The European Space Agency (ESA) Earth Explorer satellite Aeolus provides continuous profiles of the
horizontal line-of-sight wind component globally from space. It was
successfully launched in August 2018 with the goal to improve numerical
weather prediction (NWP). Aeolus data have already been successfully
assimilated into several NWP models and have already helped to significantly
improve the quality of weather forecasts. To achieve this major milestone
the identification and correction of several systematic error sources were
necessary. One of them is related to small fluctuations of the temperatures
across the 1.5 m diameter primary mirror of the telescope which cause
varying wind biases along the orbit of up to 8 m s-1. This paper presents a
detailed overview of the influence of the telescope temperature variations
on the Aeolus wind products and describes the approach to correct for this
systematic error source in the operational near-real-time (NRT) processing.
It was shown that the telescope temperature variations along the orbit are
due to changes in the top-of-atmosphere reflected shortwave and outgoing
longwave radiation of the Earth and the related response of the telescope's
thermal control system. To correct for this effect ECMWF model-equivalent
winds are used as a reference to describe the wind bias in a multiple linear
regression model as a function of various temperature sensors located on the
primary telescope mirror. This correction scheme has been in operational use
at ECMWF since April 2020 and is capable of reducing a large part of the
telescope-induced wind bias. In cases where the influence of the temperature
variations is particularly strong it was shown that the bias correction can
improve the orbital bias variation by up to 53 %. Moreover, it was
demonstrated that the approach of using ECMWF model-equivalent winds is
justified by the fact that the global bias of model u-component winds with respect to
radiosondes is smaller than 0.3 m s-1. Furthermore, this paper presents the
alternative of using Aeolus ground return winds which serve as a zero-wind
reference in the multiple linear regression model. The results show that the
approach based on ground return winds only performs 10.8 % worse than the
ECMWF model-based approach and thus has a good potential for future
applications for upcoming reprocessing campaigns or even in the NRT
processing of Aeolus wind products.
Introduction
The European Space Agency (ESA) Earth Explorer satellite Aeolus was
successfully launched into space in August 2018 with an intended mission
lifetime of 3 years (Kanitz et al., 2019;
Reitebuch et al., 2020). Aeolus, built by Airbus, is equipped with the
first-ever functioning space-borne Doppler wind lidar (DWL) instrument
ALADIN (Atmospheric LAser Doppler
INstrument) and provides globally distributed
vertically resolved wind measurements from the ground up to 30 km (ESA, 1999; Reitebuch, 2012a). It measures the
component of the wind vector along the instrument's line of sight by
emitting ultraviolet (UV) laser pulses into the atmosphere and detecting the
frequency-shifted backscatter signal from molecules and particles (ESA, 2008). The main goal of Aeolus is to improve
numerical weather prediction (NWP) by filling gaps for global wind
measurements in the Global Observation System of the World Meteorological
Organization (WMO), especially in the tropics and the Southern Hemisphere (Andersson, 2018; Stoffelen et al., 2005, 2020). Another goal is to improve our understanding
of the atmospheric dynamics, especially in the tropics. As spin-off data
products, Aeolus provides continuous information about aerosol and cloud
distribution, including vertical profiles of backscatter and extinction
coefficients (Ansmann
et al., 2007; Flamant et al., 2008).
The operational assimilation of Aeolus observations into the European Centre
for Medium-Range Weather Forecasts (ECMWF) NWP system was started (Rennie and Isaksen, 2020) on 9 January 2020, followed by other
weather centers around the world, such as the German weather service DWD
(Deutscher Wetterdienst), Météo-France and the UK Met Office. A
prerequisite for this major milestone was the quick identification and
correction of the two most important systematic error sources of the Aeolus
wind measurements (Reitebuch et al., 2020;
Rennie, 2018). The first one was linked to dark current anomalies, so-called
“hot pixels”, on the Aeolus detectors which cause systematic wind errors
of up to several meters per second. This issue was successfully mitigated on 14 June 2019
by applying appropriate correction methods based on dedicated dark signal
calibration measurements (Weiler et al.,
2021). The second one, independent of the hot pixel issue, was linked to
unexpectedly large systematic errors which strongly vary with geolocation.
Thanks to the collaborative effort of the teams within the Aeolus Data
Innovation and Science Cluster (DISC) (Reitebuch et al., 2019) and
the first discovery at ECMWF (Rennie and Isaksen, 2020), a
strong correlation of the wind bias with temperature variations across the
primary mirror of the telescope could be identified as the root cause of the
latter issue.
The small primary mirror temperature variations of 0.3 ∘C, which
are related to varying outgoing top-of-atmosphere (TOA) radiation and
corresponding response of the primary mirror's thermal control (TC) to that, lead
to varying wind errors along the orbit of up to 8 m s-1. Thermal changes in
the instrument's components along the orbit were already expected before
launch. However, it was assumed that these variations would be of smaller
error magnitude and would be mainly of a harmonic orbit-related nature (Reitebuch et al., 2018b). As the telescope-induced bias
turned out to be strongly scene-dependent and not perfectly harmonic, bias
correction tools, which were developed before the Aeolus launch, could not
be applied to the discovered complexity. As a consequence, a new bias
correction method using the temperatures of the Aeolus telescope from the
Aeolus housekeeping telemetry as independent variables was developed and has
been successfully implemented into the operational near-real-time (NRT)
processing chain of Aeolus since 20 April 2020.
This article aims to provide a detailed overview of the influence of the
telescope temperature variations on the Aeolus winds and the method to
correct for the telescope temperature-induced wind bias. Section 2 of the
paper briefly describes the measurement principles of Aeolus, the design and
thermal control of the telescope, and the Aeolus wind data products.
Section 3 depicts the telescope-induced wind bias and explains the bias
correction method in detail. Section 4 demonstrates the performance of the
wind bias correction scheme based on a case study with special settings for
the telescope temperatures and also shows the reliability of the method when
applied to the complete observation period of 6 months using Aeolus data
from the first data reprocessing campaign from June to December 2019.
The paper concludes with a summary and an outlook for further analysis.
Instrument and datasets
This section gives an overview of the measurement principle of ALADIN
followed by a description of the instrument's telescope and its thermal
control. Finally, the Aeolus data products and variables necessary for this
study are presented. For more detailed information about the instrument,
please refer to ESA (2008), Reitebuch et al. (2018a), Reitebuch (2012a), or Lux et al. (2021).
ALADIN configuration and measurement principle
Aeolus flies in a sun-synchronous dusk/dawn orbit at a mean altitude of 320 km with a repeat cycle of 7 d. The satellite carries one single payload,
the direct-detection Doppler wind lidar which is pointing toward the Earth
under a 35∘ off-nadir angle towards the dark side of the
terminator, the line separating the sunlit from the nighttime areas (Reitebuch, 2012a). The instrument consists of three main
components, the laser transmitter, the telescope and the receiver unit. The
ultra-violet laser transmitter emits nanosecond pulses with a pulse
repetition frequency of 50.5 Hz and an energy of ∼ 60 mJ into
the atmosphere (Lux et al., 2020a) where the light is
scattered on air molecules, aerosols and cloud particles (Reitebuch, 2012b). The backscattered light from the
atmosphere is collected by a Cassegrain-type telescope which consists of two
mirrors. The primary mirror collects the light and the secondary mirror
reflects it through a hole in the primary mirror to the receiver unit where
the Doppler frequency shift of the backscatter light is analyzed. The
receiver combines a Fizeau interferometer (FIZ) to analyze the narrow
spectral bandwidth backscatter signal from aerosols and cloud particles (Mie
channel) and two sequential Fabry–Pérot interferometers (FPIs) (Rayleigh
channel) to measure the broad bandwidth backscatter signal from molecules.
