Scale considerations Flashcards
Definitions
Particular character of objects with respect to time or space (1D, 2D, 3D, etc.)
Objects with scale
- Processes
- Observations
- Models
Special definitions of scale
(1) Extent → Total dimension, total time period
(2) Support → discretisation, raster, time steps
(3) Coverage → Observed/ modelled/ considered part of elements from total number of elements
Model structure:
Why distributed modelling?
(1) Variability of input variables (e.g. precipitation)
(2) Variability of basin characteristics (e.g. land use, soils)
(3) Considering different model approaches (e.g. urban, rural)
Model structure:
Conditions for model structuring:
(1) Problem appropriate (goals: target gauge, long term trends)
(2) Information appropriate (depends on available input data)
(3) Adequate for processes (floods vs. water balance)
Model structure:
Two types for model structuring:
- Horizontal structuring (→ runoff concentration, flood routing)
- Vertical structuring (→ runoff generation)
Spatial model structure – horizontal
a) Subcatchments, river sections
c) Quadratic raster network:
a) Subcatchments, river sections
Advantage:
- Natural flow direction
- 1D simulation possible
- Fast computing
- Many models available
- Further structuring into hydrotopes easy possible
Disadvantage:
- Poor distribution in space
- no fully specification of location possible
- Input scaling required
- Hydraulics only for river sections possible
c) Quadratic raster network:
Advantages:
- Fully explicit specification of locations!
- Data usually available as raster data (e.g. elevations, weather radar rainfall)
- Simple geometry for hydraulic approaches available
Disadvantages:
- Flow direction not well defined
- Real processes might take place at not-rectangular land forms
- Uniform resolution required
- Parameter intensive approach
- Computationally expensive
Implicit, location independent structuring:
Hydrotopes
Homogeneous with respect to hydrological behaviour
Building of hydrotopes by combination of catchment properties
Hydrotopes are also called HRU „hydrological response unit“ or HSU „hydrological similar units“
Implicit, location independent structuring:
Typical catchment characteristics
used for hydrotope building:
Topography (Elevation, slope, etc.)
Land use / coverage, vegetation
Soil properties and
Hydrogeology
Spatial model structure – vertical
Application for each hydrotope class or raster cell or subcatchment
Horizonal variation in model structure possible
Further distribution within one simulation unit by statistical distribution of parameters possible
Scaling
In a narrower sense → change of support for variables or
parameters (change of temporal or spatial resolution)
In a wider sense → spatial or temporal transfer of variables or
parameters between two different scales
Regionalisation
transfer of variables or parameters from known to unknown
points in space or time
Parameter estimation:
Calibration
- Manual or automatic estimation (optimisation) of some model parameters
- Repeated simulation with modified parameters (e.g. rainfall → runoff )
- Maximize simulation performance comparing observed and simulated target variable (e.g. discharge)
Parameter estimation:
Validation
- Test of model performance using a different data set and keeping model parameters constant
- Using split sampling (two parts sample) or cross validation (leaf one out method) for separation of the data sets in calibration and validation data set
Note: Most often used criterion for the assessment of hydrological model performance is comparison of observed and simulated discharge
Basic considerations for calibration
Use as small as possible number of parameters for calibration
Use parameters which cannot be derived from basin properties
Try to restrict parameters to physically feasible range
Use parameters with high sensitivity
Analysis of parameter sensitivity
Estimation of the sensitivity of the hydrological model output depending on change in parameters
Sensitivity is often assessed with regard to model performance
Theoretically analysis of a n-dimensional response surface corresponding to an n-dimensional parameter space
Practically often only 1D sequential analysis changing one parameter at a time is carried out
Model performance:
General comments
Performance criteria are used both for optimisation in the objective function and for validation of the model
Using simultaneously several criteria in optimisation (multi criteria optimisation) allows more robust parameter estimation
Using additional criteria for validation is good test
Performance criteria are usually calculated for each time step and then averaged over the total period
Typical performance measures
mean error or bias: =0
Absolute/relative standard error: min
Nash-Sutcliff-criterion: 1 (-indefinite < NS <= 1
Optimisation:
Local optimisation
Locates the nearest optimum relative to the starting point no matter if it’s a local or global optimum
One Parameter: e.g. univariate gradient method
Several pars: downhill simplex (Nelder & Mead, 1965, HECHMS);
Gauss-Marquardt-Levenberg (Doherty, 2004, PEST)
Optimisation:
Global optimisation
Finds global optimum; different types of optimisation: deterministic, probabilistic, combination methods
Well known example for combination methods is „Shuffled complex evolution“ algorithm (SCE) (Duan et al., 1992)
Model Uncertainty
All models are uncertain!
Uncertainty can result from
a) Uncertain knowledge about processes
b) Uncertain model parameters
c) Uncertain input variables
d) Uncertain target/ reference variable(s)
In modelling the uncertainty should be quantified:
a) The simplest way is by discussing the performance measures
b) Better is to provide results with confidence bands (Baye’sche uncertainty estimation, GLUE, different Monte-Carlo experiments, …)
General Likelihood Uncertainty Estimation (GLUE):
Basic idea
Because of our inability to represent exactly in a model how nature works there is no one optimal parameter set or model.
Instead it is assumed that there are many good (behavioural) parameter sets equally suitable for simulation (equifinality).
The different parameter sets are supposed to represent the uncertainties a) and b) (see above)
General Likelihood Uncertainty Estimation (GLUE):
Procedure
Find a representative set of parameter vectors and use these to assess model uncertainty together with predictions
Realized by ensemble simulation using behavioral parameter sets weighted acc. to its prediction performance likelihood
