Monte Carlo analysis of the Copano Bay fecal coliform model

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Monte Carlo analysis of the Copano Bay fecal
coliform model

• Prepared by,
• Ernest To

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Copano Bay model domain
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Copano Bay schematic network
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The concept of Monte Carlo Analysis
Parameters
Decay rate, Kd
Inputs
Output
EMCs
Flows, Q
10 of population lt 43 cfu/100 ml
median of population lt 14 cfu/100 ml
To use uncertainties in the inputs and parameters
to estimate uncertainties in the model output.
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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
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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-simulati
on.html
http//www.brighton-webs.co.uk/distributions/image
s/pdf_beta.gif
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Variables of the Copano Bay Fecal Coliform model
Ldownstream Lupstreamexp(-KdTau)
Lwatershedexp(-KdTau_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
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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.
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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
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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 A2 and B2.

Beta
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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)
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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

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On to the demo..
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Remaining tasks

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

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Acknowledgements

• Dr. David Maidment
• Carrie Gibson

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Questions?