Mountain Scholar :: Browsing by Author "Eykholt, Richard, committee member"

Browsing by Author "Eykholt, Richard, committee member"

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Open Access
A search for Lorentz and CPT violation in the neutrino sector of the standard model extension using the near detectors of the Tokai to Kamioka neutrino oscillation experiment
(Colorado State University. Libraries, 2016) Clifton, Gary Alexander, author; Toki, Walter, advisor; Berger, Bruce, committee member; Eykholt, Richard, committee member; Hulpke, Alexander, committee member
The Tokai to Kamioka (T2K) neutrino experiment is designed to search for electron neutrino appearance oscillations and muon neutrino disappearance oscillations. While the main physics goals of T2K fall into conventional physics, T2K may be used to search for more exotic physics. One exotic physics analysis that can be performed is a search for Lorentz and CPT symmetry violation (LV and CPTV) through short baseline neutrino oscillations. The theoretical framework which describes these phenomena is the Standard Model Extension (SME). Due to its off-axis nature, T2K has two near detectors. A search for LV and CPTV is performed in each detector. The search utilizes charged-current inclusive (CC inclusive) neutrino events to search for sidereal variations in the neutrino event rate at each detector. Two methods are developed; the first being a Fast Fourier Transform method to perform a hypothesis test of the data with a set of 10,000 toy Monte-Carlo simulations that do not have any LV signal in them. The second is a binned likelihood fit. Using three data sets, both analysis methods are consistent with no sidereal variations. One set of data is used to calculate upper limits on combinations of the SME coefficients while the other two are used to constrain the SME coefficients directly. Despite not seeing any indication of LV in the T2K near detectors, the upper limits provided are useful for the theoretical field to continue improving theories which include LV and CPTV.
Open Access
A tropical radiation and cloud system feedback modulated by sea surface temperature
(Colorado State University. Libraries, 2011) Igel, Matthew R., author; Stephens, Graeme, advisor; van den Heever, Susan, committee member; Eykholt, Richard, committee member
A large domain, high resolution cloud system resolving model set up in the tropics over fixed sea surface temperatures (SST) of 298 K and 302 K and run to radiative convective equilibrium has been analyzed with the focus on well equilibrated, domain mean results. The Regional Atmospheric Modeling System (RAMS) is used. The modeled convection organizes into disturbed, convective and undisturbed, subsidence regions. The mean profiles of state variables such as temperature, relative humidity (RH), and convective mass flux are analyzed and found to depend on SST in both predictable and unpredictable ways. The characteristics of rain depend on SST such that higher surface temperatures produce greater variability in intensity and lesser frequency. Next, the large-scale mean state is used to understand the convective system-scale setup. A focus is on the controls in the undisturbed regions of the disturbed region, deep convective anvil detrainment. Upper tropospheric radiation, through diabatic convergence, is used as a paradigm to understand the height at which detrainment occurs. The dependence of upper tropospheric radiation on RH is derived explicitly for the first time. From this new equation, temperature and RH are found to control anvil detrainment. The addition of RH as an anvil detrainment control explains why the model leads to an understanding of cooler anvils with higher SST - a positive climate feedback on the system. Other anvil feedbacks exhibited by the model are similar to those proposed in the Iris and Thermostat hypotheses. The convective system components are shown to enhance one another such that the overall system dependence on SST is nonlinear. To understand the circulation system, a heat engine analogue is made that shows the warmer state is able to more efficiently circulate or move heat. Finally, observational evidence from Cloudsat and CALIPSO shows that some of the modeled results are also apparent in nature.
Open Access
Aerosol impacts on deep convective storms in the tropics: a combination of modeling and observations
(Colorado State University. Libraries, 2012) Storer, Rachel Lynn, author; van den Heever, Susan C., advisor; Stephens, Graeme L., committee member; Johnson, Richard H., committee member; Eykholt, Richard, committee member
It is widely accepted that increasing the number of aerosols available to act as cloud condensation nuclei (CCN) will have significant effects on cloud properties, both microphysical and dynamical. This work focuses on the impacts of aerosols on deep convective clouds (DCCs), which experience more complicated responses than warm clouds due to their strong dynamical forcing and the presence of ice processes. Several previous studies have seen that DCCs may be invigorated by increasing aerosols, though this is not the case in all scenarios. The precipitation response to increased aerosol concentrations is also mixed. Often precipitation is thought to decrease due to a less efficient warm rain process in polluted clouds, yet convective invigoration would lead to an overall increase in surface precipitation. In this work, modeling and observations are both used in order to enhance our understanding regarding the effects of aerosols on DCCs. Specifically, the area investigated is the tropical East Atlantic, where dust from the coast of Africa frequently is available to interact with convective storms over the ocean. The first study investigates the effects of aerosols on tropical DCCs through the use of numerical modeling. A series of large-scale, two-dimensional cloud-resolving model simulations was completed, differing only in the concentration of aerosols available to act as CCN. Polluted simulations contained more deep convective clouds, wider storms, higher cloud tops and more convective precipitation across the entire domain. Differences in the warm cloud microphysical processes were largely consistent with aerosol indirect theory, and the average precipitation produced in each DCC column decreased with increasing aerosol concentration. A detailed microphysical budget analysis showed that the reduction in collision and coalescence largely dominated the trend in surface precipitation; however the production of rain through the melting of ice, though it also decreased, became more important as the aerosol concentration increased. The DCCs in polluted simulations contained more frequent, stronger updrafts and downdrafts, but the average updraft speed decreased with increasing aerosols in DCCs above 6 km. An examination of the buoyancy term of the vertical velocity equation demonstrates that the drag associated with condensate loading is an important factor in determining the average updraft strength. The largest contributions to latent heating in DCCs were cloud nucleation and vapor deposition onto water and ice, but changes in latent heating were, on average, an order of magnitude smaller than those in the condensate loading term. It is suggested that the average updraft is largely influenced by condensate loading in the more extensive stratiform regions of the polluted storms, while invigoration in the convective core leads to stronger updrafts and higher cloud tops. The goal of the second study was to examine observational data for evidence that would support the findings of the modeling work. In order to do this, four years of CloudSat data were analyzed over a region of the East Atlantic, chosen for the similarity (in meteorology and the presence of aerosols) to the modeling study. The satellite data were combined with information about aerosols taken from the output of a global transport model, and only those profiles fitting the definition of deep convective clouds were analyzed. Overall, the cloud center of gravity, cloud top, rain top, and ice water path were all found to increase with increased aerosol loading. These findings are in agreement with what was found in the modeling work, and are suggestive of convective invigoration with increased aerosols. In order to separate environmental effects from that due to aerosols, the data were sorted by environmental convective available potential energy (CAPE) and lower tropospheric static stability (LTSS). The aerosol effects were found to be largely independent of the environment. A simple statistical test suggests that the difference between the cleanest and most polluted clouds sampled are significant, lending credence to the hypothesis of convective invigoration. This is the first time evidence of deep convective invigoration has been demonstrated within a large region and over a long time period, and it is quite promising that there are many similarities between the modeling and observational results.
