Spatio-temporal data analysis is crucial in many research fields. However, modelling large-scale spatio-temporal data presents challenges such as high computational demands, complex correlation structures, and the separation of mixed sources. To address these issues, we are developing 4DModeller (fdmr), a robust and user-friendly R package designed to model spatio-temporal data within a Bayesian framework. The software package offers a comprehensive solution for visualizing, analyzing and modelling different types of spatio-temporal data in various disciplines. By incorporating Bayesian hierarchical models, "fdmr" allows for the flexible integration of prior knowledge and data uncertainty into the modelling process. By utilizing the Integrated Nested Laplace Approximations (INLA) algorithm and the stochastic partial differential equations (SPDE) method for model inference, "fdmr" significantly reduces the computational complexity of handling high-resolution, highdimensional spatio-temporal data. Furthermore, "fdmr" provides intuitive and interactive visual analytics tools that facilitate the exploration of data patterns across both space and time. This paper aims to introduce the "fdmr" package, and outline its core modelling framework through an example study on the spread of COVID-19 infection rates in England from 19 December, 2020 to 20 March, 2021.

Within the last decade, the Greenland ice sheet (GrIS) and its surroundings have experienced record high surface temperatures (Mote, 2007; Box et al., 2010), ice sheet melt extent (Fettweis et al., 2011) and record-low summer sea-ice extent (Nghiem et al., 2007). Using three independent data sets, we derive, for the first time, consistent ice-mass trends and temporal variations within seven major drainage basins from gravity fields from the Gravity Recovery and Climate Experiment (GRACE; Tapley et al., 2004), surface-ice velocities from Inteferometric Synthetic Aperture Radar (InSAR; Rignot and Kanagaratnam, 2006) together with output of the regional atmospheric climate modelling (RACMO2/GR; Ettema et al., 2009), and surface-elevation changes from the Ice, cloud and land elevation satellite (ICESat; Sørensen et al., 2011). We show that changing ice discharge (D), surface melting and subsequent run-off (M/R) and precipitation (P) all contribute, in a complex and regionally variable interplay, to the increasingly negative mass balance of the GrIS observed within the last decade. Interannual variability in P along the northwest and west coasts of the GrIS largely explains the apparent regional mass loss increase during 2002-2010, and obscures increasing M/R and D since the 1990s. In winter 2002/2003 and 2008/2009, accumulation anomalies in the east and southeast temporarily outweighed the losses by M/R and D that prevailed during 2003-2008, and after summer 2010. Overall, for all basins of the GrIS, the decadal variability of anomalies in P, M/R and D between 1958 and 2010 (w.r.t. 1961-1990) was significantly exceeded by the regional trends observed during the GRACE period (2002-2011). © 2012 Elsevier B.V.

Large uncertainties remain in the current and future contribution to sea level rise from Antarctica. Climate warming may increase snowfall in the continents interior, but enhance glacier discharge at the coast where warmer air and ocean temperatures erode the buttressing ice shelves. Here, we use satellite interferometric synthetic-aperture radar observations from 1992 to 2006 covering 85 of Antarcticas coastline to estimate the total mass flux into the ocean. We compare the mass fluxes from large drainage basin units with interior snow accumulation calculated from a regional atmospheric climate model for 1980 to 2004. In East Antarctica, small glacier losses in Wilkes Land and glacier gains at the mouths of the Filchner and Ross ice shelves combine to a near-zero loss of 4±61 Gt yr1. In West Antarctica, widespread losses along the Bellingshausen and Amundsen seas increased the ice sheet loss by 59 in 10 years to reach 132±60 Gt yr1 in 2006. In the Peninsula, losses increased by 140 to reach 60±46 Gt yr1 in 2006. Losses are concentrated along narrow channels occupied by outlet glaciers and are caused by ongoing and past glacier acceleration. Changes in glacier flow therefore have a significant, if not dominant impact on ice sheet mass balance. © 2008 Nature Publishing Group.

High-resolution (∼11 km) regional climate modeling shows total annual precipitation on the Greenland ice sheet for 1958-2007 to be up to 24% and surface mass balance up to 63% higher than previously thought. The largest differences occur in coastal southeast Greenland, where the much higher resolution facilitates capturing snow accumulation peaks that past five-fold coarser resolution regional climate models missed. The surface mass balance trend over the full 1958-2007 period reveals the classic pattern expected in a warming climate, with increased snowfall in the interior and enhanced runoff from the marginal ablation zone. In the period 1990-2007, total runoff increased significantly, 3% per year. The absolute increase in runoff is especially pronounced in the southeast, where several outlet glaciers have recently accelerated. This detailed knowledge of Greenland's surface mass balance provides the foundation for estimating and predicting the overall mass balance and freshwater discharge of the ice sheet. Copyright 2009 by the American Geophysical Union.

We use satellite and airborne altimetry to estimate annual mass changes of the Greenland Ice Sheet. We estimate ice loss corresponding to a sea-level rise of 6.9 ± 0.4 mm from April 2011 to April 2020, with a highest annual ice loss rate of 1.4 mm/yr sea-level equivalent from April 2019 to April 2020. On a regional scale, our annual mass loss timeseries reveals 10-15 m/yr dynamic thickening at the terminus of Jakobshavn Isbræ from April 2016 to April 2018, followed by a return to dynamic thinning. We observe contrasting patterns of mass loss acceleration in different basins across the ice sheet and suggest that these spatiotemporal trends could be useful for calibrating and validating prognostic ice sheet models. In addition to resolving the spatial and temporal fingerprint of Greenland's recent ice loss, these mass loss grids are key for partitioning contemporary elastic vertical land motion from longer-term glacial isostatic adjustment (GIA) trends at GPS stations around the ice sheet. Our ice-loss product results in a significantly different GIA interpretation from a previous ice-loss product.

The Greenland Ice Sheet is the largest land ice contributor to sea level rise. This will continue in the future but at an uncertain rate and observational estimates are limited to the last few decades. Understanding the long-term glacier response to external forcing is key to improving projections. Here we use historical photographs to calculate ice loss from 1880-2012 for Jakobshavn, Helheim, and Kangerlussuaq glacier. We estimate ice loss corresponding to a sea level rise of 8.1 ± 1.1 millimetres from these three glaciers. Projections of mass loss for these glaciers, using the worst-case scenario, Representative Concentration Pathways 8.5, suggest a sea level contribution of 9.1-14.9 mm by 2100. RCP8.5 implies an additional global temperature increase of 3.7 °C by 2100, approximately four times larger than that which has taken place since 1880. We infer that projections forced by RCP8.5 underestimate glacier mass loss which could exceed this worst-case scenario.