# Seasonal gradient in flow across Melbourne

There is a seasonal gradient in flow across Melbourne. Out in the rural east, the rivers flow as you would expect; high flows in winter (maximum in August) with dry conditions in January, February and March.  As we track west, the seasonal signal is lost and we get similar flows in all months.

Lets look at monthly discharges in seven streams from the Bass River, near Phillip Island, around to the Werribee River.

Flow in the Bass River at Glen Forbes South is strongly seasonal.  The graph below shows the flow volume in each month. The horizontal lines are the monthly averages with vertical lines representing volumes for each month as recorded in the years 2000 to 2015.

As we track west, winter flows become less pronounced; see the discharges for the Bunyip River below.

There is a small seasonal signal in Eumemmerring Creek (near Dandenong), but in the streams in urbanised catchments (from east to west – Gardiners, Merri and Kororoit) there is no evidence of seasonality.   For these streams, the high flow months are November and February.  This is partly driven by some unusually large events, for example, the flood of Feb 2005 stands out on these figures.

For the highly regulated Werribee River, average monthly volumes are higher in summer and spring.  The small number of large vertical spikes show this pattern is influenced by a few rare events.

Its difficult to tease out the cause of the differences in seasonality as these streams are affected by gradients in urbanisation, climate, and regulation.  Certainly, urbanisation has a strong influence. The impervious surfaces in urban areas will produce runoff all year round; they aren’t influenced by the seasonal wetting and drying that occurs in the rural catchments.

And the consequences?  We know that fish, for example, respond to seasonal flow changes to migrate and spawn.  But changes in seasonality are probably only a small influence in comparison with the large number of factors affecting the ecology of these streams.

# 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)

# Munging rating tables

The Victorian water monitoring site includes rating tables for stream gauges but they are in a format that is not easy to work with.   An example is shown in Figure 1 below.

Figure 1: Extract of rating table

The following steps can be used to extract and convert the data into a useable format.

1. Download and save rating table.  Click the button shown to get the rating table as a text file.

Figure 2: Save the rating table

2. Re-format the data to create columns of levels and flows.  You’ll need to use your favourite tool for this munging step.  An example using R is available as a gist.

3. Plot and compare with the online version

Figure 2: Rating plot (source: data.water.vic.gov.au/monitoring.htm?ppbm=404216&rs&1&rscf_org)

Figure 3: Rating plot using data from rating table

4. Save as a csv file for further use.

R code is available here.

Related posts:

# Converting between EY, AEP and ARI

The latest version of Australian Rainfall and Runoff (ARR2016) proposes new terminology for flood risk (see Book 1, Chapter 2.2.5).  Preferred terminology is provided in Figure 1.2.1 which is reproduced below.

Definitions:

• EY – Number of exceedances per year
• AEP – Annual exceedance probability
• AEP (1 in x) – 1/AEP
• ARI – Average Recurrence Interval (years)

Australian Rainfall and Runoff preferred terminology

For floods rarer than 5%, the relationship between the various frequency descriptors can be estimated by the following straightforward equations.

$\mathrm{EY} = \frac{1}{\mathrm{ARI}}$
$\mathrm{EY} = \mathrm{AEP}$
$\mathrm{AEP(1\; in\; x \;Years)} = \frac{1}{\mathrm{AEP}}$
$\mathrm{ARI} = \mathrm{AEP(1\; in \; x \; Years)}$
$\mathrm{AEP} = \frac{1}{\mathrm{ARI}}$

For common events, more complex equations are required (these will also work for any frequency):

$\mathrm{EY} = \frac{1}{\mathrm{ARI}}$
$\mathrm{AEP(1\; in\; x \;Years)} = \frac{1}{\mathrm{AEP}}$
$\mathrm{AEP(1\; in\; x \;Years)} = \frac{\exp(\mathrm{EY})}{\left( \exp(\mathrm{EY}) - 1 \right)}$
$\mathrm{ARI} =\frac{1}{-\log_e(1-AEP)}$
$\mathrm{AEP} = \frac{\exp(\frac{1}{\mathrm{ARI}}) - 1}{\exp(\frac{1}{\mathrm{ARI}})}$

A key result is that we can’t use the simple relationship ARI = 1/AEP for frequent events.  So, for example, the 50% AEP event is not the same as the 2-year ARI event.

### Example calculations

For an ARI of 5 years, what is the AEP:

$\mathrm{AEP} = \frac{\exp(\frac{1}{\mathrm{5}}) - 1}{\exp(\frac{1}{\mathrm{5}})} = 0.1813$

For an AEP of 50%, what is the ARI?

$\mathrm{ARI} =\frac{1}{-\log_e(1-0.5)} = 1.443$

R functions and example calculation available as a gist.

# Highlights from ARR Book 7

Book 7 of Australian Rainfall and Runoff is titled Application of Catchment Modelling Systems.  It has been written by experienced people and there is some great information. A few, paraphrased, highlights follow.

• Its often challenging to get good calibrations for all the available historical events and there may good reasons why.

Difficulties in calibrating a model to observed flood events of different magnitude should be taken as an indication of the changing role of processes.