The Mie channel uses the fringe-imaging technique which is based on
measuring the wind-speed-dependent horizontal displacement of interference
patterns (McKay, 1998). The Rayleigh channel
incorporates the double-edge technique which uses two FPIs as spectral
filters that are symmetrically placed around the transmitted laser wavelength (Chanin et al., 1989;
Flesia and Korb, 1999; Garnier and Chanin, 1992). In the presence of a
Doppler frequency shift the Rayleigh spectrum is shifted towards the
spectral peak transmission of one of the two filters. Thus, from the
contrast between the transmission of two filters the wind speed along the
line of sight of the instrument can be determined. Afterwards, a projection
to the horizontal plane, the so-called horizonal line of sight (HLOS), is
obtained.
For both channels accumulation charged-coupled devices (ACCDs) are used to
image the output of the spectrometers (ESA, 2008; Weiler et al.,
2021). In the 16×16 pixel illuminated imaging area the return signal is
integrated over time based on the vertical range gate settings. The
integration time is adjustable and can be changed from 2.1 to 16.8 µs which corresponds to vertical sampling of 250 to 2000 m,
considering the 35∘ off-nadir angle of the instrument. Afterwards,
the signals of each range gate are binned together and are continuously
shifted downwards to the non-illuminated memory zone of the ACCD which
consists of 16×16 pixels in which each row corresponds to one range gate. In
the memory zone the return signals of 18 consecutive laser pulses are
accumulated to so-called measurements with a duration of 0.4 s
(∼ 2.9 km horizontal resolution). Afterwards, the accumulated
charges are digitized with 16-bit accuracy and converted into numbers of
least significant bits (LSBs). In the on-ground processing the signal of
typically 30 measurements is accumulated to so-called observations with a
duration of 12 s which corresponds to a spatial horizontal resolution of
86.4 km (see Fig. 1) for a satellite ground track
speed of 7.34 km s-1.
(a) Aeolus observational geometry (adapted from Lux et al., 2020b) and (b) the
setup of the Aeolus telescope consisting of the M1 primary and M2 secondary
mirrors and the mounting struts (adapted from https://directory.eoportal.org/web/eoportal/satellite-missions/a/aeolus,
last access: 23 August 2021).
Aeolus telescope
Aeolus is operated in a mono-axial transceiver configuration which means
that the same telescope is used to transmit and receive the light. The
Cassegrain telescope consists of a parabolic 1.5 m diameter primary “M1”
mirror and a convex, spherical 46 mm diameter secondary “M2” mirror
attached to three mounting struts (see Fig. 1).
The main components of the telescope are made of silicon carbide (SiC).The
wave front error, defined as the deviation of the telescope's wave front
from the perfect spherical, was determined after the instrument assembly to
be below 150 nm rms (root mean square) which is within the specification of
340 nm rms (Korhonen et al., 2008). The distance
between the M1 and M2 mirrors is 1.32 m. The main specifications of the
Aeolus telescope are summarized in Table 1. A baffle
around the complete telescope structure is used to shield the secondary
mirror and the mounting struts from direct sun illumination. On the
sun-remote side of the satellite the baffle is shortened to reduce mass and
air drag. As Aeolus is facing different thermal conditions on its orbit
which influence the thermal stability of the M1 mirror, an active thermal
control system is used. The thermal control of the M1 mirror aims to keep
the temperature of the M1 mirror stable at a fixed temperature setpoint of
12 ∘C throughout the orbit, using thermal control (TC) thermistors
located on the back side of the mirror. For additional temperature
monitoring further temperature sensors also located on the back side of the
mirror, the so-called accurate housekeeping thermistors (AHTs), are
available. The AHT sensors are not used in the active thermal control system
of the telescope. Measurements of both sensor types are provided for each
observation every 12 s in the Aeolus data products. The location of
the sensors on the M1 mirror is indicated in Fig. 2. The sensors TC-23, TC-29 and TC-32 which are mounted on the bottom and
lateral shields of the mirror are not indicated in the figure and are not used
in the thermal control loop of the telescope.
A schematic illustration of the Aeolus M1 mirror. The red and
orange dots indicate the positions of the thermal control (TC) and accurate
housekeeping (AHT) thermistors. X indicates the flight direction. Note that
TC-23, TC-29 and TC-32 are not shown.
To control the focus of the telescope the thermal control of the struts and
the M2 mirror can be adjusted using dedicated heaters. This allows us to change
the distance between the M1 and the M2 mirrors which affects the focus of the
telescope. So-called instrument telescope refocus (ITR) measurements are
carried out on a regular basis to determine the best focus with respect to the
radiometric performance of the instrument and using the spot width on the
Rayleigh channel ACCD as a measure for the telescope's focus. During these
measurements, the temperature setpoints of the strut's and M2 control
thermistors are varied in the range between 6 to 16 ∘C in order to derive the optimum setpoint with the best focus.
Aeolus telescope specifications.
ParametersValueTypeCassegrain concept, silicon carbideDiameterPrimary mirror M1: 1.5 m, parabolicSecondary mirror M2: 46 mm, spherical-convexMass67 kgOptical qualitySpecification <340 nm rms wave front errorAeolus data products
The Aeolus data processing which is managed by ESA's Payload Data Ground
Segment (PDGS) includes several stages to process the raw detector counts up
to the main wind product, namely the Level 2B (L2B) data product which
contains the fully processed horizontal line-of-sight (HLOS) winds for the
Mie and Rayleigh channels (Straume, 2018; Rennie et
al., 2020). To continuously improve the quality of the Aeolus data products
for use of Aeolus products in operations at NWP centers, the operational
processors are usually updated twice a year. Updates for auxiliary files
which are used to control certain settings of the processors do not follow
a fixed schedule and are updated more often. The term “baseline” is part
of the PDGS administration and is used to describe a collection of products
that have been produced in a similar way, i.e., using processor versions with
similar major version numbers and mostly unchanged algorithm settings.
Level 1B
In the L0 and L1A steps, the housekeeping information which consists of
various satellite and instrument parameters (e.g., temperatures, pressure,
currents, etc.) is processed, and the raw signal data are geo-referenced. The
L1B processor provides processed ground echo data and preliminary winds
which are not corrected for atmospheric temperature and pressure influences (Reitebuch et al., 2018a) at the so-called observation
level which corresponds to a temporal resolution of 12 s corresponding to a
spatial horizontal resolution of 86.4 km (see Fig. 1). Within the various processing steps, the L1B processor uses a ground
detection scheme to flag return signals as ground return signals (Weiler, 2017) with the aim to use these ground detections for
zero-wind calibration (ZWC). Solid ground is assumed to be a non-moving
object and thus can be used as a zero-wind speed reference. In addition,
this also allows possible ground-affected range bins to be flagged since
mixing ground and atmospheric backscatter in the same range bin will lead to
incorrect wind retrievals. In a first step, the L1B ground detection
algorithm identifies ground bin candidates based on a signal-gradient
threshold approach (Weiler, 2017). Next, several checks are
performed to further restrict the selection of ground bins. For instance,
the distance of the ground bin candidates to a model of the Earth's surface
is evaluated, and the signal intensity of the ground bin candidates is also
assessed to identify valid ground bins. In a final step, the wind retrieval
is applied to the valid ground bin signals to retrieve the ZWC winds (Reitebuch et al., 2018a). The ZWC
winds are contained for each channel at observation level in the L1B
products and can be used as reference for the M1 bias correction (see Sect. 3.3). The sensitivity of the ground detection algorithm can be controlled by
several parameters. For the presented work reprocessed Aeolus L1B data
products, processed using the same processor versions as for baseline 1B11
but with custom ground detection settings, from June to December 2019
were used. For these data products quite relaxed parameter settings for the
ground detection were used. The minimum ground useful signal thresholds were
set to zero for both channels, which leads to a high number of ground returns
in the L1B product. Since also the ground return signal is reported in the
L1B product, it is possible to use the ground useful signal as quality
criterion by applying a minimum threshold. In the framework of this
analysis, a minimum useful signal threshold of 9700 LSBs is applied to the
Rayleigh ZWC winds, making sure that gross outliers are removed from the
dataset.
