Simple Numerical Modeling in R – Part 1: Exercises

The modeling process is just one of the methods to find a solution for a certain problem. It can be a combination between empirical simulation approaches. The empirical method is data-based analysis that relies upon mathematical function and often has no meaning in real life. An approach using simulation is more based on scientific understanding of a process. Designing a model is consist of three stages; design, development, and evaluation (figure 1 below).

Natural environment is a continuous system that consists of discrete units/events. In this exercise, we will try to build continuous relationships that consist of a discrete event. The continuous relationship is represented with a simple calculation that repeats over and over. The model needs to count the space and time variables to make it continuous. In this case, we will use a rainfall catchment as an example that represents water flow through the water tank. Download the data-set used for this exercise here.

Answers to these exercises are available here. If you obtained a different (correct) answer than those listed on the solutions page, please feel free to post your answer as a comment on that page.

Exercise 1
Load and plot the data table. Assume variable 1 as time and variable 2 as the water level in the tank.
Imagine the amount of water that flows out from the system is dependent on the reduction of water levels inside the water tank. Furthermore, the reduction of water levels is caused by air pressure that is acting on the surface of the water. This is the mechanistic model that needs to be found and fully understood first.

Exercise 2
Try to write the mechanistic model mathematically that says that the water level in the tank is equal to the change of water in time.

Exercise 3
Let’s say we have a bucket with 15 cm of water in it and we know and assume that k= 0.05. Between 0 and 1 seconds, how much water would we expect to lose? What is the new water level? Do the same calculation from 1 to 2 seconds.
The “k” parameter represents how fast water flows from the tank.

Exercise 4
Try to create a loop that consists of the calculations in exercise 3. Consider thinking about time, initial water level, model parameter, time step, and final time step.

Exercise 5
Plot the water level based off the tank over the time.