Tag Archives: floods

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

Links for more information:

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.

ARR update from the FMA conference

There were several papers related to Australian Rainfall and Runoff at the FMA conference last week.  Once the papers become available on the FMA website, it would be worth checking, at least these three:

  • What Do Floodplain Managers Do Now That Australian Rainfall and Runoff Has Been Released? – Monique Retallick, WMAwater.
  • Australian Rainfall and Runoff: Case Study on Applying the New Guidelines -Isabelle Testoni, WMAwater.
  • Impact of Ensemble and Joint Probability Techniques on Design Flood Levels -David Stephens, Hydrology and Risk Consulting.

There was also a workshop session where software vendors and maintainers discussed how they were updating their products to become compliant with the new ARR.

A few highlights:

1. The ARR team are working on a single temporal pattern that can be used with hydrologic models to get a preliminary and rapid assessment of flood magnitudes for a given frequency. This means an ensemble or Monte Carlo approach won’t be necessary in all cases but is recommended for all but very approximate flood estimates.

2. The main software vendors presented on their efforts to incorporate ARR2016 data and procedures into models. This included: RORB, URBS, WBMN, RAFTS. Drains has also included functionality. All the models use similar approaches but speakers acknowledged further changes were likely as we learn more about the implications of ARR2016. The modelling of spatial rainfall patterns did not seem well advanced as most programs only accept a single pattern so don’t allow for the influence of AEP and duration.

3. WMA Water have developed a guide on how to use ARR2016 for flood studies. This has been done for the NSW Office of Environment and Heritage (OEH) and looks to be very useful as it includes several case studies. The guide is not yet publicly available but will be provided to the NFRAG committee so may released.

4. Hydrologists need to take care when selecting the hydrograph, from the ensemble of hydrographs, to use for hydraulic modelling. A peaked, low-volume hydrograph may end up being attenuated by hydraulic routing. We need to look at the peaks of the ensemble of hydrographs as well as their volumes. The selection of a single design hydrograph from an ensemble of hydrographs was seen as an area requiring further research.

5. Critical duration – The identification of a single critical duration is often much less obvious now we are using ensemble rainfall patterns. It seems that many durations produce similar flood magnitudes. The implications of this are not yet clear. Perhaps if the peaks are similar, we should consider hydrographs with more volume as they will be subject to less attenuation from further routing.

6. There was lots of discussion around whether we should use the mean or median of an ensemble of events.  The take away message was that in general we should be using the median of inputs and mean of outputs.

7. When determining the flood risk at many points is a large catchment, different points will have different critical durations. There was talk of “enveloping” the results. This is likely to be an envelope of means rather than extremes.

8. The probabilistic rational method, previously used for rural flood estimates in ungauged catchments, is no longer supported. The RFFE is now recommended.

9. The urban rational method will only be recommended for small catchments such as a “two lot subdivision”.

10. There was no update on when a complete draft of ARR Book 9 would be released.

11. Losses should be based on local data if there is any available. This includes estimating losses by calibration to a flood frequency curve. Only use data hub losses if there is no better information. In one case study that was presented, the initial loss was taken from the data hub and the continuing loss was determined by calibration to a flood frequency curve.

12. NSW will not be adopting the ARR2016 approach to the interaction of coastal and riverine flooding. Apparently their current approaches are better and have an allowance for entrance conditions that are not embedded in the ARR approach.

13. NSW will not be using ARR approaches to estimate the impacts of climate change on flooding. Instead they will use NARCLIM.

14. NSW have mapped the difference between the 1987 IFD and the 2016 IFD rainfalls and use this to assist in setting priorities for undertaking flood studies.

15. A case study was presented for a highly urbanized catchment in Woolloomooloo. There was quite an involved procedure to determine the critical duration for all points in the catchment and the temporal patterns that led to the critical cases. Results using all 10 patterns were mapped, gridded and averaged. I didn’t fully understand the approach as presented but there may be more information in the published version of Isabelle Testoni’s paper once it becomes available.

There is still much to learn about the new Australian Rainfall and Runoff and much to be decided.  The papers at the FMA conference were a big help in understanding how people are interpreting and responding to the new guideline.

Flood frequency and the rule of 3

There is a ‘rule of three‘ in statistics that provides a rapid method for working out the confidence interval for flood occurrence.

From Wikipedia:

If a certain event did not occur in a sample with n subjects, the interval from 0 to 3/n is a 95% confidence interval for the rate of occurrences in the population.

For example, if a levee hasn’t been overtopped since it was built 100 years ago, then it can be concluded with 95% confidence that overtopping will occur in fewer than 1 year in 33 (3/100).  Alternatively the 95% confidence interval for the Annual Exceedance Probability of the flood that would cause overtopping is between 0 and 3/100 (3%).  Of course you may be able to get a better estimate of the confidence interval if you have other data such as a flow record, information on water levels and the height of the levee.

The rule of 3 provides a reasonable estimate for n greater 30.

Old flood levels on railway bridge plans

Historic flood levels are an important input to flood studies to help with hydraulic model calibration and to improve the precision of flood frequency analysis.  A collection of old bridge plans from Victorian Railways (Victoria, Australia) is available that includes information on flood levels from some of the largest floods from the late 19th and early 20th Century.  From newspaper reports, we know these were big floods, but information on levels is hard to find which means the observations noted on these plans are a valuable resource.

A link to a PDF file with 409 plans is here:

I’ve pulled out some examples in the following figures.

Mitchell River, 1870 flood level at Bairnsdale


Figure 1: Mitchell River at Bairnsdale, 1870 flood level (link to plan)

Nicholson River, 1893 flood level at the Nicholson Bridge

The 1893 flood was a very significant event in this area, resulting in a change in course in the nearby Tambo River which isolated a wharf which was important for river traffic at the time (Erskine et al., 1990).


