AMTAtmospheric Measurement TechniquesAMTAtmos. Meas. Tech.1867-8548Copernicus GmbHGöttingen, Germany10.5194/amt-8-109-2015Generation of a bending angle radio occultation climatology
(BAROCLIM) and its use in radio occultation retrievalsScherllin-PirscherB.barbara.pirscher@uni-graz.athttps://orcid.org/0000-0003-4969-7462SyndergaardS.FoelscheU.https://orcid.org/0000-0002-9899-6453LauritsenK. B.Wegener Center for Climate and Global Change (WEGC) and Institute
for Geophysics, Astrophysics, and Meteorology/Institute of Physics
(IGAM/IP), University of Graz, Graz, AustriaDanish Meteorological Institute, Copenhagen, DenmarkB. Scherllin-Pirscher (barbara.pirscher@uni-graz.at)9January20158110912424July20148August201421November201425November2014This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://www.atmos-meas-tech.net/8/109/2015/amt-8-109-2015.htmlThe full text article is available as a PDF file from https://www.atmos-meas-tech.net/8/109/2015/amt-8-109-2015.pdf
In this paper, we introduce a bending angle radio occultation
climatology (BAROCLIM) based on Formosat-3/COSMIC (F3C)
data. This climatology represents the monthly-mean atmospheric state
from 2006 to 2012. Bending angles from radio occultation (RO)
measurements are obtained from the accumulation of the change in the
raypath direction of Global Positioning System (GPS) signals. Best
quality of these near-vertical profiles is found from the middle
troposphere up to the mesosphere. Beside RO bending angles we also
use data from the Mass Spectrometer and Incoherent Scatter Radar
(MSIS) model (modified for RO purposes) to expand BAROCLIM in a spectral model, which
(theoretically) reaches from the surface up to infinity. Due to the
very high quality of BAROCLIM up to the mesosphere, it can be used
to detect deficiencies in current state-of-the-art analysis and
reanalysis products from numerical weather prediction (NWP) centers.
For bending angles derived from European Centre for Medium-Range
Weather Forecasts (ECMWF) analysis fields from 2006 to 2012, e.g.,
we find a positive bias of 0.5 to 1 % at
40 km, which increases to more than 2 % at
50 km. BAROCLIM can also be used as a priori information in
RO profile retrievals. In contrast to other a priori information
(i.e., MSIS) we find that the use of BAROCLIM better preserves the
mean of raw RO measurements. Global statistics of statistically
optimized bending angle and refractivity profiles also confirm that
BAROCLIM outperforms MSIS. These results clearly demonstrate the
utility of BAROCLIM.
Introduction
Global data sets of the lower and middle atmosphere (troposphere
to upper mesosphere) provide important information to understand
atmospheric dynamics of the Earth's climate system.
Observational data as well as analysis/reanalysis data and
atmospheric models are used, e.g., to study specific atmospheric
phenomena such as MJO (Madden Julian Oscillation), ENSO (El
Niño–Southern Oscillation), or the QBO (Quasi
Biennial Oscillation). Long-term observational records,
reanalysis data sets, and atmospheric models can also be used to
investigate atmospheric climate change.
Simple empirical atmospheric models are of high utility if a quick but
reasonable estimate of the atmospheric state is of main interest. This
is of importance, e.g., for simulation studies in the field of
atmospheric remote sensing or within the retrieval of atmospheric
parameters from remote sensing measurements. For this purpose several
research communities use early empirical models like CIRA (Committee
on Space Research (COSPAR) International Reference Atmosphere)
or MSIS
(Mass Spectrometer and Incoherent Scatter Radar) .
Published in the early 1960s, the CIRA model was the earliest
comprehensive climatological model of the atmosphere to contain
information up to the thermosphere. This model is based on
observational data such as radiosondes, rocket data, and satellite
observations. Its fourth version, CIRA-86, includes
thermosphere models as well as tables of monthly-mean zonal-mean
temperature, pressure, geopotential height, and zonal wind from the
surface to an altitude of 120 km. The most recent CIRA
version (CIRA-2012) contains updated versions of empirical
models of the Earth's upper atmosphere (above 120 km)
.
Recent MSIS model versions (MSIS-90 and NRLMSIS-00)
provide information on atmospheric composition, total mass density,
and temperature from the ground up to the exosphere also using
observations from ground, rockets, and satellites. The MSIS model
output depends on time (day of year, universal time, local solar
time), location (altitude, latitude, longitude), geomagnetic activity
(represented by the magnetic index Ap), and solar
activity (represented by the 10.7 cm solar radiation flux,
F10.7).
An overview on principal features of a number of global and regional
models of the middle atmosphere and thermosphere is given by
, summarizing their model content, uncertainties, and
limitations. compared middle-atmosphere
climatologies from approximately 10 to 80 km –
including historical measurements from rocketsonde winds and
temperatures (1970 to 1989), lidar temperature data (1990s), global
meteorological analyses, and satellite data – and found notable
differences between these data sets. Some biases found in atmospheric
analyses were caused by the low vertical resolution of these data as
well as the low vertical resolution of some assimilated satellite
measurements.
Since 2004 research initiatives have tried to understand and eliminate
errors of previous middle-atmosphere models, building new,
state-of-the-art analysis and reanalysis products. However, there are
still uncertainties and differences in current reanalysis products,
and the SPARC (Stratosphere-troposphere Processes And their Role in
Climate) Reanalysis/analysis Intercomparison Project S-RIP;
aims at understanding and reasonably interpreting
these differences and contributing to future reanalysis improvements
in the middle atmosphere.
In this study, we aim at compiling and investigating a global
climatological model from recent high-resolution radio occultation
(RO) bending angles.
The RO method is an active limb
sounding technique that utilizes radio signals continuously broadcast by
Global Positioning System (GPS) satellites. The measured quantity
is the phase change of the GPS signal as a function of time, which
is a measure for physical atmospheric parameters, in particular
bending angle and radio refractivity, from which density, pressure,
geopotential height, temperature, and humidity profiles can be derived
with very high accuracy (though in the lower moist troposphere
auxiliary information is necessary to separate dry-air and moist-air
contributions to the refractivity). Precise and stable oscillators
aboard the GPS satellites ensure measurement stability and
consistency between various RO missions, without the need for
instrument-dependent calibrations
.
