considered in the wind vector Eq.(A1).This allows to estimate the maximum potential uncertainty by sensor setup and wind model description.The results for the maximum overall uncertainty bounds are 0.66 and 0.57 m s −1 for the horizontal (v m uv ) and vertical (v m w ) wind components, respectively.Figure 10 shows the results of all wind square flights.For wind velocities > 2 m s −1 v m uv determined for individual legs deviate less than 10% from the average for the entire square.The residuals did not scale with the average wind velocity, to a greater degree they are likely to result from an incomplete removal of wind field inhomogeneities over the 12 km long flight paths.Therefore a horizontal wind velocity of 2 m s −1 can not be considered as a detection limit for wind measurements from WSMA.Also no systematic deviation for aircraft orientation could be detected.However v m w shows a slight sensitivity of −0.05 on v tas (R 2 = 0.46).Using the cardinal direction evaluation criteria Eq. ( 6), RMSD in α ∞ , β ∞ and |v m tas | were computed to 0.31, 0.33 and 0.26 m s −1 , respectively.These compare well to the results from the uncertainty propagation (Tables 5 and 6), which amount to 0.31, 0.36 and 0.34 m s −1 for α A , β A and v tas , respectively.
Figure 11  based wind measurement was further quantified by calculating RMSD and BIAS for all measurements accepted for the comparison (Table 3).The impact of calibration steps C-G on these measures is displayed in Fig. 12.The measurement of the horizontal wind components (v m uv ) was mainly improved (14%, relative to the initial uncertainty) by means of the in-flight dynamic pressure correction (step D).After the wind square analysis (step E) the measurement was not further improved nor deteriorated.Yet the vertical wind measurement (v m uv ) receives its greatest improvement (31%) during steps F-G, i.e. variance optimization and vertical wind specific patterns: During these steps BIAS and dBIAS, i.e. its dependence on v tas , were reduced.In contrast to the findings from the wind square analysis, with a sensitivity of ≈ +0.05 a slight positive dependence of all wind components on v tas remained.Considering all data couples between WSMA and ground based measurements, RMSD and BIAS amount to 0.50 and −0.07 m s −1 for v m uv and 0.37 and −0.10 m s −1 for v m w , respectively.In addition to the above mentioned outlier, two more suspects were identified for the flight on 18 October 2008, again concurrent for v m v and v m w .A possible explanation is the increased land surface heterogeneity sensed by the aircraft while travelling through the wind field.On the northern and western limbs of the aircraft cross pattern, forest patches of ≥ 200 m edge length interrupt the flat arable land immediately upwind.Therefore WSMA measurements can include turbulence and wake effects generated at the forest edges.In contrast tower measurements are not subject to comparable roughness changes until ≈ 2 km in upwind direction.Omitting the three outliers from the statistics, RMSD and BIAS between WSMA and ground based measurements improve to 0.39 and −0.11 m s −1 for v m uv and 0.27 and −0.10 m s −1 for v m w , respectively.

Discussion
Distortions of the wind measurement originating from the aeroelastic wing and trike structural features were successfully handled for straight, vertically accelerated flight.Yet the treatments integral to Eqs. (A7), ( 7) and ( 8) still leave room for improvement: Compared to ground based measurements the aircraft underestimated the wind components ≈ −0.1 m s −1 .A possible reason could be the discarded offset during the dynamic pressure (p q ) in-flight calibration (Sect.4.1).Rather forcing the linear fit to zero would slightly enhance the slope of p q and with it compliance to the aircraft's inertial speed.
During the wind square and comparison flights contradictory sensitivities (regression slope −0.05 versus +0.05) of the wind components on the true airspeed were found.For the variability in v tas during a thermally turbulent flight in the atmospheric boundary layer (σ = 1.24 m s −1 , Fig. 4) this corresponds to ±0.06 m s −1 deviation in the wind components.Since this deviation is one order of magnitude lower than the system's input uncertainty, it was not further treated.
The lift coefficient is used as sole explanatory variable in the linear calibration models Eqs. ( 7) and ( 8).This treats the influence of aircraft trim (i.e.dynamic pressure) and vertical acceleration (i.e.loading factor) on the wind measurement with similar sensitivity.The study by Visbal and Shang (1989) however shows that the flow field response of airfoils to pitch oscillations depends on the excitation frequency.This indicates that an independent upwash correction is desirable for steady state and dynamic flight modes.Such procedure would however require infinitely more in-flight data and analytical effort in order to isolate independent parameters.In return it could address forenamed dependence of the wind components on v tas and additionally allow for superior wind measurements during horizontal manoeuvres.

