2016/12/19 by Dionissios T. Hristopulos, Hristopulos, Dionissios T., Ivi C. Tsantili +1
Environmental Science · Agricultural and Biological Sciences · #Ecosystem dynamics and resilience #Greenhouse Technology and Climate Control #Remote Sensing in Agriculture
paper · pdf · doi:10.48550/arxiv.1612.06146
The generation of non-separable, physically motivated covariance functions is\na theme of ongoing research interest, given that only a few classes of such\nfunctions are available. We construct a non-separable space-time covariance\nfunction based on a diffusive Langevin equation. We employ ideas from\nstatistical mechanics to express the response of an equilibrium (i.e., time\nindependent) random field to a driving noise process by means of a linear,\ndiffusive relaxation mechanism. The equilibrium field is assumed to follow an\nexponential joint probability density which is determined by a spatial local\ninteraction model. We then use linear response theory to express the temporal\nevolution of the random field around the equilibrium state in terms of a\nLangevin equation. The latter yields an equation of motion for the space-time\ncovariance function, which can be solved explicitly at certain limits. We use\nthe explicit covariance model obtained in one spatial dimension and time. By\nmeans of the turning bands transform, we derive a non-separable space-time\ncovariance function in three space dimensions and time. We investigate the\nmathematical properties of this space-time covariance function, and we use it\nto model a dataset of daily ozone concentration values from the conterminous\nUSA.\n