Introduction
Wind is a key parameter of dynamics throughout the atmosphere.
In the troposphere, wind is directly related to weather phenomena.
Dynamics in the stratosphere also have an influence on tropospheric dynamics and
thus on weather phenomena . Hence, many
numerical weather prediction models have extended their upper limit to the
mesosphere region in the past few years. At the same time, it is a fact that
nearly no measurements of wind speeds in the upper stratosphere
and the lower mesosphere exist. This region roughly corresponds to the so called
radar gap, where too few scatterers for radar observations are present. The
first wind radiometer WIRA proved Doppler microwave radiometry to be a
suitable method to achieve wind profile observations between 35 and 75 km
altitude on a campaign basis as well as for long term stationary measurements
. In contrast, Rayleigh–Mie
Doppler wind lidar techniques can also reach the upper stratosphere or even
the mesosphere at 80 km .
Lidar systems can provide wind profiles with a high temporal and spacial
resolution; however, they always need clear sky conditions and measurements
during daytime are difficult to achieve. In addition, they are not operating
autonomously and are thus not very well suited for continuous wind
measurements.
observed the 11 GHz ozone line using low-cost satellite
television electronics and derived seasonal and local solar time aggregated
wind speeds at 95 km altitude using 5 years of measurements.
Spaceborne instruments like the Microwave Limb Sounder (MLS) measured wind
speeds between 70 and 95 km using the Doppler shift
introduced to the 118 GHz emission line of oxygen and proposed to extend
this range towards 40 km by using other emission lines. The Superconducting
Submillimeter Wave Limb-Emission Sounder (SMILES) observed winds between
October 2009 and April 2010 between 30 and 80 km by observing the Doppler
shift of the 625 GHz ozone emission line and the HCl emission line at
625 GHz .
Ground-based passive microwave instruments are autonomous and independent of
daylight or clouds and can thus deliver continuous measurements, even though
with lower spacial and temporal resolution compared to lidar. Such
measurements are important for the validation of models and other
instruments, as demonstrated by . In addition
showed that microwave wind radiometry is a valuable
complement to other techniques like lidar and infrasound at multi instrument
sites and contributes to the general understanding of middle atmospheric
dynamics.
The WIRA-C instrument (Wind Radiometer for Campaigns) presented here,
represents the newest development in microwave wind radiometry. It is capable
to deliver 12 hourly resolved wind profiles in an altitude range of 35 to
75 km. Compared to the WIRA instrument , it is more
compact, and thus easier to deploy and operate on campaigns. All optical
elements, including the calibration target and the corrugated feed horn
antenna, are integrated in a single housing with a stable temperature and stay
dry and clean at all times, which allows us to resume high-quality observations
immediately after rainfall. Furthermore, we apply a three-dimensional
retrieval method that has never been used for ground
based radiometry before.
After a short introduction of the measurement principle, we present the
instrument, its optics and receiver system in Sect. . The
data processing and the retrieval process used to obtain wind profiles from
radiometric measurements is presented in Sect. .
Also in Sect. , we present error estimations for
random and systematic errors of our retrieval. Finally, the results from the
1-year campaign of WIRA-C on the Maïdo observatory on Réunion
are shown in Sect. and we compare our measurement
data to the European Centre for Medium-range Weather Forecasts (ECMWF)
operational model that is widely used in middle atmospheric research and to
coincident lidar measurements.
Measurement principle
WIRA-C measures the spectral intensity of the 142.17504 GHz ozone rotational
transition emission line. Wind information is introduced to the emission line
by the classical Doppler shift, the linear relation between the line-of-sight
speed of an emitter drifting with the wind flow vlos and the
observed frequency shift Δν:
Δν=vloscν0.
Further, the emission line is pressure broadened, meaning that information
about the altitude of the emitters is encoded in the spectrum. This allows
the retrieval of wind profiles up to approximately 75 km, where the
altitude-independent Doppler broadening effect starts to dominate.
Because the Doppler shift is proportional to the emitted frequency ν0,
it is advantageous to use a high observation frequency. We chose the 142 GHz
emission line of ozone because of its strong magnitude and because the
troposphere is more transparent in this frequency range than at higher
frequencies. This limits the tropospheric contribution to the observed
spectrum and increases the signal-to-noise ratio for middle atmospheric
emission signals.
Passive microwave wind radiometers require a stable frequency reference as
the ratio between observation frequency and the Doppler shift is in the order
of 10-8 to 10-7 for typical atmospheric wind speeds of
10 m s-1 or 100 m s-1, respectively. Given our observation
frequency of 142.17504 GHz, the Doppler shift introduced by line-of-sight
wind speeds is 4.75 kHz per 10 m s-1. Further, we rely on opposing
measurement directions, for example eastwards vs. westwards, to derive an
absolute wind speed in the presence of possible frequency drifts and shifts
not related to wind. This implies that we assume the horizontal wind speed to
be constant over the horizontal distance spanned by the two opposing
line-of-sights. For an elevation angle of 22∘, this horizontal
distance would be 150 km at 30 km altitude and 370 km at 70 km altitude.
The WIRA-C instrument as installed on the Maïdo observatory on
Réunion. It measures 0.6×0.75×0.5 m and
contains the optics, the receiver, a spectrometer, a computer and power
supplies. Radiation from the sky enters the instrument through the scan
drum (a), which is at the same time the air outlet. The air filters (b) are placed below the
instrument and the GNSS
antenna and a rain sensor (c) are attached on top .
[t]
The instrument
WIRA-C has been designed to be compact and autonomous. As depicted in
Fig. , it fits into one single housing with the
dimensions 0.6×0.75×0.5 m and is set up on a tripod. It only
needs an ethernet and a power connection and thus requires no additional
laboratory space. Once set up, it measures autonomously and we supervise and
configure the measurement process via remote connection. This makes
WIRA-C an ideal instrument for campaigns at remote locations as well
as for long term continuous observations.