Figure 2: Nicholson River at Bairnsdale, 1983 flood level (link to plan)

I’ve looked through all the plans and found flood levels for about 15 waterways as noted in the following table. Not all of these will be useful but there are a few gems such as the 1934 flood levels in Orbost which include velocity estimates.

Table 1: Waterways and page numbers in the PDF file of plans
Waterway Location Page number in PDF Comment
Back Ck Taradale 381 “Max” flood level
Goulburn River Toolamba 400 1870 flood
Jacksons Ck Sunbury 361 1916 flood
Maribrynong River 168 ‘Adopted’ flood level
Mitchell River Bairnsdale 178 1870 flood
Moonee Ponds Ck Jacana 221 ‘Adopted’ flood level
Moorabool River 223
MurrayRiver Albury 265 Flood sometime prior to 1882
Murray River Tocumwal 388 Flood prior to 1892
Nicholson River Nicholson 275 1893 flood
Saltwater River
Footscray 334 1906 flood
Snowy River Orbost 301 1934 flood
Stoney Ck 351
Tambo River Bruthen 371
Thomson River Sale 317 Flood prior to Nov 1874
Yarra River Richmond 310 1863 flood
Woady Yallock Ck 405 1909 flood
Wombat Ck 407

Weekly cycle of storms

Are storms more likely on Friday or Monday?  An recent article in Geophysical Research Letters (Yang et al., 2016) suggests there is a weekly cycle to thunderstorms over parts of China that is related to the buildup of air pollution during the week that dissipates over the weekend.   Depending on the type of pollution, this can either increase or decrease the number of storms.  So in some areas there are fewer storms on Monday than Friday with the opposite effect in other areas.  There has been similar work in the US (Bell et al., 2008), Moscow and Atlanta. There is also a good review article (Sanchez-Lorenzo et al. 2012)

In Melbourne, Australia, Simmonds and Kaval (1986) found that rainfall increased during the week from a minimum on Sunday to a Maximum on Thursday.  A later study (Simmonds and Keay, 1997) showed that temperatures and rainfall tended to be higher on weekdays compared to weekends.

The Bureau of Meteorology maintains a Severe Storms Archive.  I grabbed the data for Victoria and looked at the frequency of storms on different days of the week.  There are 237 records from 1 Jan 2010 to 11 Mar 2016.  A quick analysis suggests the number of storms is lower on Monday with an increase through to Friday.


If this result was confirmed by a more thorough analysis it could have implications for planning for emergency response.

Data and analysis is available as a gist.




Rain, soil moisture and urbanisation

The amount of runoff from a catchment depends on the amount of rain, but it also the case that the amount of rain depends on the catchment.  Catchments influence the amount of rain in different ways in rural, irrigated and urban areas.

In rural catchments, some recent work has shown a relationship between summer afternoon rain and soil moisture.  When there is a lot of soil moisture around i.e. in wet summers, rainfall is more frequent – that is to be expected – but the rain is most likely to fall over areas of dry soil.  This is because sun shining on these dry areas produces the warmest air that rises further and faster.  Moisture in the air then condenses to form rain.  There is a nice summary of the research here and in this letter to Nature.

Now, new research has suggested rainfall is less likely over irrigated, compared to non-irrigated areas.  Air is more stable over irrigated regions because they are cooled by evaporating water.  The air doesn’t rise as far, or as fast on a warm afternoon so rain is less frequent.  This causes more dry days and reduced rainfall totals.  A summary of the research is available here.

There is likely a similar effect in urban areas.  In summer, cities tend to be warmer than surrounding non-urban land which can lead to more frequent and more intense afternoon rainfall (see some great research on rainfall over Houston).  However the total amount of rain over an urban area can decrease because the effect of development can lead to less water in the landscape.  This is consistent with cities being dry and hot in summer.   For example research in the large urban area of Beijing showed fewer but more intense summer rainfall events.

Increased rainfall intensity isn’t the only factor contributing to changes in flooding regime caused by urbanisation.  The flood regime of a stream can change under the influence of three factors:

  1. Atmospheric processes e.g. increased rainfall intensity, as mentioned above.
  2. Catchment processes e.g. an increase in impermeable areas or other landuse change.
  3. Alteration to a stream e.g. improving hydraulic efficiency – piping and lining, decreasing floodplain storage, or extending the drainage network – the underground drainage system that reaches to the furthest corners of a developed catchment.

In urban areas, all three factors are at work, so floods become larger and more frequent following urbanisation.  Plus there are are a lot more people and assets that are vulnerable to flooding.


The three-headed dog of urbanisation impacts on flooding

Further reading

Burian, S. J. and Shepherd, J. M. (2005) Effect of urbanization on diurnal rainfall pattern in Houston.  Hydrological Processes 19(5):1089-1103 (link).

Konrad, C. P. (2014) Effects of urban development on floods.  U. S. Geological Survey. Fact Sheet 076-03 (link) (pdf).

Selman, C. and Mishra, V. (2016) The sensitivity of southern US climate to varying irrigation vigor.  Journal of Geophysical Research Atmos.  DOI: 10.1002/2016JD025002 (link).

Taylor, C. M., de Jeu, R. A. M., Guichard, F., Harris, P. P. Dorigo, W. A. (2012) Afternoon rain more likely over drier soils.  Nature doi:10.1038/nature11377 (link).

Viglione, A., Merz, B. Dung, N. V., Parajka, J., Nester, T. and Bloschl, G. (2016) Attribution of regional flood changes based on scaling fingerprints.  Water Resources Research DOI: 10.1002/2016WR019036 (link).