Eulerian-Lagrangian analysis of transport conditioned on hydraulic data 3. Spatial moments, travel time distribution, mass flow rate, and cumulative release across a compliance surface

Zhang Dongxiao Zhang, Shlomo P Neuman

Research output: Contribution to journalArticle

29 Citations (Scopus)

Abstract

In paper two the effects of log transmissivity and hydraulic head data on conditional predictions of concentration due to instantaneous point and nonpoint sources are examined. In this paper the same approach is used directly to estimate mass flow rate across a "compliance surface', cumulative mass release, and the probability distribution of travel times across this surface and the associated uncertainty. Contrary to some other methods in the literature, the approach requires neither a special theory for travel times nor a prior assumption about their probability distribution. It is shown how one can compute explicitly the second spatial moment of the conditional mean plume about its center of mass, the conditional mean second spatial moment of the actual plume about its center of mass, and the conditional covariance of the plume center of mass. These quantities and the effect of conditioning on some of them are illustrated by considering instantaneous point, line, and area sources in a two-dimensional, statistically homogeneous, isotropic, mildly varying log transmissivity field under uniform prior (unconditional) mean flow. -from Authors

Original languageEnglish (US)
Pages (from-to)65-75
Number of pages11
JournalWater Resources Research
Volume31
Issue number1
StatePublished - 1995
Externally publishedYes

Fingerprint

Lagrangian analysis
mass flow
Travel time
compliance
travel
Probability distributions
travel time
fluid mechanics
Flow rate
Hydraulics
hydraulics
probability distribution
plume
transmissivity
conditioned behavior
hydraulic head
uncertainty
conditioning
prediction
rate

ASJC Scopus subject areas

  • Aquatic Science
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology

Cite this

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abstract = "In paper two the effects of log transmissivity and hydraulic head data on conditional predictions of concentration due to instantaneous point and nonpoint sources are examined. In this paper the same approach is used directly to estimate mass flow rate across a {"}compliance surface', cumulative mass release, and the probability distribution of travel times across this surface and the associated uncertainty. Contrary to some other methods in the literature, the approach requires neither a special theory for travel times nor a prior assumption about their probability distribution. It is shown how one can compute explicitly the second spatial moment of the conditional mean plume about its center of mass, the conditional mean second spatial moment of the actual plume about its center of mass, and the conditional covariance of the plume center of mass. These quantities and the effect of conditioning on some of them are illustrated by considering instantaneous point, line, and area sources in a two-dimensional, statistically homogeneous, isotropic, mildly varying log transmissivity field under uniform prior (unconditional) mean flow. -from Authors",
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N2 - In paper two the effects of log transmissivity and hydraulic head data on conditional predictions of concentration due to instantaneous point and nonpoint sources are examined. In this paper the same approach is used directly to estimate mass flow rate across a "compliance surface', cumulative mass release, and the probability distribution of travel times across this surface and the associated uncertainty. Contrary to some other methods in the literature, the approach requires neither a special theory for travel times nor a prior assumption about their probability distribution. It is shown how one can compute explicitly the second spatial moment of the conditional mean plume about its center of mass, the conditional mean second spatial moment of the actual plume about its center of mass, and the conditional covariance of the plume center of mass. These quantities and the effect of conditioning on some of them are illustrated by considering instantaneous point, line, and area sources in a two-dimensional, statistically homogeneous, isotropic, mildly varying log transmissivity field under uniform prior (unconditional) mean flow. -from Authors

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