The Korea Institute of Atmospheric Prediction Systems (KIAPS) has been developing a new global numerical weather prediction model and an advanced data assimilation system. As part of the KIAPS package for observation processing (KPOP) system for data assimilation, preprocessing, and quality control modules for bending-angle measurements of global positioning system radio occultation (GPS-RO) data have been implemented and examined. The GPS-RO data processing system is composed of several steps for checking observation locations, missing values, physical values for Earth radius of curvature, and geoid undulation. An observation-minus-background check is implemented by use of a one-dimensional observational bending-angle operator, and tangent point drift is also considered in the quality control process. We have tested GPS-RO observations utilized by the Korean Meteorological Administration (KMA) within KPOP, based on both the KMA global model and the National Center for Atmospheric Research Community Atmosphere Model with Spectral Element dynamical core (CAM-SE) as a model background. Background fields from the CAM-SE model are incorporated for the preparation of assimilation experiments with the KIAPS local ensemble transform Kalman filter (LETKF) data assimilation system, which has been successfully implemented to a cubed-sphere model with unstructured quadrilateral meshes. As a result of data processing, the bending-angle departure statistics between observation and background show significant improvement. Also, the first experiment in assimilating GPS-RO bending angle from KPOP within KIAPS-LETKF shows encouraging results.

Global positioning system radio occultation (GPS-RO; Kursinski et al., 1997) is a limb-geometry remote-sensing technique whereby the time delay of GPS radio signals that have passed through the limb of the Earth's atmosphere are used to determine vertical profiles of measurements related to the refractive index. GPS satellites transmit two microwave signals (1.2 and 1.5 GHz) to receivers on low Earth orbit (LEO) satellites. An occultation occurs when the microwave signals transmitted by one of the GPS satellites as it rises or sets pass through the Earth's atmosphere. During an occultation, the ray connecting the GPS and LEO satellites scans the atmosphere, providing vertical information of the atmosphere from the refraction of the GPS radio signals as measured by the receiver in a low Earth orbit. The raw measurements of radio occultations are the phase and amplitude of radio signals transmitted by the GPS satellites. Based on these measurements and knowledge of the precise positions and velocities of the GPS and LEO satellites, vertical profiles of bending angle and atmospheric refractivity are derived by use of the local spherical symmetry assumption and the Abel inversion (Phinney and Anderson, 1968). The observations have high vertical resolution (0.1 km near surface to 1 km tropopause) and global coverage, even though the horizontal resolution is relatively poor (hundreds of kilometers). Also, they show high accuracy (equivalent to < 1 K; average accuracy < 0.1 K) and precision (0.02–0.05 K) (Anthes, 2011) for a temperature in the vertical range of 10 to 40 km and equal accuracy over either land or ocean (Cucurull et al., 2013). The most powerful benefits of the GPS-RO measurements are no satellite bias and minimal effect on the data by clouds or precipitation compared to other satellite observations. Because of these benefits, many operational numerical weather prediction centers, such as the Met Office of the United Kingdom, ECMWF, NCEP, Météo-France, Environment Canada, and JMA, have started incorporating GPS-RO soundings into their assimilation systems with clear positive impacts on weather forecasting (e.g., Healy, 2008; Buontempo et al., 2008; Cucurull and Derber, 2008; Aparicio et al., 2009; Rennie, 2010). In particular, GPS-RO data assimilation shows strong sensitivity to upper atmosphere temperature structures, an area that is only weakly constrained by other observations in the analysis and that is prone to large model uncertainties (Anlauf et al., 2011).

