John is cured (why I'm here part 2)

The next step in modeling is to calibrate the model. This means that I tinker with variables to try and get my model to match my observations as best as I can. In the example from the other day, this would mean that I could try to change X, because perhaps John was going faster or slower than I thought.

The final step in modeling is to apply the model. This is usually the final goal. So, in our example, the question was, "where is John", and I can apply my calibrated model to guess where John is at any given time! Sweet!

However, the model I am developing, calibrating and applying is a bit more complicated than a man walking only from east to west.
Let's say suddenly John is cured from his crazy disorder! Ahhhh! Now he can walk west to east or east to west (which would be the negative of west to east) and north to south or south to north (negative of north to south). In fact, he can even walk at an angle, heading north-east or south-east. This makes my model a bit more complicated. Here's another figure for you to ponder:

So, now his velocity is a little bit more complicated because its not straight west to east. However, I can still try to guess his location, but my model gets a bit more complicated (now its two dimension!)

deltat = t/n
DO i = 1, n
D(i) = D_start + X_es*deltat + X_ns*deltat
END DO

So, this time I have two parameters (X_es anc X_ns) that I can tinker with to calibrate. Once its calibrated, again I can apply.

So, to understand what I am modeling, lets say there are 10,000 John's lining the street, they can go any direction, even jump up and down. And instead of John's on a street, its water molecules in a river. That's the initial part of my model, the movement of water. But, instead of trying to model individual molecules, I group them all together and model the mass movement of the water. In addition to modeling how the water moves, I model how certain chemical reactions occurs in the water and affect the quality.