Monte Carlo analysis of the Copano Bay fecal coliform model

1. Monte Carlo analysis of the Copano Bay fecal coliform model Prepared by, Ernest To

2. Copano Bay model domain

3. Copano Bay schematic network

4. λ α β θ The concept of Monte Carlo Analysis Parameters Decay rate, Kd Inputs Output EMCs Flows, Q median of population < 14 cfu/100 ml 10% of population < 43 cfu/100 ml To use uncertainties in the inputs and parameters to estimate uncertainties in the model output.

5. The goal of Monte Carlo Analysis To match the variation in actual fecal coliform monitoring data Cumulative Density Function (CDF) of Fecal Coliform Concentration (CFU/100mL) at Schemanode 75

6. Beta What is Monte Carlo? • Monte-Carlo analysis uses random numbers in a probability distribution to simulate random phenomena. • For each uncertain variable (whether inputs or parameters), possible values are defined with a probability distribution. Distribution types include: http://www.decisioneering.com/monte-carlo-simulation.html http://www.brighton-webs.co.uk/distributions/images/pdf_beta.gif

7. Variables of the Copano Bay Fecal Coliform model Ldownstream = Lupstream*exp(-Kd*Tau) + Lwatershed*exp(-Kd*Tau_w) Lupstream Kd = decay rate Tau = residence time in river Schema link for river Schema link for watershed Inputs: EMCwatershed’ Qwatershed Parameters: Kd, Tau, Tau_w Lwatershed = EMCwatershed * Qwatershed Kd = decay rate Tau_w = residence time in watershed Ldownstream

8. Lognormal Flow (Q) • Matched flow distributions at USGS gages using lognormal distributions. • Applied matched distribution (with adjustments) to other schemanodes along the river. Measured and simulated cumulative distributions for flow at USGS gage 08189700.

9. Event mean concentrations (EMCs) • Defined as total storm load (mass)/ divided by the total runoff volume. • According Handbook of Hydrology by Maidment et al., EMC for fecal coliform in combined sewer outfalls follows a lognormal distribution with a coefficient of variation of 1.5. (where coefficient of variation = standard deviation/mean) Lognormal

10. Decay rate (Kd) • Decay rate is an experimentally derived property • Difficult to determine the distribution of Kd • Most likely within a finite range and has a central tendency. • Therefore assume beta distribution, with parameters A=2 and B=2. Beta

11. Program concept Results Table Schematic Processor SchemaNode New EMCs Success Random number generators Process Schematic SchemaLink Abort New flow and decay rates Loop for N times (where N = integer specified by user)

12. Implementation • Wrote simple program that performs a similar function as Schematic Processor in Excel • Imported schemalink and schemanode tables into Excel • Programmed random number generators for Kd, Q and EMCs. • Programmed a simple “for” loop to execute function multiple times. • Created a simple user-interface

13. On to the demo…..

14. Remaining tasks • Complete calibration of model to Fecal Coliform monitoring data. • Perform kriging on bay fecal coliform data (challenging because of fluctuation of data)

15. Acknowledgements Dr. David Maidment Carrie Gibson

16. Questions?