TOWARDS A SYSTEMS APPROACH TO THE VISUALIZATION OF SPATIAL UNCERTAINTY Phaedon C. Kyriakidis

Introduction Uncertainty is endemic in spatial data due to the imperfect means of recording, processing, and representing spatial information (Zhang and Goodchild, 2002). The characterization (modeling and portrayal) of spatial uncertainty, as well as its propagation to geographical modeling and its impact on decision-making, has been identified as a critical research priority in Geographic Information Science (GIScience), e.g., UCGIS (1996). Early cartographic work on the portrayal of spatial uncertainty focused on the adaptation of Bertin's visual variables (location, size, value, shape, texture, color and orientation) for representing uncertainty measures, such as standard errors of predictions in an interpolation setting, or of posterior probabilities of class occurrence in a classification setting. Bertin's variables, along with additional ones such as color saturation, were thus used in the context of static verity visualization, i.e., the simultaneous depiction of the origina

Efficient uncertainty propagation of lognormal hydraulic conductivity in a three dimensional hydrogeological model of flow and transport on very large regular grids

Proceedings of IAMG 2015 - 17th Annual Conference of the International Association for Mathematical Geosciences 2015, Pages 369-377This work illustrates an efficient method for Monte Carlo uncertainty analysis in a three dimensional hydrogeological context involving very large grids. Although Monte Carlo simulation using Simple Random (SR) sampling is the de facto method for such an uncertainty analysis, it quickly becomes expensive in terms of time and computer resources, particularly for the case of complex models. To alleviate this problem, a new Latin Hypercube (LH) sampling method is proposed in this work for efficiently generating realizations of secondorder stationary lognormal random fields on large (order of million pixels) regular grids. he performance of the proposed LH sampling method is compared to that of SR sampling in the context of a 3D hydrogeological flow and transport model. The results show that the proposed LH sampling is more efficient than SR sampling, in that it can overall reproduce to a similar extent statistics of the conductivity (and associated concentration) field, yet with smaller sampling variability than the latter

A spatial time series framework for modeling daily precipitation at regional scales

In this paper, a framework for stochastic spatiotemporal modeling of daily precipitation in a hindcast mode is presented. Observed precipitation levels in space and time are modeled as a joint realization of a collection of space-indexed time series, one for each spatial location. Time series model parameters are spatially varying, thus capturing space-time interactions. Stochastic simulation, i.e., the procedure of generating alternative precipitation realizations (synthetic fields) over the space-time domain of interest (Deutsch and Journel, 1998), is employed for ensemble prediction. The simulated daily precipitation fields reproduce a data-based histogram and spatiotemporal covariance model, and identify the measured precipitation values at the rain gauges (conditional simulation). Such synthetic precipitation fields can be used in a Monte Carlo framework for risk analysis studies in hydrologic impact assessment investigations

A spatial time series framework for modeling daily precipitationat regional scales

In this paper, a framework for stochastic spatiotemporal modeling of daily precipitation in a hindcast mode is presented. Observed precipitation levels in space and time are modeled as a joint realization of a collection of space-indexed time series, one for each spatial location. Time series model parameters are spatially varying, thus capturing space-time interactions. Stochastic simulation, i.e., the procedure of generating alternative precipitation realizations (synthetic fields) over the space-time domain of interest (Deutsch and Journel, 1998), is employed for ensemble prediction. The simulated daily precipitation fields reproduce a data-based histogram and spatiotemporal covariance model, and identify the measured precipitation values at the rain gauges (conditional simulation). Such synthetic precipitation fields can be used in a Monte Carlo framework for risk analysis studies in hydrologic impact assessment investigations