Besides the more compact structure, several technical improvements have been
made over the WIRA prototype presented by . Firstly,
WIRA-C has a better signal-to-noise ratio than WIRA, thanks to the better low
noise amplifier (LNA) in the receiver chain. Secondly, while WIRA observes at
a fixed elevation angle of 22∘, WIRA-C can freely select the
elevation and azimuth angle to look at the sky thanks to independent
elevation and azimuth drives. This makes WIRA-C a true all-sky microwave
radiometer, similar to the concept of ASMUWARA , and we
will benefit from this flexibility in the future, e.g. for the
characterisation of tropospheric inhomogeneities in the context of tipping
curve calibration. At the moment we use the all-sky mode only for the
geometrical alignment by scanning the sun. For wind measurements we use the
same well-established observation scheme as for WIRA because 22∘
elevation provide an optimum in terms of projection of horizontal wind speed
to the line-of-sight vs. decreasing signal to noise ratio with increasing
path length through the troposphere. Further, the ambient temperature
calibration target is embedded inside the housing and thus better protected
against environmental influence such as inhomogeneous heating by solar
radiation. In particular, the optics and the calibration target are fully
protected against rain. As no highly absorbing water can be deposited on the
optical components, the instrument can resume the measurement immediately
after rainfall has stopped. In addition many smaller technical improvements
have been implemented, for example the path length modulator to mitigate
standing waves between calibration target and receiver. The key
specifications of WIRA-C are summarised in Table 1.
WIRA-C optics with flat mirror M3 (inside the scan-drum), flat
mirror M2 (on a linear stage), elliptical mirror M1, elliptical mirror M4
(slewable, drawn in inactive state), hot load and the front end with the feed
horn.
Receiver optics
Figure shows the optical system with its four mirrors.
Radiation from the sky enters the instrument through the scan drum that
contains the flat mirror M3 and is rotatable to select any elevation angle.
Together with the azimuthal drive at the bottom of the instrument, all
cardinal directions (north, east, south, west) can be observed. This is
important for robust wind retrievals, as the observation of opposite
directions allows us to compensate for possible shifts in absolute frequency
scale and also makes the calibration more robust as will be explained in
Sect. .
From mirror M3, the radiation is deflected by the flat mirror M2 and coupled
into the feed horn antenna by the elliptical mirror M1. The mirror M2 is
mounted on a linear stage that can be shifted back and forth to make a
λ/4 difference in optical path length between two measurements. This
path length modulation is especially useful for calibration with the internal
hot load as it mitigates standing waves between the receiver and the
calibration target by destructive interference.
Key specifications of the WIRA-C microwave Wind Radiometer for
Campaigns.
Optics
Ultra-Gaussian feed horn + elliptical and
flat mirrors
Beam width
2.3∘ FWHM
Receiver type
Pre-amplified single-side band heterodyne
Frequency
142.17504 GHz
Bandwidth
2×120 MHz
Backend
Ettus Research USRP, FFTS
Spectral resolution
12.2 KHz
System Temperature
550 K
Calibration
Hot load + tipping curve
Elevation range
All sky
The calibration target is an aluminium wedge with a half angle of
12∘, coated with absorbing material Eccosorb MMI-U. This absorber
type from Laird NV is particularly well suited for those frequencies as shown
by . Mirror M4 can be moved into the optical path to
perform a hot load measurement and because of its elliptical shape focuses
the beam to fit the load aperture, which results in a very compact
calibration wedge. The calibration wedge is placed with its plane of
incidence perpendicular to the electric field, which is generally referred to
as transversal-magnetic (TM) mode. As measured with the setup described in
, the calibration wedge performs well with a reflectivity
lower than -60 dB at 142 GHz.
Measured and simulated far-field beam cuts of the whole instrument
when pointing to zenith direction. Panel (a) shows the cut along the
Y-Z-plane which is also the plane of reflection on the last mirror (see
Fig. for the coordinate system). Panel (b) shows
the perpendicular cut. The gray dashed line marks the -35 dB level.
A narrow beam with low side lobes is required for a well defined pointing.
This is important for ground based radiometric measurements of the middle
atmosphere, as the path length through the troposphere, and thus the
tropospheric signal, increases rapidly with decreasing elevation angle,
especially at low elevation angles used for wind measurements. The antenna of
WIRA-C is an ultra low side lobe Gaussian corrugated feed horn with a
divergence angle of Θfeed=14.3∘. The elliptical
mirror M1 transforms this beam to the near-pencil instrument beam that has a
full width at half maximum divergence angle of Θinstr=2.1∘.
We measured the beam pattern of the instrument using a vector network
analyzer (VNA) in the near-field. The experimental setup for this measurement
includes an open-ended waveguide probe placed in front of the instrument on a
linear scanning stage that allows scanning along the x and y axis (see
Fig. for the coordinate system). The VNA source signal at
142 GHz is coupled into the optics by the WIRA-C feed horn.
Figure shows the far-field transformation of the scanning
along the two axes as well as the corresponding physics simulations carried
out with GRASP . The measurements and simulations agree on a
full width at half maximum of the beam of 2.1∘ and confirm the side
lobes to be below -35 dB.
Block diagram of the WIRA-C single side-band receiver with
radiometer front end (a) and USRP spectrometer (b) with
channels A and B. The oven-controlled and GPS-disciplined crystal oscillator
(OCXO) (c) provides
the 10 MHz reference frequency for all local oscillators (LO) in the front
and back end.
Receiver electronics
The receiver front end (Fig. ) of WIRA-C contains a
temperature-stabilised heterodyne single side-band receiver. The observed
radio frequency (RF) of 142 GHz is collected by the feed horn and then
amplified by the low noise amplifier (LNA) by 20 dB (3.29 dB noise figure at
142 GHz and 293 K). This LNA has been built by the Fraunhofer IAF based on
the 50 nm M-HEMT technology described by . After
subsequent selection of a single side band, the sub-harmonic mixer is fed by
a local oscillator (LO) with 72.9 GHz, which gives an intermediate frequency
(IF) of 3.65 GHz. The microwave components of the front end are all mounted
on a rigid aluminium plate that is temperature stabilised by
thermo-electrical elements to maintain a stable temperature at 295 K.
