Normal mode analysis is a Laplace-transform method for calculating the surface-loading response of laterally homogeneous spherical Earth models with linear viscoelasticity which delivers modal decay times and amplitudes. It can locally fail owing to numerical singularities arising from the viscoelastic parameters, leading to an incomplete accounting of the surface-loading response. Collocation methods were developed to circumvent this issue. The mixed collocation method includes least-squares fitting to the Laplace-transformed Earth response to determine amplitudes assuming the normal mode decay times are known, while the pure collocation method assumes a series of logarithmically regularly spaced inverse decay times for which amplitudes are determined numerically. Both collocation methods may determine amplitudes that are physically unrealistic and all three methods produce crustal motion predictions that differ significantly. The hybrid normal mode-collocation method presented here applies the normal mode analysis, and then applies the pure collocation to the resulting residuals. This retains the modal structure, while providing an improved fit. Our implementation avoids numerical singularities that may arise from Rayleigh-Taylor instabilities occurring at large times and can be automated. Vertical crustal motions predicted by the hybrid method for North America with the ICE-6G_C loading model and the VM5a viscosity structure have a root mean square (RMS) of 4.49 mm/yr and RMS differences with the normal mode, pure, and mixed collocation method of 0.06, 0.23, and 0.25 mm/yr, respectively. Maximum differences reach 0.20, 0.87, and 0.63 mm/yr. The differences increase for a viscosity profile with a greater viscosity increase with depth that exhibits stronger singularity issues. The Earth's response to past and present-day ice mass change is known as glacial isostatic adjustment (GIA). GIA induces crustal motion and gravitational change and is an important element for understanding regional sea-level change. The goal of this study was to develop a computer modeling method that can be used to accurately calculate the Earth's GIA response, subject to some simplifying assumptions about the nature of Earth structure and its flow properties, while also being more robust than previous methods. To do this, we created a new method (Hybrid Normal Mode-Collocation) from two previously published methods to minimize the documented issues of these prior methods. The hybrid method is shown to be robust, produce a more accurate predicted Earth model response, and avoid most of the problems of the previous methods. The hybrid method uses normal mode analysis and pure collocation to calculate the surface-loading response for Maxwell viscoelastic Earth models The hybrid method retains all the significant modal structure that can be found and fits the residual component well There are significant differences in the calculated crustal response (vertical and horizontal) between the hybrid method and previously published methods

Responses to Canada's Changing Climate", which brings together articles that describe and quantify

The Mackenzie Delta is an extensive river-mouth depocentre, the second largest delta on the Arctic Ocean, and lies in the zone of continuous permafrost. We report the first measurements of natural consolidation subsidence in a high-latitude delta with ice-bonded sediments. Several years of episodic GPS records on a network of 15 stable monuments throughout the central and outer delta reveal downward motion between 1.5 ± 0.7 and 5.3 ± 1.1 mm/year relative to a nearby monument on bedrock. Additional shallow subsidence results from loss of near-surface excess ice with deeper seasonal thaw in a warming climate. Isostatic adjustment is a third component of subsidence, captured in the NAD83v70VG crustal velocity model. Sedimentation rates over much of the outer delta are less than the rate of subsidence combined with rising sea level. Scenarios for future inundation are evaluated using interpolated IPCC AR5 projections, NAD83v70VG, and a LiDAR DEM with realistic consolidation, thaw subsidence, and sedimentation rates, on time scales of 40 and 90 years. These reveal increases in area flooded at mean water level from 33% in 2010 to 65% or as much as 85% in 2100, depending on the emissions scenario, driving delta-front retreat and removing a large proportion of avian nesting habitat. The three components of subsidence together increase the relative sea-level rise by a factor of two to eight, depending on the scenario. Consolidation subsidence may also contribute to rising low-flow water levels in the central delta, increasing river-lake connectivity, with negative impacts on aquatic biodiversity and productivity.

Including sea-level rise (SLR) projections in planning and implementing coastal adaptation is crucial. Here we analyze the first global survey on the use of SLR projections for 2050 and 2100. Two-hundred and fifty-three coastal practitioners engaged in adaptation/planning from 49 countries provided complete answers to the survey which was distributed in nine languages – Arabic, Chinese, English, French, Hebrew, Japanese, Korean, Portuguese and Spanish. While recognition of the threat of SLR is almost universal, only 72% of respondents currently utilize SLR projections. Generally, developing countries have lower levels of utilization. There is no global standard in the use of SLR projections: for locations using a standard data structure, 53% are planning using a single projection, while the remainder are using multiple projections, with 13% considering a low-probability high-end scenario. Countries with histories of adaptation and consistent national support show greater assimilation of SLR projections into adaptation decisions. This research provides new insights about current planning practices and can inform important ongoing efforts on the application of the science that is essential to the promotion of effective adaptation. Coastal practitioners in countries with longer histories and more national support show greater assimilation of sea level rise projections in adaptation planning, according to quantitative and qualitative analysis of a global survey.

