# EVRF2019

- Data
- Realization of the Datum
- Epoch of the measurements
- Tidal corrections
- Adjustment results
- EVRF2019 heights

**Data**

Since the first EVRS realization in 1998, most of the national leveling data have been replaced at least once. New included national leveling networks extended the UELN far to the East.

Since the publishing of EVRF2007 in December 2008, more than half of the data have been changed (see figure 1). Furthermore, the following countries provided their leveling data for the first time:

- Russia - European part of the network (2012)
- Belarus (2017)
- Ukraine (2018)
- North Macedonia (2019)

###### Data of Great Britain

In former EVRS realizations, systematic differences occur between the national ODN (Ordnance Datum Newlyn) heights and the EVRF2000 or EVRF2007 heights. ODN heights were computed by an adjustment of the 3^{rd} leveling epoch (1951-1956), in which the results of the 2^{nd} epoch (1912-1952) were held fix because of suspected systematic errors in the 3^{rd} leveling epoch. But only the observations of the 3^{rd} epoch are available in the UELN data base and have been used in the EVRF2000 and EVRF2007.

In order to avoid systematic errors in the EVRF2019 heights over Great Britain and to make them more consistent with the national heights of Great Britain, the measurement through the channel tunnel was used in the UELN adjustment to compute the datum shift between EVRF2019 and ODN. The EVRF2019 heights in Great Britain were determined subsequently by a transformation of the national heights applying this datum shift parameter.

In the mean-tide system, the difference between EVRF2019 and ODN is constant:

To determine the EVRF2019 heights of British points in the zero-tide system, the correction is dependent by the latitude.

**Data of France**

Already since 1971, a tilt of 23 cm in North-South direction has been suspected in the French leveling network IGN69, deduced from comparison with tide gauge observations. In the meantime, a zero-order leveling network named NIREF is being developed, which is more accurate and not affected by such a systematic. But the network density of NIREF is too low to replace IGN69 completely.

In 2015, France delivered a new data set to the UELN data center, consisting of NIREF data, measured between 1983 and 2014, and some new measured lines of IGN69 in the northern part of France. The NIREF observations and the IGN69 network were combined in the UELN adjustment. In order to eliminate the influence of the tilt of IGN69, the observations of this network were supplied with very low weights: The original variances were multiplied with factor 100.

## Realization of the Datum

EVRF2019 was computed based on the definitions and standards of EVRS, described in Ihde et al 2008). Accordingly, NAP is the datum of EVRF2019. For the realization of the height datum we have to specify:

- the datum points
- the heights or geopotential numbers of these datum points
- the velocity of the datum points

In the EVRF2007, the datum was realized by 13 datum points with their heights in EVRF2000, converted to zero-tide. It was assumed that the velocities of these points were zero (no temporal height changes), although two of the points in Denmark were in the area of influence of the postglacial rebound (see figure 2).

For the EVRF2019 the following criteria, requirements and assumptions were adopted:

- The datum should be realized using multiple datum points in order to avoid possible undetected height changes of an individual benchmark. The datum realization has to be unconstrained.
- The datum points should be widely distributed across the European leveling network in order to avoid a systematic influence in a certain part of the network. This explicitly includes also these countries, which were not part of the EVRF2000.
- There should be only one datum point per country.
- The datum points have to be outside of areas known to be influenced by vertical land movements. This also includes regions like Scandinavia and the Alps, where models about the vertical velocities are available. This is to avoid the influence of possible uncertainties of these models on the datum realization of the EVRF2019.
- The datum points should not be affected by known systematic errors in the leveling networks, especially in EVRF2007. The differences between the heights in EVRF2019 and EVRF2007 have to be reasonable small, that is, in the magnitude caused by the random error of the leveling network. This excludes datum points in Great Britain as well as the western part of the leveling network (France, Spain and Portugal, southern Italy).

Finally, after different computations and investigations a new set of 12 datum points shown in Figure 2 was used for height datum realization of the EVRF2019. The heights of the datum points were obtained from the EVRF2007 adjustment and it was assumed that these heights have not changed (velocity 0 mm/a). According to the condition equation in the adjustment the sum of the height changes of all datum points is zero. The maximum differences between the heights in EVRF2007 and EVRF2019 are in the range of ± 1.5 cm.

## Epoch of the measurements

At the UELN data center, velocity models are available only for two areas in Europe: for the area of the Scandinavian land uplift and for Switzerland. The used models are NKG2016LU_lev (Vestøl et al 2016), published by the Nordic Geodetic Commission, and a set of velocities, provided by A. Schlatter and U. Marti from swisstopo.