Open Access
An analysis of total lightning characteristics in tornadic storms: preparing for the capabilities of the GLM
(Colorado State University. Libraries, 2017) Reimel, Karly Jackson, author; Rutledge, Steven, advisor; Miller, Steven, advisor; Rasmussen, Kristen, committee member; Eykholt, Richard, committee member
Numerous studies have found that severe weather is often preceded by a rapid increase in the total lightning flash rate. This rapid increase results from numerous intra-cloud flashes forming around the periphery of an intensifying updraft. The relationship between flash rates and updraft intensity is extremely useful to forecasters in severe weather warning decision making processes, but total lightning data has not always been widely available. The Geostationary Lightning Mapper (GLM) will be the first instrument to detect lightning from geostationary orbit, where it will provide a continuous view of lightning over the entire western hemisphere. To prepare for the capabilities of this new instrument, this thesis analyzes the relationship between total lightning trends and tornadogenesis. Four supercellular and two non-supercellular tornadic storms are analyzed and compared to determine how total lightning characteristics differ between dynamically different tornadic storms. Supercellular tornadoes require a downdraft to form while landspout tornadoes form within an intensifying updraft acting on pre-existing vertical vorticity. Results of this analysis suggest that the supercellular tornadoes we studied show a decrease in flash rate and a decrease in lightning mapping array (LMA) source density heights prior to the tornado. This decrease may indicate the formation of a downdraft. In contrast, lightning flash rates increase during landspout formation in conjunction with an intensifying updraft. The total lightning trends appear to follow the evolution of an updraft rather than directly responding to tornadogenesis. To further understand how storm microphysics and dynamics impact the relationship between lightning behavior and tornadogenesis, two of the tornadic supercells were analyzed over Colorado and two were analyzed over Alabama. Colorado storms typically exhibit higher flash rates and anomalous charge structures in comparison to the environmentally different Alabama storms that are typically normal polarity and produce fewer flashes. The difference in microphysical characteristics does not appear to affect the relationship between total lightning trends and tornadogenesis. The capabilities of GLM are yet to be determined because the instrument is still in its calibration/validation stages. However, as part of the GLM cal/val team, we were in a unique position to examine the first-light GLM data and contribute to the assessment of its performance for noteworthy thunderstorm events during the Spring/Summer seasons of 2017. The final chapter of this thesis displays a preliminary analysis of GLM data. A first look into GLM performance is established by comparing GLM data with data from other lightning detecting instruments. Overall, GLM appears to detect fewer flashes than other lightning detecting networks and instruments in Colorado storms, more so for intense storms compared to weaker storms.
Open Access
Analyzing the detection efficiency of the Geostationary Lightning Mapper in isolated convection
(Colorado State University. Libraries, 2021) Clayton, Adam Wayne, author; Rutledge, Steven, advisor; Miller, Steven, advisor; Chiu, Christine, committee member; Eykholt, Richard, committee member
The Geostationary Lightning Mapper (GLM) flying on GOES-16 and GOES-17 has provided near-hemispheric lightning detection for nearly two years. Since operation began, several attempts have been made to compare flash rate observations from GLM against ground-based lightning detection systems. While GLM captures a high percentage of flashes in the field-of-view of GOES-16 and GOES-17, some studies have shown reduced detection efficiency at storm-scale. The problem of analyzing lightning from space is a complex one. Several factors such as: flash area, flash length, cloud water and ice contents, flash height, flash brightness and position relative to satellite nadir affect the detection efficiency of GLM. This study analyzes numerous convective cells in the Alabama, Colorado, and W. Texas regions to further analyze the detection efficiency of GLM. Lightning data from VHF-based lightning mapping arrays (LMAs) in each region were compared directly to measurements from GLM. The GLM/LMA ratio for each cell was computed during the lifetime of the thunderstorm. Additionally, graupel echo volumes, precipitation ice water paths, and cloud ice and cloud water paths were calculated to access the microphysics of each cell. This study features an in-depth analysis of thunderstorms that vary in size and severity from each region. Further, a statistical analysis of all of the variables was performed to determine the major factors that affect GLM detection efficiency. This study found that flash rate, flash brightness and near cloud-top water and ice water paths significantly affect GLM detection efficiency. Specifically, thunderstorms with increased flash rates, cloud-top water paths, and decreased flash size/brightness are often characterized by low (< 20%) GLM detection efficiencies. These characteristics are common in so-called "anomalous" charge structure thunderstorms that frequent the northern Colorado region. Additionally, this study confirmed results from previous studies which found that the GLM DE decreases as the distance from nadir increases. These results will be helpful for meteorologists utilizing GLM observations to assist with decisions regarding severe weather.