The RO bending angle can be used as a climate variable
. In the upper troposphere and above (where
moisture is negligible), it mainly depends on atmospheric
density, which again depends on pressure and temperature. This
means that a change in bending angle can be caused by changes of
all these parameters. This has to be kept in mind when analyzing
atmospheric variability in terms of bending angle. However, the
use of bending angle as a climate variable is superior to other
RO-derived atmospheric quantities that are sensitive to the
additional use of a priori information used in the retrieval
(see below).
First RO profiles of the Earth's atmosphere were provided by the
GPS/MET experiment in intermittent periods from 1995 and 1997
. Since 2001, RO data have been continuously
available from a number of RO satellite missions: CHAMP RO
measurements from 2001 to 2008 are supplemented with measurements from
SAC-C (launched in 2000), GRACE (2002), Metop-A (2006),
TerraSAR-X (2007), C/NOFS (2008), OceanSat-2 (2009),
Tandem-X (2010), SAC-D (2011), Megha-Tropiques (2011),
Metop-B (2012), FY-3C (2013), and KOMPSAT-5 (2013) as well
as from the first six-satellite RO constellation, Formosat-3/COSMIC
(F3C; launched in 2006).
Atmospheric profiles from RO are used for data assimilation in
numerical weather prediction (NWP)
e.g., and in atmospheric and
climate research seefor reviews.
Most studies utilize RO profiles in the upper troposphere and lower
stratosphere (UTLS) region, i.e., the altitude range from
approximately 5 to 35 km, where RO profiles of
pressure, geopotential height, and temperature are known to be of best
quality .
The top altitude of RO measurements depends on the instrument
settings but is at least 80 km (e.g., Metop-A and
Metop-B). For F3C it is usually about 120 km or
higher. However, at these altitudes, individual RO profiles are
dominated by measurement noise and ionospheric disturbances, because
neutral atmospheric density gradients are small. To derive
refractivity profiles via the Abel integral transform
, and since noisy and erroneous information from
high altitudes propagates downwards in the retrieval process, bending
angles are combined with a priori information, e.g., from
a climatology, usually applying statistical optimization
.
Formally, the upper limit in the Abel integral transform is infinity
. If a climatology is used for statistical
optimization, it is therefore necessary that it is able to provide
a good measure of the bending angle to very high altitudes. Usually,
the climatology is used as an extrapolation above the altitude range
where the statistical optimization is performed (or some other form of
extrapolation is necessary for high-accuracy purposes). However,
biases in the a priori information are inevitable. At high enough
altitudes biases are non-negligible (in a fractional sense) and
affect the quality of derived atmospheric profiles
. Therefore high-quality a priori
information is of particular importance.
and introduced a new approach to
derive GPS RO climatological products. Instead of averaging
individual refractivity profiles, they calculated monthly-mean bending
angles and computed mean refractivity as the Abel inversion of the
mean bending angle. showed that the maximum altitude
through which the F3C measurements are useful increased
substantially, which leads to a reduced bias in climatological
averages of refractivity. The main drawback of this approach,
however, is that it can only be used to obtain mean atmospheric fields
and is not applicable to individual RO profiles.
The generation of the bending angle radio occultation
climatology (BAROCLIM) described in this paper is mainly based
on the work by and
. BAROCLIM is based on
measurements from 2006 to 2012. Since this period is much
shorter than the standard period for climate normals (30 years),
BAROCLIM does not represent a long-term mean. However, it is
of very high utility to obtain a quick and reasonable estimate
of the atmospheric mean state as required, e.g., within the
retrieval of atmospheric parameters from remote sensing
measurements.
Section gives a detailed description of the RO data
set as well as of reference data used in this study. In
Sect. we present the method used to construct
BAROCLIM, and in Sect. we discuss potential
systematic errors and evaluate the model by comparing it to reference
data from NWP analysis fields provided by the European Centre for
Medium-Range Weather Forecasts (ECMWF). In
Sect. we show that
BAROCLIM can further be used as a priori information for statistical
optimization in RO profile retrievals. Conclusions are drawn in
Sect. .
Data
For the generation of BAROCLIM, we used ionosphere-corrected bending
angles as a function of impact altitude (impact parameter with the
local radius of curvature and geoid undulation subtracted). These
profiles were retrieved with the Wegener Center for Climate and Global
Change (WEGC) Occultation Processing System version 5.6
(OPSv5.6) and interpolated on a regular
200 m grid.
Input data to the WEGC processing system are profiles of excess phase and
amplitude as well as precise orbit information of GPS and low Earth orbit
(LEO) satellites (level 1a data) provided by other data centers. Currently
WEGC uses level 1a data provided by University Corporation for Atmospheric
Research (UCAR)/COSMIC Data Analysis and Archive Center (CDAAC) for all
RO satellite missions. Since recent UCAR/CDAAC processing versions vary
for different missions and GPS receivers used for RO measurements are not
of the same quality e.g., found different bending angle noise for
different missions, we decided to use only data from the
F3C constellation. The UCAR/CDAAC processing version of F3C data used
in this study was 2010.2640 for the entire time period starting in 2006.
The processing system at UCAR/CDAAC relies on the Bernese software
package to obtain precise orbits of F3C satellites and applies single
differencing to remove F3C clock offsets . In the
inversion retrieval, WEGC first corrects orbits for the Earth's oblateness
, removes outliers from L1 and L2 excess phase
profiles, and smooths data with a regularization filter
. Doppler shift profiles are then calculated from
excess phase profiles via numerical differentiation. In the upper troposphere
and above, bending angles are computed from Doppler shift profiles based on
geometric optics . Wave optics retrieval is applied in
the lower and middle troposphere
. To remove the ionospheric
contribution to the bending angle, WEGC applies ionospheric correction on
bending angle level following and .
