Estimates of Future Sea-Level Changes for Norway

Transcription

1 Estimates of Future Sea-Level Changes for Norway March 26, 2012 Matthew Simpson, Kristian Breili, Halfdan Pascal Kierulf, Dagny Lysaker, Mohammed Ouassou and Even Haug Please reference this report as Simpson, M., Breili, K., Kierulf, H. P., Lysaker, D., Ouassou, M. and Haug, E. (2012). Estimates of Future Sea-Level Changes for Norway. Technical Report of the Norwegian Mapping Authority.

2 2 Estimates of Future Sea-Level Changes for Norway Abstract In this work we establish a framework for estimating future regional sea-level changes for Norway. We consider how different physical processes drive non-uniform sea-level changes by accounting for spatial variations in (1) ocean density and circulation (2) ice and ocean mass changes and associated gravitational effects on sea level and (3) vertical land motion arising from past surface loading change and associated gravitational effects on sea level. An important component of past and present sea-level change in Norway is glacial isostatic adjustment. Central to our study, therefore, is a reassessment of vertical land motion using a far larger set of new observations from a permanent GPS network. We find that uplift rates along the Norwegian coast vary between 1 and 5 mm/yr. We also examine extreme sea levels and trends in sea-level changes using tide gauge records. If we assume that observed rates for the last 30 years continue unchanged, sea-level changes in Norway will vary between -6.5 and 6 cm for the period 2000 to Our 21 st century sea level estimates are split into two parts. Firstly, following Slangen et al. [2011] we show regional projections largely based on findings from the 4 th IPCC assessment and dependent on the emission scenarios A2, A1B and B1. These indicate that 21 st century regional sea-level changes in Norway will vary between -20 to 30 cm. Secondly, we explore the high-end scenario presented by Katsman et al. [2011], in which a global atmospheric temperature rise of up to 6 C and emerging collapse for some areas of the Antarctic ice sheets is assumed. Using this approach we tentatively estimate the upper bound of 21 st century relative sea-level changes in Norway as between 70 and 130 cm. We attach no likelihood to any of our projections owing to the lack of understanding of some of the processes that cause sea-level change.

3 3 Estimates of Future Sea-Level Changes for Norway Contents Abstract... 2 Contents Introduction Determining Sea-Level Changes Previous Work The IPCC s Fourth Assessment Report (AR4) Observed Sea-Level Changes Projected Sea-level Changes Progress Following the IPCC s 4th Assessment National Efforts to Estimate Future Sea-Level Changes The United Kingdom s Climate Projections Report The Delta Commission Past Studies for Norway Present-Day Vertical Land Motion in Norway Observed Vertical Land Motion in Norway The GPS network GPS Analysis-Strategies and Determining Vertical Velocities Time-Series Analysis Defining a Vertical Velocity Field for Norway Statistical Interpolation Glacial Isostatic Adjustment Modeling Discussion Comparison of GIA Modeling and Previous Work Reference Frame Issues Uncertainties in the Crustal Velocity Field Solution Conclusions... 29

4 4 Estimates of Future Sea-Level Changes for Norway 4. Observed Sea-level Changes for Norway Tide Gauge Records Global Sea-Level Changes From Tide Gauge Records The Norwegian Tide Gauge Records Satellite Altimetry Altimetry Measurements for Norway Discussion Conclusions Projected 21 st Century Sea-level Changes for Norway Data and Model Descriptions Model of Vertical Land Motion and Associated Gravity Changes The Climate Models (AOGCMs) Future Ocean Density and Circulation Changes Future Ocean Mass Changes Future Non-Uniform Sea-Level Changes due to Land Ice Changes Analysis Global Mean Sea-Level Changes Regional Sea-Level Changes Regional 21 st Century Sea-Level Projections for Norway Discussion A High-End Scenario of Sea-level Change for Norway High-End Global Mean Sea-Level Changes High-End Regional Sea-Level Changes High-End Regional 21 st Century Sea-Level Projections for Norway Conclusions Extreme Sea Levels Observed Extreme Sea Levels Statistical Methods Estimated Return Levels Changes in Observed Extreme Sea Levels Future Changes in Extreme Sea Levels Conclusions... 72

5 5 Estimates of Future Sea-Level Changes for Norway 7. Summary Comparisons to the DSB-Report Acknowledgements Appendix I: Projected 21 st Century Sea Levels Projected 21 st Century GIA Effects and Vertical Land Motion Projected 21 st Century Sea Surface Changes Projected High-End 21 st Century Sea Surface Changes Appendix II: Notes on the Reference Levels The National Vertical Reference Systems of Norway The Connection Between Mean Sea Level and the Vertical Reference System Which Reference Level Should be Used? References... 96

6 6 Estimates of Future Sea-Level Changes for Norway 1. Introduction There are potentially serious socio-economic consequences of continued global sea-level rise through the 21 st Century [Stern, 2007]. Higher sea-levels can have a variety of impacts, for example: the inundation of coastal areas, increased risk of flooding, erosion of the coastline and the salinization of ground waters. There is, however, large uncertainty associated with projections of future sea-levels. This uncertainty is, in part, due to our lack of understanding of some of the processes that drive sea-level changes. In particularly, the potential icedynamic contributions of the large ice sheets [e.g. Alley et al., 2005]. In a recent review by Pfeffer [2011], it was underscored that for planners and coastal engineers, the people that make decisions based on projections from scientists, information on future sea levels is best presented in a probabilistic form. That is, for a specific future date, an assessment is made of the probability of a certain sea level occurring. Given our current limited understanding of the causes of sea-level change, however, the scientific community has not yet been able to deliver such a product to decision makers. Although, efforts are now underway to improve projections of the contributions of ice mass changes to future sea-level rise (e.g. It is also important to note that there has been significant progress in other areas of sea level research [e.g. Cazenave et al., 2009]. Following the publication of the Fourth Assessment Report from the Intergovernmental Panel for Climate Change (hereafter IPCC AR4), there has been increased interest in regional and/or local projections of sea-level change [e.g. Katsman et al., 2008, 2011; Slangen et al., 2011]. Observations show that past sea-level changes have been spatially variable (or nonuniform), so we expect that future changes will also be of this nature [Milne et al., 2009]. Thus, identifying the processes causing sea-level changes at regional scales [e.g. Landerer et al., 2007] and improving our future projections of the spatial variability of sea-level change [e.g. Gomez et al., 2010] have become an important focus for scientific researchers.

7 7 Estimates of Future Sea-Level Changes for Norway The move towards regional projections has also led to several countries commissioning national reports into future sea-level changes. For example, the Delta Commissie [2008] report for the Netherlands and the United Kingdom s climate projections [see Lowe et al., 2009]. In this vein, we present here a new assessment of future sea-level change for Norway. The main aim of this report is, therefore, to demonstrate that a methodology used to determine local or regional sea-level projections can successfully be applied to the Norwegian coast. The secondary aims of the work, which assist in the evaluation of our future projections, are: (1) to compare observed and modeled land motion in Norway, (2) analyze present and recent past observed patterns of local sea-level changes and (3) examine data on regional extreme sea levels. The report is structured as follows: Chapter 1, this chapter, outlines the motivation of the work and defines how we determine sea-level changes. The previous work is described in Chapter 2, this includes the main findings of the IPCC AR4 and progress since then, it also discusses the past sea level studies for Norway and the approach taken in other national reports. Chapter 3 examines vertical land motion in Norway, an important component of present sea-level change in Scandinavia, which we constrain using new GPS measurements. In Chapter 4 we analyze observed sea-level changes in Norway from tide gauge records and satellite altimetry data. Our projections of 21 st century sea-level change for Norway are given in Chapter 5. These are largely based on the results of the IPCC AR4 which, closely following the methodology of Slangen et al. [2011], are used to determine future regional sea-level changes. Chapter 6 analyses extreme sea-levels for the Norwegian coast and Chapter 7 summarizes our results Determining Sea-Level Changes Determining sea-level changes can be thought about in two separate ways: relative sea-level change which is measured with respect to the ocean bottom. Whereas, absolute sea-level change is measured with respect to the Earth s centre of mass. As the focus of this report is regional sea-level changes for the Norwegian coast, we concentrate on data and projections that show relative sea-level changes.

8 8 Estimates of Future Sea-Level Changes for Norway Fig The processes that cause sea-level change. Taken from Milne et al. [2009]. There are a number of different processes which drive sea-level changes (see Fig. 1.1). Over the 20 th century, changes in (1) ocean mass; the exchange of mass between the oceans, land based ice and terrestrial water storage (2) ocean density; changes to the temperature and salinity of sea water (also called steric changes), dominated mean global sea-level changes [see Lemke et al., 2007]. This will also be the case over the 21 st century. The reader should note that all the physical processes shown in Figure 1.1 produce a nonuniform sea-level change. Thus, on a regional scale, it is important to take account of the spatial variability of these separate contributions. Effects other than ocean mass and ocean density changes can also play an important role in determining local sea-level changes. Indeed, for the case of Norway, it is clear that the process of Glacial Isostatic Adjustment (GIA) produces a significant and ongoing regional pattern of Earth response [e.g. Milne et al., 2001]. The influence of GIA on relative sea-level changes is, therefore, carefully considered in this analysis.

