Lesson 10 - Viewing Contaminant Transport Results

Now that we have explored how the system is defined, in this Lesson we will look at some results.

Run the model now.  The results of interest can be found in the Results Container.  Enter that Container now.  We’ve already previously examined the Key System Flows.  Double-click on the Mass Release Rates Result element to view that result:

This displays the rate at which contaminant mass is added to the pond from the pipeline (an external input to the model), as well as the release rates from each of the pathways we discussed in the previous Lessons. As can be seen, each pathway tends to delay and disperse the original input of mass from the pipeline.  If we integrate each of these over time, they should all converge on the same value (25 kg) since contaminant mass is conserved.  This can be seen in Cumulative Mass Release Result element:

The Concentrations Result element displays the concentrations exiting each of the pathways:

Due to dilution, the Aquifer and Stream concentrations are difficult to view on a linear scale.  Plotting the concentrations on a log scale (the Log Concentrations Result element) makes these clearer:

Recall that our objective is to predict the peak concentration of the contaminant in the stream.  What is the best way to do this?  Obviously, we want to see the peak value on the plot above for the stream concentration.  We could attempt to do this manually (looking at the curve it appears to be on the order of 2E-4 mg/l), but GoldSim provides a specialized element to do just that: the Extrema element (which is discussed in detail in Unit 12, Lesson 5 of the Basic Course). We can view the output of the Extrema element superimposed on top of the stream concentration in the Peak Concentration in Stream Result element:

The final value of the Extrema element is the desired result (in this case, by holding the cursor over the curve we see it is equal to approximately 2.38E-4 mg/l).  Since we have only run a single realization, we can also view this value if we hold our cursor over the Extrema element (the final value of an element is displayed when you do this):

Now that we have our result, let’s briefly address a modeling decision we made that we have not yet discussed: the timestep. As discussed in Unit 6, Lesson 3 of the Basic Course, as a general rule, the timestep for a model should be 3 to 10 times shorter than the timescale of the fastest process being simulated in the model. If we examine the conceptual model and inputs, what we will see is that there are two changes to the model that we want to capture accurately: 1) the “spike” input of mass from the pipeline; and 2) the seasonal change in the stream flow.  The rest of the processes are likely to be slower than these. In this model, the timestep was selected to be 1 day.  Given the timescale of the other processes, it is likely that this is sufficiently small. 

Although the rule of thumb we mentioned above is useful, the only way to really be certain if the timestep is small enough is to run the model multiple times with different timesteps.  You can do this now yourself if you wish, but you don’t need to; the results of this little experiment are summarized below:

As can be seen, the result does not change (within three significant figures) if we use a smaller timestep than 1 day.  In fact, even a larger timestep would probably be sufficient for our needs (as we will note in  the next Lesson, the uncertainty in our inputs for a real world problem would almost certainly be much greater than the error generated by using a larger timestep). 

In the next Lesson, we will take a quick look at a probabilistic version of the model in order to illustrate some key concepts associated with representing uncertainty in contaminant transport models.