The smoothness of HASM

To smooth noises inherent in uniformly sampled dataset, the smoothness of high accuracy surface modeling (HASM) was explored, and a smoothing method of HASM (HASM-SM) was developed based on a penalized least squares method. The optimal smoothing parameter of HASM-SM was automatically obtained by means of the generalized cross-validation (GCV) method. For an efficient smoothing computation, discrete cosine transform was employed to solve the system of HASM-SM and to estimate the minimum GCV score, simultaneously. Two examples including a numerical test and a real-world example were employed to compare the smoothing ability of HASM-SM with that of GCV thin plate smoothing spline (TPS) and kriging. The numerical test indicated that the minimum GCV HASM-SM is averagely more accurate than TPS and kriging for noisy surface smoothing. The real-world example of smoothing a lidar-derived Digital Elevation Model (DEM) showed that HASM-SM has an obvious smoothing effect, which is on a par with TPS. In conclusion, HASM-SM provides an efficient tool for filtering noises in grid-based surfaces like remote sensing–derived images and DEMs.     

Map errors that could account for deviations from a uniform intensity of land change

Intensity Analysis is a mathematical framework that compares a uniform intensity to observed intensities of temporal changes among categories. Our article summarizes Intensity Analysis and presents a new method to compute the minimum hypothetical error in the data that could account for each observed deviation from a uniform intensity. A larger hypothetical error gives stronger evidence against a hypothesis that a change is uniform. The method produces results for five groups of measurements, which are organized into three levels of analysis: interval, category, and transition. The method applies generally to analysis of changes among categories during time intervals, because the input is a standard contingency table for each time interval. We illustrate the method with a case study concerning change during three time intervals among four land categories in northeastern Massachusetts, USA. Modelers can perform the analysis using our computer program, which is free.     

雷达测雨误差及其对淮河流域径流模拟的影响

将雷达测雨数据与分布式水文模型相耦合进行径流过程模拟,分析雷达测雨误差及其径流过程模拟效果,研究雷达测雨误差对径流过程模拟的影响效应.在对淮河流域气象中心业务化的5种淮河流域雷达测雨数据进行误差分析的基础上,采用雷达测雨数据驱动HEC-HMS水文模型,模拟分析淮河息县水文站以上流域2007年7月1-10日强降雨集中期的径流过程.结果表明:利用雷达测雨数据的径流模拟结果与实测资料的模拟结果基本吻合,各种雷达测雨数据误差经过HEC-HMS水文模型传递后,误差明显减小.联合校准法对应的模拟效果最好,过程流量相对误差NBs'和洪峰流量相对误差Z'分别为-20.2%和-13.3%.     

基于粒子群优化的多目标体中梯电阻率异常反演

在采用中梯装置的电阻率剖面法应用中,特别是在环境、水文和工程等领域,经常遇到需要对多个异常目标体进行快速定位以便及时进行相应处理的情况.利用倾斜椭球体来近似模拟这些电阻率异常目标体,使得正演计算可以采用解析表达式来实现,提高正演计算的时效性.相应的地球物理模型也可简化为由椭球体个数、中心点位置、倾角、轴径以及电阻率等参数构成的粒子,多个粒子组成的粒子群在粒子群优化算法的控制下在给定的搜索空间中并行地搜索最优模型.通过对粒子群优化算法参数的合理设计,利用其良好的全局与局部均衡的搜索能力实现对多个异常目标体的同时反演.数值实验结果表明该反演方法能有效实现对多个目标体的同时反演,计算速度快、反演拟合精度较高、同时具有一定的抗噪音能力.快速的多目标体反演,可以实时准确的定量解译中梯剖面法圈定的异常目标体,较好地满足工程等领域的高时效性要求.     

Accuracy of the half-power bandwidth method with a third-order correction for estimating damping in multi-DOF systems

A third-order correction was recently suggested to improve the accuracy of the half-power bandwidth method in estimating the damping of single DOF systems.This paper analyzes the accuracy of the half-power bandwidth method with the third-order correction in damping estimation for multi-DOF linear systems.Damping ratios in a two-DOF linear system are estimated using its displacement and acceleration frequency response curves,respectively.A wide range of important parameters that characterize the shape of these response curves are taken into account.Results show that the third-order correction may greatly improve the accuracy of the half-power bandwidth method in estimating damping in a two-DOF system.In spite of this,the half-power bandwidth method may significantly overestimate the damping ratios of two-DOF systems in some cases.     

Review of the Kalman-type hydrological data assimilation

ABSTRACT

There is great potential in Data Assimilation (DA) for the purposes of uncertainty identification, reduction and real-time correction of hydrological models. This paper reviews the latest developments in Kalman filters (KFs), particularly the Extended KF (EKF) and the Ensemble KF (EnKF) in hydrological DA. The hydrological DA targets, methodologies and their applicability are examined. The recent applications of the EKF and EnKF in hydrological DA are summarized and assessed critically. Furthermore, this review highlights the existing challenges in the implementation of the EKF and EnKF, especially error determination and joint parameter estimation. A detailed review of these issues would benefit not only the Kalman-type DA but also provide an important reference to other hydrological DA types.

