Mathematical Submodels in Water Quality Systems

394 Pages·2013·20.343 MB·English

by  S.E. Jørgensen and M.J. Gromiec (Eds.)

1. ENERGY AND ECOLOGICAL MODELLING
edited by W.J. Mitsch, R.W. Bossermann and J.M. Klopatek
1981 839 pp.
2. WATER MANAGEMENT MODELS IN PRACTICE:
A CASE STUDY OF THE ASWAN HIGH DAM
by D. Whittington and G. Guariso
1983 xxii + 246pp.
3. NUMERICAL ECOLOGY
by L. Legendre and P. Legendre
1983 xvi + 419pp.
4A. APPLICATION OF ECOLOGICAL MODELLING IN ENVIRONMENTAL MANAGEMENT
PART A
edited by S.E. Jorgensen
1983 viit + 735 pp.
4.B APPLICATION OF ECOLOGICAL MODELLING IN ENVIRONMENTAL MANAGEMENT
PARTB
edited by S.E. Jorgensen and W.J. Mitsch
1983 viii+438pp.
5. ANALYSIS OF ECOLOGICAL SYSTEMS: STATE-OF-THE-ART IN ECOLOGICAL MODELLING
edited by W.K. Lauenroth, G.V. Skogerboe and M. Flug
1983 992 pp.
6. MODELLING THE FATE AND EFFECT OF TOXIC SUBSTANCES IN THE ENVIRONMENT
edited by S.E. Jorgensen
1984 viii + 342pp.
7. MATHEMATICAL MODELS IN BIOLOGICAL WASTE WATER TREATMENT
edited by S.E. Jergensen and M.J. Gromiec
1985 vi + 802pp.
8. FRESHWATER ECOSYSTEMS: MODELLING AND SIMULATION
by M. StraSkaba and A.H. Gnauck
1985 309 pp.
9. FUNDAMENTALS OF ECOLOGICAL MODELLING
by S.E. Jorgensen
1986 389 pp.
10. AGRICULTURAL NONPOINT SOURCE POLLUTION:
MODEL SELECTION AND APPLICATION
edited by A. Giorgini and F. Zingales
1986 409 pp.
11. MATHEMATICAL MODELLING OF ENVIRONMENTAL AND ECOLOGICAL SYSTENS
edited by J.B. Shukla, T.G. Hallam and V. Capasso
1987 xii + 254pp.
12. WETLAND MODELLING
edited by W.J. Mitsch, M. Straskraba and S.E. Jorgensen
1988 x + 228p.
13. ADVANCES IN ENVIRONMENTAL MODELLING
edited by A. Marani
1988 691pp.
Developments in Environmental Modelling, 14
Mathematical Submodels
in Water Quality Systems
Edited by
S.E. Jorgensen
Langkaer Vaenge 9, 3500 Vaerl0se, Copenhagen, Denmark
and
M.J. Gromiec
Instytut Meteorologii i Gospodarki Wodnej, 01-673 Warszawa u.
Podlesna 61, Poland
ELSEVIER
Amsterdam — Oxford — New York — Tokyo 1989
ELSEVIER SCIENCE PUBLISHERS B.V.
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Distributors for the United States and Canada:
ELSEVIER SCIENCE PUBLISHING COMPANY INC.
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Library of Congress Catalog1ng-1n-Publtcatlon Data
Mathematical submodels in water quality systems / edited by S.E.
Jergensen and M.J. Gromlec.
p. cm. — (Developments 1n environmental modelling ; 14)
Bibliography: p.
Includes Index.
ISBN 0-444-88030-5
1. Hater quality—Mathematical models. 2. Aquatic ecology-
-Mathematlcal models. 3. Hydrology—Mathematical models.
