Environmental Engineering Reference
In-Depth Information
Chapter 18
Compartment Graphs and Linear Systems
18.1 Compartments and Graphs
Seen from the process perspective, compartment models are the simplest type of
environmental models. This type of model is based on quite rigorous conditions.
There is probably no environmental system at all, where the conditions are fulfilled
exactly. Nevertheless, as a first guess and in order to give a rough idea about the
interactions between compartments, the simplicity justifies the application.
Compartment models consist of a network of compartments. An example
for such a network is given in Fig.
18.1
, representing the terrestrial part of the
hydrological cycle.
There are four compartments to be modelled in the system of Fig.
18.1
: inter-
ception, soil moisture, groundwater and surface water, visualized by rectangular
boxes. Systems of compartments are the simplest concept in environmental
modeling. A compartment is part of an environmental system which is spatially
not further resolved. The analogue in chemical engineering is the continuously
stirred chemical reactor. A compartment model can thus only be an approximation
of a real system if there are no steep gradients within the real environment.
Several processes induce fluxes between compartments, visualized in Fig.
18.1
by
arrows. Groundwater recharge is a flux from the soil to the groundwater, overland
flow from interception to the surface water compartment. There is interflow from
unsaturated soil moisture to the surface water compartment.
Rounded boxes illustrate processes connecting to the outer world, which is not
explicitly taken into account in the model. Ocean and atmosphere are compartments
within the hydrological cycle not being treated within the conceptual model
demonstrated by Fig.
18.1
.
A system of compartments, shown in a flux diagram, can be represented by
a matrix. The
adjacency matrix
represents each compartment in one line and one
column. It has a one-entry at the corresponding position, if there is a flux from the
row compartment to the column compartment; otherwise there is a 0-entry.
The adjacency matrix for the system of Fig.
18.1
is:
