Nonhydrostatic effects and the determination of icy satellites’ moment of inertia

We compare the moment of inertia (MOI) of a simple hydrostatic, two layer body as determined by the Radau–Darwin Approximation (RDA) to its exact hydrostatic MOI calculated to first order in the parameter q = Ω²R³/GM, where Ω, R, and M are the spin angular velocity, radius, and mass of the body, and G is the gravitational constant. We show that the RDA is in error by less than 1% for many configurations of core sizes and layer densities congruent with those of solid bodies in the Solar System. We then determine the error in the MOI of icy satellites calculated with the RDA due to nonhydrostatic effects by using a simple model in which the core and outer shell have slight degree 2 distortions away from their expected hydrostatic shapes. Since the hydrostatic shape has an associated stress of order ρΩ²R² (where ρ is density) it follows that the importance of nonhydrostatic effects scales with the dimensionless number σ/ρΩ²R², where σ is the nonhydrostatic stress. This highlights the likely importance of this error for slowly rotating bodies (e.g., Titan and Callisto) and small bodies (e.g., Saturn moons other than Titan). We apply this model to Titan, Callisto, and Enceladus and find that the RDA-derived MOI can be 10% greater than the actual MOI for nonhydrostatic stresses as small as ∼0.1 bars at the surface or ∼1 bar at the core–mantle boundary, but the actual nonhydrostatic stresses for a given shape change depends on the specifics of the interior model. When we apply this model to Ganymede we find that the stresses necessary to produce the same MOI errors as on Titan, Callisto, and Enceladus are an order of magnitude greater due to its faster rotation, so Ganymede may be the only instance where RDA is reliable. We argue that if satellites can reorient to the lowest energy state then RDA will always give an overestimate of the true MOI. Observations have shown that small nonhydrostatic gravity anomalies exist on Ganymede and Titan, at least at degree 3 and presumably higher. If these anomalies are indicative of the nonhydrostatic anomalies at degree 2 then these imply only a small correction to the MOI, even for Titan, but it is possible that the physical origin of nonhydrostatic degree 2 effects is different from the higher order terms. We conclude that nonhydrostatic effects could be present to an extent that allows Callisto and Titan to be fully differentiated.     

Observations of the Labrador Sea eddy field

This paper is an observational study of small-scale coherent eddies in the Labrador Sea, a region of dense water formation thought to be of considerable importance to the North Atlantic overturning circulation. Numerical studies of deep convection emphasize coherent eddies as a mechanism for the lateral transport of heat, yet their small size has hindered observational progress. A large part of this paper is therefore devoted to developing new methods for identifying and describing coherent eddies in two observational platforms, current meter moorings and satellite altimetry. Details of the current and water mass structure of individual eddy events, as they are swept past by an advecting flow, can then be extracted from the mooring data. A transition is seen during mid-1997, with long-lived boundary current eddies dominating the central Labrador Sea year-round after this time, and convectively formed eddies similar to those seen in deep convection modeling studies apparent prior to this time. The TOPEX / Poseidon altimeter covers the Labrador Sea with a loose “net” of observations, through which coherent eddies can seem to appear and disappear. By concentrating on locating and describing anomalous events in individual altimeter tracks, a portrait of the spatial and temporal variability of the underlying eddy field can be constructed. The altimeter results reveal an annual “pulsation” of energy and of coherent eddies originating during the late fall at a particular location in the boundary current, pinpointing the time and place of the boundary current-type eddy formation. The interannual variability seen at the mooring is reproduced, but the mooring site is found to be within a localized region of greatly enhanced eddy activity. Notably lacking in both the annual cycle and interannual variability is a clear relationship between the eddies or eddy energy and the intensity of wintertime cooling. These eddy observations, as well as hydrographic evidence, suggest an active role for boundary current dynamics in shaping the energetics and water mass properties of the interior region.     

