Estimating and modeling spatio-temporal complex-valued covariance functions

Mapping Intimacies ◽

10.5194/egusphere-egu21-16382 ◽

2021 ◽

Author(s):

Sabrina Maggio ◽

Donato Posa ◽

Sandra De Iaco ◽

Claudia Cappello

Keyword(s):

Complex Data ◽

Temporal Dependence ◽

Covariance Functions ◽

Covariance Models ◽

Unit Of Measurement ◽

Oceanographic Data ◽

Spatio Temporal ◽

Complex Valued ◽

Vectorial Data

Oceanographic data belong to the wide class of vectorial data, for which the decomposition in modulus and direction is meaningful, and the vectorial components are characterized by homogeneous quantities, with the same unit of measurement. Another feature of oceanographic data is that they exhibit spatio-temporal dependence. In Geostatistics, such data can be properly modelled by recalling the theory of complex-valued random fields. However, in the literature, only techniques for modeling and predicting the spatial evolution of these phenomena were proposed; while the temporal dependence was analyzed separately from the spatial one, or just time-varying complex covariance models were used. Thus, the novelty of this paper regards some advances of the complex formalism for analyzing complex data in space-time and new classes of spatio-temporal complex covariance models. A case study on spatio-temporal complex estimating and modeling with oceanographic data is provided and a comparison between two classes of complex covariance models is also proposed.

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Spatio-Temporal Visualisation of Reflections from Building Integrated Photovoltaics

10.20944/preprints201805.0271.v1 ◽

2018 ◽

Author(s):

Roland Schregle ◽

Christian Renken ◽

Stephen Wittkopf

Keyword(s):

Reference Material ◽

Distribution Functions ◽

High Temporal Resolution ◽

Complex Data ◽

3 Dimensional ◽

Building Integrated Photovoltaics ◽

Computational Workflow ◽

Spatio Temporal ◽

The Impact

With the increasing adoption of building integrated photovoltaics (BIPV), concerns arise about potential glare. While recommended criteria to assess glare exist, it is challenging to apply these in the spatial and temporal domains and communicate the complex data to planning authorities and clients. In this paper we present a new computational workflow using annual daylight simulation, material modelling using bi-directional scattering distribution functions (BSDFs) and image-based postprocessing to obtain 3-dimensional renderings of cumulative annual irradiance and glare duration on the built environment. The annual daylight simulation considers relevant sun positions in high temporal resolution (15-minute timesteps) and measured BSDFs to model different PV materials. The postprocessing includes a relative irradiance visualisation comparing the impact of a proposed PV proportional to a reference material. It also includes a new spatio-temporal workflow to assess the glare duration based on recommended thresholds. We demonstrate this workflow with a case study of a proposed PV roof for a church, assessing the glare potential of two different PV materials. Our visualisations indicate glare durations well below the thresholds with satinated PVs, and in noncritical zones outside observer positions with standard PVs. Thus the proposed PV roof does not cause any disturbing glare.

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Spatio-Temporal Visualisation of Reflections from Building Integrated Photovoltaics

10.20944/preprints201805.0271.v2 ◽

2018 ◽

Author(s):

Roland Schregle ◽

Christian Renken ◽

Stephen Wittkopf

Keyword(s):

Reference Material ◽

Distribution Functions ◽

High Temporal Resolution ◽

Complex Data ◽

3 Dimensional ◽

Building Integrated Photovoltaics ◽

Computational Workflow ◽

Spatio Temporal ◽

The Impact

With the increasing adoption of building integrated photovoltaics (BIPV), concerns arise about potential glare. While recommended criteria to assess glare exist, it is challenging to apply these in the spatial and temporal domains and communicate the complex data to planning authorities and clients. This paper presents a new computational workflow using annual daylight simulation, material modelling using bi-directional scattering distribution functions (BSDFs) and image-based postprocessing to obtain 3-dimensional renderings of cumulative annual irradiance and glare duration on the built environment. The annual daylight simulation considers relevant sun positions in high temporal resolution (15-minute timesteps) and measured BSDFs to model different PV materials. The postprocessing includes a relative irradiance visualisation comparing the impact of a proposed PV proportional to a reference material. It also includes a new spatio-temporal workflow to assess the glare duration based on recommended thresholds. This workflow is demonstrated with a case study of a proposed PV roof for a church, assessing the glare potential of two different PV materials. The visualisations indicate glare durations well below the thresholds with satinated PVs, and in noncritical zones outside observer positions with standard PVs. Thus the proposed PV roof does not cause any disturbing glare.

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Modeling spatio-temporal complex covariance functions for vectorial data

Spatial Statistics ◽

10.1016/j.spasta.2021.100562 ◽

2022 ◽

pp. 100562

Author(s):

C. Cappello ◽

S. De Iaco ◽

S. Maggio ◽

D. Posa

Keyword(s):

Covariance Functions ◽

Spatio Temporal ◽

Vectorial Data

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Spatio-Temporal Visualisation of Reflections from Building Integrated Photovoltaics

Buildings ◽

10.3390/buildings8080101 ◽

2018 ◽

Vol 8 (8) ◽

pp. 101 ◽

Cited By ~ 2

Author(s):

Roland Schregle ◽

Christian Renken ◽

Stephen Wittkopf

Keyword(s):