We use a Universal Software Radio Peripheral (USRP X310 with CBX-120
daughterboard, see ) as Fast Fourier Transform Spectrometer
(FFTS). It has a bandwidth of 200 MHz and a channel width of 12.2 kHz but
due to some constraints by filters in the USRP, only the central 120 MHz of
the full bandwidth can be used for our measurements. As shown in
Fig. , the USRP provides two channels with independent local
oscillators and AD converters. In the current setup, the primary channel
(channel A) is centred around the resonance frequency of the ozone thermal
emission line at 142 GHz while the secondary channel is offset by 120 MHz
to extend the spectrum towards the off-resonance frequencies. The Fast
Fourier Transformation (FFT) and accumulation algorithms are implemented
using LabVIEW and programmed on the FPGA chip aboard the USRP.
The system noise temperature of the single-sideband receiver system is 510 K
at 142 GHz, as measured in the laboratory by a hot–cold calibration using
liquid nitrogen and confirmed by the routine tipping curve calibration. This
is about 300 K lower than for the WIRA instrument, mainly due to the better
quality of the 20 dB low noise amplifier.
As wind measurements require a stable frequency reference, we use a GPS
disciplined and oven-controlled quartz oscillator to improve the long and
short-term stability of the local oscillators of the front end and the
back end.
The receiver gain typically drifts with time and periodical calibration is
important to get consistent measurements. The Allan variance computation
scheme gives a timespan for which a receiver can be
considered stable. Figure shows the Allan variance for a
14 h measurement with the WIRA-C receiver. The noise of the WIRA-C receiver
drops for an integration time up to 4 min for a single channel with a
bandwidth of 14.6 kHz, then starts to increase again because of drifts.
The duration of one measurement cycle was thus chosen to be 2 min.
Allan variance of the receiver measured for a bandwidth of 14.6 kHz
compared to the radiometric noise formula. The minimal Allan variance is
reached after 4 min of integration.
Data processing
The primary measurement cycle of WIRA-C alternates between the six targets,
which are the hot load, zenith (used as cold load), and the four 22∘
elevation observations (north, south, east, west). For all six targets the
linear stage is placed in two different positions to make a difference in
path length of λ/4. The integration time for each position of the
linear stage is 10 s and the two measurements are averaged prior to
calibration to cancel standing waves. Notably, we use the time during the
relatively slow rotation around the azimuthal axis for the zenith and
hot-load measurements to save valuable integration time. The twelve
measurements of one cycle are then processed further, as described in the
following sections.
Calibration
Compactness and low maintenance requirements were major design goals of
WIRA-C, ruling out liquid nitrogen or a Peltier calibration target
as cold reference that is needed in addition to the hot
reference for radiometric calibration. This is why we opted for an ambient
temperature hot load complemented with the tipping curve method for the
radiometric calibration. Essentially, this method has been explained by
and uses the sky as cold load by assuming a mean tropospheric
temperature and fitting the tropospheric opacity to a set of observations at
different elevation angles. We use the measurements at 22∘ elevation
and zenith, and estimate the mean tropospheric temperature Tm
according to from the ambient temperature Tamb
as Tm22=Tamb-9.8 K and Tm90=Tamb-10 K, respectively.
The temperature of the hot load is measured by two temperature sensors
mounted on its aluminium backing and follows the internal temperature of the
instrument which we stabilise at about 10 K above the typical maximum
ambient temperature by regulating air flow and additional heaters.
In order to include as little wind information in the tipping calibration
process as possible, we average the northwards and southwards measurement to
provide the input for the 22∘ elevation measurement to the tipping
curve algorithm. We prefer that in favour of the eastwards and westwards
measurements, as zonal winds are expected to be stronger and thus the slight
broadening of the spectral line when averaging the two measurements would be
increased.
Tropospheric correction
The calibrated brightness temperature as seen on the ground,
Tb(z0), can be modelled as a sum of the tropospheric contribution
driven by the same mean temperature Tm used above and a
middle-atmospheric contribution Tb(ztrop) that would be
observed if the instrument was above the troposphere :
Tb(z0)=Tm1-exp-τ/sinη+Tbztropexp-τ/sinη,
where τ is the zenith opacity of the troposphere and η is the
elevation angle of the observation. The opacity itself can be estimated in
different ways. We are applying the same technique as
and use the brightness temperature at the wings of the measured spectra, as
far away from the ozone rotational transition resonance frequency as
possible. In practice we use an average over 10 MHz at the left wing of the
spectrum measured by the second spectrometer channel (USRP channel B)
depicted in Fig. . The Zenith opacity is then given by
τ=-sinηlnTm-Tboff-resonanceTm-Tbg,
where we set the background temperature Tbg to 2.7 K. We apply
this estimation for all four cardinal directions independently and thus
account for direction-dependent tropospheric conditions.
Opacity τ at the off-resonance observation frequency obtained
from tipping calibration for three days in June (a) and
September (b) at the Maïdo observatory. The gray areas mark
nighttime, with sunrise and sunset at 02:00 and 14:00 UTC,
respectively.
As described in Sect. , the second channel of the USRP is
offset by 120 MHz, giving us information up to 180 MHz off-resonance. At
this offset from the line centre the ozone signal is still relatively strong
and we see more than just the microwave background Tbg. However, for
wind measurements we are more interested in a normalisation of the spectra of
the four cardinal directions against each other to compensate for the
tropospheric inhomogeneities than in absolute brightness temperature
calibration.
This gives us an estimate on τ for each observation direction and we can
estimate the non-tropospheric contribution through
Tbztrop=Tb(z0)-Tm1-exp-τ/sinηexp-τ/sinη.
As Eq. () is not linear in τ, it does not hold
exactly for average values of τ and Tb for long integration
times or highly variable tropospheric conditions. We encounter such
conditions, for example, on the Maïdo observatory on Réunion
(21.4∘ S, 55.9∘ E). There, during nighttime, the conditions
are optimal for radiometric observations because the observatory is located
at 2200 m above sea level and near the free troposphere during the night
. However, during daytime, when microclimatic effects and
convection are dominant, the opacity is highly variable as shown in
Fig. . At the same time the signal-to-noise ratio for
wind measurements is quite low and long integration times of several hours
are required. The high variability of the opacity and the long integration
times are the reasons why we apply the tropospheric correction directly to
the calibrated spectra before integration and use the 12 h integration of
the corrected brightness temperatures Tb(ztrop) for the
wind retrievals. This integration time showed to be suited for the objective
of instrument validation, but for other studies one might also consider
shorter or longer integration times.
