The Water Balance Model ​

In Trench, the fundamental water balance equation is:

or

which can also be expressed as

Trench assumes that LTAR and wastewater volume are unchanging on a monthly or daily basis. The only variables, which usually (but need not necessarily) change, are retained rainfall and evapotranspiration. When you provide climatic data, LTAR and wastewater volume, it is a simple matter to calculate the only remaining unknown (change in storage).

Trench expresses the change in storage in a trench/bed/irrigation area/lagoon, etc. as a depth of wastewater, and displays a graph which shows how the depth varies monthly (or daily).

By changing depth and width, and setting allowable minimum and maximum levels for the wastewater, you can quickly select a combination of dimensions which, for the given inputs, avoids wastewater overflow in any month. This is usually the objective of the exercise, but, alternatively, you can allow monthly overflow to calculate discharges from, for example, treatment lagoons or irrigation areas. On a daily basis, overflow may be used to calculate the required volume of on-site storage.

Schematic diagram of the water balance model ​