9 9 Estimates of Future Sea-Level Changes for Norway 2. Previous Work 2.1. The IPCC s Fourth Assessment Report (AR4) The task of the IPCC s Working Group 1 is to critically review and assess the most recent scientific work pertaining to climate change. The issue of sea-level change is addressed in a number of chapters of the AR4, however, we only examine the findings from Chapters 5 and 10. Chapter 5 covers observed sea-level changes [Bindoff et al., 2007] while Chapter 10 presents projections of future sea-level changes [Meehl et al., 2007]. In the below we briefly summarize the relevant findings of the IPCC AR4, beginning with observed sea-level changes Observed Sea-Level Changes Observations from the global tide gauge network and satellite altimetry provide information on 20 th century sea-level changes. Using tide gauge records, the IPCC assesses the rate of global mean sea-level rise as 1.8 ± 0.5 mm/yr for 1961 to 2003 and 1.7 ± 0.5 mm/yr for the 20 th century [e.g. Holgate and Woodworth, 2004; Leuliette et al., 2004; Church and White, 2006]. For the period 1993 to 2003, satellite altimetry observations indicate the current rate of sea-level rise as 3.1 ± 0.7 mm/yr [see Cazenave and Nerem, 2004]. It is not yet apparent if this increased rate of rise is short-term variation or a change in the long-term trend Projected Sea-level Changes The AR4 gives global average sea-level projections for the 21 st century which include contributions from thermal expansion and land based ice (salinity changes are only important on regional scales). The results are based on projections from 17 different Atmosphere Ocean General Circulation Models (AOGCMs) using 6 different future greenhouse gas emission scenarios (the methods of the IPCC are explained in more detail in Chapter 5). For the period 2090 to 2099 relative to 1980 to 1999, future global sea-level change is projected to range from 18 to 59 cm [Meehl et al., 2007]. A significant issue with these results, however, was that no likelihood was attached to the AR4 projections. As briefly discussed in Chapter 1, it is currently not possible to assess the probability of future sea-level changes owing to our (the scientific community s) lack of understanding of some of

10 10 Estimates of Future Sea-Level Changes for Norway the processes that drive sea-level change. For this reason, the AR4 does not give a best estimate or upper bound for future sea-level changes. Fig Local sea-level changes for the period 2090 to 2099 relative 1980 to Sealevel changes are shown as deviations from the global mean. Projections are forced using the A1B emissions scenario and generated from 16 AOGCMs. The shaded areas indicate a value of 1 or greater for the multi-model mean divided by the multi-model standard deviation. Taken from Meehl et al. [2007]. The IPCC also briefly addresses geographical patterns of future sea-level change. As shown in the AR4, projected local sea-level changes driven by ocean density and circulation changes are given in Figure 2.1. The results generated from the AOGCMs generally show poor agreement; there are few areas where the mean of the model projections exceeds the standard deviation Progress Following the IPCC s 4th Assessment Following the publication of the AR4, significant progress has been made in sea level research. In a review by Milne et al. [2009], the authors highlight two main advances: (1) the correction of biases discovered in the ocean temperature measurements [Willis et al., 2007] and (2) our ability to combine different observation systems (namely GRACE, altimetry and Argo) to better constrain the contributions to sea-level change.

11 11 Estimates of Future Sea-Level Changes for Norway As mentioned, there is large uncertainty associated with current projections of sea-level change and, in particular, the potential ice-dynamic contributions of the large ice sheets [e.g. Alley et al., 2005] (the limitations of the current generation of ice sheet models is briefly discussed in Chapter 5). Work since the AR4 has suggested that larger future contributions from Greenland and Antarctica are plausible [e.g. Pfeffer et al., 2008]. New observations, using two independent methods, indicate an increased (and accelerating) contribution from the ice sheets [Rignot et al., 2011]. If these observed trends continue then the IPCC AR4 sealevel projections for the 21 st century will be exceeded. It is not clear, however, if these changes are the beginning of a sustained response to recent warming. Other studies have examined the relationship between observed sea-level change and global averaged temperature changes or changes in radiative forcing, they are generally known as semi-empirical models [e.g. Rahmstorf, 2007; Vermeer and Rahmstorf, 2009]. Semi-empirical models give higher sea-level projections when compared to more complex physical models (e.g. as used in the IPCC AR4) and have suggested that global sea-level rise by the end of the 21 st century could approach 2 m. They offer an interesting alternative to the way in which we project or assess the risk of future sea-level changes, but their results should be used with caution. Most importantly, it remains uncertain whether a simple historical relationship between sea-level change and, for example, global temperature change will hold in the future. This is a major limitation of semi-empirical models and should be kept in mind when interpreting their results. The reader should also be aware that the use of such models for future projections has faced other criticisms [Holgate et al., 2007; Schmith et al., 2007; Rahmstorf, 2008; von Storch et al., 2008]; a summary of the main outstanding issues is detailed by Church et al. [2011]. Given these concerns, therefore, we decide not to adopt projections from semi-empirical models in this report. Moreover, the focus of this work is on regional sea-level projections and current semi-empirical models only give global sea-level rise estimates.

12 12 Estimates of Future Sea-Level Changes for Norway 2.3. National Efforts to Estimate Future Sea-Level Changes Several countries have begun working towards regional projections of sea-level change. Owing to their vulnerability to sea-level rise, significant efforts to better constrain future sea-level changes have been made in both the Netherlands and U.K The United Kingdom s Climate Projections Report The United Kingdom s climate projection report provides information on many aspects of future climate (see Chapter 3 deals with changes to mean sea level [Lowe et al., 2009]. Relative sea-level changes for the 21 st century ( relative to ) are reported as 0.21 to 0.68 m for London and 0.07 to 0.54 m for Edinburgh (5 th to 95 th percentile for a medium emissions scenario). For a fossil fuel intensive scenario, the 95 th percentile for relative sea-level change over the same period in London is 0.83 m and Edinburgh 0.7 m. The report also discusses a high-end scenario and, based on geological observations [Rohling et al., 2008], indicates a range of 0.93 to 1.9 m for the 21 st century. The authors consider the occurrence of high-end changes to be very unlikely, however, no formal assessment of their probability can be made The Delta Commission The 2 nd Delta commission was organized to come up with recommendations on how the Dutch coast can be protected against the consequences of climate change. In 2008 the commission published the Delta-report Working together with water *Delta Commissie, 2008] (see in which projections of future sea level and increased river discharge are presented. The sea level projections given in the Delta-report are based on the work of Vellinga et al. [2008] (see also Katsman et al. [2011]). Regional 21 st century sea-level changes were computed for a high-end scenario, corresponding to a global temperature increase of 2 to 6 C, and a warm scenario as detailed in KNMI [2006]. For these two scenarios, the resulting regional sea-level changes for the Dutch coast are 0.55 to 1.20 m and 0.40 to 0.80 m, respectively. In addition to the 21 st century projection, the Delta-report indicates a possible

13 13 Estimates of Future Sea-Level Changes for Norway sea level rise of 2 to 4 m along the Dutch coast within It should be noted that the final sea level projections given in the Delta-report do not include the effect of vertical land motion or gravitational effects on sea level due to land ice mass changes [e.g. Mitrovica et al., 2001] Past Studies for Norway Official projections for the 21 st century sea level change along the Norwegian coast are found in the report Havnivåstigning *Vasskog et al., 2009] based on a study by Drange et al. [2007]. The report was prepared mainly by the Bjerknes Centre for Climate Research and the work was organized by the Directorate for Civil Protection and Emergency Planning (DSB). Hereafter, the report will be denoted the DSB-report. In the summary, Chapter 7, we compare the findings of the DSB-report to our estimates of future sea-level changes for Norway. The projections found in the DSB-report are the ones presently recommended for land use planning in Norway. The report presents storm-surge heights and sea-level changes for 2050 and 2100 with respect to the level in Generally speaking, sea level is expected to rise by 70 cm along the southern and western part of the Norwegian coast, by 60 cm in the north of Norway, and by 40 cm in the inner part of Trondheims- and Oslofjorden over the 21 st century. Spatial variation in sea-level change is only due to variations in vertical land motion; ranging from 1 to 5 mm/yr along the Norwegian coast. The authors of the DSB-report recognize that IPCC AR4 does not provide a likelihood nor an upper bound for future sea-level change. They conclude, therefore, that IPCC AR4 should not be used for future land use planning in coastal areas. Instead, a projection based on the semi-empirical approach of Rahmstorf [2007] was adopted. Using this study, the DSB-report indicates the most likely sea-level change as 31 (-8 to +14) cm for 2050 and 80 (-20 to +35) cm for For 2100, a regional correction of 10 cm, taken from Fig IPCC AR4, was added to the semi-empirical estimate. This figure indicates sea-level changes due to ocean density and circulation changes larger than the global average along the Norwegian coast. After applying this correction, the total absolute sea level change is 90 cm for Finally,

14 14 Estimates of Future Sea-Level Changes for Norway relative sea-level changes were computed for 279 coastal municipals by subtracting the effect of vertical land motion. The land uplift rates were computed from the rates presented in Vestøl [2006]. These rates are relative rates, i.e. uplift with respect to local ocean surface change. Apparent uplift rates in the DSB-report are transformed into absolute uplift rates by adding 1.4 mm/yr (see also Section 3.3.1). The report also discusses extreme sea levels for the Norwegian coast due to storm-surges. Extreme sea level in the DSB-report is defined as that with a return period of 100 years or over. This level was computed from time series of tide gauges along the Norwegian coast. Based on a study by Lowe and Gregory [2005], storm-surge heights are expected to increase by 5 ± 2.5 cm for 2050 and 10 ± 5 cm for Hence, these corrections were added to the computed storm-surge heights. Storm-surge heights were then added to the highest observed astronomical tides and referred to the national geodetic height datum of Norway (NN1954, see Appendix II for additional details about the vertical reference systems of Norway).

