A gauge model for quantum mechanics on a stratified space

In the Hamiltonian approach on a single spatial plaquette, we construct a quantum (lattice) gauge theory which incorporates the classical singularities. The reduced phase space is a stratified K\"ahler space, and we make explicit the requisite singular holomorphic quantization procedure on this space. On the quantum level, this procedure furnishes a costratified Hilbert space, that is, a Hilbert space together with a system which consists of the subspaces associated with the strata of the reduced phase space and of the corresponding orthoprojectors. The costratified Hilbert space structure reflects the stratification of the reduced phase space. For the special case where the structure group is $\mathrm{SU}(2)$, we discuss the tunneling probabilities between the strata, determine the energy eigenstates and study the corresponding expectation values of the orthoprojectors onto the subspaces associated with the strata in the strong and weak coupling approximations.Comment: 38 pages, 9 figures. Changes: comments on the heat kernel and coherent states have been adde

Upper gila, salt, and verde rivers: Arid land rivers in a changing climate

The major tributary of the Lower Colorado River, the Gila River, is a critical source of water for human and natural environments in the Southwestern US. Warmer and drier than the Upper Colorado River basin (UCRB), with less snow, and a bi-modal precipitation regime, the Gila River is controlled by a set of climatic conditions that is different from the controls on Upper Colorado River flow. Unlike the Colorado River at Lees Ferry, the Upper Gila River and major Gila River tributaries, the Salt and Verde Rivers, do not yet reflect significant declines in annual streamflow, in spite of warming trends. Annual streamflow is dominated by cool season precipitation, but the monsoon influence is discernable as well, variable across the basin and complicated by an inverse relationship with cool season precipitation in the Salt and Verde River basins. Major multi-year streamflow droughts in these two basins have frequently been accompanied by wet monsoons, suggesting that monsoon precipitation may partially offset the impacts of a dry cool season. While statistically significant trends in annual streamflow are not evident, decreases in fall and spring streamflow reflect warming temperatures and some decreases in spring precipitation. Because climatic controls vary with topography and the influence of the monsoon, the impacts of warming on streamflow in the three sub-basins is somewhat variable. However, given relationships between climate and streamflow, current trends in hydroclimate, and projections for the future, it would be prudent to expect declines in Gila River water supplies in the coming decades.6 month embargo; published online: 16 November 2021This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

A Long View of Southern California Water Supply: Perfect Droughts Revisited

The impact of drought on water resources in arid and semiarid regions can be buffered by water supplies from different source regions. Simultaneous drought in all major source regions - or perfect drought - poses the most serious challenge to water management. We examine perfect droughts relevant to Southern California (SoCal) water resources with instrumental records and tree-ring reconstructions for the Sacramento and Colorado Rivers, and SoCal. Perfect droughts have occurred five times since 1906, lasting two to three years, except for the most recent event, 2012-2015. This number and duration of perfect droughts is not unusual in the context of the past six centuries. The modern period stands out for the relatively even distribution of perfect droughts and lacks the clusters of perfect drought documented in prior centuries. In comparison, perfect droughts of the 12th Century were both longer (up to nine years) and more widespread. Perfect droughts of the 20th and 21st Centuries have occurred under different oceanic/atmospheric patterns, zonal and meridional flow, and ENSO or non-ENSO conditions. Multidecadal coherence across the three regions exists, but it has varied over the past six centuries, resulting in irregular intervals of perfect drought. Although the causes of perfect droughts are not clear, given the long-term natural variability along with projected changes in climate, it is reasonable to expect more frequent and longer perfect droughts in the future.California Department of Water Resources [4600011071]; U.S. Department of Energy, Office of Science Innovative and Novel Computational Impact on Theory and Experiment (DOE INCITE) ProgramUnited States Department of Energy (DOE); U.S. Department of Energy, Office of Biological and Environmental Research (BER)United States Department of Energy (DOE); National Oceanic and Atmospheric Administration Climate Program OfficeNational Oceanic Atmospheric Admin (NOAA) - USA12 month embargo; published online: 8 January 2020This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Five Hundred Years of Hydrological Drought in the Upper Colorado River Basin

