In this tutorial we will explore the use of index lists in modelling. It is recommended that you first read Tutorial 2-Creating a compartment model, where a basic description of the concept of Materials and Index lists is given.
The conceptual model
Consider a model that describes the turnover of a group of contaminants in a simple environmental system with two compartments: Upper_Soil and Lower_Soil. The contaminants enter the system from an atmospheric source via deposition on upper soil. This is represented in the model using a parameter called “input”, which has different values for different contaminants.
The transfer rate from the Upper_Soil to Lower_Soil is represented in the model with the help of a parameter “TC”. The same parameter is used to determine the transfer rate out from the system.
The mathematical model
The following ordinary differential equations describes the mass balance of the contaminants in the upper soil layer:
dAUpper Soil/dt = Input - TCUpper to Lower * AUpper Soil
dALower Soil/dt = TCUpper to Lower * AUpper Soil - TCLower to Sink * ALower Soil
AUpper Soil is the contaminant inventory in the upper soil layer.
ALower Soil is the contaminant inventory in the lower soil layer.
Input is the contaminant deposition rate.
TCUpper to Lower is the transfer rate from the upper to the lower soil layer.
TCLower to Sink is the transfer rate of contaminants leaving the system from the lower soil layer.