BinSq: visualizing geographic dot density patterns with gridded maps

ABSTRACT

Dot maps have become a popular way to visualize discrete geographic data. Yet, beyond showing how the data are spatially distributed, dot maps are often visually cluttered in terms of consistency, overlap, and representativeness. Existing clutter reduction techniques like jittering, refinement, distortion, and aggregation also address this issue, but do so by arbitrarily displacing dots from their exact location, removing dots from the map, changing the spatial reference of the map, or reducing its level of detail, respectively. We present BinSq, a novel visualization technique to compare variations in dot density patterns without visual clutter. Based on a careful synthesis of existing clutter reduction techniques, BinSq reduces the wide variety of dot density variations on the map to a representative subset of density intervals that are more distinguishable. The subset is derived from a nested binning operation that introduces order and regularity to the map. Thereafter, a dot prioritization operation improves the representativeness of the map by equalizing visible data values to correspond with the actual data. In this paper, we describe the algorithmic implementation of BinSq, explore its parametric design space, and discuss its capabilities in comparison to six existing clutter reduction techniques for dot maps.     

River catchment rainfall series analysis using additive Holt–Winters method

Climate change is receiving more attention from researchers as the frequency of occurrence of severe natural disasters is getting higher. Tropical countries like Malaysia have no distinct four seasons; rainfall has become the popular parameter to assess climate change. Conventional ways that determine rainfall trends can only provide a general result in single direction for the whole study period. In this study, rainfall series were modelled using additive Holt–Winters method to examine the rainfall pattern in Langat River Basin, Malaysia. Nine homogeneous series of more than 25 years data and less than 10% missing data were selected. Goodness of fit of the forecasted models was measured. It was found that seasonal rainfall model forecasts are generally better than the monthly rainfall model forecasts. Three stations in the western region exhibited increasing trend. Rainfall in southern region showed fluctuation. Increasing trends were discovered at stations in the south-eastern region except the seasonal analysis at station 45253. Decreasing trend was found at station 2818110 in the east, while increasing trend was shown at station 44320 that represents the north-eastern region. The accuracies of both rainfall model forecasts were tested using the recorded data of years 2010–2012. Most of the forecasts are acceptable.     

A method of time-dependent analysis using elastic solutions for nonlinear materials

The formulation of viscoelastic solutions from elastic equations using the ‘correspondence principle’ and an inverse Laplace transform has been discussed extensively in the literature. Because this method has been developed, many time-dependent solutions can be obtained from closed form elastic solutions and conditions have been delineated in which the ‘quasi-elastic’ approximation of the viscoelastic solution is within acceptable tolerance. This communication shows the feasibility of the application of these methods to formulate approximate nonlinear viscoelastic solutions with nonlinear stress-strain materials, and for want of a specific nonlinear model to demonstrate this, the hyperbolic model was selected. The ‘power law’ is used to model the relaxation modulus of the viscoelastic materials. There are five related development that are discussed here using a simple numerical example to illustrate each of them and they are: (1) a linear elastic solution, (2) a linear viscoelastic solution, (3) a nonlinear elastic solution, (4) a nonlinear viscoelastic solution and finally, (5) a ‘regression’ approximation of the nonlinear viscoelastic solution which is suggested by the series form of the elastic solution. All of these are related to one another and each provides an acceptably accurate solution of the problem it addresses. The latter is of particular practical interest since it can be used to provide answers to problems involving nonlinear viscoelastic materials while requiring only very small calculation times. The problem used as an example is the calculation of the displacement of a circular hole in an infinite plate made of a material with a nonlinear time-dependent stress-strain relationship. The nonlinear elastic form of the solution was developed by matching results from nonlinear finite element analysis.     

Exploring variations in upper ocean structure for the last 2 Ma of the Nansha area by means of calcareous nannofossils

A great number of calcareous nannofossils have been found in the deep-sea sediments of 2.32 Ma at ODP Site 1143 located in the Nansha area, the southern South China Sea. The number of coccoliths varies from about 0.5×10⁶ up to almost 53×10⁶ coccoliths/g sediment, with an average of 16×10⁶ coccoliths/g sediment. The accumulation rate of total coccoliths varies from 1×10⁶ to 278×10⁶ coccoliths/cm² ka. The nannofossil assemblages are usually dominated by a lower-photic species-Florisphaera profunda, of which the average percentage is about 70% in all samples. The absolute abundance and the accumulation rate of nannofossils as well as the percentage ofF. profunda display significant oscillations on two different time scales. One is the fluctuation coincident with the glacial-interglacial cycle, and the other is the long-term changes on a time scale longer than 100 ka. Six evolutionary stages of calcareous nannofossils could be divided for the last 2.32 Ma, from which we can reconstruct the changes in the depth of nutricline of the Nansha area. In this paper, the possible mechanism resulting in these variations is also discussed.     