Measured spectrum of the ozone line from a single calibration cycle
on 25 June 2017 at 09 h (UTC). Panel (a) shows the eastward and
westward measurement after calibration, panel (b) shows the same
measurement but with tropospheric correction applied. Channel A of the USRP
has 12.2 kHz resolution and is centred around the line centre while
channel B has 97.7 kHz resolution and observes the line
wing.
Figure shows an example of a measured spectrum from one
calibration cycle before and after tropospheric correction. Without
tropospheric correction, the measurements in eastward and westward direction
differ by 20 K because of tropospheric inhomogeneities. If we apply the
tropospheric correction as described above using the left wing as reference,
the spectra are on the same level and have the same magnitude. While we use
the measurement form channel A for the retrieval of wind speeds, channel B is
used solely for the tropospheric correction.
Retrieval of wind profiles
We retrieve wind information from the measured spectra by inverting a
radiative transfer model that describes the relation between the atmospheric
state vector x and the measurement vector y as x=F(y). The inversion thereof is typically ill-posed because many
(unphysical) configurations of the atmosphere lead to the same measured
brightness temperature. The optimal estimation method uses an a priori value
with associated uncertainties for the atmospheric configuration to regularise
the inverse problem as described by .
The WIRA-C retrieval of zonal wind uses the brightness temperature measured
in eastern and western direction and combines these measurements to retrieve
a single wind profile. The retrieval of the meridional wind is set up
analogously. This is in contrast to the wind retrieval procedures used for
WIRA, where wind profiles have been estimated for east and west separately
and are then averaged to get a single zonal wind profile
. By combining both observations in one inversion, we
can effectively maximise the a posteriori likelihood of the wind profile
given our two measurements in opposite directions. This is especially
important in the presence of frequency shifts or drifts that are not related
to wind. Such shifts are of a systematic or random nature and can originate
from instrumental instabilities or offsets or even uncertainties in the
molecular resonance frequency.
Fitting one atmosphere to two measurements drastically increases the
overdetermination of the retrieval as the number of measurements is
increased. This is explicitly wanted for wind and frequency shift where we
need to combine all our measurements, but not ideal for ozone abundance that
is also being retrieved to fit the observed line. Fitting one common ozone
profile to the eastward and westward direction constrains the retrieval too
much resulting in non-convergence or oscillations of the ozone profiles. This
might be due to actual spatial variations in ozone abundances, which we
consider to be unlikely as they are not expected to be that big in tropical
latitudes. More probably, tropospheric inhomogeneities or clouds affecting
the eastward and westward observations differently could have an influence on
the ozone profile. However, this is not expected to have an influence on the
retrieved wind speed, as the Jacobian of the forward model is completely
antisymmetric with regard to wind as elaborated in .
This is why we model a three-dimensional atmosphere and include independent
ozone profiles, and thus more freedom in our retrieval for the opposing
observations.
In case of WIRA-C, the state vector x and the measurement vector
y have the following form for the zonal wind retrieval (and analogous
for the meridional wind retrieval):
x=uxO3,1…xO3,MΔfb⊺,y=Tb,eastTb,west⊺,
where the elements of x are itself vectors. For example the zonal
wind speed profile is given by u=u(p1)u(p2)…u(pN) for N pressure levels. Besides the zonal wind
profile u, the x vector also contains the profiles of volume
mixing ratio of ozone xO3 at M different spacial grid
points as well as the frequency shift parameter Δf and one or more
baseline parameters b. Finally, the temperatures
Tb,east and Tb,west are the
calibrated and corrected brightness temperatures from Eq. ().
The optimal estimation method then minimizes the cost function
χ2=x^-xa⊺Sa-1x^-xa+y-Fx^⊺Sϵ-1y-Fx^,
for finding the most probable atmospheric state x^ given the a
priori profile xa and the measurement y. It does so
using the assigned statistics in form of the covariance matrices
Sa and Sϵ for the a priori data and
the measurement, respectively.
They are constructed as block diagonal matrices, analogous to the x
and y vectors in Eqs. () and ():
Sa=Sa,uSa,XO31,1…Sa,XO31,M⋮⋱⋮Sa,XO3M,1…Sa,XO3M,MSa,ΔfSa,b,Sϵ=STb,eastSTb,west=σyI,
where the off-diagonal elements Sa,XO3i,j(i≠j) describe the covariance of the spatially distributed ozone
profiles. Details about the setup of covariance matrices for
multi-dimensional retrievals are described by . The
value σy on the diagonal of Sϵ is directly
determined as the Allan-deviation of the measurement vector y by
σy2=12〈yn+1-yn2〉.
Following and using a linearised form of the forward
model with Jacobian K, the solution that minimizes
Eq. () in a linear case is
x^=xa+Gy-Kxa,
where G is the gain-matrix and describes the sensitivity of the
retrieved profile to changes in the spectra:
G=∂x^∂y=KTSϵ-1K+Sa-1-1KTSϵ-1.
As the frequency shift introduced by wind has a non-linear impact on the
brightness temperature, the final solution x^ is found by a
Levenberg–Marquardt algorithm and Eq. () is applied
iteratively while updating the point of linearisation for K but
leaving xa fixed.
Assuming that Sϵ characterises the radiometric noise on
the spectra, the uncertainty of the retrieved profiles due to thermal noise,
the so called observational error σo, is defined as
σo2=diagGSϵGT.
We assume that the major contribution to the uncertainty on the retrieved
profiles is due to radiometric noise and thus use the observational error
σo as a measure for the uncertainty in this study. It is
important to note, that the observational error is influenced by the a priori
statistics via Eq. () and the observational error grows with
increasing a priori covariance because then the measurement and its noise
have a bigger impact on the retrieved quantity. We accept this as an inherent
property of the optimal estimation method: for a given thermal noise on the
spectrum, the uncertainty of the retrieved value is smaller if there is less
ambiguity in the a priori state.
Another measure for quality of our retrieved state x^ is the
averaging kernel matrix given by
A=∂x^∂x=GK.
Each row of the matrix A is called an averaging kernel and
describes the smoothing of information. We use the averaging kernels for
quality control as described in Sect. .
