The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics

J. R. Schramski, B. C. Patten, C. Kazanci, D. K. Gattie, Nadia Kellam

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.

Original languageEnglish (US)
Pages (from-to)3225-3232
Number of pages8
JournalEcological Modelling
Volume220
Issue number22
DOIs
StatePublished - Nov 24 2009
Externally publishedYes

Fingerprint

ecological modeling
energetics
ecosystem
network analysis
energy flow
mathematics
mass transport
reef
thermodynamics
engineering
history
energy

Keywords

  • Control surface
  • Control volume
  • Ecological modeling
  • Ecological network analysis
  • Ecosystem energetics
  • Eulerian
  • Reynolds transport theorem

ASJC Scopus subject areas

  • Ecological Modeling

Cite this

The Reynolds transport theorem : Application to ecological compartment modeling and case study of ecosystem energetics. / Schramski, J. R.; Patten, B. C.; Kazanci, C.; Gattie, D. K.; Kellam, Nadia.

In: Ecological Modelling, Vol. 220, No. 22, 24.11.2009, p. 3225-3232.

Research output: Contribution to journalArticle

Schramski, J. R. ; Patten, B. C. ; Kazanci, C. ; Gattie, D. K. ; Kellam, Nadia. / The Reynolds transport theorem : Application to ecological compartment modeling and case study of ecosystem energetics. In: Ecological Modelling. 2009 ; Vol. 220, No. 22. pp. 3225-3232.
@article{ba77d496a1ac4f3eb990e01c06445dfb,
title = "The Reynolds transport theorem: Application to ecological compartment modeling and case study of ecosystem energetics",
abstract = "The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.",
keywords = "Control surface, Control volume, Ecological modeling, Ecological network analysis, Ecosystem energetics, Eulerian, Reynolds transport theorem",
author = "Schramski, {J. R.} and Patten, {B. C.} and C. Kazanci and Gattie, {D. K.} and Nadia Kellam",
year = "2009",
month = "11",
day = "24",
doi = "10.1016/j.ecolmodel.2009.08.009",
language = "English (US)",
volume = "220",
pages = "3225--3232",
journal = "Ecological Modelling",
issn = "0304-3800",
publisher = "Elsevier",
number = "22",

}

TY - JOUR

T1 - The Reynolds transport theorem

T2 - Application to ecological compartment modeling and case study of ecosystem energetics

AU - Schramski, J. R.

AU - Patten, B. C.

AU - Kazanci, C.

AU - Gattie, D. K.

AU - Kellam, Nadia

PY - 2009/11/24

Y1 - 2009/11/24

N2 - The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.

AB - The Reynolds transport theorem (RTT) from mathematics and engineering has a rich history of success in mass transport dynamics and traditional thermodynamics. This paper introduces RTT as a complementary approach to traditional compartmental methods used in ecological modeling and network analysis. A universal system equation for a generic flow quantity is developed into a generic open-system differential expression for conservation of energy. Nonadiabatic systems are defined and incorporated into control volume (CV) and control surface (CS) perspectives of RTT where reductive assumptions in empirical data are then formally introduced, reviewed, and appropriately implemented. Compartment models are abstract, time-dependent systems of simultaneous differential equations describing storage and flow of conservative quantities between interconnected entities (the compartments). As such, they represent a set of flexible and somewhat informal, assumptions, definitions, algebraic manipulations, and graphical depictions subject to influence and selectively parsed expression by the modeler. In comparison, RTT compartment models are more rigorous and formal integro-differential equations and graphics initiated by the RTT universal system equation, forcing an ordered identification of simplifying assumptions, ending with clearly identified depictions of the transfer and transport of conservative substances in physical space and time. They are less abstract in the rigor of their equation development leaving less ambiguity to modeler discretion. They achieve greater consistency with other RTT compartment style models while possibly generating greater conformity with physical reality. Characteristics of the RTT approach are compared with those of a traditional compartment model of energy flow in an intertidal oyster-reef community.

KW - Control surface

KW - Control volume

KW - Ecological modeling

KW - Ecological network analysis

KW - Ecosystem energetics

KW - Eulerian

KW - Reynolds transport theorem

UR - http://www.scopus.com/inward/record.url?scp=70350119620&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350119620&partnerID=8YFLogxK

U2 - 10.1016/j.ecolmodel.2009.08.009

DO - 10.1016/j.ecolmodel.2009.08.009

M3 - Article

AN - SCOPUS:70350119620

VL - 220

SP - 3225

EP - 3232

JO - Ecological Modelling

JF - Ecological Modelling

SN - 0304-3800

IS - 22

ER -