Hydrostratigraphy and geochemistry at a coastal sandfill in Singapore

A characterization study was carried out in a 10-m-thick sandfill, formed by hydraulic filling with marine sand, in Singapore. Placement methods and compaction were found to influence hydrostratigraphy. The deepest part of the sandfill consists of a loose sand layer and is overlain by a medium sand layer extending to mean sea level (MSL). At certain locations, a thin silty-sand layer was found. The different layers within the saturated zone were found to have different values for hydraulic conductivity (K) and groundwater flow velocity. Estimates for K increase according to the following sequence of methods: repacked sand column, step-pumping test, grain-size analysis and slug test. Slug tests and grain-size analysis yielded comparable estimates of K. The freshwater lens in the older part of the sandfill is about 2 m thicker than in a recently completed area. Comparisons of Ca²⁺/Cl^?, Mg²⁺/Cl^?, K ⁺/Cl^? and \({\text{Cl}}^{{\text{ - }}} {\text{/}}{\left( {{\text{Cl}}^{{\text{ - }}} {\text{ + HCO}}^{{\text{ - }}}_{{\text{3}}} } \right)}\) ratios indicate that the chemical composition of the groundwater at shallower depths has probably been altered by mineral dissolution. Weathering of carbonate minerals was found to be a major contributor to the major ions at these depths. The molar ratios approach the value for seawater at greater depths. The groundwater is close to equilibrium with calcite.     

Generalized inversion of a global numerical weather prediction model

Summary We construct the generalized inverse of a global numerical weather prediction (NWP) model, in order to prepare initial conditions for the model at time t=0 hrs. The inverse finds a weighted, least-squares best-fit to the dynamics for –24<t<0, to the previous initial condition att=–24, and to data att=–24,t=–18,t=–12 andt=0. That is, the inverse is a weak-constraint, four-dimensional variational assimilation scheme. The best-fit is found by solving the nonlinear Euler-Lagrange (EL) equations which determine the local extrema of a penalty functional. The latter is quadratic in the dynamical, initial and data residuals. The EL equations are solved using iterated representer expansions. The technique yields optimal conditioning of the very large minimization problem, which has 10⁹ hydrodynamical and thermodynamical variables defined on a 4-dimensional, space-time grid.In addition to introducing the inverse NWP model, we demonstrate it on a medium-sized problem, namely, a study of the impact of reprocessed cloud track wind observations (RCTWO) from the 1990 Tropical Cyclone Motion Experiment (TCM-90). The impact is assessed in terms of the improvement of forecasts in the South China Sea att=+48 hours. The calculation shows that the computations are manageable, the iteration scheme converges, and that the RCTWO have a beneficial impact.     

Large motion analysis of compliant structures using euler parameters

The large motions that a compliant offshore structure experiences were analysed using Euler parameters. Firstly, the equations of motion of a rigid body undergoing large translations and rotations were obtained using the Lagrangian formulation. Secondly, the hydrodynamic forces acting on the structure were calculated using the modified Morison's equation. A tension-leg platform (TLP) subjected to an oblique incident wave was then analysed using the above formulation. This was followed by an analysis of an articulated tower for comparison with the results of other researchers. An example showing the tower undergoing subharmonic oscillations was also included.     

Euler–Lagrange equations for the spectral element shallow water system

We present the derivation of the discrete Euler–Lagrange equations for an inverse spectral element ocean model based on the shallow water equations. We show that the discrete Euler–Lagrange equations can be obtained from the continuous Euler–Lagrange equations by using a correct combination of the weak and the strong forms of derivatives in the Galerkin integrals, and by changing the order with which elemental assembly and mass averaging are applied in the forward and in the adjoint systems. Our derivation can be extended to obtain an adjoint for any Galerkin finite element and spectral element system.We begin the derivations using a linear wave equation in one dimension. We then apply our technique to a two-dimensional shallow water ocean model and test it on a classic double-gyre problem. The spectral element forward and adjoint ocean models can be used in a variety of inverse applications, ranging from traditional data assimilation and parameter estimation, to the less traditional model sensitivity and stability analyses, and ensemble prediction. Here the Euler–Lagrange equations are solved by an indirect representer algorithm.