Monte Carlo analysis of the Copano Bay fecal coliform model

Prepared by,

Ernest To

Copano Bay model domain

Copano Bay schematic network

The concept of Monte Carlo Analysis

To use uncertainties in the inputs and parameters to estimate uncertainties in the model output.

β α θ λ

Parameters

Inputs

Output

10% of population

< 43 cfu/100 ml

median of population

< 14 cfu/100 ml

EMCs

Flows, Q

Decay rate, Kd

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

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.brighton-webs.co.uk/distributions/images/pdf_beta.gif

http://www.decisioneering.com/monte-carlo-simulation.html

Beta

Variables of the Copano Bay Fecal Coliform model

Schema link for river

Schema link for watershed

Kd = decay rate

Tau = residence time in river

Kd = decay rate

Tau_w = residence time in watershed Ldownstream

Lupstream

Lwatershed

= EMCwatershed * Qwatershed

Ldownstream = Lupstream*exp(-Kd*Tau) + Lwatershed*exp(-Kd*Tau_w)

Inputs: EMCwatershed’ Qwatershed

Parameters:Kd, Tau, Tau_w

Flow (Q) Matched flow distributions at USGS gages using

lognormal distributions. Applied matched distribution (with adjustments) to other

schemanodes along the river.

Lognormal

Measured and simulated cumulative distributions for flow at USGS gage 08189700.

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

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

Program concept

Random number generators

New EMCs

New flow and decay rates

Process Schematic

SchemaNode

SchemaLink

Success

Abort

Results Table

Loop for N times (where N = integer specified by user)

Schematic Processor

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

On to the demo…..

Remaining tasks Complete calibration of model to Fecal Coliform

monitoring data. Perform kriging on bay fecal coliform data

(challenging because of fluctuation of data)

Acknowledgements

Dr. David Maidment

Carrie Gibson

Questions?