The forward model and OEM implementation is provided by ARTS/QPACK2 (version
2.3) . In the current setup for WIRA-C wind retrievals we
use 6 ozone profiles equally spaced around the instrument location inside the
east–west observation plane for zonal wind. We choose M=6 as this showed
to give superior retrieval results in terms of measurement response and
altitude resolution than lower values. This is a detail related to the grid
interpolations done by ARTS/QPACK2 and the construction of the covariance
matrix for ozone. The covariance matrices for ozone are set up using
separable statistics with a horizontal correlation length of 200 km, which
we assume to be height independent.
A priori data and model parameters
For the a priori data for wind, we always use a 0 m s-1 profile. This
equalises the probability to retrieve easterly and westerly winds, which is
desirable in case of sudden wind reversals like they are observed around
equinox and in context of sudden atmospheric events. To put it in other
words, even though wind speeds in the atmosphere are generally not normally
distributed we assume that the wind in the atmosphere is 0±su m s-1 and we use climatological statistics from
6 years of ECMWF data at the campaign location to estimate su which
then depends on altitude but not on time. The same applies for meridional
wind, and sv turns out to be smaller than su because
meridional winds are typically slower than zonal winds. We multiply these
statistics by a factor of 2 in order not to have a bias towards zero, as
elaborated by and additionally we impose a vertical
correlation length of 0.5 pressure decades to construct the covariance
matrix. Like this, our retrieved wind speeds are regularised but in no case
biased towards either direction by the a priori wind profile.
For the ozone a priori data, we rely on a F 2000 WACCM scenario from a
simulation by . This allows us to extend the retrieval grid
up to 110 km altitude and thus includes the nighttime secondary ozone
maximum at 10-3 Pa. We determine the a priori profile and variance in a
window of 11 days around the day-of-year of our measurement while only
regarding the same hours of the day that we integrated over (either day or
nighttime). Extending the retrieval grid and separating day and nighttime
retrievals is important because signals from the secondary ozone maximum can
have an influence on wind retrievals below 75 km if not properly handled as
elaborated by .
We multiply the variance of ozone by a factor of 4 for the same reasons as
above and impose a vertical correlation length of 0.3 pressure decades to get
the covariance matrix. As explained in Sect. , the horizontal
covariance of ozone is assumed to be height independent with a horizontal
correlation length of 200 km. The ozone a priori profile and covariance
matrix thus depend on altitude and time (day or night and time of year).
The forward model also needs additional information about the atmosphere,
namely it includes the temperature profile (from MLS and ECMWF complemented
with WACCM) and volume mixing ratio profiles for the less critical species
N2 and O2 (from standard atmospheres) that are known well
enough and thus will not need to be optimised.
Quality control and uncertainty
A big advantage of the optimal estimation method over other regularisation
methods is the availability of error estimations and quality control
information.
As expressed by Eq. (), the averaging kernel matrix (AVKM)
describes the sensitivity of our estimated atmospheric state x^
for the true state x. We derive three quantities from the averaging
kernel matrix: firstly, the measurement response that is the sum of the rows
of the AVKM and describes the sensitivity of our retrieved state to the true
state as can readily be seen in Eq. (). Ideally it is exactly 1,
meaning that a change in the true atmospheric state is exactly represented in
the retrieved state. Secondly, the full width at half maximum of the
averaging kernels gives information about the spatial smoothing of the data.
Ideally these kernels would be delta peaks (which would make the AVKM
diagonal). Finally, we examine the difference between the peak of the
averaging kernels to their respective nominal height. In the ideal case
(diagonal AVKM), the offset would be zero, meaning that all information is
mapped to the correct grid points. We use the information in the AVKM for
quality control of the wind retrieval: the measurement response must be
between 0.8 and 1.2 and the offset of the peak to the nominal height of the
kernel must not exceed 5 km. If these criteria are fulfilled for an extended
altitude range, the retrieved values are valid. Further, the full width at
half maximum (FWHM) of the individual kernels gives information about the
altitude resolution.
Figure shows the averaging kernels and the derived quality
control parameters for one measurement. The retrieved values are considered
to be valid between 38 and 75 km altitude. The measurement response would be
acceptable on higher altitudes but the upper points are rejected by the
offset parameter. We see the offset parameter jumping from -7 to 10 km at
approximately 80 km altitude. This is because Doppler broadening starts to
dominate the pressure broadening above approximately 75 km altitude and
signals can not be attributed to the exact height they originate from. This
means that they are attributed to lower or higher altitudes depending on the
ozone a priori profile. Even though the measurement response stays within the
bounds of validity in these altitudes, offset criteria reject these points
reliably.
The FWHM in Fig. indicates an altitude resolution between 9
and 11 km for the whole altitude range. This is an improvement in comparison
to the WIRA retrieval, where the altitude resolution for zonal wind is about
10 to 16 km . We attribute this improvement to the
lower noise of the instrument and the simultaneous inversion of the two
measurements, which gives more independent information than the inversion of
one spectrum after the other.
Further, Fig. shows the residuals for the same retrieval
shown in Fig. . The residuals look random, indicating that we
properly model our observations.
Visualisation of the averaging kernel matrix (AVKM) for the
nighttime measurement of 26 June 2017. The individual averaging kernels (rows
of the AVKM) for each altitude (a) are characterized by the
measurement response (MR), their full width at half maximum (FWHM) and the
difference of their maximum to the nominal height (Offset). The valid ranges
for all parameters are marked by the green areas. Valid components that
fulfill all criteria are shown in colours and others in gray (or dashed lines
and hollow markers, respectively).
Corrected and integrated (12 h) brightness temperature spectra as
used for the retrieval of 26 June 2017 nighttime for eastwards and westwards
direction (a) together with the residuals (observed minus computed,
b). Smoothed residuals (by binning 50 channels) are shown in black.
Characterisation of the retrieval quality for zonal and meridional
wind for the day and nighttime period of 2 days. The observation error
represents the measurement uncertainty. The full width at half maximum (FWHM)
of the averaging kernels describes the altitude resolution, which is
approximately 10 km, up to 68 km altitude. The measurement response is a
measure for the sensitivity of our retrieved wind speeds to changes in actual
wind speeds. In the perfect case it would be 1.0 but values between 0.8 and
1.2 are acceptable.