Except for the use of F3C open-loop data and the
wave optics retrieval in the lower and middle troposphere, the WEGC
OPSv5.6 bending angle retrieval is very similar to the OPSv5.4
processing described by and .
We used F3C data from August 2006 to December 2012 (more than
6 years of data). The number of F3C measurements increased from
2006 to 2007 until all F3C spacecraft were in their final orbits
(F3C/flight model no. 3 (FM-3) did not reach its final orbit
altitude because solar panels were stuck, which limited the power and
payload operation of this spacecraft). From 2007 to 2009 F3C always
tracked more than 60 000 RO events per month (exception: June 2009,
UCAR/CDAAC provided approximately 55 000 level 1a profiles).
Since 2010 the number of measurements decreased again due to battery
degradation of all spacecraft. Furthermore, F3C/FM-3 has been
out of contact since 1 August 2010. However, the minimum number of
level 1a data provided by UCAR/CDAAC per month in the period
between 2006 and 2012 was always larger than 30 000.
Since RO profiles usually do not reach higher than about
120 km (only about 80 km for Metop) and because the
true neutral atmospheric bending angle decreases nearly exponentially
with height (and therefore measurement noise dominates in a fractional
sense in the mesosphere and above), there is an upper limit to which
RO data are useful for the generation of a climatology. To extend
BAROCLIM to higher altitudes, we used bending angles based on
a modified version of the MSIS-90 empirical model of the neutral
atmosphere .
The MSIS-90 model is based on data from several satellites,
incoherent scatter radar stations, and rocket probes as well as
from tabulations from the Middle Atmosphere Program (MAP)
Handbook 16 .
modified the original MSIS-90 model by
smoothing out a discontinuity at 72.5 km and fixing the
local apparent solar time at 0 h, the solar radio flux
at F10.7=150×10-22Wm-1Hz-1,
and the magnetic index at Ap=4.
Subsequently, this modified version of the MSIS model was used to
generate spectral models of refractivity and bending angle for the use
of fast and efficient modeling and inversion of RO data. The
spectral model of refractivity, N, was obtained from the MSIS
pressure, p, and temperature, T (N=77.6p/T), for the 15th of
every month. The spectral model of bending angle was obtained from the
spectral refractivity model via the Abel integral transform. Thus,
the MSIS-based bending angles and refractivities contain no
information on atmospheric humidity and are given as a function of
month, impact height, latitude, and longitude. Both spectral models
are based on Chebychev polynomials in the vertical and spherical
harmonics in the horizontal and were constructed using an approach
similar to the one we now use for BAROCLIM described in
Sect. . The MSIS spectral models were later
incorporated into the End-to-end Generic Occultation Performance
Simulator (EGOPS) and the Radio Occultation
Processing Package (ROPP) .
To validate BAROCLIM, we used operational ECMWF analysis
fields at T42 horizontal resolution (comparable to RO
horizontal resolution) and 91 vertical levels. Profiles were
extracted at mean RO event location of those F3C
measurements, which were used to construct BAROCLIM. We
applied a forward model to derive ECMWF bending angles from
refractivity (above the ECMWF model top, refractivities were
extended with MSIS profiles scaled to fit the ECMWF model at
high altitudes).
We will show in Sect. that
BAROCLIM can be used as a priori information for the statistical
optimization in the processing of RO measurements. To investigate
the performance of BAROCLIM as a priori information, we used
level 1a data from CHAMP, GRACE-A, SAC-C, and F3C from
January 2008 and July 2008 (level 1a data were again provided by
UCAR/CDAAC; CHAMP data version was 2009.2650; other satellites
had consistent data version 2010.2640) and applied the WEGC
OPSv5.6 retrieval using BAROCLIM and MSIS as a priori
information for bending angle initialization. Retrieved atmospheric
profiles were then compared to operationally retrieved OPSv5.6
profiles that used ECMWF short-range forecasts as a priori in the
statistical optimization .
BAROCLIM generation
Flowchart of the BAROCLIM generation.
Figure summarizes the steps of the BAROCLIM
generation. Using ionosphere-corrected bending angles as a function
of impact altitude on a regular 200 m grid, we first applied
a quality control (QC) to identify and exclude bad profiles before
averaging bending angles in latitude and altitude and calculating
monthly-mean 10∘ zonal-mean bending angles. These
monthly means include data from 6 or 7 years. Since we aimed at
generating a BAROCLIM spectral model, which (theoretically) reaches
from the surface to infinity, we extended mean RO profiles with
MSIS. We refer to these bending angles as the BAROCLIM discrete
model. The BAROCLIM spectral model was then constructed by
expansion into Chebychev polynomials and zonal harmonics. Below we
describe these steps in detail.
Quality control of individual profiles
Some bending angles are very noisy and/or contain unphysical
values. They could strongly affect the quality of the bending
angle climatology if they were not properly excluded.
To avoid entering these profiles in BAROCLIM, we only used OPSv5.6
profiles that passed the external QC performed at WEGC
. This external QC comprises bending angle,
refractivity, and temperature profiles, which are compared to
co-located profiles from ECMWF analysis fields. The profile is
flagged as bad if the difference between the RO and the ECMWF profile
is larger than 20 % in bending angle, 10 % in
refractivity, and/or 25 K in temperature. However, since these
quality checks are only performed in the upper troposphere and lower
stratosphere region up to 35 km, profiles passing the external
QC can still be very noisy in the upper stratosphere and above.
The inspection of individual bending angle profiles indeed revealed
that it is imperative to perform an additional QC. We therefore
introduced a threefold approach for an additional outlier rejection.
In a first step we rejected all profiles with bending angles smaller
than -40µrad or larger than +40µrad in the
altitude range from 50 to 80 km. In this altitude
range, neutral atmospheric bending angles are usually smaller than
20 µrad, and bending angles smaller/larger than
±40 µrad result from very strong (unphysical) noise,
possibly sometimes related to ionospheric scintillations
.
To also detect very bad profiles below 50 km, we
rejected all profiles with bending angles smaller than
-20µrad below 50 km in a second step.
