Vienna Mapping Functions 1 (VMF1)

Reference + Reference (forecast)

VMF1 is based on empirical equations for the "b" and "c" coefficients of the continued fraction form, whereas the "a" coefficients are determined epoch-wise (00, 06, 12, 18 UT) from ray-traced delays at 3° elevation angle. The ray-tracing is performed through two different NWM types, resulting in two different versions of VMF1. "VMF1_OP" is based on ERA-40 NWMs up to the year 2001 and from the year 2002 onwards on OPERATIONAL NWMs. This version is provided on the day after the date of its validity. "VMF1_FC" is based on FORECAST NWMs and is provided on the day prior to the date of its validity.

Important note: The coefficients for determining "c" in Table 1 of the online paper are incorrect. The corrected table can be found in this version of the paper.

Site-wise VMF1

Site-wise VMF1 parameters are provided for DORIS, GNSS, and VLBI stations listed in the respective *_vmf1.ell file. Hydrostatic and wet "a" coefficients of VMF1 can be used as input for the routines vmf1.f/vmf1.m in order to compute the hydrostatic and wet mapping factor.

Important note: On 2018/07/01, the algorithm for calculating site-wise VMF1 parameters was modified. The values are not determined for the exact location of a site anymore, but rather are interpolated from the surrounding 2.0°x2.5° grid points. However, the change in method causes only a slight change of the values.

Important note: Up to 2014/12/1, parameters for the VLBI station ARECIBO were processed using a wrong longitude. The value erroneously used was 66° Eastern longitude instead of 66° Western longitude.

Available files:

DORIS/VMF1/VMF1_OP/*/*.vmf1_d	VMF1 data for DORIS stations based on ERA-40/OPERATIONAL NWM data (epoch-wise, daily, or yearly format)
DORIS/VMF1/VMF1_FC/*/*.vmf1_d	VMF1 data for DORIS stations based on FORECAST NWM data (epoch-wise, daily, or yearly format)
GNSS/VMF1/VMF1_OP/*/*.vmf1_g	VMF1 data for GNSS stations based on ERA-40/OPERATIONAL NWM data (epoch-wise, daily, or yearly format)
GNSS/VMF1/VMF1_FC/*/*.vmf1_g	VMF1 data for GNSS stations based on FORECAST NWM data (epoch-wise, daily, or yearly format)
VLBI/VMF1/VMF1_OP/*/*.vmf1_r	VMF1 data for VLBI stations based on ERA-40/OPERATIONAL NWM data (epoch-wise, daily, or yearly format)
VLBI/VMF1/VMF1_FC/*/*.vmf1_r	VMF1 data for VLBI stations based on FORECAST NWM data (epoch-wise, daily, or yearly format)
codes/vmf1.f	Fortran code for determining the mapping factors from VMF1 "a" coefficients
codes/vmf1.m	MATLAB code for determining the mapping factors from VMF1 "a" coefficients
station_coord_files/doris_vmf1.ell	List of ellipsoidal DORIS station coordinates used for determining VMF1 parameters
station_coord_files/gnss_vmf1.ell	List of ellipsoidal GNSS station coordinates used for determining VMF1 parameters
station_coord_files/vlbi_vmf1.ell	List of ellipsoidal VLBI station coordinates used for determining VMF1 parameters
station_coord_files/orography_ell	ellipsoidal station heights of the grid points

Column description:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	hydrostatic zenith delay [m]
(6)	wet zenith delay [m]
(7)	mean temperature of the atmosphere at the Earth surface corresponding to orography_ell [K]
(8)	pressure at the site [hPa]
(9)	temperature at the site [°C]
(10)	water vapor pressure at the site [hPa]
(11)	orthometric height of the station [m] (using geoid EGM96)

Grid-wise VMF1

VMF1 values for arbitrary sites can be determined through interpolation from grid-wise VMF1 data. For this purpose, the routines vmf1_grid.f90/vmf1_grid.m can be used, which also include the transformation of "a" coefficients and zenith delays from zero height to the desired height. Alternatively, the routines vmf1_ht.f/vmf1_ht.m can be used for calculating mapping factors from VMF1 "a" coefficients interpolated from the grid.

Available files:

GRID/2.5x2.0/VMF1/VMF1_OP/*/*.H*	VMF1 data on a global 2.0°x2.5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/2.5x2.0/VMF1/VMF1_FC/*/*.H*	VMF1 data on a global 2.0°x2.5° grid from FORECAST NWM data (epoch-wise format)
GRID/2.5x2.0/VMF1/STD_OP/*/*.h*	Compact VMF1 data on a global 2.0°x2.5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/2.5x2.0/VMF1/STD_FC/*.h*	Compact VMF1 data on a global 2.0°x2.5° grid from FORECAST NWM data (epoch-wise format)
codes/vmf1_grid.f90	Fortran code for determining mapping factors and zenith delays from VMF1 grid files
codes/vmf1_ht.f	Fortran code for determining mapping factors based on "a" coefficients
codes/vmf1_grid.m	MATLAB code for determining mapping factors and zenith delays from VMF1 grid files
codes/vmf1_ht.m	MATLAB code for determining mapping factors based on "a" coefficients
station_coord_files/orography_ell	ellipsoidal station heights of the grid points

