Areal Precipitation

Gross and Net Precipitation
The net (excess) precipitation that contributes directly to surface runoff is equivalent to the gross precipitation minus losses to interception, evaporation, depression storage, and infiltration
The relation between excess precipitation Pe and gross precipitation P is: Pe = P – ? losses

Areal Precipitation (mean precipitation over an area)
لتخمين كمية المطر الكلية الساقطة على مساحة كبيرة، فمن الضروري تحويل قراءات المقاييس المنفردة إلى متوسط عمق على تلك المساحة.

It is important to know the areal distribution of precipitation
In general, an average depth for the watershed is determined and used
For this, point precipitation readings are utilized to develop average precipitation depth over an area
There are different methods for finding the areal average rainfall for an area of interest
1- The Arithmetic-Mean Method
This is the simplest method of determining the areal average rainfall
The average rainfall depth for an area is found by computing the average of the depth values for all the gages using the following formula:
P ? = 1/n ?_(i=1)^n?(P_i )
where n is the number of gages and Pi is the rainfall recorded at gage i



2- The Isohyetal Method (most accurate method)
The isohyetal method is based on interpolation between gauges
Plot the rain gauge locations and record the rainfall amounts
Interpolation between gauges is performed
Rainfall amounts at selected increments are plotted
Identical depths from each interpolation are then connected to form isohyets (lines of equal rainfall depth)

تتلخص هذه الطريقة في رسم خطوط تساوي المطر (Isohyets) على خريطة المنطقة الموقع عليها محطات القياس وسمك المياه المتساقطة عند كل محطة. هذه الخطوط تشكل توزيعا ذا دقة كبيرة للمياه المتساقطة على المنطقة.




















Example:






















Rainfall volume (km2.mm) Average rainfall
(mm) Net area
(Km2) Area enclosed
Km2)) Isohyets
6560 80* 82 82 >75
50625 62.5 810 892 75-50
21262.5 37.5 567 1459 50-25
3240 20* 162 1621 <25
?81687.5

P= (81687.5/1621)=50.4 mm



3- Thiessen Method
The area is subdivided into subareas using rain gauges as centers
The subareas are used as weights in estimating the watershed average depth
The Thiessen network is fixed for a given gauge configuration, and
polygons must be reconstructed if any gauges are relocated

P= (? Ai * Pi) / ?Ai
P=?_(i=1)^M??P A_i/A?
Where:
p= Average depth over entire watershed
A = total area, Ai = area for station i , M = total stations
A_i/A is called the weightage factor for each station




Example:























Pi*% Total area % Total area
=ai/A ai,
(km2) Rain fall (Pi),
(mm) No.
1.2 7 119 16.5 1
7 19 308 37.1 2
9.3 19 308 48.8 3
13.7 20 324 68.3 4
7.2 10 162 71.6 5
3.1 8 130 39.1 6
12.9 17 275 75.7 7
?54.4 100% 1626 ?P=357.1

P=54.4 mm
P=(357.1/7)=51 mm by arithmetic mean method