1) Can the "box" really have a uniform mixing of pollutant along direction x?
Clearly not because upwind movement will inevitably be less than downwind movement but those interested in a more reasonable approach to this aspect, who have good mathematical ability might reasonably see GC Holzworth, US Environmental Protection Agency Report AP-101, US Govt. Printing Office, Washington DC, 1972.

2) Is the box likely to have uniform distribution of emissions of pollutants over the city?
Again this is not likely but if mixing is perfect (or assumed to be so) it does not matter.

One approach might be to break the city into smaller boxes and assign a different value of Q to each. (This will also take into account the upwind / downwind trend to some extent).

These problems were dealt with some time ago (but with limited success). For instance interested readers might consult SR Hanna," A Simple Model For Calculating Dispersion From Urban Area Sources", J Air Pollution Control Assoc, Vol 21,pp774-777, 1971.

More modern approaches tend to combine fixed box models with point source models (discussed later) and take into account the non conservative nature of many pollutants and have particular applications when applied to pollutants formed through photochemical reactions. However a study of the simple box model helps us to understand the data needs and limitations of the more complex models and points us in the direction of how we might simply model the non-rectangular city in a real rather than imaginary flat topography.

It is worth considering here the thoughts of RS Scorer of Imperial College in his excellent book Meteorology of Air Pollution (published by Ellis Horwood).

Task 2:

Imagine you are an Environmental Health Officer in a large city authority. You are given the task of producing a broad costing for instigating a modelling program for a limited range of pollutants within the city. The model to be used is based on a multiple box version of the fixed box model but is considerably more sophisticated.

List the types of data, which you think, would be required to feed into the model if it were be used. Indicate for each item whether this might be obtained directly, through data purchase or monitoring or whether there is a need for an extended period for data collection prior to its use.