Abstract Including sea-level rise (SLR) projections in coastal adaptation is increasingly recognized as crucial. Here we analyze the first global survey on the use of SLR projections comprising 253 coastal practitioners engaged in adaptation/planning from 49 countries with time frames of 2050 and 2100. While recognition of the threat of SLR is almost universally recognized, only 71% of respondents currently utilize SLR projections. Generally, developing countries have lower levels of utilization. There is no global standard in the use of SLR projections: for locations using a standard structure, 53% are planning for a single projection, while the remainder are using multiple projections, with 13% considering an unlikely high-end scenario. Countries with long histories of adaptation and consistent national support show greater assimilation of SLR projections into adaptation decisions. This research proves insightful for improving sea-level science, and informs important ongoing efforts on the application of the science which are essential to promote effective adaptation.

Sea level rise (SLR) is a long-lasting consequence of climate change because global anthropogenic warming takes centuries to millennia to equilibrate for the deep ocean and ice sheets. SLR projections based on climate models support policy analysis, risk assessment and adaptation planning today, despite their large uncertainties. The central range of the SLR distribution is estimated by process-based models. However, risk-averse practitioners often require information about plausible future conditions that lie in the tails of the SLR distribution, which are poorly defined by existing models. Here, a community effort combining scientists and practitioners builds on a framework of discussing physical evidence to quantify high-end global SLR for practitioners. The approach is complementary to the IPCC AR6 report and provides further physically plausible high-end scenarios. High-end estimates for the different SLR components are developed for two climate scenarios at two timescales. For global warming of +2°C in 2100 (RCP2.6/SSP1-2.6) relative to pre-industrial values our high-end global SLR estimates are up to 0.9 m in 2100 and 2.5 m in 2300. Similarly, for a (RCP8.5/SSP5-8.5), we estimate up to 1.6 m in 2100 and up to 10.4 m in 2300. The large and growing differences between the scenarios beyond 2100 emphasize the long-term benefits of mitigation. However, even a modest 2°C warming may cause multi-meter SLR on centennial time scales with profound consequences for coastal areas. Earlier high-end assessments focused on instability mechanisms in Antarctica, while here we emphasize the importance of the timing of ice shelf collapse around Antarctica. This is highly uncertain due to low understanding of the driving processes. Hence both process understanding and emission scenario control high-end SLR.

The geographic coincidence of the Chile Ridge slab window and the Patagonia ice fields offers a unique opportunity for assessing the effects of slab window rheology on glacial isostatic adjustment (GIA). Mass loss of these ice fields since the Little Ice Age causes rapid but variable crustal uplift, 12-24 mm/yr around the North Patagonia ice field, increasing to a maximum of 41 mm/yr around the South Patagonia ice field, as determined from newly collected or processed geodetic data. We used these observational constraints in a three-dimensional Maxwell viscoelastic finite element model of GIA response above both the subducting slab and slab window in which the upper-mantle viscosity was parameterized to be uniform with depth. We found that the viscosity of the northern part of the slab window, similar to 2 x 10(18) Pa.s, is lower than that of the southern part by approximately an order of magnitude. We propose that this along-strike viscosity contrast is due to late Cenozoic ridge subduction beneath the northern part of the slab window, which increases asthenospheric temperature and reduces viscosity.

This report provides national and regional maps and national geospatial data files (geoTIFFs) of projected relative sea-level change across Canada for 2006 and every decade from 2010 to 2100. It updates and augments previous reports which included plots and tables of projected relative sea-level change at specified locations where a measurement of vertical land motion had been made by Global Positioning System (GPS). Here, gridded projections are provided at a resolution of 0.1º in latitude and longitude encompassing all coastal regions of Canada. The relative sea-level projections are based on the Fifth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC AR5) and on the NAD83v70VG national crustal velocity model. Projections are relative to 1986-2005, and are given for the median value and 5th and 95th percentiles for Representative Concentration Pathway (RCP) scenarios RCP2.6, RCP4.5, and RCP8.5. As well, the projected sea level at 2100 is given for an enhanced scenario where Antarctica is assumed to provide an additional 65 cm of global sea-level rise to the median projection of RCP8.5. For many purposes, the upper (95th percentile) of the high-emission RCP8.5 scenario may comprise the appropriate planning level, but if tolerance to the risk of sea-level rise is low, it may be appropriate to consider a larger amount of projected sea-level rise.

Securing well-being and building resilience in response to shocks are often viewed as key goals of sustainable development. Here, we present an overview of the latest published evidence, as well as the consensus of a diverse group of scientists and practitioners drawn from a structured analytical review and deliberative workshop process. We argue that resilience and well-being are related in complex ways, but in their applications in practice they are often assumed to be synergistic. Although theoretically compatible, evidence we present here shows that they may in fact work against each other. This has important implications for policy. Well-being and resilience are considered related or even synergistic dimensions of sustainable development. This Perspective highlights how trade-offs emerging from narrow interpretations of resilience and well-being could threaten sustainable development outcomes.