Figure shows the observation error σo
for four different measurements together with the FWHM and the measurement
response. We see that the observation error for zonal wind retrievals is
approximately 15 m s-1, up to 64 km altitude for the nighttime
measurement with the chosen integration time of 12 h. Below 55 km, the
errors of the day and nighttime measurement are nearly identical, but above
60 km the error for the day time measurements increase rapidly. As
tropospheric opacity has a big impact on the signal-to-noise ratio of the
spectra, the bigger uncertainty for the daytime measurements can be explained
by the higher opacity during daytime as is shown in
Fig. . Also the ozone concentration is lower during
daytime as studied for example by , resulting in less
emitters and lower signal-to-noise ratio during daytime compared to
nighttime. The observation error is smaller for the meridional wind than it
is for the zonal wind. As elaborated in Sect. , this is because
the observation error is not independent of the a priori statistics and the
covariance for meridional wind is smaller than for zonal wind.
The full width at half maximum, that is also shown in
Fig. , describes the altitude resolution. For zonal
wind, the altitude resolution is approximately 10 km up to 68 km. For
meridional wind, the resolution is between 10 and 15 km, which is a direct
consequence of the more restrictive a priori profile for meridional wind.
While the measurement response is even between 0.9 and 1.1 (as opposed to the
quality requirement of 0.8 to 1.2) for nearly the entire altitude domain for
zonal wind indicating that our retrieval is highly sensitive to changes in
the atmospheric wind speed and largely independent of the a priori profile.
The measurement response for the meridional wind is somewhat more variable,
which is related to the constriction by the a priori profile, because a
smaller a priori covariance also implies less weight on the measurement and
thus lower sensitivity. Nevertheless, the quality requirement is fulfilled
between 38 and 65 km.
Considered uncertainties for the Monte Carlo error analysis together
with the estimated error. The resulting error is given as the maximum error
in three altitude domains: lower, from 5 to 1 hPa (36 to 48 km), middle,
from 1 to 0.2 hPa (48 to 59 km) and upper, from 0.2 to 0.02 hPa (59 to
75 km).
Estimated 1σ error, m s-1
Subject
Distribution
Type
Parameters
Lower
Middle
Upper
Temperature profile
Gaussian
absolute
2σ=10 K
0.86
0.94
0.57
Ozone a priori profile
Gaussian
absolute
2σ=0.4 ppm
0.91
1.2
3.2
Ozone covariance
Gaussian
relative
2σ=50 %
2.4
4.6
10
Wind covariance
Gaussian
relative
2σ=50 %
2.5
3.0
4.3
Elevation
uniform
absolute
±0.2∘
3.4
1.5
2.0
Calibration
uniform
relative
[1,1.3]
2.4
3.0
6.5
Total systematic
5.6
6.6
13
Retrieval noise
15
17
26
2σ=50 % means σ=14μ for a
Gaussian distribution with mean μ.
Estimation of systematic errors
In the above section, we discussed the random errors caused by thermal noise
on the spectrum as determined by the optimal estimation method. Additionally
we perform a Monte Carlo error estimation to further characterise
uncertainties not related to noise. These uncertainties are of systematic
nature, as they are inherent to the retrieval setup and choice of a priori
profiles and covariance matrices. Table gives a list of
the variables we considered in this analysis together with their expected
distribution. The Monte Carlo estimation involves sampling from these
distributions and retrieving a wind profile for every sample. The estimated
systematic error is then derived from the standard deviation of the retrieved
wind speeds.
All the profiles (temperature, a priori and covariances) are expected to
follow a Gaussian distribution as they are derived from statistics as
described in Sect. . We perturb the profiles on all
altitudes simultaneously using the value sampled from the respective
distribution. The elevation is expected to have a systematic error of maximum
±0.2∘, as this is the estimated precision we reach when levelling
the instrument. The calibration subject in Table
accounts for the uncertainty in the calibration and tropospheric correction.
This uncertainty has a random and a systematic component. We only consider
the systematic part that comes from the fact that our off-resonance
frequencies used to determine the tropospheric opacity is still somewhat
closer to the line centre than would be desirable (see
Sect. ). In our Monte Carlo estimation we simulate this
error by introducing a factor in the range 1,1.3 to the
y prior to the retrieval, which corresponds to an assumed uncertainty
of 10 % of the tropospheric opacity. Further, we neglect all correlations
between systematic errors and among systematic and random errors.
We performed the Monte Carlo estimation for four different cases (same as
shown in Fig. ). The results for the setup of one
retrieval (26 June 2017, nighttime) is shown in Table
for three different altitude domains. The biggest systematic error is evident
in higher altitude domains and comes from the ozone a priori profile. The
influence of the ozone a priori profile has been thoroughly examined by
, concluding that a careful choice of ozone a priori and
covariance data is important for the retrieval of wind speeds in higher
altitudes. The total systematic error is approximately half the retrieval
error in the worst case and by just looking at the retrieval noise, we thus
underestimate the total error by approximately 10 %.
Validation
The Maïdo campaign
From August 2016 until February 2018, the WIRA-C instrument has been operated
at the Maïdo observatory on Réunion(21.4∘ S,
55.9∘ E) at 2200 m above sea level. After having been operational
for a few days in August 2016, a very uncommon failure of the
synthesiser–multiplier chain occurred and the campaign could continue only in
mid-November. Since then, WIRA-C measured continuously, except for a period of
tropical cyclone alert and some power outages. The few measurements in August
2016 are very valuable because they coincide with three lidar measurements.
For all retrievals presented in this section, we used an integration time of
12 h, from 02:00 to 14:00 UT which is 06:00 and 18:00 local time (LT) and
roughly corresponds the times of sunrise and sunset in the tropics. We set up
the a priori profiles and covariances as described in Sect.
and most notably use an a priori of 0 m s-1 for all pressure levels
for zonal and meridional wind. Quality control for the retrieved data is done
as described in Sect. .
Comparison data
ECMWF model data
The ECMWF operational analysis provides atmospheric data on 137 layers up to
80 km altitude. However, the main focus lies on delivering data on the
atmospheric layers below 35 km for weather forecasts. Especially above
68 km the data quality is supposed to decrease because the uppermost layers
do not assimilate measurements but are artificially forced to model
stability.
