Environmental System Analysis
Kangwon National University
College of Engineering
Division of Geosystem and Environmental
Professor Joon Hyun Kim
Class Contents and Schedule
Fate and Transport of Pollutants in Water,
Air, and Soil
-JERALD L. SCHNOOR
If we are going to live so intimately with these
chemicals, eating and drinking them into the very
marrow of our bones, we had better know
something about their nature and power
-Rachel Carson, Silent Spring
1.1 SCOPE OF ENVIRONMENTAL MODELING
Why should we build mathematical models of environmental
1) To gain a better understanding of the fate and transport of
chemicals by quantifying their reactions, speciation, and
movement for the prediction of fate, transport, and persistence of
chemicals in the environment.
Classic models address conventional pollutants, eutrophication,
toxic organic chemicals, and metals in surface waters and
Recently, mathematical models have become more sophisticated in
terms of their chemistry. This book seeks to solidify the bond
between water quality modeling and aquatic chemistry. Chemical
speciation models are coupled with kinetic transport models for
determining fate and chemical speciation.
2) To determine chemical exposure concentrations to aquatic
organisms and/or humans in the past, present, or future.
It pertains to assessing the effects of chemical pollutants. New water
quality criteria are promulgated to account for acute and chronic
effects levels using frequency and duration of exposure.
These criteria result in water quality standards that are enforceable by
law and require the application of mathematical models for waste load
allocations, risk assessments, or environmental impact assessments.
Toxic chemicals-ammonia, arsenic, cadmium, chlorine, chromium,
copper, cyanide, lead, and mercury-have been regulated. The criteria
specify an acute threshold concentration and a chronic-no-effect
concentration for each toxicant as well as tolerable durations and
New criteria recognize that toxic effects are a function both of the
magnitude of a pollutant concentration and of the organism exposure
time to that concentration : (1) the 4-day average concentration of the
toxicant does not exceed the recommended chronic criterion more than
once every three years on the average and (2) the 1-hour average
concentration does not exceed the recommended acute criterion more
than once every three years on the average.
3) To predict future conditions under various loading scenarios or
management action alternatives.
Waste load allocations and exposure models for risk assessment fall
into this category.
Regardless how much monitoring data are available, it will always be
desirable to have an estimate of chemical concentrations under
different conditions, results for a future waste loading scenario, a
predicted "hindcast" or reconstructed history, or estimates at an
alternate site where field data do not exist.
For all these reasons we need chemical fate and transport models, and
we need models that are increasingly sophisticated in their chemistry,
as we move toward site-specific water quality standards and chemical
speciation considerations in ecotoxicology.
To model aquatic chemical systems, we begin with a simple mass
balance based on the principle of continuity: matter is neither created
nor destroyed in macroscopic chemical, physical, and biological
1.2 MASS BALANCES
Water quality may be defined as "something inherent or distinctive about water."
These distinctive characteristics can be chemical, physical, or biological
Mass balance serves for determining the fate of water quality parameters in
natural waters and to assess degree of pollution expected under various conditions
The fate of chemicals in the aquatic environment is determined by
the rate of their physical transport through the environment
Mathematical models are simply useful accounting procedures for the calculation
of these processes
To the extent that we can accurately predict the chemical, biological, and physical
reactions and transport of chemical substances, we can "model" their fate and
persistence and the inevitable exposure to aquatic organisms
Key elements in a mass balance (see Fig.1.1):
(i) A clearly defined control volume.
(ii) A knowledge of inputs and outputs that cross the boundary of the
(iii) A knowledge of the transport characteristics within the control
volume and across its boundaries.
(iv) A knowledge of the reaction kinetics within the control volume.
Figure 1.1 Generalized
approach for mass
balance models utilizing
concept and transport
A control volume:
can be as small as an infinitesimal thin
slice of water in a swiftly flowing
stream or as large as the entire body
of oceans on the planet earth.
The important point: the boundaries
are clearly defined with respect to
their location (element i) so that the
volume is known and mass fluxes
across the boundaries can be
determined (element ii).
Transport in adjacent or surrounding
control volumes may contribute mass
to the control volume, so transport
across the boundaries of the control
volume must be known or estimated
knowledge of the chemical,
biological, and physical reactions that
the substance can undergo within the
control volume (element iv) is needed.
Classification of substances relative to their reactions in water
Mass Balance of Water (Water Balance, Water Budget)
If the system is nearly isothermal, then the mass of storage is
accounted for by the volume of inflows and outflows.
inflows: the volumetric inputs of tributaries and overland flow
outflows: all discharges from the water body
direct precipitation: water that falls directly on the surface
evaporation: volume of water that leaves the surface of the water
body to the atmosphere.
In case of inputs/outputs of groundwater, the piezometric surface of the
groundwater adjacent to the water body must be measured .
