# API and inital loss

In an earlier blog I wrote about the relationship between the Antecedent Precipitation Index (API) and initial loss – In this context, initial loss is the amount of rain that is ‘lost’ and does not contribute to a flood hydrograph.  This post provides more information on the use of API in the new Australian Rainfall and Runoff.

Although API was in favour in the 1970s when it was used in several studies by Ian Cordery, it is barely mentioned in ARR1987 and is discounted in favour of pre-storm baseflow in the influential report on rainfall losses by Hill et al. (1998).  Recent work has shown that in some catchments API could explain much of the variance in initial loss while in others it provided no explanation (See Figure 6.19 in Hill et al., 2014a).

The usefulness of API led to its inclusion in an equation to estimate design values for initial loss in one region of Australia (the ‘GSAM coastal and inland region’) in a study undertaken for the new ARR (ARR2016 – Project 6) (Hill et al., 2014).  GSAM stands for Generalised South Australian Method which is a procedure to estimate the probable maximum precipitation (PMP).  A rough definition of the PMP is the largest possible rainfall.  (See this link for more details, or the Bureau of Meteorology website).  The GSAM region is the greenish area shown in Figure 1.

Figure 1: Zones where the different generalised methods can be used to estimate long duration probable maximum precipitation (PMP).  Initial loss has been related to API in the GSAM coastal and inland regions (source: BoM)

In the GSAM coastal and inland region:

$IL_s = 16.7+0.141 P_{24h}^{2\%} - 0.291\, \mathrm{median}(API)$     (3)

The median API is 37.6 mm (based on daily rainfall data from 1889 to 2016).  The procedure to calculate API is explained here and computer code is here.

The 24 hour 2% rainfall depth $P_{24h}^{2\%}$ can be obtained from the Bureau of Meteorology website (here).  The centroid of the catchment above creswick is approximately (37.4S, 143.9E), so the required rainfall depth is 106 mm.

$16.7 + 0.141 \times 106 - 0.291 \times 37.6 = 20.7 \, \mathrm{mm}$.

Interestingly, when the material from the project 6 reports was incorporated in the draft Australian Rainfall and Runoff, the API didn’t make the cut.  The regions were changed from these from those shown in Figure 1.  The current ‘Loss Regions’ are shown in Figure 2.  It will be interesting to see if API makes a comeback in the next version of the ARR draft.

Figure 3: Regions defined for recommending loss values (ARR2016, Book 5, Figure 5.5.16)

Other approaches to calculating API have been proposed.

In the UK, the formula for the API is a little different to that used in the US and Australia (Reed, 2011).

$API = r^{0.5} \left( P_{-1} +r \left( P_{-2} + r \left( P_{-3} + ... \right) \right) \right)$     (4)

For daily data $P_{-i}$ is precipitation on the ith day before the event and $r$ is the recession factor $0 . The $r^{0.5}$ term is used so that $API$ represents the catchment wetness at the beginning of the current day.

UK practice is to only use the first 5 terms of the series (Reed, 2011).

Heggen (2001) proposed a formula to normalise the API to average conditions for a catchment.  I plan to explore this in a future post.

(Edit 15 July 2015) Recent work by researchers at the University of Adelaide (Deng et al., 2016) has developed an ‘Antecedent effect ratio’ to describe the importance of a catchment’s antecedent moisture content on overall runoff volume.   Catchments with high AER values (where antecedent moisture content was highly influential),  were likely where precipitation regimes were highly seasonal.

### References

Heggen, R. (2001) Normalized antecedent precipitation index.  Journal of Hydrologic Engineering 6(5): 377-381 (link to abstract).

Kohler, M. A., Linsley, R. K. (1951) Predicting runoff from storm rainfall. Res. Paper 34, U. S. Weather Bureau, Washington, D. C. (link to PDF).

Cordery, I. (1970b). Initial Loss for Flood Estimation and Forecasting. Journal of the Hydraulics Division 96(12): 2447-2466 (link to abstract).

Cordery, I. (1970a). Antecedent wetness for design flood estimation. Civil Engineering Transactions CE12(2):181-184.

Mein, R. G. Nandakumar, N. and Siriwardena, L. (1995) Estimation of initial loss from soil moisture indices (pilot study).  CRC for Catchment Hydrology. Working Document 95/1.

Hill, P., Mein, R. and Siriwardena, L. (1998) How much rainfall becomes runoff? Loss modelling for flood estimation.  Cooperative Research Centre for Catchment Hydrology (link).

Hill, P. I., Graszkiewicz, Z., Taylor, M. and Nathan, R. J. (2014) Loss models for catchment simulation.  State 4 Analysis of rural catchments. May 2014.  ARR Revision project 6  (link to project 6 reports).

Reed, D. W. (2011) Letters in applied hydrology.  Lulu (link)