15 15 Estimates of Future Sea-Level Changes for Norway 3. Present-Day Vertical Land Motion in Norway Observations of Glacial Isostatic Adjustment (GIA) in Fennoscandia 1 have traditionally been used to infer details of Earth s viscosity structure and the region s ice history [e.g. Fjeldskaar, 1994; Lambeck et al., 1998a; Milne et al., 2001]. They also inform us on vertical land motion, which is an important component of present-day relative sea-level change for Norway. The development of GPS, in particular, has enabled us to image crustal deformation to a high degree of precision. These observations show that present-day vertical Earth deformation across Fennoscandia is dominated by the ongoing relaxation of the Earth in response to past ice mass loss [e.g. Milne et al., 2001]. In this Chapter we investigate present-day vertical land motion in Norway using new GPS observations [Kierulf et al., in prep.]. We focus on the vertical component of motion as it is this, rather than horizontal movements, that is important for estimating present and future sea-level changes. Using the new GPS observations we use two different techniques to determine a crustal velocity field for Norway by (1) a method of interpolation called kriging and (2) a forward model of GIA. In our analysis, we compare these two methods and examine how our results differ to the land uplift model of Vestøl [2006], which has been applied in the previous DSB-report of sea-level changes in Norway Observed Vertical Land Motion in Norway In a landmark project named BIFROST (Baseline Inferences for Fennoscandian Rebound Observations Sea Level and Tectonics), a network of GPS observations from across Fennoscandia was used to investigate regional present-day crustal motion [Milne et al., 2001; Johansson et al., 2002]. These studies included measurements from the GPS networks in Sweden and Finland but data from only 1 GPS site in Norway. Results from the BIFROST analyses show a pattern of present-day Earth response with highest rates of uplift corresponding to areas of thickest ice during the last glacial period ( 21,000 years ago). Since the early 2000s, members of the BIFROST project have continued to update their 1 Fennoscandia is defined here as the geographic regions of Norway, Finland and Sweden.

16 16 Estimates of Future Sea-Level Changes for Norway results and incorporate new GPS observations into their analyses [Lidberg et al., 2007, 2010]. In addition to these efforts, a model of land uplift based on a collocation method was proposed by Vestøl [2006]. He used observations from leveling, tide gauges and GPS data from Fennoscandia and the nearby areas of continental Europe (the GPS velocities used in his analysis are the same as in Lidberg et al. [2007]). The model of Vestøl [2006], as mentioned above, is the land motion component that has been used in earlier analyses of sea-level change for Norway The GPS network Today 140 permanent GPS stations exist in Norway, although, only around half have been operating for sufficiently long that reliable velocity estimates can be determined from the data (see Section 3.1.2). The land motion model of Vestøl [2006] includes velocity estimates from 6 of the Norwegian GPS sites. In the following section, we outline the analysis of Kierulf et al. [in prep.] in which all the existing Norwegian GPS stations are examined and, from which, they determine a new vertical crustal velocity field for Norway. Fig Locations of the 139 permanent GPS stations on the Norwegian mainland. Symbols correspond to length of time-series relative to the start of Stars indicate more than 10 years of data, diamonds more than 5 years and circles more than 3 years. Dots mark stations with less than 3 years of data; these observations are not included in this report.

17 17 Estimates of Future Sea-Level Changes for Norway GPS Analysis-Strategies and Determining Vertical Velocities Three different approaches (software packages) are used in the analysis of the GPS data, these are: (1) the GPS Analysis Software of MIT (GAMIT) [King and Bock, 2003] (2) the GPS Inferred Positioning System/Orbit Analysis and Simulation Software (GIPSY/OASIS-II) [Zumberge et al., 1997] and (3) Bernese [Hugentobler et al., 2001]. All solutions are given in the ITRF2008 reference frame. Vertical velocities are determined using a least squares analysis and maximum likelihood estimation [e.g. Williams et al., 2004] Time-Series Analysis In a number of tests, Kierulf et al. [in prep.] assess the stability, uncertainty and consistency of the velocity estimates determined using the GAMIT, GIPSY and Bernese software. For the stability test, velocities estimated from shorter time-series are compared to the velocity determined from a 10 year observation period. This provides a guide as to what length timeseries is required to obtain results similar to the 10 year estimate (i.e. it tells us how quickly velocities converge on our 10 year velocity result). The RMS of the differences between the velocities determined from the shorter time-series and the 10 year period is given as: Eq Where is the station specific rate for a chosen time-series length and is the station specific rate for the 10 year period. The total number of GPS stations is given by. For the Norwegian GPS stations Kierulf et al. [in prep.] find that the GAMIT solution is generally slightly more stable than results from the other analysis strategies. In Figure 3.2 we show calculated using the vertical velocities from the GAMIT, GIPSY and Bernese software. For the GAMIT solution, velocities based on 3 years of data agree to within 0.5 mm/yr of the 10 year estimate. Velocities based on 5 years of data agree to within 0.2 mm/yr.

18 18 Estimates of Future Sea-Level Changes for Norway Fig The RMS of the differences in calculated velocities for a time-series of a given length and the 10 year estimate (see Eq. 3.1). Lines show solutions from GAMIT (green), GIPSY (blue) and Bernese (yellow). The length of the time-series is plotted relative to The aim of this work is to determine a crustal velocity field for Norway. We want to include as much of the available GPS data as possible but, clearly, our solution also has to be stable and reliable. In this case, we opt to use velocities calculated from the GAMIT software and using data from GPS stations that have been operating for 3 years or more (and are therefore within 0.5 mm/yr of our 10 year long-term estimates). Of the 139 stations considered, 66 have been operating for 3 years or longer. This means we lack GPS observations for the middle of Norway (the area north of Trondheim and south of Bodø) and the central mountainous areas of the south (see Fig. 3.1) Defining a Vertical Velocity Field for Norway To establish a continuous crustal velocity field in areas where we have (1) no GPS receivers or (2) the observation period is too short to obtain reliable results, either interpolation or modeling is required. In the first part of this Section (3.2.1) we show results from a statistical interpolation method called kriging. Section presents results from a GIA forward model constrained by the GPS data. The observed vertical velocities used here are based on the GAMIT solution using GPS time-series of 3 years or longer.

19 19 Estimates of Future Sea-Level Changes for Norway Statistical Interpolation We make use of a spatial interpolation theory called kriging [Cressie, 1993]. The methods used are described in Kierulf et al. [in prep.]. In Figure 3.3 we show predicted values for the 277 coastal municipalities and locations of the 66 GPS stations used in the kriging solution. Vertical velocities for the coastal municipalities are predicted to vary between 2 and 5 mm/yr. In their analysis, Kierulf et al. [in prep.] find that the kriging performs very well for locations inside of the GPS network (i.e. points with GPS observations available in several different directions like southern Norway). Outside of the GPS network, however, then the solution is less reliable. Thus, for parts of the far north and the area north of Trondheim and south of Bodø, we have little confidence in the predicted values. Fig Predicted vertical velocities (mm/yr) for the 277 coastal municipalities using the kriging statistical interpolation method. Black triangles mark the 66 GPS observations used in our solution.

20 20 Estimates of Future Sea-Level Changes for Norway Glacial Isostatic Adjustment Modeling Description of the GIA Model The GIA model employed is composed of three components: a model of grounded past ice evolution (for Fennoscandia and other ice covered areas), a sea level model to compute the redistribution of ocean mass for a given ice and Earth model, and an Earth model to compute the solid Earth deformation associated with the ice ocean loading history. The GIA model used here, and the method used to calculate present-day land motion, is the same as applied by Milne et al. [2001] except that the sea level component of the model was improved as discussed in Mitrovica and Milne [2003] and Kendall et al. [2005]. Note that the global ice model used in the analysis of Milne et al. [2001] is made up of two parts: The Fennoscandian and Barents Sea ice sheets are represented by the model of Lambeck et al. [1998a], which has been shown to provide good fit to paleo sea level data from the region. For other areas of the globe, they use the ICE-3G ice sheet reconstruction of Tushingham and Peltier [1991] Earth Model Sensitivity Test and Determining a Best-Fit Model Past GIA modeling studies have used both paleo sea level data [e.g. Lambeck et al., 1998a] and/or GPS observations [e.g. Milne et al., 2001; 2004] to help constrain Earth model parameters. These investigations have shown that it is not yet possible to uniquely constrain Earth s viscosity structure for the Fennoscandian region. Such studies, however, are able to provide us with a range of Earth parameter values that satisfy the various GIA observables. Given our limited knowledge of Earth s viscosity structure, we generate predictions of present-day vertical land motion using a suite of 297 Earth viscosity models. The range of values we explore is similar to those in Milne et al. [2001; 2004], namely; lithospheric thickness is varied from 71 to 120 km, upper mantle viscosity from 0.05 x to 5 x Pas and lower mantle viscosity from to 50 x Pas. To determine an optimal Earth model (i.e. the model which gives best-fit to the GPS data) we conduct a simple statistical test. We compute vertical velocities at all 66 GPS stations

21 21 Estimates of Future Sea-Level Changes for Norway considered for each of the 297 Earth models introduced above and quantify the goodness of fit for each Earth model using the criterion: Eq The value indicates the difference between the predicted ( ) and observed vertical velocity ( ) for a specified observational error ( ) and given GPS station ( ). A value of 1 or less indicates fit to the data. Fig The results for 297 different Earth viscosity models (see text for details). Each frame is based on a fixed value for lithospheric thickness. The 95% confidence level is marked by the white dashed line. Figure 3.4 shows how goodness of fit to the GPS observations varies with Earth model parameters. Encouragingly, we find similar results to Milne et al. [2001; 2004], namely that the vertical velocities favor an Earth model with a relatively stiff upper mantle. Differences between values for the various lithospheric thicknesses are small. Results from a more comprehensive investigation, however, suggest a preference for a lithosphere of 100 km or thicker [Milne et al., 2004]. For the models with a 120 km lithospheric thickness, an upper mantle viscosity of 3 x Pas and lower mantle viscosity of 5 x Pas gives best-fit to the GPS data. In the remainder of this analysis, we only use predictions from this model (hereafter referred to as our best-fit GIA model).