Editor D. Koutsoyiannis; Associate editor F. Pappenberger     

Recent progress in estimating uncertainty in geomagnetic field modeling

Abstract

Recent work pertaining to estimating error and accuracies in geomagnetic field modeling is reviewed from a unified viewpoint and illustrated with examples. The formulation of a finite dimensional approximation to the underlying infinite dimensional problem is developed. Central to the formulation is an inner product and norm in the solution space through which a priori information can be brought to bear on the problem. Such information is crucial to estimation of the effects of higher degree fields at the Core-Mantle boundary (CMB) because the behavior of higher degree fields is masked in our measurements by the presence of the field from the Earth's crust. Contributions to the errors in predicting geophysical quantities based on the approximate model are separated into three categories: (1) the usual error from the measurement noise; (2) the error from unmodeled fields, i.e. from sources in the crust, ionosphere, etc.; and (3) the error from truncating to a finite dimensioned solution and prediction space. The combination of the first two is termed low degree error while the third is referred to as truncation error.

The error analysis problem consists of “characterizing” the difference δz = z—z, where z is some quantity depending on the magnetic field and z is the estimate of z resulting from our model. Two approaches are discussed. The method of Confidence Set Inference (CSI) seeks to find an upper bound for |z—?|. Statistical methods, i.e. Bayesian or Stochastic Estimation, seek to estimate E(δz² ), where E is the expectation value. Estimation of both the truncation error and low degree error is discussed for both approaches. Expressions are found for an upper bound for |δz| and for E(δz² ). Of particular interest is the computation of the radial field, B., at the CMB for which error estimates are made as examples of the methods. Estimated accuracies of the Gauss coefficients are given for the various methods. In general, the lowest error estimates result when the greatest amount of a priori information is available and, indeed, the estimates for truncation error are completely dependent upon the nature of the a priori information assumed. For the most conservative approach, the error in computing point values of B_r at the CMB is unbounded and one must be content with, e.g., averages over some large area. The various assumptions about a priori information are reviewed. Work is needed to extend and develop this information. In particular, information regarding the truncated fields is needed to determine if the pessimistic bounds presently available are realistic or if there is a real physical basis for lower error estimates. Characterization of crustal fields for degree greater than 50 is needed as is more rigorous characterization of the external fields.     

Reconstruction of the rainy season precipitation in central Jordan

Abstract

Concurrent reconstructions of October—April precipitation at Madaba and Rabba gauging sites in central Jordan back to the year 1777 using a multivariate regression model are presented. The reconstruction model was calibrated using concurrent precipitation and tree-ring data for the period 1953–1981 The regression equation is significant (p < 0.05), while reconstructions account for 53% and 48% (adjusted for lost degrees of freedom) of the total variability of the precipitation at the Madaba and Rabba sites, respectively. The validation statistic obtained indicates the existence of worthwhile information in the reconstructions. A threshold of 1 standard deviation below the mean is used to define extremely dry years. The concurrent analysis of the reconstructed precipitation at both sites indicates the occurrence of 24 regional extremely dry periods of between 1 and 2 years' duration. Dry periods of more than 2 years' duration rarely occur. This study indicates the occurrence of noticeable extremely dry individual years: 1800, 1827, 1895 and 1933. The estimated mean recurrence times of extreme droughts are 9.3 and 51.3 years for droughts of 1-year and 2-years duration, respectively.     

A note on the applicability of log-Gumbel and log-logistic probability distributions in hydrological analyses: II. Assumed pdf

Abstract

Applicability of log-Gumbel (LG) and log-logistic (LL) probability distributions in hydrological studies is critically examined under real conditions, where the assumed distribution differs from the true one. The set of alternative distributions consists of five two-parameter distributions with zero lower bound, including LG and LL as well as lognormal (LN), linear diffusion analogy (LD) and gamma (Ga) distributions. The log-Gumbel distribution is considered as both a false and a true distribution. The model error of upper quantiles and of the first two moments is analytically derived for three estimation methods: the method of moments (MOM), the linear moments method (LMM) and the maximum likelihood method (MLM). These estimation methods are used as methods of approximation of one distribution by another distribution. As recommended in the first of this two-part series of papers, MLM turns out to be the worst method, if the assumed LG or LL distribution is not the true one. It produces a huge bias of upper quantiles, which is at least one order higher than that of the other two methods. However, the reverse case, i.e. acceptance of LN, LD or Ga as a hypothetical distribution, while the LG or LL distribution is the true one, gives the MLM bias of reasonable magnitude in upper quantiles. Therefore, one should avoid choosing the LG and LL distributions in flood frequency analysis, especially if MLM is to be applied.     

Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies

Abstract

The collocation technique has become a popular tool in oceanography and hydrology for estimating the error variances of different data sources such as in situ sensors, models and remote sensing products. It is also possible to determine calibration constants, for example to account for an off-set between the data sources. So far, the temporal autocorrelation structure of the errors has not been studied, although it is known that it has detrimental effects on the results of the collocation technique, in particular when calibration constants are also determined. This paper shows how the (triple) collocation estimators can be adapted to retrieve the autocovariance functions; the statistical properties as well as the structural deficencies are described. The coupling between the autocorrelation of the error and the estimation of calibration constants is studied in detail, due to its importance for analysing temporal changes. In soil moisture applications, such time variations can be induced, for example, by seasonal changes in the vegetation cover, which affect both models and remote sensing products. The limitations of the proposed technique associated with these considerations are analysed using remote sensing and in situ soil moisture data. The variability of the inter-sensor calibration and the autocovariance are shown to be closely related to temporal patterns of the data.

Editor D. Koutsoyiannis

Citation Zwieback, S., Dorigo, W., and Wagner, W., 2013. Estimation of the temporal autocorrelation structure by the collocation technique with an emphasis on soil moisture studies. Hydrological Sciences Journal, 58 (8), 1729–1747.