Summary Data and Models in Earth Surface & Water Systems (MIDTERMS)| UU| 2026/27

Data and Models in Earth Surface & Water
Systems




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,Contents
Lecture 1: Modelling concepts .................................................................................. 3
Lecture 2: Data, wrangling & visualization ................................................................ 11
Lecture 3: Basic statistical modeling and inference .................................................. 20
Lecture 4: Time-Series Analysis ............................................................................... 38




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,Lecture 1: Modelling concepts
What is a model?

Purposeful simplification of a system. Represents selected variables or processes. Links
information to an answer. Leaves some aspects of reality out.




Modelling approaches:

- Physical: for example the metronome, smaller physical representation of a
system
- Data-driven; statistical, time-series and machine learning models. You only have
data to predict a certain change in a system.
- Empirical; relations derived from observations/experiments. For example the soil
loss equation. Tied to the environment of the observation
- Process-based; physical mechanisms represented with equations; often solved
numerically.
- Hybrid; combines data-driven and process-based approaches.

Model forms

- Conceptual; Simplified, qualitative representation of a system; Verbal and
Graphical
- Mathematical; Relations expressed with symbols and equations
- Computational; Relations and equations implemented as code


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,One model may use all three forms.



Core structure of a model:




Model boundary

- Defines what is represented inside the model; simulated vs external processes;
simulated spatial domain vs outside world
- Chosen according to the model purpose and represented system
- Boundary conditions prescribe values or fluxes at the domain edge

For example: Incoming upstream river flow, offshore water level.

Settings and parameters

Settings: choices that configure how the model is run; define the numerical or
experimental setup; usually selected by the modeler.

Examples: file paths, time step, resolution, simulation period, algorithm choice.

Parameters: values that control model behaviour; represent physical or empirical
system properties; often measured or estimated using observations; may be constant or
vary across space.

Examples: infiltration capacity, roughness, recession constant.

States and fluxes

States: quantities that change during the simulation; represent the current condition of
the system; updated as model progresses; carry information between successive times;
give models memory of previous conditions.

Examples: soil moisture storage, ice thickness, sediment concentration.

Fluxes: rates of transfer between states; calculated from model relationships; change
the states during each time step; often expressed per unit time.

Examples: runoff, glacier melt, sediment transport.



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,Inputs

- Observations used to estimate parameters; e.g. observed discharge, ice flow
velocity.
- Initial conditions of states; e.g. initial soil moisture.
- Boundary conditions.
- Forcing: external drivers that vary through time; e.g. precipitation, temperature,
wind.
- Predictors (data-driven models): variables used to estimate or classify the
output.

Outputs

- Quantities produced by the model.
- Primary outputs: directly address the modelling question; e.g. predicted
discharge, shoreline change, glacier mass loss.
- Diagnostic outputs: reveal internal states, fluxes, or intermediate calculations;
help explain and evaluate model behaviour; e.g. soil moisture, sediment
transport rate, energy balance.
- Output forms: single value, time series, map or spatial field, probability
distribution.




Static vs dynamic

Static: No evolving internal state

Dynamic: System changes through time; Modelled at discrete time steps (t); t indexes
successive model times or time steps.




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,Lumped vs distributed

Lumped(a): One value for entire area of interest; Internal spatial variation ignored

Semi-distributed(b): Area divided into units with their own states; Variation between
units represented

Distributed(c): Values vary continuously across grid cells; Spatial interactions explicitly
represented




Deterministic vs stochastic

Deterministic: same inputs and parameters give the same
output; repeated runs are identical. represents one
prescribed system response

Stochastic: random variability is represented explicitly;
repeated runs can give different outputs; many runs form
an output distribution; useful for probabilities, ranges, and
extreme-event risk.

Important considerations: deterministic does not mean
certain, both can have uncertain inputs, parameters, and
model structure.

Modelling solutions

Analytical solutions: Equations solved directly

Numerical solutions:

- Differential equations often cannot be solved
analytically. Solving equations on temporal or spatial
grid.
- Discretisation needed: breaking down continuous
functions into small pieces; approximate solutions
computed step by step; Introduces numerical error
(proportional to step/grid size).
- Several numerical solvers exist (e.g. Finite Difference
Method). Some schemes require sufficiently small time
steps to remain stable.


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