A new analytical solution of tidal water table fluctuations in a coastal unconfined aquifer

This paper presents a new perturbation solution of the non-linear Boussinesq equation for one-dimensional tidal groundwater flow in a coastal unconfined aquifer. Built upon the work of Parlange et al. [Parlange, J.-Y., Stagnitti, F., Starr, J.L., Braddock, R.D., 1984. Free-surface flow in porous media and periodic solution of the shallow-flow approximation, J. Hydrol., 70, 251–263], the solution adopts a new perturbation parameter that is by definition less than unit, and thus is applicable to a wider range of physical conditions within the constraint of the Boussinesq approximation. This approach avoids a secular term in the third-order perturbation equation of Parlange et al. (1984), enabling the derivation of the third- and higher-order solutions. In comparison with a numerical (“exact”) solution, the new perturbation solution is shown to be slightly more accurate than that of Parlange et al. (1984) with the second-order approximation. The obtained third-order solution exhibits considerable improvement in accuracy. In relatively simple analytical forms, the present perturbation solution will help to understand better the non-linear characteristics of tidal water table fluctuations in as modeled by the non-linear Boussinesq equation coastal unconfined aquifers.     

遥测地表温度与比辐射率的迭代反演方法──理论推导与数值模拟

首先在地表比辐射率为已知的条件下,提出一个非线性迭代温度反演模型,我们对不同的地表和大气条件进行了模拟计算,结果表明当大气温度廓线误差－２Ｋ－２Ｋ,水汽廓线误差±２０％时的温度均方根误差为０．４８Ｋ。当大气模式误差一个模式时反演的温度均方根误差为０．８５Ｋ。在此基础上,引人相邻像元的概念,相邻像元的大气状况可以认为是相同的,应用两个时相的遥感影像数据,假定在两个相近时相之间地表比辐射率值不变,建立地表比辐射率与温度的反演模型。我们对不同的地表和大气条件进行了模拟计算,结果表明当大气温度廓线误差－２Ｋ－２Ｋ,水汽廓线误差±２０％时地表温度均方根误差小于１．５Ｋ,地表比辐射率均方根误差小于０．０２,地表辐射均方根误差为１％;当大气温度廓线误差－２Ｋ－２Ｋ,水汽廓线误差±１０％时,地表温度均方根误差小于１．０Ｋ,地表辐射均方根误差小于０．６％。     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

A higher-order non-hydrostatic σ model for simulating non-linear refraction–diffraction of water waves

A higher-order non-hydrostatic σ model is developed to simulate non-linear refraction–diffraction of water waves. To capture non-linear (or steep) waves, a 4th-order spatial discretization is utilized to approximate the large horizontal pressure gradient. A higher-order top-layer pressure treatment is further implemented to resolve wave propagation. The model's characteristics including linear wave dispersion and non-linearity are carefully examined. The accuracy of the present model using only two vertical layers is validated by laboratory data and the available results predicted by the non-linear Schrödinger equation, Boussinesq-type equations, the non-linear mild slope equation, and the Laplace equation. Features of harmonic generation as well as the influences of dispersion and non-linearity on wave energy transfer processes are discussed.     

Evolution of natural risk: analysing changing landslide hazard in Wellington,Aotearoa/New Zealand

This paper addresses the temporal variation of rainfall-triggered landslide hazard within the broader context of natural risk evolution. Analysis of a sequence of aerial photos covering a period of 60 years allowed the establishment of a record of landsliding for a site in the Wellington region, New Zealand. The data show one very dominant peak in the magnitude of landslide occurrence in the late 1970s, followed by a continuous decrease. Landslide hazard can be expressed by the frequency and magnitude of the landslide events, with the total surface area affected used as a surrogate for magnitude. However, the distinct decline of landslide magnitude through time from the 1980s onwards indicates that landslide hazard may change with time. This possibility is further explored by correlating potential landslide triggering storms with the magnitude of the landslide event, using the ‘Antecedent Soil Water Status’ model in combination with daily rainfall. The relation between magnitudes of rainfall and magnitudes of landslide events is found to be weak, suggesting that a given ‘Critical Water Content’ (antecedent soil water status and rainfall on the day) does not produce similar magnitudes of landsliding. Furthermore, the study shows that reactivation of previous landslides before the peak landslide occurrence of the late 1970s is low, while the situation is reversed after this peak and reactivation in the subsequent years plays a larger role. It is concluded that the pattern of landsliding cannot be explained by the pattern of rainfall and other factors are controlling the variation of landslide hazard in time. A possible explanation is a change of the geomorphological system with time, instigated by a massive period of landsliding (the late 1970s peak). Subsequent sediment exhaustion of source areas resulting from this period appears to alter the system’s subsequent reaction to an external trigger such as rainfall. The study demonstrates that landslide hazard analysis in general should not rely on the integral of the frequency–magnitude relationship only, but should include potential non-linear changes of system settings to increase the understanding of future system behaviour, and therefore hazard and risk.