Time series of zonal wind speeds measured by WIRA-C (a) and
ECMWF analysis data (b) between 14 November 2016 and 31 December
2018 for the altitude range of 35 to 75 km with a time resolution of 12 h
(day and nighttime). The ECMWF data has been convolved with the averaging
kernels of the retrieval in order to get the same spatial and temporal
resolution for both datasets. Invalid data points are grayed out, resulting
in different altitude ranges for different days. The few data gaps are due to
a tropical cyclone and power outages.
Zonal WIRA-C wind measurements on 10 distinct pressure levels
between 35 km (a) to 71 km (j). The fully convolved ECMWF
model data as well as the ECMWF data from the nearest pressure level (but
still smoothed in time) is given for comparison. Often the raw and convolved
ECMWF curves coincide. Time resolution is 12 h (day and nighttime). The
light-blue area represents the uncertainty σo of the WIRA-C
data.
The ECMWF operational analysis has a higher time and altitude grid resolution
than the WIRA-C retrieval. The time resolution is 6 h, whereas WIRA-C has a
time resolution of 12 h. Thus, to check the two datasets for consistency we
always average the two ECMWF time steps which are within the respective
integration period of WIRA-C.
To adapt the vertical resolution of the model to our retrieval, we convolve
the model data with the averaging kernels of the retrieval.
Integrated forecast system cycles Cy41r2, Cy43r1 and Cy43r3 have been used
for this study.
The Rayleigh–Mie Doppler wind lidar
The Rayleigh–Mie Doppler wind lidar is an active sounder, measuring the
Doppler shift of backscattered visible light using Fabry–Perot
interferometry and can provide wind profiles from 5 up to approximately
60 km. Up to 30 km, the vertical resolution is 100 m and the accuracy is
better than 1 m s-1 for 1 h integration time. Because of decreasing
density of molecular backscatters and the inverse-square law of light, the
uncertainties of the lidar measurements increase with altitude and finally
limit the altitude domain to approximately 60 km depending on integration
time. Between 30 and 60 km, the vertical resolution varies between 0.5 to
3 km and the measurement error is 10 m s-1 at 50 km altitude for an
integration time of 3 h. The instrument and the retrieval scheme is
described in and references therein.
Same as Fig. but for meridional wind.
Time series of meridional wind speeds measured by WIRA-C (a) and
ECMWF analysis data (b) between 14 November 2016 and 1 January 2018
for the altitude range of 35 to 75 km with a time resolution of 12 h (day
and nighttime). The ECMWF data has been convolved with the averaging kernels
of the retrieval in order to get the same spatial and temporal resolution for
both datasets. Invalid data points are grayed out, resulting in different
altitude ranges for different days. The few data gaps are due to a tropical
cyclone and power outages.
The lidar only measures at nighttime and has a variable integration time that
depends on meteorological conditions (clear sky) and available man power. As
the integration time often is below 4 h, we cannot run a retrieval for the
microwave radiometer for exactly the same integration time because of the
noise. We currently have no opportunity to adapt our measurement to the short
integration times of the lidar and thus we just compare the nighttime
measurement of WIRA-C and the lidar while noting the respective integration
times. For the vertical resolution we convolve the lidar data with the
averaging kernels of the retrieval to have comparable altitude resolution of
the profiles.
The lidar measures at an elevation angle of 45∘ as opposed to the
22∘ of WIRA-C. However, the difference between the two lines-of-sight
is not relevant, as WIRA-C retrieves a wind profile that best fits both
observations in opposing directions. As the retrieval is not linear, this
does not necessarily deliver the mean profile but an approximation thereof.
For our retrieval and comparisons, we thus assume that the variation of
horizontal wind speeds are negligible for 12 h integration time and
horizontal distances from 150 km at 30 km altitude up to 370 km at 75 km
altitude.
Results
Figures and show
an overview over the zonal and meridional measurements from the Maïdo
campaign, together with the corresponding ECMWF data, convolved in space and
time. A more detailed view is given in Figs.
and for zonal and meridional wind, respectively.
There, besides the convolved ECMWF data, the model data of the nearest
level is also given for comparison. At the lowest and highest levels, the
difference between the fully convolved and the original ECMWF data is quite
obvious. This difference is an indicator for the smoothing error, and is a
consequence of the slightly worse altitude resolution and accuracy at the
lowest and uppermost levels compared to the central levels where the
difference nearly vanishes.
Same as Fig. but for meridional wind. WIRA-C
measurements on 10 distinct pressure levels between 35 km (a) to
71 km (f) for 1 June 2017 to 19 September 2017. The data before
June 2017 and after September 2017 (shown in Fig. )
is not represented here in order to focus on the period with more
variability. The fully convolved ECMWF model data as well as the ECMWF data
from the nearest pressure level (but still smoothed in time) is given for
comparison. Time resolution is 12 h (day and nighttime). The light-blue area
represents the uncertainty σo of the WIRA-C data.
In general, the zonal and meridional wind for WIRA-C and ECMWF are
consistent: firstly, the zonal wind reversal around equinox is resolved by
the model as well as WIRA-C and they agree on the time of this event as well
as on the magnitude. Secondly, the well-defined periods of stronger westward
winds between 35 and 55 km in June are present in both datasets. Further,
the increased variability with a period of approximately 10 days present at
the layers between 50 and 60 km in August and September 2017 are also
present in both datasets.
Seven coincident observations of zonal wind from WIRA-C and Doppler
lidar from August 2016 and June 2017 together with radio soundings and ECMWF
operational model data at different times, WIRA-C measurements start at
14:00 UT (18:00 LT) and lidar measurements typically between 17:00 and
20:00 UT (21:00 and 24:00 LT). The measurement time for WIRA-C is 12 h for
every profile while the measurement time for the lidar observation (given in
parenthesis) is typically between 3 and 3.5 h, with the exception of 21 and
22 June 2017, where measurement took 8.8 and 9.7 h, respectively. Source of
radiosonde data: Météo-France.