The Korea Institute of Atmospheric Prediction Systems (KIAPS) is a government-funded, non-profit research and development institute that was established in 2011 by the Korea Meteorological Administration (KMA). The goal of the KIAPS is to develop the next-generation operational global numerical weather prediction (NWP) system, which can be used for global modeling as well as local areas, particularly optimized to topographic and meteorological features of the Korean Peninsula. The KIAPS has been developing an advanced data assimilation system in addition to a global model (KIAPS integrated model with spectral element dynamic core, or KIM). As one of the data assimilation systems, a local ensemble transform Kalman filter (LETKF) (Hunt et al., 2007) has been successfully implemented for the National Center for Atmospheric Research Community Atmosphere Model with Spectral Element dynamical core (CAM-SE) (Dennis et al., 2012), which has the same grid structure on the cubed sphere as KIM. After a successful evaluation of the KIAPS-LETKF data assimilation system with various observing system simulation experiments (OSSEs) (Kang and Park, 2013), assimilation of real observations of surface and rawinsonde data from NCEP preprocessed data has been performed (Jung et al., 2014). In preparation for GPS-RO data assimilation, preprocessing and quality control modules for bending-angle measurements of GPS-RO data are well implemented in the KIAPS Package for Observation Processing (KPOP) to provide optimal observation for the data assimilation. Finally, we have tested GPS-RO bending-angle data assimilation within the KIAPS-LETKF system to see whether our first version of the GPS-RO data assimilation cycle works well in a coupled system of KIAPS-LETKF and KPOP.

In this paper, we describe the GPS-RO data processing system for bending-angle data assimilation and present preliminary results from bending-angle data assimilation experiments with the KIAPS-LETKF system. In Sect. 2, we present the GPS-RO processing system in KPOP. In this section, background ingest and spatial interpolation step, observation operator for bending angle, quality control procedure, and results from the quality control process for bending-angle data assimilation are introduced. In Sect. 3, description of analysis cycles within the KIAPS-LETKF system and its preliminary result are presented. Section 4 contains a summary and plans for future work.

The observation needs to be compared with the model background for quality
control and observation monitoring. Here, operational global model forecasts
of the KMA are used as a model background. The global model is the Unified
Model (UM; Davies et al., 2004), which was developed by the UK Met Office.
It is a non-hydrostatic, grid-point model, with the Charney–Phillips grid in
a vertical direction. The horizontal resolution is approximately 25 km
(N512/

To produce the simulated observation by use of model background fields, the
spatial interpolation of model variables to the observation space is
required. We used a bi-linear interpolation method to transform model
variables into the observation space in the horizontal direction. In the
vertical coordinate of the UM, model information is provided on a staggered
height grid, with pressure and density on

The purpose of data assimilation is to find an optimal analysis state, depending on the difference between observation and model background (i.e., innovations) and their error statistics. To have such innovations, one should have the observation operator that maps atmospheric variables in the model grid space into the observed variables in observation space (Eyre, 1994). Therefore, the observation operator (forward model) is one of the most important components in the data assimilation system that calculates the simulated observation by use of model variables.

GPS-RO measurements have a two-dimensional limb geometry that, ideally,
should be accounted for when they are assimilated into numerical weather
prediction systems. Generally, the ray-tracing operator (Gorbunov and
Kornblueh, 2003) for the bending angle is reported to lead to best results
in terms of standard deviation of the difference between observation and
model background (Pingel and Rhodin, 2009). However, the use of a
ray-tracing operator requires a high computational cost, so most numerical
weather prediction centers (e.g., ECMWF, UK Met Office, DWD, and
Météo-France) currently use one-dimensional observation operators
for the bending-angle assimilation and inflate the observation errors to
partially compensate for this source of forward model error (Anlauf et al.,
2011). The assumption of spherical symmetry enables calculation of the
bending angle from a one-dimensional integration of the background
refractivity lapse-rate profile located at the vertical level of the
observation point. Recently, ECMWF has tested the two-dimensional bending-angle operator in their numerical weather prediction system and planned to
implement it into the next model cycle. For the same reason as
most other operational centers, however, we adhere to a one-dimensional bending-angle operator that is included in the Radio Occultation Processing
Package (ROPP) developed by the European Organization for the Exploitation
of Meteorological Satellites (EUMETSAT) Radio Occultation Meteorology
Satellite Application Facility (ROM SAF). The one-dimensional bending-angle
operator in ROPP solves Eq. (1) by use of the algorithm of Healy and
Thépaut (2006). It calculates the integral of the bending angle (e.g.,
Kursinski et al., 1997), given the observed impact parameter

