ARR2019 – Areal Reduction Factors

With the publication of the 2019 edition of Australian Rainfall and Runoff most, but not all, of the ambiguities around the calculation of Areal Reduction Factors have been fixed.

Equations are provided that allow calculation of Areal Reduction Factors (ARFs) for:

  • Short durations

Durations less than 12 hours; a single equation for the whole of Australia

  • Long durations

Durations between 24 hours and 168 hours, with different coefficients required for each of 10 regions (Figure 1).

These equations, and the long duration coefficients, are available from the data hub and from from Australian Rainfall and Runoff (ARR) (Book 2, Chapter 4.3).  The reference is to ‘coefficients’ in ARR and to ‘parameters’ on the data hub but they are the same thing.

2059

Figure 1: ARF regions

What the data hub doesn’t make clear is that procedures used to calculate an ARF depend on both duration and area.  Details are in ARR Book 2, Table 2.4.1.  There are 11 separate cases to consider which I list in 5 groups below.

1. Very small catchments:

1.1. Catchment area ≤ 1 km2, ARF = 1 for any duration

2. Very large catchments:

2.1. Catchment area > 30,000 km2, ARF can not be calculated using the generalised equations

3. Catchments between 1000 km2 and 30,000 km2

3.1. Short durations: for duration ≤ 12 hours, ARF can not be calculated using the generalised equations

3.2. Long durations: for duration ≥ 24 hours calculate ARF using the long duration equation

3.3. Between long and short durations (between 12 and 24 hours);  interpolate between the long duration and short duration ARFs.  So, although it is not valid to use the short duration ARFs in catchments of this size, the guidance suggests the 12 hour short duration ARF can be used as one terminal in the required interpolation.

4. Catchments between 10 km2 and 1000 km2

4.1. Short durations: use the short duration equation for durations ≤ 12 hours

4.2. Long durations: use the long duration equation for durations ≥ 24 hours

4.3. Between long duration and short duration: interpolate

5. Catchments between 1 km2  and 10 km2

5.1. Short duration: interpolate for the area between an ARF of 1 at 1 km2 and the short duration ARF for 10 km2.

5.2. Long duration: interpolate for the area between an ARF of 1 at 1 km2 and the long duration ARF for 10 km2.

5.3. Between long duration and short duration: Interpolate for the duration between the long duration ARF and short duration ARF for a catchment of 10 km2.  Then interpolate for the area between an ARF of 1 at 1 km2 and the value for a 10 km2 catchment.

Note, that for the area-based interpolations in 5.1 and 5.2, equation 2.4.4 is required (below).  For the duration based interpolations, equation 2.4.3 should be used.  There is an error in Table 2.4.1 in ARR where the wrong interpolation formula is referred to.

\mathrm{ARF} = \mathrm{ARF_{12hour} + (ARF_{24hour} -ARF_{12 hour}) \frac{(duration-720)}{720}}     (2.4.3)

\mathrm{ARF} = 1-0.6614(1 - \mathrm{ARF_{10km^2}} ) ( \mathrm{A}^{0.4} - 1 )     (2.4.4)

Another thing to be careful of is that the unrealistic negative values are calculated for large catchments and short durations.  For example, the ARF for a 1000 km2 catchment, 1 minute duration and AEP of 1% in the Southern Temperate zone is -0.79.  Of course, most practitioners are not interested in situations like this but if a Monte Carlo approach is used, these odd results may come up unless the parameter bounds are set carefully.

When setting up an ARF spreadsheet or script it is probably worth setting any values less than zero, to zero.  But also check that your hydrologic model won’t crash if ARF is zero.

The smallest duration considered in the derivation of the ARFs was 60 min so anything shorter than that is an extrapolation (Stensmyr et al., 2014).  If the critical case ends up being less than 60 min, check that the ARFs are realistic.

Example

There is a worked example in ARR Book 2, Chapter 6.5.3.

Region = East Coast North,  Area = 245.07, AEP = 1%, Duration = 24 hour (1440 min)

ARF = 0.929

ARF calculator

I’ve developed a simple ARF calculator as a web app here. The code is available as a gist.

Test cases

The test cases I used when developing the ARF calculator are here.  This gives ARFs for a range of AEPs, durations and areas that correspond to the 11 cases listed above, along with other checks.  I calculated these manually.  Please let me know if you think any are incorrect.

References

Stensmyr, P., Babister, M. and Retallick, M. (2014) Spatial patterns of rainfall.  Australian Rainfall and Runoff Revision Project 2. http://arr.ga.gov.au/__data/assets/pdf_file/0020/40556/ARR_Project2_Report_Short_ARF.pdf

 

 

 

 

 

 

Coronavirus resources

Sources of information on the COVID-19 epidemic.  These are sites that I’m looking at.

Data

Modelling and forecasting

General information

 

Tidy Pre-burst data

Pre-burst rainfall data can be obtained from the ARR data hub but its not in a form that is easy to work with.  It’s not ‘tidy’.  Tidy data has one observation per row with information in neighbouring columns about that observation.  Once the data is in tidy format, its easy to use tools in R or pivot tables in excel to undertake analysis.  You spend a lot less time munging tidy data than the usual case when data is messy.

A tidy data structure for pre-burst data would look like the table below.  ‘Type’ can be either depth or ratio, available percentiles are 10, 25, 50, 75, 90, standard AEPs are 1, 2, 5, 10, 20, 50.  The value is either a depth in mm or the pre-burst to burst ratio.  The value is the observation.  Everything else is information about the observation.

Duration (min) Duration (hour) Type Percentile AEP Value
60 1 depth 10 50 0
60 1 ratio 10 50 0
2880 48 depth 90 1 15.1
2880 48 ratio 90 1 0.105

I’ve written a function Get_tidy_prebust that will return the pre-burst data in tidy format given the latitude and longitude of a location.  After that its easy.  Below is an example for Axe Creek. First we get the tidy data, and can then graph it in a variety of formats.  See the gist for all the details.

Axe = Get_tidy_prebust(lat =-36.9, lon = 144.36)
Axe %>%
filter(type == 'ratio') %>%
ggplot(aes(x = dur_hour, y = preburst, colour = factor(percentile))) +
geom_line() +
geom_point()+
facet_wrap(~AEP) +
labs(x = 'Preburst ratio',
y = 'Duration (hour)') +
scale_colour_discrete(name = 'Percentile')
Axe_dur_ratio

Figure 1: Relationship between pre-burst ratio and duration as a function of AEP and percentile

Axe_percentile_ratio

Figure 2: Relationship between pre-burst ratio and percentile as a function of AEP and duration

 

Scraping the data hub

The Australian Rainfall and Runoff data hub provides information to support modelling of design floods.  The usual way to get the required data is via a web interface but it is also possible to scrape the data.  Instructions are here under the heading ‘Advanced Use:’.

In R the getURI function from the RCurl package can be used.  A basic command is:
RCurl::getURI(glue("https://data.arr-software.org/?lon_coord={lon}&lat_coord={lat}&type=text&Preburst=1&OtherPreburst=1"))

Where ‘lon’ and ‘lat’ are the longitude and latitude of the location of interest.  This will return a text file with information on median prebust (Preburst=1) and preburst for other percentiles (OtherPreburst=1).  The text file can then be processed to extract required information.  Many other options are available.  For example if All=1 is used, information on a large number of parameters is returned including rainfall temporal patterns.

As an example, I’ve written a function, Get_burst, which extracts the preburst information for a percentile, latitude and longitude.  It is also necessary to specify if depths or ratios are required.  Example usage is shown below.

Get_preburst(percentile = 90, type = 'depth', lat = -36.9, lon = 144.36)   


   dur_min dur_hour AEP_50 AEP_20 AEP_10 AEP_5 AEP_2 AEP_1
 1      60      1     22.3   25.2   27.1  29    30.6  31.8
 2      90      1.5   24.2   25.4   26.1  26.9  31.5  35  
 3     120      2     27.2   33.4   37.5  41.5  43.6  45.2
 4     180      3     23.3   27.1   29.6  32    43.4  52  
 5     360      6     19.5   24.3   27.5  30.6  42.5  51.4
 6     720     12     12.8   20.3   25.3  30.1  34.4  37.6
 7    1080     18     15.6   18.1   19.7  21.3  25.7  29  
 8    1440     24     14.6   18.8   21.6  24.2  24.3  24.4
 9    2160     36      9     11.2   12.6  14    22.3  28.5
10    2880     48      1.1    2.7    3.7   4.7  10.7  15.1
11    4320     72      0.2    1.9    3     4    12.5  18.9

This approach is much quicker when working on a large number of sites and could be used to automate entry into other programs such as RORB.

The function Get_losses, returns initial and continuing loss from the data hub for any location.

# # Exampe usage
# lat = -33.87
# lon = 151.206
#
# Get_losses(lat = lat, lon = lon)
# $ILs
# [1] 28
#
# $CL
# [1] 1.6

 

When to plan a paddling trip on the King River

The King River in northeast Victoria is a fun kayaking destination but its only worth going when there is enough flow.  The best white water is the reach between Lake William Hovel and Cheshunt South (map).  According to the Whitehouse Canoe Club, the minimum level for paddling is 0.6 m at the Cheshunt gauge; a good level is 1.0 m.

