Creation of Histograms for Data in Various Mineral Resource and Engineering Problems: A Review of Existing Methods and a Proposed New Method to Define Bin Number

Histograms are widely used in geosciences for data analysis and visualization. In cases where a distribution is not fitted to data, histograms are often used to address various sampling- and interpolation-related aspects. However, the results of these applications are substantially affected by the histogram’s number of bins as determined by several binning methods. This paper proposes a new binning approach and compares it with various standard approaches to demonstrate the relative performance of the new approach. Cut-off grade optimization for polymetallic deposits, Monte-Carlo modeling, and derivation of conditional distribution, all of which use histograms, are used as case studies. The proposed technique is based on calculating the squared error for each bin in a histogram, and combining the error values to evaluate the total error for each histogram. The new technique then selects the bin number which minimizes the total error. The results showed that the new binning approach is well suited for binning small datasets and can be used in geoscience applications if needed.     

A brief summary of Dr. G. V. Rao’s research interests

A brief summary of Dr. G. V. Rao's research interests is presented. Many of his earlier studies were in conjunction with the summer Monsoon Experiment of 1979 (MONEX-79). These included: 1) the structure of the Somali jet based on aerial observations; 2) sea-level air trajectories over the equatorial Indian Ocean; 3) structural features of the east African low-level flow; 4) effects of Indian Ocean surface temperature anomaly patterns on the summer monsoon circulations; 5) structures of the monsoon low-level flow over the Arabian Sea; 6) characteristics and momentum-flux budgets of the Arabian Sea convective bands; and 7) evaporation and precipitation over the Arabian Sea during the monsoon seasons. Dr. Rao's research efforts in recent years had focused on case studies of mesocyclones spawned by tropical cyclones (TCs) in Florida using Doppler radar data and a mesoscale numerical model. These included: 1) research on tornadic mesocyclones spawned by TC Earl in 1998; 2) documentation of subtle differences between tornadic and non-tornadic mesocyclones in TC Floyd in 1999; and 3) numerical simulation of the tornadic environment observed in peninsular Florida during TC Earl in 1998. Preliminary findings show that the supercells' cold pools interacted with an existing boundary resulting in increased baroclinicity and horizontal vorticity, and a maximization of the tornado production potential by the updrafts. The model successfully simulated the mesoscale features of the mesocyclones and the tornadic environment observed during TC Earl. A 24 h simulation of accumulated rainfall within the inner domain agreed well with the observed precipitation pattern over the region.     

Multiple-pumped-well aquifer test to determine the anisotropic properties of a karst limestone aquifer in Pasco County, Florida, USA

Groundwater-level data from an aquifer test utilizing four pumped wells conducted in the South Pasco wellfield in Pasco County, Florida, USA, were analyzed to determine the anisotropic transmissivity tensor, storativity, and leakance in the vicinity of the wellfield. A weighted least-squares procedure was used to analyze drawdowns measured at eight observation wells, and it was determined that the major axis of transmissivity extends approximately from north to south and the minor axis extends approximately from west to east with an angle of anisotropy equal to N4.54°W. The transmissivity along the major axis ${\left( {T_{{\xi \xi }} } \right)}$ is 14,019 m² day^–1, and the transmissivity along the minor axis ${\left( {T_{{\eta \eta }} } \right)}$ is 4,303 m² day^–1. The equivalent transmissivity $T_{e} = {\left( {T_{{\xi \xi }} T_{{\eta \eta }} } \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} = 7,767{{\text{m}}^{2} } \mathord{\left/ {\vphantom {{{\text{m}}^{2} } {{\text{day}}^{{ - {\text{1}}}} }}} \right. \kern-0em} {{\text{day}}^{{ - {\text{1}}}} }$ , and the ratio of anisotropy is 3.26. The storativity of the aquifer is 7.52?×?10^?4, and the leakance of the overlying confining unit is 1.37?×?10^?4 day^?1. The anisotropic properties determined for the South Pasco wellfield in this investigation confirm the results of previous aquifer tests conducted in the wellfield and help to quantify the NW–SE to NE–SW trends for regional fracture patterns and inferred solution-enhanced flow zones in west-central Florida.     

