## 1 Introduction

[2] Tropospheric slant delays used in the analysis of GNSS (Global Navigation Satellite System), VLBI (Very Long Baseline Interferometry), and DORIS (Doppler orbitography by radiopositioning integrated on satellite) observations are normally modeled as the sum of a hydrostatic and a wet part (Davis *et al*. 1985), each of them being the product of zenith delay and corresponding mapping function. Whereas wet zenith delays are usually estimated, hydrostatic zenith delays can be derived from the pressure value at the observation site following Saastamoinen (1972). Knowledge of the instantaneous local pressure arises from barometric recordings, the gridded surface pressure output of a numerical weather model (NWM), or global empirical models, which approximate the spatial and temporal pressure variability. Nowadays, the common empirical model used in GNSS/VLBI/DORIS processing is GPT (Global Pressure and Temperature) (Böhm *et al*. 2007); see Petit and Luzum (2010)).

[3] Both hydrostatic and wet mapping functions are expressed by the coefficients {*a*,*b*,*c*} given in the continued fraction form of Herring (1992). These coefficients are different for the hydrostatic and wet mapping functions and can be calculated in several ways. Within the currently used models, like the Isobaric Mapping Function (IMF (Niell, 2001)) or the Vienna Mapping Function 1 (VMF1 (Böhm *et al*. 2006b)), the coefficients of the hydrostatic and wet terms are obtained from operational analysis and forecast fields of NWMs, and issued for download. If they are not accessible, one may deploy empirical mapping models that are based on average values derived from NWMs. The Global Mapping Function (GMF (Böhm *et al*. 2006a)), which depends only on the station coordinates and the day of year (doy), can be noted as such an auxiliary model.

[4] There are some weaknesses to both models (GPT, GMF). These have been improved within a new combined model named GPT2. See Table 1 for a comprehensive overview. In the first place, GPT/GMF parameters are expanded to spherical harmonics of degree and order 9, leading to a coarse horizontal resolution of about 20°. Hence, the models’ capability of representing large height variations and the associated change of parameters is restricted. As a second issue, considerable height differences ( > 1 km) have to be dealt with when reducing meteorological quantities from the model surface to the actual station height. Within GPT2, a refined horizontal resolution of 5° partly compensates for these problems. The data used are monthly mean profiles of the latest ECMWF (European Centre for Medium-Range Weather Forecasts) Re-Analysis (ERA-Interim [*Dee et al.*, 2011]). Temporal coverage (2001–2010), vertical resolution (37 isobaric levels), and quality of the ERA-Interim data surpass the characteristics of ERA-40 fields [*Uppala et al.*, 2005] that were utilized for GPT/GMF (three years of monthly mean profiles at 23 isobaric levels). In those models, only mean and annual variation (phase fixed to 28 January) of the parameters were estimated within a least-squares adjustment at mean sea level. In addition to that, GPT2 incorporates semi-annual harmonics in order to better account for regions where very rainy periods or very dry periods dominate. Furthermore, GPT2 replaces GPT's constant temperature lapse rate of − 6.5°C∕km by mean values and (semi-)annual variations of the temperature lapse rate at each grid point. This amendment improves the reduction of the temperature from the height of the grid to the height of the site. For the analogous reduction in terms of pressure values, GPT2 reverts to the virtual temperature (i.e., the temperature at which a parcel of dry air would have the same pressure and density as the equivalent parcel of moist air). Information about the humidity of the troposphere is accounted for by the water vapor pressure (see Table 1). The new parameters water vapor pressure, temperature, and lapse rate are beneficial for determining a priori values of zenith wet delays. Furthermore, annual and semi-annual temperature variations can be used for modeling the thermal deformation of VLBI radio telescopes.

GPT/GMF | GPT2 | |
---|---|---|

NWM data | Monthly mean profiles from ERA-40 (23 pressure levels): 1999–2002 | Monthly mean profiles from ERA- Interim (37 levels): 2001–2010 |

Representation | Spherical harmonics up to degree and order 9 at mean sea level | 5° grid at mean ETOPO5-based heights |

Temporal variability | Mean and annual terms | Mean, annual, and semi-annual terms |

Phase | Fixed to January 28 | Estimated |

Temperature reduction | Constant lapse rate − 6.5°C∕km assumed | Mean, annual, and semi-annual terms of temperature lapse rate estimated at every grid point |

Pressure reduction | Exponential based on standard atmosphere | Exponential based on virtual temperature at each point |

Output parameters | Pressure (p), temperature (T), mapping function coefficients (a_{h}, a_{w}) | p, T, lapse rate ( dT), water vapor pressure (e), a_{h}, a_{w} |

[5] This paper describes the development and workings of GPT2 in sections 2 and 3. The new model is compared to GPT and successfully validated on the basis of in situ barometric observations in section 4. Finally, we confirm the improved performance of GPT2 with respect to GPT/GMF within global VLBI solutions (section 4.3).