## 1. Introduction

[2] One of the key characteristics of GPS radio occultation (GPSRO) measurements is that they can be assimilated into operational numerical weather prediction (NWP) and reanalysis systems without bias correction. This is possible because the assimilated GPSRO quantities, usually either bending angle profiles or refractivity profiles, are derived from precise measurements of a time delay with an atomic clock. In addition, the forward problem is relatively straightforward when compared with the assimilation of satellite radiance measurements, partly because it is not considered to be reliant upon poorly known spectroscopic parameters, or the assumed concentrations of well-mixed gases. In fact, the forward modeling of GPSRO measurements does require empirically derived refractivity coefficients, but to date the level of confidence in these values has been very high. The refractivity coefficients used operationally at European Centre for Medium-Range Weather Forecasts (ECMWF) and the Met Office were derived by *Smith and Weintraub* [1953] (hereafter referred to as SW53), but their accuracy has been reinforced in more recent work by, for example, *Hasegawa and Stokesberry* [1975] (hereafter referred to as HS75) and *Bevis et al.* [1994] (hereafter referred to as BEV94). In particular, there has been a broad consensus in the literature that the *k*_{1} coefficient, which accounts for the dry air contribution to the total refractivity (see section 2), is *k*_{1} = 77.6 K hPa^{−1}, and this has effectively become the “standard value” used in GPSRO studies. However, *Rüeger* [2002] (hereafter referred to as RU02) has proposed a new set of “best average” refractivity coefficients, and the new *k*_{1} coefficient is 0.115% larger than the standard value. The new coefficients are based on a thorough reappraisal of experimental work from the 1950s to the 1970s.

[3] In the context of NWP, Rüeger's coefficients were tested for GPSRO data monitoring at Météo-France, but they were not used in assimilation experiments (P. Poli, personal communications, 2009). They are now used operationally at Environment Canada [*Aparicio and Deblonde*, 2008].

[4] ECMWF has recently conducted forecast impact experiments comparing SW53 coefficients and the RU02 best average coefficients, and we have found that the RU02 coefficients cool the mean state in the troposphere by ∼−0.1 K. This cooling reduces the biases in the short-range forecast fit to radiosonde temperature and height measurements in the Northern Hemisphere but increases the biases in the tropics and Southern Hemisphere. Experiments show that the cooling is caused primarily by the change in the “*k*_{1}” refractivity coefficient. Interestingly, the increased bias with respect to radiosonde measurements in the Southern Hemisphere appears to be qualitatively similar to the results presented by J. Aparicio (Environment Canada) at the ECMWF/Global navigation satellite system Receiver for Atmospheric Sounding (GRAS) Satellite Application Facility (SAF) workshop in 2008. *Aparicio et al.* [2009] use the Rüeger coefficients operationally but also advocate the inclusion of nonideal gas effects in GPSRO operators in order to reduce geopotential height biases against radiosondes. Furthermore, National Centers for Environmental Prediction (NCEP) has also recently reported difficulties with the RU02*k*_{1} value, suggesting it is too large [*Cucurull*, 2010], and they have retained *k*_{1} = 77.6 K hPa^{−1} in their refractivity forward model by adopting the BEV94 coefficients.

[5] Given the difficulties with the RU02 coefficients in NWP impact experiments, we have attempted to reconcile the differences between the standard (i.e., SW53/HS75/BEV94) and RU02*k*_{1} values. This exercise has shown that there is more uncertainty in the *k*_{1} coefficient than is generally recognized by the NWP community. It has highlighted small numerical discrepancies in how the refractivity coefficients are derived from refractivity measurements by different authors, and a misunderstanding over whether the contribution of CO_{2} is accounted for when deriving the coefficient. A similar analysis is also presented by *Cucurull* [2010]. We have also investigated the connection between the choice of refractivity coefficients and the inclusion of nonideal gas effects in the GPSRO observation operator. In section 2, we introduce and compare the standard values of the refractivity coefficients given by SW53, BEV94, and others, with the new RU02 estimates. The forecast impact experiments examining the sensitivity to the SW53 and RU02 coefficients, and investigating the inclusion of nonideal gas effects are described in section 3. The discussion and conclusions are given in section 4.