Level 2B
The L2B processing (Tan et al., 2008)
includes a correction of the Rayleigh winds for temperature and pressure
broadening effects (Dabas et
al., 2008). This correction is based on a priori temperature and pressure
information from short-range forecasts from the ECMWF weather forecast
model. Moreover, the measurement signals (∼ 2.9 km horizontal
resolution) from the Mie and Rayleigh channels are classified according to
their optical properties based on the scattering ratio and signal-to-noise
ratio (SNR) derived from the Mie channel. This allows for the classification of
measurements into so-called “clear” (molecular backscatter) and “cloudy”
(particulate backscatter) results to avoid contamination from spectrally
narrow bandwidth Mie signals in the Rayleigh channel, which would result in
errors in the retrieved wind speed (when not accounted for). The classified
measurements are then grouped together and horizontally accumulated to
optimize the signal-to-noise ratio. The accumulation length is variable and
depends on the processor settings and the characteristics of the measurement
signals. Due to the different SNR characteristics of the Mie and Rayleigh
signals, the accumulation length is also different for both channels. For
the Mie channel, the signals are typically accumulated over a horizontal
scale of at most ∼ 10 km, whereas the accumulation length for
the Rayleigh (clear air) signals is at most ∼ 86 km. It should
be noted that for mixed scenes containing both clear and cloudy sections,
the accumulation length may be smaller, and this may differ for different
altitudes. Afterwards, the wind retrieval is separately applied to each
accumulated signal portion to yield two HLOS so-called “wind results” for
each channel: Rayleigh clear and cloudy; and Mie clear and
cloudy. In general, the focus lies on the Rayleigh clear and Mie
cloudy wind results since they are of better quality. It should be noted
that the Mie clear wind results are physically not meaningful and are a
result of the classification process. As part of the wind retrieval, a
cross-talk correction is applied to the Rayleigh wind results to further
minimize Mie contamination (Rennie et al., 2020). Moreover,
the L2B products also contain quality flags and wind error estimates for
each wind result.
For the presented work Aeolus L2B data products produced by the PDGS,
labeled with baseline 2B10, from June to December 2019 were used.
ECMWF model and O-B statistics
For monitoring purposes, equivalent HLOS winds from the ECMWF model are
calculated for each L2B wind result. For this, information from the Aeolus
auxiliary meteorological files (AUX_MET) which amongst many
variables contains wind vector information along the predicted Aeolus track
is used (Rennie et al., 2020). The information in the
AUX_MET file is updated every 12 h and is based on short-range forecasts obtained from the operational ECMWF high-resolution model
TCO1279 (∼ 9 km grid spacing, cubic-octahedral spectral
transform with spectral truncation of n=1279) (Malardel et al., 2016) with a maximum forecast range of
up to 30 h. The information in the AUX_MET files is
provided every 3 s along the orbit at 137 model levels interpolated
(nearest neighbor) to the Aeolus track. To compute observation minus
background (O-B) statistics, the L2B processor uses a nearest-neighbor
approach in the horizontal and uses the closest profile in the
AUX_MET file in the selected time window. In the vertical
dimension a spline interpolation is used to get a value at the proper
altitude. The O-B statistics have been used to analyze the systematic and
random wind errors of the Aeolus observations at a global scale (Martin et
al., 2021). The term “background” refers to the background model forecast
which serves as a priori information for the next analysis run in the data
assimilation (Rennie and Isaksen, 2020). From 20 April 2020 (as
implemented in L2BP v.3.30, starting with Level 2B products labeled
baseline 09) onwards, O-B statistics also have been added to the operational
Aeolus L2B products. The first reprocessed dataset from June to
December 2019 also includes this improvement.
For the following analysis of the dependency of the wind bias on the M1
temperatures, a representative average O-B value “E(O-B)” is calculated
from the L2B O-B values. For this only L2B wind results with the overall
validity flag set to “true” are used. In addition, HLOS error estimates,
reported for each L2B wind result, are used as quality criterion. Only Mie
and Rayleigh wind results with HLOS error estimates smaller than 4 and 8 m s-1, respectively, are considered. As mentioned above, the O-B values are
available for each L2B wind result. However, to decrease the variance of the
bias, the O-B values are horizontally averaged to the L1B observation
granularity (12 s temporal and 86.4 km horizontal resolution). For long wind result accumulation lengths, the L1B observation might be covered by only
one single wind result. In such cases, no averaging is performed.
Afterwards, the O-B values are averaged over all range gates to yield the
E(O-B) value. This is justified by the lack of altitude dependency of the
M1 bias effect as the measured M1 temperatures are constant over all
altitudes. Figure 3 shows the typical distribution
of the center-of-gravity altitudes of the L2B Mie cloudy and Rayleigh clear
wind results. This plot indicates that for the Mie channel a large fraction of
wind results in the lower altitudes contribute to the E(O-B) statistics.
In contrast, the Rayleigh wind results show a broad distribution with an equal
contribution of the wind results in the altitude range between 5000 and
18 000 m. As explained in the following sections, the E(O-B) value is used to
derive the fit coefficients for the M1 bias correction. Thus, the
information from Fig. 3 should be kept in mind when
analyzing the altitude dependency of the error of M1 bias-corrected L2B wind
results.
Density curves of the center-of-gravity altitudes of the Mie
cloudy (blue) and Rayleigh clear (orange) L2B wind results. A total of 74 202 Mie and
132 042 Rayleigh wind results obtained from 8 August 2019 were used to derive
the probability density curves. Only valid wind results with HLOS error
estimates smaller than 4 and 8 m s-1 for the Mie and Rayleigh channels,
respectively, are shown.
It is obvious that the use of the NWP model for the bias correction
introduces some NWP model bias dependency since the ECMWF model wind biases
are not zero. However, this is justified by the fact that on average the
global bias of the model wind u components with respect to reference measurements
based on radiosondes is relatively small. This is demonstrated in
Fig. 4, which shows the time series of daily
averages of E(O-B) values of the ECMWF's u-component winds computed for
radiosondes and pilots (radiosondes that only measure wind). It should be
mentioned that the comparison is restricted to locations where radiosondes
and pilots are available, which is mainly above the Northern Hemisphere land
surface. Thus, it is difficult to accurately assess the model bias in the
Southern Hemisphere or above oceans. Nevertheless,
Fig. 4 shows that during all days the bias is
clearly below 0.3 m s-1, which is significantly smaller than the Aeolus M1-related bias (for the Rayleigh), justifying the choice of the ECMWF model as
a reference for the bias correction. To mitigate the influence of model wind
bias, 24 h of global model winds averaged over all altitudes are used in
the M1 bias correction. On the one hand, this makes sure that localized
small-scale model biases (e.g., in the tropics) appear only as a noise source
in the fit procedure. On the other hand, averaging over all altitudes
ensures that any altitude-varying model bias is not an issue.
Time series of global (at all available radiosonde and pilot
locations) 24 h averages of E(O-B) values of ECMWF's u-component winds
computed for radiosondes and pilots (radiosondes that only measure wind) at
all model levels.
Methods
The following section describes the correlation between the wind bias and
the M1 telescope temperatures. Moreover, the approach to remove the M1-dependent bias using O-B values and ZWC winds as a bias reference is
explained, and its limitations are discussed.
Telescope-induced wind bias
Before launch, harmonic (with respect to the orbit phase) bias contributors,
induced by thermal effects and pointing variations of the attitude control
system that mainly depend on the latitudinal position of the satellite and
the orbit phase, were expected to be dominant. These kinds of error
contributors were supposed to be corrected with the so-called harmonic bias
estimator (Reitebuch et al., 2018b). This tool was set up
before launch based on end-to-end simulations of the assumed harmonic errors
using ZWC winds as a reference to correct for harmonic bias variations.
However, it turned out that this kind of correction was far from being
sufficient to correct the bias variation as seen in Aeolus in-orbit data
despite the wind biases having some harmonic behavior.
Figure 5 shows in-orbit measurements of the Rayleigh
clear E(O-B) values as a function of the orbit phase angle (argument of
latitude) on 11 August (blue) and 11 November (orange) 2019. The
argument of latitude describes the position of the satellite and is defined
as 0∘ at the ascending node Equator crossing and 360∘ at
the descending node Equator crossing. For both cases the bias shows complex
and non-perfectly harmonic dependencies with the orbit phase. Moreover, it
was found that the bias structure changes over the seasons and is strongly
dependent on the atmospheric scene, i.e., cloudiness and the TOA temperature.
Comparing both cases in Fig. 5 shows smaller bias
amplitudes in the Southern Hemisphere in November than in August. On top of
that, the bias shows strong longitudinal dependencies, i.e., non-harmonic
elements, which are indicated by the large spread of the bias at a fixed
orbit phase, e.g., at around 45∘ argument of latitude for the
August case.
Rayleigh clear E(O-B) HLOS statistics as a function of the
argument of latitude on 11 August (blue) and 11 November (orange) 2019.
The argument of latitude describes the position of the satellite along its
orbit in the ascending (asc., dark grey) and descending (desc., light grey)
orbit phase (EQ: Equator; NP: North Pole; SP: South Pole). The blue and
orange dots indicate the E(O-B) values which correspond to averaged O-B
values over all altitudes at observation level (introduced in Sect. 2.4). The
blue and the orange lines show the E(O-B) values as binned averages using a
bin size of 5∘ for the argument of latitude.
Bell et al. (2008) found strong
correlations between housekeeping temperature data and biases for the Special Sensor Microwave Imager/Sounder (SSMI/S)
mission, so easy access to housekeeping data for Aeolus was requested early
on during the design of the ground segment. The comparison of the O-B statistics
with available housekeeping data then revealed a high correlation of the
Rayleigh bias with the M1 temperatures. In particular, a strong linear
correlation was found between the Rayleigh bias and the radial temperature
gradients of the M1 telescope mirror. This relationship was first discovered
at ECMWF and is described in more detail in Rennie and Isaksen (2020). The radial temperature gradient can be described by the following
combination of the sensors located at the outer and inner parts of the
telescope (see Fig. 2): (mean(AHT_27, TC_20, TC_21) – mean(AHT_24, AHT_25, AHT_26, TC_18,
TC_19)). Thus, negative values for the radial temperature
gradient indicate a warmer central part of the telescope and vice versa.
Further investigations have shown that the orbital variations in the radial
temperature gradient are linked to changes in TOA radiation.
Figure 6 shows the relationship between the radial
temperature gradient measured by Aeolus and the outgoing longwave radiation
(OLR) obtained from the NOAA Climate Data Record (CDR) of daily OLR. This
dataset is derived from observations from imagers on board several
geostationary satellites such as the High-resolution Infrared Radiation
Sounder (HIRS) instrument on board the NOAA19 satellite, and it provides daily
averages of global OLR measurements (Lee and NOAA CDR
Program, 2011). OLR measurements from 1 October 2019 were collocated with
Aeolus measurements from the same day and averaged along the Aeolus orbit
for 60 observations (720 s) resulting in 1388 collocations. It has to be
noted that the relationship was found to be not perfectly linear (depicted
by the red line in Fig. 6), and for other days the
nonlinearity seems to be stronger. But due to the response of the thermal
control of the telescope to the changing environment and the fact that shortwave radiation is not considered in the regression analysis, no perfectly
linear relation is expected. However, the results depicted in
Fig. 6 clearly demonstrate the correlation between
TOA OLR and changes in the radial temperature gradient of the M1 telescope
and motivated further studies of the wind bias correlation with the radial
temperature gradient.
Correlation between the radial M1 mirror temperature gradient and
the daily-averaged TOA outgoing longwave radiation measured by the HIRS
instrument on board several NOAA satellites on 1 October 2019 (Lee and NOAA CDR Program, 2011). The red line shows the
radial M1 temperature gradient as a function of the outgoing longwave
radiation as binned averages (5 W m-2 bin size).
To illustrate the relationship between the Rayleigh bias and the mirror
temperatures Hovmöller diagrams are generated. Hovmöller diagrams
allow us to analyze temporal as well as spatial characteristics of a quantity
at the same time. Typically, time is plotted on the x axis, and the spatial
variable, in this case the latitude of the observation, is used as the y axis.
In the Hovmöller diagrams of Fig. 7, the mean
over all M1 temperature sensors (top), the radial temperature gradients
(middle) and the Rayleigh clear E(O-B) values (bottom) are shown at
observation level for the complete observation period. It shows that the
mean M1 temperature values vary quite remarkably with geolocation and time
in the range between 12.9 and 14.5 ∘C. The observed
patterns suggest that the variations are due to the changes in the TOA
short- and longwave radiation of the Earth and the response of the thermal
control to that. The mean M1 temperatures show a quadrupole-like structure
which is visible for ascending as well as descending orbits. Minimum values
appear in Northern Hemisphere summer (June to July) and winter (November to
February) in the region of the North Pole and South Pole, respectively. Two
dominant maximum regions occur in the Southern Hemisphere between July and
November and in the Northern Hemisphere between September and January.
During polar summer in both hemispheres the high outgoing shortwave
radiation fluxes in the polar regions heat up the M1 mirror. This is then
compensated for by the thermal control system which explains the colder mean M1
temperature values in these regions for these periods. In a similar way the
positive anomalies during Northern Hemisphere and Southern Hemisphere winter can be
explained. Here, the reduced reflected solar radiation cools down the M1
mirror which is compensated for by actively heating up the M1 mirror. It is
remarkable that the intertropical convergence zone (ITCZ) which is
characterized by low longwave outgoing radiation is visible in the M1
temperatures. When the satellite passes by the ITCZ, the thermal control
reacts by heating the mirror which increases the mean M1 temperatures after
the ITCZ. Comparing the mean M1 temperatures between ascending and
descending orbits indicates a slight phase shift of the structures between
both phases. This can be explained by the inertia of the thermistors and the
reaction of the thermal control system. When the satellite crosses the
relatively cold ITCZ it takes some time for the thermal control to respond.
As a result, the ITCZ appears slightly shifted to the north and south for
ascending and descending orbits, respectively.
Hovmöller diagrams of the average over all M1 temperatures
(a, b), the radial temperature gradient of the M1 telescope (c, d) and the
Rayleigh clear E(O-B) HLOS values (e, f) from 28 June to 31 December 2019
split up into ascending (a, c, e) and descending (b, d, f) orbit phases.
The middle panel of Fig. 7 shows the radial
temperature gradients (as introduced above) along the M1 mirror. Knowing
that the central part of the mirror is more exposed to radiation changes,
many of the features can be explained such as the difference of the radial
gradients between ascending and descending orbits around the South Pole during
Southern Hemisphere winter. Here, the satellite crosses the very cold areas
of the Southern Hemisphere polar vortex which makes the central part of the
mirror relatively cold (red colors). Afterwards, on the ascending orbit
phase the thermal control responds by heating the central part, which results
in relatively warmer inner telescope temperatures (blue colors). Comparing
the radial temperature gradients (middle) with the Rayleigh clear E(O-B)
values (bottom) demonstrates the strong correlation between the bias and the
M1 radial temperature gradients. Note that sometimes the bias is due to
other issues than changes in the M1 temperatures. For instance, the striking
bias anomalies close to the Equator for descending paths around mid-August or
mid-September are related to the star tracker of the spacecraft being
blinded by the moon leading to an incorrect determination of the satellite-induced LOS velocity and thus systematic wind errors.
The radial temperature changes in the M1 mirror along the orbit which are up
to 0.4 ∘C most likely affect the shape of the mirror. This would
change the focus of the telescope and other higher order aberrations, and
hence, it causes slightly different angular illumination patterns (e.g.,
incidence angle and divergence) of the light passing through the field stop
and illuminating both spectrometers. Both spectrometers are sensitive
towards angular changes in the incoming light and thus produce an apparent
frequency shift which manifests as wind bias. Further analysis also shows
that the radiometric performance of the instrument is affected by the thermal
variations in the telescope (Flament et al., 2021).
It should be noted that also sensitivity of the Mie bias to the M1
temperatures was thoroughly investigated. The sensitivity was found to be
∼ 10 times less than for the Rayleigh channel. This could be
explained by the fact that the beam for the Mie spectrometer is increased by
a beam expander in front of the Mie spectrometer by a factor of 1.8, thus reducing the divergence of the light. Furthermore, the Rayleigh
spectrometer is specifically sensitive to the incidence angle variation
because of its sequential implementation of the two Fabry–Pérot
interferometers (Reitebuch, 2012b). Hence, the focus of the
analysis below is on the correction of the Rayleigh wind bias.
Bias correction using the ECMWF model
The discovery of the strong linear correlation between the radial gradients
of the M1 telescope temperatures (Rennie et al., 2021) and the
wind bias paved the way towards the development of an operational bias
correction scheme. For this, a multiple linear regression (MLR) approach
choosing all available thermistors as independent variables is used to
describe the E(O-B) values as a function of the following 15 M1
temperatures: AHT-22, AHT-23, AHT-24, AHT-25, AHT-26, AHT-27, TC-18, TC-19,
TC-20, TC-21, TC-23, TC-25, TC-27, TC-29 and TC-32
(Fig. 2). A prerequisite for the operational
correction was the adaption of the L1B and L2B processors to include these
variables in the operational data products (since baseline 2B09), which was a
huge achievement by the DISC team given the short amount of time for
preparation. With this information the MLR model can be defined as follows:
EO-B=β0+β1⋅AHT22+β2⋅AHT23+⋯+β15⋅TC32+ε,
where β0 is the intercept, β1⋯β15
are the coefficients for each temperature variable, and ε
denotes the error term. In terms of reducing the bias, it turned out that
the MLR showed better mathematical performance than a linear model that is
based on the radial physical temperature gradient of the telescope (see Sect. 3.1; Rennie and Isaksen, 2020).
Figure 8 demonstrates that the MLR model described
in Eq. (1) is a suitable choice for this task. For the diagnosis, in the
same way as is done for the NRT processing, past data, in this case from 11
August 2019, are used to predict the bias on 12 August 2019. Note that for
the reprocessing data from the same time period are used to derive the fit
coefficients. The big advantage for reprocessing is the availability of the
complete dataset which makes it possible to apply the MLR model to the same
time period that was used to train the model. This even further improves the
performance of the bias correction scheme as no predictions with unseen data
have to be performed. The left scatter plot indicates the high
correspondence between the model prediction and the measured bias values.
This is demonstrated by the high R2 value of 0.78. The right
panel of Fig. 8 is generally used to indicate if
the model residuals show remaining patterns that are not fully captured by
the model (James et al., 2014). This is done by
plotting the model residuals against the predicted values. In our case, the
residuals are equally scattered around zero without dominant patterns
justifying the MLR approach. There seems to be a slight hint for remaining
residual bias (<0.3 m s-1) in the range between 0 to 2 m s-1. This
is shown by the smooth curve fitted using weighted least squares (red line)
fit to the residuals which shows slightly negative values in this region.
Diagnostic plots for the multiple linear regression with the
measured Rayleigh clear E(O-B) values (a) and the model residual (b)
as a function of the predicted bias (a). Data from 11 August 2019 are used
to predict the bias on 12 August 2019. The red line in (a)
indicates the diagonal. In the text box of (a) values for the
coefficient of determination (R2 ), standard deviation (SD) ]and the bias of the corrected values, as well as the number of data points
(N) used in the regression, are shown. The red line in (b)
indicates the smooth function obtained after applying locally weighted
smoothing. The color coding in both panels indicates the kernel density.
Figure 9 demonstrates the application of the M1 bias
correction for 12 August 2019. For this example, the model fit coefficients
β0,⋯β15 are derived from Rayleigh clear
E(O-B) values from 11 August 2019 and are used to predict the Rayleigh clear
E(O-B) values on the next day. The panels compare corrected (orange) with
uncorrected (blue) E(O-B) values as a function of time (Fig. 9a) and the
argument of latitude (Fig. 9b). To measure the performance of the bias
correction approach to decrease the bias variation along the orbit, the
standard deviation of the E(O-B) values, i.e., SD(E(O-B)), can be used. In the case depicted in
Fig. 9, this value is reduced by 52.8 % from
2.89 to 1.36 m s-1 (also see the text box in Fig. 8), which clearly demonstrates how well this method works to reduce most of
the M1-induced bias variation along the orbit. The remaining residual
variation of 1.36 m s-1 is considered to be of a random nature arising from
instrumental and forecast model random errors, and it does not contain any
obvious regular patterns. It should be noted that this value of the standard
deviation is representative for altitude averages of the E(O-B) value at L1B
observation granularity, in contrast to the wind random error which is
defined as the standard deviation of each single observation within a
vertical profile.
Rayleigh clear E(O-B) HLOS values as a function of time (a) and
the argument of latitude (b) during 12 August 2019. The blue and the
orange dots indicate the bias without and with M1 bias correction,
respectively. The blue and the orange lines show
temporal (5 min interval) and binned (5∘ bin size for the
argument of latitude) averages of the E(O-B) values, respectively. The M1 bias
correction coefficients are derived from data from 11 August 2019.
For the M1 bias correction in the operational processing chain, dedicated
software was developed which was put into operation on 20 April 2019
(starting with Level 2B products labeled baseline 09).
