Jaakko Mäkinen

Mean sea surface topography in the Baltic Sea and its transition area to the North Sea: A geodetic solution and comparisons with oceanographic models

A consistent height system designed for comparisons between geodesy and oceanography is presented for the Baltic Sea area. Mean sea surface topography is computed geodetically in this height system at 42 reliable long-term sea level stations, connected by high-precision levelings, along the coasts of the Baltic Sea, the Kattegat, the Skagerrak, and the adjacent part of the North Sea. Based on this, a map is drawn of the mean sea surface topography in the Baltic Sea and its transition area to the North Sea. The general agreement between our geodetic solution and recent oceanographic models turns out to be excellent; the discrepancies rarely exceed 2–3 cm. Hence the mean sea surface topography in the Baltic Sea area to a dominating extent is caused by the distribution of salinity. There are two main characteristics of the sea surface topography found here. First, there is a continuous increase of the sea surface height from the North Sea into the Baltic Sea, the height difference between the inner part of the Gulf of Bothnia and the Skagerrak amounting to 35–40 cm. The main reason behind this is the considerable difference in salinity, close to the maximum possible one. Second, there is a steep sea level gradient in the border zone between the Kattegat and the Skagerrak, reaching 2 cm per 10 km. This reflects the salinity front there, separating the brackish Baltic Sea water from the saline North Sea water, and the associated Baltic current. A local maximum in the sea surface can be seen in the Oslo Fiord, reflecting an accumulation of low-salinity water there. An area where there is still no oceanographic model agreeing sufficiently with the geodetic solution is the Belt Sea/southwestern Kattegat.

The permanent tide in GPS positioning

The treatment of the permanent tidal deformation of the Earth in GPS computation has been an almost unmentioned topic in the GPS literature. However, the ever increasing accuracy and the need to combine the GPS based coordinates with other methods requires a consistent way to handle the tides. Our survey shows that both the ITRF-xx coordinates and the GPS based coordinates are nowadays reduced to a “non-tidal” crust, conventionally defined using physically meaningless parameters. We propose to use instead the zero-crust concept which corresponds to concepts already accepted in the resolution of IAG in 1983 for gravimetric works.

The European Comparison of Absolute Gravimeters 2011 (ECAG-2011) in Walferdange, Luxembourg: results and recommendations

We present the results of the third European Comparison of Absolute Gravimeters held in Walferdange, Grand Duchy of Luxembourg, in November 2011. Twenty-two gravimeters from both metrological and non-metrological institutes are compared. For the first time, corrections for the laser beam diffraction and the self-attraction of the gravimeters are implemented. The gravity observations are also corrected for geophysical gravity changes that occurred during the comparison using the observations of a superconducting gravimeter. We show that these corrections improve the degree of equivalence between the gravimeters. We present the results for two different combinations of data. In the first one, we use only the observations from the metrological institutes. In the second solution, we include all the data from both metrological and non-metrological institutes. Those solutions are then compared with the official result of the comparison published previously and based on the observations of the metrological institutes and the gravity differences at the different sites as measured by non-metrological institutes. Overall, the absolute gravity meters agree with one another with a standard deviation of 3.1 µGal. Finally, the results of this comparison are linked to previous ones. We conclude with some important recommendations for future comparisons.

The Fennoscandian Land Uplift Gravity Lines 1966–2003

The Fennoscandian Land Uplift Gravity Lines (sometimes called Nordic Land Uplift Gravity Lines) consist of four east-west profiles across the Fennoscandian postglacial rebound area, along the approximate latitudes 65°, 63°, 61°, and 56°N. Repeated relative gravity measurements have been so far performed 1975–2000 (65°N), 1966–2003 (63°N), 1976–1983 (61°N), and 1977–2003 (56°N). The line 63°N has most observations. From the measurements along it up to 1993, Ekman and Makinen (1996) deduced the ratio −0.20 μgal/mm between surface gravity change and uplift relative to the Earth’s center of mass. Since that time, more gravity measurements have been taken. On the eastern part of the line 63°N, they result in slightly smaller estimates for the rate of gravity. New estimates of uplift and model predictions are also available. The updated gravity change combined with various estimates of uplift gives ratios between −0.16 and −0.20 μgal/mm. On the western part of the line 63°N an apparently anomalous change in gravity difference requires further study. In the future, the measurements will be performed using absolute gravity techniques.

