# Lesson 3 – Building Complex, Multi-Dimensional Models Using GoldSim Pathways

In the Examples and Exercises we have seen in previous Units, the spatial dimensionality of the system was quite simple.  Models that consisted of a single Cell were essentially zero-dimensional (there was no spatial component at all), while other models involving a series of Cells or an Aquifer or Pipe pathway were one-dimensional.

Of course, real-world systems are three-dimensional.  So how do we represent such systems using the GoldSim pathways? Essentially, you do so by building networks of simple components (Cells, Aquifers and Pipes) to represent multi-dimensional systems. When doing so, however, it is critical to keep in mind two points that we have discussed previously:

• As pointed out in Lesson 2, the complexity and detail that you include in your model should be consistent with the amount of uncertainty in the system. As a result, you should take a “top-down” modeling approach for complex models and details should only be added only to those processes that are identified as being important with respect to your modeling objectives and where additional detail will reduce the uncertainty resulting from model simplifications. (The “top-down” modeling approach was discussed in Unit 3, Lesson 9).
• When designing your model, it is important to keep in mind the objectives of your modeling effort, as this should inform the amount of detail required. For example, as discussed in Unit 9, Lesson 4, for most applications, what you will typically be interested in predicting is a mass discharge rate into a particular feature (e.g., a well, a river or some other surface water body). This mass is then mixed (and diluted) by additional water.  Hence, what we are typically interested in is not a concentration at a point in space, but one that is averaged (due to mixing within the downstream feature). This has major implications for how you design your model (e.g., a detailed, fully three-dimensional representation of an aquifer may not be required and a simpler one-dimensional representation may be appropriate).

By keeping these two points in mind, you should be able to represent many different kinds of complex multi-dimensional systems using the simple components we have described in this Course (Cells, Aquifers and Pipes). In fact, the very first model we looked at in Unit 4 was multi-dimensional:

We represented that system with using Cells and Aquifers:

Admittedly, this is still a very simple model. However, you should be able to see how you could use a similar approach to represent much more complex systems (involving perhaps many tens if not hundreds of GoldSim pathways).

Of course, there may be some systems that cannot be realistically represented using Cells, Aquifers and Pipes. That is, there may be some parts of complex systems in which you will need to represent in much greater detail (e.g., linking GoldSim to an external mass transport code).  We will discuss this in Lesson 9.