Figure 10 depicts the flow chart of the M1 bias
correction for the Aeolus NRT operational processing chain. The
AUX_TEL software uses 24 h of past L2B data as input,
performs the MLR (see Eq. 1) and writes the model coefficients β0⋯β15 into an auxiliary telescope
(AUX_TEL_12) file. The generation of the
AUX_TEL_12 file is updated every 12 h. The
AUX_TEL_12 file is used as input by the L2B
processor for the M1 bias correction of the wind results. This is done by
solving Eq. (1) using measured M1 temperatures and the derived model fit
coefficients to yield an M1 bias correction value for each L2B wind result of
both channels. As a next step, the bias correction values are subtracted
from the measured wind results and provided in the L2B products as bias-corrected winds. Note that bias correction values are also written into the
Earth Explorer format L2B product, which allows users to undo the M1 bias
correction.
Flow chart of the operational M1 bias correction of the L2B wind
results. In the AUX_TEL software, 24 h of past L2B data
with the E(O-B)-values as dependent and the 15 M1 temperatures as
independent variables are used as input for the multiple linear regression
(MLR) model. The model software produces an AUX_TEL file
which contains the model coefficients β0⋯β15. Afterwards,
the L2B processor uses the AUX_TEL files to make a prediction
for the wind bias and to correct the wind results of the subsequent 12 h
window. Then, the AUX_TEL file is updated in the same way.
The high update frequency of 12 h for the AUX_TEL_12 generation is necessary because the model parameters
β0⋯β15 are slowly changing with time, which
indicates that the sensitivity of the instrument towards telescope
temperature variations is changing over time. Moreover, this allows us to
capture the slowly drifting global average bias. Investigations have shown
that the global average bias changes are due to a slow drift of illumination
of the Rayleigh spectrometers in the internal path (particularly for the second laser, the Flight Model (FM)-B laser). In order to capture this effect, it was decided to implement an
intercept term, β0 (see Eq. 1), into the model which makes sure
that the mean of the model residuals, i.e., the mean [E(O-B)] value of the
analyzed period, is zero. To avoid large constant bias offsets from the
model, the mean winds are anchored to the ECMWF model twice per day, and the
AUX_TEL_12 generation is updated every 12 h. The introduced bias offset depends on the change rate of the internal
reference response in the 12 h interval. For the analyzed period, the maximum
change (worst case) was considerably small at 0.78 m s-1. To make sure that
the sample size is large enough and the fit coefficients are derived with a
sufficiently high enough accuracy, 24 h of past data (∼
6500 samples) are used in the MLR.
As mentioned before, the Mie cloudy winds are much less affected by thermal
variations in the M1 mirror. However, it was decided to also use the same
correction approach for the Mie winds mainly for the reason to correct for
global bias offsets of the Mie cloudy winds, again related to internal path
drifts.
Bias correction using ground return winds
The operational M1 bias correction procedure makes use of ECMWF model winds
and thus introduces some dependency on the NWP model. But as mentioned in
Sect. 2.4, this is justified by the low model wind bias
with respect to radiosondes (see Fig. 4). In addition,
the M1 bias correction uses 24 h of global model winds averaged over all
altitudes, which is why small-scale model biases (e.g., in the tropics)
appear only as an additional noise source in the fit procedure. Moreover,
altitude-dependent ECMWF model bias is not an issue as vertically averaged
E(O-B) statistics are used in the MLR model.
However, to overcome this issue of model dependency, it is also possible to
use Aeolus' L1B ground return winds (see Sect. 2.3) as a reference instead of
E(O-B) values. Ground return winds can be seen as a zero-wind reference to
correct for systematic wind error sources such as the M1 temperature-induced
wind bias. However, the use of ground return winds as reference is hampered
by the limited spatial and temporal coverage of ground returns. The
availability of ground returns with high enough ground signals is mainly
restricted to polar regions with high surface albedo. The top panel of
Fig. 11, which displays Rayleigh clear O-B HLOS and
ZWC winds before the application of the M1 correction as a function of the
argument of latitude during 11 August 2019, shows the large difference of
the data availability between O-B and ZWC values. In this case, the
availability of winds is mainly restricted to the ice-covered regions around
Antarctica, which results in a rather small sample size of 659 ZWC winds
compared to 6897 O-B values. However, it turned out that the coverage of ZWC
winds is sufficiently high, i.e., enough different O-B values are covered, to
use ZWC winds as a bias reference in the M1 bias correction. The plot shows a
large correspondence between O-B and ZWC values as both indicate the same M1-dependent bias structure. Note that the constant offset of about 3 m s-1
between O-B and ZWC values is due to the different calibration procedure
between L1B and L2B winds and is quite consistent with time (Dabas et
al., 2008; Reitebuch et al., 2018a; Rennie et al., 2020). It is not
considered to be a problem for the bias correction since this offset could
be corrected in the data processing.
(a) Rayleigh clear O-B HLOS values (red) and Rayleigh ZWC HLOS
winds (grey) without M1 correction as a function of the argument of latitude
during 12 August 2019. (b) The red and grey points indicate the
Rayleigh clear O-B HLOS values after the M1 correction using O-B values and
ZWC values as a bias reference, respectively. The M1 bias correction
coefficients for both approaches (ZWC, O-B) are derived from data from 11
August 2019.
In contrast to the MLR model defined in Eq. (1) a slightly different approach
is used to describe the ZWC winds as a function of the M1 temperatures. Due
to the lower sample size a simplified model with fewer independent variables
has to be used. In the case that the sample size is small compared to the number of
model coefficients, overfitting can occur, meaning that the model tends to
describe the noise rather than the physical relationship in the data. In
such a case, the capability of the model performing predictions with unseen
data is drastically reduced. To avoid this issue, different MLR model
combinations were tested, and for each combination the skill in predicting
the bias was evaluated. It was found that a grouping of the thermistors into
two groups which describe the temperature at the outer and inner parts of
the M1 mirror provides the best results: G1 = mean(AHT27, TC20, TC21) and G2 = mean(AHT24, AHT25, AHT26, TC18, TC19). The bias correction model is then described as follows:
ZWC=α0+α1⋅G1+α2⋅G2+ε,
where α0 is the intercept, α1 and α2 are the
coefficients for each temperature group G1 and G2, and ε denotes
the error term. For the M1 bias correction of L2B winds Eq. (2) is solved using
measured M1 temperatures and the derived model coefficients α1 and α2 to yield an M1 bias correction value for each L2B wind
result. The bottom panel of Fig. 11 shows the
application of the ZWC-based M1 correction for 12 August 2019. The grey
curve indicates the Rayleigh clear O-B HLOS values after the ZWC-based M1
correction. To compare both approaches, the O-B bias after the ZWC-based M1
correction (grey) is shown together with the operational O-B-based bias
correction (red). This demonstrates that also the ZWC-based approach is
capable of reducing most of the M1 temperature-induced bias variation. The
ZWC approach reduces the SD(E(O-B)) from 2.89 to 1.40 m s-1, which is only slightly worse than the O-B-based approach achieving a
reduction to 1.36 m s-1. The offset between both curves is a result of the
different calibration procedure between L1B and L2B winds as discussed
above. The similar performance of the ZWC approach also helps us to confirm
that the O-B approach is doing the correct thing and not introducing too
many ECMWF model bias-related artifacts.
Results
In this section, it is demonstrated that the M1 bias correction also works
with different temperature set point conditions for the thermal control
thermistors of the primary telescope mirror (see Sect. 2.2). Moreover, the
performance of the M1 bias correction using O-B values is evaluated for the
completed observation period from 28 June to 31 December 2019, demonstrating
the reliability of this method. In addition, the performance of the bias
correction using ground return winds is shown.
