[1] Incorporating hydro(geo)logical data, such as head and tracer data, into stochastic models of (subsurface) flow and transport helps to reduce prediction uncertainty. Because of financial limitations for investigation campaigns, information needs toward modeling or prediction goals should be satisfied efficiently and rationally. Optimal design techniques find the best one among a set of investigation strategies. They optimize the expected impact of data on prediction confidence or related objectives prior to data collection. We introduce a new optimal design method, called PreDIA(gnosis) (Preposterior Data Impact Assessor). PreDIA derives the relevant probability distributions and measures of data utility within a fully Bayesian, generalized, flexible, and accurate framework. It extends the bootstrap filter (BF) and related frameworks to optimal design by marginalizing utility measures over the yet unknown data values. PreDIA is a strictly formal information-processing scheme free of linearizations. It works with arbitrary simulation tools, provides full flexibility concerning measurement types (linear, nonlinear, direct, indirect), allows for any desired task-driven formulations, and can account for various sources of uncertainty (e.g., heterogeneity, geostatistical assumptions, boundary conditions, measurement values, model structure uncertainty, a large class of model errors) via Bayesian geostatistics and model averaging. Existing methods fail to simultaneously provide these crucial advantages, which our method buys at relatively higher-computational costs. We demonstrate the applicability and advantages of PreDIA over conventional linearized methods in a synthetic example of subsurface transport. In the example, we show that informative data is often invisible for linearized methods that confuse zero correlation with statistical independence. Hence, PreDIA will often lead to substantially better sampling designs. Finally, we extend our example to specifically highlight the consideration of conceptual model uncertainty.

A new type of glyph is introduced to visualize unsteady flow with static images, allowing easier analysis of time-dependent phenomena compared to animated visualization. Adopting the visual metaphor of radar displays, this glyph represents flow directions by angles and time by radius in spherical coordinates. Dense seeding of flow radar glyphs on the flow domain naturally lends itself to multi-scale visualization: zoomed-out views show aggregated overviews, zooming-in enables detailed analysis of spatial and temporal characteristics. Uncertainty visualization is supported by extending the glyph to display possible ranges of flow directions. The paper focuses on 2D flow, but includes a discussion of 3D flow as well. Examples from CFD and the field of stochastic hydrogeology show that it is easy to discriminate regions of different spatiotemporal flow behavior and regions of different uncertainty variations in space and time. The examples also demonstrate that parameter studies can be analyzed because the glyph design facilitates comparative visualization. Finally, different variants of interactive GPU-accelerated implementations are discussed.

[1] Many hydro(geo)logical problems are highly complex in space and time, coupled with scale issues, variability, and uncertainty. Especially time-dependent models often consume enormous computational resources, but model reduction techniques can alleviate this problem. Temporal moments (TM) offer an approach to reduce the time demands of transient hydro(geo)logical simulations. TM reduce transient governing equations to steady state and directly simulate the temporal characteristics of the system, if the equations are linear and coefficients are time independent. This is achieved by an integral transform, projecting the dynamic system response onto monomials in time. In comparison to classical approaches of model reduction that involve orthogonal base functions, however, the monomials for TM are nonorthogonal, which might impair the quality and efficiency of model reduction. Thus, we raise the question of whether there are more suitable temporal base functions than the monomials that lead to TM. In this work, we will derive theoretically that there is only a limited class of temporal base functions that can reduce hydro(geo)logical models. By comparing those to TM we conclude that, in terms of gained efficiency versus maintained accuracy, TM are the best possible choice. While our theoretical results hold for all systems of linear partial or ordinary differential equations (PDEs, ODEs) with any order of space and time derivatives, we illustrate our study with an example of pumping tests in a confined aquifer. For that case, we demonstrate that two (four) TM are sufficient to represent more than 80% (90%) of the dynamic behavior, and that the information content strictly increases with increasing TM order.Citation: Leube, P. C., W. Nowak, and G. Schneider (2012), Temporal moments revisited: Why there is no better way for physically based model reduction in time, Water Resour.

No abstract

No abstract