A new form of the cokriging equations

Myers developed a matrix form of the cokriging equations, but one that entails the solution of a large system of linear equations. Large systems are troublesome because of memory requirements and a general increase in the matrix condition number. We transform Myers’s system into a set of smaller systems, whose solution gives the classical kriging results, and provides simultaneously a nested set of lower dimensional cokriging results. In the course of developing the new formulation we make an interesting link to the Cauchy-Schwarz condition for the invertibility of a system, and another to a simple situation of coregionalization. In addition, we proceed from these new equations to a linear approximation to the cokriging results in the event that the crossvariograms are small, allowing one to take advantage of a recent results of Xie and others which proceeds by diagonalizing the variogram matrix function over the lag classes.     

A parameterisation for the threshold shear velocity to initiate deflation of dry and wet sediment

A new parameterisation for the threshold shear velocity to initiate deflation of dry and wet particles is presented. It is based on the balance of moments acting on particles at the instant of particle motion. The model hence includes a term for the aerodynamic forces, including the drag force, the lift force and the aerodynamic-moment force, and a term for the interparticle forces. The effect of gravitation is incorporated in both terms. Rather than using an implicit function for the effect of the aerodynamic forces as reported earlier in literature, a constant aerodynamic coefficient was introduced. From consideration of the van der Waals force between two particles, it was further shown that the effect of the interparticle cohesion force between two dry particles on the deflation threshold should be inversely proportional to the particle diameter squared. The interparticle force was further extended to include wet bonding forces. The latter were considered as the sum of capillary forces and adhesive forces. A model that expresses the capillary force as a function of particle diameter squared and the inverse of capillary potential was deduced from consideration of the well-known model of Fisher and the Young–Laplace equation. The adhesive force was assumed to be equal to tensile strength, and a function which is proportional to particle diameter squared and the inverse of the potential due to adhesive forces was derived. By combining the capillary-force model and the adhesive force model, the interparticle force due to wet bonding was simplified and written as a function of particle diameter squared and the inverse of matric potential. The latter was loglinearly related to the gravimetric moisture content, a relationship that is valid in the low-moisture content range that is important in the light of deflation of sediment by wind. By introducing a correction to force the relationship to converge to zero moisture content at oven dryness, the matric potential–moisture content relationship contained only one unknown model parameter, viz. moisture content at −1.5 MPa. Working out the model led to a rather simple parameterisation containing only three coefficients. Two parameters were incorporated in the term that applies to dry sediment and were determined by using experimental data as reported by Iversen and White [Sedimentology 29 (1982) 111]. The third parameter for the wet-sediment part of the model was determined from wind-tunnel experiments on prewetted sand and sandy loam aggregates. The model was validated using data from wind-tunnel experiments on the same but dry sediment, and on data obtained from simulations with the model of Chepil [Soil Sci. Soc. Am. Proc. 20 (1956) 288]. The experiments showed that soil aggregates should be treated as individual particles with a density equal to their bulk density. Furthermore, it was shown that the surface had to dry to a moisture content of about 75% of the moisture content at −1.5 MPa before deflation became sustained. The threshold shear velocities simulated with our model were found to be in good agreement with own observations and with simulations using Chepil's model.     

Groundwater control of mangrove surface elevation: Shrink and swell varies with soil depth

We measured monthly soil surface elevation change and determined its relationship to groundwater changes at a mangrove forest site along Shark River, Everglades National Park, Florida. We combined the use of an original design, surface elevation table with new rod-surface elevation tables to separately track changes in the mid zone (0–4 m), the shallow root zone (0–0.35 m), and the full sediment profile (0–6 m) in response to site hydrology (daily river stage and daily groundwater piezometric pressure). We calculated expansion and contraction for each of the four constituent soil zones (surface [accretion and erosion; above 0 m], shallow zone [0–0.35 m], middle zone [0.35–4 m], and bottom zone [4–6]) that comprise the entire soil column. Changes in groundwater pressure correlated strongly, with changes in soil elevation for the entire profile (Adjusted R² = 0.90); this relationship was not proportional to the depth of the soil profile sampled. The change in thickness of the bottom soil zone accounted for the majority (R² = 0.63) of the entire soil profile expansion and contraction. The influence of hydrology on specific soil zones and absolute elevation change must be considered when evaluating the effect of disturbances, sea level rise, and water management decisions on coastal wetland systems.     