Complexity, self-organisation and variation in behaviour in meandering rivers

River meanders are natural features on the surface of Earth that present some degree of regularity of form. They range from being highly dynamic to being stable under present conditions. Conventional theory is that meanders develop to an equilibrium form which is related to discharge and sediment load. Other research has demonstrated that many highly active meanders exhibit a continuous evolution over time and a non-linearity in rate of development. Ideas of autogenesis and of self-organised criticality as being an explanation of some meander changes have been proposed. In this paper data from rivers around the world are examined for further evidence of autogenic, self-organised or non-linear behaviour through analysis of change in sinuosity over time for reaches and change in individual bend form, particularly bend curvature and bend elongation. Some examples do exhibit trends of increasing sinuosity over time and a few show limits from which large decreases occur. Several case studies show non-linearity of behaviour and increasing complexity of form. Other case studies, however, do not exhibit such trends. Phase space plots are used to help uncover emergent behaviour but show a variety of patterns. The example of a reach in which multiple cut-offs occurred is analysed for mechanisms of self-organisation of the planform and in the pool-riffle pattern. Riffles are more closely spaced and also more transient in the more rapidly changing and higher sinuosity parts of the channel. Hypothetical trajectories of different meander behaviour, including for bedrock meanders, are plotted but the challenge remains to uncover the conditions for occurrence and for divergence of tendencies to stability and instability. Identification of attractors and phase space of behaviour of different meandering systems offer the potential for application to sustainable channel management.     

Quantification of soil non-linearity based on simulation

Recent earthquake studies have demonstrated that non-linear behavior of soft soil can be significant compared to other effects affecting seismic motion. Therefore, the question is to know when sediment non-linearity is a first-order effect and when it is not. In this study, we propose a method for quantifying non-linear effects based on simulations. An elasto-plastic model is used to simulate the behavior of four materials (sands and clays). For each computation, the non-linearity is quantified by the use of a ‘non-linear parameter’ and compared to four non-linearity indicators. These computations suggest that the efficiency of an indicator depends on the nature of the soil underlying the recorder and that the most efficient indicator should be based on the high frequencies content rather than on the resonant frequency changes.     

地球静止卫星云图象点定位方法之比较

在假定ＧＭＳ－４地球静止卫星所发定位网格数据的精度满足要求的基础上，通过数学原理分析、改变二维插值顺序、比较插值结果与实际分布等手段，对比分析了利用线性和非线性插值方法给每一个象点定位的结果，发现非线性插值所得结果明显优于线性插值，更加符合实际情况。线性插值的误差在经度方向上较小。可以忽略，但是在纬度方向的误差，即经度误差极为明显。在星下点的左上部，误差由东南向西北迅速增大，有相当一部分地区内经度     

Finite element models for use in mechanics including geological engineering

A number of finite element (FE) models have been developed, starting with a purely magnetic one. The magnetic model was verified against analytical solutions and the commercial FE-programme ANSYS. The magnetic model was then coupled to the wave-equation, resulting in a model governing linear magnetostriction. In the magnetostrictive model a property of two degrees of freedom, that is, displacements, was coupled to a property of one degree of freedom, that is, magnetic potential. To make this possible, non-quadratic coupling matrices had to be developed. This linear model was then verified against analytical solutions, with a good conceptual agreement. In the next step the still linear system of equations was time-propagated, using the Newmark method. This model was verified by comparing the differential step-response of the system calculated with the time propagation method, to the frequency function of the system, calculated with the harmonic model. Further, non-linear and non-linear transient models were developed and discussed. The non-linear transient model was developed for a situation where a Terfenol rod was assumed to collide periodically with a rigid wall, thus indicating a tool for analysing a Terfenol based resonant system, which could be used, for example, for ultrasonic cutting of hard and brittle materials and also for rock-blasting.