A Lagrangian Box Model

FIGURE 25.5 Concentration as a function of travel time across an urban area predicted by a Lagrangian box model assuming length 200km and a constant windspeed of 2.8 m s 1. 

Lagrangian models The next step in model development was the use of Lagrangian models depicted in Fig. f6.20 (Wayne et at., 1973). These models consider a column of air containing certain initial pollutant concentrations and follow its trajectory as it moves along a trajectory. In effect, it is an expansion of a simple box model to a series of adjacent, interconnected boxes. 

Shon and Kim (2002) compared data from two Lagrangian flights during ACE-1 with a constrained box model and found a better agreement regarding total O3 loss and the timing (i.e., sunrise ozone destruction) when they included halogen chemistry. The effects were mainly caused by bromine oxide but also by iodine oxide. 

The above described results illustrate the strengths and weaknesses of the two box models. The Eulcrian box model is easy to apply but oversimplifies everything by assuming a homogeneous airshed. The Lagrangian model can provide more information, such as, for example, a spatial distribution of concentrations, but by neglecting horizontal dispersion, it may predict higher concentrations downwind of emission sources. 

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