# 2. Model Theory content¶

## 2.1. Introduction to land surface process modelling¶

### 2.1.1. Key topics¶

- General introduction to land surface process modelling.
- Forward modelling
- Aims of modelling
- Model development cycle

### 2.1.2. Literature for exam¶

Wainwright, J. and Mulligan, M., 2004, Modelling and model building, in: Environmental Modelling: finding simplicity in complexity, Second Edition. J. Wainwright, M. Mulligan (eds), p. 7-26, Wiley, Chichester.

Karssenberg, D., 2010, Introduction to dynamic spatial environmental modelling.

Burrough, P.A., McDonnel, R. & Lloyd, C.D., 2015, Principles of Geographical Information Systems, Oxford University press, Chapter 12, Space-time modelling and error propagation, p. 251-260.

### 2.1.3. Reading material¶

Karssenberg, D., Bridge, J.S., 2008, A three-dimensional numerical model of sediment transport, erosion and deposition within a network of channel belts, flodplain and hill slope: extrinsic and intrinsic controls on floodplain dynamics and alluvial architecture, Sedimentology, 55, 1717-1745. Link.

### 2.1.4. Lectures, e-Lectures¶

Lecture slides Introduction to land surface process modelling

### 2.1.5. Short paper assignment 1¶

Please read the excerpt from Wainwright & Mulligan (first edition) The excerpt distinguishes three type of models: empirical models, conceptual models, and physically based models. Read the paper by Karssenberg & Bridge (2008, reading material for this topic). Consider the following questions:

- What type of model is the model described in the paper (empirical, conceptual or physically based)?
- Would it be possible to model the same system using another approach (empirical, conceptual, or physically based)?

Write a 1-1.5 page (12 points font size, single line spacing) short paper that gives a short summary of the paper, poses the above questions and provides an answer (and discussion) to these questions. Hand in by uploading to Blackboard (assignments section in Blackboard).

## 2.2. Local (point) models¶

### 2.2.1. Key topics¶

- Dynamic point models
- Numerical solution of differential equations

### 2.2.2. Literature for exam¶

Kreyszig, E., 1999, Numerical Methods for Differential Equations, in Advanced Engineering Mathematics, New York, N.Y., Wiley: p. 942-952.

### 2.2.3. Lectures, e-Lectures¶

Lecture slides Local point models

## 2.3. Spatio-temporal models: neighbourhood interaction¶

### 2.3.1. Key topics¶

- Neighbourhood interaction
- Neighbourhoods by a defined topology
- Dynamic neighbourhood models: cellular automata

### 2.3.2. Literature for exam¶

Burrough, P.A., McDonnel, R. & Lloyd, C.D., 2015, Principles of Geographical Information Systems, Oxford University press, Chapter 7, Analysis of discrete entities in space, p. 127-145, and Chapter 10, Analysis of continuous fields, p. 201-229.

Favis-Mortlock, D., 2004, Non-linear dynamics, self-organization and cellular automata models, in: Environmental Modelling: finding simplicity in complexity, J. Wainwright, M. Mulligan (eds), p. 45-67, Wiley, Chichester.

### 2.3.3. Reading material¶

Saco, P.M., Willgoose, G.R., Hancock, G.R., 2007, Eco-geomorphology of banded vegetation patterns in arid and semi-arid regions, Hydrology and Earth System Sciences, 11: 1717-1730. Link.

### 2.3.4. Lectures, e-Lectures¶

e-Lecture Neighbourhood interaction

e-Lecture slides Spatio-temporal models: neighbourhood interaction, pdf

### 2.3.5. Working group session¶

We will have a working group session on this topic.

To prepare for the session:

- Listen to the e-Lecture (see above for the link)
- Study the literature for the exam (related to this topic, see above)
- Create a group (consisting of two students)
- Prepare a 10 minute presentation (one per group), for topics see below

During the working group session:

- Bring your presentation (powerpoint or pdf) on a usb stick (computer is available).
- Each group gives a 10 minute presentation.
- After each presentation: 5 minutes discussion with questions

The presentation should describe an example of either 1) the use of cellular automata or 2) self organisation in the earth sciences (or related fields). Search the literature (use a bibliographic database, e.g. http://www.scopus.com) to find at least one paper on one these topics. Prepare a presentation which explains how cellular automata are used in the article or what kind of self organisation is described. If you want you can add items for discussion at the end.

### 2.3.6. Short paper assignment 2¶

Favis-Mortlock (2004, in the reader) discusses self-organizing systems and why feedback mechanisms may lead to self-organization. Read the paper by Saco et al. (reading material). In a short paper (1-1.5 pages, 12 points font, single line spacing), explain the concept of self-organization and discuss why the system studied by Saco et al. is a self-organizing system. In addition, provide the main feedback mechanisms that lead to the observed self-organization. Hand in by uploading in Blackboard.

## 2.4. Stochastic models (and error propagation)¶

### 2.4.1. Key topics¶

- Stochastic variables
- Probability distributions, categorial and continuous variables
- Properties of probability distributions: percentiles, confidence intervals
- Stochastic variables to represent uncertain model inputs and parameters
- Solving stochastic models: Monte Carlo simulation

### 2.4.2. Literature for exam¶

Karssenberg, D. de Jong, K., 2005, Dynamic environmental modelling in GIS: 2. Modelling error propagation. International Journal of Geographical Information Science, 19, p. 623-637.

