During the period of June 29 through July 6, 2002, an extreme precipitation event occurred over Texas, resulting in catastrophic flooding. Operational forecasts performed poorly, neither predicting the copious amounts of rain nor its longevity. The Penn State University/NCAR Mesoscale Model version 5 (MM5) was used to conduct predictability experiments, which follow closely to the research conducted by Zhang et al. A control simulation initialized at 00Z 1 July is established over a 30-km grid. First, practical predictability experiments are performed by exploring the impacts due to different lead-times, resolution dependence, and different physics parameterizations. Second, intrinsic predictability is investigated by inducing a random temperature perturbation in the initial conditions, followed by numerous simulations with various perturbed initializations. Similar results to those found by Zhang et al. were discovered here: the prominent initial error growth is associated with moist processes leading to convection. Eventually these errors grow from the convective scale to sub-synoptic scale, essentially below 1000 kilometers. This indicates that as the forecast time extends further beyond initialization, the resulting errors will impact forecasts of larger-scale features such as differences in the positioning and intensity of positive PV anomalies and distribution of precipitation from the control simulation.

This dissertation examines the performance of an ensemble Kalman filter (EnKF) implemented in a mesoscale model in increasingly realistic contexts from under a perfect model assumption and in the presence of significant model error with synthetic observations to real-world data assimilation in comparison to the three-dimensional variational (3DVar) method via both case study and month-long experiments. The EnKF is shown to be promising for future application in operational data assimilation practice. The EnKF with synthetic observations, which is implemented in the mesoscale model MM5, is very effective in keeping the analysis close to the truth under the perfect model assumption. The EnKF is most effective in reducing larger-scale errors but less effective in reducing errors at smaller, marginally resolvable scales. In the presence of significant model errors from physical parameterization schemes, the EnKF performs reasonably well though sometimes it can be significantly degraded compared to its performance under the perfect model assumption. Using a combination of different physical parameterization schemes in the ensemble (the so-called “multi-scheme” ensemble) can significantly improve filter performance due to the resulting better background error covariance and a smaller ensemble bias. The EnKF performs differently for different flow regimes possibly due to scale- and flow-dependent error growth dynamics and predictability. Real-data (including soundings, profilers and surface observations) are assimilated by directly comparing the EnKF and 3DVar and both are implemented in the Weather Research and Forecasting model. A case study and month-long experiments show that the EnKF is efficient in tracking observations in terms of both prior forecast and posterior analysis. The EnKF performs consistently better than 3DVar for the time period of interest due to the benefit of the EnKF from both using ensemble mean for state estimation and using a flow-dependent background error covariance. Proper covariance inflation and using a multi-scheme ensemble can significantly improve the EnKF performance. Using a multi-scheme ensemble results in larger improvement in thermodynamic variables than in other variables. The 3DVar system can benefit substantially from using a short-term ensemble mean for state estimate. Noticeable improvement is also achieved in 3DVar by including some flow dependence in its background error covariance.

