## 1. Introduction

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.