Observing Fennoscandian Gravity Change by Absolute Gravimetry

The Nordic countries Norway, Sweden, Denmark and Finland are a key study region for the research of glacial isostasy, and, in addition, it offers a unique opportunity for validating and testing the results of the GRACE experiment. Over a period of five years, the expected life time of GRACE, a temporal geoid variation of 3.0 mm is expected in the centre of the Fennoscandian land uplift area, corresponding to a gravity change of about 100 nm/s2. This is expected to be within the detection capabilities of GRACE. With terrestrial absolute gravimetry, the gravity change due to the land uplift can be observed with an accuracy of ±10 to 20 nm/s2 for a 5-year period. Thus, the terrestrial insitu observations (ground-truth) may be used to validate and test the GRACE results.

The effect of the Baltic Sea level on gravity at the Metsähovi station

Abstract The loading effect of the Baltic Sea is immediately recognizable in the gravity record of the superconducting gravimeter T020 in Metsahovi, Finland, by simply inspecting residual gravity together with the tide gauge record at Helsinki 30 km away. The station is 10 km from the nearest bay of the Baltic Sea and 15 km from the open sea. Sea level variations in the Baltic are non-tidal and driven at short periods primarily by wind stress, at longer periods by water exchange through the Danish straits. Locally they can have a range of 2–3 m. Loading calculations show that a uniform layer of water covering the complete Baltic Sea increases the gravity in Metsahovi by 31 nm/s 2 per 1 m of water, and the vertical deformation is −11 mm. The observed gravity response to the local sea level is generally less, since the variations at short periods are far from uniform areally, the same water volume just being redistributed to different places. Regression of the whole gravity record (1994-2001) on local sea level gives 50–70% of the uniform layer response, as do loading calculations using actual water distributions derived from 11 tide gauges. However, both fits are dominated by some extreme values of short duration, and parts of the gravity record with long-period variations in sea level are close to the uniform layer response. The gravity observations can be used to test corrections for other co-located geodetic observations (GPS, satellite laser ranging) which are influenced by the load effect but not sensitive enough to discriminate between models.

The deviation of mean sea level from the mean geoid in the baltic sea

The mean sea level along the Swedish coast has been recomputed, taking into account the effect of the permanent tide on the height system. The recomputed data show the deviation of mean sea level (1960) from the mean geoid, i.e. the oceanographic deviation of mean sea level, with NAP as zero. On the basis of a conversion between the Finnish and Swedish height systems, mean sea level data from the Finnish coast are reduced to the same system as on the Swedish coast.The geodetically determined mean sea level values are compared with oceanographic model calculations. On the whole, the agreement between geodesy and oceanography is found to be good. Nevertheless, oceanography tends to yield somewhat larger deviations of the mean sea level than geodesy, especially in the extreme parts of both the Gulf of Bothnia and the Gulf of Finland. This might indicate that the oceanographic model has overestimated some effect. However, across the Gulf of Bothnia the oceanographic model predicts slightly smaller mean sea level differences than the geodetic data suggest.

CCM.G-K2 key comparison

In November 2013 an International Key Comparison, CCM.G-K2, was organized in the Underground Laboratory for Geodynamics in Walferdange. The comparison has assembled 25 participants coming from 19 countries and four different continents. The comparison was divided into two parts: the key comparison that included 10 NMIs or DIs, and the pilot study including all participants. The global result given by the pilot study confirms that all instruments are absolutely coherent to each other. The results obtained for the key comparison confirm a good agreement between the NMI instruments. Main text. To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Gravity change and land uplift in Fennoscandia 1966–1984

An analysis is made of the results from all repeated gravity measurements of the Fennoscandian land uplift gravity line 63°. The line is, thereby, divided into two separate parts: one part west of the land uplift maximum, and the other part east of the land uplift maximum. A statistically significant change of gravity is found both for the western part and the eastern one. Both parts give a relation between gravity change and land uplift of about −0.22μgal/mm.

Baltic Sea Mass Variations from GRACE: Comparison with In Situ and Modelled Sea Level Heights

The monthly variation in the water mass of the semi-enclosed Baltic Sea is about 60 Gt RMS over an area of \(390,000 \textrm{km}^2\). The Baltic has a dense network of tide gauges (TGs), and several high-resolution regional hydrodynamic models, making it one of the best-monitored seas for mass variations of this size in the world. We investigate the performance of different GRACE gravity field solutions to recover this oceanic mass variation using in situ measurements of sea-level heights. For GRACE, we use both the standard monthly solutions as well as regional solutions to estimate the total water storage in the Baltic Sea.