Information on the accuracy of meteorological observation is essential to
assess the applicability of the measurements. In general, accuracy information
is difficult to obtain in operational situations, since the truth is unknown.
One method to determine this accuracy is by comparison with the model
equivalent of the observation. The advantage of this method is that all
measured parameters can be evaluated, from 2 m temperature observation
to satellite radiances. The drawback is that these comparisons also contain
the (unknown) model error. By applying the so-called triple-collocation
method

Quantifying observation errors is of major importance to correctly use or
interpret the measured information. For example, the optimal use of
observations in assimilation, using variational techniques, is directly
related to the assignment of the correct observation error values. An
underestimation of the error will result in a model initialization, which is
too tight to the observation, while an overestimation of the error will
result in a too weak constraint and thus observations will not be optimally
exploited. Determining the measurement error can be performed in laboratory
environments, which try to mimic the reality as well as possible. Intercomparison studies can also serve as a valuable source for information on the
error characteristics of an observation

A method to avoid the information on the truth while estimating the
uncertainty of three collocated observations in space and time was developed
by

Although radiosonde observations are regarded as a reference in meteorology,
these observations are not exploited in this study. At present, due to budget
cuts, only one launch per day at 00:00 UTC is performed. At that time the number
of aircraft landing at or departing from Schiphol airport is very low (i.e. 01:00 LT or 02:00 LT depending on summer- or wintertime),
and thus this will
hamper the number of collocations, especially in the boundary layer.
Furthermore, the distance between the radiosonde launch site (De Bilt) and
the airport is more than 30 km. Nevertheless, radiosonde observations are a
valuable source for detecting model deficiencies

This paper is organized as follows. In Sect.

In this section the data sources used in the present study are described. First a description is given of Mode-S EHS observations, followed by radar and sodar. The used NWP model is described last.

Aircraft are equipped with sensors for flight efficiency and safety. For this
purpose, an aircraft measures the speed of the aircraft, its position, and
ambient temperature and pressure. For a few decades a selection of these
observations are transmitted to a ground station using the AMDAR system. An
atmospheric profile can be generated when measurements are taken during
take-off and landing. See

An SSR has a typical interrogation frequency of once every 4 to 20 s.
Consequently, wind and temperature are observed at these same rates, and with
a typical cruising speed of 250 m s

The difference between Mode-S EHS and AMDAR lies in the method of retrieving the data. AMDAR data are transmitted through a dedicated relay system, and AMDAR observations are initiated on request of the meteorological community. Not all aircraft are AMDAR equipped; only selected aircraft have the AMDAR software implemented on their on-board computer.

The focus of this paper is on wind, although (mean-layer) temperature is also available in Mode-S EHS or ADS-B information; temperature will be investigated in future research.

A Doppler weather radar is capable of determining one component of the
velocity of scattering particles. Only the velocity component along the line
of sight, the so-called radial velocity, can be determined. A Doppler radar
is commonly associated with measurements of frequency shifts because of the
low velocities of hydrometeors. However, these shifts cannot be observed
directly. The phase of the scattered electromagnetic waves is employed to
determine the Doppler frequency shift instead. During pulse-pair processing,
the velocity is effectively deduced from the phase jump of the received
signal. The unambiguous velocity interval of the instrument, especially for
C-band radars, is enhanced by applying a dual-pulse repetition frequency
(PRF). The two Royal Netherlands Meteorological Institute (KNMI) radars
are C-band with a wavelength of 5.3 cm. The high PRF is chosen to be four-thirds of
the low PRF, resulting in an unambiguous velocity of 4 times the low PRF
unambiguous velocity, which is 23 m s

A sodar (sonic detection and ranging) is a ground-based remote-sensing
instrument for measuring wind and turbulence in the lower atmosphere. A
mono-static sodar is operated and maintained by KNMI at Amsterdam Airport
Schiphol (AAS) since March 2006. A sodar emits short acoustic pulses into the
atmosphere and receives atmospheric echoes generated by small-scale density
fluctuations that are associated only with thermally driven turbulence, which
is not always present. The transmitted signals can be phase shifted to point
the beam in different directions. At Schiphol, three are in use for the
instrument, and one antenna is oriented vertically. The zenith angle of the other
beams is dependent on the transmit frequency and varies between 10 and 30

The non-hydrostatic HARMONIE

HARMONIE main characteristics.

