Lagrangian Stochastic Modeling in Coastal Oceanography

Lagrangian stochastic (LS) modeling is a common technique in atmospheric boundary layer modeling but is relatively new in coastal oceanography. This paper presents some fundamental aspects of LS modeling as they pertain to oceanography. The theory behind LS modeling is reviewed and an introduction to the substantial atmospheric literature on the subject is provided. One of the most important properties of an LS model is that it maintains an initially uniform distribution of particles uniform for all time—the well-mixed condition (WMC). Turbulent data for use in an oceanic LS model (LSM) are typically output at discrete positions by a general circulation model. Tests for the WMC are devised, and it is shown that for inhomogeneous turbulence the data output by an oceanic general circulation model is such that the WMC cannot be demonstrated. It is hypothesized that this is due to data resolution problems. To test this hypothesis analytical turbulence data are constructed and output at various resolutions to show that the WMC can only be demonstrated if the resolution is high enough (the required resolution depending on the inhomogeneity of the turbulence data). The output of an LSM represents one trial of possible ensemble and this paper seeks to learn the ensemble average properties of the dispersion. This relates to the number of particles or trials that are performed. Methods for determining the number of particles required to have statistical certainty in one’s results are demonstrated, and two possible errors that can occur when using too few particles are shown.

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