Open Access
Assessing the impacts of cloud condensation nuclei on cumulus congestus clouds using a cloud resolving model
(Colorado State University. Libraries, 2011) Sheffield, Amanda M., author; van den Heever, Susan C., advisor; Kreidenweis, Sonia, committee member; Eykholt, Richard, committee member
Cumulus congestus clouds are mid-level clouds that form part of the trimodal tropical cloud distribution. They act to moisten the atmosphere and may become mixed-phase in their lifetime. Congestus typically surpass the tropical trade wind inversion from where they may either develop into deeper convection, or alternatively remain as terminal congestus. Such growth is dependent on multiple factors, including those which alter the local environment and the microphysical structure of the cloud. This study investigates the impacts of cloud condensation nuclei (CCN) on cumulus congestus clouds through the use of large domain, cloud-resolving model (CRM) simulations in radiative convective equilibrium (RCE). Previous studies have focused on the convective invigoration of congestus and their subsequent growth to deep convection in association with ice processes. This study will focus on the response of congestus clouds to more polluted conditions, with particular emphasis on the development and growth of congestus from the warm phase to beyond the freezing level. It is found that convection is invigorated in the more polluted cases in association with the enhanced latent heat released during the vapor diffusional growth of cloud droplets in the warm phase. Such invigoration results in stronger updraft speeds, enhanced vertical lofting of cloud water, and a subsequent increase in the number of clouds growing to above the freezing level. The lofted cloud water is available to form more ice, however the ice water produced is smaller in magnitude compared to cloud water amounts above the freezing level. The low amounts of ice result in relatively insignificant contributions of the latent heat of freezing to the updraft strength. The impacts of enhanced CCN concentrations on various other cloud characteristics and microphysical processes are also investigated.
Open Access
Assessing the impacts of microphysical and environmental controls on simulated supercell storms
(Colorado State University. Libraries, 2018) Freeman, Sean William, author; van den Heever, Susan C., advisor; Rasmussen, Kristen L., committee member; Eykholt, Richard, committee member
Supercell thunderstorms are some of the most dangerous single-cell storms on the planet. These storms produce many hazards to life and property, including tornadoes, floods, damaging straightline winds, strong updrafts and downdrafts, and lightning. Although these hazards are not unique to supercells, some of them are often at their strongest when supercell-produced. Because of the destructive power of supercell hazards, supercells have been the subject of scientific research for decades. In this thesis, two of these hazards will be examined: supercell rainfall and supercell tornadoes, with the overarching goal to improve both our process-level understanding and forecasts of these hazards. The first part of this study focuses on supercell rainfall forecasts. Rainfall prediction by weather forecasting models, including supercell rainfall prediction, is strongly dependent on the microphysical parameterization being utilized in the model. As forecasting models have become more advanced, they are more commonly using double moment bulk microphysical parameterizations, which typically predict the hydrometeor number concentration and mass mixing ratio. While these double moment schemes are more sophisticated and require fewer a priori parameters than single moment parameterizations, a number of parameter values must still be fixed for quantities that are not prognosed or diagnosed. Two such parameters, the width of the drop size distribution and the choice of liquid collection efficiencies, are examined in Chapter 2. Simulations of a supercell were performed in which the collection efficiency dataset and the a priori width of the rain drop size distribution (DSD) were independently and simultaneously modified. Analysis of the results show that the a priori width of the DSD was a larger control on the total accumulated precipitation (a change of up to 130%) than the choice of the collection efficiency dataset used (a change of up to 10%). While the total precipitation difference when changing collision efficiency is relatively small, it does have a larger control on the warm rain process rates (including autoconversion and liquid accretion) than changing the rain DSD width does. The decrease in rainfall as the DSD width narrows is due to a combination of three main factors: (a) decreased rain production due to increased evaporation, (b) decreased rain production due to decreased ice melting, and (c) slower raindrop fall speeds which leads to longer residency times and changes in rain self-collection. The decreasing precipitation rate and accumulated precipitation with narrower DSD is consistent with observations of continental convection. This part of the study emphasizes that, in order to improve rainfall and flooding forecasts, the number of a priori parameters required by microphysical parameterizations should be reduced. Improvements in rainfall forecasts can be made immediately through the further development and implementation of triple-moment microphysical schemes, which do not require an a priori specified DSD width. The second part of this study focuses on supercell tornado forecasts. Supercell-produced tornadoes make up a majority of the most violent tornadoes and result in 90% of tornado-related deaths. Improving lead times and reducing false alarm rates is therefore critical. However, this requires an enhanced understanding of the controls that environmental conditions have on supercell tornadogenesis as well as improved observational platforms that are able to better detect environments that can produce tornadic supercells in advance. Therefore, the goals of the research presented in Chapter 3 are to (1): understand the storm processes that change as environmental conditions of supercells are perturbed and (2): determine how sensitive platforms, especially space based platforms, would need to be in order to distinguish between environments that can produce tornadic supercells from those that will produce nontornadic supercells. To address the goals, a suite of experiments were performed with a numerical model where the Convective Available Potential Energy (CAPE), Lifted Condensation Level (LCL), and low level wind shear are independently perturbed. The presented research shows that a platform with high accuracy in temperature and wind shear measurements can add value to supercell tornado forecasting. Further, several processes that influenced tornadogenesis, including cold pool strength and the role of horizontal vorticity, are found to have an impact on tornadogenesis. This part of the study emphasizes the need for new observational platforms that can more accurately observe environmental conditions in order to improve supercell tornado forecasting. Overall, the research presented here highlights supercell flooding and tornado forecast improvements that can be made with forecasting models and observational systems. Careful selection of a priori parameters, such as the width of the rain DSD, or reducing the number of those parameters required by microphysical parameterizations could improve supercell rainfall forecasts, therefore improving flooding forecasts. Supercell tornado forecasts can be improved by the addition of accurate space-based observational platforms which can help to distinguish between tornadic and nontornadic environmental conditions.
