A simple formula for interpolation inn-dimensional space

n¶rt;m u u¶rt; umnu n-a nmam, ma ¶rt;mm n¶rt; u (auum m um ¶rt;uam, aum ua¶rt;m umnua uu). ¶rt;a nu¶rt;um nmu u¶rt; ma umnu u m ma.     

A simple model for spatial rainfall fields

Spatial rainfall amounts accumulated over short to medium periods of time, say a few days, tend to have a probabilistic structure with very distinctive features. Some of these that are specially relevant for the purpose of spatial modeling are the presence of mixed sampling distributions, right skewed distributions conditional on rainfall occurrence, and a complex spatial association structure. The goal of this work is to construct a family for the bivariate distributions of spatial rainfall fields that incorporates these distinctive features. It is based on the separate modeling of spatial occurrence of rainfall and the spatial distribution of positive rainfalls. The main properties of the bivariate distributions are derived, and some properties of the random field realizations are illustrated through simulation. Some limitations of the proposed model are also discussed.     

A simple oblique dip model for geomagnetic micropulsations

It is pointed out that simple models adopted so far have tended to neglect the obliquity of the magnetic field lines entering the Earths surface. A simple alternative model is presented, in which the ambient field lines are straight, but enter wedge shaped boundaries at half a right-angle. The model is illustrated by assuming an axially symmetric, compressional, impulse type disturbance at the outer boundary, all other boundaries being assumed to be perfectly conducting. The numerical method used is checked from the instant the excitation ceases, by an analytical method. The first harmonic along field lines is found to be of noticeable size, but appears to be mainly due to coupling with the fundamental, and with the first harmonic across field lines.     

A simple pore water hydrogen diffusion syringe sampler

Molecular hydrogen (H(2)) is an important intermediate product and electron donor in microbial metabolism. Concentrations of dissolved H(2) are often diagnostic of the predominant terminal electron-accepting processes in ground water systems or aquatic sediments. H(2) concentrations are routinely measured in ground water monitoring wells but are rarely measured in saturated aquatic sediments due to a lack of simple and practical sampling methods. This report describes the design and development (including laboratory and field testing) of a simple, syringe-based H(2) sampler in (1) saturated, riparian sediments, (2) surface water bed sediments, and (3) packed intervals of a fractured bedrock borehole that are inaccessible by standard pumped methods.     

A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.     

A simple model of a building cumulus cloud

Summary A model of a building cumulus structure is described. The one-stage model published in[1] was used to describe ascent of two cloudy parcels that a cloud is supposed to be formed of. The other ascent is assumed to take place after the first cloud element sinks back as a result of evaporative cooling. The numerical results and their evaluation are given for various rates of mixing at the cloud top level of the first cloud volume.     

A simple model of seasonal open ocean convection

 Aspects of open ocean deep convection variability are explored with a two-box model. In order to place the model in a region of parameter space relevant to the real ocean, it is fitted to observational data from the Labrador Sea. A systematic fit to OWS Bravo data allows us to determine the model parameters and to locate the position of the Labrador Sea on a stability diagram. The model suggests that the Labrador Sea is in a bistable regime where winter convection can be either “on” or “off ”, with both these possibilities being stable climate states. When shifting the surface buoyancy forcing slightly to warmer or fresher conditions, the only steady solution is one without winter convection.  We then introduce short-term variability by adding a noise term to the surface temperature forcing, turning the box model into a stochastic climate model. The surface forcing anomalies generated in this way induce jumps between the two model states. These state transitions occur on the interannual to decadal time scale. Changing the average surface forcing towards more buoyant conditions lowers the frequency of convection. However, convection becomes more frequent with stronger variability in the surface forcing. As part of the natural variability, there is a non-negligible probability for decadal interruptions of convection. The results highlight the role of surface forcing variability for the persistence of convection in the ocean.     

A probability-weighted moment test to assess simple scaling

We present a statistically robust approach based on probability weighted moments to assess the presence of simple scaling in geophysical processes. The proposed approach is different from current approaches which rely on estimation of high order moments. High order moments of simple scaling processes (distributions) may not have theoretically defined values and consequently, their empirical estimates are highly variable and do not converge with increasing sample size. They are, therefore, not an appropriate tool for inference. On the other hand we show that the probability weighted moments of such processes (distributions) do exist and, hence, their empirical estimates are more robust. These moments, therefore, provide an appropriate tool for inferring the presence of scaling. We illustrate this using simulated Levystable processes and then draw inference on the nature of scaling in fluctuations of a spatial rainfall process.     

A simple model of seasonal open ocean convection

 A simple tutorial model of open-ocean deep convection is presented, based on the seminal box model of Welander. The model is extended to include prognostic variables of the deep box. An approximate analytical solution is found and discussed for a surface forcing which includes a seasonal cycle. The model helps to illustrate, e.g., the basic balances at work in determining the duration of the winter convection season or the rate dependence of the response of convection to surface warming.     