Column description:

(1)	latitude [°]
(2)	longitude [°]
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	hydrostatic zenith delay [m]
(6)	wet zenith delay [m]

File description of compact format:

ah*.h*	hydrostatic "a" coefficient
aw*.h*	wet "a" coefficient
tm*.h*	mean temperature of the atmosphere at the Earth surface corresponding to orography_ell [K]
zh*.h*	hydrostatic zenith delay [m]
wh*.h*	wet zenith delay [m]

Linear Horizontal Gradients (LHG)

Reference

Complementary to VMF1, the VMF Data Server provides linear horinzontal gradients for the same stations as VMF1 site-wise products. A reduction factor of 0.53 for the hydrostatic gradients and 0.71 for the wet gradients needs to be applied. The ellipsoidal coordinates of the stations can be found in the respective *_vmf1.ell files. Please note that these coordinate files are slightly different from the ones used for VMF3/GRAD.

The provision of LHG gradients ended in 2017. Please refer to the GRAD gradients from then on.

Available files:

DORIS/LHG/*/*.lhg_d	LHG data for DORIS stations (daily or yearly format)
GNSS/LHG/*/*.lhg_g	LHG data for GNSS stations (daily or yearly format)
VLBI/LHG/*/*.lhg_r	LHG data for VLBI stations (daily or yearly format)
station_coord_files/doris_vmf1.ell	List of ellipsoidal DORIS station coordinates
station_coord_files/gnss_vmf1.ell	List of ellipsoidal GNSS station coordinates
station_coord_files/vlbi_vmf1.ell	List of ellipsoidal VLBI station coordinates

Column description:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic north gradient [mm] (to be multiplied with 0.53)
(4)	hydrostatic east gradient [mm] (to be multiplied with 0.53)
(5)	wet north gradient [mm] (to be multiplied with 0.71)
(6)	wet east gradient [mm] (to be multiplied with 0.71)

Vienna Mapping Functions 3 (VMF3)

Reference

VMF3 is the successor of VMF1. It is based on empirical "b" and "c" coefficients of the continued fraction form, whereas the "a" coefficients are determined epoch-wise (00, 06, 12, 18 UT) from ray-traced delays at 3° elevation and eight equally spaced azimuth angles. The ray-tracing is performed through different NWM types, resulting in different versions of VMF3. Furthermore, the extended output format *.v3gr additionally includes linear horizontal gradients of the GRAD model.

Available versions:

ERA-Interim ("EI")	starting in 1980; only published in blocks every few months by the ECMWF, therefore not available in real-time
Operational ("OP")	starting in 2008; made available at about 18 UT for the previous day
Forecast ("FC")	starting in 2018; made available in real-time at about 09 UT for the following day

Site-wise VMF3

Site-wise VMF3 parameters are provided for DORIS, GNSS, and VLBI stations listed in the respective *.ell file. Hydrostatic and wet "a" coefficients of VMF3 can be used as input for the routines vmf3.f90/vmf3.m in order to compute the hydrostatic and wet mapping factor.

Available files:

DORIS/VMF3/VMF3_EI/*/*.vmf3_d	VMF3 data for DORIS stations based on ERA-Interim NWM data (daily or yearly format)
DORIS/VMF3/VMF3_OP/*/*.vmf3_d	VMF3 data for DORIS stations based on OPERATIONAL NWM data (daily or yearly format)
DORIS/VMF3/VMF3_FC/*/*.vmf3_d	VMF3 data for DORIS stations based on FORECAST NWM data (daily or yearly format)
GNSS/VMF3/VMF3_EI/*/*.vmf3_g	VMF3 data for GNSS stations based on ERA-Interim NWM data (daily or yearly format)
GNSS/VMF3/VMF3_OP/*/*.vmf3_g	VMF3 data for GNSS stations based on OPERATIONAL NWM data (daily or yearly format)
GNSS/VMF3/VMF3_FC/*/*.vmf3_g	VMF3 data for GNSS stations based on FORECAST NWM data (daily or yearly format)
VLBI/VMF3/VMF3_EI/*/*.vmf3_r	VMF3 data for VLBI stations based on ERA-Interim NWM data (daily or yearly format)
VLBI/VMF3/VMF3_OP/*/*.vmf3_r	VMF3 data for VLBI stations based on OPERATIONAL NWM data (daily or yearly format)
VLBI/VMF3/VMF3_FC/*/*.vmf3_r	VMF3 data for VLBI stations based on FORECAST NWM data (daily or yearly format);
DORIS/V3GR/V3GR_EI/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on ERA-Interim NWM data (daily or yearly format)
DORIS/V3GR/V3GR_OP/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on OPERATIONAL NWM data (daily or yearly format)
DORIS/V3GR/V3GR_FC/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on FORECAST NWM data (daily or yearly format)
GNSS/V3GR/V3GR_EI/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on ERA-Interim NWM data (daily or yearly format)
GNSS/V3GR/V3GR_OP/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on OPERATIONAL NWM data (daily or yearly format)
GNSS/V3GR/V3GR_FC/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on FORECAST NWM data (daily or yearly format)
VLBI/V3GR/V3GR_EI/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on ERA-Interim NWM data (daily or yearly format)
VLBI/V3GR/V3GR_OP/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on OPERATIONAL NWM data (daily or yearly format)
VLBI/V3GR/V3GR_FC/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on FORECAST NWM data (daily or yearly format)
codes/vmf3.f90	Fortran code for determining the mapping factors from VMF3 "a" coefficients
codes/vmf3.m	MATLAB code for determining the mapping factors from VMF3 "a" coefficients
station_coord_files/doris.ell	List of ellipsoidal DORIS station coordinates
station_coord_files/gnss.ell	List of ellipsoidal GNSS station coordinates
station_coord_files/vlbi.ell	List of ellipsoidal VLBI station coordinates

