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| <slide title="Model Connections">
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| [[File:Allmods.png|center]]
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| </slide>
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|
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| <slide title="Aggregate System Models">
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| * Population: population, land uses, energy
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| * Resources: water flows, infrastructure, energy
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| * Sentiments: Pro-market vs. pro-environment, inequality, conflict
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| * Diet Model: livestock, wild-caught, nourishment, prices
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| </slide>
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|
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| <slide title="Aggregate Model: Population and Resources">
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| [[File:Agg1.png|center]]
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| </slide>
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|
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| <slide title="Aggregate Model: Sentiments">
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| [[File:Politics.png|center]]
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| </slide>
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|
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| <slide title="Aggregate System 1 Calibration" hide="true">
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| * 12.7-37 kg ha-1 per mm = 25: French, R. J., & Schultz, J. E. (1984). Water use efficiency of wheat in a Mediterranean-type environment. I. The relation between yield, water use and climate.
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| Crop and Pasture Science, 35(6), 743-764.
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| * 1961: 49% agriculture, 1.66% urban = 2.6% urban in 2002 * 183.7e6 pop / 287.6e6 pop (Major Uses of Land in the United States, 2002)
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| </slide>
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|
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| <slide title="Politics: Dynamic Optimization">
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| [[File:Dynamicopt.png|center]]
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| Used for making discrete decisions, in politicized context.
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| </slide>
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|
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| <slide title="Spatial Optimization">
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| Used for building infrastructure, and making spatial decisions.
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| * Hydropower dams, given population centers, slopes, streamflow
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| * Other power plants, given population centers and streamflow
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| * Agriculture, given soil and water availability
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| * Urban sprawl, given land values and existing urban centers
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| * Well digging, given agriculture potential, groundwater resources
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| </slide>
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|
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| <slide title="Network Model: Hydrological Modeling">
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| [[File:Netmap_ext.png|center]]
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| </slide>
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|
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| <slide title="Network Model: District Population Shifts">
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| [[File:Districtnetwork2.png|center]]
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| </slide>
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|
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| <slide title="Demand Model">
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| == Neoclassical Approach ==
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| Representative firm profit and consumer utility maximization.
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|
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| <math>\pi = \left(q - \frac{r}{e} - g(e)\right) f(\vec{x}) - c(\vec{p}, \vec{x})</math>
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| == VAR-style Dynamic Statistic General Equilibrium Model ==
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| Statistical model, fit to observed macroeconomic series.
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|
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| == Agent-based Economic Model ==
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| "Heterogeneous agents, statistical dynamics, multiple equilibria, and endogenous learning."
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| </slide>
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|
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| <slide title="Demand: Neoclassical" hide="true">
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| <math>\pi = \left(q - \frac{r}{e} - g(e)\right) f(\vec{x}) - c(\vec{p}, \vec{x})</math>
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| * General form of profit maximization, except for terms with e.
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| * e is the water efficiency of the chosen technology; r is the water rate; g(e) is the (increasing) cost of the higher-efficiency technologies.
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|
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| Let <math>g(e) = e^d</math>, so optimal <math>e = \left(\frac{r}{b d}\right)^{1 / d+1}</math>.
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| </slide>
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|
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| <slide title="Proposed Networked VAR Model">
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| * Smets and Wouters (2007):
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| VAR model with output (GDP), prices (CPI), wages, hours worked,
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|
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| interest rates (TB yields), consumption, investment.
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|
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| http://www.mathworks.com/help/econ/examples/modeling-the-united-states-economy.html
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| * Add water rates and water extractions series.
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| * Estimate separately for national, state-wide, and Metropolitan Statistical Areas,
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|
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| and do Bayesian Hierarchical Coupling.
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| </slide>
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|
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| <slide title="Bayesian Hierarchical Coupling">
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| [[File:Amalgelt2.png]]
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| </slide>
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|
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| <slide title="Coupling between Demand and Aggregate">
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| [[File:Amalgelt1.png]]
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| </slide>
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|
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| <slide title="OpenWorld Core Elements" hide="true">
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| [[File:Elements.png|center]]
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| </slide>
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|
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| <slide title="Smart Variables: Dimensions" hide="true">
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| * <math>3</math> vs. <math>3</math> [tonnes] vs. <math>1350487537</math> [seconds since Jan. 1, 1970]
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| * Dimensional analysis at the heart of science
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| * Automatic model checking, unit conversion
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| </slide>
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|
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| <slide title="Smart Variables: Maps" fs="1.5em" hide="true">
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| "Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).
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| Maps of different resolutions can be manipulated transparently. Example:
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|
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| <syntaxhighlight lang="cpp">
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| GeographicMap<double>& degreeDayMelt =
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| (degreeDayFactor + degreeDaySlope * elevation)
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| * (snowCover / 100) * (surfaceTemp - ZERO_CELSIUS)
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| * (surfaceTemp >= ZERO_CELSIUS);
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| </syntaxhighlight>
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|
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| * elevation is a static map at <math>1 km</math> resolution
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| * surfaceTemp is a daily varying map at <math>.25^\circ</math> resolution, read from the file 1 day at a time
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| * snowCover is a weekly varying map at <math>.33^\circ</math> resolution, reconstructed for past years
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| </slide>
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|
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| <slide title="Smart Variables: Relations" hide="true">
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| Variables can represent relationships or differential equations between other variables.
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|
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| Example (the heat equations):
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| <syntaxhighlight lang="cpp">
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| q = -k * Grad(u);
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| Diff(u) = (-1 / c_p * rho) * Div(q);
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| </syntaxhighlight>
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|
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| The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so the model can be run.
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| </slide>
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|
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| <slide title="Networked System Dynamics">
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| [[File:ssdarch-mod.png]]
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|
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| (Ahmad et al 2004; flood management, water resources modeling, invasive species spread)
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| </slide>
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|
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| <slide title="Multiple Networks">
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| Models use multiple networks simultaneously
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| * Different paths on which stocks flow
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| * Disaggregations into structured classes
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| * Capturing network properties
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| [[File:Ohionet.png]]
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| </slide>
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|
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| <slide title="Disaggregating System Models">
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| [[File:Popmod-vensim.png|center]]
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|
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| [[File:Popmod.png|center]]
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| </slide>
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|
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| <slide title="Computational Tools">
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| * Evaluate model performance (Barlas 1996)
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| * Identify driving feedback loops
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| * Identify tipping and leverage points
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| * Construct simplified models for communication
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| * System Regression: construct models from data
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| * Data for calibration, validation, fictional forces
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| </slide>
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