The effect of nested grid sampling on the parameter estimation of a spatial Gompertz diffusion

This paper evaluates the effects of using data observed on regular nested grids on the parameter estimates of a two-parameter Gompertz diffusion model. This new spatial diffusion process represents a technically more complex stage of Gompertz modeling. Firstly, the diffusion model is introduced through an appropriate transformation of a two-parameter Gaussian diffusion process. Probabilistic characteristics of this model, such as the transition densities and the trend functions, are obtained. Secondly, statistical estimation is considered using data obtained on a regular or irregular grid; the explicit expression of the likelihood equations and the parameter estimators are given for regular grids. Finally, a simulation experiment illustrates the results of this paper.     

An improved method of least-squares parameter estimation with pumping-test data

Least-squares estimation of storativity and transmissivity from pumping-test data has been concerned with finding the lowest point on a mathematical surface. Since there is no guarantee that such surfaces do not contain local minima, the accuracy of the estimate may be dependent upon the selection of “good” initial values.

An improved estimation procedure can be obtained by converting the two-dimensional minimisation problem into an equivalent form in one dimension. The resulting line function can then be easily evaluated through any given feasible interval. This approach avoids the requirement of initial estimates and always returns the true estimates after a single computation sequence.

Examples are given of the application of the method to both drawdown and recovery data, together with a simple model for the determination of estimation error.     

MODFLOW-Style parameters in underdetermined parameter estimation

In this article, we discuss the use of MODFLOW-Style parameters in the numerical codes MODFLOW_2005 and MODFLOW_2005-Adjoint for the definition of variables in the Layer Property Flow package. Parameters are a useful tool to represent aquifer properties in both codes and are the only option available in the adjoint version. Moreover, for overdetermined parameter estimation problems, the parameter approach for model input can make data input easier. We found that if each estimable parameter is defined by one parameter, the codes require a large computational effort and substantial gains in efficiency are achieved by removing logical comparison of character strings that represent the names and types of the parameters. An alternative formulation already available in the current implementation of the code can also alleviate the efficiency degradation due to character comparisons in the special case of distributed parameters defined through multiplication matrices. The authors also hope that lessons learned in analyzing the performance of the MODFLOW family codes will be enlightening to developers of other Fortran implementations of numerical codes.     

A numerical investigation into effects of single and multiple frequency earthquake motions

During dynamic centrifuge modelling for earthquakes there is a decision to be made about the type of base input motion that should be imparted to the soil model. Motions can either be a tone burst of single frequency or a multi-frequency event simulating a real earthquake. In this paper a series of numerical analyses is reported which endeavours to capture the effects of loading rate on liquefiable soil. Non-linear dynamic finite element analysis in terms of effective stress was carried out using the FE code SWANDYNE. The numerical model was subjected to four types of input motion. Results are presented in terms of excess pore pressure ratios for different frequencies. It was seen that the interplay between frequency content of the seismic motion and generation of excess pore pressure could change the dynamic response of a system. It was concluded that simplicity of the input motion leads to a soil response that is less difficult to analyse.     

Validity limits for the van Genuchten–Mualem model and implications for parameter estimation and numerical simulation

The calculation of the relative hydraulic conductivity function based on water retention data is an attractive and widely used approach, since direct measurements of unsaturated conductivities are difficult. We show theoretically under which conditions an air-entry value for water retention data is definitely required when using the statistical approach of Mualem. Moreover we rigorously specify the conditions for which the classical van Genuchten–Mualem model leads to wrong predictions of relative hydraulic conductivity and, hence, an alternative formulation including an air-entry value should be used. Significant consequences are demonstrated for the inverse parameter estimation based on multistep outflow experiments. Furthermore it is shown that the use of a physically correct formulation of the water retention curve including an air-entry value and the derived hydraulic conductivity function influences not only the stability of numerical simulations but also their final results. This is especially grave as simulations with van Genuchten–Mualem parameters are frequently used to compare experiments and simulations and to draw conclusions on the correctness of Richards’ equation.     