I. Jargensen, Sven Erik, 1934- . II. Gromlec, Marek Jerzy.
III. Series.
TD370.M43 1989
628.1'61 — dc20 89-16789
CIP
ISBN 0-444-88030-5 (Vol. 14)
ISBN 0-444-41948-9 (Series)
© Elsevier Science Publishers B.V., 1989
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Printed in The Netherlands
LIST OF TABLES
Chapter 2: VOLATILIZATION
2.1 Concentration of ammonia (NH + NH +) which contains a non-ionized
3 4
ammonia concentration of 0.025 mg NH I-1
3
2.2 Evaporation rate of chemical compounds (Dilling et al., 1975 and
Hutzinger et al., 1974)
Chapter 3: REAERATION
3.1 Theoretical models for the reaeration coefficient
3.2 Differential equations and boundary conditions used in the develop-
ment of theoretical reaeration models
3.3 Values of parameters for models in studies of Shastry et al. (1969)
as estimated by Bard's method
3.4 Reaeration coefficients for lakes
3.5 Statistical test of selected predictive models (Tsivoglou and
Wallance, 1972)
3.6 Error analysis of various predictive models for reaeration coef-
ficient (Bennett and Rathbun, 1972)
3.7 Predictive performance of various models for reaeration coefficient
(Wilson and Macleod, 1974)
Chapter 4: ADSORPTION AND ION EXCHANGE
4.1 Freundlich's constant for adsorption of some organic compounds on
activated carbon
4.2 Adsorption determinations
Chapter 14: PREDATOR-PREY INTERACTIONS
14.1 Proposed functions for description of dependency of predation rate
on prey concentration
14.2 Source of proposed functions for description of dependency of
digestion rate on temperature
Chapter 15: PRIMARY PRODUCTIVITY
15.1 Representative parameter values from CE-QUAL-R1
Chapter 16: FISH GROWTH
16.1 Energy budget at different feeding levels
Chapter 17: SEDIMENT-WATER EXCHANGE MODELS
17.1 6 (out of 17) Glums0-model state variables, describing the indepen-
dent phosphorus cycle
17.2 Characteristics of various sediment phosphorus models (from Kamp-
Nielsen, 1983)
17.3 Rate constants (reciprocal residence time) for a dissolved species in
a lake, for diffusional flux at the sediment-water interface (l/t ),
d
sedimentation and growth of pure water volume (l/t ), water out-
u
flow (l/t ) and first-order chemical removal or decay (l/t). All
w r
values have the dimension year1
10.2 Hydrolysis rates at 25°C and pH 7 of some halogenated compounds
10.3 Equilibrium constants for selected redox reactions
10.4 Review: Chemical oxidation of organic compounds
10.5 Rate constants of oxidation by singlet oxygen in water at 25°C. The
concentration of singlet oxygen can be estimated as 10"12 M
10.6 Standard electrode potentials at 25°C
Chapter 12: MICROBIAL DECOMPOSITION
12.1 Reaeration coefficient K for different rivers and streams. After
2
Hydroscience (1971)
12.2 Stream slope dependance of coefficient of bed activity n. After
Bowie et al. (1985). K, = K,j + n (n/H)
12.3 Comparison of experimental and calculated values of the A coef-
ficient, according to Bosco and Novotny, for Holston River, Tenessee.
After Novotny et al. (1974)
12.4 Graphical and mathematical K, procedures compared by Hewitt et al.
(1975)
12.5 Deoxygenation rate constants, K After Bansal (1975)
v
Chapter 13: NITRIFICATION
13.1 Typical values of kinetics constants for nitrifying organisms
13.2 Effects of dissolved oxygen
13.3 Different types of inhibition model
13.4 Temperature coefficients for nitrifying microorganisms
Chapters; HEAT EXCHANGE
5.1 Total dust depletion coefficient for two levels of optival air mass,
m. d = d + d
s a
5.2 Estimated values of total reflectivity of the ground, R
g
5.3 Radiation absorbed in the first meter below the water surface (after
TVA, 1972)
Chapter 6: SEDIMENTATION
6.1 Phytoplankton settling velocities
6.2 Detritus, settling rate
Chapter 8: PRECIPITATION
8.1 Negative logarithms of solubility products of heavy-metal hydrox-
ides (total ionization constants), carbonates and sulphides (pH = 7 at
25°C)
Chapter 9: COMPLEX FORMATION
9.1 Coordination numbers of pertinent metal ions
9.2 Concentration of ligand in interstitial seawater (M) (reducing con-
ditions)
9.3 Gross stability constants for complex equilibria of environmental
importance
9.4 Classification in accordance with the HSAB system
Chapter 10: HYDROLYSIS AND CHEMICAL REDOX PROCESSES
10.1 Examples of hydrolysis and redox processes in the environment
CHAPTER 1
INTRODUCTION
by
Sven Erik Jcrgensen
1.1 THE APPLICATION OF SUBMODELS
Environmental models may be divided into empirical and mechanistic
models. The latter type is based on quantitative descriptions of physical,
chemical and biological processes in the environment. The description
attempts to describe the mechanism behind the process on a sound
scientifical basis.
