Multiple Parameter Regularization: Numerical Solutions and Applications to the Determination of Geopotential from Precise Satellite Orbits

Kaula’s rule of thumb has been used in producing geopotential models from space geodetic measurements, including the most recent models from satellite gravity missions CHAMP. Although Xu and Rummel (Manuscr Geod 20 8–20, 1994b) suggested an alternative regularization method by introducing a number of regularization parameters, no numerical tests have ever been conducted. We have compared four methods of regularization for the determination of geopotential from precise orbits of COSMIC satellites through simulations, which include Kaula’s rule of thumb, one parameter regularization and its iterative version, and multiple parameter regularization. The simulation results show that the four methods can indeed produce good gravitational models from the precise orbits of centimetre level. The three regularization methods perform much better than Kaula’s rule of thumb by a factor of 6.4 on average beyond spherical harmonic degree 5 and by a factor of 10.2 for the spherical harmonic degrees from 8 to 14 in terms of degree variations of root mean squared errors. The maximum componentwise improvement in the root mean squared error can be up to a factor of 60. The simplest version of regularization by multiplying a positive scalar with a unit matrix is sufficient to better determine the geopotential model. Although multiple parameter regularization is theoretically attractive and can indeed eliminate unnecessary regularization for some of the harmonic coefficients, we found that it only improved its one parameter version marginally in this COSMIC example in terms of the mean squared error.     

A case for a reassessment of the risks of extreme hydrological hazards in the Caribbean

There is an urgent need for the development and implementation of modern statistical methodology for long-term risk assessment of extreme hydrological hazards in the Caribbean. Notwithstanding the inevitable scarcity of data relating to extreme events, recent results and approaches call into question standard methods of estimation of the risks of environmental catastrophes that are currently adopted. Estimation of extreme hazards is often based on the Gumbel model and on crude methods for estimating predictive probabilities. In both cases the result is often a remarkable underestimation of the predicted probabilities for disasters of large magnitude. Simplifications do not stop here: assumptions of data homogeneity and temporal independence are usually made regardless of potential inconsistencies with genuine process behaviour and the fact that results may be sensitive to such mis-specifications. These issues are of particular relevance for the Caribbean, given its exposure to diverse meteorological climate conditions.In this article we present an examination of predictive methodologies for the assessment of long-term risks of hydrological hazards, with particular focus on applications to rainfall and flooding, motivated by three data sets from the Caribbean region. Consideration is given to classical and Bayesian methods of inference for annual maxima and daily peaks-over-threshold models. We also examine situations where data non-homogeneity is compromised by an unknown seasonal structure, and the situation in which the process under examination has a physical upper limit. We highlight the fact that standard Gumbel analyses routinely assign near-zero probability to subsequently observed disasters, and that for San Juan, Puerto Rico, standard 100-year predicted rainfall estimates may be routinely underestimated by a factor of two.     

A level-set corrector to an adaptive multiscale permeability prediction

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zonation, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.     

一种基于正则化方法的SAR图像边缘检测算法

提出了一种基于正则化方法的SAR图像边缘检测算法,并用MSTAR(moving and stationary target acquisitions and recognition)数据进行大量的仿真实验。实验表明,与经典的边缘检测方法相比,该方法能保持图像的细节特征,较好地解决了边缘断裂和抗噪问题,具有较好的边缘检测能力。     

Calculation of the Inverse of the Covariance

In reservoir characterization, the covariance is often used to describe the spatial correlation and variation in rock properties or the uncertainty in rock properties. The inverse of the covariance, on the other hand, is seldom discussed in geostatistics. In this paper, I show that the inverse is required for simulation and estimation of Gaussian random fields, and that it can be identified with the differential operator in regularized inverse theory. Unfortunately, because the covariance matrix for parameters in reservoir models can be extremely large, calculation of the inverse can be a problem. In this paper, I discuss four methods of calculating the inverse of the covariance, two of which are analytical, and two of which are purely numerical. By taking advantage of the assumed stationarity of the covariance, none of the methods require inversion of the full covariance matrix.     

