Academic literature on the topic 'Dynamic meteorology Mathematics'

Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis. Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction model based on long short-term memory (LSTM) is used to predict PM2.5 concentration, achieving ideal results.

Air pollution is a major global problem, closely related to economic and social development and ecological environment construction. Air pollution data for most regions of China have a close correlation with time and seasons and are affected by multidimensional factors such as meteorology and air quality. In contrast with classical peaks-over-threshold modeling approaches, we use a deep learning technique and three new dynamic conditional generalized Pareto distribution (DCP) models with weather and air quality factors for fitting the time-dependence of the air pollutant concentration and make statistical inferences about their application in air quality analysis. Specifically, in the proposed three DCP models, a dynamic autoregressive exponential function mechanism is applied for the time-varying scale parameter and tail index of the conditional generalized Pareto distribution, and a sufficiently high threshold is chosen using two threshold selection procedures. The probabilistic properties of the DCP model and the statistical properties of the maximum likelihood estimation (MLE) are investigated, simulating and showing the stability and sensitivity of the MLE estimations. The three proposed models are applied to fit the PM2.5 time series in Beijing from 2015 to 2021. Real data are used to illustrate the advantages of the DCP, especially compared to the estimation volatility of GARCH and AIC or BIC criteria. The DCP model involving both the mixed weather and air quality factors performs better than the other two models with weather factors or air quality factors alone. Finally, a prediction model based on long short-term memory (LSTM) is used to predict PM2.5 concentration, achieving ideal results.

We review the scientific and engineering understanding of various types of inland and coastal flooding by considering the different causes and dynamic processes involved, especially in extreme events. Clear progress has been made in the accuracy of numerical modelling of meteorological causes of floods, hydraulics of flood water movement and coastal wind–wave-surge. Probabilistic estimates from ensemble predictions and the simultaneous use of several models are recent techniques in meteorological prediction that could be considered for hydraulic and oceanographic modelling. The contribution of remotely sensed data from aircraft and satellites is also considered. The need to compare and combine statistical and computational modelling methodologies for long range forecasts and extreme events is emphasized, because this has become possible with the aid of kilometre scale computations and network grid facilities to simulate and analyse time-series and extreme events. It is noted that despite the adverse effects of climatic trends on flooding, appropriate planning of rapidly growing urban areas could mitigate some of the worst effects. However, resources for flood prevention, including research, have to be considered in relation to those for other natural disasters. Policies have to be relevant to the differing geology, meteorology and cultures of the countries affected.

Ed Lorenz was a pioneer of chaos theory; he provided the first realization of a strange attractor based on a mathematical model of just three coupled differential equations. In addition, Ed made many seminal contributions to theoretical meteorology, not only in studies of the predictability of weather and climate, but also in advancing our basic understanding of the dynamics and thermodynamics of climate.

Dynamic data assimilation offers a suite of algorithms that merge measurement data with numerical simulations to predict accurate state trajectories. Meteorological centers rely heavily on data assimilation to achieve trustworthy weather forecast. With the advance in measurement systems, as well as the reduction in sensor prices, data assimilation (DA) techniques are applicable to various fields, other than meteorology. However, beginners usually face hardships digesting the core ideas from the available sophisticated resources requiring a steep learning curve. In this tutorial, we lay out the mathematical principles behind DA with easy-to-follow Python module implementations so that this group of newcomers can quickly feel the essence of DA algorithms. We explore a series of common variational, and sequential techniques, and highlight major differences and potential extensions. We demonstrate the presented approaches using an array of fluid flow applications with varying levels of complexity.

