Abstract
This paper describes a framework to evaluate air quality model predictions against observations. We propose the following relationship between observations and predictions from an adequate model% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% WaaSbaaSqaaiaaicdaaeqaamXvP5wqonvsaeHbfv3ySLgzaGqbaOGa% e8hkaGIaamiEamaaBaaaleaacaaIXaaabeaakiaacYcacaWG4bWaaS% baaSqaaiaaikdaaeqaaOGae8xkaKIaeyypa0Jabm4qayaajaWaaSba% aSqaaiaadchaaeqaaOGae8hkaGIaamiEamaaBaaaleaacaaIXaaabe% aakiab-LcaPiab-TcaRiabew7aLjab-HcaOiaadIhadaWgaaWcbaGa% aGOmaaqabaGccqWFPaqkaaa!4F93!\[\hat C_0 (x_1 ,x_2 ) = \hat C_p (x_1 ) + \varepsilon (x_2 )\],where x 1 refers to the inputs used in the model prediction C p(x 1), and x 2denotes unknown variables which affect the observed concentration C 0. The hats associated with C pand C 0denote transformations to convert the residual ɛ to a ‘white noise’ sequence which is normally distributed. In this paper we assume % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabm4qayaaja% GaeyyyIORaciiBaiaac6gacaWGdbaaaa!3B39!\[\hat C \equiv \ln C\].
The standard deviation of ɛ determines the expected deviation between model prediction and observation. The purpose of model improvement is to make this deviation as small as possible.
The formalism we have proposed is applied to the evaluation of two models developed by this author. We show how careful analysis of residuals can lead to improvements in the model. We have also estimated Σɛ for each of the models.
In the last part of the part of the paper we show how the statistics of ɛ can be used to interpret model predictions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Box, G. E. P. and Jenkins, G. M.: 1976, Time Series Analysis: Forecasting and Control, Holden-Day, San Francisco, 575 pp.
Box, G. E. P., Hunter, W. G., and Hunter, J. S.: 1978, Statistics for Experimenters, John Wiley and Sons, New York, 653 pp.
Csanady, G. T.: 1973, Turbulent Diffusion in the Environment, D. Reidel Publ. Co., Dordrecht, Holland, 248 pp.
Draper, N. and Smith, H.: 1981, Applied Regression Analysis, Second edition. John Wiley and Sons, Inc., N.Y. 709 pp.
Fox, D. G. (chairman): 1981, Judging Air Quality Model Performance. A summary of the AMS workshop on dispersion model performance. Woods Hole, Mass., 8–11 September, 1980. Bull. Amer. Meteorol. Soc. 62, 599–609.
Venkatram, A.: 1981, ‘Model Predictability with Reference to Concentrations Associated with Point Sources’, Atmos. Envir. 15, 1517–1522.
Venkatram, A.: 1980, ‘Dispersion from an Elevated Source in a Convective Boundary Layer’, Atmos. Envir. 14, 1–10.
Weil, J. C.: 1977, Evaluation of the Gaussian Plume Modelat Maryland Power Plants, Report No. PPSP-MP-16, Martin Marietta Corporation, Baltimore Maryland.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Venkatram, A. A framework for evaluating air quality models. Boundary-Layer Meteorol 24, 371–385 (1982). https://doi.org/10.1007/BF00121601
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00121601