Case study
In order to decrease the orbital variation in the wind bias and increase the
atmospheric return signal, in-orbit tests were carried out to optimize the
thermal control of the telescope from 6 to 10 July 2020. The main goal of
the tests was to decrease the orbital variations in the M1 mirror radial
thermal gradients by modifying the control law coefficients of the heater
lines. The thermal control of the M1 mirror is based on a proportional
integration differential (PID) control loop which controls the heating
power applied to the TC sensors. The control law coefficients can be used to
optimize the response of the control loop. Figure 12a shows the evolution of the radial M1 temperatures (see Sect. 3.1)
before and during the M1 optimization tests. The radial gradients are
shifted towards higher values, and the range is also increased from
-0.3 to -0.1∘C before the test to -0.25 to 0.1 ∘C during the test. As a result, the Rayleigh clear
bias (blue line in bottom panel of Fig. 12) also changed
significantly. The panel indicates a decrease in the variability in the bias
on sub-orbital timescales but an increase in the bias variability on longer
timescales. However, the orange line that indicates the M1-corrected bias
clearly demonstrates the capability of the M1 bias correction approach to
also perform well with new temperature settings. In this case, data from the
same day are used to derive the fit coefficients. During the optimization
test the M1 bias correction improved the standard deviation of the O-B
values by 53.2 % from 5.09 to 2.70 m s-1. This example also shows how
the M1 bias correction removes the global offset introduced by changes in
the illumination in the internal path (see Sect. 3.2). In this case, the
offset improves on average from -7.49 to 0.0 m s-1.
The radial temperature gradient of the M1 telescope (a) and the
Rayleigh clear E(O-B) HLOS values (b) as a function of time during the
M1 optimization tests on 5 and 6 July 2020. The blue and the orange dots
indicate the bias without and with M1 bias correction, respectively. Data
from day N are used to predict the bias on day N. The periodicity (especially
visible in the second half of the plot) is related to the orbital phase of
the satellite which is ∼ 91 m.
This important finding implies that the M1 telescope-induced bias can be
handled by ground processing in all circumstances, and further M1
optimization tests can now be fully focused on optimizing the radiometric
performance of the instrument.
Performance time series
Figure 13 shows the performance of the M1 bias
correction for the period from 28 June to 31 December 2019. To generate the
time series, data from day N were used to predict the wind bias on day
N+1. The top panel shows daily averages of the standard deviation of the
Rayleigh values SD(E(O-B)) before and after the application of the M1
correction based on O-B and ZWC values. In general, this panel shows a
changing seasonal influence of the M1 temperature-induced Rayleigh bias. At
the beginning of the period from July to October the largest variability in
the radial gradients of the M1 temperatures along the orbit can be observed
(see Fig. 7), which leads to large M1 temperature-induced wind bias and hence a large improvement by both bias correction
approaches. For instance, on 15 July 2019 M1 bias correction drastically
reduces the SD(E(O-B)) values from 2.29 to 1.24 and 1.37 m s-1
for the O-B and ZWC approaches, respectively. For the following period
between August and October a steady decrease in the M1 influence on the
Rayleigh wind bias can be seen. This is mostly related to a seasonal effect
that decreases the orbital variability in the radial temperature gradients
on the descending orbit phase (see Fig. 7). In
October and November, the M1 temperature-induced bias variability reaches
its minimum. During this period, the influence of the bias correction on the
Rayleigh wind bias is very small. The plateau of increased standard
deviation values between 28 October and 15 November is during a campaign
period with a special range gate setting with smaller range gates to achieve
finer altitude resolution around the tropopause, resulting in higher random
wind errors. Afterwards, the seasonal effect on the M1 temperature
variations slowly starts to increase again.
Performance of the O-B (red) and ZWC M1 bias correction (grey)
methods for the period from 28 June to 31 December 2019. (a) Time series
of daily averages (15 orbits) of the standard deviation (SD) of the
Rayleigh clear E(O-B) HLOS values before (blue) and after the O-B- and ZWC-based M1 correction (red and grey, respectively). (b) Daily averages of the bias of the Rayleigh
clear E(O-B) HLOS values before (blue) and after the O-B-based M1 bias
correction (red). Data from day N are used to predict the bias on day N+1.
The difference between the performance of the O-B (red) and ZWC (grey)
approaches is not constant. On average, the ZWC approach is 10.8 % worse
than the O-B-based correction with a maximum deviation of up to 25.6 %.
However, one should bear in mind that the verification against O-B itself
will naturally favor the O-B method. Especially at the end of period, when
the M1 influence on the wind bias is low, the performance of the ZWC
approach decreases and is not able to further improve the SD(E(O-B))
values. As a consequence, it was decided to use the ECMWF model as reference
for the operational correction of the NRT products. However, methods to
further improve the performance of the ZWC-based approach are still under
investigation, which might allow us to use this approach for future
reprocessing or even NRT processing of the Aeolus data products, removing
the need for ECMWF model winds as a reference. Other NWP centers have
confirmed the low biases with respect to their own independent NWP models
following the operational implementation of the M1 temperature bias
correction, which is reassuring.
It is worth noting that the M1 bias-corrected SD(E(O-B)) values show a
steady increase of 11.3 % from 1.24 m s-1 at the beginning to 1.40 m s-1 (O-B
based) at the end of the period. This is due to a combination of decreasing
laser emitted energy from 65 to 61 mJ and a loss of the optical signal
throughput in the receive path of the instrument. Without the implementation
of the accurate M1 bias correction, it would not have been possible to
observe the increase in the random error based on wind error statistics as
the M1 effect dominates the SD(E(O-B)) values. The daily averages of the
uncorrected SD(E(O-B)) values (blue curve in the top panel of
Fig. 13) show a decrease from the beginning of the
period until October 2019, related to the changing seasonal influence of the
M1 temperature-induced bias. This decrease could be misinterpreted as a
decrease in the random wind error. Only after correcting for the M1 effect is
the true random error evolution revealed.
The bottom panel of Fig. 13 shows the temporal
evolution of daily averages of the Rayleigh clear mean(E(O-B)) values with
(red) and without (blue) O-B-based M1 correction. As mentioned in Sec. 3.2,
the M1 bias correction also removes the constant offset from the winds which
is due to changes in the illumination of the spectrometers for the internal
path. The blue curve shows that the daily averages of the mean(E(O-B))
values slowly decreased at different drift rates from +2.1 to -7.5 m s-1. To correct for this effect, the M1 bias correction is updated once per
day. In the operational processing, the updates are even performed twice per
day, which allows for a more accurate and reactive correction of the constant
bias offset. After the M1 correction the bias using O-B values (red line) is
in the range between +0.9 and -0.6 m s-1, proving the capability of bias
correction to remove the constant offset. Smaller peaks of the corrected
bias, e.g., on 15 July or 1 September, are related to larger steps in the
bias development and could be avoided by further increasing the update
frequency of the bias correction. For the reprocessing, this issue is solved
by using data from the same day to derive the MLR coefficients.