Determining the finite-amplitude preconditioned states in the hurricane embryo, which lead to tropical cyclogenesis, is a central issue in contemporary meteorology. In the embryo there is competition between different preconditioning mechanisms involving hydrodynamics and moist thermodynamics, which can lead to cyclogenesis. Here systematic asymptotic methods from applied mathematics are utilized to develop new simplified moist multi-scale models starting from the moist anelastic equations. Three interesting multi-scale models emerge in the analysis. The balanced mesoscale vortex (BMV) dynamics and the microscale balanced hot tower (BHT) dynamics involve simplified balanced equations without gravity waves for vertical vorticity amplification due to moist heat sources and incorporate nonlinear advective fluxes across scales. The BMV model is the central one for tropical cyclogenesis in the embryo. The moist mesoscale wave (MMW) dynamics involves simplified equations for mesoscale moisture fluctuations, as well as linear hydrostatic waves driven by heat sources from moisture and eddy flux divergences. A simplified cloud physics model for deep convection is introduced here and used to study moist axisymmetric plumes in the BHT model. A simple application in periodic geometry involving the effects of mesoscale vertical shear and moist microscale hot towers on vortex amplification is developed here to illustrate features of the coupled multi-scale models. These results illustrate the use of these models in isolating key mechanisms in the embryo in a simplified content.

Abstract The concept of 𝐴-level sets of real functions 𝑢(𝑥, 𝑦) (i.e., the solutions of 𝑢(𝑥, 𝑦) = 𝐴 = const) in a given domain admits numerous interpretations in applied sciences: level sets are potential lines, streamlines in hydrodynamics, meteorology and electromagnetics, isobars in gas-dynamics, isotherms in thermodynamics, etc. In fact, the level sets of 𝑢 considered for all values 𝐴 make the “map” of this function and their interpretations in different sciences make the “maps” of the corresponding processes. In this paper we study the geometry of these maps for broad classes of functions and arbitrary values 𝐴. In particular, we study how much twisted or, speaking in general, how turbulent these maps are. The concepts and results admit some immediate interpretations and can be stated in terms of flow rotation and turbulence. The study gives a new, in fact a geometric description of these applied phenomena.

Collapse calderas are defined as the volcanic depression that result from the disruption of the geometry of the magma chamber roof due to down faulting during the course of an eruption. These structures have received considerable attention due to their link to Earth's ore deposits and geothermal energy resources, but also because large pyroclastic eruptions and associated caldera collapse structures represent one of the most catastrophic geologic events that have occurred on the Earth's surface in the Phanerozoic time and in the historical time.
After several pioneering works, collapse calderas have been the subject of studies of diverse disciplines. However, some important aspects on caldera dynamics and structure remain poorly understood yet.

First, we have revised important works concerning field data about collapse calderas and summarized the most relevant aspects and results. We have created a database to record existing information about collapse calderas: Collapse Caldera DataBase (CCDB). After an exhaustive analysis of the included information we have observed two types of collapse caldera: type-A and type-B.

Experiments on caldera collapse modelling allow a qualitative study of the structural evolution of a caldera collapse process and suggest which of factors play a more relevant role. Analogue models have verified that caldera collapse formation is influenced by multiple aspects (e.g. regional tectonics). We have performed three types of semi-quantitative analyses of particular interest for volcanic hazard: the measurement of the erupted magma chamber volume fraction required to achieve each step of the collapse process, the estimation of the subsidence pattern and the study of the influence of the roof aspect ratio in the dimensions of the collapse parts at surface.

This work includes also a summary of the most important aspects concerning mathematical models of collapse calderas. In base of a mathematical analysis of the pressure evolution inside the chamber during volcanic cycles, we have defined two collapse caldera end-members: under- and overpressure calderas. We have (1) reproduced numerically some of the analogue experiments set out in this work; (2) studied the influence of the selected geometrical setting (e.g. axial symmetric or three-dimensional) in the obtained results and subsequent interpretations and (3) demonstrated that results obtained with mathematical models not strictly related to collapse caldera processes are also applicable to the study of collapse mechanisms and controlling factors.