Molybdenite in calcium-aluminum-rich inclusions in the Allende meteorite

The first observations of molybdenite in a meteorite have been made in two CaAl-rich inclusions in the Allende chondrite. The mineral occurs as single individuals completely enclosed in high Ni metal (62–64.5 wt. % Ni). The association with refractories is consistent with thermodynamic calculations which predict that Mo is a high temperature condensate even when nucleation constraints are imposed on the formation of a metal phase. Kinetic factors (including nucleation constraints) appear to have played an important role in the formation of molybdenite and the associated sulfides, magnetite and high nickel metal.     

Mid-latitude Southern Indian Ocean response to Northern Hemisphere Heinrich events

The lack of temporal resolution and accurate chronology of Southern Ocean marine cores has hampered comparison of glacial millennial-scale oscillations between the Southern Ocean, Antarctic ice and other records from both hemispheres. In this study, glacial climate variability is investigated over the last 50 ka using a multi-proxy approach. A precise chrono-stratigraphy was developed on the high-sedimentation rate core MD94-103 (Indian Southern Ocean, 45°35′S 86°31′E, 3560 m water depth) by geomagnetic synchronization between the later core and NAPIS75, and ¹⁴C dates. High-resolution time-series of δ¹⁸O in planktonic foraminifera Globigerina bulloides and Neogloboquadrina pachyderma, and sea surface temperatures (SSTs) estimated from the alkenone U^K′₃₇ index and foraminifera assemblages have been generated. Temporal evolution of the two temperature proxy records is notably different during the last glacial period. While foraminifera data indicate a consistent cooling towards the last glacial maximum, anomalous warm glacial alkenone temperatures suggest a strong advection of warm “detrital” alkenones by surface waters of the Agulhas current. Superimposed to this general trend, during Heinrich events, foraminiferal SSTs point to warmer surface waters, while concurrent alkenone SSTs exhibit apparent coolings probably caused by enhanced local alkenone production. By analogy to modern observations, possible influence of ENSO-like conditions on the subantarctic Southern Ocean SSTs is discussed.     

Mantle convection with a brittle lithosphere: thoughts on the global tectonic styles of the Earth and Venus

Plates are an integral part of the convection system in the fluid mantle, but plate boundaries are the product of brittle faulting and plate motions are strongly influenced by the existence of such faults. The conditions for plate tectonics are studied by considering brittle behaviour, using Byerlee's law to limit the maximum stress in the lithosphere, in a mantle convection model with temperature-dependent viscosity.
When the yield stress is high, convection is confined below a thick, stagnant lithosphere. At low yield stress, brittle deformation mobilizes the lithosphere which becomes a part of the overall circulation; surface deformation occurs in localized regions close to upwellings and downwellings in the system. At intermediate levels of the yield stress, there is a cycling between these two states: thick lithosphere episodically mobilizes and collapses into the interior before reforming.
The mobile-lid regime resembles convection of a fluid with temperature-dependent viscosity and the boundary-layer scalings are found to be analogous. This regime has a well defined Nusselt number–Rayleigh number relationship which is in good agreement with scaling theory. The surface velocity is nearly independent of the yield stress, indicating that the 'plate' motion is resisted by viscous stresses in the mantle.
Analysis suggests that mobilization of the Earth's lithosphere can occur if the friction coefficient in the lithosphere is less than 0.03–0.13—lower than laboratory values but consistent with seismic field studies. On Venus, the friction coefficient may be high as a result of the dry conditions, and brittle mobilization of the lithosphere would then be episodic and catastrophic.     

Water budget and vertical conductance for Lowry (Sand Hill) Lake in north-central Florida, USA

