Data Assimilation in Spatio-Temporal Models with Non-Gaussian Initial States—The Selection Ensemble Kalman Model

Assimilation of spatio-temporal data poses a challenge when allowing non-Gaussian features in the prior distribution. It becomes even more complex with nonlinear forward and likelihood models. The ensemble Kalman model and its many variants have proven resilient when handling nonlinearity. However, owing to the linearized updates, conserving the non-Gaussian features in the posterior distribution remains an issue. When the prior model is chosen in the class of selection-Gaussian distributions, the selection Ensemble Kalman model provides an approach that conserves non-Gaussianity in the posterior distribution. The synthetic case study features the prediction of a parameter field and the inversion of an initial state for the diffusion equation. By using the selection Kalman model, it is possible to represent multimodality in the posterior model while offering a 20 to 30% reduction in root mean square error relative to the traditional ensemble Kalman model.

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Spatio-Temporal Inversion Using the Selection Kalman Model

Frontiers in Applied Mathematics and Statistics ◽

10.3389/fams.2021.636524 ◽

2021 ◽

Vol 7 ◽

Author(s):

Maxime Conjard ◽

Henning Omre

Keyword(s):

Gaussian Distribution ◽

Recursive Algorithm ◽

Initial Distribution ◽

Pollution Monitoring ◽

Initial State ◽

Gaussian Distributions ◽

Initial States ◽

Spatio Temporal ◽

Spatial Histogram

Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial distribution and Gauss-linear forward and observation models. This model is contained in the class of Gaussian distribution and is therefore analytically tractable. It is however unsuitable for representing multimodality. We define the selection Kalman model that is based on a selection-Gaussian initial distribution and Gauss-linear forward and observation models. The selection-Gaussian distribution can be seen as a generalization of the Gaussian distribution and may represent multimodality, skewness and peakedness. This selection Kalman model is contained in the class of selection-Gaussian distributions and therefore it is analytically tractable. An efficient recursive algorithm for assessing the selection Kalman model is specified. The synthetic case study of spatio-temporal inversion of an initial state, inspired by pollution monitoring, suggests that the use of the selection Kalman model offers significant improvements compared to the traditional Kalman model when reconstructing discontinuous initial states.

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Pyramidal Framework: Guidance for the Next Generation of GIS Spatial-Temporal Models

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi10030188 ◽

2021 ◽

Vol 10 (3) ◽

pp. 188

Author(s):

Cyril Carré ◽

Younes Hamdani

Keyword(s):

Conceptual Models ◽

Future Generations ◽

Temporal Data ◽

Temporal Modeling ◽

Temporal Models ◽

Gis Data ◽

Spatio Temporal ◽

New Interpretation ◽

Conventional Literature

Over the last decade, innovative computer technologies and the multiplication of geospatial data acquisition solutions have transformed the geographic information systems (GIS) landscape and opened up new opportunities to close the gap between GIS and the dynamics of geographic phenomena. There is a demand to further develop spatio-temporal conceptual models to comprehensively represent the nature of the evolution of geographic objects. The latter involves a set of considerations like those related to managing changes and object identities, modeling possible causal relations, and integrating multiple interpretations. While conventional literature generally presents these concepts separately and rarely approaches them from a holistic perspective, they are in fact interrelated. Therefore, we believe that the semantics of modeling would be improved by considering these concepts jointly. In this work, we propose to represent these interrelationships in the form of a hierarchical pyramidal framework and to further explore this set of concepts. The objective of this framework is to provide a guideline to orient the design of future generations of GIS data models, enabling them to achieve a better representation of available spatio-temporal data. In addition, this framework aims at providing keys for a new interpretation and classification of spatio-temporal conceptual models. This work can be beneficial for researchers, students, and developers interested in advanced spatio-temporal modeling.