Comment on “Complete Eulerian-mean tracer equation for coarse resolution OGCMs” by M. S. Dubovikov and V. M. Canuto

Dubovikov and Canuto (Dubovikov, M.S. and Canuto, V.M., Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. Astrophys. Fluid Dyn., 2006, 100, 197–214), after averaging the tracer conservation equation in density coordinates and transforming to height coordinates, concluded that present ocean models are missing important terms in their mean tracer equations. Here we point out some errors made by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in their isopycnal averaging procedure. We draw on the temporal-residual-mean (TRM) theory and show that when the isopycnal averaging and coordinate transformation are performed correctly, the tracer equations of present ocean circulation models are recovered. We therefore conclude that present ocean circulation models are not neglecting the leading order terms identified by Dubovikov and Canuto (2006 Dubovikov, MS and Canuto, VM. 2006. Complete Eulerian-mean tracer equation for coarse resolution OGCMs. Geophys. & Astrophys. Fluid Dynam., 100: 197–214. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]).     

Intergranular diffusion rates from the analysis of garnet surfaces: Implications for metamorphic equilibration

Novel approaches to garnet analysis have been used to assess rates of intergranular diffusion between different matrix phases and garnet porphyroblasts in a regionally metamorphosed staurolite‐mica‐schist from the Barrovian‐type area in Scotland. X‐ray maps and chemical traverses of planar porphyroblast surfaces reveal chemical heterogeneity of the garnet grain boundary linked to the nature of the adjacent matrix phase. The garnet preserves evidence of low temperature retrograde exchange with matrix minerals and diffusion profiles documenting cation movement along the garnet boundaries. Garnet–quartz and garnet–plagioclase boundaries preserve evidence of sluggish Mg, Mn and Fe diffusion at comparable rates to volume diffusion in garnet, whereas diffusion along garnet–biotite interfaces is much more effective. Evidence of particularly slow Al transport, probably coupled to Fe³⁺ exchange, is locally preserved on garnet surfaces adjacent to Fe‐oxide phases. The Ca distribution on the garnet surface shows the most complex behaviour, with long‐wavelength heterogeneities apparently unrelated to the matrix grain boundaries. This implies that the Ca content of garnet is controlled by local availability and is thought likely to reflect disequilibrium established during garnet growth. Geochemical anomalies on the garnet surfaces are also linked to the location of triple junctions between the porphyroblasts and the matrix phases, and imply enhanced transport along these channels. The slow rates of intergranular diffusion and the characteristics of different boundary types may explain many features associated with the prograde growth of garnet porphyroblasts. Thus, minerals such as quartz, Fe‐oxides and plagioclase whose boundaries with garnet are characterized by slow intergranular diffusion rates appear to be preferentially trapped as inclusions within porphyroblasts. As such grain boundary diffusion rates may be a significant kinetic impediment to metamorphic equilibrium and garnet may struggle to maintain chemical and textural equilibrium during growth in pelites.     

Review: The Yucat��n Peninsula karst aquifer, Mexico

The Yucatán Peninsula karst aquifer is one of the most extensive and spectacular karst aquifer systems on the planet. This transboundary aquifer system extends over an area of approximately 165,000? km² in México, Guatemala and Belize. The Triassic to Holocene Yucatán limestone platform is located in the vicinity of the North American/Caribbean plate boundary and has been reshaped by a series of tectonic events over its long geologic history. At the end of the Cretaceous period, the Yucatán Peninsula was hit by a large asteroid, which formed the Chicxulub impact crater. The Yucatán Peninsula karst aquifer hosts large amounts of groundwater resources which maintain highly diverse groundwater-dependent ecosystems. Large parts of the aquifer are affected by seawater intrusion. Anthropogenic pollution of the aquifer has been increasing over the past few decades, owing to relentless economic development and population growth on the Peninsula. This review summarizes the state of knowledge on the Yucatán Peninsula karst aquifer and outlines the main challenges for hydrologic research and practical groundwater-resources management on the Peninsula.     

