Global positioning system radio occultation (GPS RO) soundings are currently being assimilated operationally at the major NWP centers (e.g. Healy and Thépaut, 2006; Cucurull et al., 2007; Aparicio et al., 2009). Typically, profiles of refractivity or bending angle are used with their corresponding forward operators, quality control procedures, and error structures. A detailed description of the processing of the GPS RO raw measurements, so atmospheric values can be retrieved and used in weather forecasting, can be found, for example, in the study by Kursinski et al., 1997. Briefly, profiles of bending angle are obtained with the use of the observed Doppler shift and the velocity and position of the low-Earth orbit (LEO) (receiver) and GPS (transmitter) satellites. During this step in the processing of the data, the geographic coordinates of the tangent point of the ray are assigned. There are several reasons why the tangent point trajectory retrieved from measurements is oblique rather than vertical, including the fact that the GPS and LEO satellites move at different speed, and that their orbits are at different heights and are not coplanar.
The GPS RO processing centers provide profiles of bending angle and refractivity with their corresponding geographic coordinates for modeling purposes. However, most NWP centers have been using single profile-representative geographic coordinates for all observations within a profile instead of characterizing the latitude and longitude of all the values within a profile. In this case, only the variation of the geometric height in a sounding is taken into account during the assimilation process, thus profiles are assumed to be vertical. This approximation significantly reduces the computation cost and makes the forward operator quite faster, which makes it quite attractive from a data assimilation standpoint.
US National Centers for Environmental Prediction (NCEP) has been taking into account the horizontal smearing of the tangent point trajectories since the beginning of operational use of GPS RO data in May 2007. Since then, other operational centers have adopted this approach. For example, Météo-France introduced the tangent point drift in their operational system in late 2007 (Poli et al., 2009) and more recently European Centre for Medium-Range Weather Forecasts (ECMWF) switched to the new approach (Healy, 2011, personal communication).
A GPS-RO-retrieved value represents a volume—even if we treat it as a point measurement in NWP systems. As a consequence, they have larger representativeness errors than radiosondes (Kuo et al., 2005). By misplacing the coordinates of that ‘point measurement’, we are likely increasing the representativeness error associated with that derived value. Thus, higher representativeness errors are expected when comparing RO data to other data sets (e.g. radiosonde) or model simulations if verticality of the profiles is assumed.
Foelsche et al., 2011 conducted a detailed theoretical study and quantified the errors introduced with the use of a mean (or representative) tangent point trajectory. Although the true three dimensional (3D) tangent point trajectory is only feasible in theoretical studies, their findings recommend the use of the tangent point coordinates retrieved from measurements to minimize the errors. They show that this is a much better approach than considering a profile-fixed latitude and longitude. In the NWP context, several studies analyzed the contribution of neglecting the drift of the tangent point to the error of the forward operator (Poli and Joiner, 2004; Healy et al., 2007; Pingel and Rhodin, 2009). However, these studies did not investigate the impact of the geometry of the tangent point trajectory in terms of weather forecast skill.
The potential benefits of taking into account the drift of the tangent point have recently received a lot of attention within the GPS RO community and there is an increasing need to quantify the results in the literature. This paper analyzes the impact of the tangent point trajectory by performing NWP experiments with real profiles and an operational assimilation system. The goal of this study is to investigate whether the obliquity of the profiles should be considered in order to minimize errors, so research and operational centers can make their choice of what method to use based on model performance and available computing resources. It is important to emphasize that it is not the intent of this study to quantify the benefits of using GPS RO data in NWP systems, but rather to investigate two different approaches when using GPS RO data: one that considers the drift of the tangent point and one that uses fixed coordinates. There is no doubt about the significant benefits of assimilating GPS RO data, regardless of the approach being adopted. Results on the impact of using GPS RO with different models and the two approaches have been widely published over the recent years. We refer for instance to Cucurull et al. (2008) for a detailed evaluation on the gain in weather forecast skill with the use of GPS RO data at NCEP. Results presented there might be compared with the two approaches for assimilating GPS RO investigated in this study.
The manuscript is structured as follows. First, a description of the forward operator is provided in Section 2. The design of the experiments and the results are described in Sections 3 and 4, respectively. Finally, conclusions are summarized in Section 5.
2. Forward operator
The NCEP's Global Data Assimilation System uses a local forward operator for refractivity to assimilate GPS RO data (Cucurull and Derber, 2008). Quality control and error structures have been tuned accordingly.