Q = flow rate m3d-1 I = precipitation rate md-1 A = surface area of
water body, m2 E = evaporation rate md-1 ∆t = time increment,
days ∆V = change in storage volume, m3
Figure 1.2 Schematic of a lake with inflows and outflows
for computation of a water budget
Example 1.1 Mass Balance of Water (Volume) in a Lake
Calculate the volume of a lake over time during a drought if the sum of
all inputs is 100 m3s-1 and the outflows are 110 m3s-1 and increasing 1
m3s-1 every day due to evaporation and water demand. Initial volume of
the lake is 1 × 109 m3. See Figure 1.3. (Note : Convert all units from
seconds to days.)
Figure 1.3 Plot of volume versus time for hypothetical lake
during a drought period
Example 1.2 Algebraic Mass Balance on Toxic Chemical in a Lake
Calculate the steady-state concentration of a toxic chemical in a lake
under the following conditions. Assume steady state (dC/dt = 0) and
constant volume (Qin = Qout) and a degradation rate of 50 kg d-1 for the
conditions such as : Cin=100μgL-1, Qin=Qout=10m3s-1, -Rxn=50kgd-1
Solution: Write the mass balance equation for the lake as a control volume
Accumulation = Inputs - Outflows ± Rxns , Accumulation = 0 at steady
state Outflows = Inputs - Rxn (degradation)
1.3 MODEL CALIBRATION AND VERIFICATION
O To perform mathematical modeling, four ingredients are necessary:
1) field data on chemical concentrations and mass discharge inputs
2) a mathematical model formulation
3) rate constants and equilibrium coefficients for the mathematical model
4) some performance criteria with which to judge the model
O If the model is to be used for regulatory purposes, there should be enough
field data to be confident of model results (two sets of field measurements,
one for model calibration and one for verification under somewhat
different circumstances (a different year of field measurements or an
O Model calibration involves a comparison between simulation results and
field measurements. Model coefficients and rate constants should be chosen
initially from literature or laboratory studies.
O If errors are within an acceptable tolerance level, the model is considered
calibrated. If errors are not acceptable, rate constants and coefficients must
be systematically varied (tuning the model) to obtain an acceptable
simulation. The parameters should not be "tuned" outside the range of
experimentally determined values reported in the literature.
O After you run the model, a statistical comparison is made between model
results for the state variables (chemical concentrations) and field
measurements. The model is calibrated.
Definition of Terminologies
Mathematical model-a quantitative formulation of chemical, physical,
and biological processes that simulates the system.
State variable-the dependent variable that is being modeled (in this
context, usually a chemical concentration).
Model parameters-coefficients in the model that are used to formulate
the mass balance equation (e.g., rate constants, equilibrium constants,
Model inputs-forcing functions or constants required to run the model
(e.g., flowrate, input chemical concentrations, temperature, sunlight).
Calibration-a statistically acceptable comparison between model results
and field measurements; adjustment or "tuning" of model parameters is
allowed within the range of experimentally determined values reported
in the literature.
Verification-a statistically acceptable comparison between model results
and a second (independent) set of field data for another year or at an
alternate site; model parameters are fixed and no further adjustment is
allowed after the calibration step.
Simulation-use of the model with any input data set (even hypothetical
input) and not requiring calibration or verification with field data.
Validation-scientific acceptance that (1) the model includes all major and
salient processes, (2) the processes are formulated correctly, and (3) the
model suitably describes observed phenomena for the use intended.
Robustness-utility of the model established after repeated applications
under different circumstances and at different sites.
Post audit-a comparison of model predictions to future field
measurements at that time.
Sensitivity analysis-determination of the effect of a small change in
model parameters on the results (state variable), either by numerical
simulation or mathematical techniques.
Uncertainty analysis-determination of the uncertainty (standard
deviation) of the state variable expected value (mean) due to uncertainty
in model parameters, inputs, or initial state via stochastic modeling
Statistical "goodness of fit" criteria using chi-square or KolmogorovSmirnov tests (tests of the sampling distribution of the variance).
Paired t-tests of model results and field observations at the same time (a
test of the means).
Linear regression of paired data for model predictions and field
observations at the same time.
A comparison of model results to field observations and their standard
deviation (or geometric deviation, if appropriate).
Parameter estimation techniques such as nonlinear curve-fitting
regressions (weighted or unweighted) or Kalman filters to determine
model parameters in an optimal fashion.
To verify the model, a statistical comparison between simulation
results and a second set of field data is required.
Coefficients and rate constants cannot be changed from the model
Acceptance of a model calibration of verification does not necessarily
imply that the model, itself, is validated. It is possible that the model
works well under one set of circumstances but poorly under another.
As the model is applied to different situations at various locations, we
gain confidence in the model and its robustness. The process when the
model is considered validated is gradual.
Further testing its formulation and validity.
