Environmental Modeling

1
Environmental Modeling

• ?????????????? slide ?????????? Nisai Wanakule,
  Ph.D., P.E.
• nwanakule_at_tampabaywater.org

2
What is a (computer) model?
Who use computer models?
When to use or not use a model?
Where can I apply mathematical modeling?
Why modeling becomes more attractive?
3
Types of Model

• Iconic Prototype model, ??. Model
  ?????????????? Model ???????????
• Analog ??? electrical circuit ????? simulate
  ???????????????, ??. network flow analyzer, flow
  net analysis
• Symbolic ?????????????????????, ??. digital
  ???? numerical model

4
What is the (Math.) Model?

• ????????????????????????????????
• ???????????????????????????????????????????????
• ????????????????????????????????????????
• ????????? partial differential ???????????????????
  ?
• ??????????????????????????????????????????????????
  ??
• ??????????????????????????????????????????????????
  ???????????????????????????????????? ? ???????

5
Mathematical Model

• Model ??????????????????????????
• ??????????????????????????????????????????
• ????? Model ????????????????????????????????
  ????????????????????????

6
Mathematical Model Texture

• ?????????? models ???? ? ??? ?
• ??????????? ????????????????????????
• ?????????? ???????????????????
• ???????????? ??????????????????????
• ????????????? ????????????????????
• Modularity ????????????????
• Source code ?????????? ??????????????

7
Modeling Requirements

• Computer resources
• ?? CPU speed ??? RAM size ???????
• ??????????????????????
• Local Area Network (LAN) ??? Internet Access
• ??????
• ???????? modeler ?????? modeling software
• ???????????????????? model

8
Why Modeling Becomes More Attractive?

• CPU speed ??? RAM size ???????????????????????????
  ???????????????????????????????????????
• ??????????????????????????????????????????????????
  ??????????????

9
Why Modeling Becomes More Attractive? (cont.)

• ?? pre- ??? post-processing software
  ??????????????????????? ?????????????? model
  ????????????? ???????????????
• ??????????????? database ?????????????????????????
  ????????
• ??????????????????????????????????????????????????
  ???????????????

10
Model Uses

• Model ????????????????????????????
• Simulation what if scenario ???????????????????
  ??????????
• Optimization what best if scenario
  ???????????????????????????
• Risk/Uncertainty what possible if scenario
  ????????????????????????????????
• Model ????????????????????????
• ??????? hypothesis ?????????????????????????????
• ???????????????????????????????????????????????
• ???????????????????????????????????????????????
• ????????????????????????????????

11
Environmental Management
Influence

• Human Activities
• Urbanization
• Industrialization

Ecosystem
Impacts
Information gathering
Control

• Environmental Technology
• New technology
• Legislature
• Alternative management
• Socio-economics

Ecological Model
Environmental management
12
Use of a Model to Aid in Making Complex Decisions

• ?????????????????????????????????????????? 1
  ?????????????????? 1 ??????
• ????????????????????????????
• ????????????????????????????????????????????????
• ?????????????????????????????? ?????? model
  ????????? ?
• ???????????? ?????????????????
• ??????????????????? ??????? model
  ?????????????????????????
• ?????????????????????
• Feedback ?????????????/?????????????????
  ??????????????????????

13
Modeling Concepts

• System Concepts
• Model elements
• Model Classification
• ?????????????? Model
• Calibration
• Verification
• Sensitivity Analysis

14
System Concepts

• ??????????????????????????????????????

Input
Environment
Output
Controlled
Desirable
Partially Controlled
Undesirable
System
Uncontrolled
Neutral
Feedback (dynamic)
15
System and Model Elements

• Variables
• Mathematical equations
• Parameters
• Universal constants

16
Model Classification

• ?????????
• Research model research tool
• Management model management tool
• ?????????????????????????????????????? ?
• Deterministic ??????????????????????????????????
  ?????
• Probabilistic/Stochastic ??????????????
  ??????????????????????????????????????????????????
  ???? ?
• Spatial treatment ???????
• Lumped parameters ?????????????????????????????
  ? ???????????????????????????????
• Distributed parameters ?????????????????????????
  ? ? ????????????

17
Model Classification (cont.)

• ??????????? (non-stationary ????????????????????)
• Steady state or static ????????????????????????
• Transient or dynamic ?????????????????????????
• ???????????????
• Linear
• Nonlinear input/output treatment
• Causal input/output ??????????? ?
  ????????????????????????
• Black-Box input ???????????? output

18
Model Classification (cont.)

• Model Derivative
• Physical based ???????????????????? physics
  ??????????????????? chemistry ??? biology
• Statistical based ??????????????? systems
  memory
• Empirical/Experimental ?????????????????????????
  ????????????????????????????????
• Mathematical formulation
• Compartment ?????? differential equations
• Matrix ?????? matrix ????? formulate
• Process complexity
• Reductionistic ?????????????????????????????????
  ?????????
• Holistic ????????????????????

