Ice loss from the Greenland ice sheet is one of the largest sources of contemporary sea-level rise (SLR). While process-based models place timescales on Greenland’s deglaciation, their confidence is obscured by model shortcomings including imprecise atmospheric and oceanic couplings. Here, we present a complementary approach resolving ice sheet disequilibrium with climate constrained by satellite-derived bare-ice extent, tidewater sector ice flow discharge and surface mass balance data. We find that Greenland ice imbalance with the recent (2000–2019) climate commits at least 274 ± 68 mm SLR from 59 ± 15 × 10 3 km 2 ice retreat, equivalent to 3.3 ± 0.9% volume loss, regardless of twenty-first-century climate pathways. This is a result of increasing mass turnover from precipitation, ice flow discharge and meltwater run-off. The high-melt year of 2012 applied in perpetuity yields an ice loss commitment of 782 ± 135 mm SLR, serving as an ominous prognosis for Greenland’s trajectory through a twenty-first century of warming.

ABSTRACTWhile the terms ‘glacier’ and ‘ice cap’ have distinct morphological meanings, no easily defined boundary or transition distinguishes one from the other. Despite this, the exponent of the power law function relating volume to surface area differs sharply for glaciers and ice caps, suggesting a fundamental distinction beyond a smoothly transitioning morphology. A standard percolation technique from statistical physics is used to show that valley glaciers are in fact differentiated from ice caps by an abrupt geometric transition. The crossover is a function of increasing glacier thickness, but it owes its existence more to the nature of the underlying bedrock topography than to specifics of glacier mechanics: the crossover is caused by a switch from directed flow that is constrained by surrounding bedrock topography to unconstrained radial flow of thicker ice that has subsumed the topography. The crossover phenomenon is nonlinear and rapid so that few if any glaciers will have geometries or dynamics that blend the two extremes. The exponents of scaling relationships change abruptly at the crossover from one regime to another; in particular, the volume/area scaling exponent will switch from γ = 1.375 for glaciers to γ = 1.25 for ice caps, with few, if any, ice bodies having exponents that fall between these values.

Volume‐area power law scaling, one of a set of analytical scaling techniques based on principals of dimensional analysis, has become an increasingly important and widely used method for estimating the future response of the world's glaciers and ice caps to environmental change. Over 60 papers since 1988 have been published in the glaciological and environmental change literature containing applications of volume‐area scaling, mostly for the purpose of estimating total global glacier and ice cap volume and modeling future contributions to sea level rise from glaciers and ice caps. The application of the theory is not entirely straightforward, however, and many of the recently published results contain analyses that are in conflict with the theory as originally described by Bahr et al. (1997). In this review we describe the general theory of scaling for glaciers in full three‐dimensional detail without simplifications, including an improved derivation of both the volume‐area scaling exponent γ and a new derivation of the multiplicative scaling parameter c. We discuss some common misconceptions of the theory, presenting examples of both appropriate and inappropriate applications. We also discuss potential future developments in power law scaling beyond its present uses, the relationship between power law scaling and other modeling approaches, and some of the advantages and limitations of scaling techniques.

Previous studies of the Iterated Prisoner’s Dilemma Game (IPDG) focus on the optimal strategies for accumulating points against another player or the evolution of cooperation. Instead, this paper expands upon the possible complexity in interactions by using a Cellular Automaton (CA) model to simulate large numbers of players competing within a limited space. Unlike previous works, we introduce a method for creating a wide variety of deterministic rules by mapping each possible interaction to a binary number. We then prove the computational universality of the resulting IPDG CA. An analysis of the number of interactions leads to the discovery of interesting properties when allowing only enough iterations for a strategy to use its “transient” instructions. The implications of universal computation (UC) are also discussed.

Estimating a glacier's volume by inferring properties at depth (e.g. bed topography or basal slip) from properties observed at the surface (e.g. area and slope) creates a calculation instability that grows exponentially with the size of the glacier. Random errors from this inversion instability can overwhelm all other sources of error and can corrupt thickness and volume calculations, unless problematic short spatial wavelengths are specifically excluded. Volume/area scaling inherently filters these short wavelengths and automatically eliminates the instability, while numerical inversions can also give stable solutions by filtering the correct wavelengths explicitly, as is frequently done when 'regularizing' a model. Each of the scaling and numerical techniques has applications to which it is better suited, and there are trade-offs in resolution and accuracy; but when calculating volume, neither the modeling nor the scaling approach offers a fundamental advantage over the other. Both are significantly limited by the inherently 'ill-posed' inversion, and even though both provide stable volume solutions, neither can give unique solutions.

Sea-level changes on a wide range of time and space scales. This article considers changes in mean sea level, that is, sea level averaged over a sufficient period of time to remove fluctuations associated with surface waves, tides, and individual storm surge events. Changes in sea level changes over the last hundred years or so and on how it might change over the next one hundred years are or particular interest. However, to understand these changes requires consideration of sea level since the last glacial maximum 20,000 years ago. The longer-term implications of changes in the Earth's climate arising from changes in atmospheric greenhouse gas concentrations are also considered.

Most glaciers and ice caps (GIC) are out of balance with the current climate. To return to equilibrium, GIC must thin and retreat, losing additional mass and raising sea level. Because glacier observations are sparse and geographically biased, there is an undersampling problem common to all global assessments. Here, we further develop an assessment approach based on accumulation-area ratios (AAR) to estimate committed mass losses and analyze the undersampling problem. We compiled all available AAR observations for 144 GIC from 1971 to 2010, and found that most glaciers and ice caps are farther from balance than previously believed. Accounting for regional and global undersampling errors, our model suggests that GIC are committed to additional losses of 32 ± 12% of their area and 38 ± 16% of their volume if the future climate resembles the climate of the past decade. These losses imply global mean sea-level rise of 163 ± 69 mm, assuming total glacier volume of 430 mm sea-level equivalent. To reduce the large uncertainties in these projections, more long-term glacier measurements are needed in poorly sampled regions.

Abstract. Estimating a glacier's volume by inferring properties at depth from properties observed at the surface creates an instability that grows exponentially with the size of the glacier. Random errors from this instability can overwhelm the volume calculation unless problematic short spatial wavelengths are specifically excluded. Volume-area scaling inherently filters these short wavelengths and automatically eliminates the instability, but typical numerical inversions must filter the correct wavelengths explicitly. The world's total glacier and ice cap (GIC) volume is calculated from the sum of hundreds of thousands of ice masses, dramatically reducing the random error from the "ill-posed" instability. However, the variance of the total GIC volume estimate will be exponentially larger if the instability is not carefully controlled. When all other considerations are equal, greater confidence should be placed in total volume estimates that eliminate the ill-posed instability versus those estimates that do not.

Abstract. A single large glacier can contain hundreds of millions of times the mass of a small glacier. Nevertheless, small glaciers are so numerous that their contribution to the world's total ice volume is significant and may be a notable source of error if excluded. With current glacier inventories, total volume errors on the order of 10 % are possible at both global and regional scales. However, errors of less than 1 % require glaciers that are smaller than those available in some inventories. Such accuracy requires a global list of all glaciers and ice caps (GIC) as small as 1 km2, and for regional estimates requires substantially smaller sizes. For some regions, volume errors of less than 5 % require a complete list of all glaciers down to the smallest conceivable sizes. For this reason, sea-level rise estimates and other total mass and total volume analyses cannot ignore the world's smallest glaciers without careful justification.

Agreed, and we would add the following text to the second paragraph (giving this point some prominence in the paper). “It is entirely possible that the smallest glaciers’ sealevel contribution could be underestimated, in large part for practical reasons which make a catalog of the smallest glaciers expensive, time consuming, and error prone due to difficulties of separating small glaciers from snow patches (Bolch et al., 2010). As an inventory’s size threshold is lowered, relative errors may rise, but with the smallest glaciers rapidly melting and possibly disappearing over the next few decades (Mernild et al, 2011; Radić and Hock, 2011), the potentially rapid sea-level contribution of these smallest glaciers should be considered, or systematic errors due to their exclusion should be estimated.”

A single large glacier can contain tens of millions of times the mass of a small glacier. Nevertheless, very small glaciers (with area ≤1 km2) are so numerous that their contribution to the world's total ice volume is significant and may be a notable source of error if excluded. With current glacier inventories, total global volume errors on the order of 10% are possible. However, to reduce errors to below 1% requires the inclusion of glaciers that are smaller than those recorded in most inventories. At the global scale, 1% accuracy requires a list of all glaciers and ice caps (GIC, exclusive of the ice sheets) larger than 1 km2, and for regional estimates requires a complete list of all glaciers down to the smallest possible size. For this reason, sea-level rise estimates and other total mass and total volume analyses should not omit the world's smallest glaciers. In particular, upscaling GIC inventories has been common practice in sea level estimates, but downscaling may also be necessary to include the smallest glaciers.