Ray bending above the model top is accounted for by extrapolating the
uppermost model parameters and evaluating

For the assimilation of GPS-RO bending-angle measurements, preprocessing and
quality control modules are implemented into KPOP. Figure 1 is a flowchart
that shows the structure and data processing steps of the GPS-RO processing
system. As the first step, input/output (I/O) modules for GPS-RO
data are implemented to process the binary universal format for data
representation (BUFR) data stream of the KMA by use of an ECMWF BUFR
decoder. Quality control modules in gross quality control steps are
implemented for checking observation locations, missing values for
refractivity, bending angles and their errors, physical values for Earth
radius of curvature, and geoid undulation. The criteria of physical values
correspond with those used in Météo-France. Also, this step involves
determining whether the impact height is increasing with geometric height
and the identical geolocation for each data point in the profile to screen
cases out of rule. The impact parameter is converted to impact height, which
is defined as the impact parameter minus the local radius of curvature, for
convenience. To take into account the tangent points drift, we make bins in
the vertical with 1.5 km intervals and then use the local information of
the latitude and longitude for each data point. An
observation-minus-background (O-B) check is implemented by the
one-dimensional observational bending-angle operator, as mentioned in a
previous section, to reject spurious data. This check consists of rejecting
data per element of the profile if the O-B value exceeds 5 times the
assumed observation error. The observation errors are assigned by applying
the error model described in Healy and Thépaut (2006), in which the
combination of forward model error and observation error is assumed to vary
only with impact height. The standard deviation of the error is assumed to
decrease linearly from 10 % of the observed value to 1 % for impact
heights from 0 to 10 km, and to stay at 1 % above 10 km, with an absolute
lower limit of 3

Schematic diagram of the GPS-RO data processing system implemented in KPOP.

We processed 30 days of bending-angle data from 1 to 30 November 2011, which were used for operational data assimilation at the KMA. The GPS-RO data provided by the KMA include measurements from the GRAS instrument on METOP (Loiselet et al., 2000), the constellation of six satellites launched by the Constellation Observing System for Meteorology, Ionosphere and Climate (COSMIC) program (Anthes et al., 2000), and the Communications/Navigation Outage Forecasting System (C/NOFS) Occultation Receiver for Ionospheric Sensing and Specification (CORISS) instrument. Figure 2 shows geographical coverage of GPS-RO profiles over 6 h. The number of total GPS-RO events for 6 h is approximately 500, and the data are shown to be distributed globally over land and ocean.

The KMA global model forecasts are used as model background. The operational
global forecast model used at the KMA is the UM (Davies et al., 2004),
developed by the UK Met Office. The GPS-RO data were assimilated to produce
the analysis with other kinds of observations in operational forecast cycle
at the KMA. Figure 3 presents the global mean of departure
statistics of bending angle between the observation and background
calculations for the month of November 2012. Figure 3a and b show the
global mean and standard deviation of bending-angle innovations normalized
by background and the number of observations as a function of impact height
before and after quality control, respectively. Also, Fig. 3c shows the
difference of departure statistics between Fig. 3a and b. After the
quality control, the mean agreement is best over approximately 5 to 40 km
altitude, between

Six-hour coverage of the GPS radio occultation events on 7 November 2012. The total number of profiles is 591.

We compared our results of bending-angle departure statistics to those from
the established operational quality control system of the Met Office by
Burrows et al. (2014) (not shown). The period (about 1 month) of data
processing and the types (satellites) of observations used by the Met Office are
similar to our data processing even though the year and month of
observation are not exactly matched. The comparison of results of O-B statistics
in our study with those of Met Office shows a good agreement in terms of
global mean and standard deviation. The results from CORISS instruments
show the large value of mean difference of O-B statistics under

The number of observations has been reduced by 1.07 % of the total number
of observations for the entire vertical range after the quality control. The
mean value of observation rejection for 10 km vertical intervals ranges from
0.65 % as minimum to 1.61 % as maximum, and such a difference depends
on the height. Relatively many observations are rejected under

