# EVRF2007

The European Vertical Reference Frame 2007 (EVRF2007), the new realization of the EVRS, is based on a combination strategy of three elements: the network, the vertical datum and the observation of the time evolution of the reference frame. The data is reduced, where possible, to the epoch 2000. The determination of the relationship of EVRF2007, to a Global Vertical Reference System (GVRS) is a future step. The detailed strategy is described in the paper "Conventions for the Definition and Realization of a European Vertical Reference System (EVRS)" – EVRS Conventions 2007 (Ihde et al 2008).

**Network**

Since the publication of the UELN95/98 adjustment results in January 1999 as EVRF2000 a lot of new data have been delivered to the UELN data center (Sacher et al. 2006). 14 countries made their current first order leveling networks available (see Figure 1)

Therefore a new realization of EVRS under the name EVRF2007 was computed. All participating countries were asked to contribute up-to-date data.

The measurements in the UELN data base originate from very different epochs (see Figure 2). This weak point of the project can be remedied only partly by the development of a kinematic network using information on the velocity of the points.

The data in the main area of the Fennoscandian Postglacial Rebound (PGR) is reduced to the epoch 2000 by differences of vertical velocities relative to the geoid from the land uplift model NKG2005LU (Ågren, J., Svenssonn, R., 2007). This applies to the measurements of Finland, Norway, Sweden, Denmark, Germany (northern part), Poland, Lithuania, Latvia and Estonia. Figure 3 shows a map of the model in relation to the UELN configuration.

**Datum specification**

In the UELN95/98 solution that forms the backbone of the EVRF2000, the NAP level was fixed by the reference point 000A2530 in the Netherlands (not to be confused with the datum point of the national leveling network 000A2350). The Fifth precision leveling of the Netherlands does not include this reference point. So it was not possible to relate the new adjustment of UELN to this reference, which had been used since UELN-55 (Simonsen 1960).

Therefore the UELN adjustment for the EVRF2007 is fitted to the EVRF2000 solution by choosing a number of datum points and introducing their UELN95/98 heights into the free adjustment of the current network. For the n datum points *P _{i}* it is set

For this transformation purpose it was important to choose stable marked datum points located in a stable part of the European plate. These datum points are part of both adjustments 2007 and 1998. The participating countries located in the stable part of the European plate were asked to propose datum points for the EVRF2007. Finally 13 datum points were used (see Figure 4).

**Tidal corrections and permanent tide**

The earth tides, caused by the gravitational forces of Moon and Sun, induce a permanent deformation of the earth crust. Different concepts to handle this deformation are described in Ekman 1989, Mäkinen and Ihde 2007, Ihde et al. 2008, Mäkinen 2008. The IAG resolution no. 16 recommends for the treatment of tidal corrections for gravity and station positioning the concept of zero tide. That means to retain the effect of the deformation and eliminate the effect of the tidal attraction.

Consequently the EVRS definition contains the clause: "The EVRS is a zero tidal system, in agreement with the IAG resolutions." (Ihde and Augath 2001). In the EVRF2000 this part of the definition was not realized, no reductions because of the permanent tides have been applied to the data by the UELN computing center.

The countries delivered their data in different tidal systems, and the actual systems were not known to the UELN computing center. As a result, the tidal system of the EVRF2000 is mixed. At present, we know that it is mostly mean-tide.

In EVRF2007 the geopotential differences are reduced from the mean-tidal system to zero-tide by

There was the question how to deal with the reduction of the datum points. In a first step the geopotential numbers of all datum points were corrected by

to bring them from the mean-tide system to the zero-tide system (Mäkinen, 2008).

The resulting reductions ranged between –0.030 (Italy) and –0.108 (Denmark) kgal·m. In order to minimize the differences to the EVRF2000 solution we added the constant of +0.08432 kgal·m, the value of the tidal correction of point 13600 (000A2530) with opposite sign, to the correction described in formula (2). This is equivalent to the assumption that the NAP datum of EVRF2000 is in the zero tidal system in accordance with the EVRF2000 definition (Ihde et al. 2008).

**Results**

In December 2008 the IAG Sub-Commission EUREF handed over data and information of the final solution of EVRF2007 to the participating countries. EUREF recommended to the European Commission to adopt EVRF2007 as the vertical reference for pan-European geo-information.

Table 1 compares the adjustment parameters of EVRF2000 and EVRF2007.

Parameter | EVRF2000 | EVRF2007 |

Number of datum points | 1 | 13 |

Number of unknowns | 3063 | 8133 |

Number of measurements | 4263 | 10568 |

Number of condition equations | 0 | 1 |

Degrees of freedom | 1200 | 2436 |

A-posteriori standard deviation referred to 1 km leveling distance in kgal·mm | 1.10 | 1.12 |

Mean value of the standard deviation of the adjusted geopotential numbers (heights) in kgal·mm | 19.6 | 16.2 |

Average redundancy | 0.281 | 0.231 |

Figure 5 shows the resulting differences of the adjusted geopotential numbers to the adjustment EVRF2000.

The pictured differences have three main reasons:

- New of measurering data

Between 1999 and 2008 the data of 13 countries have been changed or first added.

- Postglacial Rebound

In EVRF2007 a new land uplift model (NKG2005LU) was used for the reduction to a common epoch. In the EVRF2007 the common reference epoch is 2000 (compared to 1960 in EVRF2000). All data located in the area of the model have been reduced – in EVRF2000 only the data of Finland, Norway and Sweden.

- Different tidal systems

The EVRF2000 is in the mean tidal system, EVRF2007 in the zero tidal system. The tidal reduction depends on the latitude. Therefore the differences between EVRF2000 and EVRF2007 are in the South of Europe positive, around the latitude of the former datum point the differences are nearly zero and in the North the differences are negative. This effect is superimposed by the influence of new data and in Scandinavia by the influence of the postglacial rebound.

In December 2008 the IAG Sub-commission EUREF handed over data and information of the final solution of EVRF2007 to the participating countries. EUREF recommended to the European Commission to adopt EVRF2007 as the vertical reference for pan-European geo-information.

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