ALBERT

Description: This study explores an approach that simultaneously estimates Antarctic mass balance and glacial isostatic adjustment (GIA) through the combination of satellite gravity and altimetry data sets. The results improve upon previous efforts by incorporating a firn densification model to account for firn compaction and surface processes as well as reprocessed data sets over a slightly longer period of time. A range of different Gravity Recovery and Climate Experiment (GRACE) gravity models were evaluated and a new Ice, Cloud, and Land Elevation Satellite (ICESat) surface height trend map computed using an overlapping footprint approach. When the GIA models created from the combination approach were compared to in situ GPS ground station displacements, the vertical rates estimated showed consistently better agreement than recent conventional GIA models. The new empirically derived GIA rates suggest the presence of strong uplift in the Amundsen Sea sector in West Antarctica (WA) and the Philippi/Denman sectors, as well as subsidence in large parts of East Antarctica (EA). The total GIA-related mass change estimates for the entire Antarctic ice sheet ranged from 53 to 103 Gt yr−1, depending on the GRACE solution used, with an estimated uncertainty of ±40 Gt yr−1. Over the time frame February 2003–October 2009, the corresponding ice mass change showed an average value of −100 ± 44 Gt yr−1 (EA: 5 ± 38, WA: −105 ± 22), consistent with other recent estimates in the literature, with regional mass loss mostly concentrated in WA. The refined approach presented in this study shows the contribution that such data combinations can make towards improving estimates of present-day GIA and ice mass change, particularly with respect to determining more reliable uncertainties.

Description: The sea level contribution from glacial sources has been accelerating during the first decade of the 21st Century (Meier et al., 2007; Velicogna, 2009). This contribution is not distributed uniformly across the world's oceans due to both oceanographic and gravitational effects. We compute the sea level signature for ice mass fluxes due to changes in the gravity field, Earth's rotation and related effects for the nine year period 2000–2008. Mass loss from Greenland results in a relative sea level (RSL) reduction for much of North Western Europe and Eastern Canada. RSL rise from this source is concentrated around South America. Losses in West Antarctica marginally compensate for this and produce maxima along the coastlines of North America, Australia and Oceania. The combined far-field pattern of wastage from all ice melt sources, is dominated by losses from the ice sheets and results in maxima at latitudes between 20° N and 40° S across the Pacific and Indian Oceans, affecting particularly vulnerable land masses in Oceania. The spatial pattern of RSL variations from ice mass losses used in this study is time-invariant and cumulative. Thus, sea level rise, based on the gravitational effects from the ice losses considered here, will be amplified for this sensitive region.

Description: The sea level contribution from glacial sources has been accelerating during the 21st century (Meier et al., 2007; Velicogna, 2009). This contribution is not distributed uniformly across the world's oceans due to both oceanographic and gravitational effects. We compute the sea level signature of 21st century ice mass fluxes due to changes in the gravity field, Earth's rotation and related effects. Mass loss from Greenland results in a relative sea level (RSL) reduction for much of North Western Europe and Eastern Canada. RSL rise from this source is concentrated around South America. Losses in West Antarctica marginally compensate for this and produce maxima along the coastlines of North America, Australia and Oceania. The combined far-field pattern of wastage from all ice melt sources, is dominated by losses from the ice sheets and results in maxima at latitudes between 20° N and 40° S across the Pacific and Indian Oceans, affecting particularly vulnerable land masses in Oceania. The spatial pattern of RSL variations due to the observed ice mass loss is temporally invariant. Thus, sea level rise, based on the land ice losses considered here, will be amplified for this sensitive region.

Description: This study explores an approach that simultaneously estimates Antarctic mass balance and glacial isostatic adjustment (GIA) through the combination of satellite gravity and altimetry data sets. The results improve upon previous efforts by incorporating reprocessed data sets over a longer period of time, and now include a firn densification model to account for firn compaction and surface processes. A range of different GRACE gravity models were evaluated, as well as a new ICESat surface height trend map computed using an overlapping footprint approach. When the GIA models created from the combination approach were compared to in-situ GPS ground station displacements, the vertical rates estimated showed consistently better agreement than existing GIA models. In addition, the new empirically derived GIA rates suggest the presence of strong uplift in the Amundsen Sea and Philippi/Denman sectors, as well as subsidence in large parts of East Antarctica. The total GIA mass change estimates for the entire Antarctic ice sheet ranged from 53 to 100 Gt yr−1, depending on the GRACE solution used, and with an estimated uncertainty of ±40 Gt yr−1. Over the time frame February 2003–October 2009, the corresponding ice mass change showed an average value of −100 ± 44 Gt yr−1 (EA: 5 ± 38, WA: −105 ± 22), consistent with other recent estimates in the literature, with the mass loss mostly concentrated in West Antarctica. The refined approach presented in this study shows the contribution that such data combinations can make towards improving estimates of present day GIA and ice mass change, particularly with respect to determining more reliable uncertainties.

Description: Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.

Description: We use three methods to identify power-law scaling of multi-scale log air permeability data collected by Tidwell and Wilson on the faces of a laboratory-scale block of Topopah Spring tuff: method of moments (M), Extended Self-Similarity (ESS) and a generalized version thereof (G-ESS). All three methods focus on q-th-order sample structure functions of absolute increments. Most such functions exhibit power-law scaling at best over a limited midrange of experimental separation scales, or lags, which are sometimes difficult to identify unambiguously by means of M. ESS and G-ESS extend this range in a way that renders power-law scaling easier to characterize. Our analysis confirms the superiority of ESS and G-ESS over M in identifying the scaling exponents, ξ(q), of corresponding structure functions of orders q, suggesting further that ESS is more reliable than G-ESS. The exponents vary in a nonlinear fashion with q as is typical of real or apparent multifractals. Our estimates of the Hurst scaling coefficient increase with support scale, implying a reduction in roughness (anti-persistence) of the log permeability field with measurement volume. The finding by Tidwell and Wilson that log permeabilities associated with all tip sizes can be characterized by stationary variogram models, coupled with our findings that log permeability increments associated with the smallest tip size are approximately Gaussian and those associated with all tip sizes scale show nonlinear variations in ξ(q) with q, are consistent with a view of these data as a sample from a truncated version (tfBm) of self-affine fractional Brownian motion (fBm). Since in theory the scaling exponents, ξ(q), of tfBm vary linearly with q we conclude that nonlinear scaling in our case is not an indication of multifractality but an artifact of sampling from tfBm. This allows us to explain theoretically how power-law scaling of our data, as well as of non-Gaussian heavy-tailed signals subordinated to tfBm, are extended by ESS. It further allows us to identify the functional form and estimate all parameters of the corresponding tfBm based on sample structure functions of first and second orders.

Description: Spatial statistics of earth and environmental (as well as many other) data tend to vary with scale. Common manifestations of scale-dependent statistics include a tendency of increments to have symmetric, non-Gaussian frequency distributions characterized by heavy tails that decay with separation distance or lag; power-law scaling of sample structure functions (statistical moments of absolute increments) in midranges of lags; linear relationships between log structure functions of successive orders at all lags, known as extended self-similarity or ESS; and nonlinear scaling of structure function power-law exponents with function order, a phenomenon commonly attributed in the literature to multifractals. Elsewhere we proposed, explored and demonstrated a new method of geostatistical inference that captures all of these phenomena within a unified theoretical framework. The framework views data as samples from random fields constituting scale-mixtures of truncated (monofractal) fractional Brownian motion (tfBm) or fractional Gaussian noise (tfGn). Important questions not addressed in previous studies concern the distribution and statistical scaling of extreme incremental values. Of special interest in hydrology (and many other areas) are statistics of absolute increments exceeding given thresholds, known as peaks over thresholds or POTs. In this paper we explore for the first time the statistical behavior of POTs associated with samples from scale-mixtures of tfBm or tfGn. We are fortunate to have at our disposal thousands of neutron porosity values from six deep boreholes, in three diverse depositional environments, which we show possess the properties of such samples thus following the theory we proposed. The porosity data are of additional value in revealing a remarkable transition from one scaling regime to another at certain lags. The phenomena we uncover are of fundamental importance for the analysis of fluid flow and solute as well as particulate transport in complex hydrogeologic environments.

