Gabriel Katul

Teaching (Fall 2009):

• ENVIRON 234L.001, WATERSHED HYDROLOGY

  LSRC A211, MWF 10:20 AM-11:10 AM

  Topics:
  

  1. Introduction to Hydrology: The hydrologic cycle, hydrologic processes, conceptual models for hydrologic systems: statistical, semi-empirical, and physical.
  2. Precipitation : Formation and measurement of precipitation, areal estimation from point measurements and the concept of spatial aggregation, consistency of precipitation gages, introduction to statistical estimation theory, frequency distributions, intensity-duration-frequency analysis of point rainfall measurements. 
  3. Soil Water Flow : Subsurface water flow: Introduction to soil physics, energy-state of soil water, soil hydraulic properties - soil water characteristic curve and soil hydraulic conductivity fluction, the Buckingham-Darcy law, soil moisture and tension measurements.  Solving Richard's equation for stratified soils.
  4. Infiltration Processes: Infiltration models - empirical, semi-empirical, and physical (sorption and gravitational flow and Philip's theory), Infiltration measurements.
  5. Ground Water Hydraulics: Basic concepts, confined/unconfined aquifers, Darcy's law and steady-state models for ground water movement; Introduction to Well hydraulics and Pumping.
  6. Evaporation : Evaporation into the atmosphere, radiation balance, energy balance, the role of water vapor in climate and hydrologic systems, general equations for evaporation: turbulent transport of water vapor and aerodynamic considerations, Bowen ratio/energy balance equations, Penman's combination equations.
  7. Stream Flow: Energy state of water, classification/types of flows - uniform flow equations (emphasize on Manning's equation), concept of specific energy, concept of specific momentum, hydraulic jumps, steady non-uniform flow, estimation of water-surface profiles for simple cross-sections; introduction to computational hydraulics. An introduction to open channel design (lined and unlined and canals) will be presented. Stream velocity/discharge Measurements (theory and practical considerations, flow over weirs).
  8.  Overland Flow: Basic definitions, Hortonian overland flow, shallow water approximations, inter-flow. 
  9. Hydrograph analysis : Hydrograph separation, estimation of peak flow rates, the unit hydrograph, and flood rooting.
  10. Special Topics: Wetland Design
      

• ENVIRON 234L.01L, WATERSHED HYDROLOGY

  LSRC A247, W 01:15 PM-02:45 PM

  Laboratory work primarily focuses on problem solving in Mathematica and Matlab.

• ENVIRON 264.01, APPL DIFF EQUA ENV SCI

  LSRC A211, MW 11:40 AM-12:55 PM

  It is well recognized that many environmental problems require the construction and solution to equations (or system of equations) that involve relations between rates and states of environmental variables. The objective of this course is to illustrate the use of differential equations and analytical tools from calculus to solve such problems. The course covers basic analytical and numerical solutions to ordinary differential equations (O.D.E.) with an introduction to partial differential equations commonly encountered in environmental studies (mainly diffusion and reaction-diffusion equations). Example applications include atomic waste disposal in oceans, refined population forecasting and finite time singularities, hydrological transport problems in xylems, predator-prey systems, heat transport in soils, and spatial models of biomass-water interactions. It is envisaged that this special topics course will also serve as an applied mathematics review for students who have not been in contact with calculus in the last two years. It also introduces numerous concepts routinely used in dynamical systems theory (e.g. equilibrium, resilience, bifurcation analysis, catastrophe theory, limit cycles, etc...).