Profiles that were flagged as bad by these QC mechanisms were
outlier profiles, which could degrade the quality of
BAROCLIM. Inspecting remaining bending angle profiles after
application of these first checks, we still found some very noisy
bending angle profiles (top panel of Fig. 2) and therefore
applied an additional QC.
F3C bending angles (in µrad) in January in the
latitude band from 80 to 90∘ S before (top) and
after (bottom) the application of the 4σ-outlier rejection
criterion. The thick green line shows the mean of all profiles, the thick
yellow lines 1 standard deviation, and the thin yellow lines 4 standard
deviations. The dashed lines in the lower panel indicate the thin yellow
lines in the upper panel.
Mean F3C bending angles (in µrad) (top) and their
standard deviation (in percent) of the mean (bottom) in January (left)
and July (right) as a function of latitude and impact altitude up to
100 km.
We used all remaining profiles and
calculated mean bending angles and standard deviations for 10∘
latitude bands for multiyear monthly means and rejected all profiles
with bending angles outside of 4 standard deviations (4σ)
from the mean in the altitude range from the surface to
100 km. Figure
shows F3C profiles for the month of January before and after
application of this 4σ criterion. This figure reveals that
application of this final QC results in a considerable decrease in
standard deviation.
Table gives an overview on the number of
profiles provided by UCAR/CDAAC, retrieved at WEGC, and passing
BAROCLIM QC. The number of bending angle profiles for a given
month used to generate BAROCLIM is always larger than 200 000,
except for June, when it is slightly below. In some months, however,
the number is even larger than 260 000. These numbers are large
enough and sufficient to obtain a smooth BAROCLIM up to about
60 km.
Average over high-quality profiles
The optimal horizontal extent of the regions to calculate a typical
climatological mean from high-quality measurements is a trade-off
between a sufficiently large number of profiles and atmospheric
variability. Our experience of building atmospheric climatologies
utilizing RO data
e.g., showed that
10∘ zonal bands were a reasonable choice for calculating mean
atmospheric profiles from RO data. These bands range from
90∘ S to 90∘ N, resulting in 18 zonal bands.
The mean number of profiles per 10∘ latitudinal band varied
between 11 000 (June) and 15 000 (October). However, the
latitudinal distribution of RO events is not uniform, which is due
to the orbit characteristics of the GPS and F3C satellites (orbit
inclinations of 55∘ and 72∘, respectively). The
largest number of RO measurements per latitude band is obtained at
mid-latitudes, where more than 20 000 profiles enter BAROCLIM.
A smaller number of measurements per latitude band is
obtained at low
(approximately 8000 profiles) and high latitudes (between 2000 and
4000 profiles). We judged that 8000 tropical profiles are sufficient
to calculate mean profiles because atmospheric variability at high
altitudes is small at low latitudes. We also considered 2000
high-latitude profiles to be sufficient due to the decrease of zonal
surface area with increasing latitude. Thus, 2000 profiles are enough
to represent a small area.
Number of level 1a F3C data provided by UCAR/CDAAC (first
column), number of bending angles profiles retrieved at WEGC (second column),
and number of profiles that passed BAROCLIM quality control (last
column). Numbers are shown for every month, adding up the data from
August 2006 to December 2012.
Multiyear monthly-mean bending angles for 10∘ zonal bands for
January and July are shown in
Fig. together with their
standard error of the mean σmean=σ/N
(σ is the standard deviation, and N is here the number of
observations used to estimate the mean – not to be confused with
refractivity). Bending angles are negative (white areas) somewhat
above an altitude of 80 km, and the standard error of the mean
is larger than 10 % above 70 km in the winter
hemisphere at high latitudes. While negative mean bending angles
might be caused by residual systematic ionospheric errors
see, the high standard error of the mean (in
a fractional sense) is a result of the decreasing bending angle with
altitude. Below 60 to 70 km, however, mean bending
angles are rather smooth and the standard error of the mean generally
does not exceed 2 %.
BAROCLIM discrete model
Because of the generally decreasing bending angle with altitude, the
mean bending angle
(Fig. ) is error-dominated
above 80 km. Therefore we combined the mean bending
angles with a priori information to generate a model that is useful
also above the mesosphere. A priori information profiles can be
obtained from already-existing climatological models or profile data
sets. Current state-of-the-art analysis, reanalysis, or forecast
products from NWP centers do not reach high enough in the atmosphere
(the ECMWF model top, e.g., is at 0.01 hPa, corresponding
approximately to 80 km) and can therefore not be used for
extension to higher altitudes.
Since it is readily available, we decided to use the modified MSIS
climatology as a priori information. In order to make maximum use of
the information content of the RO data, and since the MSIS-90
climatology might be biased at high altitudes, we did not necessarily
take the MSIS profile as representative for a given latitude band
and month. Instead we performed a search in the spectral model of the
MSIS bending angle climatology on a regular 5∘×10∘ latitude–longitude grid through all months from January
to December, and we found the best match to the RO data using
a least-squares fit to the RO mean bending angle profile in the altitude
range from 60 to 80 km, where RO data quality is
still high. To correct remaining background biases, the best-fitting
MSIS profile was then multiplied with a fit factor obtained from
regression with respect to the mean RO bending angle profile at high
altitudes (least-squares adjustment from 60 to
80 km). We found fit coefficients being close to unity (0.99
to 1.01), with exceptions only in Southern Hemisphere winter at high
latitudes (80 to 90∘ S), where fit coefficients
were as small as 0.96, 0.88, and 0.91 in May, June, and July,
respectively.
To combine the mean RO bending angle profile with the
corresponding MSIS profile, we applied statistical
optimization by inverse covariance weighting
between 60 and 80 km using an error
correlation length of 2 km for the RO profile and an
error correlation length of 15 km for the adjusted
MSIS model profile. Furthermore, we assumed the MSIS
background error to increase linearly from 0 % at
80 km to 15 % at 78 km, kept it
constant at 15 % between 78 and
62 km, and then increased linearly again from
15 % at 62 km to 100 % at
60 km. All these percent values refer to the absolute
values of the MSIS bending angle at the respective impact
altitude level. While the linear increase of the relative error
at the top and the bottom end of statistical optimization avoids
too sharp transitions, the constant fraction of 15 %
was determined empirically by .
