Areal Reduction Factors

[Edit 9 Feb 2016]

Information on Areal Reduction Factors is now available from the ARR data hub http://data.arr-software.org/

Also check the latest version of Australian Rainfall and Runoff as there has been revisions to the ARF recommendations since I wrote this post.

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New Areal Reduction Factors for Australia are published in the draft version of Australian Rainfall and Runoff (Book 2, section 4.2).  You can browse to them via http://book.arr.org.au/

In a quirk of formatting, the key equations (Equation 2.4.1 and 2.4.2) can’t be seen in the epub version or the web-version.   I opened the epub version with Adobe Digital Editions and found the equations which are copied below.  You will probably need to zoom in to see the parameters.  The long duration equation (2.4.1) are suitable for durations of 24 hours or more.  The short duration equations (2.4.2) are suitable for 12 hours or less.  For durations between 12 and 24 hours a combination of these two equations is required as discussed in Table 2.4.1 in ARR.

ARR2015 Book 2, Section 4.2, Equation 2.4.1

Long duration ARFs  (>24 hours, 1440 mins) – ARR2015, Book 2, Section 4.2, Equation 2.4.1

ARR2015 Book 2, Section 4.2, Equation 2.4.2

Short duration ARFs  (< 12 hours, 720 min)- ARR2015, Book 2, Section 4.2, Equation 2.4.2

Also, note that these equations are different to those published in the final ARF research reports and, for Victoria, they differ from the commonly used Siriwardena and Weinmann equations as published in Hydrological Recipes (see section 3.1).  Based on discussion with the developers, it’s also likely the short duration equation (Equation 2.4.2) will change, as will the procedures listed in Table 2.4.1 of ARR.  The upshot is, the procedure as published is very much a draft.

Long Duration Areal Reduction Factors

The most enduring aspect of the draft procedures is likely to be the long duration approach (equation 2.4.1).

The prediction equation (2.4.1 above) has 9 parameters which vary depending on the region. Ten regions have been defined for Australia as shown in Figure 1.  Parameters are listed in Table 1 and can be downloaded here.

ARF-Regions

Figure 1:  Regions for Areal Reduction Factors (source: ARR Book 2, Section 4.2)

Table 1:  Parameters for the ARF equation (2.4.1) which depend on the region (source: ARR Book 2, Section 4.2)
Region a b c d e f g h i
East Coast North 0.327 0.241 0.448 0.36 0.00096 0.48 -0.21 0.012 -0.0013
Semi-arid Inland QLD 0.159 0.283 0.25 0.308 7.30E-07 1 0.039 0 0
Tasmania 0.0605 0.347 0.2 0.283 0.00076 0.347 0.0877 0.012 -0.00033
SW WA 0.183 0.259 0.271 0.33 3.85E-06 0.41 0.55 0.00817 -0.00045
Central NSW 0.265 0.241 0.505 0.321 0.00056 0.414 -0.021 0.015 -0.00033
SE Coast 0.06 0.361 0 0.317 8.11E-05 0.651 0 0 0
Southern Semi-arid 0.254 0.247 0.403 0.351 0.0013 0.302 0.058 0 0
Southern Temperate 0.158 0.276 0.372 0.315 0.000141 0.41 0.15 0.01 -0.0027
Northern Coastal 0.326 0.223 0.442 0.323 0.0013 0.58 -0.374 0.013 -0.0015
Inland Arid 0.297 0.234 0.449 0.344 0.00142 0.216 -0.129 0 0

An R function to calculate the ARFs is available as a gist.

I’ve made a web app to undertake the ARF calculations. It is very basic at present and uses guidance that has not yet been published in ARR. I’ll finalise it once ARR has been updated. Check the app out here.

3 thoughts on “Areal Reduction Factors

  1. Pingback: Using new Areal Reduction Factors in RORB | tonyladson

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