Finally, we compare the different results obtained by the three distinct disciplines, in order to propose a genetic classification for collapse calderas and to describe the dynamic and structural evolution of the defined end-members. We distinguish between "Cordilleran type" and "Composite volcano type" calderas. Calderas related to the first group correspond to commonly rhyolitic or dacitic, large plate/piston or trap-door calderas formed from a sill-like overpressurized magma chamber in the presence of a regional extensive stress field and a large scale doming or underplating. These calderas tend to occur in areas of thick or thin continental crust and in evolved transitional thick crust. They are associated with C-type subduction zones and areas of continental rifting. "Composite volcano type" calderas occur at the culmination of a long eruptive cycle in composite volcanoes. They take place at the summit of a long-lived volcanic edifice, which has undergone various periods of magma chamber inflation and deflation and different eruptions. The caldera-forming eruption begins with overpressure inside the chamber that triggers, once overcome the tensile strength of the host rock, magma injection into the host rock and finally, an eruption. Calderas included in this group tend to be smaller and not too voluminous.

Concluding, the combination of field studies with experimental and theoretical/mathematical and modelling allows us to identify and quantify the main factors controlling collapse calderas.

Thesis (Ph.D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences and the Woods Hole Oceanographic Institution), 2000.
Includes bibliographical references (p. 284-290).
by Brian Kenneth Arbic.
Ph.D.

The thermally-driven rotating annulus is a laboratory experiment used to study the dynamics of planetary atmospheres under controlled and reproducible conditions. The predictability of this experiment is studied by applying the same principles used to predict the atmosphere. A forecasting system for the annulus is built using the analysis correction method for data assimilation and the breeding method for ensemble generation. The results show that a range of flow regimes with varying complexity can be accurately assimilated, predicted, and studied in this experiment. This framework is also intended to demonstrate a proof-of-concept: that the annulus could be used as a testbed for meteorological techniques under laboratory conditions. First, a regime diagram is created using numerical simulations in order to select points in parameter space to forecast, and a new chaotic flow regime is discovered within it. The two components of the framework are then used as standalone algorithms to measure predictability in the perfect model scenario and to demonstrate data assimilation. With a perfect model, regular flow regimes are found to be predictable until the end of the forecasts, and chaotic regimes are predictable over hundreds of seconds. There is a difference in the way predictability is lost between low-order chaotic regimes and high-order chaos. Analysis correction is shown to be accurate in both regular and chaotic regimes, with residual velocity errors about 3-8 times the observational error. Specific assimilation scenarios studied include information propagation from data-rich to data-poor areas, assimilation of vortex shedding observations, and assimilation over regime and rotation rate transitions. The full framework is used to predict regular and chaotic flow, verifying the forecasts against laboratory data. The steady wave forecasts perform well, and are predictable until the end of the available data. The amplitude and structural vacillation forecasts lose quality and skill by a combination of wave drift and wavenumber transition. Amplitude vacillation is predictable up to several hundred seconds ahead, and structural vacillation is predictable for a few hundred seconds.

Crop development models are commonly used in research. However, their use as crop management tools for growers is rare. Decision support systems (DSS), which combine crop models with expert systems, are being developed to provide management assistance to growers. Researchers at Oregon State University are in the process of developing a DSS. Research was conducted to develop a computer program to provide current and generated weather data for use by the DSS. The objectives of this research were to obtain a weather station, develop a set of quality control procedures to check data from the station, obtain a weather generator program, and create a weather data manager program to implement the above objectives. A weather station was obtained and was placed near two existing weather stations for ten months. Data from the weather station was compared with the other two stations for values of monthly average maximum temperature, minimum temperature, and daily total solar radiation and monthly total precipitation. The weather station performed well. Only measurements of total daily solar radiation were consistently different from the other stations. Based on a comparison of the weather station with an Eppley pyranometer, a factor was calculated to correct the solar radiation readings. The quality control procedures used on the weather data were adapted from automated procedures given in the literature. When tested, the procedures performed as desired. When used on actual data from the weather station, values that failed the procedures were apparently legitimate values. Options were added to the data manager program that allow the user to quickly decide what to do with failed values. For a weather data generator, WGEN was chosen from the generators presented in the literature. An input parameter file was created for the Corvallis, Oregon area and thirty years of data were generated. Monthly means from this data were compared with thirty-year historical monthly means for Corvallis. Precipitation data from WGEN compared well with the historical data. The generated data for maximum and minimum temperature and daily total solar radiation had great differences from the historical data. It is believed that the input parameters for the Corvallis area suggested by the authors of WGEN are not appropriate. The weather data manager program was written in the C programming language, and occupies approximately 98 kilobytes of disk space, not including the eleven files created directly and indirectly by the program. The main functions of the program are: 1) retrieving data from the weather station and performing quality control procedures on the data (allowing the user to decide what to do with values that failed QC); 2) viewing and editing of files by the user; 3) weather data generation (creating a file of only generated data or appending generated data to the file of current data from the weather station to create a file containing a full year of weather data); and 4) miscellaneous functions (monitoring the weather station, setting the calendar in the station's datalogger, and changing information used by the data manager program). It is hoped that this program will be a significant contribution towards the development of a decision support system.
Graduation date: 1992

