2019/12/04 by Denis Allard, Allard, Denis, Xavier Emery +5 · 2 citations
Decision Sciences · Earth and Planetary Sciences · Environmental Science · #3D Surveying and Cultural Heritage #Computation (stat.CO) #FOS: Computer and information sciences #Methodology (stat.ME) #Probabilistic and Robust Engineering Design #Remote Sensing and LiDAR Applications #Soil Geostatistics and Mapping #Wind and Air Flow Studies
paper · pdf · doi:10.48550/arxiv.1912.02026
openalex publication_date 2019/12/04 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
Two algorithms are proposed to simulate space-time Gaussian random fields with a covariance function belonging to an extended Gneiting class, the definition of which depends on a completely monotone function associated with the spatial structure and a conditionally negative definite function associated with the temporal structure. In both cases, the simulated random field is constructed as a weighted sum of cosine waves, with a Gaussian spatial frequency vector and a uniform phase. The difference lies in the way to handle the temporal component. The first algorithm relies on a spectral decomposition in order to simulate a temporal frequency conditional upon the spatial one, while in the second algorithm the temporal frequency is replaced by an intrinsic random field whose variogram is proportional to the conditionally negative definite function associated with the temporal structure. Both algorithms are scalable as their computational cost is proportional to the number of space-time locations, which may be unevenly spaced in space and/or in time. They are illustrated and validated through synthetic examples.