Mathematics in the Environment: Modelling Pollution Hierarchy of Models

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Mathematics in the EnvironmentModelling
PollutionHierarchy of Models

• Graeme Wake
• Centre for Mathematics in Industry
• Massey University
• Auckland
• g.c.wake_at_massey.ac.nz

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1.First Pond model

• One- off dump.P(t) pollution, O(t) oxygen
• dP - kp P, P(t 0) Po,
• dt
• dO - koP, O(t 0) 100
• dt

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• Tasks..
• Solve
• Units, what are they????
• Develop decision-support procedure
• Po lt Pcrit ? O(t ? 8 ) gt 30
• Whats Pcrit ??

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2. Second Pond Model

• Oxygen restoration
• One- off dump. P(t) pollution, O(t) oxygen
• dP - kp P, P(t 0) Po,
• dt
• dO - koP k(100 O) , O(t
  0) 100
• dt

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Tasks to discuss

• Whats the oxygen term?
• Solve
• Produce a modified decision-support
• scheme
• Po lt Pcrit ? O(t ? 8 ) gt 30
• Whats Pcrit ??
• Suggest strategies for improvement within the
  suggested goals
• Po as big as possible
• O(t large) lt 30

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• 3. Third pond model
• Constant dump. P(t) pollution, O(t) oxygen
• dP - kp P po,
  P(t 0) 0, Easier!!
• dt addition at
• constant rate
• dO - koP oxygen , O(t 0)
  100
• dt

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Tasks

• Solve
• Produce a modified decision-support
• scheme
• po lt pcrit ? O(t ? 8 ) lt 30
• Whats pcrit ??
• Suggest strategies for improvement within the
  suggested goals
• po as big as possible
• O(t large) lt 30

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n. Ultimate model

• Factors to incorporate in model
• Position
• Tidal flow
• Dumping strategy
• HOW??????? Discuss.

How?? Discuss??