A suite of forward GIA model predictions, spanning a wide range of layered mantle viscosity and lithospheric thickness values, is compared to observed horizontal crustal motions in North America to discern optimal model parameters in order to minimize a root-mean-square (RMS) measure of the velocity residuals. To obtain the Earth model response, a combination of the full normal mode analysis and the collocation method is implemented. It provides a means to determine the surface loading response automatically and robustly to 1-dimensional (radially varying) Earth models, while retaining as much of the physics of the normal mode method as numerically feasible, given documented issues with singularities along the negative inverse-time axis in the Laplace transform domain. This method enables the exploration across a wide parameter range (for the lower mantle, transition zone, asthenosphere, and thickness of the elastic lithosphere) to find optimal combinations to explain horizontal crustal motion in North America. The analysis utilizes crustal motion rates from approximately 300 GNSS sites in central North America (Canada and United States) provided by the Nevada Geodetic Laboratory. Preliminary results indicate that horizontal crustal motion predictions generated with a thin lithosphere, 40 – 60 km, produce horizontal motions that are strongly discrepant with the observations and have velocity residuals larger than the null model (modelled horizontal motion set to zero). As the lithospheric thickness increases, from 80 km to 240 km, the horizontal motion residuals gradually decrease with no minimum apparent for the thicknesses thus far considered. The residual velocities for the best-fitting models appear to carry a remaining signal, confirming previous inferences of limitations to spherically symmetric Earth models in modeling horizontal crustal motions in North America.

The Coast Mountains in British Columbia and southeastern Alaska contain around 9040 km2 of glaciers and ice fields at present. While these glaciers have followed an overall trend of mass loss since the Little Ice Age (or LIA around 300 years before present), the past decade has seen a significant increase in melting rate that is likely to continue due to the effects of climate change. The region is home to a complex tectonic setting, having proximity to the Queen Charlotte-Fairweather transform plate boundary in the northern region and the Cascadia subduction zone (CSZ) in the southern region, which has an associated active volcanic arc underlying the glaciated area. Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) glacier melt data collected between 2000 and 2019 represent a melt rate that is averaged between periods of relatively low mass loss (2000-2009) and high mass loss (2010-2019). As a preliminary test, this average melt rate was assumed to be constant back to the LIA. A history of gridded ice thicknesses was calculated to create an ice loading model for input to a series of forward modelling calculations to determine the crustal response. Predictions of vertical crustal motion are compared to available Global Navigation Satellite System (GNSS) measurements of uplift rate to constrain Earth rheology. The results using this simplified loading model favour a thin lithosphere (around 20-40 km thick) and asthenospheric viscosities on the order of 1019 Pa s. These values are significantly lower than those of rheological profiles used in extant global GIA models, but are in general agreement with previous GIA modelling of the forearc region of the CSZ. To improve the glacial history model, the Open Global Glacier Model (OGGM), driven by historic climate data and statistically downscaled climate projections, is being employed to create a more accurate loading model and refine our estimates of Earth rheology and regional crustal motion. The best-fitting models will be employed to separate GIA and tectonic components of crustal motion and to generate improved regional sea-level projections.

Modeled ray paths and comparisons to picked arrivals are shown here for the refractions in sediment layers 1 (Fig. S1) and 2 (Fig.S2), the reflections from the bottoms of sediment layers 1 (Fig. S3) and 2 (Fig. S4), the refraction from the bottom of the crustal velocity layer (Fig. S5), and the head-wave from the bottom of the crustal-velocity layer (Fig. S6).

A national-scale crustal velocity model has been developed for Canada as part of the current realisation of NAD83(CSRS), delivered as a set of 3 national grids, for each of the North, East and Up (N, E and U) components. It is used to propagate coordinates to different reference epochs, and to support scientific studies such as natural hazards, climate change, and groundwater change. The previous velocity model was based on continuous and campaign GPS data between 1994 and 2011.3. The new model includes new stations in key areas, six more years of data (to the end of 2017), and newly reprocessed historical data using the latest software and GPS products. We include data from continuous GPS sites in Canada, the northern portions of the US, all of Greenland, and a set of globally distributed sites used to define the reference frame; and from repeated high accuracy campaign surveys in Canada. A new type of model is introduced for the vertical grid. It incorporates GPS observations with the crustal uplift predictions of Glacial Isostatic Adjustment (GIA) and elastic rebound models, which are especially important in areas with sparse coverage. Gridded uncertainty estimates are provided for each component of NAD83v70VG.

Baseline mapping of coastal characteristics and understanding of the dynamic response of coastal sensitivity to environmental changes provide a strong foundation for climate change adaptation in Canada's coastal regions. CanCoast is a collection of datasets that describe the physical characteristics of Canada's marine coasts. It includes datasets that are not expected to change through time (such as coastal materials and backshore slope), and some that are projected to change as climate changes (such as wave height and mean sea level). CanCoast includes: sea-level change (early and late 21st century); wave-heights including the effects of sea ice (early and late 21st century); ground ice content; coastal materials; tidal range; and backshore slope. These are mapped to a common high-resolution shoreline and used to calculate indices that show the generalised coastal sensitivity of Canada's marine coasts in early and late 21st century climates, and the spatially-variable change in sensitivity between the early and the late 21st century. Because of the scales of the input data, the generalised indices are best used to identify regions that differ in sensitivity to changing climate, rather than local properties or coastal infrastructure with specific characteristics that cannot be resolved in this national-scale approach.