Each value within a profile is assimilated with its own latitude, longitude, and geometric height. Model variables of surface pressure, moisture, and temperature are interpolated to the location of the retrieved value. Then, the model refractivity is computed. The following expression is used to simulate the values of refractivity:
which is a simplification of the refractivity equation provided by Thayer (1974) by ignoring the nonideal behavior of atmospheric gases. In the expression above, Pd is the pressure of the dry air, Pw the pressure of the water vapor, and T the absolute temperature. The k1, k2, and k3 are the atmospheric refractivity constants. The NCEP's operational configuration uses the refractivity coefficients provided by Bevis et al., 1994 (Cucurull, 2010) rather than the original values provided by Thayer (1974). The operational configuration only assimilates GPS RO data up to 30 km.
Theoretically, one could perform a full 3D ray tracing through the atmosphere and simulate the real tangent profile trajectory during an occultation. In practice, the processing of GPS RO products assumes spherical symmetry of the atmosphere. Under this condition, the values of the bending angle and refractivity only depend on the vertical coordinate and, by definition, horizontal dependence (latitude and longitude) does not exist. This 1D profile can a posteriori be assigned to a fixed latitude and longitude (profile-representative geographic coordinates). A better approach is to estimate the latitude and longitude at each ray tangent point height from the derived bending angles and positions of the GPS and LEO satellites. In this case, we assign a latitude and longitude to each retrieved value within the profile, accounting thus for some horizontal drift of the tangent point trajectory. Such slant profile is a better representation of the truth (Sokolovskiy, 2009, pers. comm.; Foelsche et al., 2011).
Another concern when ignoring the non-obliquity of the profiles is how the profile-representative tangent point is defined. Different definitions exist among different processing centers, which complicates the interpretation of the comparison between different GPS RO profiles even further. For example, GFZ uses the lowest point of the GPS RO profile, while UCAR/CDAAC uses a point with height ∼3–4 km. On the other hand, EUMETSAT uses a higher point still (∼16 km).
3. Experiment design
We performed two experiments in order to evaluate the impact of taking into account the horizontal drift of the tangent point trajectories in the GPS RO soundings. The control experiment (PRCNTL) accounted for the horizontal smearing of the tangent point within a profile, i.e. each GPS-RO-retrieved value was assimilated with its corresponding derived latitude, longitude, and geometric height.
A second experiment (PRNDTP) assumed no horizontal drift of the tangent point trajectory. In PRNDTP, the profile-mean tangent point height provided by the data providers was used. Both experiments performed from 2 February 2010 to 7 March 2010 and used the operational version of the NCEP's model.
The parallel experiments assimilated GPS RO soundings from COSMIC 1-6, GRAS/MetOp, and GRACE-A. A distribution of the number of profiles per RO sensor is shown in Figure 1. Over 95% of the data below 30 km were assimilated in both experiments. The remaining data were rejected because of several internal quality control procedures (differences with the background field too large, below model topography, etc.). The number of retrieved refractivities that passed the quality control was slightly larger (∼1%) in PRCNTL than PRNDTP, caused by the fact that the retrieved values were closer to the model simulations of refractivity in PRCNTL than in PRNDTP, thus less refractivities were rejected by this quality control procedure. This is expectable since the values in PRCNTL are a better representation of the state of the atmosphere because their assigned horizontal coordinates are more accurate, resulting in smaller differences between the retrieved values and the background field simulations.
Statistics of the difference between the GPS RO profiles and model simulations as a function of the geometric height are shown in percentage of refractivity in Figure 2 (top-left) for one of the COSMIC satellites (FM4). The figure only includes data that passed all the quality control procedures. Consequently, the statistics stops at 30 km.
The mean and the standard deviation of the differences are shown for the Southern Hemisphere extratropics (latitude below 20S), but the results are similar for other latitude ranges. Although the mean difference between PRCNTL and PRNDTP is very similar, the variability of these differences is larger in PRNDTP below ∼3 km and above ∼4 km, in particular, between ∼10 and 22 km. This is expected because it is at these heights where the deviations between considering a profile-assigned tangent point and the actual tangent point are expected to be larger for the COSMIC satellites.
The differences between data and model simulations normalized by the data error are shown in Figure 2 (top-right) for the same RO instrument and latitudinal range. After the assimilation cycle, one expects this difference to be ∼1. Normalized differences are larger in PRNDTP, in particular, between ∼10 and 25 km. This indicates that PRCNTL has a better behavior than PRNDTP within the assimilation system. The averaged normalized differences are also lower in the stratosphere in PRCNTL than PRNDTP.
Since the height assigned to the fixed tangent point depends on the processing center, the deviations in statistics will depend on the RO satellite as well. For example, as EUMETSAT uses a higher fixed height, the differences in statistics between using a fixed tangent point height or an observation dependent height will be less significant in the stratosphere than for the COSMIC satellites. This is shown in Figure 2 (bottom-left), where the statistics is shown for the GRAS satellite. The lower deviations for GRAS were already noticed by Healy, 2011 (pers. comm.). Normalized differences still show slightly better results when the drift of the tangent point is taken into account (Figure 2, bottom-right).
Anomaly correlation scores for the 5-day geopotential heights are shown in Figure 3 for the Northern and Southern Hemisphere extratropics. Results are presented for the 700-, 500-, and 250 mb pressure levels. As seen in the figure, accounting for the drift of the tangent point provides higher anomaly correlation values at all levels and for both hemispheres. Although the differences between the experiments are larger for the higher pressure levels, they are still noticeable ∼700 mb. The results are statistically significant at the 95% confidence level.
By considering the obliquity of the profiles in the assimilation system, tropospheric and stratospheric global winds improve as well. For example, wind root-mean-squared errors (rms) at day 3 are shown in Figure 4 for the 200 mb pressure level and different latitude ranges. The results are verified against own analysis (Figure 4(a)) and against a consensus analysis between the NCEP, ECMWF, and UK Met Office analyses (Figure 4(b)). The results are statistically significant at the 95% confidence level for the Northern and Southern Hemisphere extratropics. Regardless of the analysis being used, results are best when the drift of the tangent point within a profile is taken into consideration in the assimilation system.
The rms wind errors at day 3 for the Southern Hemisphere extratropics are shown in Figure 5 for several pressure levels. Again, considering the obliquity of the profiles gives the lowest rms errors. Results are statistically significant at the 95% confidence level. Differences are found for low and high-pressure levels, and the improvement is independent of the verification analysis used. The better performance of PRCNTL extends to other latitude ranges. Comparison against radiosondes shows improvement in the mid-upper tropospheric winds and temperature at 24-h forecast as well.
The assumption of treating GPS RO as vertical profiles has been explored within a global data assimilation system. From a theoretical point of view, GPS RO soundings are more accurate if their obliquity is considered (Foelsche et al., 2011). Although a full 3D ray tracing of the atmosphere is necessary to compute the true tangent point trajectory, a more realistic approach is to use multiple latitudes and longitudes obtained from each of the measurements within a profile.
This study shows that not just from a theoretical point of view, but from an NWP point of view as well, results are better when the horizontal smearing of the tangent point trajectory is taken into consideration in the assimilation algorithms. The impact, although not too large, is already noticeable with a global model. This impact is expected to be larger with a regional model since a profile with an oblique tangent point trajectory would cover a larger number of grid points and the verticality assumption would project all the information to a single grid point through the adjoint of the forward operator. In addition, the effects in NWP model skill will likely be larger when a denser RO observing system becomes available (e.g. with the planned COSMIC-2 mission), as the information on the atmospheric conditions that otherwise would extend to a larger number of grid points (larger profile density would cover a more extended area) would get reduced to a lower number of grid points.
This paper corroborates the theoretical results found in the study by Foelsche et al., 2011 by performing NWP experiments with real data and an operational assimilation system. Overall improvement in NWP skill is found when the obliquity of the profiles is considered. The improvement is found for the different latitude ranges and pressure levels, thus emphasizing the use of the slant geometry of the GPS RO profiles, whenever possible. Since the use of the drift of the tangent point will be associated with some increase in computational cost—how much will depend on the specific design and implementation of the forward operator and the particular analysis system—users will need to perform additional testing to evaluate if the improvement in forecast skill is cost effective for their specific needs.
The author acknowledges UCAR, NSPO, EUMETSAT, GRAS SAF, and GFZ for providing the different GPS RO profiles assimilated in the experiments. The author is also thankful to Dr John Derber for reviewing the manuscript and to the two anonymous reviewers for their comments and suggestions.