School of Surveying & Spatial Information Systems

The University of New South Wales

GIS Analysis of Areal Reduction Factors for Design Rainfall Estimation

by Leah Howell

Supervised by Assoc. Prof. J. E. Ball

Co-supervisor A. Hobson

Edited by J. M. Rüeger

November 2003


Design rainfall information is generally expressed in terms of point rainfall intensity, which is the rainfall depth (mm) at a location per hour. However, for flood estimates of large catchments, an estimate of the average areal rainfall intensity across the catchment is required. This is the mean rainfall depth per hour over the entire catchment. Areal reduction factors (ARFs) for the catchment can then be determined by the ratio of point rainfall intensities and average areal rainfall intensities. ARFs are applied to point rainfall depths to convert them to equivalent measurements for the whole catchment area. With recent developments in computer processing power, it is now possible to take a geographical information system (GIS) approach to determine and assess areal reduction factors.

GIS Approach

A geographical information system (GIS) was employed to determine average areal rainfall values using the spline surface method. This method of spatial interpolation fits a surface to an area using known points. It calculates new values from the three closest known observations on the curve. Daily rainfall depths were obtained from the Commonwealth Bureau of Meteorology for seven Sydney stations and used to create spline surfaces for 3145 days of measurement between the years of 1960 and 2003. The average areal rainfall for each day over three catchments of sizes 262 km2, 1675 km2 and 6003 km2 (see Figure 1) was determined from the spline surfaces using a 100 m2 grid. This procedure took approximately 50 hours of processing.

Figure 1: Sydney Catchments of 262 km2, 1675 km2 and 6003 km2

A log-Pearson Type III frequency distribution was then applied to the series of annual maximum rainfall depths, determined for each station and across the three catchments for rainfall durations of 24, 48 and 72 hours. This allowed the determination of design point rainfall intensities and design average areal rainfall intensities for annual exceedance probabilities (AEPs) of 0.01, 0.02, 0.05, 0.10, 0.18, and 0.39. (The term AEP refers to the probability between rainfalls of certain intensities. An AEP of 0.01 refers to a rainfall intensity which occurs once every 100 years.) Areal Reduction Factors (ARFs) were derived for each combination of catchment size, duration and AEP by dividing the design areal intensity of the catchment with the design point intensity of the Sydney (Observatory Hill) station.



The areal reduction factors (ARFs) derived for the Sydney region in this study differed from those recommended in Australian Rainfall and Runoff (1987) (see Figures 2 and 3), which were determined using techniques adopted from the U.S. The ARFs calculated for the 262 km2 and 1675 km2 catchments were notably lower than the recommended values. The derived values for the 6003 km2 catchment were higher than those calculated for the smaller catchments. This variation was attributed to the extensive extrapolation required by the spline surface which, in some cases, caused unrealistic estimates of the rainfall depths.

Figure 2: Derived Areal Reduction Factors for an AEP of 0.01

Figure 3: Areal Reduction Factors given in Australian Rainfall and Runoff to cover all AEPs

To spatially assess the accuracy of the generated spline surfaces, the GIS was used to view the spatial distribution of point rainfall across the catchment and to examine the estimated areal rainfall patterns. Figure 4 illustrates the 24-hour rainfall depth (mm) measured at the seven stations on 11 April 1998.

Figure 4: Twenty-four hour point rainfall (mm) on 11/04/98

The rainfall surface over the 6,003 km2 catchment (see Figure 5) illustrates high rainfall at the south-west and north-east boundaries. The spatial interpolation between the stations was consistent with the point rainfall distribution. However, beyond these points the gradient of the surface continued the measured rainfall pattern. The curve follows the increase towards the north-east and escalates to an unrealistic maximum value of 480.7 mm of rainfall at the outer boundary. The decreasing rainfall pattern is modelled with large portions of the southern and north-western parts of the catchment depicting 0.0 mm of rainfall. The calculated average rainfall for this catchment was 131.3 mm.

Figure 5: Spatial rainfall pattern over 6003 km2 catchment on 11/04/98
Conclusions and Recommendations

In this study, the rain gauge stations were not spread across the entire catchment area. They were primarily located in the east and mid-catchment regions causing the spline surface to extrapolate to the outer boundaries. This caused rainfall values calculated at the southern, northern and western boundaries to be generally higher or lower than expected. Therefore, it is recommended that, for the use of a spline surface to calculate areal rainfall, stations be uniformly distributed across the catchment. The use of a geographical information system proved to be a feasible method of calculating areal rainfall. It was beneficial for the analysis and assessment of derived areal rainfall as it allowed the distribution of point and areal rainfall patterns to be visualised.


Further Information

For more information, please contact:


School of Surveying and Spatial Information Systems
University of New South Wales

Phone: +61-2-9385-4182
Fax: +61-2-9313-7493