# Instructions

On the left is a floodplain. On the floodplain are two villages, one on the hilltop and one in the valley. At the moment the level of the river is normal but there is a flood coming!

In Drag Mode click and drag to look around the floodplain.

A mathematical model has been built to predict the flood. It is a very simple model. As inputs it takes the amount of extra water w, and some parameters a, b and c. The output is a prediction of the extent of the flood, it is shown on the floodplain as a red line.

The trouble is we don't know the values of these parameters! In reality the flood will depend on friction which will vary across the whole floodplain. If we tried to model this accurately we would have 1000s of parameters which are too complicated to measure directly.

In our simple model we approximate friction, so our three parameters need to account for all the friction across the floodplain. We have no idea what the values of a, b and c could be, so how can be approximate them?

We can calibrate the model!

Calibrating the model means that we use the model to predict something we already know the answer to. We already know where the river is when the water level is normal so we can adjust the parameters of our model so it predicts this better.

Open the Constant Controller and select a from the drop-down menu. Use the arrow buttons to adjust the value of a.

Adjust b and c in the same way until you are happy with the model.

Notice how sometimes the red line goes into the river and sometimes it is outside the river. These correspond to two types of error in prediction. What are they?

Which error do you think it is more important to avoid?

Now that we have calibrated our model we can use these values of a, b and c when we predict the flood.

In the Constant Controller, select w from the drop-down menu. Press Play.

The amount of extra water w will slowly increase and our model prediction will adjust. In practice we would normally create the prediction before the flood arrives but it is nice to see the two together so we can see how our model performs during the flood.

How did your model perform during the flood?

In the Constant Controller, select w from the drop-down menu. Press Stop. Change the value to 0 and adjust the values of your parameters again to see if you can improve your prediction. Select w from the drop-down menu. Press Play.

Is your prediction any better?

You may find that your prediction is better in some areas of the floodplain and worse in others. There is not one correct value for each of the parameters.

In this activity we have covered many different aspects of calibration. In Bayesian calibration we can see the uncertainty in our predictions by making the following changes:

1. We said we had no knowledge of the parameters before using the model to predict an observed event. In practice experts may have some subjective knowledge of what the values should be. This knowledge can be provided as a probability distribution for the parameters called the Prior.
2. We simply compared the model prediction to the observed river edge by eye. For rigorous calibration we need to provide a probability distribution which is the Likelihood of the observed data given our model output.
3. We used single values of the parameters for prediction. In practice we can use the prior and the likelihood to calculate the probability distribution for the parameters called the Posterior. Then we can provide probabilities of flooding across the floodplain.