Column description VMF3 data:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	pressure at the site [hPa]
(8)	temperature at the site [°C]
(9)	water vapor pressure at the site [hPa]

Column description V3GR data:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	pressure at the site [hPa]
(8)	temperature at the site [°C]
(9)	water vapor pressure at the site [hPa]
(10)	hydrostatic north gradient Gn_h [mm]
(11)	hydrostatic east gradient Ge_h [mm]
(12)	wet north gradient Gn_w [mm]
(13)	wet east gradient Ge_w [mm]

Grid-wise VMF3

VMF3 values for arbitrary sites can be determined through interpolation from the grid-wise VMF3 data. For this purpose, the routines vmf3_grid.f90/vmf3_grid.m can be used, which also include the transformation of "a" coefficients and zenith delays from zero height to the desired height. Alternatively, the routines vmf3_ht.f/vmf3_ht.m can be used for calculating mapping factors from VMF1 "a" coefficients interpolated from the grid. The grid-wise VMF3 data is available in a horizontal resolution of 5°x5° as well as 1°x1° for the grid point coordinates listed in gridpoint_coord_5x5.txt and gridpoint_coord_1x1.txt, respectively.

Important note: All VMF3 data on the 5°x5° grid have been re-calculated on May 2, 2018, because wrong ellipsoidal heights had been used for some few grid points before.

Available files:

GRID/5x5/VMF3/VMF3_EI/*/*.H*	VMF3 data on a global 5°x5° grid from ERA-Interim NWM data (epoch-wise format)
GRID/5x5/VMF3/VMF3_OP/*/*.H*	VMF3 data on a global 5°x5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/5x5/VMF3/VMF3_FC/*/*.H*	VMF3 data on a global 5°x5° grid from FORECAST NWM data (epoch-wise format)
GRID/1x1/VMF3/VMF3_EI/*/*.H*	VMF3 data on a global 1°x1° grid from ERA-Interim NWM data (epoch-wise format)
GRID/1x1/VMF3/VMF3_OP/*/*.H*	VMF3 data on a global 1°x1° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/1x1/VMF3/VMF3_FC/*/*.H*	VMF3 data on a global 1°x1° grid from FORECAST NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_EI/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from ERA-Interim NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_OP/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_FC/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from FORECAST NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_EI/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from ERA-Interim NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_OP/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_FC/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from FORECAST NWM data (epoch-wise format)
codes/vmf3_grid.f90	Fortran code for determining mapping factors and zenith delays from VMF3 grid files
codes/vmf3_ht.f90	Fortran code for determining mapping factors based on "a" coefficients
codes/vmf3_grid.m	MATLAB code for determining mapping factors and zenith delays from VMF3 grid files
codes/vmf3_ht.m	MATLAB code for determining mapping factors based on "a" coefficients
station_coord_files/gridpoint_coord_5x5.txt	List of 5°x5° grid point coordinates (based on the model ETOPO5)
station_coord_files/gridpoint_coord_1x1.txt	List of 1°x1° grid point coordinates (based on the model ETOPO5)
station_coord_files/orography_ell_5x5	Ellipsoidal station heights of the grid points listed in gridpoint_coord_5x5.txt
station_coord_files/orography_ell_1x1	Ellipsoidal station heights of the grid points listed in gridpoint_coord_1x1.txt

Column description VMF3 data:

(1)	latitude [°]
(2)	longitude [°]
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]

Column description V3GR data:

(1)	latitude [°]
(2)	longitude [°]
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	hydrostatic north gradient [mm]
(8)	hydrostatic east gradient [mm]
(9)	wet north gradient [mm]
(10)	wet east gradient [mm]

A priori horizontal gradients (GRAD)

Reference

Complementary to VMF3, the GRAD model provides hydrostatic and wet horizontal gradients for the same stations as VMF3 site-wise products, as well as grid-wise data on a 5°x5° and a 1°x1° grid. The gradients are derived from ray-traced delays, consistently with VMF3 products, and are intended for the gradient formula by Chen and Herring (1997). The ray-tracing is performed through different NWM types, resulting in different versions of the GRAD model. Furthermore, the extended output format *.v3gr combines VMF3 and GRAD model parameters.

Available versions:

ERA-Interim ("EI")	starting in 1980; only published in blocks every few months by the ECMWF, therefore not available in real-time
Operational ("OP")	starting in 2008; made available at about 18 UT for the previous day
Forecast ("FC")	starting in 2018; made available in real-time at about 09 UT for the following day

Site-wise GRAD

Site-wise GRAD parameters are provided for DORIS, GNSS, and VLBI stations listed in the respective *.ell file. Please note that these coordinate files are slightly different from the ones used for VMF1/LHG.