Departure statistics between the observation and background
calculations of bending angles for the month of November 2012. (

We also investigated the bending-angle departure statistics when the tangent point drift is taken into account in GPS-RO data processing. Figure 4 shows the difference of the bending-angle departure statistics between the results from data processing with and without considering the tangent point drift. In data processing, which does not consider the tangent point drift, horizontal location of each data point in a vertical profile is assumed to be fixed, with mean value of latitude and longitude extracted from the BUFR file for all vertical levels. Although no significant difference is seen between the two treatments over most of the area, certain differences have been found at altitudes below 5 km over the tropics in latitude bands. Furthermore, the total number of data points remaining after quality control with tangent point drift consideration is slightly smaller than the other results with 0.08 %.

Difference of the bending-angle departure statistics for global

The forecast model used for the analysis cycles in this study is the CAM-SE,
which was developed for climate projection rather than weather prediction.
It has a relatively coarse vertical resolution with 30 layers, and its top
is near 2.25 Pa (

For the ensemble data assimilation experiments, we had 30 ensemble members
and a 6-hourly analysis cycle. Within the 6 h assimilation window, we
considered background ensembles and GPS-RO data every hour, based on a
4D-LETKF algorithm (e.g., Fertig et al., 2007; Harlim and Hunt, 2007) that
deals with flow-dependent background uncertainty in space as well as in
time. Adaptive multiplicative inflation (Miyoshi, 2011) was implemented,
which greatly helped in estimating background error covariance accurately
(e.g., Miyoshi and Kunii, 2012; Kang et al., 2012). Within the 4D-LETKF data
assimilation, the analysis mean

To assimilate GPS-RO bending-angle data within the KIAPS-LETKF system, we
ran ROPP implemented in KPOP, as an observation operator, as many times as
the ensemble size. Then, background ensembles at the GPS-RO observation
space

For the bending-angle data assimilation within the KIAPS-LETKF system, we first processed the GPS-RO data with hourly background ensembles from the CAM-SE forecast within KPOP system. All processing steps described in Sect. 2.3 are applied for the GPS-RO data processing with CAM-SE background. The data processing for ensemble data assimilation was done using each member of background ensembles of CAM-SE forecasts from every 6 h analysis for 2 weeks. The observations passed through the KPOP processing with all 30 ensemble backgrounds are used for the bending-angle assimilation within the KIAPS-LETKF system. The background ensembles at the initial time of bending-angle data assimilation cycles are the forecasts from the analysis assimilating sonde and surface pressure station data only. Once the the data assimilation cycle with RO data (EXP_RO cycle) is initiated, the background ensembles used for the data processing are CAM-SE forecasts starting from the analysis assimilating bending angle in addition to sonde and surface pressure data.

Figure 5 presents departure statistics between the observation and
background of the bending angle from 15 to 30 November 2012. The
background of the bending-angle results from an ensemble mean of 30
background states. Figure 5a and b show the global mean of
departure statistics normalized by background and the number of observations
as a function of impact height before and after quality control,
respectively. Also, Fig. 5c shows the difference of departure statistics
between Fig. 5a and b. Figure 5d and e show the zonal mean and the
standard deviation of bending-angle departures between observations and
background after the processing. The data processing clearly improves the
bending-angle departure statistics in terms of global mean and standard
deviation for the vertical range from 10 to 35 km. The global mean
departure statistics show best agreement between observation and background
over approximately 5 to 30 km of the impact height. The zonal mean
feature of departure statistics shows large value over the tropic regions.
About 13 % of the total number of observation is rejected during the data
processing. The number of rejected observations widely ranges from 2.9
to 32 % in the vertical profile. Note that the number of observations
around

When compared with the results obtained from use of the KMA forecast as a background, as presented in Sect. 2.4, the departure statistics show a larger variability with the CAM-SE background than with the KMA background in terms of global and zonal mean features of statistics. Also, the number of observations is significantly reduced compared to results of KMA forecasts after the data processing. This again implies that the CAM-SE background has poorer forecasts of atmospheric conditions than the KMA background. If we recall the lower horizontal and vertical resolution of the CAM-SE model and some limitations of climate models for good weather prediction as mentioned in a previous section, the finding looks reasonable. Another factor is that the KMA backgrounds already include the operational data assimilation effects of GPS-RO and many other observations on the analysis, whereas our CAM-SE background is the forecast from the analysis assimilating sonde, surface pressure station data, and GPS-RO bending angle only.

