Types of Water Pollution • We can classify types of pollution in a few different ways: • Source – We can distinguish between point source pollution, where the origin of the material can be identified and measures can be taken, and non-point source pollution, where there is no singular source of the pollution, usually because the material originates throughout the landscape • Ecological Impacts – We can group pollutants based on how they effect the ecosystem, e.g. pollutants that lower dissolved oxygen content vs. pollutants that mimic estrogenic compounds etc. David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Types of Water Pollution • General Types – We can group pollutants based on the nature of the material (or energy) in question: 1. Heat (thermal) pollution – As we heat the water (either by returning heated water to the system directly, or indirectly), the solubility of dissolved oxygen in the water is decreased 2. Silt & Sediment – Erosion of soils from a variety of activities increases turbidity, which decreases light penetration, decreasing photosynthesis in aquatic plants, which lowers the dissolved oxygen content 3. Nutrients – Through careless fertilizer use, increased N and P can boost algal growth, again blocking light penetration etc.

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Types of Water Pollution 4. Organic Wastes – When we add organic material to wastewater effluent, it can decompose in the water and reduce dissolved oxygen content 5. Microorganisms – Also associated with organic material, these can transmit infectious disease 6. Acids – Whether through acid precipitation or industrial effluent (including mining), by changing the pH of surface waters we can create conditions where some key organisms in an ecosystem cannot survive 7. Various chemicals – Any number of toxic compounds, such as heavy metals, organochloranes etc., sources from pesticides and industrial discharges can be damaging to organisms

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Dissolved Oxygen • The concentration of dissolved oxygen (DO) in fresh water is a particularly important criterion of water quality, because most aquatic life depends on a certain amount of oxygen being present • A few processes can reduce the DO content of water: 1. Dumping organic waste in the water provides organic carbon compounds in the presence of DO and various decomposers, thus organic waste + O2 Æ CO2 + H20 + various compounds 2. Aquatic plants photosynthesize and provide the DO, but excessive algal growth due to nutrients slows this 3. Some aquatic organisms use the DO (e.g. fish etc.) David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Henry’s Law • In order to model the dissolved oxygen content in an aquatic ecosystem, we first need to understand the physical law that determines how much dissolved oxygen the water can hold • The amount of DO that water can hold is a function of Henry’s constant and partial pressures, based on Henry’s Law: CO2 = KO2 * PO2 where:

CO2

is the concentration of DO in H2O (mg/L)

PO2

is the partial pressure of O2 at the atmosphere – water boundary (atm) is Henry’s Constant which varies inversely with temperature (mg/L*atm)

KO2

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Biochemical Oxygen Demand • From our previous listing of processes that diminish the DO in an aquatic system, we know that adding organic waste can reduce DO levels through the decomposition of that waste • The amount of oxygen required to decompose a certain amount of waste is its biochemical oxygen demand (BOD), and like DO is measured in concentration units (such as mg/L) • BOD is a useful way to describe the general water quality of a sample because it indirectly measures the amount of organic waste present in the water • Ultimate BOD (BODult) is used to describe the total amount of DO required to oxidize all the organic waste

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Processes and Model Structure • We will model the resulting DO concentration in the river using a two-step approach: 1. We will establish initial values of DO and BOD immediately after the river water and effluent are mixed using a mass-balance approach 2. We will predict the expected downstream DO levels, taking into account some processes that will occur as the water moves downstream that change the DO: • Reoxygenation (or aeration) will absorb O2 from the atmosphere as the water moves downstream • Deoxygenation will consume DO in the river through the consumption of the organic waste David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Initial Stage: River and Effluent Mixing DOa = (DOsVs + DOpVp) / (Vs + Vp) where:

DOa DOs Vs DOp Vp

is the DO conc. in the mixed water (mg/L) is the DO conc. in the river water (mg/L) is the volume of river water before mixing (L) is the dissolved oxygen concentration in the effluent (mg/L) is the volume of effluent (L)

• For flowing water, we can use flow rates (Q in L/sec) instead of volumes, yielding: DOa = (DOsQs + DOpQp) / (Qs + Qp)

• We can apply the very same mass-balance principles to calculate the BOD values immediately after mixing the river water and the effluent

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Predicting Downstream DO Levels Outflows Inflows •BOD (and linked •Organic material enters the river Biochemical Oxygen Demand DO) is consumed by decomposition naturally at a constant rate BODout(t) = k1BOD(t) BODin(t) = A

•DO is recharged by O2 from the atm. up to DOsat DOin(t) = k2[DOsat (t) – DO(t)]

Dissolved Oxygen

•DO (linked to BOD) is consumed by decomposition DOout(t) = k1BOD(t) David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Predicting Downstream DO Levels – Steady-State Conditions BOD =

