Browsing by Author "Kirby, Michael J., committee member"
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Item Open Access A parametric classification of directed acyclic graphs(Colorado State University. Libraries, 2017) Chaturvedi, Mmanu, author; McConnell, Ross M., advisor; Kirby, Michael J., committee member; Rajopadhye, Sanjay V., committee member; Oprea, Iuliana, committee memberWe consider four NP-hard optimization problems on directed acyclic graphs (DAGs), namely, max clique, min coloring, max independent set and min clique cover. It is well-known that these four problems can be solved in polynomial time on transitive DAGs. It is also known that there can be no polynomial O(n1-ϵ)-approximation algorithms for these problems on the general class of DAGs unless P = NP. We propose a new parameter, β, as a measure of departure from transitivity for DAGs. We define β to be the number of vertices in a longest path in a DAG such that there is no edge from the first to the last vertex of the path, and 2 if the graph is transitive. Different values of β define a hierarchy of classes of DAGs, starting with the class of transitive DAGs. We give a polynomial time algorithm for finding a max clique when β is bounded by a fixed constant. The algorithm is exponential in β, but we also give a polynomial β-approximation algorithm. We prove that the other three decision problems are NP-hard even for β ≥ 4 and give polynomial algorithms with approximation bounds of β or better in each case. Furthermore, generalizing the definition of quasi-transitivity introduced by Ghouilà -Houri, we define β-quasi-transitivity and prove a more generalized version their theorem relating quasi-transitive orientation and transitive orientation.Item Open Access Convective cold pools: characterization and soil moisture dependence(Colorado State University. Libraries, 2016) Drager, Aryeh Jacob, author; van den Heever, Susan C., advisor; Davis, Christopher A., committee member; Kirby, Michael J., committee member; Schubert, Wayne H., committee memberConvective cold pools play an important role in Earth's climate system. However, a common framework does not exist for conceptually defining and objectively identifying convective cold pools in observations and models. The first part of this thesis begins with a review of the identification methods used in previous works. This is followed by an investigation of convective cold pools within a high-resolution simulation of rainforest convection simulated using the Regional Atmospheric Modeling System (RAMS), an open-source cloud-resolving model with a coupled land-surface model. Multiple variables are assessed for their potential for identifying convective cold pool boundaries, and a novel technique is developed and tested for identifying and tracking convective cold pools in numerical model simulations. This algorithm is based on surface rainfall rates and radial gradients in the density potential temperature field. The algorithm successfully identifies near-surface cold pool boundaries and is able to distinguish between connected cold pools. Once cold pools have been identified and tracked, composites of cold pool evolution are then constructed, and average cold pool properties are investigated. One novel result is the presence of moist patches that develop within the centers of cold pools where the ground has been soaked with rainwater. These moist patches help to maintain cool temperatures and prevent cold pool dissipation, which has implications for the development of subsequent convection. The second part of this thesis explores how the properties of convective cold pools are modulated by soil moisture. Three high-resolution simulations of tropical rainforest convection are performed using the RAMS, and the initial soil moisture is varied between 25% and 75% saturation. The cold pool identification algorithm developed in the first part of the thesis is used to construct composites of cold pools within each simulation, and the composites are compared. When soil moisture is decreased, stronger convective cold pools result. These stronger cold pools are also smaller because increased sensible heat fluxes in the reduced soil-moisture simulations cause the cold pools to dissipate more quickly as they expand. Finally, the rings of enhanced water vapor that have been documented in previous studies of tropical cold pools disappear when soil moisture is reduced. These results emphasize the role that land surface properties can have in modulating convective cold pool properties.Item Open Access Diabatic and frictional forcing effects on the structure and intensity of tropical cyclones(Colorado State University. Libraries, 2013) Slocum, Christopher J., author; Schubert, Wayne H., advisor; DeMaria, Mark, advisor; Schumacher, Russ S., committee member; Kirby, Michael J., committee member; Fiorino, Michael, committee memberTropical cyclone intensity forecasting skill has slowed in improvement for both dynamical and statistical-dynamical forecasting methods in comparison to gains seen in track forecasting skill. Also, forecast skill related to rapid