We also see the ensemble spread of background states in the observation space of bending angle in Fig. 6. Because the initial background ensembles for the RO data assimilation experiment come from background states of analyses assimilating only sonde and surface pressure data, the ensemble spread over the Northern Hemisphere is smaller than over the Southern Hemisphere. That is, meteorological variables are relatively well constrained by sonde data over the Northern Hemisphere, so the ensemble spread (standard deviation of ensemble perturbations), representing background uncertainty, has small values there. Therefore, we expect that the impact of GPS-RO bending-angle data would be significant over the regions with large ensemble spread (e.g., Southern Hemisphere) when the observation error of bending-angle data is relatively small.

We conducted two experiments: a 1-month (November 2011) data assimilation experiment that included sonde and surface pressure station data only (hereafter referred to as CTRL_SONDE) and a 2-week data assimilation experiment that starts from ensemble background after 2 weeks of CTRL_SONDE analysis (15 November 2011) but starts assimilating GPS-RO bending-angle data in addition to sonde and surface pressure station data (hereafter referred to as EXP_RO). Thus, we would like to see if EXP_RO gives reasonable analysis increments compared with CTRL_SONDE, for the last 2 weeks of the analysis period.

Same as Fig. 3 for the month of November 2012 except for the use of CAM-SE ensemble backgrounds.

Zonal mean of ensemble spread in the bending-angle observation space (unit: rad) at the initial time of EXP_RO at 00Z of 15 November 2011, which is from CTRL_SONDE.

Figure 7 shows a vertical cross section of zonally averaged analysis
increment differences of

Horizontal analysis increment at the level where many bending-angle data of GPS-RO are assimilated is presented in Fig. 8. As expected, significant increments occur where sonde data do not sufficiently constrain the background. Since the initial ensembles of EXP_RO were already constrained by conventional data for 2 weeks of CNTRL_SONDE, analysis increments look dominant where the conventional data do not exist, especially for the 2-week analysis period of EXP_RO. Recall that the spinup period usually shows significant analysis increments where observations are newly assimilated. We expect that the system will show more comparable increments even in the Northern Hemisphere as the forecast-analysis cycles are repeated.

To examine a posteriori uncertainties between CTRL_SONDE and
EXP_RO, we looked at the relative uncertainty reduction in
Fig. 9 through the following equation:

We found significant uncertainty reduction estimated over the areas where the analysis increments are shown in Fig. 8. This illustrates that GPS-RO data are assimilated and reduce uncertainties of background and analysis over the areas with many data and relative inaccuracy of background states. Because we used the adaptive multiplicative inflation method (Miyoshi, 2011), which computes inflation parameters in a way that has large inflation where and when innovation is large, to avoid underestimation of background uncertainty, background/analysis tends to have greater inflation factors than unity. In contrast, the multiplicative inflation parameter is not adaptively estimated when there is no observation (no O-B information), and a very small inflation factor (only 1 % inflation) is set. Therefore, background states in EXP_RO tend to be inflated more than those in CTRL_SONDE. Despite greater inflation factors multiplied in EXP_RO than in CTRL_SONDE, resultant analysis of EXP_RO shows significant reduction of analysis spread as a result of assimilating additional data. Before verifying our analysis, we confirmed that GPS-RO bending-angle data are assimilated effectively for the first test with the KIAPS-LETKF system in a way that reduces analysis uncertainty where the data are expected to contribute.