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Concrete is a highly non-homogeneous composite with large heterogeneities of quasi-brittle character. Failure of concrete structures is usually accompanied by cracking of concrete, which is strongly affected by the mesoscale structure and the behaviour of the interface between the aggregates and the mortar matrix, especially under complex stress conditions. Analysis of the failure mechanisms of concrete at the mesoscale is therefore crucial for a better understanding of the macroscopic behaviour of the material, which can in turn contribute to improved design of concrete structures and finding new ways to enhance the material properties. This research aims to investigate the intrinsic failure mechanisms of concrete-like materials from a mesoscale point of view. To do this, continued developments from existing work on mesoscale modelling are carried out to cater the needs of realistically simulating the damage process in concrete under complex loading conditions. The new developments focus on two key aspects. Firstly, techniques to realistically simulate the fracture process of concrete are developed and these involve the incorporation of a combined cohesive and contact mechanisms for the interface between aggregates and mortar matrix. Such interface modelling allows the crack initiation and propagation at the mesoscale to be explicitly represented. Secondly, a full 3D mesoscale finite element model for concrete-like materials with random aggregates and the possibility of high packing density is developed. Use is then made of these enhanced mesoscale models to explore the intrinsic mechanism governing the fundamental behaviour of concrete such as fracture propagation in tension and compression, the well-known size effect and the dynamic strain rate effect. The research investigation begins with an analysis of the size effect in plain concrete beams under three-point bending using a generic 2D mesoscale model. The analysis aims to provide preliminary insight into the use of a mesoscopic computational tool for examining the concrete damage mechanisms with the well-known size effect phenomenon as a benchmark scenario. The shapes and the sizes of the fracture process zone (FPZ) during the whole fracture process are captured. The role of detailed FPZ features is discussed accordingly. On the other hand, the results also point out the deficiencies of the continuum-based mesoscale framework at capturing the evolution of the local fracture process, and to resolve this problem requires explicit simulation of the initiation and propagation of the micro-cracks and thus a realistic reproduction of the fracture process zone, and this becomes the subject of research in much of the later chapters of the thesis. To cater to the needs of better representing the fracture process in concrete, a coupled cohesive-contact interface approach is proposed to model the crack initiation, crack propagation and the friction mechanism within the transition zone between the coarse aggregates and the mortar matrix. The cohesive-contact combined model is verified to perform well under simple as well as complex loading conditions. The interface approach in a mesoscale model framework provides a new platform for investigating the failure mechanisms in terms of the cohesive fracture process and the contact friction process. A more comprehensive and robust mesoscale interface modelling approach, in which the cohesive plus contact interface is inserted along all mesh grids, is developed to study the complex dynamic behaviour of concrete with the consideration that fractures can spread in a fine distributed manner within larger damage areas including the strong aggregate, particularly under high loading rate. By allowing local fractures to develop explicitly, the issues with fracture damage description with a continuum material model can be largely resolved. The effectiveness of such an approach is demonstrated and employed in an investigation into the intrinsic mechanisms governing the sensitivity of the dynamic tension resistance with the loading rate. Subsequently, a re-visit of the size effect in terms of the evolution of the fracture process zones using the mesoscale model with cohesive plus contact interface model is conducted and the results are presented. The preliminary observations from using the continuum-based mesoscale model are examined and verified. Additional insight into the fracture processes in the concrete beams with various sizes is obtained and the intrinsic mechanisms of the size effect are further discussed. On the real 3D mesoscale modelling methodology, the new development focuses on achieving a realistic representation of the actual shapes and sizes of aggregate particles and at the same time allowing for high volumetric ratios of aggregates (packing density) to be attained. In addition to specific techniques to enhance the conventional take-and-place procedure, an algorithm to generate supplementary aggregates to allow increased packing density is proposed and implemented. Example 3D mesoscale specimens so created are then verified against standard experimental tests such as uniaxial compression, uniaxial tension and compression with lateral confinements, and applied to examine the dynamic behaviour of concrete under high strain rate compression.

Mesoscale convective vortices (MCVs), which typically form within the stratiform rain of some mesoscale convective systems (MCSs), may persist for days, often regenerating convection daily. Long-lived MCVs can produce as much precipitation as a landfalling hurricane and lead to catastrophic flooding. The number of studies using multi-Doppler radar observations for validation of the kinematics, or three-dimensional (3-D) wind structure, of MCV genesis is limited. For this study, the Oklahoma City (KTLX) and Tulsa, Oklahoma (KINX) Weather Surveillance Radar – 1988 Doppler (WSR-88D) were used to examine the genesis of a long-lived MCV from 0000 to 0300 UTC on 11 June 2003. Traditional dual-Doppler techniques were used to determine the 3-D wind field. To relate MCV genesis within the associated larger MCS, time series of convective and stratiform precipitation, divergence, vertical vorticity, and vertical velocity were created for multiple levels within the MCS. The role of vertical vorticity generated in the convective region in MCV development was determined using vertical profiles of the terms in the vorticity tendency equation at 15 minute temporal resolution during the three hour period of investigation. The results of this study provide a detailed three hour examination for the initiation and early evolution of a long-lived MCV and can provide model validation of MCV generation.

Mesoscale convective vortices (MCVs), which typically form within the stratiform rain of some mesoscale convective systems (MCSs), may persist for days, often regenerating convection daily. Long-lived MCVs can produce as much precipitation as a landfalling hurricane and lead to catastrophic flooding. The number of studies using multi-Doppler radar observations for validation of the kinematics, or three-dimensional (3-D) wind structure, of MCV genesis is limited. For this study, the Oklahoma City (KTLX) and Tulsa, Oklahoma (KINX) Weather Surveillance Radar – 1988 Doppler (WSR-88D) were used to examine the genesis of a long-lived MCV from 0000 to 0300 UTC on 11 June 2003. Traditional dual-Doppler techniques were used to determine the 3-D wind field. To relate MCV genesis within the associated larger MCS, time series of convective and stratiform precipitation, divergence, vertical vorticity, and vertical velocity were created for multiple levels within the MCS. The role of vertical vorticity generated in the convective region in MCV development was determined using vertical profiles of the terms in the vorticity tendency equation at 15 minute temporal resolution during the three hour period of investigation. The results of this study provide a detailed three hour examination for the initiation and early evolution of a long-lived MCV and can provide model validation of MCV generation.