Post audits of model results are an important test of the usefulness of
the model (they are performed after model predictions have been made
as data become available in the future). Very few post audits have been
reported in the literature. More are needed.
Example 1.3 Calibration and Criteria Testing of a DO Model for a
A water discharge with biochemical oxygen demand (BOD) at km 0.0
causes a depletion in dissolved oxygen in a stream (D.O. sag curve). Model
calibration results are tabulated below (D.O. model) together with field
measurements (D.O. field) expressed in concentration units, mg L-1. See
Determine if the model calibration is acceptable according to the following
a. Chi-square goodness of fit at a 0.10 significance level (a 90% confidence
b. Paired t-test (difference between the mean and zero) at significance level
c. Linear least-squares regression of model results (D.O. model on x-axis)
versus observed data (D.O. field data on y-axis) with r2 > 0.8.
Figure 1.4 Dissolved oxygen model calibration and
comparison to field measurements.
Chi-Square Fitness Test
where the observed values are the D.O. field data, and the expected values
are the D.O. model results. α is the confidence level and χ02 is the chisquare distribution value for n-1 degrees of freedom. χ02 =4.17 for n = 10
and α = 0.9. The value for χ02 = 4.17 was determined from a statistical
table for the chi-square distribution with 9 degrees of freedom (n-1) and P
The table below shows that 0.1254≤4.17. Therefore the model passes the
goodness of fit test at a 0.10 significance level.
di - difference between values in data pairi. The acceptance criterion for
the t-test for n-1 degrees of freedom is
In D.O model the value 1.833 wart determined from a table t-values with
9 degrees of freedom and P = 0.10. The above shows
The test statistic can be calculated
The model results are found to be indistinguishable from the field data at
a significance level of 0.10 from the paired t-test because 0.3699≤1.833.
Linear Least Square Regression Analysis Test
Perfect model predictions would yield
The D.O. model meets the linear regression criteria of r2>0.8.
It would have been better to have more observations (field data) to
test the model.
All three models become more powerful (in the statistical sense) as
n→30 data points.
1.4 ENVIRONMENTAL MODELING AND ECOTOXICOLOGY
Environmental modeling is the attempt to understand better the fate of
chemicals in our environment and the role of humans in those chemical cycles.
We are impacting larger and larger domains: oceans, not just coastal waters;
the stratosphere, not just urban air; deep groundwater aquifers, not just
In industrialized nations, the anthropogenic energy flow per unit area exceeds
photosynthesis by a factor of about 10.
Despite intensive research, we only partially understand how chemical
pollutants move between atmosphere, land, and water and what
transformations they undergo during transport. .
Some 1000-1500 new chemicals are manufactured each year with perhaps
60,000 chemicals in daily use (mostly organic chemicals). Table 1.2: list of some
priority pollutants with their various transformation reactions.
We have made progress during the past ten years at predicting rates of
reaction and partitioning. However, less progress has been made on predicting
Heavy metal pollutants are pervasive and, perhaps, are a greater problem than
organic chemicals based on their persistence .
Generally human activities cause elevated concentrations of metals (Figure
Figure 1.5 Periodic table and average
Phosphate, nitrate, and ammonium are nonpoint source problems from
agricultural runoff that continue to cause the eutrophication of surface
waters, oxygen depletion of sediments, habitat alteration, and ecological
changes in the structure and function of the ecosystem that are often
difficult to detect, quantify, and prevent .
The ability of a trace element to pose an environmental hazard depends
not only on its enrichment in the atmosphere or hydrosphere but also
on its chemical speciation (form of occurrence) and the details of its
biochemical cycling. Bioavailability and toxicity depend strongly on the
chemical species. For algae and lower organisms, the free metal aquo
ions often determine the physiological and ecological response .
At present the open ocean and many lakes are more affected by
pollution impacts through tropospheric transport than through riverine
transport. Elements are termed atmophile when their mass transport to
the sea is greater from the atmosphere than from transport by streams.
This is the case for Cd, Hg, As, Se, Cu, Zn, Sn, and Pb. Atmophile
elements are either volatile, or their oxides or other compounds have
low boiling points.
The elements Hg, As, Se, Sn, and perhaps Pb can also become
methylated and are released in gaseous form into the atmosphere. The
elements Al, Ti, Mn, Co, Cr, V and Ni are termed lithophiles because
their mass transport to the ocean occurs primarily by streams.
