Spatio-temporal Modelling of Remote-sensing Lake Surface Water Temperature Data

Remote-sensing technology is widely used in environmental monitoring. The coverage and resolution of satellite based data provide scientists with great opportunities to study and understand environmental change. However, the large volume and the missing observations in the remote-sensing data present challenges to statistical analysis. This paper investigates two approaches to the spatio-temporal modelling of remote-sensing lake surface water temperature data. Both methods use the state space framework, but with different parameterizations to reflect different aspects of the problem. The appropriateness of the methods for identifying spatial/temporal patterns in the data is discussed

Functional PCA for Remotely Sensed Lake Surface Water Temperature Data

Functional principal component analysis is used to investigate a high-dimensional surface water temperature data set of Lake Victoria, which has been produced in the ARC-Lake project. Two different perspectives are adopted in the analysis: modelling temperature curves (univariate functions) and temperature surfaces (bivariate functions). The latter proves to be a better approach in the sense of both dimension reduction and pattern detection. Computational details and some results from an application to Lake Victoria data are presented

Consistent numerical methods for state and control constrained trajectory optimisation with parameter dependency

The article of record as published may be found at https://doi.org/10.1080/00207179.2020.1717633This paper describes and proves the consistency of a flexible numerical method for producing solutions to state and control constrained control problems with parameter dependencies. This method allows for the use of a variety of underlying discretisation schemes, which can be catered to differing numerical chal- lenges of specific problems, such as rapid convergence or large parameter spaces. The paper first provides a broad formulation for optimal control problems with parameter dependencies which includes multiple types of state, control, and end time constraints to enable a wide scope of application. For this formula- tion, the consistency of these methods for state and control constrained problems is then proved. Finally, a numerical example of an optimal search problem with constraints is demonstrated.This work was supported by Office of Naval Research [N001415WX01451, N001417WX01098, N001418WX01204].This work was supported by Office of Naval Research [N001415WX01451, N001417WX01098, N001418WX01204]

Modeling and Control of Large-Scale Adversarial Swarm Engagements

We theoretically and numerically study the problem of optimal control of large-scale autonomous systems under explicitly adversarial conditions, including probabilistic destruction of agents during the simulation. Large-scale autonomous systems often include an adver sarial component, where different agents or groups of agents explicitly compete with one another. An important component of these systems that is not included in current theory or modeling frameworks is random destruction of agents in time. In this case, the modeling and optimal control framework should consider the attrition of agents as well as their position. We propose and test three numerical modeling schemes, where survival probabilities of all agents are smoothly and continuously decreased in time, based on the relative positions of all agents during the simulation. In particular, we apply these schemes to the case of agents defending a high-value unit from an attacking swarm. We show that these models can be successfully used to model this situation, provided that attrition and spatial dynamics are coupled. Our results have relevance to an entire class of adversarial autonomy situations, where the positions of agents and their survival probabilities are both important.ONR SoA programNPS CRUSER progra

Density functional modeling of the binding energies between aluminosilicate oligomers and different metal cations

Interactions between negatively charged aluminosilicate species and positively charged metal cations are critical to many important engineering processes and applications, including sustainable cements and aluminosilicate glasses. In an effort to probe these interactions, here we have calculated the pair-wise interaction energies (i.e., binding energies) between aluminosilicate dimer/trimer and 17 different metal cations Mn+ (Mn+ = Li+, Na+, K+, Cu+, Cu2+, Co2+, Zn2+, Ni2+, Mg2+, Ca2+, Ti2+, Fe2+, Fe3+, Co3+, Cr3+, Ti4+ and Cr6+) using a density functional theory (DFT) approach. Analysis of the DFT-optimized structural representations for the clusters (dimer/trimer + Mn+) shows that their structural attributes (e.g., interatomic distances) are generally consistent with literature observations on aluminosilicate glasses. The DFT-derived binding energies are seen to vary considerably depending on the type of cations (i.e., charge and ionic radii) and aluminosilicate species (i.e., dimer or trimer). A survey of the literature reveals that the difference in the calculated binding energies between different Mn+ can be used to explain many literature observations associated with the impact of metal cations on materials properties (e.g., glass corrosion, mineral dissolution, and ionic transport). Analysis of all the DFT-derived binding energies reveals that the correlation between these energy values and the ionic potential and field strength of the metal cations are well captured by 2nd order polynomial functions (R2 values of 0.99–1.00 are achieved for regressions). Given that the ionic potential and field strength of a given metal cation can be readily estimated using well-tabulated ionic radii available in the literature, these simple polynomial functions would enable rapid estimation of the binding energies of a much wider range of cations with the aluminosilicate dimer/trimer, providing guidance on the design and optimization of sustainable cements and aluminosilicate glasses and their associated applications. Finally, the limitations associated with using these simple model systems to model complex interactions are also discussed

State space functional principal component analysis to identify spatiotemporal patterns in remote sensing lake water quality

Satellite remote sensing can provide indicative measures of environmental variables that are crucial to understanding the environment. The spatial and temporal coverage of satellite images allows scientists to investigate the changes in environmental variables in an unprecedented scale. However, identifying spatiotemporal patterns from such images is challenging due to the complexity of the data, which can be large in volume yet sparse within individual images. This paper proposes a new approach, state space functional principal components analysis (SS-FPCA), to identify the spatiotemporal patterns in processed satellite retrievals and simultaneously reduce the dimensionality of the data, through the use of functional principal components. Furthermore our approach can be used to produce interpolations over the sparse areas. An algorithm based on the alternating expectation–conditional maximisation framework is proposed to estimate the model. The uncertainty of the estimated parameters is investigated through a parametric bootstrap procedure. Lake chlorophyll-a data hold key information on water quality status. Such information is usually only available from limited in situ sampling locations or not at all for remote inaccessible lakes. In this paper, the SS-FPCA is used to investigate the spatiotemporal patterns in chlorophyll-a data of Taruo Lake on the Tibetan Plateau, observed by the European Space Agency MEdium Resolution Imaging Spectrometer