Research Commons
      • Browse 
        • Communities & Collections
        • Titles
        • Authors
        • By Issue Date
        • Subjects
        • Types
        • Series
      • Help 
        • About
        • Collection Policy
        • OA Mandate Guidelines
        • Guidelines FAQ
        • Contact Us
      • My Account 
        • Sign In
        • Register
      View Item 
      •   Research Commons
      • University of Waikato Research
      • Science and Engineering
      • Science and Engineering Papers
      • View Item
      •   Research Commons
      • University of Waikato Research
      • Science and Engineering
      • Science and Engineering Papers
      • View Item
      JavaScript is disabled for your browser. Some features of this site may not work without it.

      Temporal moments of a tracer pulse in a perfectly parallel flow system

      Bardsley, W. Earl
      Thumbnail
      Files
      commons_temporal_moments.pdf
      396.4Kb
      DOI
       10.1016/S0309-1708(03)00047-2
      Find in your library  
      Citation
      Export citation
      Bardsley, W.E. (2003). Temporal moments of a tracer pulse in a perfectly parallel flow system. Advances in Water Resources, 26(6), 599-607.
      Permanent Research Commons link: https://hdl.handle.net/10289/3574
      Abstract
      Perfectly parallel groundwater transport models partition water flow into isolated one-dimensional stream tubes which maintain total spatial correlation of all properties in the direction of flow. The case is considered of the temporal moments of a conservative tracer pulse released simultaneously into N stream tubes with arbitrarily different advective–dispersive transport and steady flow speeds in each of the stream tubes. No assumptions are made about the form of the individual stream tube arrival-time distributions or about the nature of the between-stream tube variation of hydraulic conductivity and flow speeds. The tracer arrival-time distribution g(t,x) is an N-component finite-mixture distribution, with the mean and variance of each component distribution increasing in proportion to tracer travel distance x. By utilising moment relations of finite mixture distributions, it is shown (to r=4) that the rth central moment of g(t,x) is an rth order polynomial function of x or φ, where φ is mean arrival time. In particular, the variance of g(t,x) is a positive quadratic function of x or φ. This generalises the well-known quadratic variance increase for purely advective flow in parallel flow systems and allows a simple means of regression estimation of the large-distance coefficient of variation of g(t,x). The polynomial central moment relation extends to the purely advective transport case which arises as a large-distance limit of advective–dispersive transport in parallel flow models. The associated limit g(t,x) distributions are of N-modal form and maintain constant shapes independent of travel distance. The finite-mixture framework for moment evaluation is also a potentially useful device for forecasting g(t,x) distributions, which may include multimodal forms. A synthetic example illustrates g(t,x) forecasting using a mixture of normal distributions.
      Date
      2003-06
      Type
      Journal Article
      Publisher
      Elsevier
      Rights
      This is an author’s accepted version of an article published in the journal: Advances in Water Resources. © 2003 Elsevier.
      Collections
      • Science and Engineering Papers [3122]
      Show full item record  

      Usage

      Downloads, last 12 months
      57
       
       
       

      Usage Statistics

      For this itemFor all of Research Commons

      The University of Waikato - Te Whare Wānanga o WaikatoFeedback and RequestsCopyright and Legal Statement