Modelling and Model Building - Environmental Modelling: Finding Simplicity in Complexity - page 12

we should invest in parameter measurement according to
how big an effect the parameter has on the model output
of interest. The magnitude of the effect of parameters on
model output is known as the sensitivity of a model to its
parameters. This important stage of analysis will be dealt
with in more detail below.

purpose of the model. A robust validation of the key model
output would tend to indicate that the model has per-
formed well in a predictive sense. This outcome does not
mean that the results have been obtained for the correct
reasons, in other words good prediction is no guarantee
of good explanation. In this way, if one were to validate
the output of a catchment hydrological model using mea-
sured discharge data and obtain good agreement between
model and data, this success can come about as the result
of many different configurations of the driving variables
for discharge. It is thus important in validation to validate
the output required but also some internal variable that
would indicate whether that output has been arrived at
for the correct reasons, in this case the spatial distribution
of soil moisture around the catchment.
The techniques used for measurement will depend
upon a number of logistic constraints such as availability,
cost, dependence on power supplies, training required
for use and safety but must also depend upon the spatial
and temporal structure of the model for which these
techniques will provide data since it is important that
the model and the data are representing the same thing.
A good example is soil moisture. Soil is a three-phase
medium consisting of the soil matrix, rock fragments
greater than 2 mm in diameter and of a porosity. Soil
moisture occupies the porosity, which is usually around
half of the soil volume. In many soils, rock-fragment
content can be in excess of 30% (van Wesemael et al .,
2000) and whilst rock fragments sometimes have a small
porosity, it is usually quite insignificant for the purposes
of moisture retention. Volumetric measurement of soil
moisture usually provides an output of m 3 water per m 3
soil fine fraction which does not usually contain rock
fragments. The latter tend to be avoided in the installation
of, and not accounted for in calibration of, electronic sen-
sors of soil moisture and tend to be avoided or sieved out
of gravimetric samples. Soil-moisture measurements are
usually an aggregate of small sample measurements of the
fine soil fraction. However soil tends to be represented as
large blocks with dimensions of tens to hundreds of metres
in hydrological models. The move to this larger-scale
representation must therefore incorporate a significant
loss of available porespace because of the presence of rock
fragments and thus the nature of soil moisture at this scale
is quite different to that at the point scale of measurement.
The need to balance data and model attributes is partic-
ularly clear where indirect measurements, in particular
remote sensing, are used for model parameterization.
Over recent decades there has been a move away from
lumped models in which spatial heterogeneity is not

2.2.1 Definingthesamplingstrategy

Like models, measurements are also abstractions of real-
ity, the results of a measurement campaign will depend
as much upon the timing, technique, spatial distribution,
scale and density of sampling as on the reality of the
data being measured. As in modelling, it is imperative
that careful thought is given to the conceptualization and
design of a sampling strategy appropriate to the parameter
being measured and the objective of the measurement.
This is particularly true when the sampled data are to be
used to parameterize or to validate models. If a model
underperforms in terms of predictive or explanatory
power this can be the result of in appropriate sampling
for parameterization or validation as much as model per-
formance itself. It is often assumed implicitly that data
represents reality better than model does (or indeed that
data is reality). Both are models and it is important to be
critical of both.
We can think of the sampling strategy in terms of (i) the
variables and parameters to be measured for parame-
terization, calibration and validation, (ii) the direct or
indirect techniques to be used in measurement and their
inherent scale of representation, (iii) the spatial sampling
scheme (distributed, semi distributed, lumped) and its
density, (iv) the temporal sampling scheme (duration
and temporal resolution). Choosing which variables will
be measured for parameterization and the intensity of
measurement will depend very much of the sensitivity
of the significant model outputs to those (see below).
Highly sensitive parameters should be high on the agenda
of monitoring programmes but as model sensitivity to a
parameter is usually also dependent on the value of other
parameters, this is not always as straightforward as it might
at first appear. Where variables are insensitive either they
shouldnotbeinthemodelinthefirstplaceortheir
measurement can be simplified to reflect this. Calibration
parameters should be, as much as possible, those without
physical meaning so as not to compromise the physical
basis of the model and their measurement will be neces-
sary for the application of models to new environments
or epochs. Validation parameters and variables should be
those that are the critical model outputs in terms of the