The observational error was set to the mean
background error between 62 and 78 km and was
constant with height (in absolute value, not percentagewise). Using
these settings, we obtained smooth statistically optimized bending
angles, for which the height where the retrieval to a priori error
ratio equals 50 % is 67.2 km for
all profiles. Outside of the transition region from 60 to
80 km, the statistically optimized bending angle equals that
of MSIS (above 80 km) or that of the mean RO profiles
(below 60 km).
Even though Fig.
indicates that the mean bending angles reach down to the surface
(2 km impact altitude approximately corresponds to
0 km altitude), mean bending angle quality also decreases in
the lower troposphere. This is mainly because of the strongly
decreasing number of measurements in the lower troposphere see
also but is also due to reduced quality of the
measurements. Besides this, averaging bending angles at low impact
altitudes is tricky, since the lowest impact altitude in
individual
profiles (even if profiles are tracked all the way to the surface)
depends on the bending angle. For the ray grazing the surface in one
occultation event with a large bending angle, the impact altitude is
larger than for the ray grazing the surface in another occultation
event with smaller bending angle. It thus becomes dubious to talk
about bending angle at the lowest impact altitude for the mean
profile.
Being aware that MSIS is a dry-air climatology (no humidity is
included in this model) and accepting that BAROCLIM will not reflect
real atmosphere conditions at the lowest altitudes, we decided to use
this model to extend BAROCLIM down to the surface. BAROCLIM is
therefore, like MSIS, a dry-air model, being clearly wrong in
regions were moisture is usually abundant, but for technical reasons
smooth bending angles in the lower troposphere close to the surface
are necessary when generating the BAROCLIM spectral model.
To extend mean RO bending angles down to the surface, we first
extracted the MSIS profile for the given month and latitude
and searched for the best fit in longitude. We then applied a
gradual transition using a cosine weighting function from the
mean RO bending angle αRO to the MSIS
bending angle αMSIS. This weighting function
was defined as w(z)=1/21+cosπ(ztop-z)/Δz, and the
tropospheric bending angle αtrop was obtained
from αtrop=w(z)αRO(z)+(1-w(z))αMSIS.
Since the amount of water
vapor in the lower troposphere depends on latitude, we performed
RO–MSIS transition between 5 and 10 km from
60∘ S/N to 90∘ S/N, between 7 and
12 km from 30∘ S/N to 60∘ S/N, and between
10 and 15 km from 30∘ S to 30∘ N.
To sum up, our BAROCLIM discrete model is available for every month
(January to December) and has a horizontal resolution of
10∘ zonal bands and a vertical gridding of 200 m. It
relies 100 % on RO data from the upper troposphere up to
60 km. Above 80 km and below 5,
7, or 10 km (depending on latitude), it consists of
data-driven adjusted MSIS profiles.
BAROCLIM spectral model
For fast and easy access to BAROCLIM at any latitude and impact
altitude, and to make the functionality similar to the MSIS bending
angle and refractivity spectral models in EGOPS and ROPP, we
expanded the BAROCLIM discrete model in Chebychev polynomials and
zonal harmonics. Since the bending angle scale height is more finely
structured than the smooth, almost exponentially decreasing bending
angle, we expanded a function into Chebychev polynomials, which
depends on the bending angle scale height.
First we introduced the variable z=h-hsurf (z≥0),
where h is impact altitude and hsurf is the lowest
possible impact altitude corresponding to a hypothetical ray grazing
the surface. The lowest impact altitude was estimated from the MSIS
climatology using hsurf=NsurfMSIS×10-6RE, where
RE=6371km is the mean radius of the Earth and
NsurfMSIS is MSIS refractivity at the surface
extracted at the specific month and latitude and at longitude λ=0∘. The bending angle α(z) was then extracted from
the BAROCLIM discrete model by interpolation to a number of discrete
impact heights evaluating z(x)=100(ln2-ln(1-x)) at
kmax values of x given by
xk=cos(π(k-12)/kmax) (k=1,…,kmax). This mapping yields a finer vertical
spacing at low altitudes and coarser vertical spacing at higher
altitudes. Having α(z) at these discrete impact heights, the
bending angle scale height HS(z) was calculated as
HS(z)=zlnαsurf/α(z),
where αsurf is the bending angle at z=0 (also
extracted from the BAROCLIM discrete model).
Chebychev coefficients, cj, were obtained from
cj=2kmax∑k=1kmaxG(xk)cosπ(j-1)k-12kmax,
where
G(x)=HS(z(x))-(mz(x)+b)
and m and b are slope and intercept, respectively, of a straight line fit to the
scale height at high altitudes. Finally, j=1,…,kmax, and kmax is the number of extracted Chebychev coefficients
for kmax-1 Chebychev polynomials .
The Chebychev coefficients were then expanded into zonal
harmonics. Besides the Chebychev coefficients, also hsurf,
αsurf, m, and b were expanded into zonal
harmonics.
In general, zonal harmonics coefficients An are obtained from
a given function f(y), where normally y=cosθ (θ is
co-latitude (polar distance)) as see, e.g.,An=2n+12∫-1+1f(y)Pn(y)dy,
where Pn are Legendre polynomials, n=1,…,nmax,
and nmax is the number of extracted zonal harmonics
coefficients. In our case f(y) was cj,
hsurf, αsurf, m, or b. Thus, the
final output of the BAROCLIM spectral model was nmax
zonal harmonics coefficients of kmax Chebychev
coefficients, surface impact altitude, surface bending angle, and
slope and intercept of the straight line.
To reconstruct the bending angle from the BAROCLIM spectral model
for a given impact altitude and latitude, we first applied Clenshaw's
recurrence formula for zonal harmonics to obtain the
Chebychev coefficients cj as well as hsurf,
αsurf, m, and b. We also applied Clenshaw's
recurrence formula to reconstruct G(x) (where x=1-2exp(-z/100))
before reconstructing bending angles using
α(z)=αsurfexp-zHS(z).