The recent extreme hydrological extremes over the globe highlight the importance of understanding the role of atmospheric dynamics and climate variability on the occurrence of these extreme events and the associated temporal and spatial characteristics of sequences of the precipitation events. Most of the studies have been focusing on overall average impacts of long-term global climate change on extremes. Majority are driven largely by considering the changes of the moisture holding capacity as a function of temperature, as indicated by the Clausius-Clapeyron equation. Given the complex dynamical structure of the atmosphere, one needs to also consider the attendant atmospheric circulation and moisture transport mechanisms that lead to extreme precipitation and subsequent floods as evidenced in the recent major floods. This study first develops insights into the causative climatic factors associated with precipitation induced regional floods events and understand the roles of Atmospheric Rivers (AR) or Tropical Moisture Exports (TME) and atmospheric circulation patterns associated with the frequency and/or persistency of such events in the midlatitudes. The second part explores the spatiotemporal relationship between climate variability and global extreme precipitation occurrence using a graph based approach based upon the concept of reciprocity to investigated the linkages and influences of the slowly changing boundary conditions on the development or propagation of atmospheric circulations, to assess the predictability of global precipitation extremes given the leading modes of identified climate dipole networks. A multi-timescale statistical, climate informed, stochastic streamflow forecast model serves as the bridge linking the first two parts to the application in the third part: application on water resources management by developing a multi-timescale climate informed stochastic hybrid stimulation-optimization model for multi-purpose reservoir systems, which enables the utilization of the streamflow forecast. The novel reservoir operation model attempts to change the game of water resources management from its conservative, rigid rule-following scheme to a robust, market-based, reliable water allocation strategy. Part I. Tropical Moisture Exports, Extreme Precipitation and Major Flood Atmospheric Rivers are being increasingly identified as associated with some extreme floods. More generally, such floods may be associated with tropical moisture exports that exhibit relatively robust teleconnections between moisture source regions and flood regions. First, a large-scale flood event that persisted over Western Europe in January 1995 is studied. During the last ten days of the month, two rare flooding events, associated with heaviest rainfall in 150 years, occurred in two places, one over Brittany (West of France), and the second in the France-Germany border region and parts of neighboring countries. In this study, we explore the month-long evolution of tropical moisture exports (TME) and their connection to the precipitation events that led to the Brittany event. The persistent large-scale atmospheric circulation patterns that led to the birth, death and evolution of these TME as atmospheric rivers with landfalls in Western Europe are identified, and the relationship of daily extreme precipitation to these patterns is examined. Singular value decomposition (SVD) analysis and a generalized linear model (GLM) are used to assess whether knowledge of the atmospheric circulation patterns from the prior record is useful for explaining the occurrence of their rare events. The analysis establishes the importance of both global and regional atmospheric circulation modes for the occurrence of such persistent events and the hydrologic importance of diagnosing global atmospheric moisture pathways. Part II. Seasonal to Interannual Variability of Tropical Moisture Exports, Extremes and ENSO A statistically and physically based framework is put forward that investigates the relationship between Tropical Moisture Exports (TMEs), Extreme Precipitation and Floods. TMEs is the more general phenomena than Atmospheric Rivers (ARs) in terms of (1) facilitates the poleward transport of warm and moist air masses from low latitudes, primarily tropical oceanic areas, to higher latitudes; (2) contributes to the global climatology precipitation and its extremes; (3) closely relates to floods events, especially in the midlatitudes. The TMEs itself has seasonal and interannual variability that is regulated by slowly changing boundary conditions and climate variability, such El Niño Southern Oscillation (ENSO), while the trajectories and movements are presumably led by atmospheric circulations patterns driven by the balance of global energy