22 22 Estimates of Future Sea-Level Changes for Norway As discussed above, the vertical component of motion is most important when considering sea-level changes. The intent of the GIA modeling work performed here is, therefore, to find a land motion model that best fits the observed vertical velocities, rather than as an investigation of Earth viscosity structure. We note that other studies have inferred Earth viscosity values differing to ours and indicate significant lateral variations of Earth structure across Fennoscandia [see Steffen and Wu, 2011] Modeled Vertical Velocity Field and Residuals Predicted vertical velocities generated using our best-fit GIA model (Fig. 3.5) show a pattern of land motion similar to previous work [Milne et al., 2001]. All of mainland Norway is predicted to be uplifting, rates along the Norwegian coast vary between 1 and 5 mm/yr. Fig Predicted vertical velocities (mm/yr) for Fennoscandia using our best-fit GIA model. White triangles mark the 66 GPS observations used to constrain our model. Residuals between the best-fit GIA model and GPS data show that the model tends to slightly over predict rates of uplift in the middle of Norway, around 64 N, and under predict towards the south (Fig. 3.6). However, no clear pattern of misfit is apparent. At 39 of the 66 GPS stations examined, differences between the modeled and observed vertical velocities are less than the uncertainty on the observed value. In other words, at these positions less than 1 and the model provides a good fit to the GPS data. is

23 23 Estimates of Future Sea-Level Changes for Norway Fig Residuals; observed vertical velocities from the GAMIT solution minus our bestfit GIA model prediction for the 66 GPS stations examined (units are mm/yr). Circles with a horizontal line through have a residual value less than the uncertainty of the observed velocity (i.e. a value of 1 or less) Modeled Sea Surface Changes Associated With GIA The GIA model can also be used to predict geoid (i.e. ocean surface) changes associated with ongoing land motion and the movement of mantle material. Previous studies have suggested that these ocean surface changes are 6 % of the vertical land motion signal in Fennoscandia [e.g. Ekman and Mäkinen, 1996; Vestøl, 2006]. This means that at the centre of uplift where vertical velocities are around 10 mm/yr, we would expect a sea-level rise due to GIA of 0.6 mm/yr. This is a significant effect and, therefore, is included in our future sealevel projections for Norway. Note that ocean surface changes associated with GIA also need to be carefully considered when analyzing tide gauge records (see also Section and ).

24 24 Estimates of Future Sea-Level Changes for Norway Fig Predicted geoid changes (mm/yr) for Fennoscandia using our best-fit GIA model. White triangles mark the 66 GPS observations used to constrain our model. Predicted geoid rates generated using our best-fit GIA model (Fig. 3.7) show a similar pattern of change to our predicted vertical velocities. Maximum rates at the centre of uplift are around 0.6 mm/yr, this is slightly larger than the 0.4 ± 0.1 mm/yr found by Milne et al. [2001] although there are differences in our model setup. (Using a similar range of Earth model parameters as we explore here, Milne et al. [2001] show the sensitivity of the geoid rates to changes in Earth viscosity structure is no larger than ± 0.1 mm/yr). Geoid rates along the Norwegian coast vary between 0.2 to 0.5 mm/yr Discussion We have shown two different approaches to predicting vertical crustal velocities for the coastal municipalities; statistical interpolation (kriging) and GIA modeling. It is of clear interest to determine which method best describes land motion for coastal Norway and, therefore, which is preferable when calculating future sea-level changes. In a simple test of the two methods, we first remove the 10 longest time-series from the original 66 GPS stations examined. The kriging and modeling analysis is then repeated based on this reduced dataset of 56 time-series. For the GIA modeling Earth sensitivity analysis, we arrive at a slight

25 25 Estimates of Future Sea-Level Changes for Norway different result; a best-fit model with a 120 km lithosphere, upper mantle viscosity of 5 x Pas and lower mantle viscosity of 3 x Pas. Note that this model is within the 95 % confidence value of our earlier results (see Fig. 3.4). Kriging and GIA model predictions are then generated for the 10 sites that have been removed from the dataset. This allows us to test how well the predicted velocity fields fit to observations which have not been used to constrain our solutions. Observed kriging Observed GIA model (mm/yr) (mm/yr) RMS difference Table 3.1. RMS differences between the 10 longest time-series of observed vertical velocities and those calculated from kriging and GIA modeling (with a best-fit model of 120 km lithosphere, upper mantle viscosity of 5 x Pas and lower mantle viscosity of 3 x Pas). See above text for details. We find that the RMS error value is lower for the GIA model than for the kriging solution (Table 3.1). For this reason, we opt to use vertical velocities generated from the GIA model in the remainder of the report. An RMS error of 0.69 gives us reasonable confidence in the ability of the model to predict vertical velocities in areas where currently we have no observations (it is not so different to the observed errors which are typically 0.5 mm/yr). In comparison to the GIA model, kriging is generally more sensitive to outliers and, unsurprisingly, is not able to give as reliable predictions where there are limited GPS observations [Kierulf et al., in prep.]. As more GPS observations become available, eventually covering all of mainland Norway, then the reliability of the kriging solution will improve Comparison of GIA Modeling and Previous Work As discussed above, it is the land motion model of Vestøl [2006] which was used in the previous DSB-report of future sea-level change for Norway. The model is based on observations from leveling, tide gauges and GPS data from across Fennoscandia and the nearby areas of continental Europe. These separate observations measure different things; tide gauge and leveling data give information on relative sea-level and land height changes, whereas, the GPS data provide absolute height changes.

26 26 Estimates of Future Sea-Level Changes for Norway Differences between rates calculated from these separate measurement techniques can be used to investigate sea-level changes. For example, Milne et al. [2001] show the following relation between tide gauge and GPS observations: Eq Where spatially varying relative sea-level changes ( ) can be considered as being made up of varying vertical crustal velocities ( ), varying geoid (or ocean surface) changes ( ) and a uniform ocean surface change ( ). The non-uniform processes are a function of ( ) latitude and ( ) longitude. In his analysis, Vestøl [2006] determines (1) to be a scale factor (5.7 %) of the vertical crustal velocity term and (2) as a uniform regional ocean surface change of 1.32 mm/yr. Vertical crustal velocities are presented as an apparent uplift model (values are given relative to ocean surface height changes). It is important to note, however, that the accurate determination of absolute land motion cannot be achieved by correcting the apparent uplift rates presented by Vestøl [2006] using the above numbers (as done in the DSB-report). Doing this means that regional variations in sea surface height will, to some extent, be included in your solution (e.g. see Fig. 5 of Milne et al. [2001] and Marcos and Tsimplis [2007]). We caution against the use of land motion models partly based on relative sea-level observations for the detailed study of sea-level changes or, indeed, future estimates of sealevel change.

27 27 Estimates of Future Sea-Level Changes for Norway Fig The land motion model of Vestøl [2006] minus the velocity field predicted from our best-fit GIA model (note that to make this comparison the model of Vestøl [2006] was transformed to absolute values). The left panel shows the spatial pattern across Fennoscandia. The right panel shows the differences for the 277 coastal municipalities, black triangles mark the 66 GPS stations used to constrain our model. Units are in mm/yr. In comparison with earlier GIA modeling work [Lambeck et al., 1998b], the Vestøl [2006] model generally indicates smaller rates of uplift over Norway. A comparison to our best-fit GIA model shows a similar pattern of results (Fig. 3.8). Differences over the rest of Fennoscandia should be interpreted with care as our model is only constrained by the Norwegian GPS observations. For the coastal municipalities we find some notable differences in our results; in some locations GIA model rates of uplift are up to 2 mm/yr higher than the absolute rates calculated from Vestøl [2006]. This corresponds to a 20 cm difference in land height by Reference Frame Issues In Table 3.2 we show estimated vertical velocities obtained from four different GPS analyses, each study has employed different analysis strategies. Some of the differences between the separate estimates will be due to different reference frame realizations. For example, Kierulf et al. [2009] reports differences of 1 mm/yr in the vertical component between the

28 28 Estimates of Future Sea-Level Changes for Norway ITRF2000 and ITRF2005 realizations over Fennoscandia. (ITRF2008 shows negligible differences to ITRF2005). The Vestøl [2006] uplift model makes use of vertical velocities presented by Lidberg [2007] which are in ITRF2000. Whereas, our best-fit GIA model solution is constrained by results from Kierulf et al. [in prep.] which are in ITRF2008. Differences shown in Figure 3.8 will, therefore, largely reflect differences between ITRF2000 and ITRF2008. Comparisons of the two different realizations indicate ITRF2008 to be the far more precise solution [Altamimi et al., 2011]. Thus, we have more confidence in the vertical velocities presented by Kierulf et al. [in prep.] but note that ITRF2008 will still contain uncertainties. Oslo Stavanger Trondheim Tromsø Vardø Johanssen et al. [2002] 4 Lidberg et al. [2007] ITRF Lidberg et al. [2010] ITRF Kierulf et al. [in prep.] ITRF Table Estimated vertical velocities (mm/yr) obtained in different analyses for 5 of the Norwegian GPS stations Uncertainties in the Crustal Velocity Field Solution We estimate the uncertainty of the best-fit GIA model and kriging vertical crustal velocity solutions as 0.5 mm/yr (1-sigma). This is the RMS of the differences between velocities from the model/kriging and all the GPS observations but with some outliers removed [see Kierulf et al., in prep.]. We note that our vertical velocity solutions are constrained by observations in the ITRF2008 reference frame, which also has uncertainties [Altamimi et al., 2011; Wu et al., 2011]. The uncertainties in geocenter motion and scale of the reference frame are important for the vertical velocity estimates and, consequently, our regional sea-level projections. Reference frame uncertainties are hard to quantify due to lack of independent measurements. Recent work by Wu et al. [2011], however, presents an estimate of these uncertainties by combining data from GRACE, ocean bottom pressure measurements and ITRF2008 results. They find the geocenter of ITRF2008 is consistent with the center of mass of the Earth at 0.5 mm/yr and that the accuracy of the scale of the reference frame is 0.2

