Scale considerations

Question 1

Definitions

Answer 1

Particular character of objects with respect to time or space (1D, 2D, 3D, etc.)

Question 2

Objects with scale

Answer 2

1. Processes
2. Observations
3. Models

Question 3

Special definitions of scale

Answer 3

(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

Question 4

Model structure:

Why distributed modelling?

Answer 4

(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)

Question 5

Model structure:

Conditions for model structuring:

Answer 5

(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)

Question 6

Model structure:

Two types for model structuring:

Answer 6

1. Horizontal structuring (→ runoff concentration, flood routing)
2. Vertical structuring (→ runoff generation)

Question 7

Spatial model structure – horizontal

Answer 7

a) Subcatchments, river sections

c) Quadratic raster network:

Question 8

a) Subcatchments, river sections

Answer 8

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

Question 9

c) Quadratic raster network:

Answer 9

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

Question 10

Implicit, location independent structuring:

Hydrotopes

Answer 10

 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“

Question 11

Implicit, location independent structuring:
Typical catchment characteristics
used for hydrotope building:

Answer 11

 Topography (Elevation, slope, etc.)
 Land use / coverage, vegetation
 Soil properties and
 Hydrogeology

Question 12

Spatial model structure – vertical

Answer 12

 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

Question 13

Scaling

Answer 13

 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

Question 14

Regionalisation

Answer 14

 transfer of variables or parameters from known to unknown

points in space or time

Question 15

Parameter estimation:

Calibration

Answer 15

• 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)

Question 16

Parameter estimation:

Validation

Answer 16

• 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

Question 17

Basic considerations for calibration

Answer 17

 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

Question 18

Analysis of parameter sensitivity

Answer 18

 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

Question 19

Model performance:

General comments

Answer 19

 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

Question 20

Typical performance measures

Answer 20

mean error or bias: =0

Absolute/relative standard error: min

Nash-Sutcliff-criterion: 1 (-indefinite < NS <= 1

Question 21

Optimisation:

Local optimisation

Answer 21

 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)

Question 22

Optimisation:

Global optimisation

Answer 22

 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)

Question 23

Model Uncertainty

Answer 23

 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, …)

Question 24

General Likelihood Uncertainty Estimation (GLUE):

Basic idea

Answer 24

 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)

Question 25

General Likelihood Uncertainty Estimation (GLUE):

Procedure

Answer 25

 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