Radio occultation (RO) and radiosonde (RS) comparisons provide a means of
analyzing errors associated with both observational systems. Since RO and RS
observations are not taken at the exact same time or location, temporal and
spatial sampling errors resulting from atmospheric variability can be
significant and inhibit error analysis of the observational systems. In
addition, the vertical resolutions of RO and RS profiles vary and vertical
representativeness errors may also affect the comparison. In RO–RS
comparisons, RO observations are co-located with RS profiles within a fixed
time window and distance, i.e. within 3–6

Radio occultation (RO), a relatively new method of atmospheric measurement,
has established itself as an important atmospheric observational system. By
measuring the phase delay of radio waves sent from Global Positioning System (GPS) satellites traversing quasi-horizontally through Earth's atmosphere to
low-Earth orbiting satellites, RO obtains accurate and precise vertical
profiles of bending angles

Since the proof-of-concept GPS/MET mission in 1995

One of the main difficulties associated with RO–RS comparisons comes from
temporal and spatial differences between nearby RS and RO soundings. Since
both measurements are not taken at the exact same time or location, temporal
and spatial errors (sampling errors) can be a significant part of the
computed RO–RS differences. To reduce the effects of sampling errors, the
majority of previous studies have restricted co-located RO observations to
within a fixed time range and distance, typically within 3–6

We apply two methods to reduce sampling errors caused by atmospheric
variability in RO–RS comparisons. First, we restrict co-location pairs to
within ellipses oriented along the direction of wind flow rather than
circles. Temperature and water vapor gradients in the free atmosphere tend to
be perpendicular to wind flow, resulting in refractivity (a function of both
temperature and water vapor pressure) gradients to also approximately lie
perpendicular to wind flow. Therefore, we hypothesize that the spatial
variability of refractivity within ellipses of semi-major axis

Although this paper considers RO–RS comparisons, the vertical filtering and methods of reducing sampling errors can be applied to comparisons of other data pairs, such as any two sounding systems or observations and models. However, the amount of filtering and the geometric constraints on the co-location pairs may have to be adjusted for different comparisons. For example, comparisons of RO or RS soundings with IR or microwave soundings, which have much different vertical resolutions, would require a greater filtering of the RO or RS profiles to make them comparable to the lower-resolution profiles.

The first section describes the data sets, filtering methods, and methodology implemented in this study. Next, we discuss aspects of the ellipse co-location method conducted using the Lindenberg RS station. The following section describes the results of co-locations using both the ellipse and sampling correction methods at four different RS stations. In the final section we summarize the results and discuss further impacts and implications, followed by an appendix which includes mean and standard deviation differences and further discussion of the spatial–temporal sampling correction.

All RO profiles are provided by the COSMIC Data Analysis and Archive Center
(CDAAC), which can be found at

Map of the GRUAN RS network. Labeled locations with red dots are RS
stations used in this study, and black dots mark the other GRUAN network RS
stations. For more information about these and other GRUAN stations, see

All RS profiles are provided by the Global Climate Observing System (GCOS)
Reference Upper-Air Network

We chose four stations in different climates for this study for the time periods of 2014, 2013, 2012, and
2011–2013, respectively: Lindenberg,
Germany (LIN); Ny-Ålesund, Norway (NYA); Tateno, Japan (TAT); and Nauru,
Nauru (NAU). (Nauru is the only station in which the full
period of activation was used; this is due to the low number of RS launches
during 2011 through late August 2013.) Figure

For refractivity comparisons, RS refractivity is computed under the
assumption of a neutral atmosphere

We generate two data sets: an unfiltered data set which contains all original RO and RS profiles and a filtered data set containing the vertically filtered versions of the original RO and RS profiles.

Representativeness errors result from two different aspects of the RO and RS
observations. Firstly, GRUAN RS have a temporal resolution of 1

To remove small-scale, unrepresentative structures in both the RO and RS
profiles, we applied the Savitzky–Golay low-pass filter

500

We co-located RO and RS observations using the ellipse method every
10

Figure

For each RS at a given time and pressure level, RO profiles are co-located
with the RS profiles under the time and geometric constraints discussed
above. There can be (and often are) multiple co-location pairs with the same RS
at a given time and pressure level. We computed differences for each
co-location pair:

Schematic of the sampling correction applied to RO and RS co-location.

Applying a spatial–temporal sampling correction to the RO–RS differences is
an alternate method of reducing sampling errors in the presence of an
auxiliary data set. This method has been applied in previous studies and is
not restricted to RO–RS comparisons.

Here, we apply a spatial–temporal sampling correction double difference
computed with model data and assess its effects on reducing sampling errors.
We use ERA-Interim data to subtract the model background from both the RO and
RS observations, removing spatial and temporal sampling differences and
isolating the observational errors associated with the RO and RS pair. As
shown in Fig.

The spatial–temporal sampling corrected differences (

The spatial–temporal corrected difference (

Preliminary proof-of-concept testing of the ellipse method using only ERA-Interim data demonstrated a significant reduction in RMS refractivity differences within the ellipse relative to both the large circle and circles of similar area to the ellipse (not shown here). In the following two sections, aspects of the ellipse co-location are analyzed at the Lindenberg station. The final section presents the results of both the ellipse co-location and sampling correction at all four RS stations.