A k1

DO = DOsat - A k2

• Note that the DO level will never reach DOsat as long as there is some BOD naturally entering the system at rate A, as is usually the case • However, if the reoxygenation coefficient (k2) is a sufficiently large value when compared to A, then the denominator of the term is big enough to make the overall term quite small, which results in the steadystate condition for the DO reservoir only being slightly smaller than the DOsat value David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Greenhouse Gases and Global Warming • What are greenhouse gases (GHG) ? – Amongst the constituents of the atmosphere are some gases that have a particular property: They contribute to the Earth’s ability to retain energy received from the Sun – These gases include CO2, CH4, N2O, CFCs and H2O – The concentration of CO2 in the atmosphere is of particular interest because the abundance of this gas in the atmosphere has increased substantially of late through human activity

• What is global warming? – Modeling results indicate an average temperature increase for the Earth over time, with an estimated increase of 2-5 degrees C by 2050 – This does not imply warming everywhere (thus global climate change is a valid term as well), but it does imply warming on average

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

The Earth’s Portion of Solar Power • When it comes to the Earth’s share of that energy, we have to consider that the solid angle that describes the radiation emitted by the Sun that the Earth will receive is only a small portion of the total: The Sun @ 5780K P = 3.9 x 1026 watts

R = 149,597,870,660 meters (= 1 AU)

Energy flux emitted at a given distance (R) can be calculated using a sphere w/ area = 4πR2

The Earth

Given the Sun’s power calculated using Stefan-Boltzmann, and the area of a sphere of radiation at distance R, we can figure out the energy flux from the Sun at that distance David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

The Earth’s Profile • The Earth can intercept the Sun’s energy flux over an area equal to a circle with a radius equivalent to the Earth’s radius (r):

r

Solar Radiation

r

The Earth w/ radius (r)

We could then use this information to estimate the amount of energy the Earth will receive from solar radiation

Shadow circle of area ~ πr2 David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Average Earth Temperature • Using the steady-state derived energy balance for ΩE and the Stefan-Boltzmann equation (assuming the Earth radiates as a black body, which it nearly does), we can come up with the expected average temperature on the surface of the Earth: ΩE = σT4

T4

ΩE = σ

ΩE T= σ

1/4

(1 - a)ΩS T= σ

1/4

• Using a = 0.31 and ΩS = 343 W/m2 in this equation, we would calculate an expected average earth surface temperature of 255 degrees K, which is –18 degrees C • This is considerably colder than the observed average temperature of about 15 degrees C • Where did we go wrong?

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Atmospheric Gases and Photons • High energy (a.k.a. UV or shortwave) photons are capable of breaking the bonds of some gas molecules: After

Before High energy

-

Photon

+ Atmospheric Gas Molecule

Ions

• Low energy (a.k.a. infrared or longwave) photons have a very different effect on these gas molecules: Low energy Photon Atmospheric Gas Molecule

The bond vibrates

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Conceptual Diagram for the System Sun (7)

(1)

(2)

Atmosphere

(8) (3)

(5) (6)

(4) Earth

(1) Reflected solar flux (2) Solar flux absorbed by atm. (3) Solar flux absorbed by Earth (4) LE and S transfer from Earth to atmosphere (5) Earth radiated flux absorbed by atmosphere (6) Atmospheric radiated flux absorbed by Earth (7) Atmospheric radiated flux radiated towards space (8) Earth radiated flux radiated to space David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Components of a Model

Nix, S.J. 1994. Urban Stormwater Modeling and Simulation. Lewis Publishers, U.S.A., p. 23.

Mathematical models have three basic components: The input data, the algorithmic portion that does the modeling, and outputs that describe the results David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Spatial Ecosystem Modeling with GIS • However, the discipline of Geography is equally interested (or perhaps more interested) in the change of phenomena (in ecosystems or other contexts) in space • Thus, the STELLA-style approach we have used so far in this course ignores some key aspects of describing ecosystems which are popular with geographers: – Phenomena work differently in different locations – We can better understand those phenomena and the underlying processes that make them function by describing them in terms of their distribution in space (mapping) – We can subdivide ecosystems into smaller units and study each in isolation to figure out how things are working – We can model the interactions between the smaller units David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Lumped vs. Distributed Models • We can distinguish between two types of models: • Lumped Models – These are the sorts of STELLA models we have used so far in this course – They represent inputs and responses in terms of the dimensions of time and whatever is being modeled (issues of location and associated dimensions of length, area and volume are often absent) – No account is taken of variation within the entity being modeled: It is assumed to be homogenous and wellmixed, i.e. Suppose we were running the model from Lab 5 for a particular forest stand. Even though there are likely various types of trees, canopy heights and densities, variations in soil etc. we model that forest stand using a single LAI and K, and with uniform soil characteristics etc. David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Lumped vs. Distributed Models • Distributed Models – These sorts of models take the variation of phenomena in space into account in their model structure – Both inputs and responses have a spatial aspect to them, i.e. mapped information is required as part of the input, and the output includes spatial pattern information – Distributed models are thus very useful when it comes to representing and studying variation. While the modeled sub-units still usually use the assumptions of homogeneity and being well-mixed, the units’ size and shape are adjusted to make these assumptions as reasonable as possible, i.e. Perhaps the forest stand we are modeling consists of 2 or 3 distinctly different sub-units, each with distinct species, and canopy and soil characteristics. We could then model each of these sub-units with its own parameters. David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Representing the Real World w/ Models • The figure to the left depicts a hierarchy for (spatial) models of knowledge about the real world • This set of spatial models includes a few sorts of spatial representations that can be used in conjunction with RHESSys

Maidment, D.R. 1993. GIS and Hydrologic Modeling. In Goodchild, M.F., B.O. Parks, and L.T. Steyeart (Eds.). Environmental Modeling and GIS, Oxford University Press, New York, p. 157.