Description: Climate change causes global mean sea level to rise due to thermal expansion of seawater and loss of land ice from mountain glaciers, ice caps and ice sheets. Locally, sea level can strongly deviate from the global mean rise due to changes in wind and ocean currents. In addition, gravitational adjustments redistribute seawater away from shrinking ice masses. However, the land ice contribution to sea level rise (SLR) remains very challenging to model, and comprehensive regional sea level projections, which include appropriate gravitational adjustments, are still a nascent field (Katsman et al., 2011; Slangen et al., 2011). Here, we present an alternative approach to derive regional sea level changes for a range of emission and land ice melt scenarios, combining probabilistic forecasts of a simple climate model (MAGICC6) with the new CMIP5 general circulation models. The contribution from ice sheets varies considerably depending on the assumptions for the ice sheet projections, and thus represents sizeable uncertainties for future sea level rise. However, several consistent and robust patterns emerge from our analysis: at low latitudes, especially in the Indian Ocean and Western Pacific, sea level will likely rise more than the global mean (mostly by 10–20%). Around the northeastern Atlantic and the northeastern Pacific coasts, sea level will rise less than the global average or, in some rare cases, even fall. In the northwestern Atlantic, along the American coast, a strong dynamic sea level rise is counteracted by gravitational depression due to Greenland ice melt; whether sea level will be above- or below-average will depend on the relative contribution of these two factors. Our regional sea level projections and the diagnosed uncertainties provide an improved basis for coastal impact analysis and infrastructure planning for adaptation to climate change.

Description: Climate change causes global mean sea level to rise due to thermal expansion of seawater and loss of land ice from mountain glaciers, ice caps and ice-sheets. Locally, sea-level changes can strongly deviate from the global mean due to ocean dynamics. In addition, gravitational adjustments redistribute seawater away from shrinking ice masses, an effect currently not incorporated in climate models. Here, we provide probabilistic projections of sea level changes along the world's coastlines for the end of the 21st century under the new RCP emission scenarios, taking into account uncertainties across the cause-effect chain from greenhouse-gas emissions to ocean heat uptake and regional land-ice melt. At low latitudes, especially in the Indian Ocean and Western Pacific, sea level will likely rise more than the global mean (mostly by 10–20%, but up to 45% in Tokyo area). Around the North Atlantic and the North-Eastern Pacific coasts, sea level will rise less than the global average or, in some rare cases, even fall. Our probabilistic regional sea level projections provide an improved basis for coastal impact analysis and infrastructure planning for adaptation to climate change.

Description: We analyze the scaling behaviors of two field-scale log permeability data sets showing heavy-tailed frequency distributions in three and two spatial dimensions, respectively. One set consists of 1-m scale pneumatic packer test data from six vertical and inclined boreholes spanning a decameters scale block of unsaturated fractured tuffs near Superior, Arizona, the other of pneumatic minipermeameter data measured at a spacing of 15 cm along three horizontal transects on a 21 m long and 6 m high outcrop of the Upper Cretaceous Straight Cliffs Formation, including lower-shoreface bioturbated and cross-bedded sandstone near Escalante, Utah. Order q sample structure functions of each data set scale as a power ξ(q) of separation scale or lag, s, over limited ranges of s. A procedure known as extended self-similarity (ESS) extends this range to all lags and yields a nonlinear (concave) functional relationship between ξ(q) and q. Whereas the literature tends to associate extended and nonlinear power-law scaling with multifractals or fractional Laplace motions, we have shown elsewhere that (a) ESS of data having a normal frequency distribution is theoretically consistent with (Gaussian) truncated (additive, self-affine, monofractal) fractional Brownian motion (tfBm), the latter being unique in predicting a breakdown in power-law scaling at small and large lags, and (b) nonlinear power-law scaling of data having either normal or heavy-tailed frequency distributions is consistent with samples from sub-Gaussian random fields or processes subordinated to tfBm or truncated fractional Gaussian noise (tfGn), stemming from lack of ergodicity which causes sample moments to scale differently than do their ensemble counterparts. Here we (i) demonstrate that the above two data sets are consistent with sub-Gaussian random fields subordinated to tfBm or tfGn and (ii) provide maximum likelihood estimates of parameters characterizing the corresponding Lévy stable subordinators and tfBm or tfGn functions.