Universal Kriging of functional data: Trace-variography vs cross-variography? Application to gas forecasting in unconventional shales

Menafoglio, Alessandra; Grujic, Ognjen; Caers, Jef

doi:10.1016/j.spasta.2015.12.003

Cited by 25 publications

(12 citation statements)

References 26 publications

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“…This was expected since the boundaries between areas cannot be entirely steady. Considering the presence of 3 different areas in the SWTA demonstrating a lack of thermohaline stationarity in the SWTA domain, an alternative approach for future studies accounting for the no stationarity would be the use of Universal Kriging (Menafoglio et al, 2016(Menafoglio et al, , 2013, which supposes that the random field has an expectation that depends of the area.…”

Section: Discussionmentioning

confidence: 99%

3D characterisation of the thermohaline structure in the southwestern tropical Atlantic derived from functional data analysis of in situ profiles

Assunção

Silva²,

Roy

et al. 2020

Progress in Oceanography

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The dynamic of the thermohaline structure of the upper ocean, which depends on ocean-atmosphere interactions, drives most near surface oceanic processes, including the control of gases and heat fluxes, and nutrient availability in the photic layer. The thermohaline structure of the southwestern tropical Atlantic (SWTA), a key region for diagnosing variation of the Atlantic Meridional Overturning Circulation, has prime impact on global climate. Characterising the thermohaline structure is typically based on the application of classical statistical methods on vertical profiles. Such approach has important limitations since classical methods do not explicitly contemplate the vertical nature of the profiles. Functional Data Analysis (FDA) is a new alternative to solve such drawbacks. Here, we apply an FDA approach to characterise the 3D canonical thermohaline structure of the SWTA in austral spring and fall. Our results reveal a clear spatial pattern with the presence of three areas with significantly different thermohaline structure. Area 1, mostly located along the continental slope, reflects the western boundary current system, with low static stability and high frequency of occurrence of barrier layer (BL). Conversely, Area 2, located along the Fernando de Noronha chain, presents strong static stability with a well-marked thermocline. This area, under the influence of the eastern Atlantic, is characterised by a low BL frequency, which is seasonally modulated by the latitudinal oscillation of the Intertropical Convergence Zone, controlling the regime of precipitation. In turn, Area 3 behaves as a transition zone between A1 and A2 with the presence of the water core of maximum salinity in subsurface, and therefore presence of strong-moderate BL. Beyond this study, FDA approach emerges as a powerful way to describe, characterise, classify and compare ocean patterns and Please note that this is an author-produced PDF of an article accepted for publication following peer review. The definitive publisher-authenticated version is available on the publisher Web site.processes. It can be applied to in situ data but could also be used to deeply and comprehensively explore ocean model output. Highlights► The thermohaline structure drives most near surface oceanic processes. ► A functional data analysis approach is used to characterise in 3D the thermohaline structure of the southwestern tropical Atlantic in spring and fall. ► We reveal a clear spatial pattern with the presence of three areas with significantly different thermohaline structure. ► The picture provided can serve as a reference for diagnosing future variation in the Atlantic Meridional Overturning Circulation.

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Section: Discussionmentioning

confidence: 99%

3D characterisation of the thermohaline structure in the southwestern tropical Atlantic derived from functional data analysis of in situ profiles

Assunção

Silva²,

Roy

et al. 2020

Progress in Oceanography

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“…We assume square integrability, that is

for all

. We can thus define the expectation

of the process as

, and the trace-covariogram ( Menafoglio et al, 2013 , Menafoglio and Petris, 2015 , Menafoglio et al, 2016a ) of the process as

where, for all

that is the infinite-dimensional analogue of the covariogram of a real-valued process ( Cressie, 1993 ). If we assume second-order stationarity and isotropy, the trace-covariogram reduces to a function of a real non-negative variable, i.e.…”

