Chapter 1

Question 1

What is a system?

Answer 1

Limited part of reality that contains interrelated elements. The totality of relations within the system is called “system structure”.

Question 2

What is a model?

Answer 2

A simplified representation of a system.

Question 3

How does the modelling scheme go?

Answer 3

Reality - System -Model

Question 4

What are the two basic assumptions of a model (dynamic)?

Answer 4

1. The state of a system can be always quantified.
2. Changes in the states (rates) can be described by mathematical equations.

Question 5

What is the dimension (unit) of 1. State variables, 2. Rate variables, 3. Driving variables?

Answer 5

1. state = amount
2. rate = amount/time
3. driving = not known beforehand

Question 6

What is a simulation?

Answer 6

1. The building of a model
2. and the study of the model behaviour in respect to its system

Question 7

What are the type of models? (in respect to time and characteristics)

Answer 7

Time:
Static
Dynamic
Characteristic:
Descriptive
Explanatory

Question 8

What is a static model?

Answer 8

A model that does not include the time dimension.

Question 9

What is a dynamic model?

Answer 9

A model that includes the time dimension.

Question 10

What is a descriptive model?

Answer 10

A model that shows the
existence of relations
between the elements of a
system without any
explanation.

Question 11

What is an explanatory model?

Answer 11

A model that explains the
behaviour of a system at
an upper integration level
by integrating processes of
a lower integration level

Question 12

What is an important thing to keep in mind when thinking about a system’s boundaries?

Answer 12

Choose a boundary such that the environment might influence the system, but that the system
does not affect the environment significantly.

Question 13

What is a state variable?

Answer 13

An element of a system structure that represents a quantity; this quantity should
be additive.

Question 14

What is a rate variable?

Answer 14

Variable indicating the rate at which the
state variables change.

Question 15

What is a parameter?

Answer 15

A variable with a value that does not
change during the simulation and is
provided beforehand.

Question 16

What is a driving variable?

Answer 16

Characterization of the influence of
external actors on the system, which are not influenced by the processes within the
system.

Question 17

What is a variable of extension?

Answer 17

Variables represent an amount, meaning that they can be added or
subtracted

Question 18

What is a variable of intensity?

Answer 18

Variables of intensity cannot be added or subtracted. Examples are temperatures and concentrations. But these variables of intensity can be calculated from variables of extension.

Question 19

What are the basic rules of Unit Analysis?

Answer 19

1. both sides of the equal sign should have the same units.
2. ONLY values with the same units can be added/subtracted.
3. Log and exponentials
   OR
4. The terms that are added, subtracted or
   compared must have the same dimensions or units. So both sides operators (=, +, -, <, > or combinations of these must have the same dimension and unit.
5. The dimensions and units of the expressions on both sides of the equal sign should be identical.
6. In multiplication reciprocal dimensions cancel out.
   In division identical dimensions cancel out (a division is the same as a multiplication with its reciprocal).
7. The arguments of exponentials, logarithms and angles should be dimensionless.

Question 20

What are the theoretical phases of systems analysis?

Answer 20

1. Concept model formulation
2. Quantitative model specification
3. Model evaluation
4. Model use

Question 21

What are relational diagrams?

Answer 21

Diagrammatical representation of system’s components and their relationships, which collectively form our conceptual model, using symbols that indicate the specific nature of the relationships.

Question 22

Objects in relational diagrams (most important: squares etc)

Answer 22

State - rectangle
Rate - valve
Parameters - line with circle in middle
Auxiliary variable - circle
Influence - dotted line
source - cloud

Question 23

What is feedback?

Answer 23

The influence of a state on its own rate of change.

Question 24

How can models be solved?

Answer 24

Analytically
Numerically

Question 25

What is the difference between analytical solutions and numerical solutions?

Answer 25

1. Analytical solutions are only available for relatively simple problems (needs the primitive function for the determined integral). 2. A model can be always solved numerically. 3. Calculating a new state of the system * Integrate all derivatives in the model

Question 26

What is a time coefficient (tau)?

Answer 26

The time needed for a model to reach its equilibrium state when the rate is kept constant.

Question 27

What is a time step (delta t)?

Answer 27

Instead of representing time continuously, models discretize time into intervals. The time step (Δt) determines the size of these intervals.

Question 28

What are the rules for choosing the correct time step (delta t)?

Answer 28

1. Based on an analysis of the time coefficients (tau) within the system (rule of thumb) 2. Time step should be small enough to track the dynamics of driving variables 3. Time step should make sure that time-driven discontinuities will take place in the simulation A pragmatic approach to test the choice of the time step is the ‘trial and error’ approach.

Question 29

What is the relationship between integration levels, characteristic times and generalisation potential?

Answer 29

High integration level (Vegetation) - Low Generalisation level - Large Characteristic time Low integration level (molecule) - High Generalisation level - Small Characteristic time

Question 30

In a numerical solution, what does error depend on?

Answer 30

1. Value of ∆𝑡 : the time-step (the higher the vale the higher the error) 2. Choice of numeric integration method (Euler more basic than Runge Kutta 4th order) 3. Processes in the system: characteristic time or time coefficient

Question 31

What is the equation for the time coefficient (tau)?

Answer 31

tau =|(State in equilibrium (S_eq) - State at time t (S_t))/rate of change of state (dS_t/dt)|

Question 32

Systematic Problem Approach

Answer 32

1. Think of the question clearly, reformulate it 2. Rewrite information that are given 3. design problem solving strategy: see what info is missing (rewrite equations) 4. Derive information that is lacking by external source. 5. Use info to answer original question.

Question 33

How can we determine the usefulness of models?

Answer 33

1. Are they testable? a. yes - Verifiable models (repeatable systems or recurring) (allows their predictions to be tested and validated against observed data) b. no - Speculative models (used to explore potential scenarios, generate hypotheses, or simulate systems where empirical data may be limited or uncertain) 2. How general are they (Generality)? a. Spatial/temporal limitations taken into consideration? b. Are all relevant processes included?