# Graphing a water balance

The water balance for a urban catchment equates the change in storage during a certain period, with the difference between water inputs (precipitation and mains water) and water outputs (evaporation, stormwater runoff and wastewater discharge).

$\Delta s = (P+I) - (E_a + R_s + R_w)$
where:

$\Delta s$ change in catchment storage
$P$ precipitation
$I$  imported water
$E_a$ actual evaportranspiration
$R_s$ stormwater runoff
$R_w$ wastewater discharge

Mitchell et al., (2003) provides data on the water balance for Curtin, ACT for 1979 to 1996.  The water balance for the average, wettest and driest years are shown in the table below.

When presenting financial statements, a common approach is to use a waterfall chart which shows how the components of a financial balance contribute to an overall result.  Here I’ve used a waterfall chart to show the water balance for Curtin for the driest and wettest year as reported by Mitchell et al., (2003).

Figure 1: Water balance for Curtin, ACT in (A) and driest and (B) the wettest years as estimated by Mitchell et al., (2003).

Does this approach to visualising a water balance help understanding?  A few things stand out:

• In the driest year, more water was input from the mains than from rainfall
• In the driest year, actual evapotranspiration was larger than rainfall and mains inputs.
• Evapotranspiration and stormwater change with climate, with large variation between the wet and dry years.  Wastewater doesn’t change all that much.
• Precipitation is highly variable, ranging from 247 mm to 914 mm.

There is a guide to making a waterfall chart in excel here.  The R code to produce the graphs shown in this blog is available as a gist, which draws on this blog.

### References

Mitchell, V. G., T. A. McMahon and R. G. Mein (2003) Components of the Total Water Balance of an Urban Catchment. Environmental Management 32(6): 735-746. (link)