Available files:

DORIS/GRAD/GRAD_EI/*/*.grad_d	GRAD data for DORIS stations based on ERA-Interim NWM data (daily or yearly format)
DORIS/GRAD/GRAD_OP/*/*.grad_d	GRAD data for DORIS stations based on OPERATIONAL NWM data (daily or yearly format)
DORIS/GRAD/GRAD_FC/*/*.grad_d	GRAD data for DORIS stations based on FORECAST NWM data (daily or yearly format)
GNSS/GRAD/GRAD_EI/*/*.grad_g	GRAD data for GNSS stations based on ERA-Interim NWM data (daily or yearly format)
GNSS/GRAD/GRAD_OP/*/*.grad_g	GRAD data for GNSS stations based on OPERATIONAL NWM data (daily or yearly format)
GNSS/GRAD/GRAD_FC/*/*.grad_g	GRAD data for GNSS stations based on FORECAST NWM data (daily or yearly format)
VLBI/GRAD/GRAD_EI/*/*.grad_r	GRAD data for VLBI stations based on ERA-Interim NWM data (daily or yearly format)
VLBI/GRAD/GRAD_OP/*/*.grad_r	GRAD data for VLBI stations based on OPERATIONAL NWM data (daily or yearly format)
VLBI/GRAD/GRAD_FC/*/*.grad_r	GRAD data for VLBI stations based on FORECAST NWM data (daily or yearly format)
DORIS/V3GR/V3GR_EI/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on ERA-Interim NWM data (daily or yearly format)
DORIS/V3GR/V3GR_OP/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on OPERATIONAL NWM data (daily or yearly format)
DORIS/V3GR/V3GR_FC/*/*.v3gr_d	Combined VMF3+GRAD data for DORIS stations based on FORECAST NWM data (daily or yearly format)
GNSS/V3GR/V3GR_EI/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on ERA-Interim NWM data (daily or yearly format)
GNSS/V3GR/V3GR_OP/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on OPERATIONAL NWM data (daily or yearly format)
GNSS/V3GR/V3GR_FC/*/*.v3gr_g	Combined VMF3+GRAD data for GNSS stations based on FORECAST NWM data (daily or yearly format)
VLBI/V3GR/V3GR_EI/*/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on ERA-Interim NWM data (daily or yearly format)
VLBI/V3GR/V3GR_OP/*/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on OPERATIONAL NWM data (daily or yearly format)
VLBI/V3GR/V3GR_FC/*/*.v3gr_r	Combined VMF3+GRAD data for VLBI stations based on FORECAST NWM data (daily or yearly format)
station_coord_files/doris.ell	List of ellipsoidal DORIS station coordinates
station_coord_files/gnss.ell	List of ellipsoidal GNSS station coordinates
station_coord_files/vlbi.ell	List of ellipsoidal VLBI station coordinates

Column description GRAD data:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic north gradient Gn_h [mm]
(4)	hydrostatic east gradient Ge_h [mm]
(5)	wet north gradient Gn_w [mm]
(6)	wet east gradient Ge_w [mm]

Column description V3GR data:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	pressure at the site [hPa]
(8)	temperature at the site [°C]
(9)	water vapor pressure at the site [hPa]
(10)	hydrostatic north gradient Gn_h [mm]
(11)	hydrostatic east gradient Ge_h [mm]
(12)	wet north gradient Gn_w [mm]
(13)	wet east gradient Ge_w [mm]

Grid-wise GRAD

GRAD values for arbitrary sites can be determined through interpolation from the grid-wise GRAD data. For this purpose, the routines grad_grid.f90/grad_grid.m can be used. The grid-wise GRAD data is available in a horizontal resolution of 5°x5° as well as 1°x1° for the grid point coordinates listed in gridpoint_coord_5x5.txt and gridpoint_coord_1x1.txt, respectively.

Important note: All GRAD data on the 5°x5° grid have been re-calculated on May 2, 2018, because wrong ellipsoidal heights had been used for some few grid points before.

Available files:

GRID/5x5/GRAD/GRAD_EI/*/*.H*	GRAD data on a global 5°x5° grid from ERA-Interim NWM data (epoch-wise format)
GRID/5x5/GRAD/GRAD_OP/*/*.H*	GRAD data on a global 5°x5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/5x5/GRAD/GRAD_FC/*/*.H*	GRAD data on a global 5°x5° grid from FORECAST NWM data (epoch-wise format)
GRID/1x1/GRAD/GRAD_EI/*/*.H*	GRAD data on a global 1°x1° grid from ERA-Interim NWM data (epoch-wise format)
GRID/1x1/GRAD/GRAD_OP/*/*.H*	GRAD data on a global 1°x1° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/1x1/GRAD/GRAD_FC/*/*.H*	GRAD data on a global 1°x1° grid from FORECAST NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_EI/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from ERA-Interim NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_OP/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/5x5/V3GR/V3GR_FC/*/*.H*	Combined VMF3+GRAD data on a global 5°x5° grid from FORECAST NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_EI/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from ERA-Interim NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_OP/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from OPERATIONAL NWM data (epoch-wise format)
GRID/1x1/V3GR/V3GR_FC/*/*.H*	Combined VMF3+GRAD data on a global 1°x1° grid from Forecast NWM data (epoch-wise format)
codes/grad_grid.f90	Fortran code for interpolating gradients from GRAD grid files
codes/grad_grid.m	MATLAB code for interpolating gradients from GRAD grid files
station_coord_files/gridpoint_coord_5x5.txt	List of 5°x5° grid point coordinates (based on the model ETOPO5)
station_coord_files/gridpoint_coord_1x1.txt	List of 1°x1° grid point coordinates (based on the model ETOPO5)

Column description GRAD data:

(1)	latitude [°]
(2)	longitude [°]
(3)	hydrostatic north gradient Gn_h [mm]
(4)	hydrostatic east gradient Ge_h [mm]
(5)	wet north gradient Gn_w [mm]
(6)	wet east gradient Ge_w [mm]

Column description V3GR data:

(1)	latitude [°]
(2)	longitude [°]
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	hydrostatic north gradient Gn_h [mm]
(8)	hydrostatic east gradient Ge_h [mm]
(9)	wet north gradient Gn_w [mm]
(10)	wet east gradient Ge_w [mm]

Vienna Mapping Functions 3 - optical (VMF3o)

Reference

VMF3o is an adaption of VMF3, dedicated for observations in the optical frequency range (e.g. SLR). It is based on empirical "b" and "c" coefficients of the continued fraction form, whereas the "a" coefficients are determined epoch-wise (00, 06, 12, 18 UT) from ray-traced delays at 5° elevation and eight equally spaced azimuth angles. The ray-tracing is performed through different NWM types, resulting in different versions of VMF3.

Available versions:

ERA-Interim (_EI)	starting in 1990; only published in blocks every few months by the ECMWF, therefore not available in real-time
OPERATIONAL (_OP)	starting in 2008; made available at about 18 UT for the previous day
OPERATIONAL Forecast (_FC)	starting in 2019; made available in real-time at about 09 UT for the following day

Site-wise VMF3o are provided for past and active SLR stations listed in the slr.ell file. The subroutine vmf3o_b_c.m can be used for calculating "b" and "c" coefficients of the continuous fraction form, based on the Spherical Harmonics coefficients saved in anm_*.txt and bnm_*.txt.

VMF3o parameters are designed for a signal wavelength of 532nm. A description and the coefficients of a wavelength correction formula can be found in the file CF_ABC.txt. With this correction formula, VMF3o parameters can be transformed to signal wavelenghts between 350nm and 1064nm. A transformation of "b" and "c" coefficients is not needed, since the effect is absorbed in the correction for the "a" coefficients.

Available files:

SLR/VMF3o/VMF3o_EI/*/*.vmf3o	VMF3o data for SLR stations based on ERA-Interim NWM data (daily or yearly format)
SLR/VMF3o/VMF3o_OP/*/*.vmf3o	VMF3o data for SLR stations based on OPERATIONAL NWM data (daily or yearly format)
SLR/VMF3o/VMF3o_FC/*/*.vmf3o	VMF3o data for SLR stations based on FORECAST NWM data (daily or yearly format)
codes/CF_ABC.txt	Description and coefficients of wavelength correction formula
codes/vmf3o_b_c.m	MATLAB code for calculating "b" nd "c" coefficients
codes/vmf3o_SH/anm_bh.txt	Spherical Harmonics coefficients for "b_h"
codes/vmf3o_SH/anm_bw.txt	Spherical Harmonics coefficients for "b_w"
codes/vmf3o_SH/anm_ch.txt	Spherical Harmonics coefficients for "c_h"
codes/vmf3o_SH/anm_cw.txt	Spherical Harmonics coefficients for "c_w"
codes/vmf3o_SH/bnm_bh.txt	Spherical Harmonics coefficients for "b_h"
codes/vmf3o_SH/bnm_bw.txt	Spherical Harmonics coefficients for "b_w"
codes/vmf3o_SH/bnm_ch.txt	Spherical Harmonics coefficients for "c_h"
codes/vmf3o_SH/bnm_cw.txt	Spherical Harmonics coefficients for "c_w"
station_coord_files/slr.ell	List of ellipsoidal SLR station coordinates

Column description VMF3o data:

(1)	station name
(2)	modified Julian date
(3)	hydrostatic "a" coefficient
(4)	wet "a" coefficient
(5)	zenith hydrostatic delay [m]
(6)	zenith wet delay [m]
(7)	pressure at the site [hPa]
(8)	temperature at the site [°C]
(9)	water vapor pressure at the site [hPa]
(10)	hydrostatic north gradient Gn_h [mm]
(11)	hydrostatic east gradient Ge_h [mm]
(12)	wet north gradient Gn_w [mm]
(13)	wet east gradient Ge_w [mm]

Mapping Functions

Global Mapping Functions (GMF)

Reference

GMF is the first empirical mapping function developed by TU Wien. Similar to NMF, the input parameters are day of year, latitude, longitude, and height.

