Geostatistical analysis of time series of short LAeq values

2011

2011

Geoderma, 2008

Geostatistics is commonly used to describe and predict the variation of soil properties over the landscape. However, many geostatistical methods require the assumption that our observed data are a realization of a random function which is intrinsically stationarity. Under stationarity, observations of a single realization of the random function at different positions can be treated as a form of replication. There are various ways in which a random function may breach the assumption of intrinsic stationarity and numerous geostatistical techniques have been developed that are able to cope with some forms of non-stationarity. What is currently needed is a set of diagnostic tools capable of detecting and identifying when data cannot plausibly be treated as a realization of a process which is stationary in the variance.

Statistical quality control is used to detect changes in the parameters values of the process which usually are estimated under the assumption of independence of the sampling units with respect to the quality characteristic. However, this is questionable for many processes. The main objective of this paper is to present estimators for the variance of autocorrelated processes by using Geostatistics methodology. With this new procedure the usual Shewhart's control charts still can be used to monitor the quality of the process. A Monte Carlo simulation study showed that the proposed estimators have good performance.

2002

Geostatistics is a set of statistical techniques that is increasingly used to characterize spatial dependence in spatially referenced ecological data. A common feature of geostatistics is predicting values at unsampled locations from nearby samples using the kriging algorithm. Modeling spatial dependence in sampled data is necessary before kriging and is usually accomplished with the variogram and its traditional estimator. Other types of estimators, known as non-ergodic estimators, have been used in ecological applications. Non-ergodic estimators were originally suggested as a method of choice when sampled data are preferentially located and exhibit a skewed frequency distribution. Preferentially located samples can occur, for example, when areas with high values are sampled more intensely than other areas. In earlier studies the visual appearance of variograms from traditional and non-ergodic estimators were compared. Here we evaluate the estimators' relative performance in prediction. We also show algebraically that a non-ergodic version of the variogram is equivalent to the traditional variogram estimator. Simulations, designed to investigate the effects of data skewness and preferential sampling on variogram estimation and kriging, showed the traditional variogram estimator outperforms the non-ergodic estimators under these conditions. We also analyzed data on carabid beetle abundance, which exhibited large-scale spatial variability (trend) and a skewed frequency distribution. Detrending data followed by robust estimation of the residual variogram is demonstrated to be a successful alternative to the non-ergodic approach.

Mathematical Geology, 2001

tics as it gives the uncertainty of the variogram estimates. This assessment, however, is repeatedly overlooked in most applications mainly, perhaps, because a general approach has not been implemented in the most commonly used software packages for variogram analysis. In this paper the authors propose a solution that can be implemented easily in a computer program, and which, subject to certain assumptions, is exact. These assumptions are not very restrictive: second-order stationarity (the process has a finite variance and the variogram has a sill) and, solely for the purpose of evaluating fourth-order moments, a Gaussian distribution for the random function. The approach described here gives the variance-covariance matrix of the experimental variogram, which takes into account not only the correlation among the experiemental values but also the multiple use of data in the variogram computation. Among other applications, standard errors may be attached to the variogram estimates and the variance-covariance matrix may be used for fitting a theoretical model by weighted, or by generalized, least squares. Confidence regions that hold a given confidence level for all the variogram lag estimates simultaneously have been calculated using the Bonferroni method for rectangular intervals, and using the multivariate Gaussian assumption for K-dimensional elliptical intervals (where K is the number of experimental variogram estimates). A general approach for incorporating the uncertainty of the experimental variogram into the uncertainty of the variogram model parameters is also shown. A case study with rainfall data is used to illustrate the proposed approach.

As mentioned in the preceding additional information (hereafter called Part I), a series of strong earthquakes with magnitudes between 5.2 and 5.9-units occurred during the two weeks period: 3 to 19 April, 2006 with epicenters lying at distances 80 to 100 km west of PAT station. Here, we show that the analysis in the natural time of the seismicity that occurred after the Seismic Electric Signals (SES) activity on February 13, 2006, specifies the occurrence time of the initiation of the aforementioned earthquake activity within a narrow range around two days. Furthermore, we provide the most recent information on some points mentioned in the main text.

Journal of Time Series Analysis, 2017

The covariance function and the variogram play very important roles in modelling and in prediction of spatial and spatio-temporal data. The assumption of second order stationarity, in space and time, is often made in the analysis of spatial data and the spatio-temporal data. Several times the assumption of stationarity is considered to be very restrictive, and therefore, a weaker assumption that the data is Intrinsically stationary both in space and time is often made and used, mainly by the geo-statisticians and other environmental scientists. In this paper we consider the data to be intrinsically stationary. Because of the inclusion of time dimension,the estimation and derivation of the sampling properties of various estimators related to spatio-temporal data become complicated. In this paper our object is to present an alternative way, based on Frequency Domain methods for modelling the data. Here we consider Discrete Fourier Transforms (DFT) defined for the (Intrinsic) time series data observed at several locations as our data, and then consider the estimation of the parameters of spatiotemporal covariance function, estimation of Frequency Variogram, tests of independence etc. We use the well known property that the Discrete Fourier Transforms of stationary time series evaluated at distinct Fourier Frequencies are asymptotically independent and distributed as complex normal in deriving many results considered in this paper. Our object here is to emphasize the usefulness of the Discrete Fourier transforms in the analysis of spatio-temporal data. Under the intrinsic stationarity condition we consider the estimation, discuss the sampling properties of the Frequency Variogram (FV) introduced in an earlier paper by Subba Rao et al. (2014) which was proposed as an alternative to the classical space, time variogram. We show that the FV introduced is a frequency decomposition of the space-time variogram, and can be computed using the Fast Fourier Transform algorithms. Assuming that the DFT's of the intrinsically stationary processes satisfy a Laplacian type of model, an analytic expression for the space-time spectral density function is derived for the intrinsic processes and also an expression for the Frequency Variogram in terms of the spectral density function is also derived. The estimation of the parameters of the spectrum is also considered. A statistical test for spatial independence of spatio-temporal data is also briefly mentioned, and is based on the test proposed earlier by Wahba (1971) for testing independence in multivariate stationary (temporally) time series.

Academia Letters, 2022