• Login
    View Item 
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    •   Home
    • UA Graduate and Undergraduate Research
    • UA Theses and Dissertations
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of UA Campus RepositoryCommunitiesTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournalThis CollectionTitleAuthorsIssue DateSubmit DateSubjectsPublisherJournal

    My Account

    LoginRegister

    About

    AboutUA Faculty PublicationsUA DissertationsUA Master's ThesesUA Honors ThesesUA PressUA YearbooksUA CatalogsUA Libraries

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    A stochastic snow model.

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Thumbnail
    Name:
    azu_td_hy_e9791_1974_350_sip1_w.pdf
    Size:
    4.056Mb
    Format:
    PDF
    Description:
    azu_td_hy_e9791_1974_350_sip1_w.pdf
    Download
    Author
    Cary, Lawrence Ernest,1941-
    Issue Date
    1974
    Keywords
    Hydrology.
    Snow -- Mathematical models.
    Committee Chair
    Fogel, Martin M.
    
    Metadata
    Show full item record
    Publisher
    The University of Arizona.
    Rights
    Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
    Abstract
    The purpose of this study was to develop a stochastic model of the snowfall, snow accumulation and ablation process. Snow storms occurring in a fixed interval were assumed to be a homogeneous Poisson process with intensity X. The snow storm magnitudes were assumed to be independent and identically distributed random variables. The magnitudes were independent of the number of storms and concentrated at the storm termination epochs. The snow water equivalent from all storms was a compound Poisson process. In the model, storms then occurred as positive jumps whose magnitudes equaled the storm amounts. Between storms, the snowpack ablated at a constant rate. Random variables characterizing this process were defined. The time to the occurrence of the first snowpack, generated by the first storm, was a random variable, the first snow-free period. The snowpack lasted for a random duration, the first snowpack duration. The alternating sequence of snow-free periods followed by snowpacks of random duration continued throughout the fixed interval. The snow-free periods were independent and identically distributed random variables as were the snowpack durations. The sum of each snow-free period and the immediately following snowpack duration formed another sequence of independent and identically distributed random variables, the snow-free, snow cycles. The snow-free, snow cycles represented the interarrival times between epochs of complete ablation, and thus defined a secondary renewal process. This process, called the snow renewal process, gave the number of times the snowpacks ablated in the interval. Distribution functions of the random variables were derived. The snow-free periods were exponentially distributed. The distribution function of the snowpack durations was obtained using some results from queueing theory. The distribution function of the first snow-free, snow cycle was derived by convoluting the density function of the first snowfree period and the first snowpack duration. The distribution of the sum of n snow-free, snow cycles was then the n-fold convolution of the first snow-free, snow cycle with itself. The probability mass function of the snow renewal process was evaluated numerically, from a known relationship with the sum of snow-free, snow cycles. The snowpack ablation rate was considered to be a random variable, constant within a season, but varying between seasons. The snowpack durations and snow-free, snow cycles were conditioned on the ablation rate, then unconditional distributions derived. An application of the model was made in the case where snow storm magnitudes were exponentially distributed. Specific expressions for the distribution functions of the random variables were obtained. These distributions were functions of the Poisson parameter X, the exponential parameter of storm magnitudes, Ne l, and the snowpack ablation rate. The snow model was compared with data from the climatological station at Flagstaff, Arizona. Snow storms were defined as sequences of days receiving 0.01 inch or more of snow water equivalent separated from other storms by one or more dry days. Snow storms occurred approximately as a homogeneous Poisson process. Storm magnitudes were exponentially distributed. Empirical distributions of snowpack ablation rates were obtained as the coefficients of a regression analysis of snowpack ablation. Two methods of estimating the Poisson parameter were used. The theoretical distribution functions were compared with the observed. The method of moments estimate generally gave more satisfactory results than the second estimate.
    Type
    Dissertation-Reproduction (electronic)
    text
    Degree Name
    Ph. D.
    Degree Level
    doctoral
    Degree Program
    Watershed Management
    Graduate College
    Degree Grantor
    University of Arizona
    Collections
    Dissertations

    entitlement

     
    The University of Arizona Libraries | 1510 E. University Blvd. | Tucson, AZ 85721-0055
    Tel 520-621-6442 | repository@u.library.arizona.edu
    DSpace software copyright © 2002-2017  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service operated by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.