Open Access
Characteristics of linear mesoscale convective systems during DYNAMO
(Colorado State University. Libraries, 2019) Messina, Joseph, author; Rutledge, Steven, advisor; Xu, Weixin, committee member; Rasmussen, Kristen, committee member; Eykholt, Richard, committee member
Mesoscale convective systems (MCSs) have long been known to play a large part in the vertical transport of horizontal momentum. They also contribute to the vertical redistribution of heat and radiative forcing. The Madden Julian Oscillation (MJO) is a tropical disturbance that propagates across the central Indian Ocean and western Pacific Ocean with an intraseasonal cycle of 30-60 days. Many studies have explored the kinematic characteristics and organization of MCSs in the tropics, while others investigated the characteristics of convective systems within the MJO. However, there remains a gap in current literature on the connection between MJO phase and kinematics of precipitating tropical convection. Those studies that did examine MCSs in the tropical environment did so with limited observations. This study used radar, sounding, and meteorological data from the Dynamics of the Madden Julian Oscillation (DYNAMO) field campaign in the central Indian Ocean to examine the influence of vertical shear on the orientation of linear MCSs, effects of cold pools on propagation of linear systems, and the mesoscale flow features of the MCSs over the phases of the MJO. DYNAMO took place from October-December 2011 and produced a vast dataset for the analysis of tropical convection during multiple MJO events. Our results show that convection during DYNAMO was consistent with studies from previous tropical field campaigns. That is, convective lines are frequently oriented perpendicular to strong low-level shear. In the absence of strong low-level shear, they are oriented parallel to strong mid-level shear. Linear systems were more prevalent during active MJO phases. Cold pools did not play a substantial role in tropical squall line propagation. Kinematic features are also consistent with previous works. The presence of a jump updraft and descending rear inflow were ubiquitous in our samples. The absence of a downdraft outflow was common. This result shows that the MCSs studied were transporting front to rear horizontal momentum from low- to mid-levels and rear to front horizontal momentum from low- to mid-levels.
Open Access
Computational modeling of low-density ultracold plasmas
(Colorado State University. Libraries, 2017) Witte, Craig, author; Roberts, Jacob L., advisor; Eykholt, Richard, committee member; Kruger, David, committee member; Sambur, Justin, committee member
In this dissertation I describe a number of different computational investigations which I have undertaken during my time at Colorado State University. Perhaps the most significant of my accomplishments was the development of a general molecular dynamic model that simulates a wide variety of physical phenomena in ultracold plasmas (UCPs). This model formed the basis of most of the numerical investigations discussed in this thesis. The model utilized the massively parallel architecture of GPUs to achieve significant computing speed increases (up to 2 orders of magnitude) above traditional single core computing. This increased computing power allowed for each particle in an actual UCP experimental system to be explicitly modeled in simulations. By using this model, I was able to undertake a number of theoretical investigations into ultracold plasma systems. Chief among these was our lab's investigation of electron center-of-mass damping, in which the molecular dynamics model was an essential tool in interpreting the results of the experiment. Originally, it was assumed that this damping would solely be a function of electron-ion collisions. However, the model was able to identify an additional collisionless damping mechanism that was determined to be significant in the first iteration of our experiment. To mitigate this collisionless damping, the model was used to find a new parameter range where this mechanism was negligible. In this new parameter range, the model was an integral part in verifying the achievement of a record low measured UCP electron temperature of 1.57 ± 0.28K and a record high electron strong coupling parameter, Γ, of 0.35 ± 0.08. Additionally, the model, along with experimental measurements, was used to verify the breakdown of the standard weak coupling approximation for Coulomb collisions. The general molecular dynamics model was also used in other contexts. These included the modeling of both the formation process of ultracold plasmas and the thermalization of the electron component of an ultracold plasma. Our modeling of UCP formation is still in its infancy, and there is still much outstanding work. However, we have already discovered a previously unreported electron heating mechanism that arises from an external electric field being applied during UCP formation. Thermalization modeling showed that the ion density distribution plays a role in the thermalization of electrons in ultracold plasma, a consideration not typically included in plasma modeling. A Gaussian ion density distribution was shown to lead to a slightly faster electron thermalization rate than an equivalent uniform ion density distribution as a result of collisionless effects. Three distinct phases of UCP electron thermalization during formation were identified. Finally, the dissertation will describe additional computational investigations that preceded the general molecular dynamics model. These include simulations of ultracold plasma ion expansion driven by non-neutrality, as well as an investigation into electron evaporation. To test the effects of non-neutrality on ion expansion, a numerical model was developed that used the King model of the electron to describe the electron distribution for an arbitrary charge imbalance. The model found that increased non-neutrality of the plasma led to the rapid expansion of ions on the plasma exterior, which in turn led to a sharp ion cliff-like spatial structure. Additionally, this rapid expansion led to additional cooling of the electron component of the plasma. The evaporation modeling was used to test the underlying assumptions of previously developed analytical expression for charged particle evaporation. The model used Monte Carlo techniques to simulate the collisions and the evaporation process. The model found that neither of the underlying assumption of the charged particle evaporation expressions held true for typical ultracold plasma parameters and provides a route for computations in spite of the breakdown of these two typical assumptions.
Open Access
Conjugacy classes of matrix groups over local rings and an application to the enumeration of abelian varieties
(Colorado State University. Libraries, 2012) Williams, Cassandra L., author; Achter, Jeffrey, advisor; Eykholt, Richard, committee member; Hulpke, Alexander, committee member; Penttila, Tim, committee member
The Frobenius endomorphism of an abelian variety over a finite field Fq of dimension g can be considered as an element of the finite matrix group GSp2g(Z/lr). The characteristic polynomial of such a matrix defines a union of conjugacy classes in the group, as well as a totally imaginary number field K of degree 2g over Q. Suppose g = 1 or 2. We compute the proportion of matrices with a fixed characteristic polynomial by first computing the sizes of conjugacy classes in GL2(Z/lr) and GSp4(Z/lr. Then we use an equidistribution assumption to show that this proportion is related to the number of abelian varieties over a finite field with complex multiplication by the maximal order of K via a theorem of Everett Howe.
