Mathematical Foundations of Computational Engineering

The importance of prior error correlations in data assimilation has long been known; however, observation-error correlations have typically been neglected. Recent progress has been made in estimating and accounting for observation-error correlations, allowing for the optimal use of denser observations. Given this progress, it is now timely to ask how prior and observation-error correlations interact and how this affects the value of the observations in the analysis. Addressing this question is essential to understanding the optimal design of future observation networks for high-resolution numerical weather prediction. This article presents new results, which unify and advance upon previous studies on this topic.The interaction of the prior and observation-error correlations is illustrated with a series of two-variable experiments in which the mapping between the state and observed variables (the observation operator) is allowed to vary. In an optimal system, the reduction in the analysis-error variance and spread of information is shown to be greatest when the observation and prior errors have complementary statistics: for example, in the case of direct observations, when the correlations between the observation and prior errors have opposite signs. This can be explained in terms of the relative uncertainty of the observations and prior on different spatial scales. The results from these simple two-variable experiments are used to inform the optimal observation density for observations of a circular domain (with 32 grid points). It is found that dense observations are most beneficial when they provide a more accurate estimate of the state at smaller scales than the prior estimate. In the case of second-order auto-regressive correlation functions, this is achieved when the length-scales of the observation-error correlations are greater than those of the prior estimate and the observations are direct measurements of the state variables.

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“…The trace of C is a constant (

\sum_{i = 0}^{n - 1} λ_{i}^{c} = n

). However, the determinant of C,

\det false(C false) = \prod_{i = 0}^{n - 1} λ_{i}^{c}

, is sensitive to the structure of the correlations and is known to satisfy

0 < \det false(C false) \leq 1 .

This is a special case of Hadamard's inequality (see Pahl and Damrath, , p914). The upper bound is attained when C = I , i.e.…”

Section: Variational Data Assimilationmentioning

confidence: 80%

On the interaction of observation and prior error correlations in data assimilation

Fowler

Dance

Waller

2017

Quart J Royal Meteoro Soc

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“…where ⇀ ∇ is vector differential operator, also called nabla operator [29], and ⃗ expresses the velocity vector including the velocities components of , V, and , responding to , , and direction, respectively, and the effective viscosity is eff = mix + , where mean viscosity was defined by…”

Section: =1mentioning

confidence: 99%

Numerical Analysis on Flow Behavior of Molten Iron and Slag in Main Trough of Blast Furnace during Tapping Process

Wang

Pan

Cheng

2017

Advances in Numerical Analysis

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The three-dimensional model was developed according to number 4 of the main trough of blast furnace at China Steel Co. (CSC BF4). The -equations and volume of fluid (VOF) were used for describing the turbulent flow at the impinging zone of trough, indicating fluids of liquid iron, molten slag, and air in the governing equation, respectively, in this paper. The pressure field and velocity profile were then obtained by the finite volume method (FVM) and the pressure implicit with splitting of operators (PISO), respectively, followed by calculating the wall shear stress through Newton's law of viscosity for validation. Then, the operation conditions and the main trough geometry were numerically examined for the separation efficiency of iron from slag stream. As shown in the results, the molten iron losses associated with the slag can be reduced by increasing the height difference between the slag and iron ports, reducing the tapping rate, and increasing the height of the opening under the skimmer.

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“…node 1 in Figure 8) and ANDjoins (e.g. node T4' in Figure 8), which is a well-known problem (Tauscher, 2011;Pahl and Damrath, 2001). For this class of failure, an automated conflict-solving algorithm is integrated into the software framework that, in this example, revises the XOR-split by the insertion of pseudo nodes resulting in a correct connection of variants and parallel construction processes (Figure 9).…”

Section: Mapping Phase -Stepmentioning

confidence: 99%

Automated Generation of Construction Sequences using Building Information Models

Tauscher

Smarsly

König

et al. 2014

Computing in Civil and Building Engineering (2014)

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Construction scheduling is usually limited to the documentation of one final construction schedule, and construction alternatives that might have been considered during the planning process are usually not included in the final schedule. Moreover, a formal control of construction schedules in terms of completeness and correctness is very limited, because existing methods, such as 4D visualization, are insufficiently integrated into the construction planning process. This paper addresses the development of a software framework that has been designed to support the process of construction scheduling. As will be shown in this paper, the process of construction scheduling, which is usually carried out manually, is conducted automatically to a large extent using building information models (BIM) and 4D visualization. Due to the logical interconnections of BIM objects and construction tasks, flexible schedules and visual representations of construction processes are automatically generated without permanent human interaction.

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Mathematical Foundations of Computational Engineering

Cited by 33 publications

References 0 publications

On the interaction of observation and prior error correlations in data assimilation

On the interaction of observation and prior error correlations in data assimilation

Numerical Analysis on Flow Behavior of Molten Iron and Slag in Main Trough of Blast Furnace during Tapping Process

Automated Generation of Construction Sequences using Building Information Models

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