利用GCV优化的正则化方法对硬X射线望远镜图象重建研究

图象重建是一个求逆过程具有不适定性。本文介绍的是一种从少数投影数据进行图象重建的线性代数法－Ｐｈｉｌｌｉｐｓ－Ｔｉｋｈｏｎｏｖ正则化方法,同时选择优化工具ＧＣＶ确定最优的正则参数。为验证该方法,我们对日本Ｙｏｈｋｏｈ卫星上塔载的硬Ｘ射线望远镜（ＨＸＴ）拍摄的太阳图象进行重建。     

A proposal for comparing the reliabilities of alternative seismic hazard models

Differences between statistical unertainty and modeling uncertainty are briefly discussed. It is pointed out that, when different models are proposed for the interpretation of reality, the uncertainty cannot be described in terms of mean value and coefficient of variation. The important question is: which of the proposed models is more reliable than the others? The attention, then, is concentrated on the comparison between different models proposed for the estimate of the required quantity, looking for a criterion leading to the selection of the most reliable one. A criterion for comparison of different models is suggested. In the example of application considered in this paper, it proved to be effective, so that the continuation of numerical experiments, exploring different and more complex situations, seems promising.     

Using regional regression within index flood procedures and an empirical Bayesian estimator

Studies have illustrated the performance of at-site and regional flood quantile estimators. For realistic generalized extreme value (GEV) distributions and short records, a simple index-flood quantile estimator performs better than two-parameter (2P) GEV quantile estimators with probability weighted moment (PWM) estimation using a regional shape parameter and at-site mean and L-coefficient of variation (L-CV), and full three-parameter at-site GEV/PWM quantile estimators. However, as regional heterogeneity or record lengths increase, the 2P-estimator quickly dominates. This paper generalizes the index flood procedure by employing regression with physiographic information to refine a normalized T-year flood estimator. A linear empirical Bayes estimator uses the normalized quantile regression estimator to define a prior distribution which is employed with the normalized 2P-quantile estimator. Monte Carlo simulations indicate that this empirical Bayes estimator does essentially as well as or better than the simpler normalized quantile regression estimator at sites with short records, and performs as well as or better than the 2P-estimator at sites with longer records or smaller L-CV.     

Bayesian analysis of stage–fall–discharge models for gauging stations affected by variable backwater

Parsimonious stage–fall–discharge rating curve models for gauging stations subject to backwater complications are developed from simple hydraulic theory. The rating curve models are compounded in order to allow for possible shifts in the hydraulics when variable backwater becomes effective. The models provide a prior scientific understanding through the relationship between the rating curve parameters and the hydraulic properties of the channel section under study. This characteristic enables prior distributions for the rating curve parameters to be easily elicited according to site‐specific information and the magnitude of well‐known hydraulic quantities. Posterior results from three Norwegian and one American twin‐gauge stations affected by variable backwater are obtained using Markov chain Monte Carlo simulation techniques. The case studies demonstrate that the proposed Bayesian rating curve assessment is appropriate for developing rating procedures for gauging stations that are subject to variable backwater. Copyright © 2009 John Wiley & Sons, Ltd.     

Each fisherman is different: Taking the environmental perception of small-scale fishermen into account to manage marine protected areas

One of the reasons for the failure of some Marine Protected Areas (MPAs) is the lack of respect for their boundaries and regulations, which intensifies the need to assess the attitudes of stakeholders affected by MPAs. To this end, it is necessary to know the perception and behavior of resource users in these areas in relation to the management process. This study addressed the perception of different groups of fishermen in three MPAs that allow sustainable use of resources on the Brazilian northeastern coast. The perception analysis was based on four aspects: biodiversity conservation, flexibility and adaptability of fishermen, participation in management and opinions about the MPA. The interviewed fishermen (n=100) were classified into natives or immigrants,≥than 40 years old or <40, predominant use of selective or nonselective fishing gear and part or full time fishermen. The results showed that younger fishermen and the ones who use selective fishing gear presented a more conservation prone perception; nonselective fishermen and part-time fishermen were more flexible and adaptable to changes; and younger fishermen tended to agree more with the establishment of the MPAs. Taking these differences in perceptions among fishermen into account could serve as a basis for improvements in the management and conservation of fishing resources, besides helping predict possible future behavior due to changes in management policies.