Download Quantitative Basis, Derivatives - Modeling of Environmental Sciences | GEOG 410 and more Study notes Geography in PDF only on Docsity! I. Quantitative Basis (1) functions: polynomial functions, exponential functions, logarithmic functions, trigonometric functions: review numerical exercises (2) Derivatives: Derivatives of simple functions (C)’=0 (x)’=1 (xn)’=nxn-1 (sin(x))’=cos(x) (cos(x))’=-sin(x) (ex)’=ex (ax)’=axln(a) (ln(x))’=1/x Derivative of compound functions: dx du du dy dx dy Example: y=sin(x2), u=x2, then xxuu dx du du dy dx dy y 2)cos()'()'(sin' 2 (3) Integration: the inverse of derivative. Here are a few examples Ckxkdx C n x dxx n n 1 1 Cedxe xx Cxdxx )sin()cos( Cxdxx )cos()sin( Definitive Integration: Newton-Leibniz Formula: )()()( aFbFdxxf b a , where f(x)=F’(x) (4) Regression: bxay ˆ Sum of squares: SST, SSR, SSE R2 Slope/intercept Positive correlation/negative correlation II. Concepts 1. Ecosystems 2. Components of System Models: a. reservoirs (stocks) b. processes (flows) c. converters (parameters) d. interrelationships 3. feedback loops a. positive feedbacks b. negative feedbacks 4. System Behavior Patterns: Linear, Exponential, Logistic, overshot/crash a. Graphic view b. System Diagrams c. Difference Equations d. Impact of model parameters on model behaviors 5. Model calibration, Validation and Sensitivity Analysis 6. Three radiation laws: a. Planck’s Equation, b. Stefen-Boltzmann’s Law c. Wien’s Law. 7. Leaf Area Index 8. Ecosystem Productions and Respirations a. GPP b. NPP c. NEP d. Ra e. Rh 9. Evapotranspiration 10. Soil water potential 11. Permanent Wilting Point 12. Field Capacity and Soil Porosity 13. Mineralization and immobilization 14. Nitrogen cycle, carbon cycle, water cycle 15. Greenhouse gases 16. Missing carbon sink III. Short Questions 1. How do you understand that Earth is a dynamic and evolving system? 2. What is the smallest ecosystem you observed in daily life, and how life is sustained within the ecosystem? 3. What is the solar elevation angle at Chapel Hill (latitude=36) at noon time on March 21? 4. How does stoma control the loss of water from plants? 5. How is transpiration different from evaporation? 6. How are soil porosity, field capacity and volumetric soil moisture related? 7. How relatively humidity, vapor pressure, saturated vapor pressure, vapor pressure deficit are related? 8. What are the sources of water for precipitation on land? 9. Draw the nitrogen cycling loop for the terrestrial ecosystem. 10. Please draw the global water/carbon cycle loop (no numbers are needed)? IV. Essay Questions