The performance of the ensemble Kalman filter (EnKF) in forced, dissipative flow under imperfect model conditions is investigated through simultaneous state and parameter estimation where the source of model error is the uncertainty in the model parameters. Two numerical models with increasing complexity are used with simulated observations. For lower complexity, a two-dimensional, nonlinear, hydrostatic, non-rotating, and incompressible sea breeze model is developed with buoyancy and vorticity as the prognostic variables. Model resolution is 4 km horizontally and 50 m vertically. The ensemble size is set at 40. Forcing is maintained through an explicit heating function with additive stochastic noise. Simulated buoyancy observations on land surface with 40-km spacing are assimilated every 3 hours. Up to six model parameters are successfully subjected to estimation attempts in various experiments. The overall EnKF performance in terms of the error statistics is found to be superior to the worst-case scenario (when there is parameter error but no parameter estimation is performed) with an average error reduction in buoyancy and vorticity of 40% and 46%, respectively, for the simultaneous estimation of six parameters. The model chosen to represent the complexity of operational weather forecasting is the Pennsylvania State University-National Center for Atmospheric Research MM5 model with a 36-km horizontal resolution and 43 vertical layers. The ensemble size for all experiments is chosen as 40 and a 41st member is generated as the truth with the same ensemble statistics. Assimilations are performed with a 12-hour interval with simulated sounding and surface observations of horizontal winds and temperature. Only single-parameter experiments are performed focusing on a constant inserted into the code as the multiplier of the vertical eddy mixing coefficient. Estimation experiments produce very encouraging results and the mean estimated parameter value nicely converges to the true value exhibiting a satisfactory level of variability.

The aim of this PhD thesis is to incorporate deformation twinning in a fullield viscoplastic crystal plasticity model based on fast Fourier transform in an effort to gain insights into its role on strain localization. This work is motivated by current experimental evidences on the important role that dislocation reactions at the twin interface play on damage initiation in materials during plastic deformation. We began first by investigating the role of slip on stress localization. To this end, we simulated the effect of macroscopic deformation path, which dictates a macroscopic stress state, as well as pre-existing microstructure in typical ferritic steel, where plastic deformation is accommodated by slip mechanism. The results show that the width of localized strain rate regions near grain boundaries is a function of the deformation path, and there is a positive correlation between local Taylor factor and local stress field, which slightly depends on deformation path. For the incorporation of mechanical twinning in twinning-induced plasticity (TWIP) steel, we implemented predominant reorientation scheme (PTR) in vpFFT, which was implemented previously in the mean field VPSC. The comparison between experimental and simulation results indicates that twin volume fraction, final texture, and stress-strain curve were satisfactorily predicted. Despite that predominant twin reorientation scheme was not suitable to capture lamellar shape of twins in the microstructure, twin domains were predicted to form and grow at or close to grain boundary regions. Finally, we surveyed current literature, which aimed at capturing the characteristic lamellar morphology of twins. Literature review shows several unsuccessful crystal plasticity simulations in capturing twin nucleation and twin lamellar shape at measocale. These inabilities can be attributed to i) twin nucleation that is controlled by local atomistic configurations and stress fluctuations at the grain boundaries, and ii) the random or stochastic nature of twin nucleation, which has been proved by EBSD observation. Based on the EBSD observations, twin nucleation depends on both microstructural (e.g, grain size, dislocation density) and loading conditions ( e.g, stress, strain). Furthermore, the propensity, frequency, and morphology of deformation twins are different among grain with the same orientation and applied boundary conditions.

Constant volume superpressure pillow balloons were flown over a mountain valley downwind from a sharp ridge line. Balloon trajectories revealed and atmospheric soundings confirmed a persistent turbulently mixed adiabatic layer over the valley at approximately ridge top height except in the immediate lee of the ridge where strong vertical motions were observed. Temporary stationarity of the relative mesoscale turbulence was found to exist on a time scale exceeding 4 hours. Power spectrum analysis of component relative velocities showed greater variance in lower wave numbers and anisotropy in mesoscale turbulence. Eddy diffusivity coefficients for turbulence above the ridge height were Kx= 1×107 , Ky = 5×106 , Kz = 1×106 (cm2 sec-1). Below the ridge line Kz was nearly constant at 2×105 cm2/sec- 1. Kz was found to vary exponentially with R, a balloon-ridge ratio; Kz ∞ exp (3R).

The structure-property relationships of Ultra-High Performance Concrete (UHPC) were quantified using imaging techniques to characterize the multiscale hierarchical heterogeneities and the mechanical properties. Through image analysis the average size, percent area, nearest neighbor distance, and relative number density of each inclusion type was determined and then used to create Representative Volume Element (RVE) cubes for use in Finite Element (FE) analysis. Three different size scale RVEs at the mesoscale were found to best represent the material: the largest length scale (35 mm side length) included steel fibers, the middle length scale (0.54 mm side length) included large voids and silica sand grains, and the smallest length scale (0.04 mm side length) included small voids and unhydrated cement grains. By using three length scales of mesoscale FE modeling, the bridge of information to the macroscale cementitious material model is more physically based.