Geology Reference
In-Depth Information
Rainfall
Table 2.1
Stages in model development.
Stage
Requirements
Objectives
Definition of problem
Required temporal and spatial scales
Required output, e.g. rates/location of
erosion/deposition
Required level of accuracy of prediction
Fig. 2.1
An example of a simple
black-box model.
Conceptualization
Understanding of system being modelled
Required level of simplicity/complexity
Experimental foundation for modelling
Definition of system variables
Definition of key processes
Decisions on which variables and
processes to include and exclude
Construction of flow diagram
Soil loss
a given catchment or at a given field site is to
undertake detailed field observations and meas-
urements of erosion and its controlling factors at
that site and, based on an analysis of the results,
to select appropriate measures to control the
problem? Unfortunately, such detailed field
measurements are often very costly and must be
carried out over many years, probably ten or
more, in order to collect representative data. In
contrast, many problems must be addressed
immediately and cannot wait for a solution some
years later by which time considerable environ-
mental damage may have occurred. The value of
an erosion model is that it can be applied now.
The question that arises, however, is how simple
or complex it needs to be for it to be valid.
Broadly, simplification can be represented at
three levels, resulting in what is usually termed
black-box, grey-box and white-box models. In
a black-box model (Fig. 2.1) a relationship exists
between one or more inputs or controlling factors,
such as rainfall or soil type and the output, such as
soil loss. There is no understanding or modelling
of the processes through which the inputs give rise
to the output. Such models are usually expressed
by some form of statistical relationship, like a lin-
ear regression equation or a correlation. A sedi-
ment-rating curve for a river channel whereby
sediment concentration is expressed as a function
of runoff is a good example of this type of model.
A grey-box model (Fig. 2.2) includes some under-
standing of the relationship between input and
output, reflecting, for example, that the effect of
rainfall on erosion alters according to slope
steepness and vegetation cover. The model is
again operated by equations based on statistical
Process description
Decisions of best available mathematical
descriptions of processes
Match between mathematical description
and process understanding
Parameterization of system variables
Availability of input data
Boundary conditions
Selection of appropriate time and space
boundaries
Continuity of mass and momentum when
routing water and sediment across
boundaries.
Sensitivity analysis
Rationality of model
Determination of most sensitive input
parameters
Required level of accuracy of input data
Calibration
Feasibility of calibration
Selection of key parameters for
calibration
Selection of dataset for calibration
Calibration procedure
Match between calibrated values and
values expected in field conditions
Validation
Criteria for goodness of fit
Selection of dataset for validation
Validation procedure
Required level of accuracy for acceptance
of model
Problems associated with uncertainty
Interpretation of results
Application
Decision on whether model is
appropriate
Data requirements
Setting-up and running of the model
Analysis of results
