152
Air Pollution and Turbulence: Modeling and Applications
A considerable amount of work has been done, especially in the United States,
on the quantitative assessment of model performances. The adopted approach varies according to whether the validation refers to the scientifi c validity of the model
or to the usefulness of the model in environmental management. In validations for
management purposes, less importance is attributed to deterministic processes (processes of cause and effect), while attention is focused on the correspondence between
observed and predicted values. For such analyses to be objective, it is necessary
to utilize different data from those adopted for the parameterization of the model
itself. Particular attention is paid, on the whole, to the comparison of concentration
maxima both with and without temporal and/or spatial simultaneity.
Generally, the attempt is made to objectivize the validation of model performances
by adopting statistical indices that describe their capacity to represent observed data.
Among them, the most widely used are (Hanna, 1988):
nmse (normalized mean square) =
2
o
p
o p
(
) /
C C
C C
−
cor (correlation) =
−
−
σ σ
o
p
o
p
o p
(
) (
)/
C C C C
æ
æ
fa2 = percentage of data for which 0.5 ≤ C o /C p ≤ 2
fb (fractional bias) =
−
+
o
p
o
p
(
)/( 0 . 5 (
) )
C C
C C
æ
æ
æ
æ
fs (fractional standard deviation) = (σ o − σ p )/0.5(σ o + σ p )
where the suffi xes o and p respectively refer to observed and predicted concentrations, and the bar indicates the mathematical mean.
REFERENCES
Beljaars, A.C.M. and Holtslag, A.A.M. (1990), A software library for the calculation of
surface fl uxes over land and sea, Environ. Soft. 5, 60–68.
Berkowicz, R.R., Olesen, H.R., and Torp, U. (1986), The Danish Gaussian air pollution model
(OML): Description, test and sensitivity analysis in view of regulatory applications.
NATO-CCMS 16th International Meeting on Air Pollution Modelling and Its Applications,
C. De Wispelaere, F.A. Schiermeier, and N.V. Gillani (Eds.), Plenum Press, New York,
pp. 453–481.
Berlyand, M.Y. (1975), Contemporary problems of atmospheric diffusion and pollution of the
atmosphere. Translated version by NERC, USEPA, Raleigh, NC.
Bowen, B.M. (1994). Long-term tracer study at Los Alamos, New Mexico. Part II: Evaluation
and comparison of several methods to determinate dispersion coeffi cients, J. Appl.
Meteorol. 33, 1236–1254.
Briggs, G.A. (1973), Diffusion estimation for small emissions, in environmental research
laboratories, air resources atmospheric turbulence and diffusion laboratory, Annual
report. USAEC Report ATDL-106, National Oceanic and Atmospheric Administration,
December 1974.
Briggs, G.A. (1975), Plume rise predictions. In Lectures on Air Pollution and Environmental
Impact Analyses. Workshop Proceedings, Boston, MA, Sept. 29–Oct. 3, 59–111.
American Meteorological Society, Boston, MA.
Briggs, G.A. (1985), Analytical parameterization of diffusion: the convective boundary layer.
J. Clim. Appl. Meteorol. 24, 1167–1186.
© 2010 by Taylor and Francis Group, LLC
Air Pollution and Turbulence: Modeling and Applications
A considerable amount of work has been done, especially in the United States,
on the quantitative assessment of model performances. The adopted approach varies according to whether the validation refers to the scientifi c validity of the model
or to the usefulness of the model in environmental management. In validations for
management purposes, less importance is attributed to deterministic processes (processes of cause and effect), while attention is focused on the correspondence between
observed and predicted values. For such analyses to be objective, it is necessary
to utilize different data from those adopted for the parameterization of the model
itself. Particular attention is paid, on the whole, to the comparison of concentration
maxima both with and without temporal and/or spatial simultaneity.
Generally, the attempt is made to objectivize the validation of model performances
by adopting statistical indices that describe their capacity to represent observed data.
Among them, the most widely used are (Hanna, 1988):
nmse (normalized mean square) =
2
o
p
o p
(
) /
C C
C C
−
cor (correlation) =
−
−
σ σ
o
p
o
p
o p
(
) (
)/
C C C C
æ
æ
fa2 = percentage of data for which 0.5 ≤ C o /C p ≤ 2
fb (fractional bias) =
−
+
o
p
o
p
(
)/( 0 . 5 (
) )
C C
C C
æ
æ
æ
æ
fs (fractional standard deviation) = (σ o − σ p )/0.5(σ o + σ p )
where the suffi xes o and p respectively refer to observed and predicted concentrations, and the bar indicates the mathematical mean.
REFERENCES
Beljaars, A.C.M. and Holtslag, A.A.M. (1990), A software library for the calculation of
surface fl uxes over land and sea, Environ. Soft. 5, 60–68.
Berkowicz, R.R., Olesen, H.R., and Torp, U. (1986), The Danish Gaussian air pollution model
(OML): Description, test and sensitivity analysis in view of regulatory applications.
NATO-CCMS 16th International Meeting on Air Pollution Modelling and Its Applications,
C. De Wispelaere, F.A. Schiermeier, and N.V. Gillani (Eds.), Plenum Press, New York,
pp. 453–481.
Berlyand, M.Y. (1975), Contemporary problems of atmospheric diffusion and pollution of the
atmosphere. Translated version by NERC, USEPA, Raleigh, NC.
Bowen, B.M. (1994). Long-term tracer study at Los Alamos, New Mexico. Part II: Evaluation
and comparison of several methods to determinate dispersion coeffi cients, J. Appl.
Meteorol. 33, 1236–1254.
Briggs, G.A. (1973), Diffusion estimation for small emissions, in environmental research
laboratories, air resources atmospheric turbulence and diffusion laboratory, Annual
report. USAEC Report ATDL-106, National Oceanic and Atmospheric Administration,
December 1974.
Briggs, G.A. (1975), Plume rise predictions. In Lectures on Air Pollution and Environmental
Impact Analyses. Workshop Proceedings, Boston, MA, Sept. 29–Oct. 3, 59–111.
American Meteorological Society, Boston, MA.
Briggs, G.A. (1985), Analytical parameterization of diffusion: the convective boundary layer.
J. Clim. Appl. Meteorol. 24, 1167–1186.
© 2010 by Taylor and Francis Group, LLC