19
Types of Mathematical Model

• Statistical based models ???????????????????????
  ??????????????????????????? ???? ??????????
  ??????????????????
• Simple linear ??? nonlinear regression
• Multiple linear ??? nonlinear regression
• Multivariate
• Time series
• Geostatistics ???????????????????

20
Types of Math. Model (cont.)

• Physical based (descriptive) models
  ???????????????????????????????? physics
  ?????????????? (chem/bio processes)
  ???????????????? what if questions, ??.
  simulation
• Lumped parameter (black box) models ?????????
• Empirical Model ????????????????????????????????
  ??????????????????
• Distributed parameter models ???????????????????
  ???????????????????????????????????? ? ??????

21
Types of Math. Model (cont.)

• Optimization models ????????????????????????????
  ???????????????? what best questions
  ???????????????????????
• Linear and Network Programming (LP)
• Mixed Integer Programming (MIP)
• Nonlinear Programming (NLP)
• Dynamic Programming (DP)
• Multi-objectives, multi-criteria

22
Types of Math. Model (cont.)

• ?????????? ?
• Stochastic optimization ????????????????????
  probability ???????????????????????????????????
• Risk and Reliability ???????????????????????????
  ??????? model ????????????????????????????????????
  ?

23
Modeling Development Process

• ??? identify ????? model objectives
• ???????? Model ??????????????????
• Conceptual diagram ?????????????????????????
• Model Formulation ??????????????????????????????
  ????????????
• Sensitivity analysis ???????????????????????????
  ????????? output ?????? ??????????????????????????
  ????????????? ? ?????? ???????????????????????????
  ?
• Calibration ????????????????????????????????????
  ????????? ? ??? input ???????? model ??????
  output ???????? match ?????????????????????
• Verification ????????????????????? model
• Applications ?????????????????
  ??????????????????????????????????????????

24
Process Flowchart
Problem and system definitions
Model Selection
Conceptual Diagram
Data Collection
Mathematical Formulation
Model Calibration
Sensitivity Analysis
Feedback
Model Verification
Model Applications
25
Modeling Aspects in Various Fields

• Kinematics
• Force ??? momentum
• Conservation ??? transportation ??????
• Conservation ??????????
• Kinetics ?? thermodynamics
• ????????????????????????????????????????

26
Domain of Models
27
Uncertainty Concepts

• Type of uncertainty in math model
• Type I model ????????????? ?????????????????????
  ????? model ??????????
• Type II model ?????????? ???????????????????????
  ??? model ??????? stochastic (??????? random
  ???????????????????)
• ??. ???????????????? modeling
• ?????????????????????????
• Hydrologic uncertainty ???????????????????????
  random ??????????
• ???????????????????????????
• ???????????????????????

28

• Time Series Analysis

29
?????

• Time Series ????????????????????????????
• ??? Continuous ??? Discrete
• Continuous ???????????????????????????
• Discrete ??????????????????????????????? ?t
  interval ?????????????????????????????????????????
  ???????????? ?t

30
Continuous and Discrete
31
?????

• A time series ?????????????????????????????
  deterministic events ???????? stochastic events
  ????????????????
• Deterministic events trend, jump, periodic
• Stochastic events random deviations

32
Stochastic and Deterministic
33
?????

• Trend ??????????????????????????????????????????
  ??????????????????????????????????????????????????
  ???????????????????
• ???????? ??????????, ??????????????????????????,
  ????????????????? ???????
• ?????????????????????????????? ??????????????,
  ????????????????? ???????

34
?????

• Jump (Shift) ??????????????????????????????????
• ???????????????????? ???? ?????????? Tsunami
  ??????????????????????????
• ?????????????????????????????? ??????????????
• Periodic ??????? astronomic cycle
• Annual Cycle stream-flow, precipitation,
  groundwater level, soil moisture
• Weekly Cycle ?????????

35
Single and Multiple Time Series

• Single Time Series
• ??????????????????????????????????????????????????
  ????????????????????
• Multiple Time Series
• ???????????????????? ?????????????????????????????
  ?????????????? network
• ??????????????????????????????? ? ???????????? ?
  ???????????

36
Optimization Model
37
????

• ?????????? WWII ??????????????????????????????????
  ??????????????? ? ????????
• ??????????????? Operations Research
  ???????Mathematical Programming
• Processes
• Problem formulation (setup)
• ?????????????????????????? model
• Solution
• Results interpretation
• ???????? model ????????? run model ???

