Mathematical Air Pollution Models: Eulerian Models
151
Examining the reasonableness of the results
•
Calculating the sensitivity of model results to change in inputs
•
Comparing evaluated concentrations from different air pollution models
•
Comparing simulated and observed concentrations
•
Usually, an air quality measurement network, whether in an urban or industrial site,
is designed according to specifi c criteria, so that it alone cannot provide all the information necessary for the validation of a model: the number of points and typology
of measurements, whether of chemical or meteorological parameters, are generally
insuffi cient to provide an overall coverage of the territory, or to guarantee a complete
range of information against which to test the model. This is perfectly understandable, since in designing a network that must function stably over an area the tendency
is to minimize the number of measurement points, which are normally fi xed, in
order to give greater evidence to the time evolution of concentrations rather than
their spatial distribution.
In general, a monitoring network can contribute to model validation, when it
is suitably integrated with other sensors during intensive measurement campaigns
specially organized for this purpose.
It must be borne in mind, when using models, that, while they are rather sophisticated instruments that ultimately refl ect the current state of knowledge on turbulent
transport in the atmosphere, the results they provide are subject to a considerable
margin of error. This is due to various factors, in particular the uncertainty of the
intrinsic variability of the atmosphere.
Models, in fact, provide values expressed as an average, that is, a mean value
obtained by the repeated performance of many experiments, while the measured
concentrations are a single value of the sample to which the ensemble average provided by models refer. This is a general characteristic of the theory of atmospheric
turbulence and is a consequence of the statistical approach used in attempting to
parameterize the chaotic character of the measured data. At the same time, the
uncertainty linked to the stochastic character of the parameterization of the atmosphere depends on turbulence intensity and is a function of the mean sampling
time. Atmospheric diffusion models ultimately present errors that can be reduced
as an uncertainty inherent in the phenomenon they describe. The reducible errors
originate from the use of an incorrect or insuffi cient set of input data and/or from
the intrinsic inadequacies of the particular model. As previously noted, irreducible errors are due to the statistical nature of the parameterization of the turbulent
fl uxes responsible for the dispersion of the material emitted into the atmosphere.
However, studies of model performance validation indicate errors in input data
(both of emission and meteorology) to be the factor responsible for the greater
contribution of the total uncertainty of models. Irwin et al. (1987), using Monte
Carlo techniques to simulate to propagation of errors from those of input data,
showed that the interval of error of the concentration maximum and of its distance
from the source may be double the interval of error of the input data. A model is
generally deemed acceptable if the estimated values are within a factor of two of
the observed data.
© 2010 by Taylor and Francis Group, LLC
151
Examining the reasonableness of the results
•
Calculating the sensitivity of model results to change in inputs
•
Comparing evaluated concentrations from different air pollution models
•
Comparing simulated and observed concentrations
•
Usually, an air quality measurement network, whether in an urban or industrial site,
is designed according to specifi c criteria, so that it alone cannot provide all the information necessary for the validation of a model: the number of points and typology
of measurements, whether of chemical or meteorological parameters, are generally
insuffi cient to provide an overall coverage of the territory, or to guarantee a complete
range of information against which to test the model. This is perfectly understandable, since in designing a network that must function stably over an area the tendency
is to minimize the number of measurement points, which are normally fi xed, in
order to give greater evidence to the time evolution of concentrations rather than
their spatial distribution.
In general, a monitoring network can contribute to model validation, when it
is suitably integrated with other sensors during intensive measurement campaigns
specially organized for this purpose.
It must be borne in mind, when using models, that, while they are rather sophisticated instruments that ultimately refl ect the current state of knowledge on turbulent
transport in the atmosphere, the results they provide are subject to a considerable
margin of error. This is due to various factors, in particular the uncertainty of the
intrinsic variability of the atmosphere.
Models, in fact, provide values expressed as an average, that is, a mean value
obtained by the repeated performance of many experiments, while the measured
concentrations are a single value of the sample to which the ensemble average provided by models refer. This is a general characteristic of the theory of atmospheric
turbulence and is a consequence of the statistical approach used in attempting to
parameterize the chaotic character of the measured data. At the same time, the
uncertainty linked to the stochastic character of the parameterization of the atmosphere depends on turbulence intensity and is a function of the mean sampling
time. Atmospheric diffusion models ultimately present errors that can be reduced
as an uncertainty inherent in the phenomenon they describe. The reducible errors
originate from the use of an incorrect or insuffi cient set of input data and/or from
the intrinsic inadequacies of the particular model. As previously noted, irreducible errors are due to the statistical nature of the parameterization of the turbulent
fl uxes responsible for the dispersion of the material emitted into the atmosphere.
However, studies of model performance validation indicate errors in input data
(both of emission and meteorology) to be the factor responsible for the greater
contribution of the total uncertainty of models. Irwin et al. (1987), using Monte
Carlo techniques to simulate to propagation of errors from those of input data,
showed that the interval of error of the concentration maximum and of its distance
from the source may be double the interval of error of the input data. A model is
generally deemed acceptable if the estimated values are within a factor of two of
the observed data.
© 2010 by Taylor and Francis Group, LLC