More details on the expansion of BAROCLIM into Chebychev polynomials
and zonal harmonics as well as their reconstruction can be found in
.
BAROCLIM spectral model (calculated with 128 Chebychev
coefficients and 18 zonal harmonics coefficients) as a function of
latitude and impact altitude for January (left) and difference between
the BAROCLIM spectral model and the BAROCLIM discrete model (right).
To settle on the order of the Chebychev polynomials and the degree of
the zonal harmonics, we calculated differences between the bending
angles from the BAROCLIM discrete model and the BAROCLIM spectral
model for different choices of kmax and nmax,
aiming at minimizing these differences. Since the BAROCLIM discrete
model has a horizontal resolution of 10∘ zonal bands (18 zonal
bands), we found minimum differences for 18 zonal harmonics
coefficients. Concerning the order of the Chebychev polynomials, we
found reasonably good agreement between the BAROCLIM discrete model
and the BAROCLIM spectral model for 64 Chebychev coefficients. When
using 128 Chebychev coefficients, the spectral model even reproduces
the sharp tropical tropopause. For this reason we decided to use 128 Chebychev coefficients when constructing the
spectral model and reconstructing the bending angle, but
lower vertical resolution bending angles can be reconstructed using
a smaller number of Chebychev coefficients. This could be useful for
applications where computational speed is more important than high
vertical resolution.
The BAROCLIM spectral coefficients (stored in a NetCDF-file)
as well as the Fortran-90 code needed to reconstruct bending
angles from these coefficients are designed to be included in a
future release of the ROPP software. ROPP is free of
charge after registration at http://www.romsaf.org.
Figure shows (as an example for the month of
January) the BAROCLIM spectral model for 128 Chebychev coefficients
and 18 zonal harmonics coefficients. The right panel of
Fig. shows that differences between the
BAROCLIM discrete model and the BAROCLIM spectral model are, in
general, within 0.5 % up to 60 km (a closer
inspection of the differences reveals that it is even within
0.3 % in most places). Larger differences are found close to
the 60 km altitude level (transition height of RO-only data
and statistically optimized RO data) and above 80 km where
the absolute amount of the bending angle is so small that even very
small differences yield a noticeable percentage value.
Systematic difference between the BAROCLIM spectral model and
ECMWF analyses forward-modeled to bending angle as a function of
latitude and impact altitude up to 60 km for January (top left), April
(top right), July (bottom left), and October (bottom right).
Evaluation of BAROCLIMError sources
Atmospheric climatological fields of RO data are affected by (i)
random statistical errors, (ii) systematic errors, and (iii) sampling
errors . Random statistical errors
include, e.g., receiver thermal noise, clock stability/differencing
errors, ionospheric noise, and statistical velocity errors see
e.g.,. Random statistical errors diminish by
averaging over a large number of profiles. Since BAROCLIM is based
on a very large number of quality-controlled RO soundings, all
contributions from statistical errors are negligible, except at the
highest altitudes
(cf. Fig. ).
Systematic errors are more important for BAROCLIM. From the RO
measurement and retrieval perspective, these errors include systematic
errors in orbit determination, local multipath, residual ionospheric
errors, and errors due to assumptions in the RO retrieval.
Systematic errors of BAROCLIM also include contributions due to the
additional use of MSIS at high and low altitudes.
investigated the uncertainty of UCAR/CDAAC
precise orbit determination (POD) of F3C satellites and found
a velocity error of 0.17 mms-1, which approximately
corresponds to an F3C bending angle error of 0.05 µrad
(1 % at 60 km). Due to the lack of an alternative
measurement system onboard F3C, could not
give an estimate of the orbit accuracy. If we assume that half of the
F3C velocity error is attributable to a systematic error component,
the corresponding BAROCLIM error will be 0.5 % at
60 km.
Errors due to local multipath depend on the spacecraft size and on the
reflection coefficient . For F3C these local
multipath errors are estimated to be smaller than
0.05 mms-1, which corresponds to
0.015 µrad in bending angle when using
velocity-error-to-bending-angle-error conversion given by . This
error corresponds to 0.3 % at 60 km.
Systematic residual ionospheric errors are important for BAROCLIM.
In general, ionospheric residual errors depend on the level of
ionization at high altitudes, which again depends on local time (i.e.,
day- versus nighttime conditions due to solar insolation) as well as
on solar activity .
showed that this error rarely exceeds
0.1 µrad
from mid-2006 to the end of 2011. When averaging over this time period, it
is even smaller than 0.05 µrad. Giving a conservative estimate
and assuming a 0.1 µrad residual ionospheric error from mid-2006
to 2012 (solar activity increased in 2012), which corresponds to
2 % at 60 km, this error is the most important
systematic error source of BAROCLIM.
Systematic errors due to assumptions in the retrieval process (such as
spherical symmetry) are assumed to be small at high altitudes
.
Another BAROCLIM systematic error component results from the
additional use of the MSIS model at low (tropospheric) and high
(mesospheric and above) altitudes. Large systematic BAROCLIM errors
in the troposphere are due to the absence of atmospheric water vapor
in the MSIS model. For this reason BAROCLIM is not generally
useful for tropospheric studies. Systematic errors from MSIS
a priori information used at high altitudes (below 70 km) are
assumed to be small due to the way MSIS was used (finding a bending
angle profile that fits the mean RO data at high altitudes).
Finally, errors in BAROCLIM are caused by discrete sampling
times and locations of RO measurements sampling error; see,
e.g.,. The
sampling error depends on the number of profiles and atmospheric
variability and can be estimated from reference data that
reflect true spatial and temporal variability. Using 6 to
7 years of RO data for BAROCLIM with more than 200 000
profiles per month (exception: June with 198 177 profiles), the
BAROCLIM sampling error is negligible. However, since
BAROCLIM is only based on measurements from 6 or 7
years, BAROCLIM might be biased relative to the long-term mean
atmospheric state over 30 years. During the BAROCLIM time
period, e.g., several major sudden stratospheric warming (SSW)
events occurred in Northern Hemisphere winter (e.g., in January
2009 and 2010), yielding an RO climatology biased towards too high
temperatures and too high atmospheric densities (i.e., too large bending
angles) at northern high latitudes in these
months. Other potential biases associated with the short RO
record (e.g., the influence of QBO and ENSO) were estimated
to be small.