Open Access
Continued exploration of nearly continuous Kakutani equivalence
(Colorado State University. Libraries, 2013) Springer, Bethany Diane, author; Shipman, Patrick, advisor; del Junco, Andres, advisor; Eykholt, Richard, committee member; Dangelmayr, Gerhard, committee member; Pries, Rachel, committee member
Nearly continuous dynamical systems, a relatively new field of study, blends together topological dynamics and measurable dynamics/ergodic theory by asking that properties hold modulo sets both meager and of measure zero. In the measure theoretic category, two dynamical systems (X, T) and (Y, S) are called Kakutani equivalent if there exists measurable subsets A subset of X and B subset of Y such that the induced transformations TA and SB are measurably conjugate. We say that a set A subset of X is nearly clopen if it is clopen in the relative topologyof a dense Gδ subset of full measure. Nearly continuous Kakutani equivalence refines the measure-theoretic notion by requiring the sets A and B to be nearly clopen and TA and SB to be nearly continuously conjugate. If A and B have the same measure, then we say that the systems are nearly continuously evenly Kakutani equivalent. All irrational rotations of the circle and all odometers belong to the same equivalence class for nearly continuous even Kakutani equivalence. For our first main result, we prove that if A and B are nearly clopen subsets of the same measure of X and Y respectively, and if ϕ is a nearly continuous conjugacy between TA and SB, then ϕ extends to a nearly continuous orbit equivalence between T and S. We also prove that if A subset of X and B subset of Y are nearly clopen sets such that the measure of A is larger than the measure of B, and if T is a nearly uniquely ergodic transformation and TA is nearly continuously conjugate to SB, then there exists B' subset of Y such that X is nearly continuously conjugate to SB'. We then introduce the natural topological analog of rank one transformations, called strongly rank one transformations, and show that all strongly rank one transformations are nearly continuously evenly Kakutani equivalent to the class containing all adding machines. Our main result proves that all minimal isometries of compact metric spaces are nearly continuously evenly Kakutani equivalent to the binary odometer.
Open Access
Covariance integral invariants of embedded Riemannian manifolds for manifold learning
(Colorado State University. Libraries, 2018) Álvarez Vizoso, Javier, author; Peterson, Christopher, advisor; Kirby, Michael, advisor; Bates, Dan, committee member; Cavalieri, Renzo, committee member; Eykholt, Richard, committee member
This thesis develops an effective theoretical foundation for the integral invariant approach to study submanifold geometry via the statistics of the underlying point-set, i.e., Manifold Learning from covariance analysis. We perform Principal Component Analysis over a domain determined by the intersection of an embedded Riemannian manifold with spheres or cylinders of varying scale in ambient space, in order to generalize to arbitrary dimension the relationship between curvature and the eigenvalue decomposition of covariance matrices. In the case of regular curves in general dimension, the covariance eigenvectors converge to the Frenet-Serret frame and the corresponding eigenvalues have ratios that asymptotically determine the generalized curvatures completely, up to a constant that we determine by proving a recursion relation for a certain sequence of Hankel determinants. For hypersurfaces, the eigenvalue decomposition has series expansion given in terms of the dimension and the principal curvatures, where the eigenvectors converge to the Darboux frame of principal and normal directions. In the most general case of embedded Riemannian manifolds, the eigenvalues and limit eigenvectors of the covariance matrices are found to have asymptotic behavior given in terms of the curvature information encoded by the third fundamental form of the manifold, a classical tensor that we generalize to arbitrary dimension, and which is related to the Weingarten map and Ricci operator. These results provide descriptors at scale for the principal curvatures and, in turn, for the second fundamental form and the Riemann curvature tensor of a submanifold, which can serve to perform multi-scale Geometry Processing and Manifold Learning, making use of the advantages of the integral invariant viewpoint when only a discrete sample of points is available.
Open Access
Evaluating the impact of deep-water channel architecture on the probability of correct facies classification using 3D synthetic seismic data
(Colorado State University. Libraries, 2021) Langenkamp, Teresa Rose, author; Stright, Lisa, advisor; Harry, Dennis, committee member; Eykholt, Richard, committee member
Modeling studies of bed-to geobody-scale architecture in deep-water channel deposits reveal that channel element stacking patterns and internal architecture strongly control connectivity. This architecture is critical to understanding hydrocarbon flow and recovery but is unresolvable in exploration-scale seismic-reflection profiles. Forward seismic reflectivity modeling of a digital outcrop models is commonly used to explore how depositional architecture is interpretable in a filtered seismic response. One limitation of forward seismic reflectivity modeling studies is that they often stop short of qualitatively assessing the link between underlying depositional architecture and seismic response. This study addresses the gap between qualitative interpretation and quantitative evaluation by calculating the prediction reliability of inverted seismic data. Specifically, this study uses synthetic 3D seismic modeling and inversion of a 3D outcrop model of deepwater channels in the Tres Pasos Formation of the Magallanes Basin of southern Chile. The model includes outcrop- (bed and geobody) to seismic- (reservoir to basin) scale architecture. The primary objective is to quantify where and when channel architecture is accurately predicted by seismic facies classification. Bayesian classification is used to test the probability of correct facies classification from P-impedance and if the classification results are dependent upon architectural styles (e.g., channel element stacking patterns). Model sensitivity variables include seismic frequency (ranging from 15 to 180 Hz) and deep versus shallow rock properties. Results show that prediction reliability increased for both channel element axis sandstone and mass transport deposits with increasing frequency. Deep reservoirs or faster seismic velocities more accurately predict facies than shallow reservoirs or slower seismic velocities due to the increasing contrast between sandstone and shale velocities. Channel axis sandstone is less easily interpreted where channel elements are vertically aggraded, reducing acoustic impedance contrasts with background shale. When channel elements are laterally stacked or disorganized, facies can be predicted from seismic attributes with a higher confidence, due to a strong contrast between channel element sandstone and background shale. This study highlights that architectural information strongly impacts 3D inverted seismic data and highlights conditions that either hinder or aid accurate interpretation from facies classification.