Reference Material ◽

Distribution Functions ◽

High Temporal Resolution ◽

Complex Data ◽

3 Dimensional ◽

Building Integrated Photovoltaics ◽

Computational Workflow ◽

Spatio Temporal ◽

The Impact

With the increasing adoption of building integrated photovoltaics (BIPV), concerns arise about potential glare. While recommended criteria to assess glare exist, it is challenging to apply these in the spatial and temporal domains and communicate the complex data to planning authorities and clients. This paper presents a new computational workflow using annual daylight simulation, material modelling using bi-directional scattering distribution functions (BSDFs) and image-based postprocessing to obtain 3-dimensional renderings of cumulative annual irradiance and glare duration on the built environment. The annual daylight simulation considers relevant sun positions in high temporal resolution (15-min timesteps) and measured BSDFs to model different PV materials. The postprocessing includes a relative irradiance visualisation comparing the impact of a proposed PV proportional to a reference material. It also includes a new spatio-temporal workflow to assess the glare duration based on recommended thresholds. This workflow is demonstrated with a case study of a proposed PV roof for a church, assessing the glare potential of two different PV materials. The visualisations indicate glare durations well below the thresholds with satinated PVs, and in noncritical zones outside observer positions with standard PVs. Thus the proposed PV roof does not cause any disturbing glare.

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Spatio-temporal variograms and covariance models

Advances in Applied Probability ◽

10.1239/aap/1127483743 ◽

2005 ◽

Vol 37 (3) ◽

pp. 706-725 ◽

Cited By ~ 30

Author(s):

Chunsheng Ma

Keyword(s):

Random Field ◽

Covariance Function ◽

Time Lag ◽

Dependent Data ◽

Covariance Functions ◽

Time Space ◽

Temporal Models ◽

Covariance Models ◽

Spatio Temporal ◽

Over Time

Variograms and covariance functions are the fundamental tools for modeling dependent data observed over time, space, or space-time. This paper aims at constructing nonseparable spatio-temporal variograms and covariance models. Special attention is paid to an intrinsically stationary spatio-temporal random field whose covariance function is of Schoenberg-Lévy type. The correlation structure is studied for its increment process and for its partial derivative with respect to the time lag, as well as for the superposition over time of a stationary spatio-temporal random field. As another approach, we investigate the permissibility of the linear combination of certain separable spatio-temporal covariance functions to be a valid covariance, and obtain a subclass of stationary spatio-temporal models isotropic in space.

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Spatio-temporal variograms and covariance models

Advances in Applied Probability ◽

10.1017/s0001867800000434 ◽

2005 ◽

Vol 37 (03) ◽

pp. 706-725 ◽

Cited By ~ 7

Author(s):

Chunsheng Ma

Keyword(s):

Random Field ◽

Covariance Function ◽

Time Lag ◽

Dependent Data ◽

Covariance Functions ◽

Time Space ◽

Temporal Models ◽

Covariance Models ◽

Spatio Temporal ◽

Over Time

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A Statistical Model for Earthquake And/Or Rainfall Triggered Landslides

Frontiers in Earth Science ◽

10.3389/feart.2020.605003 ◽

2021 ◽

Vol 8 ◽

Author(s):

Gabriele Frigerio Porta ◽

Mark Bebbington ◽

Xun Xiao ◽

Geoff Jones

Keyword(s):

Spatial Modeling ◽

Point Processes ◽

Italian Region ◽

Temporal Dependence ◽

Single Mechanism ◽

Different Types ◽

Triggering Events ◽

Spatio Temporal ◽

Secondary Hazards

Natural hazards can be initiated by different types of triggering events. For landslides, the triggering events are predominantly earthquakes and rainfall. However, risk analysis commonly focuses on a single mechanism, without considering possible interactions between the primary triggering events. Spatial modeling of landslide susceptibility (suppressing temporal dependence), or tailoring models to specific areas and events are not sufficient to understand the risk produced by interacting causes. More elaborate models with interactions, capable of capturing direct or indirect triggering of secondary hazards, are required. By discretising space, we create a daily-spatio-temporal hazard model to evaluate the relative and combined effects on landslide triggering due to earthquakes and rainfall. A case study on the Italian region of Emilia-Romagna is presented, which suggests these triggering effects are best modeled as additive. This paper demonstrates how point processes can be used to model the triggering influence of multiple factors in a large real dataset collected from various sources.

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UNIVERSAL KRIGING FOR SPATIO‐TEMPORAL DATA

Mathematical Modelling and Analysis ◽

10.3846/13926292.2003.9637230 ◽

2003 ◽

Vol 8 (4) ◽

pp. 283-290 ◽

Cited By ~ 1

Author(s):

E. Lesauskiene ◽

K. Dučinskas

Keyword(s):

Linear Prediction ◽

Real Data ◽

Universal Kriging ◽

Covariance Functions ◽

Data Prediction ◽

Optimal Linear ◽

Squared Prediction Error ◽

Covariance Models ◽

Spatio Temporal ◽

Mean Function

In this article we have used wide applicable classes of spatio‐temporal nonseparable and separable covariance models. One of the objectives of this paper is to furnish a possibility how to avoid the usage of complicated covariance functions. Assuming regression model for mean function the analytical expressions for the optimal linear prediction (universal kriging) and mean squared prediction error (MSPE) was obtained. Parameterized spatio‐temporal covariance functions were fitted for the real data. Prediction values and MSPE were presented. For visualization of results on graphics are used free available software Gstat.

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