Conclusions
We have shown that carefully computed wind vector measurements using a weightshift microlight aircraft are not inferior to those from other airborne platforms.A 10% limit of contamination of the wind components by the aircraft movement, as used by the US National Centre for Atmospheric Research, was fulfilled even during severe vertical  (Khelif et al., 1999): where ε = 0.622 is the ratio of molecular weight of water vapour to that of dry air, and e is the 5HP measured water vapour pressure.Once derived, the scalar quantity v tas has to be transformed into a vector quantity.
This can be achieved by defining the aerodynamic coordinate system (ACS, superscript a, positive forward, starboard, and downward), which has its origin at the 5HP tip.In this coordinate system the true airspeed vector has the components v a tas = (−v tas ,0,0).Since the ACS is aligned with the streamlines its orientation however varies in time.Therefore v a tas is transformed into a fixed coordinate system, that is the trike body coordinate system (BCS, superscript b, positive forward, starboard, and downward) with its origin in the INS.This is accomplished by successive rotations about the vertical axis Z a and the transverse axis Y a .Following Lenschow (1986) the rotations can be summarized in the operator with the 5HP derived airflow angles of attack α and sideslip β, and the normalization factor D as derived in Eqs.(A5)-(A7).Since v tas a carries all its information in the first 1338 vector component, it is sufficient to apply this transformation to −v tas in the wind vector Eq.(A1).Now the wind vector is known in the orientation of the BCS, yet with its origin still at the 5HP tip as initially defined in the ACS.To allow for the vector difference as required in the wind Eq. (A1) we have to account for the displacement of ACS origin (5HP tip) relative to the BCS origin (INS).This is done by considering the lever arm correction vector (Williams and Marcotte, 2000): A last step remains to obtain v m tas for use in the wind Eq. (A1), that is the transformation of the true airspeed vector from the BCS into the MCS.This is achieved by a first transformation into the geodetic coordinate system (GCS, superscript g, positive northward, eastward and downward) via successive rotations about the X b , Y b , Z b axes (Lenschow, 1986).From there the wind vector is permutated into the MCS (positive eastward, northward and upward).The transformations can be summarized in the operator  2).Uncertainty propagation is however required for v m tas , since 12 measured quantities are merged during its calculation.The magnitude of the lever arm correction Eq. (A12), and with it possible uncertainty from this source, is two orders lower than v m tas .It can therefore be neglected in the uncertainty propagation, which leaves nine measured quantities.By preprocessing Eqs.(A5)-(A10) these are further condensed to three measured quantities and three derived variables (see next paragraph for respective uncertainty propagation).Modified after V örsmann (1985) the input uncertainty of the v m tas measurement can then be calculated from a linearised uncertainty propagation model in the vector components v m tas,c (c = u, v, or w): Such a procedure is conservative, since it assumes uncertainty interference, but not cancellation.It yields the maximum possible uncertainty triggered by the combined effects of σf i .The derivatives were further simplified by small-angle approximation.This simplification allows to express the input uncertainty with sign and sensitivity as a function of Ψ b , whereas the full form yields the maximum absolute input uncertainty for different flight states.
In analogy uncertainty propagation models were formulated for the three derived variables α in Eq. (A5), β in Eq. ( A6) and v tas in Eq. (A8).These permit to express the actual uncertainties originating from the six remaining directly measured quantities, i.e. both flow angle differential pressures, dynamic-and static pressures, static temperature, and water vapour pressure.
With this setup the overall uncertainty at each stage of the wind calculation procedure can be evaluated through Gaussian uncertainty propagation (e.g., Taylor, 1997): with N being the number of (assumed linear and independent) uncertainty terms contributing to the stage investigated.