29 29 Estimates of Future Sea-Level Changes for Norway mm/yr. We, therefore, estimate the total uncertainty of our crustal velocity field as mm/yr (1-sigma) Conclusions Vertical velocities are calculated for the current 140 permanent GPS stations in Norway, the vast majority of which have not been analyzed previously. Around half of these stations have been operating for a sufficient length of time for their results to be considered reliable. Based on the new GPS data we compute a vertical crustal velocity field using statistical interpolation and preliminary GIA modeling. We note that the Earth model that gives best fit to the observed vertical velocities is similar to that determined by Milne et al. [2001]. Our best-fit GIA model shows good fit to the majority of the GPS data but with noticeable misfits in some areas. Given the existing geographical gaps in the GPS network, we consider the GIA model more suitable than the statistical interpolation approach for the analysis of regional sea-level changes. This may change as more GPS observations become available. Differences between our GIA model results and the uplift model of Vestøl [2006] are likely due to differences in the methods applied, reference frame issues and/or the use of different types of data (paleo sea level, GPS, tidegauges and leveling) to constrain the solutions.

30 30 Estimates of Future Sea-Level Changes for Norway 4. Observed Sea-level Changes for Norway Observations of present-day sea-level changes are available from the global tide gauge network and satellite altimetry. Tide gauge records provide measurements along the coastlines of the continents and at some islands. Satellite altimetry measures sea surface heights primarily in the open ocean. In the following Chapter, we first discuss global sea-level changes observed using tide gauges (Section 4.1.1) and go on to complete our own analysis of sea-level changes observed by the Norwegian tide gauges (Section 4.1.2). In the second part of the Chapter (Section 4.2) we discuss satellite altimetry and, in particular, the challenges of using this method to measure regional sea-level changes along the Norwegian coast Tide Gauge Records Records from the global tide gauge network provide a useful tool for understanding 20 th century sea-level changes and variations in sea level over multi-decade to century time scales. Tide gauges are coupled to the solid Earth, which means that they measure relative sea-level changes (i.e. both deflections of the Earth s surface and the ocean surface). Thus, to arrive at an estimate of absolute sea-level change, the tide gauge data first needs to be corrected for land motion. For Norway, vertical land motion due to GIA is an important component of contemporary sea-level change. The land motion signal can be separated from the tide gauge records using GIA modeling and/or observations from permanent GPS stations (see Chapter 3). In addition, it is worth remembering that vertical land motion also affects the Earth s gravity field and, therefore, acts to perturb the ocean surface. This effect needs to be taken in account if the tide gauge data are to be fully GIA corrected and to help us understand the separate contributions to sea-level change (see Tamisiea and Mitrovica [2011] and Section 3.3.1) Global Sea-Level Changes From Tide Gauge Records As discussed in Chapter 2, the IPCC AR4 concluded that the global sea level rate was 1.8 ± 0.5 mm/yr for 1961 to 2003 and 1.7 ± 0.5 mm/yr over the whole 20 th century. Other tide gauge studies have investigated the presence of nonlinear trends in global sea-level changes. For

31 31 Estimates of Future Sea-Level Changes for Norway example, Jevrejeva et al. [2006] determine a trend of 2.4 ± 1 mm/yr for the period 1993 to The authors find that this recent trend is similar to the observed trend between 1920 and There is also evidence of accelerations in the tide gauge records, Jevrejeva et al. [2008] reconstruct global sea level 300 years back in time from tide gauge records. The time series indicates that global sea-level change has accelerated by 0.01 mm/yr 2, starting at the end of the 18 th century. In Church and White [2006], altimetry data and tide gauge records are combined to reconstruct global sea level back to They find a sea-level rise of 1.7 ± 0.3 mm/yr over the 20 th century and reported an acceleration of ± mm/yr 2 for the same period. If this acceleration continues over the 21 st century, it corresponds to a sea level rise of 0.28 to 0.34 m. An updated analysis using five additional years with altimetry data comes to a similar conclusion; a sea-level rise of 1.7 ± 0.2 mm/yr for 1900 to 2009 and an acceleration of ± mm/yr 2 over the same period [Church and White, 2011] The Norwegian Tide Gauge Records The Norwegian Mapping Authority presently operates 22 tide gauges along the coast of Norway (Fig. 4.1). To the best of our knowledge, there are few comprehensive studies of the records from the Norwegian network but detailed analyses are forthcoming [Richter et al., in revision]. Some investigations, however, have included Norwegian stations in wider regional analyses [e.g. Douglas, 1991; Vestøl, 2006; Marcos and Tsimplis, 2007]. In a study of tide gauge records surrounding the North Sea, a trend of 1.6 ± 0.9 mm/yr (corrected for vertical land motion) was found for the period 1960 to 2000 [Marcos and Tsimplis, 2007]. As discussed in Chapter 3, Vestøl [2006] finds averaged regional sea-level change over Fennoscandia of 1.32 mm/yr (corrected for vertical land motion) for 1891 to 1990.

32 32 Estimates of Future Sea-Level Changes for Norway Fig Locations of the 18 Norwegian tide gauges used in this report. For reasons explained below, the records from Trondheim, Viker, Andøya and Vardø were not included in our analysis Analysis of the Norwegian Tide Gauges In order to better quantify observed sea-level changes along the Norwegian coast, we conduct our own analysis of tide gauge records. We use data from the Permanent Service for Mean Sea Level [Woodworth and Player, 2003] and follow their recommendation of only using the revised local reference datasets. These datasets are reduced to a common datum by making use of the tide gauge datum history provided by the supplying authority; this means that shifts in the records are eliminated. In this study, we chose to use the monthly datasets which appear to be more complete when compared to the annual records. The length of tide gauge records available from the Norwegian stations varies. The longest are from Bergen, Oslo, and Stavanger, having records beginning in 1883, 1885, and 1919, respectively. Other stations like Honningsvåg and Rørvik provide data from only 1970 to present. In a quality control of the data, we use the most complete datasets and avoid parts of the time-series that contain significant gaps. For example, in Oslo data before 1914 is removed from our analysis as the record prior to that time is not continuous. For the same reason, data before 1915 is excluded from the Bergen record. We also chose not to include the tide gauges at Trondheim, Viker, Andøya, and Vardø. In Trondheim the tide gauge was

33 33 Estimates of Future Sea-Level Changes for Norway moved in 1991, the time-series from Viker starts in 1992 and is too short for estimating a sea level trend and the time-series from both Andøya and Vardø suffer from significant data gaps. To determine long-term trends from the observed relative sea-level changes we conduct a least squares adjustment for each tide gauge (Eq. 4.1). Eq. 4.1 Here z is the observation at the epoch t, a is the intersect of the model, b is the rate of sea level change, and A, φ and f are the amplitude, phase and frequency of the annual periodic variation in the time-series. The periodic term was included because visual inspection of the monthly datasets revealed significant annual variation. If not captured by the model, the annual variation increases the standard deviation of the estimated rate of sea-level change. We compute two sets of rates. The first set makes use of all reliable data available from each tide gauge. The second set uses data from only the past 30 years (1980 to 2010) and represents present-day sea-level change along the Norwegian coast. As well as observed relative sea-level changes we also present rates that have been fully GIA-corrected. That is, the tide gauge records are adjusted for both vertical land motion and geoid changes using predictions generated from our best-fit GIA model (Chapter 3) Results From the Norwegian Tide Gauges Our estimated relative and GIA-corrected rates are listed in Table 4.1 and illustrated in Fig We estimate the uncertainties (1-sigma) of the rates to be between 0.1 and 0.3 mm/yr when using all the available reliable data. Whereas, rates determined for the period 1980 to 2010 have an uncertainty of 0.5 to 0.7 mm/yr (see Fig. 4.2). The uncertainties for the shorter time-series are therefore somewhat larger.