Karssenberg, D., Schmitz, O., Salamon, P., De Jong, K. and Bierkens, M.F.P., 2010, A software framework for construction of process-based stochastic spatio-temporal models and data assimilation. Environmental Modelling & Software, 25, pp. 489-493.

Kreyszig, E., 1999, Data Analysis. Probability Theory, in Advanced Engineering Mathematics, New York, N.Y., Wiley, Chapter 22, the following pages:

- 1050-1064, except 22.4 (Permutations and Combinations), Problem Sets and Examples

- 1069-1076, except Problem Sets and Examples

- 1085-1097, except 1086 (Distribution Function F(x)), 1087 (Theorem 1 & 2), 1089 (Examples, Binomial Distribution), 1090, Problem Sets, Examples

### 2.4.3. Reading material¶

No reading material.

### 2.4.4. Lectures, e-Lectures¶

e-Lecture Introduction to Stochastic Modelling

e-Lecture Monte Carlo simulation

e-Lecture slides Stochastic models, Monte Carlo simulation, pdf

### 2.4.5. Working group session¶

We will have a working group session on this topic. Unlike the previous session we will focus now on the theory, and the aim of the session is mainly to help you understanding the theory, and to give you some context. I have selected a number of topics (one per group, see below) for the presentations.

To prepare for the session:

- Listen to the e-Lectures on Stochastic Modelling and Monte Carlo simulation (see above for the links)
- Study the literature for the exam (related to this topic, see above)
- Use the same groups as during working group session 1
- Prepare a 10 minute presentation (one per group), for topics see below

During the working group session:

- Bring your presentation (powerpoint or pdf) on a usb stick (computer is available)
- Each group gives a ~ 7 minute presentation
- After each presentation: 5 minutes questions and/or discussion
- At the end you can ask questions (if you have) related to the theory

Topics:

- Probability functions: define/explain them, list the most widely used type of probability functions (e.g. Gaussian), and give examples of their use in the geosciences
- Realizations: explain what realizations are, and when/why they are needed in modelling, list all functions for creating realizations in PCRaster, and give examples of how they can be used
- Monte Carlo simulation: explain the procedural steps, and give an example to illustrate the concepts
- Monte Carlo simulation: explain the PCRaster Python framework for Monte Carlo simulation
- Confidence intervals, explain what it is, and how it is used in modelling, give examples
- Explain why and how error propagation modelling is used in the paper by Verstegen et al (http://www.sciencedirect.com/science/article/pii/S0198971511000883)
- Explain why and how error propagation modelling is used in the paper by Wanders et al (http://www.sciencedirect.com/science/article/pii/S0034425712003574)

## 2.5. Calibration of Environmental Models¶

### 2.5.1. Key topics¶

- Objective function
- Minimizing the objective function: hillclimbing, brute force and other techniques

### 2.5.2. Literature for exam¶

Beven, K.J., 2002, Parameter estimation and predictive uncertainty, in Rainfall-runoff modelling, the primer, Wiley, Chichester, p. 217-233.

Janssen, P.H.M, Heuberger, P.S.C., 1995, Calibration of process-oriented models, Ecological Modelling 83, 55-66.

### 2.5.3. Reading material¶

No reading material.

### 2.5.4. e-Lectures¶

e-Lecture Calibration - 01 Introduction

e-Lecture Calibration - 02 Objective Functions & Response Surfaces

e-Lecture Calibration - 02 Calibration Algorithms

Lecture slides Combining observations and models: calibration, pdf

## 2.6. Agent-based modelling¶

### 2.6.1. Key topics¶

- Agents vs Fields
- Agent representations
- Examples

### 2.6.2. Literature for exam¶

Macal, C.M., North, M.J., 2010, Tutorial on agent-based modelling and simulation. Journal of Simulation, 4, pp. 151-162.

### 2.6.3. Reading material¶

Bennett, D.A., Tang, W., 2006, Modelling adaptive, spatially aware, and mobile agents: Elk migration in Yellowstone. International Journal of Geographical Information Science, 20, pp. 1039-1066. Link.

Railsback, S.F., 2001, Concepts from complex adaptive systems as a framework for individual-based modelling. Ecological modelling, 139, pp. 47-62. Link.

### 2.6.4. e-Lectures¶

No e-Lectures.

### 2.6.5. Short paper assignment 3¶

Assignment 3: Agent-based modelling

The tutorial on agent-based modelling by Macal & North (2010) in your reader explains what Agent-based models (ABM) are. It provides the structure of an ABM (agents, relationships & interactions and environment). Read the paper of Bennet and Tang (2006) (reading material for this topic). Write an essay that explains the relationships & interactions steering agent behaviour used in the Elk model, providing examples of rules used in the model. In addition, try to identify and explain some key ABM properties in the Elk model, like emergence and path-dependence.

Write an 1-1.5 page (12 points font size, single line spacing) short paper or essay on this topic. Please hand in by uploading in Blackboard.