Kriging with external drift for functional data for air quality monitoring

Functional data featured by a spatial dependence structure occur in many environmental sciences when curves are observed, for example, along time or along depth. Recently, some methods allowing for the prediction of a curve at an unmonitored site have been developed. However, the existing methods do not allow to include in a model exogenous variables that, for example, bring meteorology information in modeling air pollutant concentrations. In order to introduce exogenous variables, potentially observed as curves as well, we propose to extend the so-called kriging with external drift—or regression kriging—to the case of functional data by means of a three-step procedure involving functional modeling for the trend and spatial interpolation of functional residuals. A cross-validation analysis allows to choose smoothing parameters and a preferable kriging predictor for the functional residuals. Our case study considers daily PM₁₀ concentrations measured from October 2005 to March 2006 by the monitoring network of Piemonte region (Italy), with the trend defined by meteorological time-varying covariates and orographical constant-in-time variables. The performance of the proposed methodology is evaluated by predicting PM₁₀ concentration curves on 10 validation sites, even with simulated realistic datasets on a larger number of spatial sites. In this application the proposed methodology represents an alternative to spatio-temporal modeling but it can be applied more generally to spatially dependent functional data whose domain is not a time interval.     

A universal kriging approach for spatial functional data

In a wide range of scientific fields the outputs coming from certain measurements often come in form of curves. In this paper we give a solution to the problem of spatial prediction of non-stationary functional data. We propose a new predictor by extending the classical universal kriging predictor for univariate data to the context of functional data. Using an approach similar to that used in univariate geostatistics we obtain a matrix system for estimating the weights of each functional variable on the prediction. The proposed methodology is validated by analyzing a real dataset corresponding to temperature curves obtained in several weather stations of Canada.     

CORRELATION PATTERNS IN CHARACTERISTICS OF SPATIALLY VARIABLE SEISMIC GROUND MOTIONS

A methodology for the investigation of the spatial variation of seismic ground motions is presented; data recorded at the SMART-1 dense instrument array in Lotung, Taiwan, during Events 5 and 39 are used in the analysis. The seismic motions are modeled as superpositions of sinusoidal functions, described by their amplitude, frequency, wavenumber and phase. For each event and direction (horizontal or vertical) analysed, the approach identifies a coherent, common component in the seismic motions at all recording stations, and variabilities in amplitudes and phases around the common component sinusoidal characteristics, that are particular for each recording station. It is shown that the variations in both the amplitudes and the phases of the motions at the station locations around the common component characteristics contribute significantly to the spatially variable nature of the motions, and, furthermore, they are correlated: increase in the variability of the amplitudes of the motions recorded at individual stations around the common amplitude implies increase in the variability of the phases around the common phase. The dispersion range of the amplitude and phase variability around their corresponding common components appear also to be associated with physical parameters. The spatially variable arrival time delays of the waveforms at the stations due to their upward travelling through the site topography, in addition to the wave passage delays identified from signal processing techniques, constitute another important cause for the spatial variation of the motions; their consideration in the approach facilitates also the identification of the correlation patterns in the amplitudes and phases. © 1997 by John Wiley & Sons, Ltd.     

Wavelet-based generation of spatially correlated accelerograms

For the seismic analysis of complex or nonlinear extended structures, it is useful to generate a set of properly correlated earthquake accelerograms that are consistent with a specified seismic hazard. A new simulation approach is presented in this paper for the generation of ensembles of spatially correlated accelerograms such that the simulated motions are consistent with (i) a parent accelerogram in the sense of temporal variations in frequency content, (ii) a design spectrum in the mean sense, and (iii) with a given instantaneous coherency structure. The formulation is based on the extension of stochastic decomposition technique to wavelet domain via the method of spectral factorization. A complex variant of the modified Littlewood-Paley wavelet function is proposed for the wavelet-based representation of earthquake accelerograms, such that this explicitly brings out the phase information of the signal, besides being able to decompose it into component time-histories having energy in non-overlapping frequency bands. The proposed approach is illustrated by generating ensembles of accelerograms at four stations.     