Observation data characteristics.

Table

Radial wind speed from the Doppler weather radar in De Bilt, location of the sodar (marked by the yellow diamond), Mode-S EHS observations (black dots), and HARMONIE (thinned) wind field at approximately 850 hPa; all valid on 3 September 2013 12:00 UTC.

The period used in this study runs from 1 January to 30 September 2013 because a rerun of HARMONIE data with version 38h1.2 is used and no more data were available overlapping the Mode-S EHS data set.

To perform a triple collocation it is essential that the data sets are collocated in space and time. In this section the method of collocation is described followed by the description of the triple-collocation methodology.

Observations are regarded at the same when the time difference is less than 5 min. Note that the model has a 3 h cycle (a new run is started every 3 h), which reduces the collocation time window to 10 min every 3 h because we use the 3 h forecast only in this study. We did not interpolate the model to the observation time and the interpolation in space was chosen to be bilinear.

The metrics of the vertical coordinate of radar and Mode-S EHS observation
differ: radar radial winds are measured at a certain elevation angle and
range, while altitude of Mode-S EHS is given as flight level. The elevation
angle and range can be converted into position and altitude (in metres), while
flight level is easily converted into pressure altitude (in hectopascals). To enable
collocation of a radar and Mode-S EHS observation, additional information on
surface pressure, and temperature and humidity profile is needed to convert
either pressure into altitude or vice versa. To perform this conversion, the
surface pressure, and temperature and humidity profile of an NWP model is
used, which is already present at the observation location since NWP is the
third data set. This may introduce a correlation between the three data sets,
but we think it is negligible. Figure

Schematic overview of the vertical collocation method. The dashed lines represent levels of constant pressure and the dotted lines of constant height. Red dots denote the Mode-S EHS observation, the blue dots the collocated radar observation.

Given a Mode-S EHS observation location, a matching radar observation is
determined by the following conditions. First of all the distance of the
observation location should be at least 50 km away from the radar, because
close to the radar the radial wind observations have a large error. The
Mode-S EHS observation will not perfectly collocate to the altitude and
position of a radar pixel; therefore, radar data points of two closest
elevations with a maximal horizontal distance of 2.5 km are considered. Next,
the elevation of the surrounding radar data points needs to be larger than
0.3

As for radar, the vertical coordinate of the sodar observation is reported in metres. We used the same algorithm based on the temperature and humidity profile to relate this altitude to pressure (or actually flight level). The quality indicators, which are output of the sodar processing, are used to screen the sodar observation prior to collocation. Since the sodar is located near the runway, a very close collocation cannot be obtained; we therefore set the maximum distance between the sodar observation and the Mode-S EHS observation to 5 km horizontal and select the sodar observation closest in altitude.

We apply the triple-collocation method

Assume we have three sets of data

The representativeness of the three observations most likely differ; there is
a residual correlation error

The data sets we use in this study consist of wind vector data (Mode-S
EHS/sodar/NWP,

Power spectral density of

The representative error has some relation to the azimuth angle (zonal
component of the wind is equal to a radial wind observed with an azimuth
angle of 90

The residual error as a function to the azimuth angle. A data set consisting of 9 months of Mode-S EHS collocations with HARMONIE was used to create a data set of radial wind for each azimuth angle. The dashed line shows the residual error using the observed distribution of azimuth angles in the Mode-S EHS/radar/NWP data set.

Now that we have estimated the residual error we can use the triple-collocation method to determine the observation errors.
Figure

Error estimates of radial wind component for Mode-S EHS- and sodar-based wind vector observations for different azimuth angles. The black vertical error bar indicates the radial wind error estimate from Mode-S EHS with the radial wind component constructed from the wind vector using the azimuth distribution of the radar data set.

