Kristian Breili

We present results from an airborne gravity campaign conducted in Norway during December 2024 by DTU Space on behalf of the Norwegian Mapping Authority (NMA). One part of the campaign covered the southwestern coast, mapping the marginal land-sea zone to support the realisation of one common future height system for land and sea areas. The second part covered Jostedalsbreen, a region experiencing large gravity variations due to rough topography including high mountains, glaciers and deep fjords. Root-mean-square-error estimates of crossover points show 1.63 mGal and 1.35 mGal, after modelling residual temperature errors in the iMAR system, in the coastal zone and Jostedalsbreen, respectively. Optimum full-width-half-maximum filtering length is found as 70 and 40 seconds for the two regions, respectively. Comparison with existing (DTU15 and DTU21) global altimetry-derived gravity in the sea area shows standard deviations in the order of 3.66 to 3.28 mGal. Comparison with a preliminary DTU26 altimetry model, including two years of data from the Surface Water and Ocean Topography (SWOT) mission, shows a standard deviation of 2.85 mGal. Outliers in marine gravity data are detected based on comparison with the airborne gravity data and DTU26. The long-wavelength pattern of the residuals between altimetry and marine gravity data coincides with existing questionable geostrophic currents based on geodetic mean dynamic topography models. This indicates erroneous long-wavelength signal in the underlying gravimetric geoids.

Horizontal dilution of precision (HDOP) is a widely used quality indicator of Global Navigation Satellite System (GNSS) positioning, considering only satellite geometry. In this study, HDOP was simulated using GNSS almanacs and high-resolution digital surface models (DSMs) along three European road sections: Oslo— Svinesund Bridge (Norway); Hamburg city center (Germany); and Rotterdam—Dutch–German border (Netherlands). This study was accomplished as part of the MODI project, which is a cross-border initiative to accelerate Cooperative, Connected, and Automated Mobility (CCAM). Our analysis revealed excellent or good overall GNSS performance in the study areas, particularly on highway sections with 99–100% of study points having a median HDOP that is categorized as excellent (HDOP < 2) or good (HDOP < 5). However, the road section in Hamburg’s city center presents challenges. When GPS is used alone, 8% of the study points experience weak or poor HDOP, and there are study points where the system is available (HDOP < 5) less than 50% of the time. Combining GNSS constellations significantly improved system availability, reaching 95% for 99% of the study points in Hamburg. To validate our simulations, we compared results with GNSS observations from a survey vehicle in Hamburg. Initial low correlation was attributed to the reception of signals from non-line-of-sight satellites. By excluding satellites with low signal-to-noise ratios, the correlation increased significantly, and reasonable agreement was obtained. We also examined the impact of using a 10 m DSM instead of a 1 m DSM in Hamburg. While the coarser spatial resolution offers computational benefits, it may miss critical details for accurate assessment of satellite visibility.

SUMMARY: Since the beginning of the 1990s, absolute gravity has been observed at several locations in Norway with FG5-type instruments to investigate the temporal gravity changes due to glacial isostatic adjustment (GIA). Previous work suggests that some of the estimated secular gravity trends may be affected by remaining unmodelled geophysical effects, such as the effect of local hydrology. In this work, we compute hydrological gravity effects from global hydrological models for the far zone and a combination of regional run-off models and modelling of residual hydrological effects for the near zone. The method developed in this paper is first tested at the geodetic observatory in Wettzell, Germany, where both high-resolution superconducting gravimeter data as well as a regional hydrological model are available. Next, the method is transferred to two Norwegian gravity sites (NMBU and TRYC), with long time-series of frequent absolute gravity observations using FG5-226. At these sites, we investigate the impact of the hydrological gravity correction on data variability as well as estimated secular gravity trends. We find that the data variability is reduced by up to 40 per cent when applying the modelled hydrological gravity effect at TRYC. The reduction is less at NMBU where the amplitude of the hydrological signal and in consequence also the signal-to-noise ratio are smaller. We also note that it is challenging to determine the near zone residual hydrological effects without carefully taking into account the hydrogeological setting of the area for modelling such effects. When utilizing the long corrected absolute gravity series to determine the gravity trends, we find that the estimated trends are not significantly different from the uncorrected observations. However, the uncertainty of the estimated trends is reduced significantly for a limited corrected gravity series. We further suggest repeatability analysis of the absolute gravimeter. From the long time-series at NMBU we find a significant step coinciding with hardware replacement. We find that the fit between observed and modelled secular trends improves when introducing the step. Further analysis of gravity rates at other stations is needed to verify the existence of a real instrumental offset.

A first national analysis of the evolution of sea-level rates along the Norwegian coast for the period 1960–2100 has been accomplished by exploring tide-gauge records, relative sea-level projections, and detection techniques for acceleration. Firstly, sea-level rates for the two study periods 1960–2020 and 1991–2020 were estimated. Along the Norwegian coast, relative sea-level rates show significant spatial variation due to glacial isostatic adjustment. Moreover, the coastal average sea-level rate for the period 1991–2020 is significantly higher than for the period 1960–2020. Accelerations were then estimated for all combinations of start years and study periods longer than 30 years by including quadratic coefficients in regression models. It was found that the estimates strongly depend on the study period and do not provide confident estimates of climate change driven variation in the sea level along the Norwegian coast. Secondly, non-linear trends in relative sea level were reconstructed from Singular-Spectrum Analysis, which at several tide gauges revealed low rates in the 1970s, maximum rates around 1990, and declining rates thereafter. From the reconstructed trends, significant positive acceleration in the relative sea level was estimated for the period 1960–2020, while accelerations less than zero were detected for the period 1991–2020. However, the estimates for the recent period appear not robust due to the influence of decadal and multidecadal variation characterizing Norwegian tide-gauge records. Finally, by artificially extending the tide-gauge records by projections, the time when unprecedented high sea-level rates emerge was identified. With projections calculated for the intensive emission scenario RCP8.5, the climate signal of the relative sea level emerges at earliest in the late 2030s. The time of emergence is typically 5 to 10 years later if reanalysis of sea-level pressure and wind speed are used to reduce decadal variation in the tide-gauge records. This is because the meteorological regressors, as a side effect, introduce serial correlations that lead to rate estimates with enlarged standard errors. An important implication of the findings is that a possible absence of record high sea-level rates in the 2020s and 2030s does not falsify that relative sea level along the Norwegian coast is consistent with projections of RCP8.5.