Water-budget components and the vertical conductance were determined for Lowry (Sand Hill) Lake in north-central Florida, USA. In this type of lake, which interacts with both the surface-water and groundwater systems, the inflow components are precipitation, surface-water inflow, groundwater inflow, and direct runoff (i.e. overland flow), and the outflow components are evaporation, groundwater outflow, and surface-water outflow. In a lake and groundwater system that is typical of many karst lakes in Florida, a large part of the groundwater outflow occurs by means of vertical leakage through an underlying confining unit to a deeper, highly transmissive aquifer called the upper Floridan aquifer. The water-budget component that represents vertical leakage to the upper Floridan aquifer was calculated as a residual using the water-budget equation. For the 13 month period from August 1994 to August 1995, relative to the surface area of the lake, rainfall at Lowry Lake was 1.55 m yr⁻¹, surficial aquifer inflow was 0.79 m yr⁻¹, surface-water inflow was 1.92 m yr⁻¹, and direct runoff was 0.01 m yr⁻¹. Lake evaporation was 1.11 m yr⁻¹, and surface-water outflow was 1.61 m yr⁻¹. The lake stage increased 0.07 m yr⁻¹, and the vertical leakage to the upper Floridan aquifer was 1.48 m yr⁻¹. Surficial aquifer outflow from the lake was negligible. At Lowry Lake, vertical leakage is a major component of the water budget, comprising about 35% of the outflow during the study period. The vertical conductance (K_V/b), a coefficient that represents the average of the vertical conductances of the hydrogeologic units between the bottom of a lake and the top of the upper Floridan aquifer, was determined to be 2.51 × 10⁻⁴ day⁻¹ for Lowry Lake.     

Pattern and process of land loss in the Mississippi Delta: A Spatial and temporal analysis of wetland habitat change

An earlier investigation (Turner 1997) concluded that most of the coastal wetland loss in Louisiana was caused by the effects of canal dredging, that loss was near zero in the absence of canals, and that land loss had decreased to near zero by the late 1990s. This analysis was based on a 15-min quadrangle (approximately 68,000 ha) scale that is too large to isolate processes responsible for small-scale wetland loss and too small to capture those responsible for large-scale loss. We conducted a further evaluation of the relationship between direct loss due to canal dredging and all other loss from 1933–1990 using a spatial scale of 4,100 ha that accurately captures local land-loss processes. Regressions of other wetland loss on canal area (i.e., direct loss) for the Birdfoot, Terrebonne, and Calcasieu basins were not significant. Positive relationships were found for the Breton (r²=0.675), Barataria (r²=0.47), and Mermentau (r²=0.35) basins, indicating that the extent of canals is significantly related to wetland loss in these basins. A significant negative relationship (r²=0.36) was found for the Atchafalaya coastal basin which had statistically lower loss rates than the other basins as a whole. The Atchafalaya area receives direct inflow of about one third of the Mississippi discharge. When the data were combined for all basins, 9.2% of the variation in other wetland loss was attributable to canals. All significant regressions intercepted the y-axis at positive loss values indicating that some loss occurred in the absence of canals. Wetland loss did not differ significantly from the coast inland or between marsh type. We agree with Turner that canals are an important agent in causing wetland loss in coastal Louisiana, but strongly disagree that they are responsible for the vast majority of this loss. We conclude that wetland loss in the Mississippi delta is an ongoing complex process involving several interacting factors and that efforts to create and restore Louisiana’s coastal wetlands must emphasize riverine inputs of freshwater and sediments.     

A one-dimensional photochemical model of the troposphere with planetary boundary-layer parameterization

The results from a one-dimensional photochemical model of the troposphere representative of summertime conditions at Northern Hemisphere mid-latitudes are presented. A parameterization of mixing processes within the planetary boundary layer (PBL) has been incorporated into the model for both the daytime convective PBL and the formation of the nocturnal PBL. One result of the parameterized PBL is that the concentrations of some trace species in the free troposphere are 20–30% higher than when mixing processes are described by a vertical eddy diffusion coefficient which is held constant with respect to height and time.The calculations indicate that the lifetime of the oxides of nitrogen (NO _x =NO+NO₂) against photochemical conversion to nitric acid (HNO₃) during summertime conditions is on the order of 6 h. This lifetime is short enough to deplete most of the NO _x in the PBL, resulting in the finding that other reactive nitrogen species (HNO₃ and peroxyacetyl nitrate) are more abundant than NO _x throughout the free troposphere, even though NO _x is the most abundant reactive nitrogen species at the surface. The effects of the inclusion of anthropogenic nonmethane hydrocarbon (NMHC) chemistry are also discussed. The inclusion of NMHC chemistry has a pronounced effect on the photochemistry of tropospheric oxone and increases thein situ column production by more than 30%.