No single flow model can simulate all possible glaciers and ice sheets without violating fundamental tenets of computational science. The root cause is not one of numerical sophistication, precision or accurate initial conditions. Instead, using flow and transport as data transmission, glaciers inadvertently function as information processors. This computational capability confers a level of complexity that inherently limits our ability to accurately and efficiently predict glacier flow and therefore, for example, to forecast those aspects of climate systems that depend on glaciers. In particular, even with considerable future advancements in glacier physics, computational theory shows that no dramatic improvements in numerical speed are likely when compared to today's glacier models. Therefore, to increase speed and resolution, the next generation of climate and sea-level models must rely on simulations tailored to specific ice-sheet geometries rather than general-purpose glacier flow models. However, because glaciers process information, entirely new computation-theoretic advances in glaciology are possible, and concepts from information entropy may help to define new glacier scaling relationships and identify which geometries will be most problematic for modeling.

Regularly spaced bumps that arise on ski slopes defy intuition by migrating uphill, even though skiers and snow move downhill.

Despite significant efforts, obesity continues to be a major public health problem, and there are surprisingly few effective strategies for its prevention and treatment. We now realize that healthy diet and activity patterns are difficult to maintain in the current physical environment. Recently, it was suggested that the social environment also contributes to obesity. Therefore, using network-based interaction models, we simulate how obesity spreads along social networks and predict the effectiveness of large-scale weight management interventions. For a wide variety of conditions and networks, we show that individuals with similar BMIs will cluster together into groups, and if left unchecked, current social forces will drive these groups toward increasing obesity. Our simulations show that many traditional weight management interventions fail because they target overweight and obese individuals without consideration of their surrounding cluster and wider social network. The popular strategy for dieting with friends is shown to be an ineffective long-term weight loss strategy, whereas dieting with friends of friends can be somewhat more effective by forcing a shift in cluster boundaries. Fortunately, our simulations also show that interventions targeting well-connected and/or normal weight individuals at the edges of a cluster may quickly halt the spread of obesity. Furthermore, by changing social forces and altering the behavior of a small but random assortment of both obese and normal weight individuals, highly effective network-driven strategies can reverse current trends and return large segments of the population to a healthier weight.

One of the most easily measured dimensions of a glacier, the accumulation area, is linked to future changes in glacier volume and consequent changes in sea level. Currently observed accumulation areas are too small, forcing glaciers to lose 27% of their volume to attain equilibrium with current climate. As a result, at least 184 ± 33 mm of sea‐level rise are necessitated by mass wastage of the world's mountain glaciers and ice caps even if the climate does not continue to warm. If the climate continues to warm along current trends, a minimum of 373 ± 21 mm of sea‐level rise over the next 100 years is expected from glaciers and ice caps. When compared to recent estimates from all other sources, melt water from glaciers must be considered as a particularly important fraction of the total sea‐level rise expected this century.

Since the mid-19th century, most glaciers have been losing area and volume. This loss of area has not been homogeneous in time and space, and direct observations are sparse, making regional and global estimates of glacier change difficult. This paper focuses on developing a single index for monitoring glacier change, one that would be particularly useful for remote-sensing applications. We combine the results of direct glacier mass-balance observations B, total glacier area S and accumulation area S(c) derived from maps or remotely sensed images. Using the accumulation-area ratio (AAR = S(c)/S), we note the differences between observed AAR, time-averaged < AAR > and the equilibrium state AAR(0), as determined by its value at B = 0 from a regression of B(AAR). We suggest that alpha(d) = (< AAR > - AAR(0))/ AAR(0) quantifies the difference between the currently observed state of glaciers and their equilibrium state and measures the delay in the dynamic response of S relative to the climatic response of S(c). Using all available observations for the period 1961-2004, alpha(d) approximate to -65% for tropical glaciers, which implies their rapid shrinkage as S continues to decrease and 'catch up' with S(c). During the same period, mid-latitude and polar glaciers show less negative values Of alpha(d). Of 86 glaciers from all latitudes and regions, only 11 show positive alpha(d) at any time between 1961 and 2004. Averaged over 1961-2004, alpha(d) is -15.1 +/- 2.2%, and < B > is -360 +/- 42 mm a(-1) w.e. Values for AAR(0) range between about 40% and 80%, but the bulk of the equilibrium values are between 50% and 60%. The average AAR(0) is 57.9 +/- 0.9% and has remained stable over time (the equilibrium AAR has not changed with climate). Overall, the observed negative alpha(d) suggests a committed retreat of glaciers and their continuing contribution to sea level even if global temperature is held constant.