34 34 Estimates of Future Sea-Level Changes for Norway First Year RSLR (mm/yr) 2010 GIA-corrected SLR (mm/yr) 2010 RSLR (mm/yr) GIAcorrected SLR (mm/yr) RSLC (cm) Oslo Oscarsborg Helgeroa Tregde Stavanger Bergen Måløy Ålesund Kristiansund Heimsjø Rørvik Bodø Kabelvåg Narvik Harstad Tromsø Hammerfest Honningsvåg Table 4.1. Observed relative sea-level rates (RSLR) for 18 of the Norwegian tide gauges. Projected total relative sea-level change (RSLC) for 2000 to 2030 is calculated on the assumption that rates observed over 1980 to 2010 continue over the next 20 years unchanged. To determine the GIA-corrected sea-level rates we adjusted the RSLR using vertical crustal velocities and geoid changes generated using our best-fit GIA model (see Chapter 3). The majority of relative sea-level rates computed from the entire time-series of reliable data are less than zero, i.e. at most sites the sea level has fallen during the 20 th century (Fig. 4.2 top panel). For most locations, therefore, 20 th century relative sea-level change is dominated by vertical land motion. We note that the lowest rates are found in Oslo and in the middle part of Norway. The highest rates are found along the west coast of Norway and at the two northernmost sites at Honningsvåg and Hammerfest. After correcting for GIA, all rates are positive and are in the range 1.4 to 3.7 mm/yr. They are generally larger than global

35 35 Estimates of Future Sea-Level Changes for Norway estimates of 20 th century sea-level rise [e.g. Church and White, 2011] but detailed comparisons are difficult and not made here. We note that the GIA-corrected rates vary considerably, which can partly be explained by the different lengths of the tide gauges records (varying between 29 and 96 years). Rates determined from the shorter time-series tend to be larger and this suggests an increased rate of sea-level rise in the past few decades. Indeed, if we then determine sea-level rates for the period 1980 to 2010 we find that rates for the majority of the stations (excluding Oscarsborg, Helgeroa, Rørvik, Narvik, and Honningsvåg) have increased (see bottom panel Fig. 4.2). Most of the relative rates are positive but range between -2.2 and 2 mm/yr. After correcting for GIA, the rates vary between 2.6 and 4.4 mm/yr excluding Kabelvåg. Here the rate is 1.4 mm/yr, this is remarkably low when compared to GIA-corrected rates determined for the nearby stations of Bodø, Narvik and Harstad. The cause of the low rate at Kabelvåg is not known. If we ignore this station then our rates for the period 1980 to 2010 are more uniform (i.e. there is less variation between locations) when compared to rates computed from the entire timeseries. Variations in the GIA-corrected rates along the Norwegian coast could be due to several different factors. Given that the GIA model is poorly constrained in some areas of Norway, however, we do not attempt to interpret this pattern. Over short time-scales, the extrapolation of present-day observations can be used as an alternative method to modeling studies. Here we assume that observed relative sea-level rates over 1980 to 2010 will continue over the next 20 years unchanged (see also Section 4.4 of Flæte et al. [2010]). Thus, relative to the 2000-level, sea level in 2030 will range between and 6 cm.

36 36 Estimates of Future Sea-Level Changes for Norway Figure 4.2. Relative (blue), adjusted for vertical motion (red) and fully GIA-corrected (open red) sea level rates estimated from tide gauge observations along the Norwegian coast. The top panel shows the rates computed from the entire time-series (which varies in length from 29 to 96 years) and the bottom panel shows rates computed for the period 1980 to 2010.

37 37 Estimates of Future Sea-Level Changes for Norway 4.2. Satellite Altimetry Over the past 20 years, satellite altimetry has been the main observation techniques for mapping sea surface topography and measuring sea-level changes. The working principle of the technique is to transmit short pulses of microwave radiation which interact with the sea surface and are partly reflected back to the satellite. From the two-way travel time of the pulses, the distance between the satellite and the sea surface can be estimated. The sea surface height is computed by subtracting this distance from the height of the satellite determined in a global reference frame. Satellite altimetry observations have been used in, for example; sea level change studies, mapping of ocean currents, mean sea surface determination, gravity field determination, lake level monitoring, river discharge studies, development of ocean tide models, and ENSO studies [see e.g. Beckley et al., 2007; Lysaker et al., 2009; Andersen et al., 1998; Hwang et al., 2005; Kouraev et al., 2004; Smith et al., 2000; Andersen et al., 2006]. Accurate sea level monitoring requires precise range measurements, precise satellite orbits (satellite positions) as well as a precise and stable reference frame. The most precise range measurements are today obtained by dual frequency radar transmitters, which directly observe the ionospheric delay, combined with microwave radiometers which measure the atmospheric water vapor delay. This allows the ranges to be determined with a precision of 3 cm. Precise orbits are determined by utilizing satellite tracking systems like GNSS (Global navigation satellite systems), DORIS (Doppler Orbitography and Radio positioning Integrated by Satellite), and SLR (Satellite Laser Ranging). The orbits of the latest altimetry missions are determined using these techniques with accuracy better than 2 cm. Averaging the sea surface height measurements over larger regions or over the whole Earth allows the sea level to be determined with a precision of some tenths of a millimeter per year. In a study by Ablain et al. [2009], the error budget of global sea level rates was assessed. The authors found a total uncertainty of 0.6 mm/yr (90 % confidence interval) for the global sea level rate estimated by combining data from the TOPEX altimeters and Jason-1 over 1993 to However, this error budget did not include systematic errors which may arise due to reference frame instabilities over time. This effect is poorly constrained, but Minster et al.

38 38 Estimates of Future Sea-Level Changes for Norway [2010] conclude that the current version of the International Terrestrial Reference Frame does not meet the requirements for 1 mm/yr sea level monitoring Altimetry Measurements for Norway Sea level can be monitored by combining the data from several succeeding altimetry missions, e.g. Topex/Poseidon, Jason-1, and Jason-2. Together, these three satellites provide nearly 20 years of observations starting in These observations indicate a global sea level rise of approximately 3 mm/yr in this interval. Satellite altimetry may also provide the local sea level change. Figure 3 in Cazenave and Llovel [2010] shows that the local sea level trend varies from -10 to +20 mm/yr. The largest rates are found in the Indian Ocean and in the Western Pacific while the lowest rates are found along the west coast of the United States. In the Norwegian Sea the rate is between 2 and 5 mm/yr, i.e. close to the global average and close to the rates estimated from the Norwegian tide gauges. This is only a rough comparison and, unlike the tide gauge records, the altimetry data is not corrected for geoid changes associated with GIA. It should also be noted that precise orbit determination is especially important for local applications. Many orbital errors have a periodic pattern which average close to zero for global applications. However, for regional applications such errors have a direct influence on the observed sea-level rate. This was demonstrated by e.g. Beckley et al. [2007] who computed sea level rates by using satellite orbits in different reference frames. The study indicates that the sea level rates may be biased by up to 1.5 mm/yr along the Norwegian coast due to errors in the orbits. This is half the size of the global rate and illustrates the importance of precise satellite orbits for regional sea level measurements. Applications of satellite altimetry in coastal areas (closer than 50 km to the land) are especially demanding tasks. This is due to returned radar waveforms and range corrections (troposphere and ocean tide) contaminated by the land areas. Sea surface heights from coastal areas can still be extracted by applying appropriate waveform retracking techniques and by using corrections tailored to coastal areas. The angle between the satellite orbit and the equatorial plane of the Earth (the orbit s inclination) controls the area observed by the satellite. The orbit of Topex/Poseidon, Jason-1

39 39 Estimates of Future Sea-Level Changes for Norway and Jason-2 has an inclination which allows the ocean areas between ±66 latitude to be observed while the European satellites ERS-1, ERS-2, and Envisat observe the ocean areas between ±81.5 latitude. From this, it is clear that the Norwegian Sea is better covered by the European satellites. Data from the ERS-1 and ERS-2 satellites, however, suffer from weakly determined orbits. This is due to the fact that ERS-1 and ERS-2 only have SLR as a technique for precise orbit determination. Hence, precise sea level monitoring at high latitude starts with the Envisat data from Table 4.2 shows available data from the main altimetry missions and also the latitudinal boundary of the datasets. Satellite Latitudinal boundary Start of mission Mission completed ERS-1 ±81.5 July 1991 June 1996 Topex/Poseidon ±66 10 August 1992 October 2005 ERS-2 ±81.5 April Jason-1 ±66 7 December 2001 In orbit Envisat ±81.5 March 2002 In orbit Jason-2 ±66 20 June 2008 In orbit Cryosat-2 ±88 8 April 2010 In orbit SARAL/Altika ±81.5 April 2012 Sentinel-3 ± Jason-3 ± Table 4.2. Overview of the latest and some future satellite altimetry missions Discussion Tide gauges and satellite altimetry are complementary techniques for measuring sea-level changes. Observations from tide gauges and from the altimetry satellites indicate presentday sea-level changes along the Norwegian coast are similar to the observed global mean. Using temperature and salinity profiles (from hydrological stations and drifters in the Argo network) could aid our interpretation of the tide gauges and altimetry observations. By combining these datasets, it may be possible to separate and quantify the contributions from ocean density and mass changes along the Norwegian coast [e.g. Richter et al., in revision].

40 40 Estimates of Future Sea-Level Changes for Norway There is also a need for regional analyses of altimetry data for Norway. Such a study would require combined use of several altimetry satellites, e.g. the Jason-satellites (below 66 N latitude), Envisat, and the future Sentinel-3. If we are to reliably resolve regional sea-level changes then, for all these satellites, it requires the computation of internal biases and the optimization of precise orbits for the Norwegian territories Conclusions Our analysis of 18 tide gauge records reveals relative sea-level rates for 1980 to 2010 range from -2.2 and 2 mm/yr along the Norwegian coast. If we assume this rate continues unchanged for the next 20 years, total sea-level change for the period 2000 to 2030 will vary between -6.5 and 6 cm. After correcting the tide gauge data for vertical land motion and associated gravity changes, we find that GIA-corrected sea-level changes over the period 1980 to 2010 are between 2.6 and 4.4 mm/yr (if we exclude the anomalous rate at Kabelvåg). Analysis of data prior to 1980 suggests that the rate of absolute sea-level rise has increased in the past few decades. Estimating regional sea-level changes for Norway from satellite altimetry measurements is challenging; largely because some satellite missions do not make observations above 66 N. In a brief review of the literature, we estimate absolute sea-level changes in the Norwegian Sea from 1992 to present as 2 to 5 mm/yr. This is similar to the rates determined in our tide gauges analysis and is not dissimilar to the observed rate of global sea level rise ( 3 mm/yr).