Open Access
Examining the impacts of convective environments on storms using observations and numerical models
(Colorado State University. Libraries, 2022) Freeman, Sean William, author; van den Heever, Susan C., advisor; Bell, Michael M., committee member; Kreidenweis, Sonia M., committee member; Eykholt, Richard, committee member
Convective clouds are significant contributors to both weather and climate. While the basic environments supporting convective clouds are broadly known, there is currently no unifying theory on how joint variations in different environmental properties impact convective cloud properties. The overaching goal of this research is to assess the response of convective clouds to changes in the dynamic, thermodynamic and aerosol properties of the local environment. To achieve our goal, two tools for examining convective cloud properties and their environments are first described, developed and enhanced. This is followed by an examination of the response of convective clouds to changes in the dynamic, thermodynamic and aerosol properties using these enhanced tools. In the first study comprising this dissertation, we assess the performance of small temperature, pressure, and humidity sensors onboard drones used to sample convective environments and convective cloud outflows by comparing them to measurements made from a tethersonde platform suspended at the same height. Using 82 total drone flights, including nine at night, the following determinations about sensor accuracy are made. First, when examining temperature, the nighttime flight temperature errors are found to have a smaller range than the daytime temperature errors, indicating that much of the daytime error arises from exposure to solar radiation. The pressure errors demonstrate a strong dependence on horizontal wind speed with all of the error distributions being multimodal in high wind conditions. Finally, dewpoint temperature errors are found to be larger than temperature errors. We conclude that measurements in field campaigns are more accurate when sensors are placed away from the drone's main body and associated propeller wash and are sufficiently aspirated and shielded from incoming solar radiation. The Tracking and Object-Based Analysis of Clouds (tobac) tracking package is a commonly used tracking package in atmospheric science that allows for tracking of atmospheric phenomena on any variable and on any grid. We have enhanced the tobac tracking package to enable it to be used on more atmospheric phenomena, with a wider variety of atmospheric data and across more diverse platforms than before. New scientific improvements (three spatial dimensions and an internal spectral filtering tool) and procedural improvements (enhanced computational efficiency, internal re-gridding of data, and treatments for periodic boundary conditions) comprising this new version of tobac (v1.5) are described in the second study of this dissertation. These improvements have made tobac one of the most robust, powerful, and flexible identification and tracking tools in our field and expanded its potential use in other fields. In the third study of this dissertation, we examine the relationship between the thermodynamic and dynamic environmental properties and deep convective clouds forming in the tropical atmosphere. To elucidate this relationship, we employ a high-resolution, long-duration, large-area numerical model simulation alongside tobac to build a database of convective clouds and their environments. With this database, we examine differences in the initial environment associated with individual storm strength, organization, and morphology. We find that storm strength, defined here as maximum midlevel updraft velocity, is controlled primarily by Convective Available Potential Energy (CAPE) and Precipitable Water (PW); high CAPE (>2500 J kg-1) and high PW (approximately 63 mm) are both required for midlevel CCC updraft velocities to reach at least 10 m s-1. Of the CCCs with the most vigorous updrafts, 80.9% are in the upper tercile of precipitation rates, with the strongest precipitation rates requiring even higher PW. Furthermore, vertical wind shear is the primary differentiator between organized and isolated convective storms. Within the set of organized storms, we also find that linearly-oriented CCC systems have significantly weaker vertical wind shear than nonlinear CCCs in low- (0-1 km, 0-3 km) and mid-levels (0-5 km, 2-7 km). Overall, these results provide new insights into the joint environmental conditions determining the CCC properties in the tropical atmosphere. Finally, in the fourth study of this dissertation, we build upon the third study by examining the relationship between the aerosol environment and convective precipitation using the same simulations and tracking approaches as in the third study. As the environmental aerosol concentrations are increased, the total domain-wide precipitation decreases (-3.4%). Despite the overall decrease in precipitation, the number of tracked terminal congestus clouds increases (+8%), while the number of tracked cumulonimbus clouds is decreased (-1.26%). This increase in the number of congestus clouds is accompanied by an overall weakening in their rainfall as aerosol concentration increases, with a decrease in overall rain rates and an increase in the number of clouds that do not precipitate (+10.7%). As aerosol particles increase, overall cloud droplet size gets smaller, suppressing the initial generation of rain and leading to clouds evaporating due to entrainment before they are able to precipitate.
Open Access
Exploring post-cold frontal moisture transport in an idealized extratropical cyclone study
(Colorado State University. Libraries, 2016) Sheffield, Amanda Marie, author; van den Heever, Susan C., advisor; Eykholt, Richard, committee member; Johnson, Richard, committee member; Kreidenweis, Sonia, committee member
Moisture transport in extratropical cyclones (ETCs) has been studied in the past in the context of the warm conveyor belt (WCB), a 'conveyor belt' transferring moisture from the warm sector boundary layer to the free troposphere both eastward and poleward of the warm front. Recent research has highlighted a different, potentially important mechanism of transporting water vapor in ETCs by post-cold frontal (PCF) clouds. PCF clouds are typically boundary layer cumulus clouds located in the cold sector of an ETC that transfer moisture to the free troposphere through convective-evaporative processes. Recent studies have suggested that these PCF cumuli may vertically transport nearly equivalent amounts of moisture as the WCB. Therefore, not only are these PCF cumuli important in venting the PCF boundary layer, they also play a role in limiting the amount of moisture available for convergence in the source region of the WCB. This limitation can have important consequences for regional weather and climate through its impact on the timing and location of precipitation, the three-dimensional redistribution of water vapor, and the distribution of clouds within ETCs. The goal of this study is to investigate the role of PCF clouds in the moisture transport of an ETC, and the impacts of environmental factors such as SST and aerosol loading on this transport role. We have achieved this goal through the use of numerical simulations of such a storm system. Previous studies have utilized model simulations with relatively coarse grid resolutions and convective parameterization schemes. Here, we simulate a wintertime ETC over the Pacific Ocean using high spatial and temporal resolution, advanced microphysics and explicitly resolved convection. The results of this research demonstrate that PCF cumuli are found to vertically ventilate BL moisture over an expansive region behind the cold front. The free tropospheric moisture contents and stability profile of the cold sector exert a strong control over the size, depth and frequency of the PCF clouds, and varies with distance from the cold front. Increased aerosol loading results in the invigoration of the PCF clouds. This is associated with an increase in the upward vertical moisture flux, increased cloud condensate formation, and reduced precipitation rates. Sea surface temperature is found to be a significantly more important factor in the development of PCF cumuli than aerosol loading, where increasing SSTs are associated with increased cloud fraction, cloud top heights, and precipitation rates. The impact of PCF clouds on vertically redistributing water vapor from the cold sector is found to depend in varying degrees on the large-scale advection of water vapor by the ETC system, the surface evaporation rates, the updraft velocities, the precipitation rates, and the cloud fraction within the PCF region. The pathways of the vertically redistributed water vapor within the ETC were then examined through the use of massless, passive tracers. The results of these experiments show that the water vapor lofted out of the PCF BL by the cumulus clouds is advected hundreds of kilometers eastward within 8-12 hours of release of tracers in the PCF BL. Furthermore, cross frontal transport from behind the cold front to the WCB source region appears to be small, in contradiction to previously hypothesized results. This is due to the fact that the cold frontal boundary provides a zone of strong vertical lifting that does not allow tracers to converge further east.
