Identifying and Evaluating Impacts - Mining and the Environment: From Ore to Metal - page 424

FIGURE 9.10
The Concept of Mathematical
Modelling in Environmental
Assessment

Source Mathematical modelling Receptor

Cross Media
Pathways

Source
Concentration

Receptor
Concentration

Geographic
Pathways

An example of a mathematical model found in practically all environmental assess-
ment studies is the simple form of the Gaussian plume dispersion equation for predicting
concentrations downstream of a source in uniform l ow, illustrated on steady-state, single
source plume dispersion modelling for air quality (total rel ection at ground level):

⎛
⎝

⎞
⎠

2

Q h

z

⎟

⎜

c exp

(9.2)

2

pss

u

2 s

yz

where c is the ground level concentration at a downstream distance of x metres along the
symmetry axis; Q is the rate of emission; u is wind velocity; h is the height of the emission
(stack height plus plume rise); and σ y and σ z are the lateral and vertical dispersion coefi -
cients calculated for the required value of x from standard empirical formulae appropriate to
the emission height, the roughness of the surrounding surface, and the atmospheric stability.
The above equation illustrates that the model prediction is only as good as the input
data allow, a simple truth that holds true for all model applications. Using the above for-
mula, an error of 20% in rate of emission will result directly in an error of 20% in the pre-
dicted concentration values. The accuracy of mathematical modelling is often controlled
by empirical model parameters. The dispersion coefi cients σ above must be dei ned with
consideration of local conditions in terms of atmospheric stability, topography, and ground
surface roughness, all of which are difi cult to derive.
The universal soil loss equation (USLE) is another example of a simple equation that
does not necessarily stand for a simple analysis; this is discussed further in Chapter Twenty.
Empirical parameters used in the USLE are equally difi cult to estimate, and long track records
of site-specii c historical data are essential for meaningful application of the soil loss model.
Uncertainties in model parameters will always require model calibration and validation,
and analyzing model sensitivities. Model calibration is essentially done by reconciliation of
predicted and observed values; then subsequent model validation compares predicted val-
ues against a series of i eld data from a period with changed conditions. At a minimum,
validation is done by comparing predicted and observed values for a data set different to
the data set used for calibration. If signii cant discrepancies exist, model input data should
be reviewed and calibration and validation cycle need to be repeated.
After calibration and validation, the mathematical model is ready for use. First, the
model is applied to existing conditions without the project (for example, evaluation of
runoff from a catchment area without the mine, or down stream water quality without

Uncertainties in model
parameters will always require
model calibration and validation,
and analyzing model sensitivities.