Seasonal and spatial variations in the scaling and correlation structure of streamflow data

Seasonal and spatial variability in scaling, correlation and wavelet variance parameter of daily streamflow data were investigated using 56 gauging stations from five basins located in two different climate zones. Multifractal temporal scaling properties were detected using a multiplicative cascade model. The wavelet variance parameter yielded persistence properties of the streamflow time series. Seasonal variations were found to be significant in that winter and spring seasons where large‐scale frontal events are dominant showed higher long‐term correlations and less multifractality than did summer and fall seasons. Coherent spatial variations were apparent. The Neches River basin located in a subtropic humid climate zone exhibited high persistence and long‐term correlation as well as less multifractality as compared with other basins. It is found that larger drainage areas tend to have smaller multifractality and higher persistence structure, and this tendency becomes apparent in regions that receive large amounts of precipitation and decreases towards arid regions. Copyright © 2012 John Wiley & Sons, Ltd.     

Site effect assessment using KiK-net data: Part 1. A simple correction procedure for surface/downhole spectral ratios

When data is available, the estimation of site effects is usually performed using the “standard spectral ratio” (SSR) technique with respect to an outcropping, reference rock site. This study uses the Japanese KiK-net network, which has more than 600 pairs of surface-downhole stations allowing the computation of empirical borehole transfer functions, consisting of mean spectral ratios of surface over downhole recordings. The borehole transfer function deviates from the SSR in two respects: the reference is located at depth, and the downhole velocity varies from one site to another. These differences bias the estimation of the transfer function with reference to a standard outcrop rock site. The goal of this paper is to develop a simple and robust methodology to correct for such bias. The proposed correction procedure consists of two steps: a depth correction designed to account, in a simplified and physically acceptable way, for the existence at depth of destructive interferences and the absence of free-surface effects in the high-frequency range; and an impedance correction designed to normalize the shear wave velocity at depth. The depth correction involves a simple, frequency-dependent curve to be adapted for each site as a function of the first destructive interference frequency at depth. The impedance normalization combines the use of “generic” rock velocity profiles and a quarter-wavelength approach, resulting in a smooth frequency-dependent amplitude correction. The proposed methodology is applied on a large subset of KiK-net data in view of analysing the correlation between site amplification factors and site parameters in a companion paper.     

A latent class MDS model with spatial constraints for non-stationary spatial covariance estimation

Multidimensional scaling (MDS) has played an important role in non-stationary spatial covariance structure estimation and in analyzing the spatiotemporal processes underlying environmental studies. A combined cluster-MDS model, including geographical spatial constraints, has been previously proposed by the authors to address the estimation problem in oversampled domains in a least squares framework. In this paper is formulated a general latent class model with spatial constraints that, in a maximum likelihood framework, allows to partition the sample stations into classes and simultaneously to represent the cluster centers in a low-dimensional space, while the stations and clusters retain their spatial relationships. A model selection strategy is proposed to determine the number of latent classes and the dimensionality of the problem. Real and artificial data sets are analyzed to test the performance of the model.     

Stochastic simulation of regionalized ground motions using wavelet packets and cokriging analysis

Performance‐based earthquake engineering often requires ground‐motion time‐history analyses to be performed, but very often, ground motions are not recorded at the location being analyzed. The present study is among the first attempt to stochastically simulate spatially distributed ground motions over a region using wavelet packets and cokriging analysis. First, we characterize the time and frequency properties of ground motions using the wavelet packet analysis. The spatial cross‐correlations of wavelet packet parameters are determined through geostatistical analysis of regionalized ground‐motion data from the Northridge and Chi‐Chi earthquakes. It is observed that the spatial cross‐correlations of wavelet packet parameters are closely related to regional site conditions. Furthermore, using the developed spatial cross‐correlation model and the cokriging technique, wavelet packet parameters at unmeasured locations can be best estimated, and regionalized ground‐motion time histories can be synthesized. Case studies and blind tests using data from the Northridge and Chi‐Chi earthquakes demonstrate that the simulated ground motions generally agree well with the actual recorded data. The proposed method can be used to stochastically simulate regionalized ground motions for time‐history analyses of distributed infrastructure and has important applications in regional‐scale hazard analysis and loss estimation. Copyright © 2014 John Wiley & Sons, Ltd.     

