Doctor of Philosophy

dissertationAccurate weather forecasting in complex terrain is of great importance, yet it is a challenging problem due to a number of difficulties, including sparse observations, terrain misrepresentation in numerical models, and model errors related to terrain complexity. Owing to these limitations, few previous studies in data assimilation have emphasized regions of complex terrain. This dissertation presents the first comprehensive evaluation of data assimilation methods and forecast error characteristics for near-surface atmospheric variables in complex terrain. The mesoscale community Weather Research and Forecasting (WRF) model and an advanced ensemble Kalman filter (EnKF) data assimilation system are employed. First, the capability of the advanced EnKF method in assimilating near-surface observations (2-m temperature and 10-m wind) is examined in an observing system simulation experiments framework and compared with the traditional three-dimensional variational data assimilation (3DVAR) method. Results indicated that the EnKF is able to effectively assimilate surface observations and improve the short-range weather forecasts, while the 3DVAR method has fundamental problems in assimilating surface observations. Next, the performance of the WRF model in predicting near-surface atmospheric temperature and wind conditions under various terrain and weather regimes is examined. The WRF model is able to simulate these weather phenomena reasonably well. Forecasts of near-surface variables in flat terrain generally agree well with observations. In complex terrain, forecasts not only suffer from the model's inability to reproduce accurate atmospheric conditions in the lower atmosphere but also struggle with representative issues due to mismatches between the model and the actual terrain. A statistical analysis during a 1-month period over the Dugway Proving Ground (DPG), Utah illustrates that forecast errors in near-surface variables depend strongly on the diurnal variation in surface conditions, especially when synoptic forcing is weak. Finally, the impact of observations from the recent field experiments of the Mountain Terrain Atmospheric Modeling and Observations (MATERHORN) is examined with EnKF. Results illustrated that the quality of the EnKF/WRF analysis is generally high and the short-range forecast errors are comparable to those of the National Centers for Environmental Prediction (NCEP) North American Mesoscale Model (NAM) forecasts for both 10-m wind speed and direction

Oligopolistic competition in heterogeneous access networks under asymmetries of cost and capacity

With the rapid development of broadband wireless access technologies, multiple wireless service provider (WSPs) operating on various wireless access technologies may coexist in one service area to compete for users, leading to a highly competitive environment for the WSPs. In such a competitive heterogeneous wireless access market, different wireless access technologies used by different WSPs have different bandwidth capacities with various costs. In this paper, we set up a noncooperative game model to study how the cost asymmetry and capacity asymmetry among WSPs affect the competition in this market. We first model such a competitive heterogeneous wireless access market as an oligopolistic price competition, in which multiple WSPs compete for a group of price- and delay-sensitive users through their prices, under cost and capacity asymmetries, to maximize their own profits. Then, we develop an analytical framework to investigate whether or not a Nash equilibrium can be achieved among the WSPs in the presence of the cost and capacity asymmetries, how the asymmetries of cost and capacity affect their equilibrium prices and what impact a new WSP with a cost and capacity advantage entering the market has on the equilibrium achieved among existing WSPs

Beating the Uncertainties: Ensemble Forecasting and Ensemble-Based Data Assimilation in Modern Numerical Weather Prediction

Accurate numerical weather forecasting is of great importance. Due to inadequate observations, our limited understanding of the physical processes of the atmosphere, and the chaotic nature of atmospheric flow, uncertainties always exist in modern numerical weather prediction (NWP). Recent developments in ensemble forecasting and ensemble-based data assimilation have proved that there are promising ways to beat the forecast uncertainties in NWP. This paper gives a brief overview of fundamental problems and recent progress associated with ensemble forecasting and ensemble-based data assimilation. The usefulness of these methods in improving high-impact weather forecasting is also discussed

Credit-based distributed real-time energy storage sharing management

Abstract: In this paper, energy storage sharing among a group of cooperative households with integrated renewable generations in a grid-connected microgrid is studied. In such a microgrid, a group of households, who are willing to cooperatively operate a shared energy storage via a central coordinator, aims to minimize their long term time-averaged costs, by jointly taking into account the operational constraints of the shared energy storage, the stochastic solar power generations and the time-varying load demands from all households, as well as the fluctuating electricity prices. This energy management problem, which comprises storage management and load control, is first formulated as a constrained stochastic programming problem. Based on the Lyapunov optimization theory, a distributed real-time sharing control algorithm is proposed to solve the constrained stochastic programming problem without requiring any statistical knowledge of the stochastic renewable energy generations and the uncertain power loads. The credit-based distributed sharing algorithm, in which each household independently solves a simple convex optimization problem without requiring any statistics of the system, is designed to quickly adapt to the system dynamics while facilitating a fair allocation of the shared energy storage with respect to individual households’ energy contributions. The performance gap of the proposed low-complexity distributed sharing algorithm is evaluated via theoretical analysis. Numerical simulations using a practical system setup are conducted to investigate the effectiveness of the proposed sharing control algorithm in terms of energy cost saving and fairness. The simulation results show that the proposed credit-based distributed sharing algorithm can not only save power consumption cost by coordinating the use the shared battery among households in a fair manner but also improve the utilization of renewable energy generation

Weighted allocations, their concomitant-based estimators, and asymptotics

Various members of the class of weighted insurance premiums and risk capital allocation rules have been researched from a number of perspectives. Corresponding formulas in the case of parametric families of distributions have been derived, and they have played a pivotal role when establishing parametric statistical inference in the area. Non-parametric inference results have also been derived in special cases such as the tail conditional expectation, distortion risk measure, and several members of the class of weighted premiums. For weighted allocation rules, however, non-parametric inference results have not yet been adequately developed. In the present paper, therefore, we put forward empirical estimators for the weighted allocation rules and establish their consistency and asymptotic normality under practically sound conditions. Intricate statistical considerations rely on the theory of induced order statistics, known as concomitants.Comment: 20 page

Research on the Teaching Design Ability of Mathematics Normal Students in Local Normal Universities in China

In order to ensure the smooth development of future work, normal university students must constantly improve their ability of teaching design. This paper uses text analysis method to study the teaching design ability of mathematics normal college students. This paper investigates the mathematics teaching design ability of normal university students from six aspects: overall teaching design, teaching objectives, key points and difficult points of teaching, teaching process, homework arrangement after class and teaching reflection. The results show that the students' overall understanding of teaching design is slightly biased, and the ability of compiling teaching objectives is not ideal, they are able to grasp the key and difficult points in teaching, but unable to put forward how to deal with the key and difficult points in teaching; The teaching process design is also deficient; Normal university students do not pay attention to homework assignment and teaching reflection. Finally, the paper puts forward some suggestions on the development of teaching design ability of mathematics normal university students. Keywords: Normal mathematics student; Teaching design ability DOI: 10.7176/JEP/13-32-08 Publication date: November 30th 202