and water budgets. In this study, we take Northwest US (NE US) to show how the TMEs is related to extreme precipitation and then floods, and the results of the variability of TMEs, coupled with atmospheric circulation patterns, on the extremes. Historical large floods events in NE US in different seasons are studied for their link to the TMEs. Major moisture sources of TMEs that contributes to precipitation, extremes and floods in NE US are identified, together with the sources' seasonally and interannually varying characterizes in terms of both birth and entrance to the NE US, with the consideration of large scale climate regulations and atmospheric circulation patterns. Part III. Correlation Networks for Identifying Predictors for Extended Range Forecasts for Extreme Precipitation Correlation networks identified from financial, genomic, ecological, epidemiological, social and climate data are being used to provide useful topological insights into the structure of high dimensional data. Strong convection over the oceans and the atmospheric moisture transport and flow convergence indicated by atmospheric pressure fields may determine where and when extreme precipitation occurs. Here, the spatiotemporal relationship between climate and extreme global precipitation is explored using a graph based approach that uses the concept of reciprocity to generate cluster pairs of locations with similar spatiotemporal patterns at any time lag. A global time-lagged relationship between pentad sea surface temperatures (SST) anomalies and pentad sea level pressure (SLP) anomalies is investigated to understand the linkages and influence of the slowly changing oceanic boundary conditions on the development of the global atmospheric circulation. We explore the use of this correlation network to predict extreme precipitation globally over the next 30 days, using a Principal Component logistic regression on the strong global dipoles found between SST and SLP. Unprecedented success of the predictive skill under cross validation for 30 days precipitation higher than the 90th percentile is indicated for selected global regions for each wet season considered. Part IV. Applications of Climate Informed Streamflow Forecasts for Water Management Streamflow forecasts at multiple time scales (e.g., season and year ahead) provide a new opportunity for reservoir management to address competing objectives. Market instruments such as forward contracts with specified reliability are considered as a tool that may help address the perceived risk associated with the use of such instruments in lieu of a traditional operation and allocation. A water allocation process that enables multiple contracts with different durations, to facilitate participatory management of the reservoir by users and system operators, is presented here. Since these contracts are based on a verifiable reliability they may in turn be insurable. A Multi-timescale climate informed Stochastic Hybrid Simulation - Optimization Model (McISH) is developed, featuring (1) dynamic flood control storage allocation at a specified risk level; (2) multiple duration energy/water contracts with user specified reliability and prices; and (3) contract sizing and updating to reflect changes in both demands and supplies. The model incorporates multi-timescale (annual and seasonal) streamflow forecasts, and addresses uncertainties across both timescales. The intended use is as part of an interaction between users and water operators to arrive at a set of short-term and long term contracts through disclosure of demand or needs and the value placed on reliability and contract duration. An application is considered using data for the Bhakra Dam, India. The issues of forecast skill and contract performance given a set of parameters are examined to illustrate the approach. Prospects for the application in a general setting are discussed.

AbstractThis chapter of Animating Unpredictable Effects charts the development of the software tools used to create uncanny simulation-based digital animations, drawing a genealogy that starts with nineteenth century mathematics, which were transformed into management and prediction tools by private and military R&D between the 1940s and 1980s. Through this, the chapter identifies a connection between these animation tools and simulation tools used in fields as diverse as meteorology, nuclear physics, and aeronautics that create unpredictability through stochastic or dynamic simulation. Using this information, the chapter offers a theoretical framework for understanding how fictional simulations in animation and visual effects make meaning through “knowing how” as opposed to cinema’s tradition approach of “knowing that,” leveraging concepts from the history of science.