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Environmental Modeling

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Scope1) Introduction2) Transport Phenomena3) Chemical Reaction Kinetics4) Equilibrium Chemical Modeling5) Goundwater Contaminants6) Eutrophication of Lakes7) Conventional Pollutants in River8) Toxic Organic Chemicals9) Modeling Trace Metals10) Atmospheric Deposition11) Global Change and Global Cycles

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Introduction

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Scope on Environmental Modeling

• To gain understanding of the fate and transport of chemical by quantifying their reactions, speciation and movement

• To determine chemical exposure concentrations to aquatics organism and/or humans in the past, present or future,

• To predict future conditions under various loading scenarios or management action alternatives

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Where do all chemicals go?

• Are they with us forever?• How rapidly are they degraded?• Example: the fate, transport and

persistence of chemical in the environment.

• Models for conventional pollutants, eutrophication, toxic organic chemicals and metals in surface water.

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Mathematical Models

• To determine chemical exposure concentrations

• To assess the effects of chemical pollutants

• For waste load allocations, risk assessment, or environmental impact assessments.

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Water quality criteria

• Aquatic organisms and their uses should not be affected unacceptably if two conditions are met:– The 4-day average concentration of the toxicants

does not exceed the recommended chronic criterion more than once every three years on the average

– The 1-hour average concentration does not exceed the recommended acute criterion more than once every three years on the average.

• The models can be developed for frequency-duration relationships of pollutant exposure.

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Environmental models

• To predict the future chemical concentrations under various scenarios or management action alternatives.

• Principle of continuity: matter is neither created or destroyed in macroscopic chemical, physical and biological interaction = mass balance

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Mass Balances• Water quality = something inherent or distinctive

about water• Distinctive (quality) parameters = chemical,

physical and biological parameters, mostly in mass quatitaties or concentration unit (mg, mg L-1, moles L-1)

• The fate of chemicals in aquatic environment:– Reactivity– Rate of their physical transport through the environment

• Mathematical model == accounting procedures

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Key elements in a mass balance:

• A clearly defined control volume• A knowledge of inputs and outputs that

cross the boundary of the control volume• A knowledge of the transport

characterisitics within the control volume and accros its boundaries

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Control Volume

• The boundaries are clearly define with respect to their location, so that :i. the volume is known and ii. mass fluxes across the boundaries can be

determinediii. Transport accross the boundaries of the control

volume must be known or estimated.iv. A knowledge of chemical, biological and

physical reactions that the substance can undergo within the control volume is needed.

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accumulation

If the system is at steady state = no change in concentration with respect to time = dC/dt = 0

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Change in storage• The accumulation of mass of water = water balance

• Inflows = volumetric inputs of tributaries and overland flow

• Outflows = all discharges from the water body• Direct precipitation = the water that falls directly on

the surface• Evaporation = the volume of the water that leaves

the surface of the water body to the atmosphere

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• If the lake or stream basin is not sufficiently “tight” with respect to inputs and outflows to groudwater, the piezometric surface of the groundwater adjacent to the water body must also be measured:

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Water budget

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Model Calibration and Verification

• To perform mathematical model, four ingredients are necessary:– Field data on chemical and mass discharge

inputs– A mathematical model formulation– Rate constants and equilibrium coefficients for

the mathematical model– Some performance criteria with which to judge

the model

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Requires two sets of field data

• For model calibration: compare between simulation result and field measurements

• For model verification: from different circumstances (a different year or an alternate site)

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Model Calibration

• Statistical comparison between model results for the state variations (chemical concentrations) and field measurements.– If errors are acceptable model calibrated.– If error are not acceptable tune the model

(constants and coefficients) obtain acceptable simulation model calibrated

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definitions• Mathematical model= a quantitative formulation of

chemical, physical and biological processes that simulates the system

• State variable = the dependent variable that is being modeled (usually a chemical concentration)

• Model parameter= coefficients in the model that are used to formulate the mass balance equation (rate constants, equilibrium constants, stoichiometric ratios, etc.)

• Model inputs = forcing functions or constants required to run the model (e.g. Flowrate, input chemical concentrations, temperature, sunlight)

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• Calibration = a statistically acceptable comparison between model results and field measurements, adjustment of model parameters is allowed within the range of experimentally determined values reported in the literature.

• Verification = a suitably acceptable comparison between model results and a second (independent) set of field data for another year or at an alternate site; model parameter are fixed and no further adjustment is allowed after the calibration step

• Simulation= use the model with any input data set (even hypothetical input) and not requiring calibration or verification with field data.

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• Validation = scientific acceptance that – (1) the model includes all major and salient

process, – (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 prediction to future field measurement at that time

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• Sensitivity analysis = determination of the effect of a small change in model parameter 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.

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Criterion for acceptance• Example: the prediction of dissolve oxygen concentration in the

stream should be within + 0.5 mg L-1 in at least 90% of the observations.

• Statistical “goodness fit” using chi-square or Kolmogorov-Smirnov tests.

• Paired t-test of model results and field measurement at the same time

• Linear regression of paired data for model prediction and field observation at the same time

• A comparison of model results to field observation and their standard deviation

• Parameter estimation techniques such as nonlinier curve-fitting regression

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Environmental Modeling and Ecotoxicology

• The role of human in the chemical cycles:– The antopogenic energy flow per unit area > 10 times

photosynthesis– Organic chemicals produced by industry = 150 kg capita-1

year-1 or 40 g m-2 year-1.• Impacted domain:

– Oceans– Stratosphere– Deep groundwater aquifiers

• 1000-1500 new chemical manufactured each year• 60,000 chemical in daily use, mostly organic chemicals

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Predicting rates of reaction and partitioning

• Four parameters for prediction rate constants for many compounds:– Octanol/water partition coefficients– Henry’s law constant– Dissociation constant– Sorption spectrum

• Reactions:– Hydrolisis– Photodegradation– Volatilization– Sorption– bioconcentration

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Heavy metal pollutants

• Pervasive and a greater problem than organic chemical based on their persistence.

• Water quality criteria can be violated by natural condition, such as Ra-226 and Ba in drinking water, and cope in clod-water fisheries.

• Human acitivities elevate metal concentration: – Hg, Pb, Cd, Cu and Zn in surface waters, – As and Se from agricultural soils– Phosphate, nitrate and ammonium from agricultural

runoff

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Trace elements pollutants

• Enrichment in the atmosphere or hydrosphere

• Its chemical speciation• Its biochemical cycling

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Atmospheric transport

• Open ocean and lakes are more affected by pollution impacts through tropospheric than through riverine transport

• Atmophile elements = their mass transport to the sea is greater from the atmosphere than from transport by streams.

• Example = Cd, Hg, As, Se, Cu, Zn, Sn and Pb.• Atmophile elements=

– Volatile or low boiling points– Methylated Hd, As, Se, Sn or Pb.

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Lithophile

• Transported by stream= Al, Ti, Mn, Co, Cr, V and Ni.

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• Volatiles = H2O, CO2, HCl, SO2 from volcanos

• Gigantic acid-base reaction with bases of the rocks (silicates, carbonates, oxides)

• Produce a stationary situation: 20.9% O2, 0.03% CO2, 79.1% N2, ocean pH ~8.