Seven coincident observations of meridional wind from WIRA-C and
Doppler lidar from August 2016 and June 2017 together with radio soundings
and ECMWF operational model data at different times, WIRA-C measurements
start at 14:00 UT (18:00 LT) and lidar measurements typically between 17:00
and 20:00 UT (21:00 and 24:00 LT). The measurement time for WIRA-C is 12 h
for every profile while the measurement time for the lidar observation (given
in parenthesis) is typically between 1 and 4 h, with the exception of 21 and
22 June 2017, where measurement took 8.8 and 9.9 h, respectively. Source of
radiosonde data: Météo-France.
There are also short periods where we can see a clear discrepancy between
the model data and the measurement. For example at the layers below 45 km
for the end of January and beginning of February 2017, where WIRA-C measured
a smaller magnitude of zonal wind than predicted by the model for several
days. This might be connected to the tropical cyclone in the Indian ocean
that was the reason for the subsequent interruption of the measurement, as
the instrument had to be dismounted and protected inside the building. At the
uppermost levels, ECMWF has the tendency to predict a higher magnitude in
zonal wind speed and to some extent also in meridional wind speed than
WIRA-C. Most prominently at the end of April 2017, the model predicts a much
higher magnitude in zonal wind but a lower variability. This might be an
effect of the artificial forcing in the model at the uppermost layers. At the
same time, our observation error increases with altitude and we cannot
completely rule out, that the variability is caused by retrieval noise.
Figures and show all seven
coincident measurements of WIRA-C and the Rayleigh–Mie Doppler wind lidar
available to date for the zonal and meridional wind component, respectively.
The lidar profiles have been acquired in August 2016 during routine
measurements and in June 2017 during the LIDEOLE-III campaign. In addition,
the corresponding ECMWF model data is shown at the four closest time steps of
the model. In case of zonal wind, these ECMWF profiles are nearly identical
but for the meridional wind, they indicate a high temporal variability in the
model data. At the lowermost levels, the radiosonde launched at the nearby
Gillot airport at noon is given for comparison where available.
For both horizontal wind components, the profiles of the three sources
(WIRA-C, lidar, ECMWF) are consistent. Especially for the lidar measurements
on 21 and 22 June 2017, where the whole night was used for lidar acquisition,
the agreement of the two independent measurements is well within their
respective uncertainties. We would like to emphasise that favourable
conditions for lidar measurements, namely clear sky and nighttime, also imply
lower uncertainties for the WIRA-C measurements. Remarkably, the zonal wind
measurements from 22 June 2017 of WIRA-C and the lidar are nearly identical,
while the ECMWF model is offset by 20 m s-1 at 55 km altitude.
For the meridional wind, the lidar shows some patterns with very large
vertical gradients in the wind speeds as on 18 August 2016 and 21, 22 and
26 June 2017 at an altitude around 40, 55, 48 and 47 km, respectively. These
patterns are not present in the other datasets and are probably caused by
internal gravity waves. For characteristics and details about such structures
observed by lidar, see . It is conceivable that the
vertical structures observed by the lidar are simply not resolved by the
ECMWF model and smoothed out by the radiometer. For example, for the
measurement of the meridional wind on 21 and 22 June 2017, we can see that
the convolved lidar profile and the WIRA-C measurement agree quite well while
the high resolution profile of the lidar shows a layer of wind speeds with
higher magnitude at 50 km altitude. This indicates that WIRA-C indeed
smoothes out the feature, but that the two measurements are consistent.
Conclusions
WIRA-C is a new passive microwave wind radiometer designed for
campaigns as well as long-term measurements. With it, the successful
prototype WIRA has been replicated and improved. The optical system and the
pre-amplified single side band heterodyne receiver and the spectrometer are
embedded in a single housing with compact dimensions. Calibration is
performed with the tipping curve scheme and tropospheric correction accounts
for tropospheric inhomogeneities and normalises the spectra acquired in the
four cardinal directions.
We applied an optimal estimation retrieval to combine observations in
opposing directions to get a single wind profile that best represents all our
measurements. The main benefit of our retrieval scheme is the availability of
quality control parameters representing the whole inversion process and the
increased altitude resolution of 9 to 11 km (as opposed to 10 to 16 km for
WIRA). The observation error gives an estimate on the uncertainty in wind
speeds caused by the thermal noise on our measurements. Its 1σ value
for zonal wind is typically around 15 m s-1 up to 68 km or 60 km for
nighttime and daytime measurements, respectively. The error on the meridional
wind is approximately 9 m s-1 due to the smaller covariance of the
a priori profile that represents the expected magnitude of the wind speeds.
To complement the estimation of the random error we performed Monte Carlo
estimations of possible systematic error sources. These estimations show that
the expected systematic errors are lower than the random errors.
The validation campaign on the Maïdo observatory on Réunion
proved that WIRA-C can provide continuous measurements of horizontal
wind speeds in the altitude range of 35 to 70 km. We presented a 1-year
dataset of measurements with a time resolution of 12 h and an altitude
resolution of approximately 10 km for zonal and 15 km for meridional wind.
Even though we retrieve ozone profiles as well, we consider them as a
by-product that is only needed to fully fit the spectrum and discussion of
them is not in the scope of this paper.
The measurements are consistent with the ECMWF operational analysis and also
show very good agreement with the available lidar measurements from the
co-located Rayleigh–Mie Doppler wind lidar. The main challenge for the
comparisons is to properly account for the different integration times and
spatial resolutions, especially for the lidar measurements with short
acquisition times. The finer structures in the wind profiles as seen by the
lidar are not resolved by WIRA-C, but the convolved profiles indicate a high
consistency of the measurements. For the lidar measurements where integration
has been performed during the whole night, the two independent measurements
agree within their respective errors in the entire altitude range of overlap
(37 to 50 km). More coincident lidar measurements would certainly be
valuable for further validation.
In total we conclude that WIRA-C provides valuable continuous measurements
of horizontal wind speeds covering the gap region between 35 and 70 km.
These measurements are complementary to the better resolved lidar
measurements, as they are continuous over more than one year and cover day
and nighttime.
The next steps in passive microwave wind radiometry will go towards
optimising the retrieval process and explore the lower limits of time
resolution. This could include a time series retrieval as performed by
for a water vapour instrument. Also, the possibility
of wind retrievals above the Doppler broadening range could be further
explored as a first comparison between WIRA and meteor radar measurements
Fig. A1 was very promising.