Soft Lewis acids, metals such as Cu+, Ag+, Cd2+, Zn2+, Hg2+, and Pb2+, and the
transition metal cations (Mn2+, Fe2+, Ni2+, Cu2+) are of environmental concern, both
from a point of view of anthropogenic emissions as well as hazard to ecosystems and
human health (chemical reactivity with biomolecules) . Considering the schematic
reaction, Igneous rock + Volatile substances = Air + Seawater + Sediments
Volatiles such as H2O, CO2, HCl, and SO2, that have been emitted from volcanos
after being leaked from the interior of the earth, have reacted in a gigantic acid-base
reaction with the bases of the rocks. On the global average, the environment with
regard to a proton and electron balance is in a stationary situation, which reflects the
present-day atmosphere (20.9% O2, 0.03% CO2, 79.1% N2), an ocean pH of～8, and
a redox potential corresponding to a partial pressure of O2 equal to 0.21 atm.
The weathering cycle is affected markedly at least locally and regionally by our
civilization. In local environments H+ and e- balances may become upset and
significant variations in pH occur.
The reactions of the oxidation of C, S, and N exceed reduction reactions in these
elemental cycles. A net production of hydrogen ions (acids) in atmospheric
precipitation is a necessary consequence. Many mere potential atmospheric
pollutants (photooxidants, polycyclic aromatic hydrocarbons smog particles, etc.) are
formed under the influence of photochemically induced interactions with OH
radicals, H2O2, ozone, and hydrocarbons with fossil fuel combustion products.
The atmosphere has become an important conveyor belt for many potential aquatic
pollutants. Many persistent pollutants are present in a vapor phase during transport
from land to fresh water and from continent to ocean. These substances include
many pesticides, such as DDT, more volatile metals (Hg), metalloids (As, Se), or their
compounds. At present the open ocean is probably more affected by metal pollution
inputs through tropospheric transport than through rival transport (Pb).
Figure 1.6 Comparison of global reservoirs
The reservoirs of atmosphere, surface fresh waters. and living biomass are
significantly smaller than the reservoirs of sediment and marine waters. The total
groundwater reservoir may be twice that of fresh water. However, groundwater is
much less accessible.
In Figure 1.6 the sizes of the various reservoirs, measured in number of molecules
or atoms, are compared. The mean residence time of the molecules in these
reservoirs is also indicated. The smaller the relative reservoir size and residence
time, the more sensitive the reservoir toward perturbation.
Obviously, the atmosphere, living biomass (mostly forests), and ground and
surface fresh waters are most sensitive to perturbation. The anthropogenic
exploitation of the larger sedimentary organic carbon reservoir (fossil fuels and
by-products of their combustion such as oxides and heavy metals and the
synthetic chemicals derived from organic carbon) can above all affect the small
The living biomass (Figure 1.6) is a relatively small reservoir and thus subject to
human interference; each species forming the biosphere requires specific
environmental conditions far sustenance and survival.
Transport of pollutants from air to water and from land to water have become
increasingly important pathways for the occurrence of water pollution (Figure
1.7). Degradation of groundwater from soil pollution is a major environmental
problem (c.g., infiltration of pesticides from agricultural applications or leachate
from hazardous waste landfills). Also, impacts of acid deposition on surface
waters and oxidants on forests and soils illustrate the importance of transport
through the airwater interface. We need to know about the aquatic chemistry of
these pollutants to estimate their speciation and fete in the environment, and we
need to know how to construct and solve mathematical models (mass balance
equations) to calculate simultaneously their transport and transformations.
Figure 1.7 Path of a pollutant through the environment
The distribution of a
pollutant in the
dependent on its specific
properties. Of particular
ecological relevance is fat
solubility or lipophilicity,
as lipophilic substances
accumulate in organisms
and the food chain.
residence time and
Figure 1.8 Transfer and transformation of pollutants in aquatic ecosystems
diluted. It can
the water by
particles or by
may also be
Figure 1.8: synopsis of the perspectives of aquatic ecotoxicology. Let us follow the
various steps from the source to the potential ecological effects of a pollutant
released into an aquatic ecosystem. The emission is measured as a flow or Input
load (capacity factor; mass per unit time or mass per unit time and volume or
area). The resulting concentration is a consequence of the dilution, transport, and
transformation of this chemical. At any point, the water condition is
characterized by the interacting physical, chemical, and biological factors.
The ecological damage of a substance depends on its interaction with organisms
or with communities of organisms (Figure 1.8). The intensity of this interaction
depends on the specific structure and activity of the substance under
consideration, but other factors such as temperature, turbulence, and the
presence of other substances are also important.
An understanding of the interaction of chemical compounds in the natural
system hinges on the recognition of the compositional complexity of the
environment requires analytical methodology: ability to predict individual
components selectively, measure them, forecast their fate. Table 1.3 lists water
quality criteria toxicity thresholds, carcinogenicity, and maximum contaminant
levels (M.C.L.) for many toxic chemicals discharged to natural waters.
Water quality criteria are the best scientific information from toxicological
studies of the maximum concentration allowable that will not cause an
observable biological effect. As ecotoxicology becomes more sophisticated as a
science, the list of chemicals will grow and species specific criteria will be
promulgated under various environmental conditions.