# 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.

# Actual ET and productivity

I was reading a post over at Dynamic Ecology presenting an appreciation of Michael Rosenzwieg, a Professor of Ecology and Evolutionary Biology at the University of Arizona. What caught my eye was his most cited paper which is on the correlation between AET (actual evapotranspiration and productivity).  Here is the abstract:

Actual evapotranspiration (AET) is shown to be a highly significant predictor of the net annual above-ground productivity in mature terrestrial plant communities. Communities included ranged from deserts and tundra to tropical forests. It is hypothesized that the relationship of AET to productivity is due to the fact that AET measures the simultaneous availability of water and solar energy, the most important rate-limiting resources in photosynthesis.

As a hydrologist I knew about actual evapotranspiration (evaporation plus transpiration) but hadn’t paid attention to the link with productivity.  To an ecologist, productivity refers to the rate of biomass production through photosynthesis –  where inorganic molecules, like water and carbon dioxide, are converted to organic material.  Productivity can be measured as mass per unit area per unit time e.g. g m-2 d-1.

In Australia, Actual evapotranspiration is mapped by the Bureau of Meteorology (Figure 1).  There are high values along the coast north of Brisbane, Cape York and ‘The Top End‘.  If Rosenzeig’s correlations hold, these areas are the most ecologically productive in Australia.  In Victoria the highest AET is around Warrnambool, Gippsland and particularly, a small area on the east coast near Mallacoota.  Many of the areas with highest AET are heavily forested.

Figure 1: Average annual areal actual evapotranspiration (link to source)

Rosenzweig quantified the relationship between AET and productivity:

$\mathrm{log_{10}NAAP} = (1.66 \pm 0.27) \mathrm{log_{10}AET} - (1.66 \pm 0.01)$

Where:

• NAAP is the net annual above-ground productivity in grams per square meter.
• AET is annual actual evapotranspiration in mm.

The 95% confidence intervals for the slope and intercept are provided.

Rosenzweig’s paper was published in 1968 and the relationship between AET and productivity is better understood now (e.g. Jasechko, S. et al., 2013).  But the simple relationship between AET and productivity does provide an interesting perspective on the Australian landscape.

### References

Michael L. Rosenzweig  (1968) Net Primary Productivity of Terrestrial Communities: Prediction from Climatological Data,” The American Naturalist 102, no. 923 (Jan. – Feb., 1968): 67-74. DOI: 10.1086/282523 (link).

Jasechko, S., Sharp, Z., Gibson, J., Birks, S., Yi, Y. and Fawcett, P. (2013) Terrestrial water fluxes dominated by transpiration.  Nature 496(7445):347-350 (link).

# 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
(Maribyrnong)
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

# Time of concentration: Pilgrim McDermott formula

There are many formulas for the time of concentration.  A previous post discussed the Bransby Williams approach. Here I look at the Pilgrim McDermott formula, which is another method commonly used in Australia and relates time of concentration to catchment area (A):

$t_c = 0.76A^{0.38}$    (hours)                                                     (equation 1)

where A is measured in km2.

This formula is a component of the Probabilistic Rational Method as discussed in Australian Rainfall and Runoff 1987 (ARR1987) Book IV and is recommended for use in:

• Eastern New South Wales
• Victoria (as developed by Adams, 1987)
• Western Australia – wheatbelt region

McDermott and Pilgrim (1982) needed a formula for the time of concentration to develop their probabilistic rational method approach which was ultimately adopted in ARR1987.  They make the point that, for their statistical method, it is not necessary that the time of concentration closely matches the time for water to traverse a catchment, rather a characteristic time is required for a catchment to determine the duration of the design rainfall.  This characteristic time must be able to be determined directly by designers and lead to consistent values of the runoff coefficient and design flood values.