Combined model state and parameter estimation with an ensemble Kalman filter in a North Sea station 1-D numerical model

The combined estimation of model state and parameters is investigated by using an ensemble Kalman filter in a 1-D numerical study of the temperature profile at a North Sea station located at 55°30??North and 0°55??East. This simplified model implementation allows to test many configurations for the sampling of the model error for the model state as well as for the parameters. Temperature profiles from thermistor data are assimilated. The influence of a vertically or non-vertically correlated model error is examined through the computation of correlation coefficients, root mean square errors, and model bias. As the CS station is located in the North Sea region stratified in summer, vertically non-correlated model error terms have a slight positive impact on the assimilative runs. The benefit of the combined estimation of the model state and parameters is examined by comparison of a simulation where the model parameters are not adjusted to simulations with the combined estimation of the model state either with one parameter or with a set of parameters related to the surface heat exchange. The optical attenuation coefficient, the sensible, and latent heat exchange coefficients are considered. The best results are obtained when a set of parameters are simultaneously adjusted.     

Systematic parameter estimation of watershed acidification model

A joint strategy for parameter estimation which can systematically identify the important model parameters is presented. the strategy includes a regionalized sensitivity analysis (RSA) and an automatic parameter calibration technique (APCT). the RSA is based on a large number of Monte-Carlo simulations to identify the sensitive parameters and to establish a range of appropriate values for each sensitive parameter. the APCT adjusts the values of the sensitive parameters based on changes in the residual variances between the predicted and observed values. the strategy is applied to the watershed acidification model—ILWAS. the strategy succeeds in identifying the sensitive parameter and increases the likelihood of obtaining a global optimal parameter set. Improvements in the model prediction of the streamflow and chemistry are obtained.     

Bulk density effects on soil hydrologic and thermal characteristics: A numerical investigation

Soil bulk density (ρ_b) is commonly treated as static in studies of land surface dynamics. Magnitudes of errors associated with this assumption are largely unknown. Our objectives were to (a) quantify ρ_b effects on soil hydrologic and thermal properties and (b) evaluate effects of ρ_b on surface energy balance and heat and water transfer. We evaluated 6 soil properties, volumetric heat capacity, thermal conductivity, soil thermal diffusivity, water retention characteristics, hydraulic conductivity, and vapour diffusivity, over a range of ρ_b, using a combination of 6 models. Thermal conductivity, water retention, hydraulic conductivity, and vapour diffusivity were most sensitive to ρ_b, each changing by fractions greater than the associated fractional changes in ρ_b. A 10% change in ρ_b led to 10–11% change in thermal conductivity, 6–11% change in saturated and residual water content, 49–54% change in saturated hydraulic conductivity, and 80% change in vapour diffusivity. Subsequently, 3 field seasons were simulated with a numerical model (HYDRUS‐1D) for a range of ρ_b values. When ρ_b increased 25% (from 1.2 to 1.5 Mg m^?3), soil temperature variation decreased by 2.1 °C in shallow layers and increased by 1 °C in subsurface layers. Surface water content differed by 0.02 m³ m^?3 for various ρ_b values during drying events but differences mostly disappeared in the subsurface. Matric potential varied by >100 m of water. Surface energy balance showed clear trends with ρ_b. Latent heat flux decreased 6%, sensible heat flux increased 9%, and magnitude of ground heat flux varied by 18% (with a 25% ρ_b increase). Transient ρ_b impacted surface conditions and fluxes, and clearly, it warrants consideration in field and modelling investigations.     

Aquifer parameter estimation from surface resistivity data

This paper is devoted to the additional use, other than ground water exploration, of surface geoelectrical sounding data for aquifer hydraulic parameter estimation. In a mesoscopic framework, approximated analytical equations are developed separately for saline and for fresh water saturations. A few existing useful aquifer models, both for clean and shaley sandstones, are discussed in terms of their electrical and hydraulic effects, along with the linkage between the two. These equations are derived for insight and physical understanding of the phenomenon. In a macroscopic scale, a general aquifer model is proposed and analytical relations are derived for meaningful estimation, with a higher level of confidence, of hydraulic parameter from electrical parameters. The physical reasons for two different equations at the macroscopic level are explicitly explained to avoid confusion. Numerical examples from existing literature are reproduced to buttress our viewpoint.     

