2. 8. Box Modeling 8.1 Box Models –Simplest of atmospheric models (simple saves $). –Species enter the box in two ways: 1. source emissions 2. atmospheric motions

3. Atmospheric motions include: –advection - transport by mean motion of air –entrainment - vertical movement from mixing

4. Species leave the box: –1. advection –2. detrainment - upward motions out of box –3. surface deposition

5. Dimension and location of the box dictated by: – 1. topic of investigation – 2. modeler

6. Key assumption: – * pollutant is completely mixed within box – * uniform atmospheric properties throughout box Box models: –often used as first estimate of temporal changes in system

7. Figure 8.1 Schematic showing the features of aero- dimensional box model of atmospheric chemistry

8. 8.2.1 Equations for Chemical Box Models

9. Separate equation for each chemical species with concentration [i] where, u = fluid velocity wv = ventilation velocity (downward) wd = surface deposition velocity L = length of box H = height of box Si = emission sources of I Ci = chemical reactions (production or loss) of i

10. Furthermore, Ci = Pi - Ki[i] where, –Pi = production reactions = –K = loss rate =1/t =

11. Determination of Ci often requires the simultaneous solution of hundreds of coupled differential equations. Time step is determined by species with shortest lifetime (ms timestep is possible) Computational and numerical solution techniques can often be the limiting part of the process.

12. 8.2.2 Steps in Box Modeling 1. Define dimensions and time variability 2. Devise mathematical representations for factors involved: – source fluxes – surface deposition – advection – entrainment 3. Decide on chemical reactions

13. 8.2.3 Types of Box Models Eulerian - compute chemical species concentrations at a fixed location – * easy to compare to measurements Lagrangian - box moves with air parcel – * advection is eliminated – * sources and sinks must change as air moves over different location – * comparison with data is difficult

14. 8.2.4 Limitations of Box Models * rely on many assumptions not completely true in nature (e.g. uniformity and rapid mixing) * tough to fit one box around a uniform area (multibox model?) * overcome these limitations by implementing spatial variability

15. –Figure 8.2 Movement of air parcel in a Lagrangian box model