# How wet is the catchment?

If a catchment is wet before a storm, more rain is likely to run off.  A wet catchment and heavy rain can lead to flooding.  Although there are remote sensing approaches to measuring soil moisture to aid flood prediction (see here and here), in this blog I look at a low tech approach.

The Antecedent Precipitation Index (API) is a running day by day measure of catchment wetness based on the rainfall that has occurred over preceding days.  The most recent rain counts more in the API than rain from previous days.  It can be though of very simply as “today’s rain plus a decay factor times yesterday’s API”.  Originally proposed for flood forecasting, it is an old idea that is still useful.

High values of API mean the catchment is wet so any rain is likely to run off.  Low values mean there hasn’t been much rain lately, the catchment is dry so rain is likely to soak into soil and wet up vegetation and not make it to a stream.  API has been related to initial loss i.e. the amount of rainfall that is ‘lost’ before runoff starts (Cordery, 1970a; 1970b).  An example for the Bobo River in northern NSW is shown in Figure 1.  As the API goes up, the catchment is wetter so the initial loss decreases and more rain will run off.

Figure 1: Bobo River, relationship between initial loss and API (Cordery, 1970)

Australian Rainfall and Runoff (Book 5, Section 5.7.4) defines the API for a particular day as:

$API_d = P_d + kP_{d-1} + k^2P_{d-2} + ...$ or     (1)

$API_d = kAPI_{d-1} + P_d$     (2)

Where

• $API_d$ is the Antecedent Precipitation Index for day $d$ a
• $k$ is an empirical decay factor less than one and
• $P_d$ is rainfall for day $d$.

Without rain, the catchment wetness (as measured by API) declines each day by the factor $k$.  Any rain tops the API up again.

The decay parameter $k$ must be less than one and is usually between 0.85 and 0.98 (Lindsay et al., 1975).  Cordery (1970a) recommended an average value of 0.92 for NSW catchments and found that $k$ varied from 0.98 in winter to 0.86 in summer.  A constant, year round, value of 0.95 was recommended by Hill et al. (2014).

### Creswick example

As an example, consider the API for the catchment upstream of Creswick.  Creswick  experienced severe flooding in 2010 and 2011.  There is no stream gauge on Creswick Creek, the creek that flows through town, and flood warning is challenging because the catchment is small so there is little lead time.  Perhaps API could indicate wet catchment conditions and the potential for high runoff if there is heavy rain.

Using daily rainfall data from SILO, I calculated API from 1889 to 2016 using a decay factor of 0.95.   A portion of the data from August to Nov 2010 are shown in Figure 2.  The graph shows the way API works.  The API was sitting at about 100 during the second part of August and then there was rain in early September (64 mm on the 4th and 26 mm on 5th).  The API peaked at 168 before decaying until the next rain in mid October.  The high rainfall in early September, on a wet catchment, led to flooding through parts of the town.

Figure 2: Daily rainfall and API for August to November 2010

We can put the conditions of 2010 into context by comparing them to past values of API.   Figure 3 shows API values for every day from 1889 to 2016, these are the grey points in the background.  The 2010 values are the black line with rainfall in blue as before.  Ninety nine percent of API values are less than 100 mm so that reinforces how wet the catchment was through August 2010 before the early September rain pushed API even higher levels.

Figure 3: Daily rainfall and API for 2010 with historical API values values shown as grey points in the background (1889 to 2016)

There is usually a yearly cycle to climate data such as rain and API and this is can be made apparent by plotting the data in polar coordinates  so that the day of the year is like the big hand on a clock with Jan 1 being straight up.  A full circuit of the clock takes us to Dec 31.  Using this approach for API highlights extreme values and the catchment wetting and drying process (Figure 4).  High daily rainfall totals push the API away from zero at the centre of the graph and it spirals back toward the centre over time.  Extreme API values are furthest from the centre, for example Figure 4 shows high API values in January 2011 and September 2010 when there was extensive flooding.  It would be interesting to know if there were flood flows on the other dates with very high API e.g. in May 1960 and 1974.  In an ungauged catchment, checking historical newspaper reports would be one way to find out.  The Trove site has some great search tools.

Figure 4: Daily API values for Creswick based on daily rainfall 1889 to 2016

Let’s check the behaviour in the Jan 2011 flood.  Figure 5 shows rainfall and API for July 2010 to June 2011.  The striking feature in Jan 2011 is the consecutive days of heavy rain and the rapid increase in API to high levels.  According to the SILO data, the rainfall totals for Jan 11 to Jan 14 were 29.4 , 37.9 , 16. 3 and 87.8  for a 4 day total of 171.4 mm.  This is only exceeded by the rain in early December 1933 (4 day total of 180 mm, based on data from 1889 to 2016).

Figure 5: API and rainfall Jul 2010 to Jun 2011

We can tell after the fact that the API values over 150 coincided with the flooding in 2010 and 2011 but it would be nice to know ahead of time if flooding was likely.  Let’s investigate an API of 90 as a threshold of concern.  A spells plot shows how often this occurs (Figure 6).   The wet periods in 2010 and 2011 are shown along with some others.  If the API was above 90 and heavy rain was forecast, perhaps that would indicate the potential for high runoff.

Figure 6: Periods of high API indicating a wet catchment

A combination of API and forecast rainfall (i.e. a forecast API) could provide some degree of flood warning for ungauged catchment such as Creswick Creek.

Code to reproduce the analysis and create the plots is available as a gist.

### References

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.

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

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).

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).

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.

### Acknowledgement

John Tilleard made a major contribution to the ideas for this blog and helped polish the writing.

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