Draft - The water requirements of Lake St. Lucia, the salinity and ecosystem response models - technical details, analytic models and detailed results.

J.A.Carter and G. Quibell

 

• Contents
• Executive summary.
• Introduction.
  • Conventions
• The Lake Salinity Model
  • Data inputs.
  • Estuary Function.
    • Effective cross-section
  • Behaviour of the Mfolozi mouth.
• Rule based ecosystem response model.
• Ecosystem response index
  • A Biomass index
  • A more responsive richness index.
• Simple analytical models for insight and understanding.
  • Very simplified version for analytic solution.
    • The Relaxation time and the half-life.
  • Very simplistic model demonstrating the effect of mouth closure.
    • Conclusions relating to lake salinity and mouth operation.
  • Why a relaxation time constant?
  • Numerical solutions of trivial problem.
    • How can one recognise when errors are playing a significant role? And what to do about it?
    • A physical picture of the time step problem.
  • Formulation of general problem.
    • Green's function solution to 1D linear Ordinary Differential equation.
    • Matrix formulation.
  • Potter's channel type problems.
    • Constant in/out flow, linear level dependent estuary.
    • Sea to lake flow.
    • Lake to sea flow.
    • From theory to practice. Filling in the numbers.
  • When is it best to make a compensation release?
    • Preventing influx of salt.
    • Flushing salt in the summer months
  • Conclusion's on the simple analytics.
• A variable step predictor corrector method. A better equation solver.
  • What is and Why use a Predictor Corrector method?
  • From Taylor's theorem to a variable step length Predictor-Corrector.
    • A second order predictor.
    • Second order correction step.
• Calibration and Verification of the model.
  • Calibration and verification of the Lake salinity model.
  • Verification of the ecosystem model.
• Sensitivity Analysis of the model.
  • How complex a model is necessary?
• Risk analysis and Bootstrapping.
• Results
  • Analysis of Potter's Channel.
  • Analysis of the Mkuze link canal.
  • Analysis of mouth operation.
    • Behaviour of the mouth under benchmark conditions.
  • What iffing. What if X increased by 20%?
  • The development spectrum.
• Caveats.
• Summary.
• An annotated bibliography
• References
• Appendix - Monte Carlo process for calculating confidence intervals.
• About this document ...