38
Classification

• Linear programming (LP)
• Network Programming
• Nonlinear programming (NLP)
• Constrained/Unconstrained
• Quadratic programming (QP)
• Mixed Integer Programming (MIP)
• Dynamic Programming (DP)
• Etc. goal programming, queuing theory
• Multiobjective optimization

39
Optimization Tree
40
Linear Programming

• Standard Form

• Short-hand

s.t.
41
Example

• Water supply sources allocation
• x1 groundwater production
• x2 surface water production
• Objective maximize profit 2x1x2
• unit profit of groundwater 2 M
• unit profit of surface water 1 M
• Constraints
• groundwater plant capacity 5 mgd
• surface water plant capacity 8 mgd
• distribution capacity 10 mgd

42
LP - Formulation

• Resource allocation
• Demand-Supply
• Transportation
• Shorted-Path (traveling salesman)
• Scheduling
• Inventory
• Etc.

43
Mathematical Programming Language (AMPL)

• Model ??????????? linear ??? nonlinear
  optimization
• Free students version ??????????????????????????
  500x500
• Web site http//www.ampl.com/

44
Groundwater Flow and Pollution Transport Models
45
Model Consideration

• Solution Method
• Analytical, Semi-Analytical, Numerical
• Flow (hydraulics)
• Saturated ???? unsaturated flow model
• Contaminant transport
• Single ???? multiple species
• Single ???? multi-phase
• Density dependent/independent

46
Groundwater Pollution Transport Processes

• Advection ???????????????????????
• Dispersion
• Molecular diffusion Ficks first law
• Mechanical mixing ?????????????????????
• Retardation
• Radioactive

47
Solute Transport PDE
Advection
Dispersion
Source/Sink
Radioactive
Retardation Factor
Average Pore Velocity
Groundwater Flow
48
Solution Methods

• Analytical Solution
• ????????????????????? ??????????????
• ?????????????????????
• laboratory, ??????????????????? plume
• ?????????????

49
Solution Methods (cont.)

• Semi-Analytical Methods
• ???????????? Multiple sinks ??? sources
• ?????????? steady state, 2-D, homogeneous
• ????? convective, ????? dispersion ??? adsorption
• Numerical Methods
• Finite difference ??????????????? cells/grids
  ??????????
• Finite Element ??????????????? geometric shapes
  ??????? ? ????????????????????

50
1-D Analytical Solution
Homogeneous, Isotropic Confined Aquifer Steady,
Uniform Groundwater Flow
Groundwater Flow
Waste Water
51
2-D Analytical Solution
Y
Waste Water
Groundwater Flow
ß
2a
X
52
Numerical Method

• Finite Difference MODFLOW and MT3D

53
???????? EPA Models

• Hydrological models
• Model ??????????????????????? runoff/infiltration
  ???????? ???????????? NRCS Curve Number Method
  (USDA-NRCS, 1986)
• Water quality models
• Model ???????????????????? simulate
  ???????????????? precipitation ??? pollutants
  ???????????????? ???????? ?????? ????????????????
  ????????????? ????????????? flows, stages ???
  pollutant concentrations

54
???????? EPA Models

• EPA SUPPORTED MODELS
• BASINS
• ???????????????????????????????????????
  ?????????????? geographical information system
  (GIS), environmental assessment ??? modeling
  tools ??????????? package ?????

55
???????? EPA Models

• EPA supported models
• Enhanced Stream Water Quality Model, Windows
  (QUAL2K)
• One dimension
• ??????????????????????????????????????????????????
  
• Steady state hydraulics.
• Diurnal heat budget. heat budget ??? ???????????
  simulate ?????????????? 1 ??? (diurnal time
  scale)
• Diurnal water-quality kinetics.
  ?????????????????? simulate ?????????? 1 ???
• Heat and mass inputs. Point ??? non-point loads
  ????????????????????

56
???????? EPA Models

• Model segmentation. Q2E ??????????????????
  reaches ?????????????????????? ? ??????? reach
  ?????????????????????????????????????
• Q2K ??? carbonaceous BOD ????????????? organic
  carbon ??????????? slow CBOD ??? fast CBOD
• ??????????? Anoxia, Denitrification
• ?? Sediment-water interactions ????????? nutrient
  flux ??????????????????????
• ?? Bottom algae
• ????????????????????????
• ?? Pathogens

57
???????? model ???? ?

• MIKE 11
• 1-dimensional
• rainfall-runoff
• advection-dispersion
• morphological
• water quality

• Parameter
• algae
• zooplankton
• detritus
• sediments
• dissolved oxygen
• temperature
• nitrogen
• phosphorus
• biochemical oxygen demand
• coliform bacteria
• metals

58
???????? model ???? ?

• GMS (groundwater modeling software)
• GMS ?????? model ???? 2D ??? 3D
• MODFLOW 2000
• MODPATH
• MT3DMS/RT3D
• SEAM3D
• ART3D
• UTCHEM, FEMWATER, PEST, UCODE, MODAEM ??? SEEP2D.