The geology of kimberlite pipes of the Ekati property, Northwest Territories, Canada

This paper reviews key characteristics of kimberlites on the Ekati property, NWT, Canada. To date 150 kimberlites have been discovered on the property, five of which are mined for diamonds. The kimberlites intrude Archean basement of the central Slave craton. Numerous Proterozoic diabase dykes intrude the area. The Precambrian rocks are overlain by Quaternary glacial sediments. No Phanerozoic rocks are present. However, mudstone xenoliths and disaggregated sediment within the kimberlites indicate that late-Cretaceous and Tertiary cover (likely <200 m) was present at the time of emplacement. The Ekati kimberlites range in age from 45 to 75 Ma. They are mostly small pipe-like bodies (surface area mostly <3 ha but up to 20 ha) that typically extend to projected depths of 400–600 m below current surface. Pipe morphologies are strongly controlled by joints and faults. The kimberlites consist primarily of variably bedded volcaniclastic kimberlite (VK). This is dominated by juvenile constituents (olivine and lesser kimberlitic ash) and variable amounts of exotic sediment (primarily mud), with minor amounts of xenolithic wall-rock material (generally <5%). Kimberlite types include: mud-rich resedimented VK (mRVK); olivine-rich VK (oVK); sedimentary kimberlite; primary VK (PVK); tuffisitic kimberlite (TK) and magmatic kimberlite (MK). The presence and arrangement of these rock types varies widely. The majority of bodies are dominated by oVK and mRVK, but PVK is prominent in the lower portions of certain kimberlites. TK is rare. MK occurs primarily as precursor dykes but, in a few cases, forms pipe-filling intrusions. The internal geology of the kimberlites ranges from simple single-phase pipes (RVK or MK), to complex bodies with multiple, distinct units of VK. The latter include pipes infilled with steep, irregular VK blocks/wedges and at least one case in which the pipe is occupied by well-defined sub-horizontal VK phases, including a unique, 100-m-thick graded sequence. The whole-rock compositions of VK samples suggest significant loss of kimberlitic fines during eruption followed by variable dilution by surface sediment and concurrent incorporation of kimberlitic ash. Diamond distribution within the kimberlites reflects the amount and nature of mantle material sampled by individual kimberlite phases, but is modified considerably by eruption and depositional processes. The characteristics of the Ekati kimberlites are consistent with a two-stage emplacement process: (1) explosive eruption/s causing vent clearing followed by formation of a significant tephra rim/cone of highly fragmented, olivine-enriched juvenile material with varying amounts of kimberlitic ash and surface sediments (predominantly mud); and (2) infilling of the vent by direct deposition from the eruption column and/or resedimentation of crater rim materials. The presence of less fragmented, juvenile-rich PVK in the lower portions of certain pipes and the intrusion of large volumes of MK to shallow levels in some bodies suggest emplacement of relatively volatile-depleted, less explosive kimberlite in the later stages of pipe formation and/or filling. Explosive devolatilisation of CO₂-rich kimberlite magma is interpreted to have been the dominant eruption mechanism, but phreatomagmatism is thought to have played a role and, in certain cases, may have been dominant.     

Glaciomarine sedimentation and bottom current activity on the north-western and northern continental margins of Svalbard during the late Quaternary

Palaeo-bottom current strength of the West Spitsbergen Current (WSC) and the influence of the Svalbard-Barents Sea Ice Sheet (SBIS) on the depositional environment along the northern Svalbard margins are poorly known. Two gravity cores from the southern Yermak Plateau and the upper slope north of Nordaustlandet, covering marine isotope stage (MIS) 1 to MIS 5, are investigated. Five lithofacies, based on grain size distribution, silt/clay ratio, content and mean of sortable silt (SS), are distinguished to characterise the contourite-dominated sedimentary environments. In addition, depositional environments are described using total organic carbon (TOC), total sulphur (TS) and calcium carbonate (CaCO₃) contents of sediments. Facies A, containing coarse SS, suggests strong bottom current activity and good bottom water ventilation conditions as inferred from low TOC content. This facies was deposited during the glacial periods MIS 4, MIS 2 and during the late Holocene. Facies B is dominated by fine SS indicating weak bottom current and poor ventilation (cf. high TOC content of 1.2–1.6%), and correlates with the MIS 4/3 and MIS 2/1 transition periods. With an equal amount of clay and sand, fine SS and high content of TOC, facies C indicates reduced bottom current strength for intervals with sediment supply from proximal sources such as icebergs, sea ice or meltwater discharge. This facies was deposited during the last glacial maximum. Facies D represents mass-flow deposits on the northern Svalbard margin attributed to the SBIS advance at or near the shelf edge. Facies E sediments indicating moderate bottom current strength were deposited during MIS 5 and MIS 3, and during parts of MIS 2. This first late Quaternary proxy record of the WSC flow and sedimentation history from the northern Svalbard margin suggests that the oceanographic conditions and ice sheet processes have exerted first-order control on sediment properties.     