Available files:

codes/gmf.f	Fortran code for calculating hydrostatic and wet mapping factors (former name: gmf_deriv.f_hu)
codes/gmf_deriv.f	Updated Fortran code for Bernese implementations including derivatives (former name: gmf_deriv.f_hu)
codes/gmf.m	MATLAB code for calculating hydrostatic and wet mapping factors (former name: gmf_f_hu.m)

Surface Meteorology Models

Global Pressure and Temperature (GPT)

Reference

GPT is an empirical model to determine pressure, temperature, and undulation from the site coordinates and the day of the year, based on spherical harmonics expansions up to degree and order 9.

Available files:

codes/gpt.f	Fortran code for calculating GPT parameters (former name: gpt.f_hu)
codes/gpt.m	MATLAB code for calculating GPT parameters

Mapping Functions + Surface Meteorology Models

Global Pressure and Temperature 2 (GPT2)

Reference

GPT2 is an updated and extended version of GPT/GMF providing additional output parameters. It is based on bilinear interpolation from a 5°x5° grid where the underlying data is contained in an external text file. GPT2 does not provide ready-to-use mapping function values, but only the "a" coefficients of the continuous fraction form. These values are, unlike the other output quantities, not valid at the height of the topography, but at sea level. In order to determine the respective mapping factors at the desired height, the routines vmf1_ht.f/vmf1_ht.m need to be applied.

Available files:

codes/gpt2.f	Fortran code for calculating GPT2 parameters
codes/vmf1_ht.f	Fortran code for determining mapping factors based on "a" coefficients
codes/gpt2.m	MATLAB code for calculating GPT2 parameters (default version)
codes/vmf1_ht.m	MATLAB code for determining mapping factors based on "a" coefficients
codes/gpt2_5.grd	Text file containing the underlying grid data for GPT2

Global Pressure and Temperature 2 wet (GPT2w)

Reference

GPT2w is the successor of GPT2 providing more precise consideration of the wet delay. The underlying grid is available optionally in 5°x5° as well as 1°x1° resolution. Again, in order to determine the mapping functions at the desired height, the routines vmf1_ht.f/vmf1_ht.m need to be applied. The output of GPT2w can be used to calculate approximations of the zenith hydrostatic delay using the routines saasthyd.f/saasthyd.m and of the zenith wet delay using asknewet.f/asknewet.m.

Available files:

codes/gpt2_1w.f	Fortran code for calculating GPT2w parameters based on a 1°x1° grid
codes/vmf1_ht.f	Fortran code for determining mapping factors based on "a" coefficients
codes/saasthyd.f	Fortran code for the determination of zenith hydrostatic delays
codes/asknewet.f	Fortran code for the determination of zenith wet delays
codes/gpt2_1w.m	MATLAB code for calculating GPT2w parameters based on a 1°x1° grid
codes/gpt2_5w.m	MATLAB code for calculating GPT2w parameters based on a 5°x5° grid
codes/vmf1_ht.m	MATLAB code for determining mapping factors based on "a" coefficients
codes/saasthyd.m	MATLAB code for the determination of zenith hydrostatic delays
codes/asknewet.m	MATLAB code for the determination of zenith wet delays
codes/gpt2w.cpp	C code for calculating GPT2w parameters (part 1)
codes/gpt2w.h	C code for calculating GPT2w parameters (part 2)
codes/gpt2_1w.grd	Text file containing the underlying 1°x1° grid data for GPT2w (former name: gpt2_1wA.grd)
codes/gpt2_5w.grd	Text file containing the underlying 5°x5° grid data for GPT2w

Mapping Functions + Surface Meteorology Models + Gradient Models

Global Pressure and Temperature 3 (GPT3)

Reference

GPT3 is the successor of GPT2w additionally including empirical horizontal gradients intended for the gradient formula by Chen and Herring (1997). The underlying grid is available optionally in 5°x5° as well as 1°x1° resolution. In order to determine the mapping functions at the desired height, the routines vmf3_ht.f90/vmf3_ht.m need to be applied. The output of GPT3 can be used to calculate approximations of the zenith hydrostatic delay using the routines saasthyd.f/saasthyd.m and of the zenith wet delay using asknewet.f/asknewet.m. Generating GPT3 parameters for a greater number of epochs or stations using gpt3.m can be fairly time-consuming (particularly the 1°x1° version). In this case it is recommended to use the faster versions of the MATLAB code.

Important note: The 5°x5° version of GPT3 has been re-calculated on April 23, 2018, because for some few grid points wrong ellipsoidal heights had been used before.