This article evaluates drought scenarios of the Upper Colorado River basin (UCRB) considering multiple drought variables for the past 500 years and positions the current drought in terms of the magnitude and frequency. Drought characteristics were developed considering water-year data of UCRB’s streamflow, and basin-wide averages of the Palmer Hydrological Drought Index (PHDI) and the Palmer Z Index. Streamflow and drought indices were reconstructed for the last 500 years using a principal component regression model based on tree-ring data. The reconstructed streamflow showed higher variability as compared with reconstructed PHDI and reconstructed Palmer Z Index. The magnitude and severity of all droughts were obtained for the last 500 years for historical and reconstructed drought variables and ranked accordingly. The frequency of the current drought was obtained by considering two different drought frequency statistical approaches and three different methods of determining the beginning and end of the drought period (annual, 5-year moving, and ten year moving average). It was concluded that the current drought is the worst in the observed record period (1923-2004), but 6th to 14th largest in terms of magnitude and 1st to 12th considering severity in the past 500 years. Similarly, the current drought has a return period ranging from 37 to 103 years based on how the drought period was determined. It was concluded that if the 10-year moving average is used for defining the drought period, the current drought appears less severe in terms of magnitude and severity in the last 500 years compared with the results using 1- and 5-year averages.National Science Foundation/[CMS-0239334]/NSF/Estados UnidosUCR::Vicerrectoría de Investigación::Unidades de Investigación::Ciencias Básicas::Centro de Investigaciones Geofísicas (CIGEFI

Tree Rings Reveal Unmatched 2nd Century Drought in the Colorado River Basin

The ongoing 22-year drought in the Upper Colorado River Basin (UCRB) has been extremely severe, even in the context of the longest available tree-ring reconstruction of annual flow at Lees Ferry, Arizona, dating back to 762 CE. While many southwestern drought assessments have been limited to the past 1,200 years, longer paleorecords of moisture variability do exist for the UCRB. Here, gridded drought-atlas data in the UCRB domain along with naturalized streamflow data from the instrumental period (1906–2021) are used in a K-nearest neighbor nonparametric algorithm to develop a streamflow reconstruction for the Lees Ferry gage starting in 1 CE. The reconstruction reveals a second-century drought unmatched in severity by the current drought or by well-documented medieval period droughts in the UCRB. Although data are sparse, analysis of individual long tree-ring records and other paleoclimatic data also support the occurrence of an exceptional second-century drought. © 2022. American Geophysical Union. All Rights Reserved.6 month embargo; first published: 09 June 2022This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Upper Colorado River Basin 20th century droughts under 21st century warming: Plausible scenarios for the future

This study builds on a collaboration with a water resource management community of practice in the Upper Colorado River Basin to develop scenarios of future drought and assess impacts on water supply reliability. Water managers are concerned with the impacts of warming on water year streamflow, but uncertainties in projections of climate make the application of these projections to planning a challenge. Instead, water managers considered a plausible scenario for future drought to be historical droughts to which warming is added. We used a simple statistical model of water year streamflow with temperatures increased by 1 °C to 4 °C, and then examined reductions in flow and runoff efficiency (RE) with each degree of warming for the six droughts defined in the observed streamflow record. In order to place these results into a management context, we employed an existing framework for system reliability, and in particular, a vulnerability assessment for water delivery metrics. Using modeled streamflow resulting from 1 °C to 4 °C warming, we found vulnerable condition thresholds for the two water delivery metrics assessed, Upper Basin Shortage and Lees Ferry Deficit, were crossed relatively infrequently at +1 °C, but with a substantially increased frequency under additional warming. Results are more relevant to resource management because the impacts of warming on Upper Colorado River streamflow were assessed in the context of management metrics and vulnerability thresholds, in collaboration with members of the water management community of practice. © 2020 The Author(s)Open access journalThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at [email protected]

Two choices good, four choices better: For measuring stereoacuity in children, a four-alternative forced-choice paradigm is more efficient than two

PURPOSE:Measuring accurate thresholds in children can be challenging. A typical psychophysical experiment is usually too long to keep children engaged. However, a reduction in the number of trials decreases the precision of the threshold estimate. We evaluated the efficiency of forced-choice paradigms with 2 or 4 alternatives (2-AFC, 4-AFC) in a disparity detection experiment. 4-AFC paradigms are statistically more efficient, but also more cognitively demanding, which might offset their theoretical advantage in young children. METHODS:We ran simulations evaluating bias and precision of threshold estimates of 2-AFC and 4-AFC paradigms. In addition, we measured disparity thresholds in 43 children (aged 6 to 17 years) with a 4-AFC paradigm and in 49 children (aged 4 to 17 years) with a 2-AFC paradigm, both using an adaptive weighted one-up one-down staircase. RESULTS:Simulations indicated a similar bias and precision for a 2-AFC paradigm with double the number of trials as a 4-AFC paradigm. On average, estimated threshold of the simulated data was equal to the model threshold, indicating no bias. The precision was improved with an increasing number of trials. Likewise, our data showed a similar bias and precision for a 2-AFC paradigm with 60 trials as for a 4-AFC paradigm with 30 trials. Trials in the 4-AFC paradigm took slightly longer as participants scanned more alternatives. However, the 4-AFC task still ended up faster for a given precision. CONCLUSION:Bias and precision were similar in a 4-AFC task compared to a 2-AFC task with double the number of trials. However, a 4-AFC paradigm was more time efficient and is therefore recommended