Snow distribution from SSM/I and its relationships to the hydroclimatology of the Mackenzie River Basin,Canada

The spatial and temporal distribution of snow cover extent (SCE) and snow water equivalent (SWE) play vital roles in the hydrology of northern watersheds. We apply remotely sensed Special Sensor Microwave Imager (SSM/I) data from 1988 to 2007 to explore the relationships between snow distribution and the hydroclimatology of the Mackenzie River Basin (MRB) of Canada and its major sub-basins. The Environment Canada (EC) algorithm is adopted to retrieve the SWE from SSM/I data. Moderate Resolution Imaging Spectroradiometer (MODIS) 8-day maximum snow cover extent products (MOD10A2) are used to estimate the different thresholds of retrieved SWE from SSM/I to classify the land cover as snow or no snow for various sub-basins in the MRB. The sub-basins have varying topography and hence different thresholds that range from 10 mm to 30 mm SWE. The accuracy of snow cover mapping based on the combination of several thresholds for the different sub-basins reaches ≈ 90%. The northern basins are found to have stronger linear relationships between the date on which snow cover fraction (SCF) reaches 50% or when SWE reaches 50% and mean air temperatures, than the southern basins. Correlation coefficients between SCF, SWE, and hydroclimatological variables show the new SCF products from SSM/I perform better than SWE from SSM/I to analyze the relationships with the regional hydroclimatology. Statistical models relating SCF and SWE to runoff indicate that the SCF and SWE from EC algorithms are able to predict the discharge in the early snow ablation seasons in northern watersheds.     

Effectiveness of post-fire salvage logging stream buffer management for hillslope erosion in the U.S. Inland Northwest Mountains

Active wildfire seasons in the western U.S. warrant the evaluation of post-fire forest management strategies. Ground-based salvage logging is often used to recover economic loss of burned timber. In unburned forests, ground-based logging often follows best management practices by leaving undisturbed areas near streams called stream buffers. However, the effectiveness of these buffers has not been tested in a post-wildfire setting. This experiment tested buffer width effectiveness with a novel field-simulated rill experiment using sediment-laden runoff (25 g/L) released over 40 min at evenly timed flow rates (50, 100 and 150 L/min) to measure surface runoff travel length and sediment concentration under unburned and high and low soil burn severity conditions at 2-, 10- and 22-month post-fire. High severity areas 2-month post-fire had rill lengths of up to 100 m. Rill length significantly decreased over time as vegetation regrowth provided ground cover. Sediment concentration and sediment dropout rate also varied significantly by soil burn severity. Sediment concentrations were 19 g/L for the highest flow 2-month post-fire and reduced to 6.9–14 g/L 10-month post-fire due to abundant vegetation recovery. The amount of sediment dropping out of the flow consistently increased over the study period with the low burn severity rate of 1.15 g L⁻¹ m⁻¹ approaching the unburned rate of 1.29 g L⁻¹ m⁻¹ by 2-year post-fire. These results suggest that an often-used standard, 15 m buffer, was sufficient to contain surface runoff and reduce sediment concentration on unburned sites, however buffers on high burn severity sites need to be eight times greater (120 m) immediately after wildfire and four times greater (60 m) 1-year post-fire. Low burn severity areas 1-year post-fire may need to be only twice the width of an unburned buffer (30 m), and 2-year post-fire these could return to unburned widths.