The basic formula for the probabilistic rational method is:

$Q_y = C_y I_{(y,t_c)} A$                                                                  (equation 2)

Where:

• $Q_y$ is the flood of $y$ years average recurrence interval.
• $C_y$ is the runoff coefficient for a particular average recurrence interval.
• $I$ is the rainfall intensity which is a function of $t_c$ (time of concentration) and $y$.
• $A$ is the catchment area.

For a catchment with a stream gauge, where flood frequency analysis can be undertaken, this will provide the $Q_y$ values on the left hand side of equation 2. We also know the catchment area ($A$). If $t_c$ can be estimated via a time of concentration formula, then the rainfall intensity can be looked up in an IFD table for the location and the only unknown is $C_y$.

$C_y = \frac{Q_y}{I_{(y,t_c)} A}$                                                              (equation 3)

This was the approach used in ARR1987. A large number of gauges were selected and $C_y$ values calculated. Ultimately $C_{10}$ values were mapped in Volume 2 of Australian Rainfall and Runoff.   For floods other than those with a 10 year average recurrence interval, frequency factors were provided to calculate the required runoff coefficient values.  This meant design floods could be estimated for ungauged catchments given information on design rainfall intensity which is available everywhere in Australia.

For this approach to work, some relationship is required between $t_c$ and catchment characteristics i.e. we need a time of concentration formula. McDermott and Pilgrim (1982) began their development of such a formula by testing the Bransby Williams approach because that had been shown to be the best of 8 methods examined by French et al. (1974). McDermott and Pilgrim found that Bransby Williams wasn’t suitable for their purposes because it often resulted in runoff coefficients greater than 1 and they thought the use of such large values would be resisted by practising engineers. Equation 2 doesn’t preclude runoff coefficient values greater than 1 but the intuitive definition of $C$ as being “the proportion of rainfall that runs off” requires it.

An alternative time of concentration formula was developed by considering the ‘minimum time of rise of the flood hydrograph’ which McDermott and Pilgrim collected or collated for 96 catchments. This is the time from when storm rainfall starts until stream discharge begins to increase. McDermott and Pilgrim adopted this as their definition of the time of concentration.

The measured times of concentration were regressed against catchment characteristics that included:

• Catchment area
• Main stream length
• Main stream equal area slope
• Main stream average slope
• Catchment shape factor
• Stream slope non-uniformity index
• Vegetation cover
• Median annual rainfall
• Soil type.

Three formulas provided a similar fit to the data with the simple relationship with catchment area ultimately adopted (equation 1).

One of the important implications of the probabilistic rational method approach is that the time of concentration used for design must be calculated using the same formula that was used in the derivation of the runoff coefficients (equation 3).   So, in Victoria (and Eastern NSW and the Wheatbelt of WA), when using the probabilistic rational method to estimate floods in ungauged catchments, it is important to adopt the Pilgrim McDermott formula for the time of concentration and not use any of the many other approaches.

### References

Adams, C. A. (1987) Design flood estimation for ungauged rural catchments in Victoria.  Road Construction Authority, Victoria. (link)

French, R., Pilgrim, D. H. and Laurenson, E. M. (1974) Experimental examination of the rational method for small rural catchments. Civil Engineering Transactions CE16: 95-102.

McDermott, G. E. and Pilgrim, D. H. (1982) Design flood estimation for small catchments in New South Wales.  Department of National Development and Energy.  Australian Water Resources Council Technical Paper No. 73, pp. 233. (link)

Pilgrim, D. H. and McDermott, G. E. (1982) Design floods for small rural catchments in eastern New South Wales. Civil Engineering Transactions.  Institution of Engineers CE24:226-234.

# Modelling impervious surfaces in RORB – II

This blog builds on the previous post; looking at the runoff coefficient approach to modelling losses and the implications for representing impervious surfaces in the RORB model.

In addition to the IL/CL model discussed in the previous post, RORB can be run using an initial loss / runoff coefficient model, where the runoff coefficient specifies the proportion of rainfall lost in each time step after the initial loss is satisfied.  This reason these different loss models are of interest is that the new version of Australian Rainfall and Runoff is recommending that the IL/CL model is used in place of the runoff coefficient model (Book 5, Section 3.3.1).  In some areas, modelling approaches will need to change and this will have implications for flood estimates.

