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

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)

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

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

An overview on principal features of a number of global and regional
models of the middle atmosphere and thermosphere is given by

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

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

The RO bending angle can be used as a climate variable

First RO profiles of the Earth's atmosphere were provided by the
GPS/MET experiment in intermittent periods from 1995 and 1997

Atmospheric profiles from RO are used for data assimilation in
numerical weather prediction (NWP)

The top altitude of RO measurements depends on the instrument
settings but is at least 80

Formally, the upper limit in the Abel integral transform is infinity

The generation of the bending angle radio occultation
climatology (BAROCLIM) described in this paper is mainly based
on the work by

Section

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)

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

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

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

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

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,

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.

Flowchart of the BAROCLIM generation.

Figure

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

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

To also detect very bad profiles below 50

F3C bending angles (in

Mean F3C bending angles (in

We used all remaining profiles and
calculated mean bending angles and standard deviations for 10

Table

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

The mean number of profiles per 10

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

Because of the generally decreasing bending angle with altitude, the
mean bending angle
(Fig.

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

To combine the mean RO bending angle profile with the
corresponding MSIS profile, we applied statistical
optimization by inverse covariance weighting

The observational error was set to the mean
background error between 62 and 78

Even though Fig.

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

Since the amount of water
vapor in the lower troposphere depends on latitude, we performed
RO–MSIS transition between 5 and 10

To sum up, our BAROCLIM discrete model is available for every month
(January to December) and has a horizontal resolution of
10

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

Chebychev coefficients,

The Chebychev coefficients were then expanded into zonal
harmonics. Besides the Chebychev coefficients, also

In general, zonal harmonics coefficients

To reconstruct the bending angle from the BAROCLIM spectral model
for a given impact altitude and latitude, we first applied Clenshaw's
recurrence formula

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

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

Figure

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

Atmospheric climatological fields of RO data are affected by (i)
random statistical errors, (ii) systematic errors, and (iii) sampling
errors

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.

Errors due to local multipath depend on the spacecraft size and on the
reflection coefficient

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

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

Finally, errors in BAROCLIM are caused by discrete sampling
times and locations of RO measurements

In December 2006 ECMWF started assimilating RO data in its
operational assimilation system

Figure

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 (

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

This comparison clearly shows that BAROCLIM is of very high
quality at least up to 60

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.

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

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

Figure

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

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

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.

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

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

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

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

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.

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