Mean Areal PrecipitationThe representative precipitation over a defined area is required in engineering

application, whereas the gaged observation pertains to the point precipitation. The areal precipitation is computed from the record of a group of rain gages within the area by the following methods:

(i) Arithmatic - mean Method

The arithmetic average method uses only those gaging stations within the topographic basin and is calculated using:

P = P 1 + P2 + P3 + ....... + Pn

n

P = Pi n where,

P = average precipitation depth (mm) Pi = precipitation depth at gage (i) within the topographic basin (mm)

n = total number of gaging stations within the topographic basin

(ii) Thiessen Polygon MethodAnother method for calculating average precipitation is the Thiessen method. This technique has the advantage of being quick to apply for multiple storms because it uses fixed sub-areas. It is based on the hypothesis that, for every point in the area, the best estimate of rainfall is the measurement physically closest to that point. This concept is implemented by drawing perpendicular bisectors to straight lines connecting each two raingages. This procedure is not suitable for mountainous areas because of orographic influences. The procedure involves:i) Connecting each precipitation station with straight lines; ii) Constructing perpendicular bisectors of the connecting lines and forming polygons with these bisectors; iii) The area of the polygon is determined.

Average precipitation = Polygon area for each station x precipitation Total polygon area

(17)

If Ai/A = wi, then wi is the percentage of area at station 1 in which the sum of total area is 100%.

(18)

Where: A = total areaP = average precipitation depthPi = p1, p2, …pn = depth of precipitation at rainfall stationAi = A1, A2, …An = sub area at station 1,2,3, ….n

St1

St2

St3

St4

St5 St6

Catchment boundary

Example 2.6

Using data given below, estimate the average precipitation using Thiessen method.

Station Area (km2) Precipitation (mm)

Area x precipitation (km2.mm)

A 72 90 6480B 34 110 3740C 76 105 7980D 40 150 6000E 76 160 12160F 92 140 12880G 46 130 5980H 40 135 5400I 86 95 8170J 6 70 420

Total 568 1185 69210

Average precipitation = Area x precipitation Area

St1

A1

A2

A3

A4

A5 A6

St2

St3

St4

St5 St6

Catchment boundary

Average precipitation = 69210 568

Average precipitation = 121.8 mm

(iii) Isohyetal MethodThe isohyetal method is based on interpolation between gauges. It closely

resembles the calculation of contours in surveying and mapping. The first step in developing an isohyetal map is to plot the rain gauge locations on a suitable map and to record the rainfall amounts. Next, an interpolation between gauges is performed and rainfall amounts at selected increments are plotted. Identical depths from each interpolation are then connected to form isohyets (lines of equal rainall depth). The areal average is the weighted average of depths between isohyets, that is, the mean value between the isohyets. The isohyetal method is the most accurate approach for determining average precipitation over an area.

where:P = mean areal precipitation A = Areap1, p2, …pn = precipitation depth for each stationA1, A2, …An = area for each site

Example 2.7

Use the isohyetal method to determine the average precipitation depth within the basin for the storm.

Isohyetal interval(mm)

Average precipitation

(mm)

Area (km 2) Area x Average

precipitation (km2.mm)

<10.0 10 0 010 - 20 15 84 126020 – 30 25 75 187530 - 40 35 68 238040 - 50 45 60 270050 - 60 55 55 302560 - 70 65 86 5590Total 428 16830

Average precipitation = Area x Average precipitation AreaAverage precipitation = 16830 428Average precipitation = 39.3 cm

10mm

20mm

36mm

45mm

57mm

42mm

51mm

p0=10mm p1=20mm p2=30mm

p3=40mm p4=50mm

p5=60mm

A1 A2

A3A4

A5 A6

P6=70mm

70mm