41 41 Estimates of Future Sea-Level Changes for Norway 5. Projected 21 st Century Sea-level Changes for Norway In this Chapter we present regional sea-level projections for Norway for the 21 st century. As discussed above, recent analyses have worked towards estimating regional and/or local projections of sea-level change [e.g. Katsman et al., 2008, 2011; Slangen et al., 2011]. In our first analysis we opt to closely follow the methodology presented by Slangen et al. [2011], which builds on the approach and results of the IPCC AR4. Slangen et al. [2011] consider how different physical processes cause non-uniform sea-level changes by accounting for spatial variations in (1) ocean density (steric changes) and circulation [e.g. Landerer et al., 2007] (2) ice and ocean mass changes and associated gravitational effects on sea level [e.g. Mitrovica et al., 2001] and (3) vertical land motion arising from past surface loading change and associated gravitational effects on sea level (see Chapter 3). This Chapter is structured as follows: First, we describe the data and models applied (Section 5.1) and outline our analysis (Section 5.2). Our 21 st century regional sea-level projections are summarized in Section 5.3 and in Appendix I. Note that here we only consider mean local sea-level changes, possible changes in extreme sea-levels are discussed in Chapter 6. As discussed above, no likelihood was attached to the IPCC AR4 sea-level estimates and, for this reason, the AR4 does not give a best estimate or upper bound for future sea-level change. This is mainly due to the large uncertainty associated with the potential ice-dynamic contributions of the large ice sheets [e.g. Alley et al., 2005]. For the period 2090 to 2099 relative to 1980 to 1999, future global sea-level change is reported in AR4 to range from 18 to 59 cm [Meehl et al., 2007]. It may be, however, that the AR4 sea-level projections for the 21 st century will be exceeded (see Chapter 2). In addition to our projections which follow the methodology of Slangen et al. [2011] and are based on the AR4 results, therefore, we also present a second analysis largely based on the high-end scenario of Katsman et al. [2011] (Section 5.5).

42 42 Estimates of Future Sea-Level Changes for Norway 5.1. Data and Model Descriptions To obtain regional sea-level estimates for the Norwegian municipalities we closely follow the methodology of Slangen et al. [2011] (Fig. 5.1). In the below Sections we describe the different contributions used in our regional sea-level analysis. Fig The methodology followed to calculate our regional sea-level change projections. Adapted from Slangen et al. [2011] Model of Vertical Land Motion and Associated Gravity Changes Predictions of vertical land motion and associated gravitational effects on sea level are taken from our best-fit GIA model (see Chapter 3). The model is constrained by observations from 66 permanent GPS stations on the Norwegian mainland (those with 3 or more years of data) analyzed using GAMIT [King and Bock, 2003]. For comparison, we also include vertical land motion predictions from kriging for areas where we believe the spatial interpolation solution to be reliable. To obtain cumulative land height and geoid changes for the period relative to we multiply our velocities (mm/yr) by 105. Note that our approach differs to Slangen et al. [2011] who, in the main part of their analysis, make use of the ICE- 5G(VM2) model [Peltier, 2004].

43 43 Estimates of Future Sea-Level Changes for Norway The Climate Models (AOGCMs) We make use of results from Atmosphere Ocean General Circulation Models (AOGCMs) which are available in the Coupled Model Intercomparison Project phase 3 (CMIP3) database. As in Slangen et al. [2011], we examine output from models forced by the IPCC SRES scenarios A2, A1B and B1 [Nakícenović and Swart, 2000]. These scenarios represent varying development pathways for society and have different greenhouse gas emission forcings. Note that the IPCC does not assign a likelihood to the different emission scenarios. To calculate regional sea-level projections requires several model outputs, this information is not available for all of the AOGCMs in the CMIP3 database (see Sections and below) Future Ocean Density and Circulation Changes To calculate regional future ocean density and circulation changes requires (1) the projected global mean, which can be approximated as the global mean thermal expansion as global salinity changes are so small and (2) the local deviation with respect to the global mean, which is called the dynamic sea level (DSL). It is related to ocean circulation, 3D density structure, and mass distribution of the ocean, i.e. it has a mass component and a steric (temperature and salinity sea water changes) component. Non-uniform sea-level changes owing to density and circulation changes ( Yin et al. [2010]): ) are given as (adapted from Eq. 5 in Eq The contributions to local sea-level change are the global mean thermal expansion ( ) and the local sea level deviation from the global mean which is also called the dynamic sea level ( ). Projections are a function of ( ) latitude and ( ) longitude and ( ) time. As in Slangen et al. [2011], the global mean thermal expansion component has been corrected for the near linear trend found in some of the AOGCMs control runs. Table 5.1 lists the models for which we calculate projected regional sea-level changes driven by ocean density and circulation changes.

44 44 Estimates of Future Sea-Level Changes for Norway Model Center Scenarios Reference BCCR BCM 2.0 Bjerknes Centre for Climate A1B, A2, Furevik et al. [2003] Research, Norway B1 CCCMA CGCM Canadian Centre for Climate A1B, A2, Flato [2005] 3.1 Modeling and Analysis, Canada B1 GFDL CM 2.0 NOAA Geophysical Fluid Dynamics Laboratory, USA A1B, A2 Delworth et al. [2006] GFDL CM 2.1 NOAA Geophysical Fluid Dynamics Laboratory, USA A1B, A2, B1 Delworth et al. [2006] GISS AOM NASA/Goddard Institute for Space Studies, USA A1B, B1 Lucarini and Russell [2002] GISS MODEL EH NASA/Goddard Institute for A1B Schmidt et al. [2006] Space Studies, USA GISS MODEL ER NASA/Goddard Institute for A1B, A2, Schmidt et al. [2006] Space Studies, USA B1, IAP FGOALS 1.0g Insitute of Atmospheric Physics, China A1B, B1 Yongqiang et al. [2002] MIROC 3.2 (hires) Center for Climate System Research, Japan National Institute for Environmental Studies, Japan Frontier Research Center for A1B, B1 Hasumi and Emori [2004] MIROC 3.2 (medres) Global Change, Japan Center for Climate System Research, Japan National Institute for Environmental Studies, Japan Frontier Research Center for Global Change, Japan A2, B1 Hasumi and Emori [2004] MIUB ECHO-g University of Bonn, Germany A1B, A2, Min et al. [2005] B1 MPI ECHAM5 Max Planck Institute for Meteorology, Germany A1B, A2, B1 Jungclaus et al. [2006] MRI CGCM 2.3.2a Meteorological Research Institute, Japan A1B, A2, B1 Yukimoto et al. [2001] NCAR CCSM 3.0 National Center for Atmospheric A1B, A2, Collins et al. [2006] Research, USA B1 NCAR PCM 1 National Center for Atmospheric Research, USA A1B, A2, B1 Washington et al. [2000] UKMO HADCM 3 Met Office, UK A1B, A2, B1 Gordon et al. [2000] UKMO HADGEM Met Office, UK A1B, A2 Johns et al. [2006] Table 5.1. The 17 AOGCMs used to calculate regional ocean density and circulation changes.

45 45 Estimates of Future Sea-Level Changes for Norway Future Ocean Mass Changes Temperature and precipitation fields from the AOGCMs are used to calculate future land ice mass changes, which can be split into the contributions from glaciers and ice caps (Section ) and from the ice sheets (Section ). All ice mass changes were provided by A. Slangen (personal communication) and are based on scenarios A2, A1B and B1 and results from around 12 of the AOGCMs available from the CMIP3 database (see Slangen et al. [2011] for details) Contributions From Glaciers and Ice Caps Slangen et al. [2011] employ a glacier model based on the volume-area scaling approach. Following this method, temperature and precipitation fields from the AOCGMs are used to calculate glacier area changes. Glacier volume ( ) is then related to glacier area ( ) using a power law [e.g. Bahr et al., 1997]: Eq Where the other values ( and ) are scaling parameters. The glacier inventory used is divided into 19 regions [Radić and Hock, 2010] and, therefore, we have separate ice mass projections for each region. Note that as no complete glacier inventory exists, upscaling was performed in 10 of the 19 regions [see Radić and Hock, 2010] Contributions From the Ice Sheets The method employed by Slangen et al. [2011] to determine future ice mass changes from the ice sheets (Greenland and Antarctica) is the same as in IPCC AR4. Projected surface mass balance changes are calculated following Gregory and Huybrechts [2006]. (Note that modeled changes in ice sheet flow are also taken into account by modifying the sea level contribution due to surface mass balance changes). In addition, we opt to use the so called scaled-up values for future ice-dynamic changes (see Meehl et al. [2007]) - where the present-day ice sheet imbalance (0.32 mm/yr for the period 1993 to 2003) scales linearly with the projected average atmospheric temperature change. Projected ice mass changes are confined to the areas of southwest Greenland and the Antarctic Peninsula.

46 46 Estimates of Future Sea-Level Changes for Norway Future Non-Uniform Sea-Level Changes due to Land Ice Changes Predictions of future sea-level changes are generated using the GIA model described in Chapter 3 except that (1) the ice model input is the projected ice sheet and glacier mass changes as detailed above and (2) the setup of the GIA model is altered so that, instead of performing past ice age calculations, it is used to predict future sea-level changes. These predictions give relative sea-level changes, which can be considered separately as perturbations to the solid Earth surface and to the ocean surface. For the Earth response, we assume that deformations over the next century will be purely elastic. Projected ice mass loss, therefore, will lead to a relatively localized elastic rebound of the Earth s surface. As both the elastic Earth response and ocean surface perturbation scales linearly with the surface loading change, non-uniform sea-level changes can be normalized by the ice mass loss [e.g. Mitrovica et al., 2001]: Eq Equation 5.3, modified from Mitrovica et al. [2001], describes how the total projected sealevel change ( ) is the sum of the normalized sea-level change ( ) from Antarctica, Greenland and the 19 glacier regions considered. Predictions of sea-level change are non-uniform being a function of ( ) latitude and ( ) longitude. Total sea-level changes are found by multiplying the normalized pattern of sea-level change by the individual projections of ice mass changes for the glaciers and ice sheets (see above) Analysis Our analysis is divided into projected global sea-level changes (Section 5.2.1) and regional sea level estimates (Section 5.2.2) Global Mean Sea-Level Changes Global mean sea-level changes are, except for the ocean density contribution where we make use of a different set of AOGCMs, the same as those presented in Slangen et al.