Open Access
Factors affecting lightning behavior in various regions of the United States
(Colorado State University. Libraries, 2014) Fuchs, Brody Robert, author; Rutledge, Steven, advisor; Lang, Timothy, committee member; van den Heever, Susan, committee member; Eykholt, Richard, committee member
Lightning activity varies greatly on a global scale. Global maps of total flash density show a strong tendency for lightning to favor continental areas over the open ocean, even in regions with similar instability. Previous studies have attributed the difference to thermodynamic and aerosol differences over continental regions, but the exact cause is still elusive. While this is not a global study, we attempt to characterize lightning activity in 4 different regions of the United States with high resolution Lightning Mapping Array (LMA) networks over one warm season. The regions of study are Washington, D.C. (DC), northern Alabama, central Oklahoma and northeast Colorado. A wide spectrum of environmental characteristics is afforded by these regions. Lightning characteristics include storm total flash rates, positive cloud-to-ground (+CG) strikes and intra-cloud (IC) to CG ratio (IC:CG). This is accomplished by using the CSU Lightning, Environmental, Aerosol and Radar (CLEAR) framework, first developed by Lang and Rutledge (2011), to objectively analyze large amounts of storm data. Lightning activity is provided by a new flash clustering algorithm, which produces total flash rates and IC flash rates when combined with NLDN CG data. The results have shown that lightning behavior has high variability throughout the regions of study. Median total storm flash rates range from approximately 1 flash/min in Alabama and DC to near 8 flashes/min in Colorado. Positive CG flash fractions exhibit a similar relationship with 10% of all CG flashes being positive polarity in Alabama and DC up to 40% in Colorado. The anomalous nature of the Colorado region is evident in all lightning metrics. Colorado is also characterized by an anomalous environment with high cloud base storms and coincident shallow warm cloud depths. Examination of all storms simultaneously has shown that relationships exist between total flash rate and environmental parameters. The similarity of these results to other studies on global scales is striking and provides evidence for the robustness of these relationships. Examination of relationships between radar and lightning intensity metrics are also performed. Similar behaviors between these intensity metrics are observed in all regions.
Open Access
Impacts of Arctic warming and sea ice loss on the Northern Hemisphere mid-latitude large-scale circulation
(Colorado State University. Libraries, 2020) Ronalds, Bryn, author; Barnes, Elizabeth A., advisor; Thompson, David, committee member; Randall, David A., committee member; Eykholt, Richard, committee member
The consequences of the rapid warming of the Arctic and associated sea ice loss on the Northern Hemisphere atmospheric circulation is still largely debated. The uncertainty in the circulation response stems from a poor understanding of the underlying physical mechanisms of the remote response, regional and seasonal differences, differences between models and experimental set-ups, the large internal variability of the system, and the short observational record. This research seeks to address some of this uncertainty, specifically the uncertainty related to the physical mechanisms, regionality, and modeling differences. The wintertime Northern Hemisphere eddy-driven jet streams over the North Pacific and North Atlantic basins exhibit differing responses to Arctic warming and sea ice loss in a fully coupled climate model. In the North Atlantic the jet weakens, narrows along the poleward flank, and shifts slightly equatorward. This response is similar to previous studies examining the Northern Hemisphere zonal mean jet response. In contrast, the North Pacific jet strengthens and extends eastward in response to Arctic sea ice loss, with no change in latitude, and narrows slightly along the poleward flank. In both cases, there are high latitude anomalous easterlies in the region of sea ice loss, where the local surface temperature gradients are weakening. This can lead to changes in locations and frequency of wave-breaking, thus leading to changes in the mean zonal winds further south, in the vicinity of the jet. This work relates the differing changes in the North Pacific and North Atlantic to these changes in wave-breaking in a simplified atmospheric model, and posits that the location of the jet relative to the region of Arctic sea ice loss is a dominant factor in determining the mean jet response to the sea ice loss and local warming. Changes in the mean wintertime Northern Hemisphere midlatitude zonal winds are found to be indicative of changes to the sub-seasonal variability of the wintertime zonal winds. The sub-seasonal circulation patterns over the ocean basins are closely linked with continental weather regimes, including changes in temperature and precipitation. While establishing a causal link between Arctic sea ice loss and changes to remote weather regimes in the observational record remains difficult, the Polar Amplification Model Intercomparison Project (PAMIP) provides insight into possible relationships and consequences. The design of the project eliminates differences in experimental set-ups across models and aids in addressing the uncertainty in regional responses. Across four climate models, Arctic sea ice loss leads to a strengthened and extended North Pacific jet in the January-February mean. This mean change is also associated with changes to the sub-seasonal, wintertime North Pacific zonal wind variability. All four models show an increase in strengthened and extended North Pacific eddy-driven jet stream events and a decrease in weakened, retracted and equatorward-shifted North Pacific jet events in January-February. Previous work has also established the relationships between North Pacific jet stream variability and downstream, North American weather regimes, and changes to the former are expected to impact the latter. Again, there is model agreement in an increase of a warm west/cold east temperature dipole over North America, associated with the strengthened and extended jet events. There is also a decrease in cold air temperature anomalies over North America, associated with weakened and equatorward-shifted jet events.