Both wind observation errors have a clear azimuth dependence and exhibit
again a bi-periodic behaviour; the errors of Mode-S EHS are between 1.2
and 1.5 m s

The trend and bias with respect to the first data set are simultaneously
estimated by the triple-collocation algorithm. Obviously, the bias has no
effect on the estimated observation errors; however, it can be informative
because it gives information on the mean difference with the truth. The trend
displays the scaling of the data set with the truth.
Figure

Error estimates of radial wind component for Mode-S EHS- and sodar-based wind vector observations for different azimuth angles. The black vertical error bar indicates the radial wind error estimate from Mode-S EHS with the radial wind component constructed from the wind vector using the azimuth distribution of the radar data set. The shaded area denotes the uncertainty in the estimates, calculated by subdivision of the data set into 10 subsets from which the mean and standard deviation of the estimate are calculated.

Next we discuss the consistency between the estimated Mode-S EHS error from
both data sets by inspection of the zonal and meridional estimates. The
radial wind is equal to the zonal component of the wind for an azimuth angle
of 90 and 270

Mode-S EHS wind component observation error estimate.

These statistics show consistency between both triple-collocation data sets
when taking into account the observed uncertainty of the estimates. Due to
the small numbers of Mode-S EHS observations satisfying the azimuth angle
conditions, the uncertainty for the estimates based on the Mode-S
EHS/radar/NWP data set is larger than for the other triple-collocation data set
(for the latter all observations can be used obviously). The uncertainty
range of the Mode-S EHS/radar/NWP estimates overlaps the uncertainty of the
Mode-S EHS/sodar/NWP. The Mode-S EHS error is approximately 1.4 to 1.5 m s

The meridional component statistics, shown also in Table

We now focus on the radial wind component of the Mode-S EHS observation
error. The result of the triple collocation for all radial wind component is
shown in Fig.

Mode-S EHS radial wind error estimates from the two triple-collocation data sets with respect to altitude. Error bar indicates the uncertainty of the error estimates based on error estimates determined from 10 subsets. The size of the data sets is denoted by the numbers on the right.

The lowest data point originates from the triple collocation of Mode-S
EHS/sodar/NWP, where we created radial wind observation from the wind vectors
using the azimuth distribution as observed by the other data set. The other
data points in Fig.

Azimuthal distribution of the data sets used to estimate the
Mode-S EHS observation error for different altitudes; in red is the azimuth
distribution of the complete data set. Azimuth bin is set to 30

Figure

Azimuthal distribution of the resampled data sets. Azimuth bin is set to 30

The resulting estimates of Mode-S EHS observation error after resampling are
shown in Fig.

Mode-S EHS radial wind error estimates from the two triple-collocation data sets with respect to altitude. The Mode-S EHS/radar/NWP data set has been resampled to have similar azimuth distributions. Error bar indicates the uncertainty of the error estimates based on error estimates determined from 10 subsets. The size of the data sets is denoted by the numbers on the right.

Trend and bias for resampled radial wind.

Finally, we present the trend and bias for the resampled radial wind data
sets (see Table

In this study we applied the triple-collocation technique to estimate the Mode-S EHS observation error. We used
two triple data sets consisting of Mode-S EHS/sodar and NWP, and Mode-S EHS,
radar, and NWP. Using the first data set an estimate of the two horizontal wind
vector components was found for observations with an altitude of at most
700 m. The estimated observation error for the wind components was around
1.40 m s

The observation error of Mode-S EHS wind vector projected on the radial
component has some dependence on altitude. The projection is performed using
the distribution of the azimuth as observed in the Mode-S EHS/radar/NWP data
set. It appears that, after resampling, from the surface to 800 hPa the
observation error is between 1.2 and 1.4 m s

In many previous studies to assess the accuracy of aircraft wind observations,
a second observing system was used. This implies that, when looking at the
statistics of the differences, the error estimates contain errors from both
systems and are in fact (at least) a factor of

The study at hand uses data over a period of 9 months. A longer period would be preferable, but the overlap of availability of Mode-S EHS and a consistent HARMONIE data set was limited to only 9 months. It is anticipated in future research to investigate seasonal effects.

Simultaneously with the estimation of the wind vector error for Mode-S EHS, the error of sodar is estimated. It turns out that the wind vector from sodar is of good quality and therefore could be used for assimilation in HARMONIE. The triple-collocation method can also be used to determine observation error correlation when the measurement systems have a good spatial coverage at collocated time.

EUROCONTROL Maastricht Upper Area Control Centre (MUAC) is kindly acknowledged for the provision of the ASTERIX CAT048 data. Edited by: A. Stoffelen Reviewed by: two anonymous referees