A simple non-separable, non-stationary spatiotemporal model for ozone

Bruno, Francesca; Guttorp, Peter; Sampson, Paul D.

doi:10.1007/s10651-008-0094-8

Cited by 26 publications

(13 citation statements)

References 26 publications

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“…that the covariance function is dependent only on the length of the separation and not on its direction). An example of a spatio-temporal covariance model where the assumptions of stationarity and separability is relaxed is presented in Bruno et al (2009), applied to tropospheric ozone data.…”

Section: Nonstationary Covariance Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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This paper presents a literature survey on timedependent statistical modelling of extreme waves and sea states. The focus is twofold: on statistical modelling of extreme waves and space-and time-dependent statistical modelling. The first part will consist of a literature review of statistical modelling of extreme waves and wave parameters, most notably on the modelling of extreme significant wave height. The second part will focus on statistical modelling of time-and space-dependent variables in a more general sense, and will focus on the methodology and models used also in other relevant application areas. It was found that limited effort has been put on developing statistical models for waves incorporating spatial and long-term temporal variability and it is suggested that model improvements could be achieved by adopting approaches from other application areas. In particular, Bayesian hierarchical space-time models were identified as promising tools for spatio-temporal modelling of extreme waves. Finally, a review of projections of future extreme wave climate is presented.

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Section: Nonstationary Covariance Modelsmentioning

confidence: 99%

Long-term time-dependent stochastic modelling of extreme waves

Vanem

2010

Stoch Environ Res Risk Assess

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“…For estimation of a deterministic trend, different forms to model complex settings have been proposed (Dimitrakopoulos and Luo 1997), which can even incorporate the seasonal effect. Additional options to accomplish specification of the trend can be derived through broad-spectrum approaches, as the generalized linear estimation (Fox 2008) or the median polish algorithm (Bruno et al 2009). We should highlight that both assumptions for the trend can provide similar predictions, when the dependence structure of the residual data is appropriately characterized (De Iaco and Posa 2012).…”

Section: Methodsmentioning

confidence: 99%

Spatial–temporal modellization of the $$\hbox {NO}_{2}$$ NO 2 concentration data through geostatistical tools

et al. 2015

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The nitrogen dioxide is a primary pollutant, regarded for the estimation of the air quality index, whose excessive presence may cause significant environmental and health problems. In the current work, we suggest characterizing the evolution of NO 2 levels, by using geostatistical approaches that deal with both the space and time coordinates. To develop our proposal, a first exploratory analysis was carried out on daily values of the target variable, daily measured in Portugal from 2004 to 2012, which led to identify three influential covariates (type of site, environment and month of measurement). In a second step, appropriate geostatistical tools were applied to model the trend and the space-time variability, thus enabling us to use the kriging techniques for prediction, without requiring data from a dense monitoring network. This methodology has valuable applications, as it can provide accurate assessment of the nitrogen dioxide concentrations at sites where either data have been lost or there is no monitoring station nearby.

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“…In [24] a spatio-temporal process was approximated using the polynomial chaos expansion (PCE), and applied to a temperature dataset obtained from an oceanographic experiment. More about theory and applications of spatio-temporal processes and their covariances can be found in [25][26][27][28][29][30]. The novelty of the current work lies in (i) using tensor decomposition techniques in approximating the covariance of a spatio-temporal process, and (ii) subsequently proposing closed-form expressions for this process using the bases found by tensor decompositions.…”

Section: Introductionmentioning

confidence: 99%

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

Ghosh

Suryawanshi

2014

Commun. comput. phys.

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A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loève (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a thirdorder tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

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A simple non-separable, non-stationary spatiotemporal model for ozone

Cited by 26 publications

References 26 publications

Long-term time-dependent stochastic modelling of extreme waves

Long-term time-dependent stochastic modelling of extreme waves

Spatial–temporal modellization of the $$\hbox {NO}_{2}$$ NO 2 concentration data through geostatistical tools

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

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