Modelling Catchment-Scale Responses to Climate Change - Climate Change Impacts on Freshwater Ecosystems - page 256

degree of equifinality so that the number of possible model structures and
parameters is reduced. One is to reduce the number of processes in the model,
but this conflicts with the requirement for model realism. Water quality
modelling is particularly difficult because the large spatial scale required means
that it is hard to constrain model parameters. For instance, a water quality
model may require the nitrogen concentration in the catchment soil, which is
potentially measurable. But given that there will be a wide range of N
concentrations in the catchment soils, which should be used? The mean of a
large number of observations? Or should soils along flowpaths or close to
rivers be given more weight? Or measurements from the upper parts of soil
profiles which may have more direct hydrological influence? Experience shows
that often models behave best with parameters that cannot be related to
measured values in any obvious way.
There are, however, methods for estimating and reducing model uncertainty,
and these have been extensively used in the Euro-limpacs modelling programme.
One of these is Monte Carlo analysis (e.g. Rubinstein 1981). This is a well-
established technique in which instead of running a model once with what is
considered the best set of parameters to generate a single result, the model is run
many times (typically thousands) with different values for input parameters
selected from their potential ranges according to some scheme. The output is then
a probability distribution which can be used to generate statistics such as confidence
intervals. Moreover, the parameters with most influence on the uncertainty of the
final result can be identified (known as sensitivity analysis) and the information
used to identify optimum targets for research aimed at reducing uncertainties.
The results of Monte Carlo analysis when applied to models can be surprising and
counterintuitive. For example, the calculation of critical loads, the deposition
thresholds used in pollution control policy, involves models which have 10-20
uncertain parameters. Monte Carlo analysis showed that the uncertainty in the
calculated critical loads was typically less than the uncertainty in any of the input
parameters (Skeffington et al . 2007). This behaviour is to be expected where
parameters are independent and subject mainly to random errors.
Monte Carlo analysis has been applied to all the INCA models to identify key
parameters and place confidence limits on model predictions (Wade et al . 2001;
Cox & Whitehead 2004; Wilby 2005; Rankinen et al . 2006; Jarritt & Lawrence
2007). The results give an idea of the kind of variability that can be expected
from water quality climate change simulations. For example, Fig. 10.6 shows the
error bounds for predictions of phosphorus concentrations in the river Lambourn
in the 2050s, using the INCA-P model (Whitehead et al . 2008). The 95%
confidence bounds show a relatively narrow band of uncertainty during lower-
flow summer months when conditions have been more stable. However, in winter
months, the uncertainty increases as flow conditions become more variable and
storms generate more run-off of water and nutrients.
One key achievement in the project has been to develop and apply a generalized
Sensitivity and Uncertainty Analysis Tool, which uses a variant of Monte Carlo
analysis called generalized sensitivity analysis. The specific method applied is that
developed by Hornberger and Spear (1980). The Monte Carlo realizations are
divided into those that best fit the observed data and the rest. The best results are