There is not enough knowledge about vertical velocities in the other parts of Europe to reduce strictly all other leveling data to a common epoch too. In these areas the epoch of EVRF2019 is determined by the date of the observations. The epoch of measurements in the UELN range between 1923 and 2018. About half of the countries provided data, which have been observed after the year 2000. Most of the remaining data were observed in the 1990th. Hence, the mean epoch of the measurements is close to the year 2000, which was already the adopted epoch for the heights of EVRF2007.

For these reasons, it was decided to reduce measurements of EVRF2019 in Scandinavia and Switzerland also to epoch 2000 using the height velocity models mentioned above. Figure 3 marks the countries whose leveling data were reduced to epoch 2000, and shows some contours of NKG2016LU_lev.

To enable the user to compute an EVRF2019 height at a particular epoch, the velocities of the points are published together with the heights.

## Tidal corrections

According to its definition, EVRS is a zero-tide system (Ihde et al 2008). So, both EVRF2007 and EVRF2019 are computed in the zero-tide system. This agrees with IAG resolution No. 16 adopted in Hamburg 1983, which recommends zero-tide for gravity field and mean-tide (= zero-tide) for 3D-positioning (Mäkinen, Ihde 2009). However, this resolution was never applied for all geodetic measurements and techniques.

The zero-tide correction is the standard for gravity measurements. The GNSS community uses conventional tide-free systems. Most of the national height systems are in mean-tide, but we find also zero-tide and non-tide height systems in Europe. For some applications it will be necessary to transform coordinates into another tidal system to make them comparable with other products. An example is the computation of geoid or quasi-geoid values as differences from ellipsoidal and leveling heights.

In the field of oceanography, heights may be compared over large or even global distances. For such applications, heights in the mean-tide system are more appropriate, because they refer to the mean undisturbed sea level.

Also, the future International Height System will be provided in the mean-tide system according to the IAG resolution No. 1 adopted in Prague 2015. The end users are not necessarily familiar with the concept of the permanent tides, just as many geodesists are not. For these reasons, the heights of EVRF2019 are additionally provided in the mean-tide system.

The EVRF adjustment was performed in the zero-tide system. The results were converted to mean-tide by

*φ* is the latitude in ETRS89.

The constant -0.08432 kgal ∙ m was first introduced in the calculation of EVRF2007 in order to achieve, that point 913600 (datum point of EVRF2000 in Amsterdam) gets the same height value both in the mean-tide and in the zero-tide system. By adding this correction, all points in the same latitude as Amsterdam have the same height in the mean- and zero-tide system.

## Adjustment results

The heights in EVRF2019 differ from EVRF2007 between -439 mm and +148 mm (see figure 4). The largest differences are in the part of Western Europe, especially in Great Britain and France. In Great Britain, we have maximum differences of half a meter. In France we find differences between -135 mm in the North and +65 mm in the South. Main reasons are the including of the zero-order network NIREF in France, which eliminates the tilt of the IGN69 network, and the modified computation of the heights for Great Britain. The largest positive height differences are in Italy, caused by the new Italian leveling data.

Table 1 shows the parameters of the adjustment. The standard deviation for 1 km leveling is in the magnitude of 1.1 mm as in EVRF2007.

Parameter | EVRF2007 | EVRF2019 |
---|---|---|

Number of datum points | 13 | 12 |

Number of unknowns | 7942 | 10758 |

Number of measurements | 10354 | 13636 |

Number of condition equations | 1 | 1 |

Degrees of freedom | 2413 | 2879 |

A-posteriori standard deviation referred to 1 km leveling distance in kgal · mm | 1.11 | 1.10 |

Mean value of the standard deviation of the adjusted geopotential numbers (heights) in kgal · mm | 16.00 | 19.26 |

Average redundancy | 0.233 | 0.211 |

## EVRF2019 heights

The following table EVRF2019_points shows the adjusted heights of EVRF2019 (update August 2020) in the zero-tide as well as in the mean-tide system.

**Should I use zero-tide or mean-tide heights?**

IAG resolution No. 16 adopted in Hamburg 1983 recommends zero-tide for gravity field and mean-tide (=zero-tide) for 3D-positioning (Mäkinen, Ihde 2009). However, this resolution was never applied for all geodetic measurements and techniques. The zero-tide correction is the standard for gravity measurements. The GNSS community uses conventional tide-free systems. Most of the national height systems are in mean-tide, but we find also zero-tide and non-tide height systems in Europe.

For some applications it will be necessary to make physical heights comparable with other geodetic products. An example is the computation of geoid or quasi-geoid values as differences from ellipsoidal and leveling heights. In these cases, you should use the heights in the **zero-tide system**.

In the field of oceanography, heights may be compared over large or even global distances. For such applications, heights in the mean-tide system are more appropriate, because they refer to the mean undisturbed sea level.

In all other cases as cross-border projects both tidal systems are applicable. But don’t mix heights of different tidal systems in the same application!

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