em1_eng

							Environmental System Analysis




            Kangwon National University
            College of Engineering
            Division of Geosystem and Environmental
            Engineering
            Professor Joon Hyun Kim
            010-9696-6354, 033-250-6354
Class Contents and Schedule
Environmental
Modeling

       Fate and Transport of Pollutants in Water,
       Air, and Soil
          -JERALD L. SCHNOOR
1. INTRODUCTION




       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
 pollutants?

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
   groundwater.
 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
    frequencies.
   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
    interactions.
    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
    parameters.
   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
     their reactivity

     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
          control volume.
    (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.
                           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
Figure 1.1 Generalized        across the boundaries of the control
approach for mass             volume must be known or estimated
                              (element iii).
balance models utilizing
                            A     knowledge of the chemical,
the control-volume            biological, and physical reactions that
concept and transport         the substance can undergo within the
across boundaries.            control volume (element iv) is needed.
Mass balance:




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.)
Solution:
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
  alternate site)
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,
     stoichiometric ratios).
    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
    techniques.
    Statistical Analysis

    Statistical "goodness of fit" criteria using chi-square or Kolmogorov-
     Smirnov 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.
    Model Verification

    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
     calibration.
    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
Hypothetical Stream
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
Figure 1.4.
Determine if the model calibration is acceptable according to the following
statistical criteria:
a. Chi-square goodness of fit at a 0.10 significance level (a 90% confidence
level).
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 chi-
square 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
= 0.10.
The table below shows that 0.1254≤4.17. Therefore the model passes the
goodness of fit test at a 0.10 significance level.
  Paired T-Test



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
    surface waters.
   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
    biotransformation.
   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
    1.5).
Table 1.2
Priority Organic
Chemicals and
Their Reactions




Significant
reactions for
selected priority
pollutant organic
chemicals in
natural waters
Figure 1.5 Periodic table and average
freshwater concentration
   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
    reservoirs.
   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
environment is
dependent on its specific
properties. Of particular
ecological relevance is fat
solubility or lipophilicity,
as lipophilic substances
accumulate in organisms
and the food chain.
Biodegradation and
chemical or
photochemical
decomposition decrease
residence time and
residual concentrations.
Figure 1.8 Transfer and transformation of pollutants in aquatic ecosystems

A substance
introduced into
the system
becomes
dispersed
diluted. It can
become
eliminated firm
the water by
adsorption on
particles or by
volatilization. It
may also be
transformed
chemically or
biologically.
   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.