Figure 14 shows the global distribution of the
Rayleigh clear (E(O-B)) values obtained from 1 week of data from 15 to
22 August 2019 before (Fig. 14a) and after the M1 bias correction (Fig. 14b), using
O-B values as a bias reference. As discussed in Sect. 3.1, the Rayleigh
bias is a complex function of the changes in the M1 radial temperatures
gradients and the response of the thermal control. During this week, the
temperature variations were particularly strong, which explains the strong
orbital bias variations in the range between -6 and 8 m s-1. However, the
M1 bias correction successfully removes latitudinal and longitudinal bias
patterns from the winds and reduces the SD(E(O-B)) value for this period
from 2.84 to 1.35 m s-1. It is important to mention that the M1 bias
correction aims at globally removing the average offset, i.e., the
mean(E(O-B)), with respect to the ECMWF model. The operational correction makes
sure that the vertically averaged mean wind bias is removed; i.e.,
mean(E(O-B)) equals zero. As a consequence, when smaller data samples,
e.g., in the framework of localized comparisons between Aeolus and
ground-based or airborne measurements, are analyzed, it might be that the
bias of M1-corrected Aeolus winds is not zero (Belova
et al., 2021; Guo et al., 2021; Martin et al., 2021). This also becomes
clear when looking closely at the bottom panel of
Fig. 14 where the bias of the corrected O-B
values, despite showing some residual effects, is in the range between -3 and 3 m s-1, depending on the geolocation. However, for the purpose of
improving NWP prediction at a global scale this approach is considered to be
the best method available at the moment, allowing for the operational assimilation
of the Aeolus wind product and demonstrating the positive impact on numerical
weather forecast (Rennie and Isaksen, 2020; Rennie et al.,
2021).
Global distribution of the Rayleigh clear E(O-B) HLOS values,
vertically averaged over all range gates, before (a) and after (b)
the M1 bias correction. A total of 1 week of data (111 orbits, only ascending orbits)
from 15 to 22 August 2019 is shown. The gaps are due to calibration
procedures such as “hot-pixel-related” calibration measurements or
calibration measurements of the internal path.
Summary
Already shortly after the successful launch of the Aeolus satellite in 2018,
the operational assimilation of Aeolus wind products started at
ECMWF in January 2020. A major milestone on the road to this achievement was
the identification and correction of one of the most important systematic
error sources for the Aeolus wind measurements. It was found that small
temperature variations of about 0.3 ∘C across the primary M1
mirror of the Aeolus telescope lead to varying wind errors along the orbit
of up to 8 m s-1. This paper presents a detailed characterization of the
telescope-induced wind bias, describes the approach to correct for this bias
source and discusses the performance of the bias correction based on data
between June and December 2019.
Our analyses have shown that the orbital variation in the Rayleigh wind bias
changes over seasons and, on top of that, strongly depends on the
atmospheric scene. It turned out that the observed bias patterns are highly
correlated with the temperatures measured at the primary telescope mirror.
The telescope temperatures vary along the orbit as a result of changing TOA
short- and longwave radiation of the Earth and the response of the
telescope's thermal control system to that. The temperature changes affect
the shape of the primary mirror which changes the focus of the telescope, and
it is assumed that this leads to a change in the angle of incidence of the
incoming light at the spectrometers of the instrument and hence to a wind
bias. Moreover, it was found that the sensitivity of the Mie bias on the M1
temperatures is ∼ 10 times less than for the Rayleigh channel.
To correct for the M1 temperature effect a dedicated operational software
was developed which describes the wind bias as a function of the M1
telescope temperature in a multiple linear regression (MLR) model. This
approach is based on ECMWF model-equivalent HLOS winds as a bias-free
reference and has been used operationally successfully at ECMWF since April
2020. The software uses 24 h of past data to derive the model fit
coefficients and is updated twice per day. In this way, also the slowly
drifting constant part of the wind bias can be corrected. It was
demonstrated that the bias correction is capable of removing a large part of
the M1-induced wind bias. In periods when the M1 influence on the wind bias
is particularly strong, the bias correction can improve the SD(E(O-B)) value of the Rayleigh clear HLOS winds by up to 53 % from 2.89 to 1.36 m s-1. The remaining residual bias variation is considered to be
of a mostly random nature and does not contain any obvious regular patterns.
Moreover, the bias correction approach was also tested under special
conditions during M1 optimization tests with changed thermal control law
coefficients for the thermal control of the telescope. The results proved
the reliability of the bias correction method even under these
circumstances, paving the way for further in-orbit tests to improve the
thermal control system of the telescope.
Despite the fact that on average the global bias of the u components of the
ECMWF model with respect to radiosonde observations is smaller than 0.3 m s-1, the use
of the numerical weather prediction model as a bias reference in the linear
regression model is not ideal. Thus, this paper also presents the
alternative of using ground return winds as a bias reference. The
availability of ground returns is mainly restricted to polar regions with
high surface albedo, which makes the task of bias modeling based on this
more challenging. Hence, a downsized MLR approach with fewer independent
variables is introduced. The results show that the approach based on ground
return winds also reduces most of the M1-induced bias variations and
performs in most cases only slightly worse than the operational ECMWF
model-based approach. However, it was also shown that the performance of the
ground return approach on average is 10.8 % worse than the ECMWF
model-based bias correction, with maximum deviations of up to 25.6 %.
Thus, it was decided to use ECMWF model winds as a bias reference.
Nevertheless, the goal is to remove the model dependence in the calculation
of winds, so for the future, further improving the performance
of the ground-return-based approach and using it for upcoming reprocessing
campaigns or even in the near-real-time-processing of the Aeolus products are planned.
In addition, more sophisticated regression models, such as random forests (Svetnik et al., 2003) or generalized additive
models (Hastie and Tibshirani, 1986), will be tested to
further improve the performance of the M1 bias correction. With the
knowledge obtained during this study, it will be possible in principle to
improve both the thermal design of the telescope and the optical setup to
reduce the bias contributions from the telescope temperature variation for a
potential follow-on wind lidar mission. The goal would be to base the bias
correction on measured ground return speeds, as was also initially
foreseen for Aeolus.
Data availability
The L1B products are processed in the framework of the second Aeolus reprocessing campaign and are available on the ADDF dissemination
server under https://aeolus-ds.eo.esa.int/oads/access/collection/L1B_Wind_Products/tree (last access date: 15 November 2021) (ESA, 2021). The CDR OLR data are available at the NOAA National Climatic Data Center (10.7289/V5SJ1HH2, Lee and NOAA CDR Program, 2011).
Author contributions
FW performed the data analysis and prepared the manuscript. MR, TK and LI
largely contributed to the development of the presented methods and the
operational M1 bias correction. EC is the thermal engineer of Aeolus at
ESA-ESTEC and provided valuable input to improve the understanding of the
thermal control of the telescope. JdK is the developer of the L2B processor
and adapted the software for the M1 bias correction. NO analyzed the
relationship between outgoing longwave radiation and the M1 radial
temperature gradient. OR is the scientific coordinator of the Aeolus DISC
and supported the investigation. All authors reviewed the initial draft
version of the manuscript and helped to continuously improve the manuscript.
Competing interests
The contact author has declared that neither they nor their co-authors have any competing interests
Disclaimer
The processor
development, improvement and product reprocessing preparation are performed
by the Aeolus DISC (Data, Innovation and Science Cluster), which involves
DLR, DoRIT, ECMWF, KNMI, CNRS/Météo-France, S&T, ABB
and Serco, in close cooperation with the Aeolus PDGS (Payload Data Ground
Segment). The analysis has been performed in the frame of the Aeolus DISC.
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Special issue statement
This article is part of the special issue “Aeolus data and their
application (AMT/ACP/WCD inter-journal SI)”. It is not associated with a conference.
Acknowledgements
The authors thank the Aeolus Space and Ground Segment Operations
teams, the Aeolus Data Innovation and Science Cluster, and the
technology centers at Airbus Defence and Space and ESA for their innovative
spirit. The authors thank Gerhard Ehret for the internal review of this
manuscript.
Financial support
The article processing charges for this open-access publication were covered by the German Aerospace Center (DLR).
Review statement
This paper was edited by Simone Lolli and reviewed by Hui Liu and two anonymous referees.
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