Filtered vs. unfiltered RMS percent differences

Filtering both the RO and RS profiles has a small, positive impact on
reducing RMS differences in refractivity, temperature, and water vapor
pressure. Compared to RMS differences computed using the unfiltered profiles
at Lindenberg, filtering both the RO and RS profiles before co-location
reduces RMS differences by about 1 % on average, up to almost 8 % in some
instances (see Table

RMS refractivity differences at Lindenberg 2014 for two sets of
RO–RS pairs separated by reported RS wind speeds: pairs with wind speeds
less than 5

The relationship between the wind direction and horizontal variability (and
sampling error) of refractivity is expected to break down for light wind
speeds – indeed we found that when wind speeds are low, the effectiveness of
orienting the ellipse along the direction of wind flow is significantly
reduced. We separated co-located RO–RS pairs at Lindenberg into two groups
based on the reported wind speed of the RS at a given time and pressure
level: (1) wind speeds less than 5

As shown in Fig.

RMS differences for RO–RS co-locations at Lindenberg, 2014. RMS
differences with ellipse method only (solid; large circle: orange; small
circle: grey; ellipse: magenta) and RMS differences with ellipse method and
sampling correction (dashed, abbreviated as SC) are shown for all three
variables:

Same as Fig.

We carried out two RO–RS comparisons at four different RS locations (Lindenberg, Ny-Ålesund, Tateno, and Nauru): first, we compared pairs with RO observations co-located within the large circle, small circle, and ellipse centered at the RS station, and second, we applied the sampling correction to the RO–RS pairs within the ellipse and two circles. We then computed RMS differences in refractivity, temperature, and water vapor pressure.

Figure

The results at Ny-Ålesund and Tateno are very similar to those at
Lindenberg, with some minor differences in the lower troposphere
(Fig.

Same as Fig.

The results at the tropical location of Nauru (Fig.

Refractivity and water vapor pressure RMS differences in the lower
troposphere (1000–700

We have shown that vertical filtering of the RO and RS profiles before
comparison reduces representativeness errors associated with different
vertical resolutions and observation types by a small amount (typically a few
percent). Using these filtered profiles, we tested two methods to reduce
spatial and temporal sampling errors during RO–RS comparisons: (1) restricting RO and RS pairs to within ellipses oriented along the direction
of wind flow and (2) applying a spatial–temporal sampling correction using
model data to remove differences caused by horizontal atmospheric gradients
and time differences in the observations. When wind speeds exceed about
5

Applying the spatial–temporal sampling correction using ERA-Interim model data showed the most significant reduction in RMS differences, more so than applying the ellipse constraint alone. The sampling correction reduced RMS differences in refractivity, temperature, and water vapor pressure by an average of 55 %. The reductions of sampling errors within both large and small circles and the ellipse tend to converge with the sampling correction applied, rendering the differences in geometric constraints of the circles and ellipse negligible. An exception to this reduction in RMS occurs at Nauru in the lower troposphere, where super-refraction associated with the atmospheric conditions of the deep tropics tends to dominate the RMS differences.

In order to reduce sampling errors for future RO–RS co-location comparisons,
our results suggest that applying the sampling correction under more lenient
co-location criteria would be most effective. By using a large distance
constraint, the sample size will be sufficiently large and applying the
sampling correction eliminates most sampling errors, even for the large
distance restriction (greater than 600

The code used in this study will be made available upon request.

In this section, we compute the mean and standard deviation (SD) of the
RO–RS differences. The mean difference is defined as

Figures

RO–RS refractivity mean (thick) and SD (thin) difference profiles
for the six co-location methods at Lindenberg

In Fig.

Same as Fig.

The biases for temperature differences (Fig.

Same as Fig.

Finally, the differences in the mean RO–RS water vapor pressure reflect the
negative refractivity bias due to super-refraction at Lindenberg, Tateno, and
especially Nauru, with little bias at the colder, drier Ny-Ålesund
station (Fig.

The SD profiles in Figs.

In Sect.

RMS

Figure

These results show that using the double-differencing method to reduce
spatial and temporal sampling errors in RO–RS comparisons allows for many
more RO–RS pairs to be included in the comparison (more than 35 000 for the
15

All co-authors contributed to developing the ideas and methodologies of this project. SG conducted the majority of the coding, data retrieval, computations, and analysis, with TR contributing to coding and data retrieval. SG prepared the manuscript with contributions from both co-authors.

The authors declare that they have no conflict of interest.

The authors thank Eric DeWeaver (NSF) and Jack Kaye (NASA) for their support of this research through NSF-NASA grant AGS-1522830. Sergey Sokolovskiy provided many useful comments and suggestions during this study. The first author was supported in part by the Significant Opportunities in Atmospheric Research and Science (SOARS) program, NSF grant AGS-1641177, and by the Constellation Observing System for Meteorology, Ionosphere, and Climate (COSMIC) program at UCAR, which is sponsored by the National Space Office in Taiwan, NSF, NASA, NOAA, and the U.S. Air Force. Thanks to CDAAC for the provided RO data sets, NOAA NCDC and GRUAN for the provided RS data sets, and the ECMWF for the provided ERA-Interim data sets. The authors thank Keith Maull for his suggestions during this study. The authors would like to thank the three anonymous reviewers for their comments and constructive suggestions which improved this paper. Edited by: Marcos Portabella Reviewed by: three anonymous referees