Available files:

codes/gpt3_5.f90	Fortran code for calculating GPT3 parameters based on a 5°x5° grid
codes/gpt3_1.f90	Fortran code for calculating GPT3 parameters based on a 1°x1° grid
codes/vmf3_ht.f90	Fortran code for determining mapping factors based on "a" coefficients
codes/saasthyd.f	Fortran code for the determination of zenith hydrostatic delays
codes/asknewet.f	Fortran code for the determination of zenith wet delays
codes/gpt3_5.m	MATLAB code for calculating GPT3 parameters based on a 5°x5° grid (default version)
codes/gpt3_5_fast.m	MATLAB code for calculating GPT3 parameters based on a 5°x5° grid (faster version, to be used together with gpt3_5_fast_readGrid.m)
codes/gpt3_5_fast_readGrid.m	MATLAB code for calculating GPT3 parameters based on a 5°x5° grid (faster version, to be used together with gpt3_5_fast.m)
codes/gpt3_1.m	MATLAB code for calculating GPT3 parameters based on a 1°x1° grid (default version)
codes/gpt3_1_fast.m	MATLAB code for calculating GPT3 parameters based on a 1°x1° grid (faster version, to be used together with gpt3_1_fast_readGrid.m)
codes/gpt3_1_fast_readGrid.m	MATLAB code for calculating GPT3 parameters based on a 1°x1° grid (faster version, to be used together with gpt3_1_fast.m)
codes/vmf3_ht.m	MATLAB code for determining mapping factors based on "a" coefficients
codes/saasthyd.m	MATLAB code for the determination of zenith hydrostatic delays
codes/asknewet.m	MATLAB code for the determination of zenith wet delays
codes/gpt3_1.grd	Text file containing the underlying 1°x1° grid data for GPT3
codes/gpt3_5.grd	Text file containing the underlying 5°x5° grid data for GPT3

Site-augmented Mode

Reference

There is also the possibility to site-augment the empirical models GPT2w and GPT3 by means of in-situ meteorological measurements. This may be relevant for real-time applications in case of no available internet connection for downloading the lastest discrete data and the user must rely on empirical models. If there is a possibility to measure temperature and/or relative humidity at the site, the performance of the empirical models can be augmented. More precisely, the augmentation is carried out through weighting coefficients, which relate the empirical values to the measured ones. Depending on whether (a) only temperature or (b) temperature and humidity are measured, there are two augmentation formulas:

(a)	zwd_augmented = zwd_GPT3 + 0.00180 * (T_meas – T_GPT3)
(b)	zwd_augmented = zwd_GPT3 + 0.00049 * (T_meas – T_GPT3) + 0.00920 * (e_meas – e_GPT3)

where zwd_GPT3 can be calculated through asknewet.f/asknewet.m using the GPT3 output quantities. The water vapor pressure is determined from temperature T (°C) and relative humidity (%) through the formula by Magnus:

e = 6.1078 * exp((17.1 * T) / (235 + T)) * hum/100;

As an alternative, the measured water vapor pressure can also be directly inserted in asknewet.f90/asknewet.m.

Converted GRIB files

The Numerical Weather Models of ECMWF are provided in so-called GRIB files (.grib). Prior to serving as input to the VieVS Ray-tracer, they are converted to text files (referred to as "grib_txt") using ecCodes following certain formatting rules. For more details see the README.md at https://github.com/TUW-VieVS/RADIATE.

For an easier application of the VieVS Ray-tracer, the convertet "grib_txt" files of the OPERATIONAL NWM of ECMWF (1°x1°, 25 pressure levels) are provided at the VMF Data Server.

Available files:

GRIB_TXT/*/*.txt.gz

Gunzipped "grib_txt" files of the epoch given in the file name

Ray-traced Delays for full VLBI history

Reference

The direct ray-traced delays for VLBI observations provided by the VMF Data Server cover the full history of geodetic VLBI. The delays are available in two different formats. *.radiate files contain the full output of the VieVS Ray-tracer. *.trp files provide a more compact format. For both formats, a column description is included in every file. Up to 2007, the ray-tracing was based on ERA-Interim NWMs, whereas from 2008 onwards, OPERATIONAL NWMs are used. The reference pressure is calculated using the empirical troposphere delay model GPT2.

Available files:

VLBI/RAYTR/RADIATE/*/*.radiate	Ray-traced delays for VLBI observations (session-wise format)
VLBI/RAYTR/TRP/*/*.trp	Ray-traced delays for VLBI observations in a more compact format (session-wise format)

Ray-tracing Comparison Campaign (2012)

Reference

In 2012 a comparison campaign between ray-tracing softwares was carried out by several institutions. NWM data from the operational analysis of ECMWF for stations Tsukuba (Japan) and Wettzell (Germany) were provided to the participants of the study. All relevant data related to the comparison campaign are accessible on the VMF Data Server.

Available files:

BMC/20080101_p0p1.wett	NWM data of ECMWF for station Wettzell
BMC/20080802_p0p1.tsuk	NWM data of ECMWF for station Tsukuba
BMC/Readme.txt	Brief description with reference to the published results
BMC/*.jpg	Result plots for stations Wettzell and Tsukuba
BMC/*.asc	Slant delays at 5 degrees elevation in meters

Reference

The VMF Data Server also provides atmospheric pressure loading (APL) data on a global 1°x1° grid as well as for DORIS, GNSS, SLR, and VLBI stations. The total atmospheric pressure loading displacements are divided into tidal and non-tidal components. For tidal components the non inverted barometer (non-IB) assumption was adopted. Mean annual surface pressure tides were extracted from 3-hourly pressure level data of the ECMWF delayed cut-off operational model (analyzed time frame: 2005.0 - 2010.12). The S3 tide was not removed from the non-tidal series. Reference epoch is 0 UTC of a mean solar day. Non-tidal radial and horizontal displacements are provided on a regular basis every 6 hours, as they are fluctuating due to weather changes. Here, the inverted barometer (IB) assumption was adopted.