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NeuCube(ST) for spatio-temporal data predictive modelling with a case study on ecological data

2014 International Joint Conference on Neural Networks (IJCNN) ◽

10.1109/ijcnn.2014.6889717 ◽

2014 ◽

Cited By ~ 20

Author(s):

Enmei Tu ◽

Nikola Kasabov ◽

Muhaini Othman ◽

Yuxiao Li ◽

Susan Worner ◽

...

Keyword(s):

Predictive Modelling ◽

Temporal Data ◽

Ecological Data ◽

Spatio Temporal

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A Case Study for Modelling Cancer Incidence Using Bayesian Spatio-Temporal Models

Australian & New Zealand Journal of Statistics ◽

10.1111/anzs.12127 ◽

2015 ◽

Vol 57 (3) ◽

pp. 325-345 ◽

Cited By ~ 4

Author(s):

Su Yun Kang ◽

James McGree ◽

Peter Baade ◽

Kerrie Mengersen

Keyword(s):

Cancer Incidence ◽

Temporal Models ◽

Spatio Temporal

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Creating and evaluating web-based visualizations of multi-dimensional spatiotemporal data

Proceedings of the ICA ◽

10.5194/ica-proc-2-145-2019 ◽

2019 ◽

Vol 2 ◽

pp. 1-8

Author(s):

Jan Wilkening ◽

Keni Han ◽

Mathias Jahnke

Keyword(s):

Spatiotemporal Data ◽

Weather Data ◽

Temporal Data ◽

Web Based ◽

Animated Maps ◽

Different Types ◽

Weather Parameters ◽

Spatio Temporal ◽

The Web

<p><strong>Abstract.</strong> In this article, we present a method for visualizing multi-dimensional spatio-temporal data in an interactive web-based geovisualization. Our case study focuses on publicly available weather data in Germany. After processing the data with Python and desktop GIS, we integrated the data as web services in a browser-based application. This application displays several weather parameters with different types of visualisations, such as static maps, animated maps and charts. The usability of the web-based geovisualization was evaluated with a free-examination and a goal-directed task, using eye-tracking analysis. The evaluation focused on the question how people use static maps, animated maps and charts, dependent on different tasks. The results suggest that visualization elements such as animated maps, static maps and charts are particularly useful for certain types of tasks, and that more answering time correlates with less accurate answers.</p>

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Comparison between VAR, GSTAR, FFNN-VAR and FFNN-GSTAR Models for Forecasting Oil Production

MATEMATIKA ◽

10.11113/matematika.v34.n1.1040 ◽

2018 ◽

Vol 34 (1) ◽

pp. 103-111 ◽

Cited By ~ 4

Author(s):

Suhartono Suhartono ◽

Dedy Dwi Prastyo ◽

Heri Kuswanto ◽

Muhammad Hisyam Lee

Keyword(s):

Forecast Accuracy ◽

Oil Production ◽

Training Data ◽

Temporal Data ◽

Monthly Data ◽

Vector Autoregressive ◽

Temporal Models ◽

Accurate Forecast ◽

Temporal Model ◽

Spatio Temporal

Monthly data about oil production at several drilling wells is an example of spatio-temporal data. The aim of this research is to propose nonlinear spatio-temporal model, i.e. Feedforward Neural Network - Vector Autoregressive (FFNN-VAR) and FFNN - Generalized Space-Time Autoregressive (FFNN-GSTAR), and compare their forecast accuracy to linear spatio-temporal model, i.e. VAR and GSTAR. These spatio-temporal models are proposed and applied for forecasting monthly oil production data at three drilling wells in East Java, Indonesia. There are 60 observations that be divided to two parts, i.e. the first 50 observations for training data and the last 10 observations for testing data. The results show that FFNN-GSTAR(11) and FFNN-VAR(1) as nonlinear spatio-temporal models tend to give more accurate forecast than VAR(1) and GSTAR(11) as linear spatio-temporal models. Moreover, further research about nonlinear spatio-temporal models based on neural networks and GSTAR is needed for developing new hybrid models that could improve the forecast accuracy.

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