The runoff coefficient loss model is selected as shown in Figure 1.

Figure 1: A runoff coefficient loss model can be selected in RORB

The user inputs the runoff coefficient, C, for a pervious surface.  For an impervious surface, there is no opportunity to specify the runoff coefficient which is hard-wired in RORB as 0.9.  For mixed sub-areas, the runoff coefficient is scaled, the equations from the RORB manual are:

$C_i = F_iC_{imp} +(1-F_i)C_{perv}, \qquad C_{perv} \le C_{imp} \qquad \mathrm{Equation \;3.5}$
$C_i = C_{imp}, \qquad C_{perv} > C_{imp}\qquad\qquad \mathrm{Equation \; 3.6}$

Where Ci is the runoff coefficient for the ith sub-area.

Example: For a fraction impervious, $F_i = 0.6$ and $C_{perv} = 0.5$
$C_i = 0.6 \times 0.9 +(1-0.6) \times 0.5 = 0.74$

The initial loss is calculated as as a weighted average of the pervious and impervious initial losses as shown in the previous post.  The impervious initial loss is always set to zero in RORB.

Let’s do the calculations for a 100% impervious surface.  RORB will set $I\!L = 0$ and $C = 0.9$.  Using the 6 hour, 1% rainfall as before, the rainfall excess hyetograph is shown in Figure 2.

Figure 2: Rainfall excess hyetograph for an impervious surface using the runoff coefficient model.  RORB sets IL to zero and the the runoff coefficient to 0.9 so 10% of rain is lost at each time step

Example calculation:

As explained in the previous post, the rainfall between 1.5 hour and 2 hour is 19.4 mm.  With a runoff coefficient of 0.9, the rainfall excess will be: 0.9 x 19.4 = 17.5 mm.

The rainfall excess hydrograph from a 10 km2 impervious sub-area can be calculated from the rainfall excess hyetograph using the method described in the previous post. The peak flow corresponding to the 17.5 mm rainfall peak is 97.2 m3s-1 (see the previous post for sample calculations).

The key point is that we have changed the peak flow from an impervious surface, just by changing the loss model.  With the IL/CL model, both initial and continuing loss for a 100% impervious surface are hard-wired to zero. The peak runoff was 107.8 m3s-1. For the runoff coefficient model, initial loss is hard-wired to zero, but the runoff coefficient is hard-wired to 0.9, i.e. we have some loss from the impervious surface. This changes the hydrograph as shown in Figure 3.

Figure 3: Comparison of rainfall excess hydrographs from a 100% impervious surface; same rainfall, different loss model

The value of the runoff coefficient for an impervious surface is noted in the RORB manual:

The impervious area runoff coefficient Cimp is set by the program to 0.9, reflecting the fact that losses occur even on nominally impervious surfaces in urban areas.

This is reasonable, but inconsistent with the treatment of the continuing loss when the IL/CL loss model is used.  In this case, CL is hard-wired to zero so there are no losses from impervious surfaces; a feature of RORB for modellers to be aware of.

Also note Equation 3.6 above.  This suggests that if the user inputs a runoff coefficient larger than the impervious coefficient (i.e. larger than 0.9) then a value of 0.9 will be used.  This isn’t actually implemented.  If a runoff coefficient of 1 is input, there is a direct conversion of rainfall to runoff i.e. there is no loss.  It is even possible to input runoff coefficients greater than 1.

Equation 3.6 may just be the result of a typo.  Some experimenting suggests the behaviour in the model is represented the combination of equation 3.5, above and the following in place of equation 3.6:

$C_i = C_{perv}, \qquad C_{perv} > C_{imp}$

That is, the runoff coefficient for an impervious surface is 0.9 unless the runoff coefficient input by the user is larger than 0.9.