Comprehensive environmental models have been used since the early
seventies. Mechanistic models are used in this context more and more,
probably because of attempts to put more ecology into the models.
Experience has shown that it is absolutely necessary to develop models on a
sound ecological basis, to find a balanced complexity and to build reality
into the models, see for instance Jorgensen (1988). One may go as far as to
state that 15-20 years ago the development of models was 75% mathematics
and 25% ecology in its widest sense. Today it is the opposite: 75% ecology
v
and 25% mathematics.
The result has been an increasing demand for the development of good
quantitative and ecological descriptions of physical, chemical and biological
processes in ecosystems. Such descriptions may be called 'submodels'.
For each process there are several and, to a certain extent, equally valid
descriptions, which vary in complexity and the number of side reactions and
details, that they include. As in the development of total models, the
selection of the right submodels is a matter for the ecosystem and its
problems (e.g. which side reactions and/or details are significant in the
considered case?), and the required accuracy, including the amount and
quality of the available data. Therefore it must not be expected that it is
possible to give a general answer to the question as to which submodel to
use for each of the relevant processes? Several submodels are presented in
this book together with the considerations needed in individual cases for
making the right selection of the submodel, best fitted to the ecosystem, the
problem and the data.
Submodels are developed similarly to total models. It means that the
Figure 1.1. is also valid for the development of a submodel, although the
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complexity and the needed data of course in most cases are less. It is
recommended to make all the steps presented in Figure 1.1 also in
development of a submodel. Some of the steps may be considered redundant,
but it is still recommended that the procedures are used to avoid exclusion
of important steps and to assure that all the required considerations are
included.
ft
Dueetfiinniittnio n of
problem
Selection of
complexity
Bounding of the problem
i n time, space and sub-
systems
^Quality of
Data requirement available data?
5
Conceptual diagram
5
Equations
Revisii on -l* 5
requi regy Verification
t 3
Sensitivity analysis
€ 5
Calibration
■£ 3
Validation
Fig. 1.1: A tentative modelling procedure.
The development or selection of a submodel is often an important part of
a total model development. New requirements often emerge in the
verification phase, as a result of sensitivity analysis or calibration. The
verification may show that something is missing in the internal logic of the
total model which of course may call for another selection of submodels or
for the development of an additional submodel. The sensitivity analysis may
reveal that the model results are particularly sensitive to the right
description of one or more processes, which implies that more detailed
submodels for these processes should be considered. If the calibration is not
- 14 -
giving acceptable results, a change to some of the applied submodels should
be considered. To a certain extent the same is also true after the validation.
In the tentative procedure Figure 1.1 also shows how the development of a
model is an iterative procedure. After the verification, sensitivity analysis,
calibration and validation, revisions may be required. These revisions may
all include development or selection of submodels.
1.2 OVERVIEW OF THE PRESENTED SUBMODELS
This book presents the most important, but not all, submodels applied in
water quality modelling. Attempts are made to include physical as well as
chemical and biological submodels to demonstrate the different classes
available.
The diffusion and advection processes have not been included among the
physical processes, because these processes are widely covered in books on
hydrodynamics.
Each of the following chapters are devoted to one process and its related
submodels. The importance of the process is discussed in the introduction of
the chapter, followed by a presentation of the most applied submodels. A
comprehensive list of applicable submodels may be presented but emphasis
is laid on the question as to which submodel to select in which case?
The chapter discusses furthermore the parameter values and how to
determine them. For some of the submodels examples of application be
considered and, finally, the state of the art of the submodel: where are we
today? Which research is needed to fill the gaps in our knowledge?
This book should not be considered a handbook in aquatic submodels.
Jargensen (1988) and Jorgensen et al (1979) already give tables of some
important submodels. The present book gives an overview of some of the
most important submodels in water quality modelling, and its scope is
rather to discuss the advantages and disadvantages of various submodels to
be applied to various case studies and total models.
Chapter two covers Volatilization i.e. the tranfer of a component from
an aquatic ecosystem to the atmosphere. It is an important process in toxic
substance models, as a substantial part of toxic organics may be lost from
aquatic ecosystems to the atmosphere by volatilization. Furthermore, the
nitrogen balance of aquatic ecosystems is often significantly influenced by
the volatilization of ammonia.
Reaeration is mentioned in chapter three and may be considered the
tranfer of gasses from the atmosphere to aquatic ecosystems. The process is
of particular importance for the oxygen balances of aquatic ecosystems, for
this process is the major source of oxygen in polluted streams.
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