predictive modelling calculations are made several other steps need to be
considered during the model application process (Figure 1). Every modelling
project should be started with clearly defined goals and objectives. This point
has to be stressed, since it influences every other consecutive step.
2. Model Application Process
different steps are:
- To collect and gather
information e.g. concerning the geology, hydrology and geochemistry of the
site. During this step the contaminated site is characterised with regard
to the modelling goals. This information is incorporated into the conceptual
site model. The established numerical model can be used in a later
step to test and verify the conceptual site model
- Selection of a computer code.
The selection of an appropriate computer code depends e.g. on the decision
whether two or three dimensional modelling is needed.
- Preparation of input files and
the incorporation of all governing equations. Assuming that all necessary
information and equations have been included a simpler model should be
applied preferentially over a more complex model.
- The calibration process is
undertaken until model simulations match the field observations to a
reasonable degree. The subsequent sensitivity analysis should be used to
test the overall responsiveness and sensitivity of the numerical model to
certain input parameters.
3. Predictive Simulations
- After calibration, the model
can be used for predictive simulations. The model can be applied as a
management tool for decisions in which the response of a system is
predicted, e.g. concentrations in groundwater at some time in the future
can be predicted.
- However the model needs to be
used with caution when applied, since uncertainties are always present and
should be addressed. The uncertainties can be divided into two general
categories: Those associated with model input parameters and those
associated with numerical and conceptual difficulties. Methods to deal
with uncertainty are sensitivity analysis and the Monte Carlo method.
- The sensitivity analysis is
used to rank important sources of variability and uncertainty. A
sensitivity analysis can involve complex mathematical and statistical
techniques such as correlation and regression analysis to determine which
factors are most important for the model output..
- The Monte Carlo Method
considers each model input parameter to be investigated as a random
variable defined by a probability density function (PDF). The PDF shows
the probability of an uncertain quantity taking on a particular value (Zheng & Bennet 2002).
Figure 1: Model Application
Process (after Bear 1992)
4. Weblinks and Guidelines:
Bear, J., Beljin, M.S., Rose, R. (1992). Fundamentals
of Ground-Water Modelling. EPA Ground Water Issue (online: http://www.epa.gov/tio/tsp/download/issue13.pdf)
(1999): RBCA Fate and Transport Models: Compendium and Selection Guidance (http://www.epa.gov/oust/rbdm)
Groundwater Services, Inc. (1996). Parameter
Estimation Guidelines for Risk Based Corrective Action (RBCA) Modeling. NGWA Petroleum Hydrocarbons Conference, Texas
Geotechnical and Geo-environmental Software Directory
Geological Survey Software Links
USEPA Center for Subsurface Modeling Support (CSMoS)
Evaluation of Selected Environmental Decision Support
Zheng, C., Bennet, G. D. (2002). Applied contaminant transport modeling
(2 ed.). New York.
Hakanson, L. (2004). Break-through in predictive modelling
opens new possibilities for aquatic ecology and management – a review. Hydrobiologia 518, 135-157
Schwarzenbach, R.P. (2003): Environmental organic chemistry (2 ed.) Wiley. New York