MODELLING AND CONTROL OF ENVIRONMENTAL SYSTEMS A.A

Transcription

1 Università di Padova SECOND CYCLE DEGREE PROGRAMME (MSC LEVEL) IN ENVIRONMENTAL ENGINEERING MODELLING AND CONTROL OF ENVIRONMENTAL SYSTEMS A.A

2 Modelling procedure Problem definition Model conceptualization Mathematical formulation Verification Numerical formulation Sensitivity Analysis Calibration Validation

3 Validation Test of "calibrated" parameters with a set of INDEPENDENT data by a similar ecosystem the same ecosystem, but in a different period

4 Validation Always desirable Data totally different from those used to calibrate On the greatest number of possible forcings Criteria established on the basis of: Model objectives Data quality

5 Constraints ( ) Topological Physical Ecological Conservation principles Reduce the Degrees of Freedom x " = f ( x,u,p,t) f ( x,u,p,t)= ν x n =V (x,!,x ν 1 n 1 )

6 Topological Delimitation of the area (size) Boundary conditions Environment inside: secure, stable outside: stochastic and uncontrollable e.g. area / mass

7 Conservation of matter V dc dt = input output + formation trasformation Net production = Ingested food - respiration - excretion - not assomilated food Efficiency = (Net production)/(ingested food) (10-20%)

8 Energy conservation First law of thermodynamics U internal energy du= Q - W is a thermodynamic potential è Exact differential: ΔU a,b = du è holds for all transformations (reversible or irreversible) b a Equivalence heat/work: è Joules experiment è mechanical equivalent of the calories J =4186 Joule/Kcal

9 Energy conservation Energy is transformed: quantityè quality decreasing quantity sun Primary production herbivores consumers increasing quality Efficiency: 0,2% 3% 1 40%

10 Energy dissipation The arrow in time: past è future The second law of thermodynamics Spontaneous processes follow predetermined lines S, entropy: state function è S is a state function è extensive è if the state varies ds=d e S+d i S Reversible Processes ΔS a,b = b a q T è d e S = Q T è d i S 0 for spontaneus processes (= 0 reversible)

11 The second law of thermodynamics For irreversible processes irrev q T > rev q T = ΔS For an adiabatic system ( q=0), the entropy can only grow, or at most rest constant, as in the case of reversible transformations b q 0 T The entropy of the universe increases! a

12 2 nd Law and Ecosystems Far fom equilibrium systems entropy production p measures energy dissipation p = ds dt 0 The system uses all available resources to help increase high quality energy storage, thereby increasing the energy dissipation dissipated Solar energy Energy storage high quality Older systems dissipate more energy!

13 Primary Production : Energy balance E solar = E ref + PP + Respiration Higher Trophic Levels : E food = E biom + E therm/resp + E not.ass Stoichiometric ratios: e.g. Redfield Ratio, C:N:P=40:7:1 plants 19,2 kj/g algae 21,3 kj/g invertebrates 23,0 kj/g vertebrates 26,3 kj/g carbohydrates 16,7 kj/g proteins 20,9 kj/g lipids 37,6 kj/g

14 Ecological constraints Carring capacity availability of resouerces (nutrient limitation, space, ecc.) e.g. N 0 in the Logistic growth Allometric relations e.g. relationship of proportion metabolism-biomass with a 3/4 exponent (Power Law) Goal functions (Orientor) structural dynamics e.g. Energy, Entropy, Exergy, Emergy

15 Stability and Equilibrium Steady state è X, constant state function dx dt = 0 Thermodynamical Static equilibrium equilibrium (thermal death) è indistinguishable (contained) from the environment è maximum constraints disorder imposed (entropy) by the environment è p=0

16 Stability and Equilibrium Dynamic equilibrium homeostasis è p 0 è linear or nonlinear depending on the intensity of the forcings homeoresis è homeostasis Dinamic evolutionary equilibrium è high complexity è continuous or discontinuous evolutionary transitions è homeoresis

17 Stability and Equilibrium homeostasis Perturbation è cancelled at a time δt x = x +Δx homeoresis Stability, various degrees è Resistance (anaelastic stab.) è Resilience (elastic stab.) R = x Δx r = 1 δt

18 Stability and Equilibrium In ecology the Steady State x è climax A state pulsing in time t è oscillations generated by forcings (long term) è induced by elements of the food chain (e.g. consumers) Maximizing performance

19 Ecological Processes Physical (abiotic) Mass, heat flows Advection, diffusion, dispersion Sedimentation, resuspension Light extinction Chemical Chemical reactions, enzymatic, acid-base Effects of temperature Adsorption Ion Exchange Volatilization Biological Biogeochemical cycling of nutrients, oxygen,. Primary production (photosynthesis, algal growth) Secondary production (zooplankton) Fish (metabolic models) Ecotoxicology