Empirical nonergodic shaking scenarios based on spatial correlation models: An application to central Italy

This paper provides a new methodological framework to generate empirical ground shaking scenarios, designed for engineering applications and civil protection planning. The methodology is useful both to reconstruct the ground motion pattern of past events and to generate future shaking scenarios, in regions where strong‐motion datasets from multiple events and multiple stations are available. The proposed methodology combines (1) an ad‐hoc nonergodic ground motion model (GMM) with (2) a spatial correlation model for the source region‐, site‐, and path‐systematic residual terms, and (3) a model of the remaining aleatory error to take into account for directivity effects. The associated variability is a function of the type of scenario generated (bedrock or site, past or future event) and it is minimal for source areas where several events have occurred and for sites where recordings are available. In order to develop the region‐specific fully nonergodic GMM and to compute robust estimation of the residual terms, the approach is calibrated on a highly dense dataset compiled for the area of central Italy. Example tests demonstrate the validity of the approach, which allows to simulate acceleration response spectra at unsampled sites, as well as to capture peculiar physical features of ground motion patterns in the region. The proposed approach could be usefully adopted for data‐driven simulations of ground shaking maps, as alternative or complementary tool to physic‐based and stochastic‐based approaches.     

基于多尺度球面小波解算GPS应变场的方法及应用

提出了利用多尺度球面小波解算GPS应变场的方法,该方法通过建立不规则分布的小波基函数以凸显测站非均匀分布的特征,获取不同空间尺度的应变场.通过对模拟数据进行对比分析验证该方法的有效性,模拟结果显示,多尺度球面小波应变计算方法稳健性较好.在位移场中加入高斯随机误差(均值为0.0mm,标准差为0.5mm)对应变计算结果的影响可忽略不计.从原有位移场随机抽取的60%的数据解算应变场时,仍然能够获取比较可靠的结果,但如果出现大范围的数据空缺,则会对应变结果产生明显影响.基于华北地区GPS测站原始观测数据,通过高精度数据处理方法解算了该区域GPS速度场,根据多尺度球面小波方法,解算了该区域的应变率场及其误差,并分析了其空间分布特征.     

Non-stationary spatial covariance structure estimation in oversampled domains by cluster differences scaling with spatial constraints

In the analysis of spatiotemporal processes underlying environmental studies, the estimation of the non-stationary spatial covariance structure is a well known issue in which multidimensional scaling (MDS) provides an important methodological approach (Sampson and Guttorp in J Am Stat Assoc 87:108–119, 1992). It is also well known that approximating dispersion by a non-metric MDS procedure offers, in general, low precision when accurate differences in spatial dispersion are needed for interpolation purposes, specially if a low dimensional configuration is employed besides a high number of stations in oversampled domains. This paper presents a modification, consisting of including geographical spatial constraints, of Heiser and Groenen’s (Psychometrika 62:63–83, 1997) cluster differences scaling algorithm by which not the original stations but the cluster centres can be represented, while the stations and clusters retain their spatial relationships. A decomposition of the sum of squared dissimilarities into contributions from several sources of variation can be employed for an exploratory diagnosis of the model. Real data are analyzed and differences between several cluster-MDS strategies are discussed.     

Application of synchrosqueezed wavelet transforms to estimate the reservoir fluid mobility

This paper presents a new methodology for estimating reservoir fluid mobility using synchrosqueezed wavelet transforms. Synchrosqueezed wavelet transforms, which adopts a reassignment method, can improve the temporal and spatial resolutions of conventional time‐frequency transforms. The synchrosqueezed wavelet transforms‐based fluid mobility estimation requires the favourable selection of sensitive low‐frequency segment and more accurate estimation of the change rate of the low frequency segment in the spectrum. The least‐squares fitting method is employed in the synchrosqueezed wavelet transforms‐based fluid mobility estimation for improving the precision of the estimation of change rate of the low‐frequency segment in the spectrum. We validate our approach with a model test. Two field examples are used to illustrate that the fluid mobility estimation using the synchrosqueezed wavelet transforms‐based method gives a better reflection of fluid storage space and monitors hydrocarbon‐saturated reservoirs well.     

