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====== Tutorial 3-Using index lists ======

===== 1/4 =====

**Overview**

In this tutorial we will explore the use of [[Index_list|index lists]] in modelling. It is recommended that you first read [[Tutorial_2-Creating_a_compartment_model|Tutorial 2-Creating a compartment model]], where a basic description of the concept of [[Material|Materials]] and [[Index_list|Index lists]] is given.

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**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.

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**The mathematical model**

The following ordinary differential equations describes the mass balance of the contaminants in the upper soil layer:

//dA<sub>Upper Soil</sub>/dt = Input - TC<sub>Upper to Lower</sub> * A<sub>Upper Soil</sub>\\
dA<sub>Lower Soil</sub>/dt = TC<sub>Upper to Lower</sub> * A<sub>Upper Soil</sub> - TC<sub>Lower to Sink</sub> * A<sub>Lower Soil</sub>//\\
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where:\\
//A<sub>Upper Soil</sub>// is the contaminant inventory in the upper soil layer.\\


//A<sub>Lower Soil</sub>// is the contaminant inventory in the lower soil layer.\\


//Input// is the contaminant deposition rate.\\


//TC//<sub>Upper to Lower</sub> is the transfer rate from the upper to the lower soil layer.\\


//TC//<sub>Lower to Sink</sub> is the transfer rate of contaminants leaving the system from the lower soil layer.\\


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**Next**

  * [[Tutorial_3-Creating_the_model_objects|Creating the model objects (2/4)]]

**References**

  * [[Tutorials|Back to Tutorials]]
  * [[start|Home]]
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