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Lecture notes: Land Surface Process Modelling (GEO4-4406)
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GEO4-4406: Land Surface Process ModellingIntroduction to simulation modelling
Simulation model: other terms used: numerical, forward, dynamic or dynamical model. These terms
have slightly different meanings, but they refer to models that calculate or mimic processes that are
taking place in a certain spatial-temporal system. It is simulating certain mechanisms in a system. The
timescale depends on the scale of the simulation.
The state = all kinds of fluxes together. The state is updated over time. In most cases, this is done with
discrete timesteps. So, for each time step, the system is updated towards the new state. The update
function in most cases stays the same over time, as processes do not change over time.
Simulation models heavily rely on the mechanisms in the system considered in addition to data which
are used as input or used to calibrate or tune the model.
Examples: hydrology (river flow, groundwater), ecology (plant growth, animals), land use science,
epidemiology (disease spreading), traffic, social science (knowledge dispersal), climate etc.
- Land use change: people move and agricultural land changes etc. They mimic processes over
several years (time step of a year, cell size 1 km). It uses neighbourhood rules to update the
land use over time. They are used to forecast land use for management and policymakers.
- Flooding of low-lying polder area: mimic the flooding of the polder after a dike breach. The
spreading can be reconstructed using historical data. However, forecasting can also be done.
In a simulation model, an update function is used. It uses state variables, parameters and inputs. Aim
of the model is to get state variables from the input with transition functions.
- The time steps have to be selected by the model builder (e.g., seconds, years, decennia) and
depend on the process that you are simulating. Balance between type of data, process and
run time.
- Inputs: drivers or boundary conditions from external. E.g. rainfall or population.
- State variables: calculated by the simulation (within the model) and are changing over time.
E.g. river discharge or land use.
- Time transition functions with parameters: model code. Describes how the model (state
variables) changes over time. It takes the input for a time step and the state in the previous
time step and based on these two it updates the state. It encodes all the rules that steer the
change over time. They need to be parameterized, so that is why they include parameters,
which are values that are included as a component in the transition function.
Why are simulation models valuable in research?
1. Formalize process knowledge. Theory of systems into a model.
2. Coupling of processes: links are defined in quantitative terms in a model.
3. Integration of observations (data): model input, calibration (inverse modelling), and data
assimilation.
,A model is a mediator between theory (abstract body) and data.
Model development cycle: we define the aim, and end with user model. It is a trial and error
procedure, and in each step we may fail and want to go back to previous steps.
1. Model structure identification: transition of
theory into a model structure
o Define conceptual model: graphical
description, description in words,
tables, equations (easily converted into
code).
o Choose type of model: differential
equation, cellular automata,
probabilistic, rule-based and agent-
based.
2. Computer programming: from model structure
to computer model. Use appropriate tools:
spreadsheet, modelling toolbox or generic
programming language. (matlab, python etc).
3. Estimation of inputs and parameters: either (or
both): direct estimation in the field or
calibration (inverse modelling).
4. Validation: test model against independent data
set. Also called evaluation. Then there is a user
model, which can be used as forecast of systems.
Spatio-temporal simulation model: mimics processes that occur in a spatio-temporal system. Runs
forward in time. The calculation stays the same over time, the only thing that changes in the input
and output, which are the changes through time.
Examples: water erosion, forecasting streamflow of large rivers, disease spreading, land use and
fluvial deposits.
You need inputs, maths, equations (from physical world to online), programming and uncertainty
assessment.
Model theory (40%), model tools (40%) and case study (20%)
, Point models and differential equations – 01
We define the aim of the model using the study site, field data
and technology we have. We use this as an input. This results in
the model structure, which describes the model on a piece of
paper. This needs to be transformed into a computer model. We
then define the parameters of the model and calibrate the
model and we need to evaluate the model's outcomes using field
data.
The numerical solutions come into play because the differential
equations need to be solved.
Differential equations:
- In dynamic models: give rate of change (how fast a
change occurs at a certain location).
- Mainly point functions (no spatial interactions in neighbouring pixels).
- Often used in model structure: vegetation growth, flow of water into or out of storages,
radio-active decay etc.
- Need to be integrated to be used in a model: analytical (often too complicated) and
numerical.
We solve the numerical solutions on a computer, so here programming comes into play.
Differential equation = rate of change given by a certain function. It involves a derivative of a certain
unknown function. By integrating, we find the function. It always gives the rate of change of the
function (graphical: the slope of the unknown function). To solve the differential equation, integration
is needed to find the unknown function.
1. Solving using the analytical technique: integrating. We need to solve an initial value problem,
which is always given by a differential equation and an initial value. We can use the integrated
differential equation, to make a plot. A while loop is used: T is the timestep times the
timestep duration, which is for each loop increased by 1 and there the thing known is
calculated.
2. Numerical mathematics: often used because:
o Many differential equations cannot be solved analytically.
o Numerical solutions are relatively simple to program.
o numerical solutions are sufficiently precise for most applications.
o modellers can’t do maths (easier).
For example: if it is raining, water is intercepted by the canopy. There
is storage and drip to the surface. With this equation the interception
storage can be determined for the next timestep: it equals the
previous interception storage and the change (fraction). If you plot
this, you get a curve. You have to define an initial value. It decreases
to zero in the end, because it is emptying over time. Delta t delta y, is
the change over time. Therefore it can be rewritten. You can take the
limit (dt/dy very small).
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