Spatiotemporal estimation of snow depth using point data from snow stakes,digital terrain models,and satellite data

Snow availability in Alpine catchments plays an important role in water resources management. In this paper, we propose a method for an optimal estimation of snow depth (areal extension and thickness) in Alpine systems from point data and satellite observations by using significant explanatory variables deduced from a digital terrain model. It is intended to be a parsimonious approach that may complement physical‐based methodologies. Different techniques (multiple regression, multicriteria analysis, and kriging) are integrated to address the following issues: We identify the explanatory variables that could be helpful on the basis of a critical review of the scientific literature. We study the relationship between ground observations and explanatory variables using a systematic procedure for a complete multiple regression analysis. Multiple regression models are calibrated combining all suggested model structures and explanatory variables. We also propose an evaluation of the models (using indices to analyze the goodness of fit) and select the best approaches (models and variables) on the basis of multicriteria analysis. Estimation of the snow depth is performed with the selected regression models. The residual estimation is improved by applying kriging in cases with spatial correlation. The final estimate is obtained by combining regression and kriging results, and constraining the snow domain in accordance with satellite data. The method is illustrated using the case study of the Sierra Nevada mountain range (Southern Spain). A cross‐validation experiment has confirmed the efficiency of the proposed procedure. Finally, although it is not the scope of this work, the snow depth is used to asses a first estimation of snow water equivalent resources.     

Modeling of spatially correlated,site-reflected,and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.     

A direct scaling analysis for the sea level rise

The estimation of long-term sea level variability is of primary importance for a climate change assessment. Despite the value of the subject, no scientific consensus has yet been reached on the existing acceleration in observed values. The existence of this acceleration is crucial for coastal protection planning purposes. The absence of the acceleration would enhance the debate on the general validity of current future projections. Methodologically, the evaluation of the acceleration is a controversial and still open discussion, reported in a number of review articles, which illustrate the state-of-art in the field of sea level research. In the present paper, the well-proven direct scaling analysis approach is proposed in order to describe the long-term sea level variability at 12 worldwide-selected tide gauge stations. For each of the stations, it has been shown that the long-term sea level variability exhibits a trimodal scaling behaviour, which can be modelled by a power law with three different pairs of shape and scale parameters. Compared to alternative methods in literature, which take into account multiple correlated factors, this simple method allows to reduce the uncertainties on the sea level rise parameters estimation.     

A composite spatial predictor via local criteria under a misspecified model

Spatial prediction and variable selection for the study area are both important issues in geostatistics. If spatially varying means exist among different subareas, globally fitting a spatial regression model for observations over the study area may be not suitable. To alleviate deviations from spatial model assumptions, this paper proposes a methodology to locally select variables for each subarea based on a locally empirical conditional Akaike information criterion. In this situation, the global spatial dependence of observations is considered and the local characteristics of each subarea are also identified. It results in a composite spatial predictor which provides a more accurate spatial prediction for the response variables of interest in terms of the mean squared prediction errors. Further, the corresponding prediction variance is also evaluated based on a resampling method. Statistical inferences of the proposed methodology are justified both theoretically and numerically. Finally, an application of a mercury data set for lakes in Maine, USA is analyzed for illustration.     

Site Response in Las Vegas Valley, Nevada from NTS Explosions and Earthquake Data

We report site response in Las Vegas Valley (LVV) from historical recordings of Nevada Test Site (NTS) nuclear explosions and earthquake recordings from permanent and temporary seismic stations. Our data set significantly improves the spatial coverage of LVV over previous studies, especially in the northern, deeper parts of the basin. Site response at stations in LVV was measured for frequencies in the range 0.2–5.0 Hz using Standard Spectral Ratios (SSR) and Horizontal-Vertical Spectral Ratios (HVR). For the SSR measurements we used a reference site (approximately NEHRP B ``rock' classification) located on Frenchman Mountain outside the basin. Site response at sedimentary sites is variable in LVV with average amplifications approaching a factor of 10 at some frequencies. We observed peaks in the site response curves at frequencies clustered near 0.6, 1.2 and 2.0 Hz, with some sites showing additional lower amplitude peaks at higher frequencies. The spatial pattern of site response is strongly correlated with the reported depth to basement for frequencies between 0.2 and 3.0 Hz, although the frequency of peak amplification does not show a similar correlation. For a few sites where we have geotechnical shear velocities, the amplification shows a correlation with the average upper 30-meter shear velocities, V₃₀. We performed two-dimensional finite difference simulations and reproduced the observed peak site amplifications at 0.6 and 1.2 Hz with a low velocity near-surface layer with shear velocities 600–750 m/s and a thickness of 100–200 m. These modeling results indicate that the amplitude and frequencies of site response peaks in LVV are strongly controlled by shallow velocity structure.     

The implications of regional variations in rainfall for reconstructing rainfall patterns using tree rings

In Australia, multidecadal periods of floods and droughts have major economic consequences. Due to the short duration of Australian instrumental precipitation records, it is difficult to determine the patterns of these multidecadal periods. Proxy records can be used to create long‐term rainfall reconstructions for regions that are lacking instrumental data. However, the spatial extent over which single‐site proxy records can be applied is poorly understood. Southeast Queensland (SEQ) is an area where tree rings can be used to reconstruct long‐term rainfall patterns, but their regional representation is unknown. In this study, the spatial variability in rainfall across SEQ is investigated from 1908 to 2007 using 140 instrumental rainfall stations. Pearson correlation analysis between stations is used to create groups at the r = 0.80, 0.85, and 0.90 correlation levels, and then annual deviations from the mean are determined. These patterns indicate that rainfall is not uniform across SEQ but can be broken into 2 main spatially consistent groups. Each of these groups is broken down into several subgroups with higher correlation levels. Long‐term streamflow records are found to be correlated to rainfall patterns local to the streamflow stations, indicating that analysis of extreme events should consider spatial precipitation variability. Finally, the only currently available proxy rainfall reconstruction for the region, a 140‐year Toona ciliata tree ring width record from Lamington National Park, is compared to rainfall groups at different correlation levels across all of SEQ. The correlation between the reconstruction and the rainfall station groupings is best for the groups within which the tree‐ring record is spatially located, and this correlation improves as rainfall group correlation increases. Correlation is nearly nonexistent for groupings located at a distance from the tree‐ring site. These results demonstrate the importance of assessing the spatial variability of precipitation so that the spatial applicability of proxy records can be assessed.     

Nonlinear estimation of spatial distribution of rainfall — An indicator cokriging approach

Indicator cokriging (Journel 1983) is examined as a tool for real-time estimation of rainfall from rain gage measurements. The approach proposed in this work obviates real-time estimation of real-time statistics of rainfall by using ensemble or climatological statistics exclusively, and reduces computational requirements attendant to indicator cokriging by employing only a few auxiliary cutoffs in estimation of conditional probabilities. Due to unavailability of suitable rain gage measurements, hourly radar rain fall data were used for both indicator covariance estimation and a comparative evaluation. Preliminary results suggest that the indicator cokriging approach is clearly superior to its ordinary kriging counterpart, whereas the indicator kriging approach is not. The improvement is most significant in estimation of light rainfall, but drops off significantly for heavy rainfall. The lack of predictability in spatial estimation of heavy rainfall is borne out in the integral scale of indicator correlation: peaking to its maximum for cutoffs near the median, indicator correlation scale becomes increasingly smaller for larger cutoffs of rainfall depth. A derived-distribution analysis, based on the assumption that radar rainfall is a linear sum of ground-truth and a random error, suggests that, at low cutoffs, indicator correlation scale of ground-truth can significantly differ from that of radar rainfall, and points toward inclusion of rainfall intermittency, for example, within the framework proposed in this work.