A simple displacement control technique for pushover analyses

This paper explains how to control in displacement any force proportional loading. Such a procedure makes it possible to derive the complete (i.e. including the possible softening branch) response curve of a structure along any radial loading path in the force space. This is exactly what is required in the so‐called pushover analysis used in the seismic assessment of structures. The proposed procedure is simple in the sense that it can be easily implemented in any classical (displacement‐based) finite element code through a standard displacement control loading process. Furthermore, it leads to an interesting definition of the controlled degree‐of‐freedom, which, in the case of the pushover analysis, could substitute the classical roof displacement. Copyright © 2006 John Wiley & Sons, Ltd.     

A methodology for simple and fast streamflow modelling

ABSTRACT

During the last few decades, hydrological models have become very powerful, capable of spatially analysing the hydrological information and accurately representing the geomorphological characteristics of the studied area. However, one of the drawbacks of this heightened intricacy is the amount of time required to set up a hydrological model. In this study, a simple methodology that requires only a minimum set-up time is presented. This methodology employs linear regression to combine the outputs of simple hydrological models to simulate hydrological responses. Two kinds of simple hydrological models are employed. The first one represents the characteristics of the streamflow attributed to overland flow, and the second the characteristics of the streamflow attributed to interflow and baseflow. The methodology was tested in 4 case studies, and the results were encouraging. The best performance was achieved in the case study with data of fine time step with significant length.     

A simple field-portable rainfall simulator for difficult terrain

A small portable rainfall simulator is described which is inexpensive to construct and use and which requires relatively little water. Although drops are produced by drop-formers a satisfactory drop-size distribution is obtained by allowing the drops to break-up by falling onto a 3 mm wire mesh. The kinetic energy of the simulated rain is lower than that of natural rainfall because of the low fall height. Characteristics of the simulated rain are described and the use of the simulator briefly illustrated by results obtained from forested areas in Luxembourg.     

A simple method of quantifying filamentous algae in microscope

A fast and simple method to quantify filamentous algae in inverted microscope is described. It is based on the number of intersections between the midline of a diametrical transect and the filaments on the chamber bottom. It is shown to be theoretically sound and is compared with the common length measurement method.     

A simple model for non-vanishing rotational hysteresis in haematite

The model, applicable to fine-grained haematite, assumes that the magnetization of a grain is constrained to lie in the basal plane, within which there is a single easy axis. Following Stoner and Wohlfarth (1948), torque curves and rotational hysteresis are calculated, for various field strengths, as a function of the orientations of the basal plane and easy axis. The results show that, for certain orientations, rotational hysteresis may be expected to persist to very high field strengths. Further, the dependence of rotational hysteresis on orientation implies that rotational hysteresis is anisotropic and thus, that, for a distribution of grains, the anisotropy of resultant rotational hysteresis will reflect the degree of preferred orientation. It may therefore serve as a rock fabric parameter. Calculated models of resultant rotational hysteresis for assumed preferred orientation distributions compare favourably with measurements on a sample of Cambrian purple slate from North Wales.     

A simple model for the formation of vegetated dunes

A simple model for the dynamics of dunes associated with vegetation is proposed. Using the model, the formation processes of transverse dunes, parabolic dunes and elongated parabolic dunes are simulated according to two environmental factors: (i) the amount of sand at the source; (ii) the wind force. The results have qualitative correspondence to the real counterpart, and the simplicity of the algorithm and the consequent ease of handling this model provide us with wide applicability for the investigation of the complex interplay between vegetation and dunes. Copyright © 2001 John Wiley & Sons, Ltd.     

A simple model of convection in the terrestrial planets

Abstract

In this paper we study analytically the simplest fluid mechanical model which can mimic the convective behavior which is thought to occur in the solid mantles of the terrestrial planets. The convecting materials are polycrystalline rocks, whose creep behavior depends very strongly on temperature and probably also on pressure. As a simple model of this situation, we consider the flow of a Newtonian viscous fluid, whose viscosity depends strongly on temperature (only), and in fact has an infinite viscosity below a certain temperature, and a constant viscosity above this temperature. This model would also be directly relevant to the convection of a melt beneath its own solid phase (e.g. water below ice, though in that case there are other physical complications).

As a consequence of this assumption, there is a vigorous convection zone overlain by a stagnant lid, as also observed in analogous laboratory experiments (Nataf and Richter, 1982). The analysis is then very similar to that of Roberts (1979), but the extension to variable viscosity introduces important differences, most notably that the boundary between the lid and the convecting zone is unknown, and not horizontal. The resulting buoyancy induced stresses near this boundary are much larger than the stresses produced by buoyancy in the side-wall plumes, and mean that the dynamics of this region, and hence also the heat flux, are independent of the rest of the cell. We give a first order approximation for the Nusselt number-Rayleigh number relationship.     

A simple correction for slug tests in small-diameter wells

A simple procedure is presented for correcting hydraulic conductivity (K) estimates obtained from slug tests performed in small-diameter installations screened in highly permeable aquifers. Previously reported discrepancies between results from slug tests in small-diameter installations and those from tests in nearby larger-diameter wells are primarily a product of frictional losses within the small-diameter pipe. These frictional losses are readily incorporated into existing models for slug tests in high-K aquifers, which then serve as the basis of a straightforward procedure for correcting previously obtained K estimates. A demonstration of the proposed procedure using data from a series of slug tests performed in a controlled field setting confirms the validity of the approach. The results of this demonstration also reveal the detailed view of spatial variations in K that can be obtained using slug tests in small-diameter installations.