B2 Uncertainty measures
For applications in the atmospheric boundary layer the comparison to a reference standard can yield an integral measure of confidence under varying conditions (e.g., Vogt and Thomas, 1995;Mauder et al., 2006).Therefore this study employs two basic bivariate criteria for the comparison of wind components.These are the root mean square deviation (RMSD) and bias (BIAS) between sample and reference (ISO, 1993): with N being the number of data couples R i and A i , R i being the i th reference observation and A i the i th observation by aircraft sensors, sampled simultaneously.RMSD is also called comparability and is a measure of overall uncertainty.BIAS is the systematic difference between the mean of the measurements and the reference.These criteria were not normalized, since no consistent dependence on the wind magnitude or the aircraft's true airspeed was found.

Appendix C Notation
Scalars and vector components are displayed in italics, vectors are displayed in bold italics, and matrices are displayed in bold roman typeface, respectively.Where applicable coordinate systems and respective axes are indicated by superscripts, whereas subscripts are used as specifiers.

C1 Operators
[M]   3. Flight campaign summary, respective locations are Lake Starnberg (ST), Lindenberg (LI), and Xilinhot (XI).Synoptic wind direction and cyclonality (CYC) were retrieved from the objective weather type data base of the German Meteorological Service (Bissolli and Dittmann, 2001).The XI flight on 31 July 2009 was supplemented with publicly available data from the US National Centre for Environmental Prediction.Prevailing wind direction throughout all flight days was south-west, anticyclonic and cyclonic conditions are indicated by a and c, respectively.Sea level pressure (p), 2 m a.g.l.maximum temperature (T max ) and cloud coverage are 24 h observations of the closest national meteorological service station on the respective day.
For the flight patterns racetrack (RACE), wind square (SQUA), variance optimization (VARI), vertical wind specific flights (VW1-VW3) and the comparison to ground based measurements (COMP) the number of available datasets for each date is given together with respective track length (km) in parenthesis.5. Uncertainty of variables entering the wind vector computation Eq. (A1): Static pressure (p s ), dynamic pressure as used in the computation of flow angles (p q,A ) and the true airspeed (p q,B ), differential pressures (p α , p β ), static temperature (T s ) and water vapour pressure (e).Sources of uncertainty (σ) are subscripted as follows: manufacturer provided sensor uncertainty (sen), calibration in laboratory (lab), wind tunnel (tun), and wind model description (mod).The 0.05 K and 0.36 K uncertainties for radiation and ram rise errors in static temperature (T s ) were accounted in σ mod .These input uncertainties were Gaussian summarized (σ gau,i ) and propagated into output uncertainties (σ) of attack angle (α), sideslip angle (β) and true airspeed (v tas ), using the sensitivities (S) in their respective computations Eqs.(A5), (A6), and (A8).Propagated output uncertainties were summed up in analogy to Eq. (B1) before Gaussian summarizing them with the non-propagated uncertainties for α and β wind tunnel measurements to the final output uncertainties (σ gau,o ).

Discussion
, spatial representativeness of measurements is a general problem.The limited coverage of ground based measurements requires strategies to Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

