Areal reduction factors and depthareaduration analysis

In designing hydraulic structures for controlling river flow, a hydrologist needs to know the areal rainfall of the area draining to the control point. Sometimes it is only the average river flow being considered, but more often the works are intended to control flood flows and knowledge of heavy rainfalls is required. There is then an issue that the rainfall depths at a point will not be the same as the average depths over a catchment area estimated by one of the interpolation techniques described above. Estimates of peak rainfall rates for points will then need to be reduced by an areal reduction factor for a catchment. Storm-centred areal reduction factors for single events can be quite variable. In hydrological analyses, fixed area reduction factors are generally used in a region. These do not refer to any particular event but are more statistical in nature, referring to the average ratio of point rainfall to areal rainfall for a given return period.

For an individual storm for which measurements are available, areal reduction factors can be analysed as follows. From the measurements made at all the rain gauges in the area, the pattern of the storm is plotted by drawing the isohyets. The areas enclosed by the isohyets are calculated by planimeter or by digitizing software. Although the average rain between isohyets is taken as the arithmetic mean, the average rain enclosed by the top isohyet has to be estimated. In the case of the extreme Martinstown storm of 1955 shown in Fig. 9.12, there were two 'unofficial' observations in the peak rainfall area (marked at H and G in Fig. 9.12) that helped in this estimation (Clark, 2005). The areal rain for each enclosing isohyet is then plotted against area. The depth-area relationship for the duration of the selected storm is thus obtained. If necessary, several similar duration storms experienced over the area can be used to provide many more data points on the depth-area graph and maximum depth values for the range of areas can be read from an enveloping curve to give design data. Short-duration storms tend to have steep rainfall gradients and hence cover smaller areas than storms of longer duration. This is well recognized in the UK, where intense thunderstorms affect limited areas, whereas prolonged heavy rainfall from an occluded front, for example, usually covers a wide area (as in the Cumbria and Dumfries floods in November 2009).

The analysis of the relationship between areal rainfall depths and area over many storms gives depth-area relationships for different specific durations. Hence in a region where particular types of storms are experienced, the areal rainfall expected from a given catchment area for the catchment response time can be taken from those depth-area relationships for that region.

In the UK, storm patterns are very variable and design rainfalls for different durations and different regions over the whole country were compiled by the Met Office for the original Flood Studies Report (Natural Environment Research Council, 1975), together with estimates of fixed area reduction factors. The resulting areal reduction factors, ARF, were also adopted for the Flood Estimation Handbook (IoH, 1999)

Area (km2)

Fig. 9.12 Rainfall isohyets and change in average rainfall with increasing area: the Martinstown Storm of 18 July 1955 that gave the highest ever recorded 24-h point total recorded in the UK until the November 2009 event in Cumbria, see Table 9.2 (after Clark, 2005, with kind permission of John Wiley & Sons).

expressed in mathematical form as

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