We can use the data from the gauge, King River at Cheshunt (403227) to work out when to plan a trip.  Figure 1 shows the average daily levels for each day in the period of record (28 June 1967 to 10 March 2020).  I’ve made the points translucent so that data can be seen in areas were there is over-plotting.  The red dashed lines are the river levels of 0.6 m and 1 m.  The blue line is the average (a loess smooth).  The river is often above 0.6 m between early July and late October.

King_daily_all

Figure 1: Daily levels, King River at Cheshunt

It is also possible to calculate an empirical estimate of the probability that the river level will be greater than 0.6 m.  This is based on the proportion of days in the record, considering each day of the year, that the river level exceeds 0.6 m (Figure 2).  The best time to plan a trip is during August and early September when the probability of being able to paddle is greater than 80%. But be prepared for cool weather, the average maximum temperature in August is only 10.8 oC.

Before you go, check the level of Lake William Hovel which is the reservoir upstream of the white-water reach.  The lake must be full and spilling over the dam before the flow will get above 0.6 m at Cheshunt.  You can check the lake levels here.

King_prob_gt0p6

Figure 2: Probability that the King River level is greater than 0.6 m for each day of the year

 

 

Stormwater walk in the Royal Botanic Gardens

[CANCELLED as at 16 March]

Melbourne Royal Botanic Gardens has successfully reduced water consumption by more than 60% since 1994, yet the gardens are still beautiful, functional and win awards.   How do they do it?

Please come and enjoy a joint event by EA Victorian Water Panel and EIANZStormwater Walk in Melbourne Royal Botanic Gardens – to discover water conservation strategies and stormwater management.

Notice: this is an event for members of EIANZ and Engineers Australia only.

Tour content:

  • The use of stormwater harvesting to offset mains irrigation demands in a large and water-thirsty public environment
  • Monitoring water quality and achieving significant improvement in key metrics including nitrogen and phosphorus reduction
  • Water treatment plant – visit and discuss the role of treatment and automated systems for irrigation
  • Not just wetlands – the various issues in managing an ornamental lake supplied by stormwater (Blue Green Algae, floating and submerged macrophytes)
  • Where to next – the use of desalinated water?

For more details, and to register, please click through to the flyer.

The Stormwater Walk in Melbourne Royal Botanic Gardens is on 19 March 2020. [Has now been cancelled]

The effect of bushfire on water quality: revisiting the 2003 fires

The 2003 Alpine fires burnt 1.3 million hectares in the Alpine and Mt Buffalo National Parks in Victoria (Figure 1). These were large fires, but much smaller than those of 2019/2020 which are still going and as of the 14th of January were estimated to have burned 18 million ha.  The water quality problems arising from the 2003 fires indicate the challenges to drinking water supplies caused by polluted runoff from burnt areas.

Fire-extent-2003

Figure 1: Area burned in the 2003 Alpine fires (EPA, 2004)

 

On 26 February 2003 there was a flash flood in the fire affected catchment of the Buckland River, a tributary of the Ovens River, that caused turbidity to spike at over 100,000 NTU (suspended solids 59,000 mg/L).  Turbidity declined as water moved downstream but peaked at 2,370 NTU in the Ovens River where water is withdrawn to supply Wangaratta a town of about 20,000 people (Figures 2 and 3).  It wasn’t just turbidity that was elevated.  Measurements show that heavy metal concentrations increased as did fecal coliform and nutrients.  For example, lead levels in the Buckland River were recorded as 0.98 mg/L, which is 98 times higher than the the Australian drinking water guideline value of 0.01 mg/L.  The baseline level, prior to the flood was < 0.001 mg/L (Leak et al., 2003).

turb

Figure 2: Turbidity in the Buckland and Ovens Rivers

 

map-3

Figure 3: Locality map

There is an interesting story of how North East Water coped with this this crisis to maintain the supply of water to Wangarratta and other affected towns (see Leak et al., 2003). The water treatment plant at Wangaratta had to be shut down for 17 hours to manage the amount of sludge being produced and chemical dosing was continuously adjusted as turbidity changed.  There was concern that Wangaratta might run out of water, restrictions were set to stage 4 – the highest level, and some water was carted in to supplement supply.

The Wangaratta plant was challenged for 17 days from 7 March 2003 to 23 March when turbidity dropped below 100 NTU.

Stuart Khan from the University of NSW recently wrote about the threats to drinking water safety from the 2019/2000 fires.  Residents of several towns have been advised to boil water before drinking it and there has been ‘do not drink’ alerts in some areas.  There are also long term risks from ash washed into water supply reservoirs and the potential for algal blooms.

Our water supply systems will need to be adapted to these challenges and to future extreme weather.