基于T-matrix的非线性参数估计方法

全波形反演可提供高精度的地下介质参数空间分布,但传统的全波形反演方法建立在Born近似的基础上,对初始模型具有一定的依赖性.为了摆脱Born近似的束缚,本文基于二维常密度声波方程,在De Wolf近似的前提下,借助传输矩阵(T-matrix)方法,深入研究了逆薄板传播算子(Inverse Thin-Slab Propagator, ITSP),实现了速度扰动的非线性估计.ITSP方法避免了Born级数方法在扰动较强、扰动区域较大时的发散性问题,且只经过一次扫描校正,计算效率较高.二维模拟数据分析验证了本文方法的可行性以及有效性.     

现代功率谱估算在反射地震剖面随机介质参数估算中的应用

由于地壳深部物质呈现出多尺度的非均质性,导致了地震剖面上反射能量弱、同相轴连续性差、多成带状分布.传统的反射地震解释方法难以有效应用到深反射地震资料解释中.统计分析的方法为深反射地震资解释提供了新的工具,地下介质这种随机分布的非均质性可以借助随机介质模型来进行描述.深反射地震剖面继承了地下介质的非均质性,因此可以通过从反射地震剖面估算随机介质参数来研究地下介质非均质性的空间分布.由于地震剖面长度有限,随机介质参数估算中自相关函数计算误差较大,导致了估算的不准确.现代功率谱估算克服了短数据自相关函数难以准确求取的问题,提高了参数估算准确性.模型计算和实际数据测算都证明了该方法能有效提高自相关函数计算精度和随机介质参数剖面的分辨率.     

Aquifer parameter estimation using an incremental area method

Theoretical well functions have been derived over the years to predict ground water level behaviour in aquifer systems under stress owing to groundwater extraction. The drawdown data collected during pump tests are typically analysed using graphical curve‐matching procedures to estimate aquifer parameters based on these well functions. Difficulty in aquifer characteristic identification and parameter estimation may arise when the field data do not perfectly match the drawdown curves obtained from the well functions. The present study provides a new method for the interpretation of aquifer pump tests which supplements the existing curve‐matching procedures in case ideal conditions do not exist; the proposed method provides a greater degree of flexibility in the data analysis for diagnostic tool purposes. The method, referred to as the Incremental Area Method (IAM) is based on integrating the logarithmic‐based drawdown curves within a discrete time and matching the results with a corresponding time integral of the Theis ( 1935 ) Well Function which governs ideal confined aquifers. The application of the proposed method to synthetically generated data and field data showed that IAM represents a viable method which yields information on potential non‐idealness of the aquifer and provides aquifer parameter estimates thus potentially overcoming drawdown data curve‐matching difficulties. Copyright © 2011 John Wiley & Sons, Ltd.     

Enhancing gradient-based parameter estimation with an evolutionary approach

Traditionally, the calibration of groundwater models has depended on gradient-based local optimization methods. These methods provide a reasonable degree of success only when the objective function is smooth, second-order differentiable, and satisfies the Lipschitz's condition. For complicated and highly nonlinear objective functions it is almost impractical to satisfy these conditions simultaneously. Research in the calibration of conceptual rainfall-runoff models, has shown that global optimization methods are more successful in locating the global optimum in the region of multiple local optima. In this study, a global optimization technique, known as shuffle complex evolution (SCE), is coupled to the gradient-based Lavenberg–Marquardt algorithm (GBLM). The resultant hybrid global optimization algorithm (SCEGB) is then deployed in parallel testing with SCE and GBLM to solve several inverse problems where parameters of a nonlinear numerical groundwater flow model are estimated. Using perfect (i.e. noise-free) observation data, it is shown SCEGB and SCE are successful at identifying the global optimum and predicting all model parameters; whereas, the commonly applied GBLM fails to identify the optimum. In subsequent inverse simulations using observation data corrupted with noise, SCEGB and SCE again outperform GBLM by consistently producing more accurate parameter estimates. Finally, in all simulations the hybrid SCEGB is seen to be equally effective as SCE but computationally more efficient.     