intensification, e.g. a 30 kt or greater increase in intensity within a 24-hour period, still remains poor. In order to make advances and gain a greater understanding, the processes that affect intensity change, especially rapid intensification, need further study. This work evaluates the roles of diabatic and frictional forcing on the structure and intensity of tropical cyclones. To assess the diabatic forcing effects on intensity change in tropical cyclones, this study develops applications of Eliassen's balanced vortex model to obtain one-dimensional solutions to the geopotential tendency and two-dimensional solutions to the transverse circulation. The one-dimensional balanced solutions are found with dynamical model outputs as well as aircraft reconnaissance combined with diabatic heating derived from microwave rainfall rate retrievals. This work uses solutions from both datasets to make short-range intensity predictions. The results show that for the one-dimensional solutions, the tangential tendency does not match the dynamical model or aircraft wind tendencies. To relax the assumptions of the one-dimensional solutions to the geopotential tendency, solutions for idealized vortices are examined by finding two-dimensional solutions to the transverse circulation. The two-dimensional solutions allow for evaluation of the axisymmetric structure of the vortex on the (r, z)-plane without setting the baroclinicity to zero and the static stability to a constant value. While the sensitivity of tangential wind tendency to diabatic forcing and the region of high inertial stability is more realistic in the two-dimensional results, the solutions still neglect the influence of friction from the boundary layer. To understand further the role of frictional forcing in the boundary layer, two analytical slab models developed in this study provide insight into recent work that demonstrates how dry dynamics plays a role in determining eyewall location and size, how potential vorticity rings develop, and how an outer concentric eyewall forms through boundary layer "shock-like" structures. The analytical models show that when horizontal diffusion is neglected, the u(∂u/∂r) term in the radial equation of motion and the u[ƒ + (∂v/∂r) + (v/r)] term in the tangential equation of motion develop discontinuities in the radial and tangential wind, with associated singularities in the boundary layer pumping and the boundary layer vorticity. The analytical models provide insight into the boundary layer processes that are responsible for determining the location of the eyewall and the associated diabatic heating that ultimately impacts the intensity of the tropical cyclone. This work shows that future research linking the roles of frictional forcing in the boundary layer to the diabatic forcing aloft while using a balanced model will be important for gaining insight into forcing effects on tropical cyclone intensity.Item Open Access Network multiple frame assignment architectures(Colorado State University. Libraries, 2001) Lu, Suihua, author; Poore, Aubrey, advisor; Kirby, Michael J., committee member; Zachmann, David W., committee member; Miranda, Rick, 1953-, committee memberMultiple target tracking methods divide into two broad classes, namely single frame and multiple frame methods. The most successful of the multiple frame methods are multiple hypothesis tracking (MHT) and multiple frame assignments (MFA). In dense tracking environments the performance improvements of multiple frame methods over single frame methods is very significant, making it the preferred solution for many tracking problems. Thus, in addition to the availability single frame processing, multiple frame data association methods are an essential class of methods for almost all tracking needs. The application of multiple frame tracking methods must consider an architecture in which the sensors are distributed across multiple platforms. Such geometric and sensor diversity has the potential to significantly enhance tracking and discrimination accuracy. A centralized architecture in which all measurements are sent to one location and processed with tracks being transmitted back to the different platforms is a simple one that is probably optimal in that it is capable of producing the best track quality (e.g., purity and accuracy) and a consistent air picture. The centralized tracker is, however, unacceptable for several reasons, notably the communication overloads and single-point-failure. Thus, one must turn to a distributed architecture for both estimation/fusion and data association. One of the simplest network-centric architectures is that of placing a centralized tracker on each platform. The architecture is called Network MFA Centralized, which removes the problem of single-point-failure. However, due to communication delays in the network, the order the measurements arrive at different platforms varies. Each composite tracker is making its own tracking decisions based on the data it receives, regardless of decisions of other platforms. Therefore, a consistent air picture may not be achieved across the network. Thus, the