Stochastic simulation of two-dimensional random fields with preservation of persistence

N. Theodoratos, Stochastic simulation of two-dimensional random fields with preservation of persistence, Diploma thesis, 69 pages, Department of Water Resources, Hydraulic and Maritime Engineering – National Technical University of Athens, Athens, July 2004.



For the rational design and management of flood-preventing works, it is important when simulating a storm to respect the spatial distribution of rainfall. Thus research is done in order to develop spatially consistent stochastic rain models. A property that seems to have a significant effect on the spatial distribution of rain is the existence of large scale dependence or persistence, which corresponds to the Hurst effect, met at the study of hydrological time series. Therefore a spatial rain model should be able to simulate the large scale persistence. Beginning from an existing one-dimensional linear model, which is usually used in simulating time series with long-term persistence, we try to expand it into two dimensions, and to find the basic formulas that describe it. The development of this two-dimensional model demands in many cases theoretical calculations in order to find the functional relationships that describe it. This model belongs to the category of Symmetric Moving Average (SMA) models. It can synthesize two-dimensional random fields, managing to preserve the average, the variance and the skewness and also the persistence of the random field. The model was tested in the reproduction of rainfall fields, with statistics obtained from radar data, and showed good performance.

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Our works that reference this work:

1. E. Rozos, and D. Koutsoyiannis, Error analysis of a multi-cell groundwater model, Journal of Hydrology, 392 (1-2), 22–30, 2010.