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UNC-Chapel Hill GEOG 110 - Modeling of Environmental Systems

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David Tenenbaum – GEOG 110 – UNC-CH Fall 2005Modeling of Environmental Systems• While the modeling of predator-prey dynamics is certainly simulating an environmental system, there is more to the environment than just organisms• Recall our definition of ecosystems:– The minimal systems on Earth that exhibit a flow of energy and a complete chemical cycling are composed of at least several interacting populations and their non-biological environment• Typically, Geography does not focus upon the populations of organisms, but studies the flows of energy and matter (including water and nutrients) in that non-biological environmentDavid Tenenbaum – GEOG 110 – UNC-CH Fall 2005Modeling of Environmental Systems• The next portion of this course will examine the balance / flows / cycling of three quantities that are present in ecosystems:– Energy– Water–Nutrients• We will look at each of these at two scales:– Global– Ecosystem• Before we can build models of these phenomena, we need to have some background on the functioning of these systems with respect to these quantitiesDavid Tenenbaum – GEOG 110 – UNC-CH Fall 2005The Global Energy Balance•We will begin with energy, because energy is the most fundamental quantity required for an ecosystem: We can think of energy as the ‘universal currency’ of ecosystems• All ecosystem processes are driven by energy, and if we trace the energy back to its source, it ultimately originates at the Sun (i.e. the Sun emits electro-magnetic radiation, some of which reaches the Earth)• Thus to understand the limitations on ecosystem activity on Earth, we must first quantify the amount of energy that the Sun emits, which can be understood in terms of three radiation lawsDavid Tenenbaum – GEOG 110 – UNC-CH Fall 2005Electromagnetic radiation energy: Wave-particle dualityparticleWavelength (λ)• EMR energy moves at the speed of light (c): c = f λ• f = frequency: The number of waves passing through a point within a unit time (usually expressed per second)• Energy carried by a photon: ε = h f [h=Planck constant (6.626×10-34Js)]• The shorter the wavelength, the higher the frequency, and the more energy a photon carries. Therefore, short wave ultraviolet solar radiation is very destructive (sunburns)Solar RadiationDavid Tenenbaum – GEOG 110 – UNC-CH Fall 20051. Planck’s Law• Planck’s Law describes the amount of energy (technically, radiant exitance) emitted by a blackbody at a given wavelength at a certain temperature–A blackbody is an idealized object that perfectly absorbs all incident electromagnetic radiation and then re-radiates it)1(252−=KThcehcMλλλπWhere: h: Planck Constant, 6.626E-34 ws2c: speed of light in vacuum 3.0E+8 m/sλ: wavelength in metersT: temperature in degrees KelvinK: Boltzman constant, 1.38054E-23 ws/KMλ: blackbody spectral exitance at T• Provided you know the temperature of the object, you can calculate the amount of energy emitted at a certain wavelength, i.e. for the Sun and the EarthDavid Tenenbaum – GEOG 110 – UNC-CH Fall 2005Electromagnetic SpectraThe atmosphere blocks much of the energy before it reaches the surface• We can use Planck’s Law to calculate both how the Sun provides energy to the Earth, and how Earth materials emit energy as they are cooling offDavid Tenenbaum – GEOG 110 – UNC-CH Fall 20052. Stefan-Boltzmann Law• Planck’s equation provides the spectral exitance for a blackbody at a given temperature and wavelength• Integrating Planck’s equation over the entire spectrum yields the Stefan-Boltzmann equation, which gives the total amount of energy emitted by a blackbody at a given temperature:41520)1(2 TdehcdMMKThcσλλπλλλ=−==−−∞∫Where σ: Stefan-Boltzmann constant (5.676E-8wm-2K-4)T: Temperature in degrees Kelvin• Given the temperature, we know how much energy a blackbody will emitDavid Tenenbaum – GEOG 110 – UNC-CH Fall 20053. Wien’s Displacement Law• From Planck’s equation, we can also derive a law that provides an easy means of finding the wavelengthwhere a blackbody emits the greatest radiation• We can do this by taking the first derivative with respect to wavelength and setting it equal to zero to find the wavelength of maximum emission (graphically this is equivalent to finding where the slope of the curve is horizontal):λmaxTAddM=⇒=max 0λλλWhere A: 2.798×10-3mKDavid Tenenbaum – GEOG 110 – UNC-CH Fall 20053. Wien’s Displacement Law• Wien’s Displacement law states that the wavelength at which the spectral exitance has its maximum value is inversely related to the temperature• According to Wien’s law, the wavelength at which the Sun emits the most energy is 0.485 µm, a value within the 0.4-0.7 µm visible light range. • Visible light is the light that we can see, and plants can use in photosynthesis• Thus, light within the wavelength range of 0.4-0.7 µm is also called photosynthetically active radiation (or PAR) Æ If we want to model plant growth we need to know how much PAR is available for photosynthesisDavid Tenenbaum – GEOG 110 – UNC-CH Fall 2005Important Concepts for Calculating Energy Received by the Earth• Radiance: Refers to the amount of radiant energy coming from a given direction to a unit area of surface perpendicular to the direction of ray, measured as watts/m2/sr (a two-dimensional solid angle)• Irradiance: Refers to the total amount of radiant energy received on a unit area of surface (from all angles), measured as watts/m2• Insolation: The irradiance of a unit horizontal area, measured as watts/m2(As has been the case with all of our models, we need to define quantities precisely, if we want the model to produce results that are predictively accurate)David Tenenbaum – GEOG 110 – UNC-CH Fall 2005Energy Received by the Earth• Before solar radiation reaches the Earth’s surface, a portion of the radiation will be reflected back into space, and a portion will be absorbed by the atmosphere• Overall, only about half of the total radiation at the top of the atmosphere will reach the Earth’s surface• The amount of solar radiation at the top of the atmosphere is the solar constant (~1360 w/m2), and this quantity is reasonably stable over the time scales we are interested in studying (2-3% variation seasonally)• When the solar radiation arrives at the Earth’s surface, a portion of it will be reflected back


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UNC-Chapel Hill GEOG 110 - Modeling of Environmental Systems

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