• In the case of our STELLA models, issues of location and spatial arrangement have been unimportant, so it was possible to skip directly from the Real World to a semantic model David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

How Does RHESSys Represent the Landscape? • It models processes at spatial and temporal scales which efficiently and effectively represent landscape heterogeneity: – Temporal - Through time step iterations of processes in the model execution (some processes are computed daily, while others are computed hourly since the hourly variation makes a difference, and reaggregated to a daily time step) – Spatial - Through a landscape representation that enforces hierarchically contained object partitions, meaning that the entire watershed’s extent is broken up into a set of basins, each basin is broken up into a set of zones, etc.

• Different processes are simulated using objects at different levels in the hierarchy David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Landscape Representation through Object Partitioning • RHESSys divides the landscape into a series of successively contained partitions:

1)

2) The method for creating a partition is determined by the processes it will represent

3) Once landscape objects in a partition are defined, parameters at that level are determined David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

What is a Model? • Just what are we talking about when we use the word model here? • There are a wide range of possible definitions, but here is a simple description that suits our purposes: – “A model can be thought of as a means of codifying how a set of processes functions, simplifying the complexity of the real world in which the processes operate.” Anderson, M.G. and T.P. Burt. 1985. Modelling Strategies. In Anderson, M.G. and T.P. Burt (Eds.), Hydrological Forecasting, John Wiley and Sons, Great Britain, 1-13.

• At the mention of the word ‘model’ you might think of computer software, or a particular STELLA file, but the model itself is the idea encoded therein, a particular representation of how something works David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Modeling in Env. Science – Synthesis & Integration 1

Observation of nature (Context: Current scientific theories and social values)

2

Form some inferences about how we think things work

3

Create a model that relates the Inferences in order to explain the observations

• One way we use models is to take our observations and expectations, and synthesize and integrate them to create a formal, coherent expression of how we think a particular system functions • Quite often in science, this is done mathematically, with some objective (statistical) criterion establish and used to see if our idea can be easily dismissed David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Modeling in Env. Science – Prediction and Forecasting

• Once we have a built a model, tested it, and decided that it is satisfactory for some purpose (i.e. possessing sufficient structural and predictive validity), we can make use of it in a few ways • The emphasis in this course has been from a problem solving point of view: Identify an environmental issue, build a model of how the system will function under a range of conditions, and use model output to help us understand what is likely to happen. We can view this problem solving process as a multi-stage linear process:

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Uncertainty, Error, and Sensitivity • We need to be able to estimate uncertainty and error associated with our input data, as errors that are present in our representation of reality are likely to result in errors in our output • We also need to be able to estimate error and sensitivity in our models’ computation: Some parameters in our model can be very sensitive to error (this is one reason we perform sensitivity analysis), such that a small change in the value input to a model can potentially result in a large error in the output

David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Precision and Accuracy •These related concepts are often confused: •Precision refers to the exactness associated with a measurement (i.e. closely clustered) •Accuracy refers to the extent of systematic bias in the measurement process (i.e. centered on the middle) x x

x

x

x x

x x

Precise & Accurate

x

x x

Precise & Inaccurate

x x

x x

Imprecise & Accurate

x

x x x

x

Imprecise & Inaccurate David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Error Propagation in our Models • When we use our input data in our model, we often combine data to produce output (through the calculation of what is in the stocks at the end of each time step in the case of using STELLA) • In order to estimate the error in the output we must combine the input errors in some fashion • Error propagation addresses the effects of errors and uncertainty on the results of modeling • Almost every input to a model is subject to error and uncertainty and in principle, every output should have confidence limits or some other expression of uncertainty that reflects the error in the analysis output David Tenenbaum – GEOG 110 – UNC-CH Fall 2005

Simplicity vs. Complexity in our Models • The difficulties associated with error propagation in complex models is amongst the reasons that we strive to make simple models – “Models should be made as simple as possible, but not simpler” Albert Einstein

• There are two ways to construct a model: 1. Make the model so simple that there are obviously no deficiencies 2. Make the model so complex that there are no obvious deficiencies • While simplicity is the more desirable approach, it is also the more difficult; we aim for parsimony David Tenenbaum – GEOG 110 – UNC-CH Fall 2005