Absolute gravity time series are available at various stations in Norway. The data have mainly been used for investigation of secular variations due to glacial isostatic adjustment. Previous work indicates that some of the estimated gravity trends suffer from unmodeled geophysical effects, like hydrological mass variations. Here we try to correct for hydrological effects by employing a combination of global and regional hydrological models. We use gravity data at two locations in the Norwegian network (NMBU and TRYC) which have frequently been observed with the absolute gravimeter FG5-226. For computing the gravity corrections, we test various Global Hydrological Models (GHMs) and combine them with a Regional Runoff Model (RRM) for Norway, run by the Norwegian Water Resources and Energy Directorate (NVE). We distinguish between an outer and an inner zone. In the outer zone, Newtonian attraction and loading effects are derived from the GHMs, while the RRM is used in the inner zone. Both types of models provide information on soil moisture and snow layers. The RRM provides groundwater variations in addition. Furthermore, we try to consider the ‘umbrella effect’ that accounts for local disturbances in subsurface water flow caused by the existence of the building in which the gravity site is located.  Neglecting the GIA trend, both NMBU and TRYC gravity time series show different amplitude and pattern. NMBU shows a lower amplitude, and with no prominent periodic pattern in the data, while TRYC shows the opposite. Significant discrepancies occurring in the NMBU gravity dataset between 2014 and 2015 are likely due to an instrumental effect, such as maintenance. The total modelled hydrological signal ranges from -4 and 4 µGal. Application of the correction reduces the standard deviation in the gravity time series, at its best, by about 33% or 0.8 µGal for NMBU, and by about 43% or two µGal for TRYC. Secular gravity rates have been derived from both, the uncorrected and the corrected time series. We find that application of the hydrological correction improves the fit of the computed secular gravity rates as compared to rates derived from the state-of-the-art Fennoscandian land uplift model NKG2016LU_abs. The uncorrected trends are 75% and 50% of the expected trend (0.77 and 1.12 µGal/year), while the hydrological corrections improve the fit to 82% and 93% for NMBU and TRYC, respectively.

Using new high-accuracy light detection and ranging (lidar) elevation data we generate coastal flooding maps for Norway. Thus far, we have mapped ∼80 % of the coast, for which we currently have data of sufficient accuracy to perform our analysis. Although Norway is generally at low risk from sea level rise largely owing to its steep topography and land uplift due to glacial isostatic adjustment, the maps presented here show that, on local scales, many parts of the coast are potentially vulnerable to flooding. There is a considerable amount of infrastructure at risk along the relatively long and complicated coastline. Nationwide we identify a total area of 400 km², 105 000 buildings, and 510 km of roads that are at risk of flooding from a 200-year storm surge event at present. These numbers will increase to 610 km², 137 000, and 1340 km with projected sea level rise to 2090 (95th percentile of RCP8.5 as recommended in planning). We find that some of our results are likely biased high owing to erroneous mapping (at least for lower water levels close to the tidal datum which delineates the coastline). A comparison of control points from different terrain types indicates that the elevation model has a root-mean-square error of 0.26 m and is the largest source of uncertainty in our mapping method. The coastal flooding maps and associated statistics are freely available, and alongside the development of coastal climate services, will help communicate the risks of sea level rise and storm surge to stakeholders. This will in turn aid coastal management and climate adaptation work in Norway.

Norway’s national sea level observing system consists of an extensive array of tide gauges, permanent GNSS stations, and lines of repeated levelling. Here, we make use of this observation system to calculate relative sea-level rates and rates corrected for glacial isostatic adjustment (GIA) along the Norwegian coast for three different periods, i.e., 1960 to 2010, 1984 to 2014, and 1993 to 2016. For all periods, the relative sea-level rates show considerable spatial variations that are largely due to differences in vertical land motion due to GIA. The variation is reduced by applying corrections for vertical land motion and associated gravitational effects on sea level. For 1960 to 2010 and 1984 to 2014, the coastal average GIA-corrected rates for Norway are 2.0 ± 0.6 mm/year and 2.2 ± 0.6 mm/year, respectively. This is close to the rate of global sea-level rise for the same periods. For the most recent period, 1993 to 2016, the GIA-corrected coastal average is 3.5 ± 0.6 mm/year and 3.2 ± 0.6 mm/year with and without inverse barometer (IB) corrections, respectively, which is significantly higher than for the two earlier periods. For 1993 to 2016, the coastal average IB-corrected rates show broad agreement with two independent sets of altimetry. This suggests that there is no systematic error in the vertical land motion corrections applied to the tide-gauge data. At the same time, altimetry does not capture the spatial variation identified in the tide-gauge records. This could be an effect of using altimetry observations off the coast instead of directly at each tide gauge. Finally, we note that, owing to natural variability in the climate system, our estimates are highly sensitive to the selected study period. For example, using a 30-year moving window, we find that the estimated rates may change by up to 1 mm/year when shifting the start epoch by only one year.