Grid-wise APL

The grid-wise APL coefficients are provided on a global 1°x1° grid for latitudes between 89.5° and -89.5° and longitudes between 0.5° and 359.5°. The tidal coefficients are constant, while the non-tidal coefficients are provided in a temporal resolution of 6 hours.

Available files:

GRID/*/*_ce_v004.apl	Non-tidal displacements calculated in the center of Earth (CoE) reference frame (epoch-wise format)
GRID/*/*_cm_v004.apl	Non-tidal displacements calculated in the center of mass (CoM) reference frame (epoch-wise format)
TIDAL/s1_s2_s3_ce_noib_grid.dat	Tidal displacements calculated in the center of Earth (CoE) reference frame
TIDAL/s1_s2_s3_cm_noib_grid.dat	Tidal displacements calculated in the center of mass (CoM) reference frame

Column description non-tidal APL data:

(1)	latitude [°]
(2)	longitude [°]
(3)	up component [m]
(4)	east component [m]
(5)	north component [m]

Column description tidal APL data:

(1)	latitude [°]
(2)	longitude [°]
(3)	S1 cosine amplitude for radial displacement [mm]
(4)	S1 sine amplitude for radial displacement [mm]
(5)	S2 cosine amplitude for radial displacement [mm]
(6)	S2 sine amplitude for radial displacement [mm]
(7)	S3 cosine amplitude for radial displacement [mm]
(8)	S3 sine amplitude for radial displacement [mm]
(9)	S1 cosine amplitude for eastward displacement [mm]
(10)	S1 sine amplitude for eastward displacement [mm]
(11)	S2 cosine amplitude for eastward displacement [mm]
(12)	S2 sine amplitude for eastward displacement [mm]
(13)	S3 cosine amplitude for eastward displacement [mm]
(14)	S3 sine amplitude for eastward displacement [mm]
(15)	S1 cosine amplitude for northward displacement [mm]
(16)	S1 sine amplitude for northward displacement [mm]
(17)	S2 cosine amplitude for northward displacement [mm]
(18)	S2 sine amplitude for northward displacement [mm]
(19)	S3 cosine amplitude for northward displacement [mm]
(20)	S3 sine amplitude for northward displacement [mm]

Site-wise APL

The site-wise APL coefficients are provided for DORIS, GNSS, SLR, and VLBI stations listed in the respective station coordinate file. The tidal coefficients are constant, while the non-tidal coefficients are provided in a temporal resolution of 6 hours. All site-wise coefficients are calculated in the center of mass (CoM) reference frame.

Available files:

DORIS/*/*.apl_d	Non-tidal displacements for DORIS stations (daily or yearly format)
GNSS/*.apl_g	Non-tidal displacements for GNSS stations (daily or yearly format)
SLR/*/*.apl_s	Non-tidal displacements for SLR stations (daily or yearly format)
VLBI/*/*.apl_r	Non-tidal displacements for VLBI stations (daily or yearly format)
TIDAL/s1_s2_s3_cm_noib_doris.dat	Tidal displacements for DORIS stations
TIDAL/s1_s2_s3_cm_noib_gnss.dat	Tidal displacements for GNSS stations
TIDAL/s1_s2_s3_cm_noib_slr.dat	Tidal displacements for SLR stations
TIDAL/s1_s2_s3_cm_noib_vlbi.dat	Tidal displacements for VLBI stations
station_coord_files/doris.ell	List of ellipsoidal DORIS station coordinates
station_coord_files/gnss.ell	List of ellipsoidal GNSS station coordinates
station_coord_files/slr.ell	List of ellipsoidal SLR station coordinates
station_coord_files/vlbi.ell	List of ellipsoidal VLBI station coordinates

Column description non-tidal APL data:

(1)	station name
(2)	modified Julian date
(3)	up component [m]
(4)	east component [m]
(5)	north component [m]

Column description tidal APL data:

(1)	station name
(2)	S1 cosine amplitude for radial displacement [mm]
(3)	S1 sine amplitude for radial displacement [mm]
(4)	S2 cosine amplitude for radial displacement [mm]
(5)	S2 sine amplitude for radial displacement [mm]
(6)	S3 cosine amplitude for radial displacement [mm]
(7)	S3 sine amplitude for radial displacement [mm]
(8)	S1 cosine amplitude for eastward displacement [mm]
(9)	S1 sine amplitude for eastward displacement [mm]
(10)	S2 cosine amplitude for eastward displacement [mm]
(11)	S2 sine amplitude for eastward displacement [mm]
(12)	S3 cosine amplitude for eastward displacement [mm]
(13)	S3 sine amplitude for eastward displacement [mm]
(14)	S1 cosine amplitude for northward displacement [mm]
(15)	S1 sine amplitude for northward displacement [mm]
(16)	S2 cosine amplitude for northward displacement [mm]
(17)	S2 sine amplitude for northward displacement [mm]
(18)	S3 cosine amplitude for northward displacement [mm]
(19)	S3 sine amplitude for northward displacement [mm]