估计辐射参数的井间电磁波层析成像技术

为了避免使用不合理初始辐射场强和方向性因子带来的误差,研究了估计辐射参数的井间电磁波层析成像技术.通过时域有限差分法模拟表明,天线长度与波长的比值、钻孔充填情况、钻孔周围介质的物性均会影响偶极天线的初始辐射场强或方向性因子;为此结合已知的分层资料,将它们设为未知参数,并设定初始辐射场强与发射点位置相关,方向性因子随射线角度而变化;采用正则化反演方法,由钻孔资料建立了模型方差目标函数,使得反演结果与钻遇的地质特征保持一致.通过理论模型试验和实例应用分析表明,相对于传统射线层析成像方法,估计辐射参数的正则化层析成像技术有助于提高反演的准确性.

     

Entropy-based parameter estimation for extended Burr XII distribution

Two entropy-based methods, called ordinary entropy (ENT) method and parameter space expansion method (PSEM), both based on the principle of maximum entropy, are applied for estimating parameters of the extended Burr XII distribution. With the parameters so estimated, the Burr XII distribution is applied to six peak flow datasets and quantiles (discharges) corresponding to different return periods are computed. These two entropy methods are compared with the methods of moments (MOM), probability weighted moments (PWM) and maximum likelihood estimation (MLE). It is shown that PSEM yields the same quantiles as does MLE for discrete cases, while ENT is found comparable to the MOM and PWM. For shorter return periods (<10–30 years), quantiles (discharges) estimated by these four methods are in close agreement, but the differences amongst them grow as the return period increases. The error in quantiles computed using the four methods becomes larger for return periods greater than 10–30 years.     

An investigation of the effects of mass distribution on pounding structures

The effects of diaphragm mass distribution are investigated for building pounding. Elastic diaphragm‐to‐diaphragm collisions are explained by considering the total momentum over the length of each diaphragm at three critical instants during collision. Expressions for collision force and collision duration are produced, providing additional information about the collision process. Equations for the post collision velocity of each diaphragm are produced and are found to appreciably differ from conventional impact—momentum equations under certain conditions. The change in post collision velocity is found to be dependent on the ratio of the axial periods of free vibration of the two diaphragms and the ratio of their masses. An equivalent lumped mass model is proposed and assessed against simplified distributed mass models with numerical modelling of two two‐storey buildings. Finally, a new parameter is introduced to represent the plasticity of an inelastic collision between the two distributed masses. This paper highlights the significant influence that diaphragm mass distribution may have on the analysis of pounding structures. Copyright © 2010 John Wiley & Sons, Ltd.     

An investigation of the significance of local site effects in Plovdiv, Bulgaria

Plovdiv is the second largest city in the Republic of Bulgaria. A large part of the city is located on Holocene alluvial sediments and the oldest neighborhoods are situated on syenitic rock outcrops. We believe that local site effects may be an important contributor to the destruction caused by earthquakes. The primary objective of this study was to estimate quantitatively the local site effects in the central area of Plovdiv in terms of fundamental site frequency and amplification factor. Another important objective was to see how these correlate with the geological structures underlying the city. Measurements of the seismic noise at more than two hundred regularly placed points were made in the central area of the city. The H/V spectra were then calculated and analyzed to determine the spatial distribution of the fundamental site frequency and the amplification factor. The results exhibit very good correlation with the local geology. They were also compared with an intensity map from the strong 1928 Plovdiv earthquake. The comparison clearly demonstrates that the local site effects were the main factor in the destruction of buildings—the zones where the most damage was observed are also the zones where we have low fundamental site frequencies and high amplifications. Similarly the areas with high fundamental site frequencies and low amplification factors cover the neighborhoods where less damage has been observed. This study may form a basis for a more comprehensive and systematic microzonation study in Plovdiv.