Calculations are available via a gist.

# Modelling impervious surfaces in RORB

The previous post looked at rainfall excess hydrographs; here I explore how these hydrographs change when modelling impervious surfaces in RORB.  This post focusses on the initial loss/continuing loss modelling approach.

Usually, losses are reduced for impervious compared to pervious surfaces and RORB sets both initial and continuing loss to zero if a surface is 100% impervious.

As an example, consider the 6 hour 1% rainfall for Melbourne, which is 83.4 mm.  If we use the ARR1987 temporal pattern (see the previous post), the hyetograph is as shown in Figure 1.

Figure 1: The 6 hour 1% rainfall (83.4 mm) multiplied by the ARR1987 temporal pattern.  For an impervious surface, RORB sets both initial and continuing loss to zero

Example calculation:

In the ARR1987 temporal pattern, the time period between 1.5 and 2 hours has 23.3 percent of the rain.  The total rainfall is 83.4 mm so the rain in this period is 83.4 x 23.3% = 19.43 mm which is consistent with Figure 1.

The corresponding rainfall excess hydrograph, for an area of 10 km2, which is 100% impervious, is shown in Figure 2 (Note that Areal Reduction Factors have not been used).

Figure 2: rainfall excess hydrograph for an area of 10 km2

Example calculation:

The instantaneous flow at a 2 hours will be

$\frac{1}{3.6} \times \frac{1}{0.5} \times 19.4 \times 10 = 107.8 \mathrm{m^3 s^{-1}}$

To explain factors at the start of the equation, 1/3.6 is for unit conversion, 1/0.5 is because the temporal pattern has a 0.5 hour time step.   The RORB output matches the calculations (Figure 3).

By default, RORB will show the rainfall excess hyetograph above the calculated hydrograph but this is  based on the initial and continuing loss as provided by the user.  In this case, I’ve specified IL = 10 mm and CL = 2 mm/h for the pervious areas.   These losses, and the hyetograph, are misleading where a sub-catchment has some impervious component.  In this case, for a 100% impervious sub-area, both IL and CL are set to zero by the program.  It would be best not to display the misleading hyetograph, which can be turned off as shown in Figure 4.

FInure 3: RORB output

Figure 4: The hyetograph can be toggled off using the button outlined in pink

If a sub-area is a combination of both impervious and pervious surfaces, this must be specified to RORB as a Fraction Impervious (Fi).  The initial and continuing losses are scaled based on this fraction.

$IL_i = (1 - F_i) I\!L_{perv}$
$CL_i = (1 - F_i) C\!L_{perv}$

Where $I\!L_{perv}$ and $C\!L_{perv}$ are the initial and continuing losses for pervious areas as input by the user.

For example, if the pervious value of IL is set to 10 mm and CL to 2 mm/h, then for a sub-area with a Fraction Impervious value of 60%, the initial and continuing losses will be:

$I\!L = (1 - 0.6) \times 10 = 4 \; \mathrm{mm}$
$C\!L = (1 - 0.6) \times 2 = 0.8 \; \mathrm{mm/h}$

The continuing loss is 0.8 mm/h which is 0.4 mm per 30 min time step.

Running the model with these parameters results in a rainfall excess hydrograph as shown in Figure 5.  Note that the start of the rise of the hydrograph is delayed because of the initial loss.  The peak is reduced by a small amount (from  108 cumec to 106 cumec because of the continuing loss).

Example calculation, flow peak:

$\frac{1}{3.6} \times \frac{1}{0.5} \times (19.4 - 0.4) \times 10 = 105.6 \mathrm{m^3 s^{-1}}$

Figure 5: Rainfall excess hydrograph

For a real catchment with a 60% fraction impervious, we would expect some early runoff from the impervious surfaces that would provide flow directly into the urban drainage system.  RORB doesn’t model this process, which may not matter, depending on the application, but as modellers we need to be aware of this limitation.

Calculations are available as a gist.