objective of this thesis is the development of two near-optimal Network-Centric MFA architectures, namely Network MFA on Local Data and Network Tracks and Network MFA on All data and Network Tracks, that preserve the quality of a centralized tracker across a network of platforms while managing communication loading and achieving a consistent air picture. One technique that has proved useful for achieving SlAP is to require that each platform be in charge of assigning its own measurements to the network tracks. In the architecture of Network MFA on Local Data and Network Tracks, only local data are used in the sliding windows and track initiations are based on local data only. In the architecture of Network MFA on All Data and Network Tracks, all data (remote and local) are used in the sliding window. Communication loading is only addressed by the architectures in that track states and their error covariances are not required to be transmitted back to the various platforms. The results of extensive computations are presented to validate the differences in four tracking architectures.Item Open Access Response of convective cold pools and precipitation to changes in soil moisture(Colorado State University. Libraries, 2020) Drager, Aryeh Jacob, author; van den Heever, Susan C., advisor; Bell, Michael M., committee member; Davis, Christopher A., committee member; Kirby, Michael J., committee member; Schubert, Wayne H., committee memberIn Part 1 of this dissertation, we examine the role of soil moisture in modulating convective cold pool properties. This investigation is performed within an idealized modeling framework featuring a cloud-resolving model coupled to an interactive land surface model. Five high-resolution simulations of tropical continental convection are conducted in which the initial soil moisture is varied. The hundreds of cold pools forming within each simulation are identified and composited across space and time using an objective cold pool identification algorithm. Several important findings emerge from this analysis. Lower initial soil moisture results in greater daytime heating of the surface, which produces a deeper, drier subcloud layer. As a result, latent cooling through the evaporation of precipitation is enhanced, and cold pools are stronger and deeper. Increased gust front propagation speed, combined with wider rain shafts, results in wider cold pools. Finally, the "water vapor rings" that surround each cold pool under wet-soil conditions disappear under dry-soil conditions, due to the suppression of surface latent heat fluxes. Instead, when soils are dry, short-lived "puddles" of enhanced water vapor permeate the interiors of the cold pools. The results are nonlinear in that the properties of the cold pools in the two driest-soil simulations depart substantially from the cold pool properties in the three simulations initialized with wetter soil. The dividing line between the resulting wet-soil and dry-soil regimes is the permanent wilting point (PWP), below which transpiration is subdued. Land surface-boundary layer-cloud interactions are found overall to play a key role in governing the properties of cold pools. During Part 1 of this dissertation, we identify a novel "intermediate-soil moisture disadvantage" regime in which soils whose initial liquid water content slightly exceeds the PWP receive the least rainfall. In Part 2, we investigate the physical mechanisms behind this result. Four suites of ten idealized, high-resolution numerical experiments are conducted using the same modeling system used in Part 1. Each suite uses a distinct combination of soil type and vegetation, and within each suite, each simulation is initialized with a different amount of soil moisture. The "intermediate soil-moisture disadvantage" from Part 1 is reproduced. This result is found to stem from differing amounts of subcloud rain evaporation across the simulations, as well as from divergent balances between the level of free convection and the strength of boundary layer vertical motions. However, the result only holds for vegetated surfaces; bare-soil surfaces are instead found to exhibit a pure "wet-soil advantage" relationship. These results have important implications for the design of future process-level studies and large-scale model parameterizations.Item Open Access Theory and applications of optimized correlation output filters(Colorado State University. Libraries, 2011) Bolme, David Scott, author; Beveridge, J. Ross, 1957-, advisor; Draper, Bruce A. (Bruce Austin), 1962-, committee member; Strout, Michelle Mills, committee member; Kirby, Michael J., committee memberCorrelation filters are a standard way to solve many problems in signal processing, image processing, and computer vision. This research introduces two new filter training techniques, called Average of Synthetic Exact Filters (ASEF) and Minimum Output Sum of Squared Error (MOSSE), which have produced filters that perform well on many object detection problems. Typically, correlation filters are created by cropping templates out of training images; however, these templates fail to adequately