Hydrographs

This article explains how hydrographs are created and used, to show the rate of rainfall or runoff over time.

In the previous video, we talked about how rainfall can become runoff in both natural and urbanized catchments. To quantify both precipitation and runoff we can use graphs called hydrographs to show the rate of rainfall or runoff over time.

For graphs showing rainfall you may also see the terms “pluviograph” or “hyetograph” used. Here we have an example of a graph showing rainfall that has been measured using a rain gauge:

Time is shown on the horizontal axis and the precipitation rate on the vertical axis. For rainfall intensity the unit we use is mm/hr (an alternative unit used is l/s ha). A rainfall rate of 1 mm/hr means that a flat, impervious surface would over the course of one hour gather a 1 mm deep layer of water from precipitation. We measure rainfall as a depth, rather than a volume, to make it easy to compare between catchments of different sizes. A rainfall depth of 1 mm also means that an area of (1m^2) will receive 1 litre of water in total. Thus, 1 mm/hr = 1 l/(m^2) hr.

In the graph above we see for example that the highest rainfall rate was 40 mm/hr between 20 and 25 minutes. However, we did not get 40 mm of rain as this intensity only lasted for 5 minutes. This is similar to how a car travelling at 80 kph only covers 40 km in half an hour. The highest intensity in this example was 40 mm/hr during a 5 minute interval, which is 1/12th of an hour. This means that the rainfall depth in that interval was 40 / 12 = 3.3 mm.

If we repeat the same operation for each interval and then add these values together, we can find the total amount of rainfall (that is the total rainfall depth in mm) during this rainfall event. A faster, but equivalent method, is to add up all the 5-minute intervals, and then divide the total by 12. Try this for yourself. You should find that the total rainfall depth was 10 mm, i.e. a volume of 10 litres on each (m^2).

If we want to show both rainfall and runoff in the same graph, we often encounter the situation where the values for the rainfall are much larger and it becomes difficult to see the runoff. In that case, we often plot the rainfall on a different vertical axis (scale) and often we plot it upside down to emphasize that the vertical axis is different:

Here the rainfall rate is shown on the vertical axis on the left, and the runoff rate is shown on the right. Note that for the runoff we again use the same unit as for the rainfall, mm/hr. If we measure runoff using a flow meter, we get a value in for example (m^3)/s or L/s (i.e. a volume per time interval). Comparing runoff to rainfall is easier when using the same unit of measurement. We achieve this by dividing the value in m3/s by the size of the catchment (in (m^2)) to obtain what is called a normalized hydrograph. However, since we are using separate vertical axes for the rainfall and the runoff, we could also continue to use and plot the flow rate in (m^3)/s. The graph would look the same, except the units and the labels on the right-hand side axis would be different.

We see that the graph for the runoff is much smoother than that for the rainfall and that – once it stops raining – it takes a while for the runoff to decline again. This is because water takes some time to flow through the catchment (on catchment surfaces, through pipes and streams) after the rain falls on the surface. This process imparts a delay on the runoff. One effect that urbanization has on the hydrological cycle is that this delay becomes smaller. This leads to the runoff peak being higher and arriving earlier. We will look at some examples of this in the next step.

You may have noticed that compared to the graph for runoff, the rainfall graph looks rather ‘blocky’. This is common for rainfall data, as we often measure the rainfall during a fixed interval (in this case, 5 minutes). Compare this to measuring how far a car moves in one minute. In this case, we only measure an average rainfall rate over that interval. This is why in these graphs we plot the rainfall intensity as a horizontal line or bar for each interval. By contrast, for hydrographs the measurements usually reflect only a single moment in time – much like a speed camera measures the speed of a car at one specific point. In this case we assume that the hydrograph changes gradually between the times where we have measurements.

For the rainfall graph you saw how we can obtain the total rainfall by summing the values for each interval, that is by calculating the area underneath the graph. For hydrographs the same principle applies – the area under the graph is the total volume.

In the next article, we will have a look at different types of urban catchments and how their hydrographs may look.

© Luleå University of Technology