Section: Modeling Death Data As Functional Compositionsmentioning

confidence: 99%

“…To set the background, we recall that over the last decades considerable work has been done on extending classical statistical methods to the case of data embedded in functional Hilbert spaces (see, e.g., Ramsay and Silverman, 2005 , Ferraty and Vieu, 2006 , Horváth and Kokoszka, 2012 , Wang et al, 2016 and references therein). Moreover, an important body of literature has focused on developing a consistent theoretical framework for geostatistical modeling and spatial prediction for functional data, developing the infinite-dimensional counterparts of techniques such as spatial variography and Kriging ( Giraldo et al, 2010 , Nerini et al, 2010 , Giraldo et al, 2011 , Ruiz-Medina, 2012 , Menafoglio et al, 2013 , Caballero et al, 2013 , Ignaccolo et al, 2014 , Menafoglio and Petris, 2015 , Menafoglio et al, 2016b , Menafoglio et al, 2016a ). Recent works have specifically targeted the case of constrained functions and other object data, in a stream of literature that we refer to as Object Oriented Spatial Statistics (O2S2) ( Menafoglio and Secchi, 2017 and references therein).…”

Section: Introductionmentioning

confidence: 99%

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

et al. 2022

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With the tools and perspective of Object Oriented Spatial Statistics, we analyze official daily data on mortality from all causes in the provinces and municipalities of Italy for the year 2020, the first of the COVID-19 pandemic. By comparison with mortality data from 2011 to 2019, we assess the local impact of the pandemic as perturbation factor of the natural spatio-temporal death process. For each Italian province and year, mortality data are represented by the densities of time of death during the calendar year. Densities are regarded as functional data belonging to the Bayes space In this space, we use functional-on-functional linear models to predict the expected mortality in 2020, based on mortality in previous years, and we compare predictions with actual observations, to assess the impact of the pandemic. Through spatial downscaling of the provincial data down to the municipality level, we identify spatial clusters characterized by mortality densities anomalous with respect to the surroundings. The proposed analysis pipeline could be extended to indexes different from death counts, measured at a granular spatio-temporal scale, and used as proxies for quantifying the local disruption generated by the pandemic.

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“…Particular attention has been paid to the problem of spatial prediction, especially to the development of novel notions of functional Kriging, both in the stationary (see, e.g., Delicado et al, 2010, for a recent review) and in the non-stationary setting (e.g., Caballero et al, 2013;Ignaccolo et al, 2014). This theory was widely applied, e.g., in climatology (prediction of daily temperature profiles, see Delicado et al, 2010, and references therein), oceanography (temperature profiles along depth of the ocean, see Nerini et al, 2010), air quality monitoring (Ignaccolo et al, 2014), wireless sensors networks (Lee et al, 2015), petroleum system modeling and production forecast (Menafoglio et al, 2016a).…”

Section: Recent Approaches To the Analysis Of Object Datamentioning

confidence: 99%

Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics

Menafoglio

Secchi

2017

European Journal of Operational Research

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We review recent advances in Object Oriented Spatial Statistics, a system of ideas, algorithms and methods that allows the analysis of high dimensional and complex data when their spatial dependence is an important issue. At the intersection of different disciplines – including mathematics, statistics, computer science and engineering – Object Oriented Spatial Statistics provides the right perspective to address key problems in varied contexts, from Earth and life sciences to urban planning. We illustrate a few paradigmatic methods applied to problems of prediction, classification and smoothing, giving emphasis to the key ideas Object Oriented Spatial Statistics relies upon

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Universal Kriging of functional data: Trace-variography vs cross-variography? Application to gas forecasting in unconventional shales

Cited by 25 publications

References 26 publications

3D characterisation of the thermohaline structure in the southwestern tropical Atlantic derived from functional data analysis of in situ profiles

3D characterisation of the thermohaline structure in the southwestern tropical Atlantic derived from functional data analysis of in situ profiles

A look at the spatio-temporal mortality patterns in Italy during the COVID-19 pandemic through the lens of mortality densities

Statistical analysis of complex and spatially dependent data: A review of Object Oriented Spatial Statistics

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