New evidence for an extended occupation of the Provo shoreline and implications for regional climate change, Pleistocene Lake Bonneville, Utah, USA

Lake Bonneville was a climatically sensitive, closed-basin lake that occupied the eastern Great Basin during the late Pleistocene. Ongoing efforts to refine the record of lake level history are important for deciphering climate conditions in the Bonneville basin and for facilitating correlations with regional and global records of climate change. Radiocarbon data from this and other studies suggest that the lake oscillated at or near the Provo level much longer than depicted by current models of lake level change. Radiocarbon data also suggest that the lake dropped from threshold control much more rapidly than previously supposed. These revisions to the Lake Bonneville hydrograph, coupled with independent evidence of climate change from vegetation and glacial records, have important implications for conditions in the Bonneville basin and during the Pleistocene to Holocene transition.     

Facies of slurry-flow deposits, Britannia Formation (Lower Cretaceous), North Sea: implications for flow evolution and deposit geometry

ABSTRACT Mud‐rich sandstone beds in the Lower Cretaceous Britannia Formation, UK North Sea, were deposited by sediment flows transitional between debris flows and turbidity currents, termed slurry flows. Much of the mud in these flows was transported as sand‐ and silt‐sized grains that were approximately hydraulically equivalent to suspended quartz and feldspar. In the eastern Britannia Field, individual slurry beds are continuous over long distances, and abundant core makes it possible to document facies changes across the field. Most beds display regular areal grain‐size changes. In this study, fining trends, especially in the size of the largest grains, are used to estimate palaeoflow and palaeoslope directions. In the middle part of the Britannia Formation, stratigraphic zones 40 and 45, slurry flows moved from south‐west and south towards the north‐east and north. Most zone 45 beds lens out before reaching the northern edge of the field, apparently by wedging out against the northern basin slope. Zone 40 and 45 beds show downflow facies transitions from low‐mud‐content, dish‐structured and wispy‐laminated sandstone to high‐mud‐content banded units. In zone 50, at the top of the formation, flows moved from north to south or north‐west to south‐east, and their deposits show transitions from proximal mud‐rich banded and mixed slurried beds to more distal lower‐mud‐content banded and wispy‐laminated units. The contrasting facies trends in zones 40 and 45 and zone 50 may reflect differing grain‐size relationships between quartz and feldspar grains and mud particles in the depositing flows. In zones 40 and 45, quartz grains average 0·30–0·32 mm in diameter, ≈ 0·10 mm coarser than in zone 50. The medium‐grained quartz in zones 40 and 45 flows may have been slightly coarser than the associated mud grains, resulting in the preferential deposition of quartz in proximal areas and downslope enrichment of the flows in mud. In zone 50 flows, mud was probably slightly coarser than the associated fine‐grained quartz, resulting in early mud sedimentation and enrichment of the distal flows in fine‐grained quartz and feldspar. Mud particles in all flows may have had an effective grain size of ≈ 0·25 mm. Both mud content and suspended‐load fallout rate played key roles in the sedimentation of Britannia slurry flows and structuring of the resulting deposits. During deposition of zones 40 and 45, the area of the eastern Britannia Field in block 16/26 may have been a locally enclosed subbasin within which the depositing slurry flows were locally ponded. Slurry beds in the eastern Britannia Field are ‘lumpy’ sheet‐like bodies that show facies changes but little additional complexity. There is no thin‐bedded facies that might represent waning flows analogous to low‐density turbidity currents. The dominance of laminar, cohesion‐dominated shear layers during sedimentation prevented most bed erosion, and the deposystem lacked channel, levee and overbank facies that commonly make up turbidity current‐dominated systems. Britannia slurry flows, although turbulent and capable of size‐fractionating even fine‐grained sediments, left sand bodies with geometries and facies more like those deposited by poorly differentiated laminar debris flows.