Describe what is meant by a model in a way that is generally understandable (how is it defined, what are its essential characteristics?)
A model is defined by 3 Key Characteristics:
1.Mapping characteristic: Model is a simplified representation of objects from the real world.
Processes
Events
Cause-effect relationships
2.Shortening characteristics: Simplifications capture the essentials but are always fuzzy! —> They do not capture all attributes but only those that are relevant.
3.Pragmatic features:
Scale level: Which temporal and spatial scales should be simulated?
Process orientation: What processes can and should be simulated?
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Purpose of Models:
to improve system understanding
to detect and simplify the systems´s complexity
as a basis for decision support
as a (low-cost) alternative to real world experiments
Limitations:
Evertying should be made as simple as possible, but not simpler!
It is impossible to develop a model that depicts the whole world and all its processes
A Model always needs a simulation software + real data!
A Model needs a time-variant input (e.g. precipitation) to create a time variant-output (e.g. runoff)
On what kind of influencing factors can model results depend on in general?
time
space
randomness
Focusing on deterministic models, which influencing factors do they depend on?
(90% of the models in Water Ressources Management are deterministic)
You should define the main characteristics of a black box model.
Please list the main characteristics of this model type
Black box:
Simulates behavior without knowledge of the internal workings
Requires mesured information based on experiments and experience (a posteriori knowledge) -input and output data and trys to perform a transfer function
parameters cant be changed —> new function
Example: Unit hydrograph (empirical models)
—> One is not aware what is happening in the box, only the input & output are known. Unlike the white box model, no parameters can be set or changed here.
White box:
Simulates processes with knowledge of the internal workings in order to test or review the functionality
Requires structural Knowledge (a priori knowledge) as an input
Example: Flow laws
—> One can see or describe what happens in the box, its transparent.
Your task is it to draw a hydrograph that indicates steady state flow as well as for an unsteady state flow condition. Please explain the differences generally understandable.
Steady state flow:
discharge rate is not changing over time —> dQ/dt = 0 discharge is independent from time
no maxima or minima
good to indicate peak discharge
Unsteady state flow:
discharge rate is changing over time —> dQ/dt =/ 0 discharge rate is dependent from time
Includes minima and maxima
good to determine volume quantities
Steady state flows und unsteady state flows are used for different tasks of design in water
resources management. Please explain when steady state flow is appropriate for design
and when to use unsteady state flows.
good to indicate max. discharge rate
—> for dimensioning a sewer system for flood events
good to determine volume
for measuring retention basins
When it comes to design flows for municipal water management tasks and large-scale
water management models there are differences. Could you please explain these
differences in easy words?
Difference regard the time and space scale
large-scale water management models: -more information, space and longer time needed for observation, steady state flow
municipal water management: shorter obersvation time, single-event, unsteady state-flow
EXTRA
Example: Deterministic models
Block Model - Detailed Model
Block Model:
Lumped (pauschal)
Rainfall is averaged over the sub-basin
just one single set of Model parameters
Runoff is only calculated at the sub-basin exit
Detailed Model:
Rainfall is determined for each cell
Model parameters can differ from cell to cell
Runoff data is available for each cell
Model Types
Descriptive model vs. Numerical Model
For which concrete application case in water management would you use a descriptive model? Justify your statement.
Descriptive model:
Describes qualitatively, qualitative variables
Effect diagram
Verbal description
e.g. rule-based model (if … then …)
Numerical model:
Describes numerical, quantitative variables
Flowchart
Equations
e.g. deterministic RR-models
Descriptive models are used in situations where a crisp representation of the process/object/system/status in numbers is not possible – instead it can be described with fuzzy, linguistic terms.
Example: during a flood event it is often difficult to state the exact water level. In this case, we would say for example “the water level is high.”
Furthermore, since they try to depict fuzzy situations, rule-based models (if…, then…) are typical descriptive models. For example: “if a flood event destroys many homes, then the people will be sad.” You see, it is not clearly stated how sad the people will be, because it is very difficult to describe it in words – the required data for mathematical equations or parameters is missing.
What are the differences between a deterministic and a stochastic model?
Deterministic models:
no randomness is involved, only depends on time & space
Output is determined by initial parameters & conditions and will always be the same for the given conditions / parameters
90% of the models are deterministic
Stochastic models:
Depends on time, space & randomness
Output can be different for the same set of parameters & conditions because it can be influenced by randomness
What Models do you know? List from large scale to small scale and name the influencing factors.
Wisdom
Monte Carlo models (space, time randomness)
Process models (space, time)
Knowledge
Fuzzy models (space, time)
Rule-Based models (space, time)
Information
Stochastic models (space, time randomness)
Neural models (space, time)
Empirical methods (space, time)
Statistical methods (space, time)
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