Modeling of Environmental Systems

Transcription

1 Modeling 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 environment

2 Modeling 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 quantities

3 The 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 electromagnetic 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 laws

4 Solar Radiation Electromagnetic radiation energy: Wave-particle duality Wavelength (λ) particle 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 ( Js)] 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)

5 1. 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 M λ = λ 5 ( e hc λkt 2 2πhc Where: h: Planck Constant, 6.626E-34 ws2 1) c: speed of light in vacuum 3.0E+8 m/s λ: wavelength in meters T: temperature in degrees Kelvin K: Boltzman constant, E-23 ws/k M λ : 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 Earth

6 Electromagnetic Spectra The 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 off

7 2. 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: M = Where 0 M hc dλ 2πhc λ λkt ( e 1) dλ σ λ = = T σ: Stefan-Boltzmann constant (5.676E -8 wm-2k-4) T: Temperature in degrees Kelvin Given the temperature, we know how much energy a blackbody will emit 4

8 3. Wien s Displacement Law From Planck s equation, we can also derive a law that provides an easy means of finding the wavelength where 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): λ max dm dλ λ = 0 λmax = A T Where A: mk

9 3. 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 µm, a value within the 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 µm is also called photosynthetically active radiation (or PAR) If we want to model plant growth we need to know how much PAR is available for photosynthesis

10 Important 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/m 2 /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/m 2 Insolation: The irradiance of a unit horizontal area, measured as watts/m 2 (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)

11 Energy 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/m 2 ), 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 into space

12 Energy Received by the Earth The Earth is also emitting energy according to the Stefan-Boltzmann law, and the atmosphere is doing the same thing, and some of the radiation being emitted by the atmosphere is being received by the Earth s surface and vice-versa Because the temperature of the Earth and atmosphere is much lower than that of the Sun, the radiation emitted from them is much longer in wavelength, thus we call it longwave radiation The difference between the outgoing longwave radiation emitted by the earth and the incoming longwave radiation from the atmosphere is called effective longwave radiation

13 Energy Received by the Earth Gates, D.M Biophysical Ecology. Springer-Verlag, Berlin and New York.

14 The Radiation Balance Equation We can describe the net radiation received by the Earth using the Radiation Balance Equation: R n = S 0 (1.0-α) + L n Where: S 0 : Shortwave radiation from the Sun α: Albedo (describing reflected rad n) L n : Net longwave radiation If R n > 0, net gain of energy (daytime, summer) R n < 0, net loss of energy (nighttime, winter) R n = 0, then we have a steady-state condition Although this is a very simple equation, it explains much of what happens in Earth s ecosystems

15 Partitioning Net Radiation After the Earth s surface receives R n radiative energy, the energy is used in the following ways: A portion of it will be used to evaporate or transpirate water from the liquid state to the gaseous state. This is called latent heat (LE) as the energy will be released when the gaseous water changes back to liquid state A portion of it will be used to heat the atmosphere, which is called sensible heat (H) A portion of it will pass through the Earth s surface to heat the soil below (Q) A small fraction of the energy is used by leaves for photosynthesis and this energy is stored in the chemical bonds of carbohydrate produced by photosynthesis (A)

16 The Energy Balance Equation We can describe the way the net radiation received by the Earth s surface is partitioned using the Energy Balance Equation: R n = LE + H + Q + A Where: LE: Latent heat H: Sensible heat Q: Energy stored in the soil A: Energy stored in photosynthate How R n is distributed among the items on the right hand side is determined by the ecosystem biophysical characteristics and has major consequences for ecosystem development and functions

17 The Radiation Budget for Earth Modified from MacCracken, M.C Carbon dioxide and climate change: Background and overview, pp In M.C. MacCracken and F.M. Luther (Eds.), Projecting the Climatic Effects of Increasing Carbon Dioxide. U.S. DOE, Er-0237, Washington, DC.

18 Energy Fluxes Change Over Time Hornberger et al Elements of Physical Hydrology. The Johns Hopkins University Press, Baltimore and London.