In many cases a significant change occurs between floods that are mostly contained within the stream channel and floods in which floodplain storage plays an important role in the routing process.

If the model has only been calibrated to in-bank floods, confidence in its ability to represent larger floods will be lower.

• Calibration needs to focus on what the model is to be used for, not just ensuring past events are well represented.

The focus of model calibration is not just to develop a model that is well calibrated to the available flood data.  Application of the model to the design requirements must be the primary focus.

It is often the case that calibration floods are relatively frequent while design applications require much rarer floods.  In this case, work in refining the model calibration to the frequent floods may not be justified.

Parameter values should account for the expected future design conditions, rather than an unrepresentative calibration event.

Calibration usually works with historic flood events while the design requirements are for probabilistic events.  The parameters calculated for the historic events may not be applicable to the design flood events.

• On using all available data.

Even if the data is of poor quality or incomplete, it is important that the model calibration be at least consistent with the available information.

Even poor quality observations may be sufficient to apply a ‘common sense test’.

…at least ensure that model performance is consistent with minimal data [available]…

• On inconsistent data

Effort should be concentrated on resolving the source of the inconsistency rather than pursing further calibration.

• Dealing with poor calibration.

It is far more important to understand why a model may not be calibrating well at a particular location than to use unrealistic parameter values to ‘force’ the model to calibrate.

• Don’t expect your model to provide a good fit to all data.

It is extremely unlikely that your simple model is perfectly representing the complex real world well, all your data has been collected without error, or is unaffected by local factors.

• The appearance of great calibrations may mean:

The model has been overfitted to the data with unrealistic parameter values, or

Some of the data, that does not fit well, has been ignored or not presented.

Calibration events should be re-run with adopted parameters and results should show at least reasonable performance for all of the calibration events.

• Confirming model suitability for design events

Model performance, for design events, should be confirmed using Flood Frequency Analysis results, if available, or regional flood frequency information.

Book 7 also has worthwhile guidance on uncertainty analysis, model checking and reporting.

# Flood frequency plots using ggplot

This post provides a recipe for making plots like the one below using ggplot2 in R.  Although it looks simple, there are a few tricky aspects:

• Superscripts in y-axis labels
• Probability scale on x-axis
• Labelling points on the x-axis that are different to the plotted values i.e. we are plotting the normal quantile values but labelling them as percentages
• Adding a title to the legend
• Adding labels to the legend
• Positioning the legend on the plot
• Choosing colours for the lines
• Using commas as a thousand separator.

Code is available as a gist, which also shows how to:

• Enter data using the tribble function, which is convenient for small data sets
• Change the format of data to one observation per row using the tidyr::gather function.
• Use a log scale on the y-axis
• Plot a secondary axis showing the AEP as 1 in X years
• Use the Probit transformation for the AEP values

# Climate change and flood investigations

One surprising finding from the review of the state of hydrologic practice in Victoria, is that climate change impacts on flooding are not being widely considered. Only half the studies reviewed (10 of 20), mention climate change.  Similar findings are reported in other work that shows some Victorian flood managers are not keeping up with their national and international colleagues in considering the additional flood risk predicted with a change in climate.

There is already evidence that rainfall intensity for short duration storms is increasing, which could lead to more frequent and larger flash floods.  This is a particular issue in towns and cities because small urban catchments are especially vulnerable.

In the corporate world, consideration of climate change is being taken seriously.   The recent Hutley opinion found that many climate change risks “would be regarded by a Court as being foreseeable at the present time” and that Australian company directors “who fail to consider ‘climate change risks’ now, could be found liable for breaching their duty of care and diligence in the future”.

The Task Force on Climate Related Financial Disclosures (TCFD), chaired by Michael Bloomberg, has recently released recommendations on how companies should report on climate change risks.  This includes the need to report on risks of “Increased severity of extreme weather events such as cyclones and floods” and “Changes in precipitation patterns and extreme weather variability”.

In the Australian flood scene, the latest Handbook 7Managing the floodplain: a guide to best practice in flood risk management in Australia – provides advice on assessing and reporting on climate change risk.  But the accompanying project brief template and guide, describe climate change aspects of a flood investigation as optional.  The latest version of Australian Rainfall and Runoff provides recommended approaches to assessing climate change impacts on flooding but recent research  argues these methods are too conservative.

On a positive note for Victoria, the Floodplain Management Strategy does encourage consideration of climate change (Policy 9A):

Flood studies prepared with government financial assistance will consider a range of floods of different probabilities, and the rarer flood events will be used to help determine the location’s sensitivity to climate change. Further climate change scenarios may be considered where this sensitivity is significant.

Figure 1: Flooding in Creswick 4 Aug 2010 (link to source)

Flood investigations lead on to decisions about land use zoning and design of mitigation works.  Are climate change risks to these measures foreseeable at the present time?  If so, then they should be considered and reported on.

Clearly this is an area where knowledge and ideas are changing rapidly. Practising hydrologists need to keep up with latest methods, and managers and boards of floodplain management authorities need to be aware of the latest thinking on governance, risk management, and disclosure.