1305
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Discussion
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1307
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1309
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | equals the aircraft's sum of vertical forces: Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Fast temperature was measured by a freely 1311 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |suspended 50 µm type K thermocouple, while water vapour pressure was measured with a capacitive humidity sensor.Time constants of thermocouple and humidity sensor are < 0.02 s and < 5 s at v tas = 27 m s −1 , respectively.Humidity readings are used solely to provide the air density correction for the v tas computation.Plug-and-socket connectors with locating pins insure a repeatable location of the 5HP with respect to the INS within < 0.1• .
to in-flight use, the five hole probe was tested in an open wind tunnel at the Technical University of Munich, Germany, Institute for Fluid Mechanics.Objectives were to (a) confirm the applicability of transformation Eqs.(A5)-(A7) and (b) determine the 5HP's uncertainty in the operational range of the WSMA.The 5HP was mounted on D-MIFU's nose-cap and measuring occurred at airflow velocities ranging from 20 to 32 m s −1 (equivalent to 2-6 hPa wind tunnel dynamic pressure).The dynamic pressure at the design stagnation point (i.e. the wind tunnel angles of attack α = 0 • and sideslip β = 0 • ) was measured at airflow velocity increments of 1 m s −1 .At increments of 2 m s −1 a total of 570 permutations of 10 predefined angles α and β, each ranging from 0 • to +20 • , were measured.In addition one-dimensional symmetry tests were performed for six predefined angles α and β ranging from −20 • to +20 • at an airflow velocity of 30 m s −1 .For the WSMA operational true airspeed of 28 m s −1 (or 4.5 hPa dynamic pressure during flight) the uncertainty of the wind tunnel airflow velocity was 1313 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | intention is to investigate the wind measurement's uncertainty constraint by sensor setup and wind model description under controlled boundary conditions.Because of flow distortion effects (Sect.2.1) the boundary conditions during flight however are less well known and might be significantly different from the laboratory.Therefore a methodology for in-flight calibration and evaluation was derived.It consists of a WSMA specific calibration model and -flight patterns.These patterns were carried out during three flight campaigns at different sites, each with its characteristic landscape and meteorological forcing: Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | . In the following, the strategies of the individual flight patterns at these three sites are categorized in five classes and briefly outlined.The first four of 1315 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Offsets and slopes for α and β were computed to minimize (a) the sum of the wind components variances plus (b) the absolute value 1317 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | attack angle (α) and pitch angle (Θ), yet with reversed sign.As compared to State 1, in State 2 the absolute uncertainties in the horizontal (|∆v m uv |) and vertical (|∆v m w |) wind components are increased by 24% and 18%, respectively.The increase however does not originate from the most sensitive-, but from formerly negligible terms such as trike roll (Φ b ).The latter now account for up to 50% of |∆v m uv | and 37% of |∆v m w |.Similar sensitivity analyses were carried out for α in Eq. (A5), β in Eq. (A6) and the thermodynamic derivation of v tas in Eq. (A8).Also here v tas = 27 m s −1 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (A5)-(A6) were most effective for deriving flow angles from our miniaturized 5HP.Root mean square deviation (RMSD) and bias (BIAS) amounted to 0.441, 0.144 • and 0.428, 0.047 • for α and β, respectively, 1323 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | layer (e.g.variance optimization flights) require a smaller lift coefficient, i.e. less wing 1325 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | pitch, than flights in the less dense air in the free atmosphere (e.g.wind square flights).
forced oscillation (VW3) flight pattern.During the flight on 25 June 2008 the wing pitching angle was modified by ±5 • and the maximum vertical velocity reached |4| m s −1 (Fig. 7).It is evident that the modelled upwash (v w up ) is linearly dependent on the lift coefficient, as defined in Eq. (3).The actual variations in measured vertical wind (v m w ) however were smaller by one order of magnitude and phase inverted compared to the modelled upwash or CL.Assuming a constant vertical wind, not necessarily but Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Paper | Discussion Paper | Discussion Paper | Discussion Paper | ) flight (both on 25 June 2008) is significantly reduced by implementing the binning procedure.Before binning, the VW1 flight shows a slight hysteresis, probably due to Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | v tas decreased from 0.42 to 0.21).The dependence on vertical movement decreased only slightly from 14.7% to 13.5% (σ), however correlation of v m w with v m,z gs is < 0.02.Due to the less calm atmosphere σ might not be representative for their cross dependence in this case.The VW2 flight on 25 June 2008 was again conducted in 1329 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | fraction.The other way around however would result in considerably higher contamination in v m w .The final calibration coefficients are summarized in Table

1331
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | shows a qualitative comparison of WSMA and ground based wind measurements for the flight on 15 October 2008.The vertical profile shows an equal number of flights at 24 and 27 m s −1 true airspeed.Despite one outlier in v m v and v m w at Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | pressure (subscript p) c p,h or constant volume (subscript v) c v,h of moist air have to be derived from the specific heat constants for dry air (subscript d) and water vapour (subscript w), c p,d = 1005 J kg and the displacement of the 5HP with respect to the INS along these axes, x b = −0.73m, y b = −0.01m, and z b = 0 m.The vector sum M ab (−v tas ) + v b lev in the wind Eq. (A1) then describes the true airspeed vector in the BCS.
b cosΘ b , 1339 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | M bm 12 = cosΨ b cosΦ b + sinΨ b sinΦ b sinΘ b , M bm 13 = sinΨ b sinΘ b cosΦ b − cosΨ b sinΦ b , M bm 21 = cosΨ b cosΘ b , M bm 22 = cosΨ b sinΘ b sinΦ b − sinΨ b cosΦ b , M bm 23 = sinΨ b sinΦ b + cosΨ b sinΘ b cosΦ b , M bm 31 = sinΘ b , M bm 32 = −cosΘ b sinΦ b , M bm 33 = −cosΘ b cosΦ b , where Φ b , Θ b , and Ψ b are the INS measured attitude angles roll, pitch and heading, respectively.Finally the movement of the BCS with respect to the MCS is described by by the inertial navigation system, together with the related uncertainty (Table derivatives of Eqs.(A11) and (A13) inserted into the wind vector Eq.(A1).Thereby the input uncertainty of v m tas can be expressed as function of the (assumed independent) input variables (f i ), with σ(f i ) being their respective uncertainty.Here f i are three quantities directly measured by the INS (i.e.pitch-(Θ b ), roll-(Φ b ) and heading-(Ψ b ) angles) and three variables derived from five hole probe measurements (i.e.attack angle (α), sideslip angle (β) and true airspeed scalar (v tas )).

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DiscussionFig. 9 .
Fig. 9. Smooth oscillation flights (VW2) on 24 June 2008 (left) and 25 June 2008 (right).In addition to the variables explained in Fig. 7 the vertical aircraft velocity (v m,z gs ) is shown.The pattern on 24 June 2008 is first carried out at 26 m s −1 (4800-5000 s), then at 28 m s −1 (5200-5400 s) true airspeed in a less calm airmass.The flight on 25 June 2008 is only conducted at 28 m s −1 true airspeed in a calm airmass.

Fig. 10 .Fig. 11 .Fig. 12 .
Fig. 10.Results from the wind square flights.For the horizontal wind components (v m uv ) the x-axis displays the residuals (leg average -square average), while the y-axis shows the wind magnitude.In contrast the vertical wind component (v m w ) is plotted against the true airspeed.Flight legs are depicted with different symbols according to their position in the square pattern.Dashed lines indicate a 10% criteria for v m uv , and the zero line for v m w .

Table 1 .
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | while Steinbrecher initiated wind-and flux measurements with the weight-shift microlight aircraft in the first place.Our gratefulness to Xunhua Zheng and her work-group at the Chinese Academy of Sciences, Institute of Atmospheric Physics, who was hosting our project and providing indispensable infrastructure.We are much obliged to Frank Beyrich of the German Meteorological Service, Richard-Aßmann-Observatory, who permitted us to carry out the evaluation flights and provided us with the corresponding SODAR-and tower data for this study.Our thanks to Jens Bange and Aline van den Kroonenberg of the Technical University of Braunschweig, Institute of Aerospace Systems (now Eberhard Karls University of T übingen, Institute for Geoscience), for their tireless advise.Stipend funding by the German Academic Exchange Service, Helmholtz Association of German Research Centrers, China Scholarship Council and the European Union under the Science and Technology Fellowship China is acknowledged.The flight in Inner Mongolia was funded by the German Research Foundation, research group 536 "Matter fluxes in grasslands of Inner Mongolia as influenced by stocking rate".Overview of sensors and electronic instrumentation used for the wind measurement.

Table 2 .
List of measured variables, sensor characteristics, signal processing and data acquisition.Individual sensor locations are described in Sect.2.2 and displayed in Figs.1 and 2. Resolution refers to the smallest change registered by the data acquisition (DAQ) units.σ is the overall sensor uncertainty provided by the manufacturer in form of one standard deviation.Signal rates are displayed for sampling, filtering and storing (Signal SFS).Data acquisition takes place in two forms, standalone (SA) and on the central DAQ unit EIDAS.For non SA devices signal forwarding via A/D converter, recommended standard 232 (RS232) or serial peripheral interface (SPI) is indicated (Interface DAQ).Continued on next page.

Table 4 .
Coefficients for static pressure (p s ), dynamic pressure (p q ), differential pressures (p α , p β ), static temperature (T s ), and flow angle measurements (α, β) during calibration steps A-G.Respective environments are laboratory (LAB), wind tunnel (TUN), comparison to ground based measurements (COMP), racetrack (RACE), wind square (SQUA), variance optimization (VARI) and vertical wind (VW) specific flight patterns.Coefficients are distinguished in offset (off) and slopes (slo), where applicable with lift coefficient in the upwash corrections (upw).Cross-calibration is referred to with the calibration steps in parentheses.Coefficients in parentheses were only used for intermediate calculations.