Comparison to ECMWF
In December 2006 ECMWF started assimilating RO data in its
operational assimilation system , which implies that
ECMWF analyses and RO measurement data are not independent
anymore. and showed that
assimilation of RO data significantly improved the forecast skill of
the ECMWF operational system in the upper troposphere and lower
stratosphere. found reduced biases in mean
ECMWF analysis fields at least up to 30 km after ECMWF
started assimilating RO. However, even though the assimilation is
performed up to 50 km, a large RO
observational error assumed in the assimilation at high altitudes
limits the impact of RO data in this region. Systematic differences
between the BAROCLIM spectral model and mean ECMWF analysis
profiles therefore provide valuable information not only about the
quality of BAROCLIM but also on the quality of ECMWF analyses,
especially at high altitudes.
Figure shows that the differences
are small (<0.5%) in the upper troposphere and lower
stratosphere region between approximately 10 and
35 km. Besides this good agreement, striking features, which
are very similar in all months, are (i) large negative differences in
the troposphere, (ii) a band of positive differences (mostly
<1%) above approximately 35 km, and (iii) large
positive differences (>2%) above 50 km.
Large negative tropospheric differences are caused by BAROCLIM
being a dry-air model. Neglecting atmospheric humidity yields
unrealistically small bending angles in regions where humidity
is high. Positive BAROCLIM minus ECMWF analysis differences
above 35 km (< 1 %) and above 50 km (> 2 %) are mainly
attributable to biases in ECMWF analyses rather than to
BAROCLIM. In general, these biases above 35 km might be
related to the bias correction of assimilated radiances from
satellite measurements, whereas the specific bias above 50 km is
most likely attributable to data from AMSU-A channel 14, which
are assimilated without bias correction (S. Healy, ECMWF,
personal communication, October 2014).
Similar ECMWF biases at high altitudes have been found with
satellite measurements from the Michelson Interferometer for
Passive Atmospheric Sounding (MIPAS) instrument on the European
environmental satellite ENVISAT and from the Microwave Limb
Sounder (MLS) instrument on the U.S. Aura satellite
. Further comparisons of ECMWF analyses and
temperature data from MIPAS and Sounding of the Atmosphere
using Broadband Emission Radiometry (SABER, an instrument on the
U.S. TIMED (Thermosphere, Ionosphere, Mesosphere Energetics and
Dynamics) satellite) also revealed a similar bias structure in
ECMWF analyses above 40 km (J. Innerkofler, WEGC,
personal communication, October 2014). All these comparisons
consistently showed that ECMWF temperatures are too high at
high altitudes, yielding a negative measurement minus ECMWF
temperature bias. When pressure biases are small, a negative
temperature bias corresponds to a positive refractivity bias,
which in turn corresponds to a positive bending angle bias
see, e.g., as shown in
Fig. .
This comparison clearly shows that BAROCLIM is of very high
quality at least up to 60 km and has the potential to
validate middle-atmosphere data.
Use of BAROCLIM in RO profile retrievals
The intended aim of BAROCLIM was its use as a priori information in
RO profile retrievals. We therefore evaluated its performance by
processing occultation data from different RO missions and comparing
retrieved atmospheric profiles obtained with different a priori
information.
As mentioned in Sect. , we used level 1a RO data
provided by UCAR/CDAAC for all missions and applied the WEGC
OPSv5.6 retrieval to obtain ionosphere-corrected bending angles.
As bending angle a priori information for statistical optimization we
used BAROCLIM and MSIS profiles co-located to RO events (termed
“BAROCLIM-Col” and “MSIS-Col”, respectively) and BAROCLIM
and MSIS profiles that best fit the ionosphere-corrected bending
angle (termed “BAROCLIM-SF” and “MSIS-SF”, respectively, where
SF means “searched” and “fit”). This best-fit algorithm was
similar to the “enhanced IGAM high-altitude retrieval scheme”
described by , searching for the best-fitting
MSIS/BAROCLIM profile between 35 and 55 km and
performing linear regression to find a multiplication factor to refine
the fit to the data from 45 to 65 km.
With this approach we do not necessarily take a profile from
MSIS/BAROCLIM corresponding to the latitude and season of
the retrieval, but one that fits the data the best at high
altitudes. Thus, with the SF approach we use MSIS/BAROCLIM
as a library of different profiles representing different
(average) atmospheric conditions on Earth. The approach should
reduce sensitivity to biases in the climatology, although it
does not guarantee that biases in the retrieved profiles are
absent.
For comparison, we also included operationally retrieved
OPSv5.6 profiles , which use ECMWF
short-range forecasts as a priori information (termed
“OPSv5.6”).
To assess the performance of BAROCLIM in RO profile retrievals we
calculated monthly statistics of raw ionosphere-corrected bending
angles minus optimized bending angles. Since the purpose of
statistical optimization is to reduce random errors, while preserving
the mean, the mean difference between raw and optimized bending angles
is an indicator of the quality of the background climatology.
Global statistics of systematic difference between raw and
statistically optimized RO bending angles for CHAMP, GRACE-A,
SAC-C, and F3C for January 2008 and July 2008. Different colors
indicate different a priori information used in the retrieval.
Figure shows mean results for
January and July 2008 for CHAMP, GRACE-A, SAC-C, and
F3C from 30 to 60 km impact altitude.
Since noise of individual ionosphere-corrected raw bending angle
profiles is high in the middle and upper stratosphere, difference
profiles have a very large standard deviation. We did not include this
information in the plot but note that it reaches approximately
15 % between 45 km (CHAMP) and 50 km
(F3C).
Figure shows that – while bending
angle systematic differences of BAROCLIM-SF, BAROCLIM-Col, and
OPSv5.6 are very close to 0 for all satellites and both months
– MSIS-Col and MSIS-SF data are slightly negatively biased above
40 and 50 km, respectively. Largest differences
(>5% above 55 km) can be found for MSIS-Col.