Finally, we compared our analysis with ERA interim reanalysis (Dee et al.,
2011) using the equation

Difference of zonally averaged analysis increments of

Difference of horizontal analysis increment of

Relative uncertainty reduction of EXP_RO from CTRL_SONDE, computed
by Eq. (9) for the variable

Improvement of EXP_RO analysis from CTRL_SONDE, toward ERA
interim, computed by the equation

Vertical cross section of zonally averaged improvement of EXP_RO
analysis from CTRL_SONDE, toward ERA interim, computed by the equation

Same as Fig. 10 except for the vertical level of 20 hPa.

We also took a look at the vertical profiles of analysis improvement in a
comparison with ERA interim data in Fig. 11. It shows significant error
reduction introduced by adding GPS-RO bending-angle data overall for 2
weeks of EXP_RO. There are considerable corrections of errors
in upper level wind and temperature. In addition, we could apparently find
positive impact of RO data even in the lower troposphere, especially over the
polar region where there is forecast imperfection due to the inactivated
sea–ice model. Figure 12 shows much greater improvement caused by GPS-RO
bending-angle data at the level of 20 hPa than the level of 100 hPa, and the
global mean of error reduction looks remarkable for both variables of

A preprocessing and quality control system for bending-angle measurements is successfully implemented in the KPOP system for GPS-RO bending-angle data assimilation. The preprocessing and gross quality control procedure consists of checks for observation locations, missing values, and physically consistent values for Earth radius of curvature and geoid undulation. An observation-minus-background check is implemented by use of a one-dimensional observational bending-angle operator that is included in the ROPP software. With this GPS-RO data processing system, we have processed bending-angle observations with background states produced by both KMA and CAM-SE forecasts to investigate the bending-angle departure statistics between observation and background. After the data processing, the mean departure statistics show better agreement between the observation and background of the bending angle. In particular, it is more apparent in the use of a CAM-SE background. Overall, the processing results show reasonable quality of departure statistics, which is consistent with previous studies (Cucurull et al., 2007; Poli et al., 2009; Rennie, 2010; Burrows et al., 2014).

We have tested GPS-RO bending-angle data processed by KPOP within the KIAPS-LETKF system. We conducted two experiments, one assimilating only sonde and surface pressure station data and the other assimilating GPS-RO bending-angle data in addition to sonde and surface pressure station data. Comparison between the two experiments shows remarkable difference of analysis increment over high altitudes, oceans, and the Southern Hemisphere, which explains the characteristics of additional data. In the KIAPS-LETKF system, we have obtained reasonable reduction of analysis uncertainty, and the positive impact of bending-angle data has been presented in the comparison with ERA interim reanalysis. What we have shown in this paper resulted from the first test assimilating the GPS-RO bending angle within the KIAPS-LETKF system. Based on this work, we will improve the KPOP and KIAPS-LETKF systems in various ways. We have started implementing the KIAPS-LETKF system in a much more advanced forecast model, KIM, which has much finer horizontal and vertical resolution with a higher top. This change will bring major improvement to the GPS-RO bending-angle data assimilation system. We can try the “localization of the variables” (Kang et al., 2011) to see if the results of bending-angle data assimilation would be improved. Moreover, in the coupled cycle of the KPOP and KIAPS-LETKF systems, we will try proactive quality control and estimate observation error by the advanced method of Hotta (2014), which estimates short-range forecast sensitivity to the observation data and to observation error within LETKF. Also, we will try to use the information from the prior ensemble statistics for the quality control of bending angle within the KPOP system. In addition, we plan to apply a two-dimensional bending-angle operator suggested (Healy et al., 2007) for advanced bending-angle preprocessing and data assimilation.

This work has been carried out through the research and development project on the development of global numerical weather prediction systems of the Korea Institute of Atmospheric Prediction Systems funded by Korea Meteorological Administration. Also, this work was partly funded by Korea Polar Research Institute project (PE15010). We thank Benjamin Ruston at the U.S. Naval Research Laboratory for his support and constructive discussion in the development of the KPOP system. Finally, we thank two anonymous reviewers for their constructive comments and suggestions to improve the manuscript. Edited by: R. Anthes