47 47 Estimates of Future Sea-Level Changes for Norway [2011]. As mentioned above, the contribution from ocean density changes can be approximated as the global mean thermal expansion because global salinity changes are so small. Fig. 5.2 shows the projected multi-model average and range of calculated thermosteric sea-level changes for the scenarios A2, A1B and B1. Fig st century global mean thermosteric sea-level change computed for the A2, A1B and B1 scenarios. For the AOGCMs considered, squares mark the average and error bars indicate the multi-model range. The projections show that the multi-model range overlaps between the scenarios (i.e. there is little difference between projections from A2, A1B and B1). Given this, we opt to use the multi-model average across all scenarios as our central value for global thermosteric sealevel change. We computed this, and the corresponding uncertainty (1-sigma), for 2030 as 0.05 ± m, for 2050 as 0.09 ± m, and for 2100 as 0.22 ± m (changes are relative to the period 1980 to 1999). The uncertainties (1-sigma) indicate that the variation between the models increases later in the 21 st century. It is important to note that the standard deviations only quantify the variability of the AOGCMs and not the uncertainty of the estimates. The uncertainty of the projected thermosteric sea-level change is difficult to assess because the uncertainty of each model and the probability of each scenario are not known.

48 48 Estimates of Future Sea-Level Changes for Norway Table 5.2 is adapted from Slangen et al. [2011], shows the contributions to projected global mean sea-level changes. We do not include the effect of GIA on ocean basin volume changes but this is predicted to be very small (less than 0.01 mm/yr). The sum of mean sea-level changes across scenarios A2, A1B and B1 is 0.47 m, this is useful to know as we can then see how different our regional projections are when compared to the global mean (see Table 8.18). Note that projected global mean sea level is split almost equally between thermal expansion and ice mass loss. Contribution to global mean sea-level change (cm) Steric 22 ± 6 (47%) Glaciers* 17 ± 4 (36%) Greenland* 7 ± 2 (15%) Antarctica* 1 ± 2 (2%) Sum 47 ± 8 Table Contributions to projected 21 st century ( relative to ) global mean sea-level change across scenarios A2, A1B and B1. Uncertainties are 1- sigma and contributions are also expressed as percentages of the global mean. *based on numbers from Slangen et al. [2011] Regional Sea-Level Changes Projected Ocean Density and Circulation Changes Before computing local sea-level changes due to ocean density and circulation changes for the 21 st century, we perform a regional assessment of the AOGCMs. In this test, we examine the ability of the AOGCMs to replicate present-day observed dynamic sea-level (DSL) changes. If the models are able to adequately reproduce present-day regional patterns of DSL change, then it gives us increased confidence in their suitability for projecting 21 st century sea-level changes for the Norwegian coast [see Yin et al., 2010; Slangen et al., 2011]. We follow a similar methodology as described by Yin et al. [2010]. Observed DSL changes, obtained from altimetry and drifting buoys, are available from 1992 to 2002 [Maximenko et al., 2009; Niiler et al., 2003]. In order to make a comparison, modeled DSL changes were averaged over the same period. We select two rectangular windows to make our regional assessment; the areas 0 14 E, N and 0 34 E, N. Note that this study

49 49 Estimates of Future Sea-Level Changes for Norway area excludes all data in the Gulf of Bothnia. Differences between models ( ) and observations ( ) were calculated by computing the RMS error [Yin et al., 2010]: Eq Where the weight of the grid-point ( ) is set equal to the area of the corresponding grid-cell and the sum of the weights ( ) corresponds to the total ocean area covered. Observed and modeled regional DSL for the period 1992 to 2002 are shown in Figure 5.3, visual inspection indicates generally good agreement between models and to the observed DSL. Some notable differences are present in the north of our study area.

50 50 Estimates of Future Sea-Level Changes for Norway Fig (below). Modeled present day (1992 to 2002) DSL from 17 AOGCMs and the observed DSL from altimetry measurements and drifting buoys [Maximenko et al., 2009; Niiler et al., 2003] (upper left panel).

51 51 Estimates of Future Sea-Level Changes for Norway RMS differences between observed DSL and the ensemble of 17 AOGCMs vary between 0.08 and 0.51 m (Fig. 5.4). We opt to use only models with a RMS error of less than 0.3 m [Yin et al., 2010]. This threshold eliminates the four models CCCMA CGCM 3.1, GISS ER, MIUB ECHO G, and MRI CGCM from further analysis. We also omit the models GISS AOM and GISS- ER because they include a contribution from land ice which cannot be separated from the steric signal [Katsman et al., 2008]. This leaves 11 AOGCMs for the calculation of future ocean density and circulation changes for Norway. Fig The root mean square error between the modeled and observed DSL from 1992 to All models with a RMS error larger than the 0.3 m threshold (dashed line) were not used for computing the DSL change for the coastal municipalities. We calculate DSL fields for 2030, 2050 and 2100 for our chosen 11 AOGCMs. (Note that in some models the global mean of the DSL is non-zero, in which case we subtract the global epoch-average of the DSL from each grid point at each epoch). The time-series of DSL change are noisy so, in a simple approach, we average the results over multi-year intervals. For example, for 2100 we examine average DSL for the period 2090 to 2100 relative to 1981 to

52 52 Estimates of Future Sea-Level Changes for Norway 2000 (i.e. essentially the same intervals as in IPCC AR4). As with the global thermosteric change, we conclude that the AOGCMs do not give a precise description of the DSL along the Norwegian coast. Still, most models point towards a sea-level change higher than the global mean. We take the ensemble average as a best guess for the regional DSL change. This gives values of 0.04 ± 0.04 m, 0.06 ± 0.04 m, and 0.09 ± 0.08 m for 2030, 2050 and 2100, respectively (Fig. 5.5). Again, it should be stressed that the standard deviations only quantify the variability of the models and not the estimated uncertainty. Fig st century regional dynamic sea-level change (the areas 0 14 E, N and 0 34 E, N) computed for the A2, A1B and B1 scenarios. For the AOGCMs considered, squares mark the average and error bars indicate the multi-model range. Spatial patterns of the local DSL change using 11 AOGCMs and for the A1B scenario are shown in Fig Visual inspection of the fields indicates that differences within our study area are no larger than a few centimeters. Thus, given the somewhat larger range between the AOGCMs (Fig. 5.5), local variations along the Norwegian coast are not taken into account.

53 53 Estimates of Future Sea-Level Changes for Norway Fig Projected 21 st century ( relative to ) dynamic sea-level changes for the A1B scenario. The 11 AOGCMs shown are those which are able to adequately reproduce observed present-day regional patterns of DSL change (see Fig. 5.4). We note that, in relation to the other AOGCMs, the MIROC3.2 (medres) and NCAR CCSM 3.0 models project significantly larger DSL changes. It is beyond the scope of this study to explain differences between the models.

54 54 Estimates of Future Sea-Level Changes for Norway Projected Non-Uniform Sea-Level Changes due to Land Ice Changes Non-uniform sea-level variations due to projected 21 st century ice sheet and glacier ice mass changes for the A1B scenario are shown in Fig The spatial patterns compare well to the projections shown by Slangen et al. [2011] (see Figs. 2 and 3), which gives us confidence in our results. Uncertainties between sea-level predictions for the different AOGCMs (1-sigma) are less than ± 5 cm over the majority of the globe, including the Norwegian coastline. Fig Projected 21 st century ( relative to ) multi-model mean sea-level changes for the A1B scenario from Greenland and Antarctica (top left) and the 19 glaciated regions (top right). Locations of ice mass changes are colored white. Corresponding uncertainties between the models (1-sigma) are shown in the bottom panels. Units are in meters. In addition, we compute non-uniform sea-level variations due to projected 21 st century ice sheet and glacier ice mass changes for the scenarios A2 and B1 (figures not show). For the Norwegian coastal municipalities, we find only small differences between the scenarios. This is not surprising as differences in projected land ice mass changes between the scenarios are small (Table 5.2). Thus, as with our ocean density and circulation projections, we opt to take the multi-model average across all scenarios. For the coastal municipalities, non-uniform

55 55 Estimates of Future Sea-Level Changes for Norway sea-level variations due to projected 21 st century ice sheet and glacier ice mass changes are shown in Fig The local uncertainty (1-sigma), which is not shown, varies between ± 3.5 and 4 cm. The projections show significant regional variations; sea-level changes in the south are approximately twice as large as those in northern Norway. This pattern can be attributed to mass loss from glaciated areas to the north of Norway. We find that the contribution from nearby Scandinavian glaciers is around -1 cm and, therefore, relatively unimportant. Projected mass loss in Svalbard affects sea levels along the Norwegian coast by between -1 and -3 cm. Fig Projected 21 st century ( relative to ) multi-model mean sea-level changes due to land ice changes across scenarios A2, A1B and B1. Units are in meters Regional 21 st Century Sea-Level Projections for Norway Here we give regional sea-level projections for the end of the 21 st century. Our sea level estimates take account of (1) ocean density (steric) and circulation changes, (2) ice and ocean mass changes and associated gravitational effects on sea-level and (3) vertical land motion arising from past surface loading change and associated gravitational effects on sea level.