Open Access
Latent heating and aerosol-precipitation interactions within mesoscale convective systems
(Colorado State University. Libraries, 2016) Marinescu, Peter James, author; van den Heever, Susan C., advisor; Kreidenweis, Sonia M., advisor; Eykholt, Richard, committee member; Schumacher, Russ S., committee member
Two studies are presented in this thesis that focus on understanding cloud processes within simulations of two mesoscale convective system (MCS) events that occurred during the Midlatitude Continental Convective Clouds Experiment (MC3E). Simulations are conducted with the Regional Atmospheric Modeling System (RAMS) and are compared with a suite of observations obtained during MC3E. It is concluded that the simulations reasonably reproduce the two MCS events of interest. Both studies provide information that can assist in the advancement of cloud process parameterizations in atmospheric models. The first study details the microphysical process contributions to latent heating profiles within MCS convective and stratiform regions and the evolution of these profiles throughout the MCS lifetime. Properly representing the distinctions between the latent heating profiles of MCS convective and stratiform regions has significant implications for the atmospheric responses to latent heating on various scales. The simulations show that throughout the MCSs, condensation and deposition are the primary contributors to latent warming, as compared to riming and nucleation processes. In terms of latent cooling, sublimation, melting, and evaporation all play significant roles. Furthermore, it is evident that throughout the MCS lifecycle, convective regions demonstrate an approximately linear decrease in the magnitudes of latent heating rates, while the evolution of latent heating within stratiform regions is associated with transitions between MCS flow regimes. The second study addresses the relative roles of middle-tropospheric and lower-tropospheric aerosol particles on MCS precipitation during the mature stage. A suite of sensitivity simulations for each MCS event is conducted, where the simulations are initialized with different aerosol profiles that vary in the vertical location of the peak aerosol particle number concentrations. Importantly, the total integrated aerosol mass remains constant between the different initialization aerosol profiles, and therefore, differences between the simulated MCS precipitation characteristics can be more directly attributed to the varied vertical location of the aerosol particles. The simulations from both MCS events demonstrate that during the mature stage, the concentrations of lower-tropospheric aerosol particles are the primary factor in determining the intensity of precipitation near the cold pool leading edge, while middle-tropospheric aerosol particles were entrained within convective updrafts, thus altering the cloud droplet properties. However, the aerosol effects on total surface precipitation is not consistent between the two simulated MCS events, suggesting that the MCS structure and environmental conditions play important roles in regulating the impacts of middle-tropospheric and lower-tropospheric aerosol particles on MCS precipitation. Lastly, changes in precipitation processes can result in dynamical feedbacks that further modify, and hence complicate, the net effect of aerosol particles on MCS precipitation. One such feedback process involving the MCS cold pool intensity and updraft tilt is discussed.
Open Access
Latent heating and mixing due to entrainment in tropical deep convection
(Colorado State University. Libraries, 2013) McGee, Clayton J., author; van den Heever, Susan, advisor; Maloney, Eric, committee member; Eykholt, Richard, committee member
Recent studies have noted the role of latent heating above the freezing level in reconciling Riehl and Malkus' Hot Tower Hypothesis (HTH) with evidence of diluted tropical deep convective cores. This study evaluates recent modifications to the HTH through Lagrangian trajectory analysis of deep convective cores in an idealized, high-resolution cloud-resolving model (CRM) simulation. A line of tropical convective cells develops within a high-resolution nested grid whose boundary conditions are obtained from a large-domain CRM simulation approaching radiative-convective equilibrium (RCE). Microphysical impacts on latent heating and equivalent potential temperature are analyzed along trajectories ascending within convective regions of the high-resolution nested grid. Changes in equivalent potential temperature along backward trajectories are partitioned into contributions from latent heating due to ice processes and a residual term. This residual term is composed of radiation and mixing. Due to the small magnitude of radiative heating rates in the convective inflow regions and updrafts examined here, the residual term is treated as an approximate representation of mixing within these regions. The simulations demonstrate that mixing with dry air decreases equivalent potential temperature along ascending trajectories below the freezing level, while latent heating due to freezing and vapor deposition increase equivalent potential temperature above the freezing level. The latent heating contributions along trajectories from cloud nucleation, condensation, evaporation, freezing, deposition, and sublimation are also quantified. Finally, the source regions of trajectories reaching the upper troposphere are identified; it is found that two-thirds of backward trajectories with starting points within strong updrafts or downdrafts above 10 km have their origin at levels higher than 2 km AGL. The importance of both boundary layer and mid-level inflow in moist environments is underscored in this study.
Open Access
Linear models, signal detection, and the Grassmann manifold
(Colorado State University. Libraries, 2014) Schwickerath, Anthony Norbert, author; Kirby, Michael, advisor; Peterson, Chris, advisor; Scharf, Louis, committee member; Eykholt, Richard, committee member
Standard approaches to linear signal detection, reconstruction, and model identification problems, such as matched subspace detectors (MF, MDD, MSD, and ACE) and anomaly detectors (RX) are derived in the ambient measurement space using statistical methods (GLRT, regression). While the motivating arguments are statistical in nature, geometric interpretations of the test statistics are sometimes developed after the fact. Given a standard linear model, many of these statistics are invariant under orthogonal transformations, have a constant false alarm rate (CFAR), and some are uniformly most powerful invariant (UMPI). These properties combined with the simplicity of the tests have led to their widespread use. In this dissertation, we present a framework for applying real-valued functions on the Grassmann manifold in the context of these same signal processing problems. Specifically, we consider linear subspace models which, given assumptions on the broadband noise, correspond to Schubert varieties on the Grassmann manifold. Beginning with increasing (decreasing) or Schur-convex (-concave) functions of principal angles between pairs of points, of which the geodesic and chordal distances (or probability distribution functions) are examples, we derive the associated point-to-Schubert variety functions and present signal detection and reconstruction algorithms based upon this framework. As a demonstration of the framework in action, we implement an end-to-end system utilizing our framework and algorithms. We present results of this system processing real hyperspectral images.