discriminate between targets and background in difficult detection scenarios. More advanced methods such as Synthetic Discriminant Functions (SDF), Minimum Average Correlation Energy (MACE), Unconstrained Minimum Average Correlation Energy (UMACE), and Optimal Tradeoff Filters (OTF) improve performance by controlling the response of the correlation peak, but they only loosely control the effect of the filters on the rest of the image. This research introduces a new approach to correlation filter training, which considers the entire image to image mapping known as cross-correlation. ASEF and MOSSE find filters that optimally map the input training images to user specified outputs. The goal is to produce strong correlation peaks for targets while suppressing the responses to background. Results in eye localization, person detection, and visual tracking indicate that these new filters outperform other advanced correlation filter training methods and even produce better results than much more complicated non-filter algorithms.Item Open Access Wake vortices and tropical cyclogenesis downstream of Sumatra over the Indian Ocean(Colorado State University. Libraries, 2015) Fine, Caitlin Marie, author; Johnson, Richard H., advisor; Schubert, Wayne H., committee member; Kirby, Michael J., committee memberA myriad of processes acting singly or in concert may contribute to tropical cyclogenesis, including convectively coupled waves, breakdown of the inter-tropical convergence zone (ITCZ), or upper-level troughs. This thesis investigates the role that topographic effects from the island of Sumatra may play in initiating tropical cyclogenesis (TC genesis) in the eastern Indian Ocean. If easterly flow is split by the mountains of Sumatra, counter-rotating lee vortices may form downstream. Because Sumatra straddles the equator, though the wake vortices rotate in opposite directions, they will both be cyclonic when winds are easterly upon Sumatra, and may intensify further into tropical cyclones. The phenomenon of cross-equatorial cyclone pairs, or "twin" tropical cyclones, in the Indian Ocean originating from Sumatra was first noted by Kuettner (1989). TC genesis appears to be particularly favored during the pre-onset phase of the Madden Julian Oscillation (MJO), when easterly flow encroaches upon Sumatra and the resulting cyclonic wake vortices encounter convectively coupled waves and enhanced moisture associated with the MJO in the Indian Ocean. Operational analysis data from the Year of Tropical Convection (YOTC) and Dynamics of the Madden Julian Oscillation (DYNAMO) campaigns were used to evaluate the impacts of Sumatra's topography upon the flow. The YOTC data encompass two years, from May 2008 to April 2010, while the special observing period of DYNAMO was conducted from October to December 2011. This research also presents three case studies of twin tropical cyclones west of Sumatra in the Indian Ocean, which were all determined to originate from Sumatran wake vortices and occurred between October and December of 2008, 2009, and 2011. Multiple cyclonic wake vortices and vorticity streamers were observed downstream of Sumatra during periods of easterly flow, most frequently between October and December. Froude numbers calculated for the region upstream of Sumatra with regard to easterly flow between October and December favored flow blocking and splitting, more so for Sumatra's northern tip due to the higher terrain there. Correlations between zonal wind and relative vorticity are more significant near Sumatra's northern tip than near and downstream of the island's southern tip. Cyclonic vorticity was maximized at the level of Sumatra's topography for most easterly wind days west of both the north and south ends of the island, suggesting that topography was contributing to vorticity generation. Thirteen tropical cyclones in the Indian Ocean during the YOTC and DYNAMO campaigns were determined to develop from cyclonic wake vortices downstream of Sumatra, including three tropical cyclone pairs. Over 75% of these tropical cyclones formed between October and December. In four cases, wake vortices were generated by anomalously easterly low-level flow that preceded the active phase of the Madden Julian Oscillation. These vortices proceeded to encounter the MJO convective envelope, which is frequently accompanied by convectively coupled waves and may have altered the environment to be more moist and favorable for tropical cyclogenesis. In many cases, equatorial westerly winds, which may have been related to westerly wind bursts from the MJO or to convectively coupled equatorial Rossby waves, intensified low-level cyclonic circulations. It is suggested that diabatic heating in the vicinity of twin tropical cyclones may disturb the atmosphere enough to invigorate extant convectively coupled Kelvin waves, or contribute to the formation of a Kelvin wave. The research presented herein describes the interaction of the flow with steep topography on Sumatra and its role in tropical cyclogenesis over the Indian Ocean, a mechanism for TC genesis that has heretofore received little attention.