Global statistics of systematic difference (left) and standard
deviation (right) between RO retrievals and ECMWF analyses for
January 2008. The top panels show (statistically optimized) bending
angle, and bottom panels refractivity. Different line types indicate
retrievals for SAC-C, GRACE-A, CHAMP, and F3C. Different colors
different indicate a priori information used in the retrieval.
Figure shows how
differences propagate from statistically optimized bending angle to
refractivity using MSIS-SF, BAROCLIM-SF, or OPSv5.6.
Since bending angle and refractivity differences shown in
Fig. are
calculated against ECMWF analyses, zero difference does not
necessarily mean that it is close to the truth
(cf. Fig. and the discussion there). Bending angle and refractivity systematic differences are
very similar for all satellites, with differences amongst the
satellites being, in general, smaller than 1.5 % up to
60 km. Comparison of the three methods reveals distinctively
larger differences in bending angle and refractivity. While
BAROCLIM-SF profiles are close to operationally retrieved
OPSv5.6 profiles in the entire altitude range, MSIS-SF clearly
performs worse compared to the other methods. Difference between
MSIS-SF and ECMWF profiles reaches 3 % at approximately
55 km in bending angle and refractivity.
Contrary to systematic differences, the magnitude of the standard
deviation features distinct satellite-dependent characteristics.
Since CHAMP data noise is larger compared to the other satellites,
OPS uses more weight of the a priori information, which results in
smoother profiles and smaller standard deviation above 40 km.
When comparing standard deviations of the three methods, larger
standard deviations are found for the two search and fit algorithms
than for OPSv5.6.
We conclude that the results using BAROCLIM seem promising, in
particular when used in combination with the SF approach. As
mentioned, such an approach should reduce the sensitivity to
possible biases in BAROCLIM because it is then merely used as
a library of different profiles representative of different
(average) atmospheric conditions. The fact that BAROCLIM is
based on data from only one mission (F3C) and from a limited
period of time (2006 to 2012) is therefore not so important in
this context; BAROCLIM can be used in this way for other RO
missions in the past and in the future as long as the climate in
the upper stratosphere does not change drastically in terms of
global variations of bending angle.
Summary, conclusions, and outlook
In this study, we used radio occultation data from the
F3C mission from August 2006 to December 2012
(more than 6 years of data) to compile a bending angle radio
occultation climatology (BAROCLIM). After careful quality control
we calculated multiyear monthly means for 10∘ zonal bands
from the surface up to 100 km. Since mean RO profiles
become noisier above 60 km (in a fractional sense) and are
error dominated above 80 km, we used a priori information from
the MSIS climatology modified for RO purposes and applied statistical optimization from 60 to
80 km to extend BAROCLIM into the thermosphere. We also
used the MSIS model to obtain smooth bending angles in the
troposphere and performed a cosine transition to mean RO profiles in
the middle troposphere. This implies that BAROCLIM is a dry-air
model in the troposphere. However, BAROCLIM relies on RO data
from the upper troposphere up to 60 km and also contains
RO-derived information higher up.
BAROCLIM spectral coefficients and the reconstruction code,
which is needed to obtain bending angles, are designed to be
included in a future release of the ROPP software.
This RO package can be downloaded for free
after registration at http://www.romsaf.org.
We showed that BAROCLIM is of very high quality in the stratosphere
and lower mesosphere, where systematic biases are small. In this
altitude range differences between BAROCLIM and ECMWF analyses (forward-modeled
to bending angle) rather show deficiencies in ECMWF analyses than in
BAROCLIM. At 40 km, e.g., we find BAROCLIM minus ECMWF
analysis bending angle differences of about 0.5 to
1.0 % and sometimes more. Above 50 km, this
difference even exceeds 2 %. This is generally consistent
with findings by , using other types of satellite
measurements.
BAROCLIM was originally developed to be used as a priori
information for bending angle initialization in RO data
processing. We thus evaluated BAROCLIM by comparing retrieved
RO profiles initialized with different a priori information
provided by BAROCLIM, MSIS, and ECMWF. These comparisons
showed that RO bending angles initialized with BAROCLIM are
close to raw (unoptimized) bending angles. This means that
BAROCLIM-initialized bending angles preserve the mean of the
raw measurements, while MSIS-initialized bending angles are
slightly negatively biased. Comparison of retrieved RO
profiles to ECMWF analyses also indicated that BAROCLIM
outperforms MSIS. These results confirmed the capability of
BAROCLIM to be used in RO profile retrievals.
The main advantage of BAROCLIM compared to the average bending
angle approach proposed by and
is that utilization of BAROCLIM yields
individual RO profiles rather than climatological fields and
individual RO profiles are known to provide accurate
information of, e.g., tropopause characteristics, occurrence of
multiple tropopauses, or the height of the atmospheric boundary
layer.
Our current BAROCLIM spectral model only includes profiles of
bending angle. An important BAROCLIM update could comprise its
inversion to refractivity, density, pressure, and temperature so
that these parameters could be used for other applications as
well.
Acknowledgements
We want to thank Gottfried Kirchengast and Josef Innerkofler
(WEGC) as well as Sean Healy (ECMWF) for valuable scientific
discussions. We are also grateful to UCAR/CDAAC for the
provision of level 1a RO data and WEGC for the provision of
level 1b RO data. Special thanks to Marc Schwärz and
Johannes Fritzer (WEGC) for the contributions in OPS system
development and operations. Furthermore, we thank ECMWF
(Reading, UK) for providing analysis data.
B. Scherllin-Pirscher and U. Foelsche were partly funded by GRAS
SAF (visiting scientist project VS14) and ROM SAF (visiting
scientist project VS19), and by the Austrian Science Fund (FWF)
under grants P22293-N21 (BENCHCLIM) and T620-N29
(DYNOCC). S. Syndergaard and K. B. Lauritsen were supported
by the ROM SAF (Radio Occultation Meteorology Satellite
Application Facility), which is an operational RO processing
center under EUMETSAT.Edited by: R. Anthes
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