Jrising at 03:55, 25 August 2013

2013-08-25T03:55:58Z

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<slide title="Model Connections">
[[File:Allmods.png|center]]
</slide>

<slide title="Aggregate System Models">
* Population: population, land uses, energy
* Resources: water flows, infrastructure, energy
* Sentiments: Pro-market vs. pro-environment, inequality, conflict
* Diet Model: livestock, wild-caught, nourishment, prices
</slide>

<slide title="Aggregate Model: Population and Resources">
[[File:Agg1.png|center]]
</slide>

<slide title="Aggregate Model: Sentiments">
[[File:Politics.png|center]]
</slide>

<slide title="Aggregate System 1 Calibration" hide="true">
* 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.
Crop and Pasture Science, 35(6), 743-764.
* 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)
</slide>

<slide title="Politics: Dynamic Optimization">
[[File:Dynamicopt.png|center]]
Used for making discrete decisions, in politicized context.
</slide>

<slide title="Spatial Optimization">
Used for building infrastructure, and making spatial decisions.
* Hydropower dams, given population centers, slopes, streamflow
* Other power plants, given population centers and streamflow
* Agriculture, given soil and water availability
* Urban sprawl, given land values and existing urban centers
* Well digging, given agriculture potential, groundwater resources
</slide>

<slide title="Network Model: Hydrological Modeling">
[[File:Netmap_ext.png|center]]
</slide>

<slide title="Network Model: District Population Shifts">
[[File:Districtnetwork2.png|center]]
</slide>

<slide title="Demand Model">
== Neoclassical Approach ==
Representative firm profit and consumer utility maximization.

<math>\pi = \left(q - \frac{r}{e} - g(e)\right) f(\vec{x}) - c(\vec{p}, \vec{x})</math>
== VAR-style Dynamic Statistic General Equilibrium Model ==
Statistical model, fit to observed macroeconomic series.

== Agent-based Economic Model ==
"Heterogeneous agents, statistical dynamics, multiple equilibria, and endogenous learning."
</slide>

<slide title="Demand: Neoclassical" hide="true">
<math>\pi = \left(q - \frac{r}{e} - g(e)\right) f(\vec{x}) - c(\vec{p}, \vec{x})</math>
* General form of profit maximization, except for terms with e.
* 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.

Let <math>g(e) = e^d</math>, so optimal <math>e = \left(\frac{r}{b d}\right)^{1 / d+1}</math>.
</slide>

<slide title="Proposed Networked VAR Model">
* Smets and Wouters (2007):
VAR model with output (GDP), prices (CPI), wages, hours worked,

interest rates (TB yields), consumption, investment.

http://www.mathworks.com/help/econ/examples/modeling-the-united-states-economy.html
* Add water rates and water extractions series.
* Estimate separately for national, state-wide, and Metropolitan Statistical Areas,

and do Bayesian Hierarchical Coupling.
</slide>

<slide title="Bayesian Hierarchical Coupling">
[[File:Amalgelt2.png]]
</slide>

<slide title="Coupling between Demand and Aggregate">
[[File:Amalgelt1.png]]
</slide>

<slide title="OpenWorld Core Elements" hide="true">
[[File:Elements.png|center]]
</slide>

<slide title="Smart Variables: Dimensions" hide="true">
* <math>3</math> vs. <math>3</math> [tonnes] vs. <math>1350487537</math> [seconds since Jan. 1, 1970]
* Dimensional analysis at the heart of science
* Automatic model checking, unit conversion
</slide>

<slide title="Smart Variables: Maps" fs="1.5em" hide="true">
"Maps" are dimension-aware functions in space-time, often tied to data streams (e.g., IRI tsvs, geotiffs).
Maps of different resolutions can be manipulated transparently. Example:

<syntaxhighlight lang="cpp">
GeographicMap<double>& degreeDayMelt =
(degreeDayFactor + degreeDaySlope * elevation)
* (snowCover / 100) * (surfaceTemp - ZERO_CELSIUS)
* (surfaceTemp >= ZERO_CELSIUS);
</syntaxhighlight>

* elevation is a static map at <math>1 km</math> resolution
* surfaceTemp is a daily varying map at <math>.25^\circ</math> resolution, read from the file 1 day at a time
* snowCover is a weekly varying map at <math>.33^\circ</math> resolution, reconstructed for past years
</slide>

<slide title="Smart Variables: Relations" hide="true">
Variables can represent relationships or differential equations between other variables.

Example (the heat equations):
<syntaxhighlight lang="cpp">
q = -k * Grad(u);
Diff(u) = (-1 / c_p * rho) * Div(q);
</syntaxhighlight>

The equations themselves are saved within <code>q</code> and <code>Diff(u)</code>, so the model can be run.
</slide>

<slide title="Networked System Dynamics">
[[File:ssdarch-mod.png]]

(Ahmad et al 2004; flood management, water resources modeling, invasive species spread)
</slide>

<slide title="Multiple Networks">
[[File:Ohionet.png|right]]
Models use multiple networks simultaneously
* Different paths on which stocks flow
* Disaggregations into structured classes
* Capturing network properties
</slide>

<slide title="Disaggregating System Models">
[[File:Popmod-vensim.png|center]]

[[File:Popmod.png|center]]
</slide>

<slide title="Computational Tools">
* Evaluate model performance (Barlas 1996)
* Identify driving feedback loops
* Identify tipping and leverage points
* Construct simplified models for communication
* System Regression: construct models from data
* Data for calibration, validation, fictional forces
</slide>

File:Amalgelt2.png - Revision history

Jrising at 03:55, 25 August 2013