131
5
Mathematical Air
Pollution Models:
Eulerian Models
Tiziano Tirabassi
CONTENTS
5.1 Introduction .................................................................................................. 131
5.2 Operative Characteristics of Mathematical Models ..................................... 132
5.3 Theoretical Characteristics of Mathematical Models .................................. 133
5.3.1 Eulerian Approach: K Models .......................................................... 134
5.3.2 Analytical Solutions.......................................................................... 136
5.3.3 Numerical Solutions ......................................................................... 139
5.3.4 Eddy Diffusivity ............................................................................... 139
5.3.5 Box Models ....................................................................................... 140
5.3.6 Gaussian Models ............................................................................... 141
5.4 Semiempirical Expressions of the σ ..............................................................143
5.5 Gaussian Model Extensions .......................................................................... 147
5.5.1 Gaussian Puff Models ....................................................................... 147
5.6 Special Algorithms Utilized in Gaussian and Analytic Models .................. 148
5.6.1 Plume Rise ........................................................................................ 148
5.6.2 Downwash ......................................................................................... 148
5.6.3 Plume Trapping ................................................................................. 148
5.6.4 Ground Deposition ............................................................................ 149
5.6.5 Chemical Reactions .......................................................................... 149
5.7 New Operative Models ................................................................................. 149
5.8 Evaluation of Model Performances and Reliability ...................................... 150
References .............................................................................................................. 152
5.1 INTRODUCTION
The management and safeguard of air quality presupposes a knowledge of the state of
the environment. Such knowledge involves both cognitive and interpretative aspects.
Monitoring networks and measurements in general, together with an inventory of
emission sources, are of fundamental importance for the construction of the cognitive picture, but not for the interpretative one. In fact, air quality control requires
© 2010 by Taylor and Francis Group, LLC
5
Mathematical Air
Pollution Models:
Eulerian Models
Tiziano Tirabassi
CONTENTS
5.1 Introduction .................................................................................................. 131
5.2 Operative Characteristics of Mathematical Models ..................................... 132
5.3 Theoretical Characteristics of Mathematical Models .................................. 133
5.3.1 Eulerian Approach: K Models .......................................................... 134
5.3.2 Analytical Solutions.......................................................................... 136
5.3.3 Numerical Solutions ......................................................................... 139
5.3.4 Eddy Diffusivity ............................................................................... 139
5.3.5 Box Models ....................................................................................... 140
5.3.6 Gaussian Models ............................................................................... 141
5.4 Semiempirical Expressions of the σ ..............................................................143
5.5 Gaussian Model Extensions .......................................................................... 147
5.5.1 Gaussian Puff Models ....................................................................... 147
5.6 Special Algorithms Utilized in Gaussian and Analytic Models .................. 148
5.6.1 Plume Rise ........................................................................................ 148
5.6.2 Downwash ......................................................................................... 148
5.6.3 Plume Trapping ................................................................................. 148
5.6.4 Ground Deposition ............................................................................ 149
5.6.5 Chemical Reactions .......................................................................... 149
5.7 New Operative Models ................................................................................. 149
5.8 Evaluation of Model Performances and Reliability ...................................... 150
References .............................................................................................................. 152
5.1 INTRODUCTION
The management and safeguard of air quality presupposes a knowledge of the state of
the environment. Such knowledge involves both cognitive and interpretative aspects.
Monitoring networks and measurements in general, together with an inventory of
emission sources, are of fundamental importance for the construction of the cognitive picture, but not for the interpretative one. In fact, air quality control requires
© 2010 by Taylor and Francis Group, LLC