REVIEW QUESTIONS

a. Explain the different methods of determining the average rainfall over a catchment
due to a storm. Discuss the relative merits and demerits of the various methods.
Arithmetic mean method: Is used for rainfall recording at various stations that does not show much
variations. Is the sum of the precipitation in all the stations between the number of stations.
Thiessen method: The rainfall is recorded at each station. It is given a weight at each gauge station
in proportion to the catchment area that is closest to that gauge. It is superior that the arithmetic
method and uses the raingauge reading outside the catchment area. You must connect the adjacent
stations with lines then constructed perpendicular lines at the midpoint of each line connecting two
stations in order two form polygons around each gauge station. Although it is widely used this
method can yield incorrect results in some circumstances.
Isohyetals method: Is the line joining points of equal rainfall magnitude. It is based on interpolation
between gauges. First you must 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.

b. Write brief notes on (i) moving average, (ii) Thiessen polygon, (iii) isohyetals, and
isopluvial maps.
Moving Average: Is the original slope of the double mass curve.
Thiessen Polygon: Is a commonly used methodology for computing the mean areal precipitation for
a catchment from raingauge observations.
Isohyetals maps: They are an interpolation of rainfall data recorded at gauged points.
Isopluvial maps: A line or a map connecting places registering the same amount of precipitation.

c. Explain a procedure for checking a rainfall data for consistency.

Double mass index: It is used to verify the consistency or homogeneity of the precipitation data
from a rainfall station. By plotting the accumulated annual precipitation for the station under
investigation against the accumulated annual precipitation of the other stations a straight line is
obtained, it can be guaranteed that the complete records for that station have been obtained under
the same conditions.
d. Explain a procedure for supplementing the missing rainfall data.
The missing rainfall data is estimated from the observations of precipitation at some other
stations as close to and as evenly spaced around the station with the missing record as
possible. There are three methods for estimating missing data. If there is a change in slope,
an explanation for the phenomenon can usually be found
1. Arithmetic mean method
2. Normal Ratio Method
3. National Weather Service Method
The arithmetic mean method has one important condition, which is that the normal annual
precipitation of the index stations must be within more or less 10% of normal annual
 precipitation. Is basically the sum of the precipitation at every station between the number
of stations. That give you the missing precipitation.
PROBLEMS
1. A catchment area has seven raingauge stations. In a year, the annual rainfall recorded by
the gauges are as follows:
 

 
a. Determine the standards error in the estimation of mean rainfall in the existing set of
raingauges.
b. For a 5% error in the estimation of the mean rainfall, calculate the minimum number
of additional raingauge stations to be established in the catchment.
 
2. The normal annual precipitation of five raingauge stations P, Q, R, S and T are
respectively 125, 102, 76, 113 and 137 cm. During a storm, the precipitation recorded by
stations P, Q, R, and S are 13.2, 9.2, 6.8 and 10.2 cm respectively. The instrument at station
T was inoperative during that storm. Estimate the rainfall at station T during that storm.
 
3. Test the consistency of the 22 years of data of the annual precipitation measured at
station A. Rainfall data for station A as well as the average annual rainfall measured at a
group of eight neighbouring stations located in a meteorologically homogeneous region are
given as follows.

 
 a. In what year is a change in regime indicated?
b. Adjust the recorded data at station A and determine the mean annual precipitation.
 
4. In a storm of 210 minutes duration, the incremental rainfall at various time intervals is
given below.

 
a. Obtain the ordinates of the hyetograph and represent the hyetograph as a bar chart
with time in chronological order in the x-axis.
b. Obtain the ordinates of the mass curve of rainfall for this storm and plot the same.
What is the average intensity of storm over the duration of the storm?
 
5.  
6. Represent the annual rainfall data of station A given below as a bar chart with time in
chronological order. If the annual rainfall less than 75% of long-term mean is taken to
signify meteorological drought, identify the drought years and suitably display the same in
the bar chart.

 
7. The watershed of a stream has five raingauge stations inside the basin. When Thiessen
polygons were constructed, three more stations lying outside the watershed were found to
have weightages. The details of Thiessen polygons surroundings each raingauge and the
recordings of the raingauges in the month of July 2012 are given below: Stations B, D and
F are outside the watershed. Determine the average depth of rainfall on the watershed in
July 2012 by (i) arithmetic mean method, and (ii) Thiessen mean method.

 
8. For a drainage basin of 600 km2, isohyetals drawn for a storm gave the following data:
 Estimate the average depth of precipitation over the catchment.
9. There are 10 raingauge stations available to calculate the rainfall characteristics of a
catchment whose shape can be approximately described by straight lines joining the
following coordinates (distances in kilometres): (30, 0), (80, 10), (110, 30), (140, 90), (130,
115), (40, 110), (15, 60). Coordinates of the raingauge stations and the annual rainfall
recorded in them in the year 2001 are given below.

Determine the average annual rainfall over the catchment by using isohyetals.
 
10. Figure 2.28 shows a catchment with seven raingauge stations inside it and three stations
outside. The rainfall recorded by each of these stations are indicated in the figure. Draw the
figure to an enlarged scale and calculate the mean precipitation by (a) Thiessen-mean
method, (b) isohyetal method, and by (c) arithmetic-mean method.
 Fig. 2.28 Problem 2.10
 
11. Annual rainfall at a point M is needed. At five points surrounding the point M the values
of recorded rainfall together with the coordinates of these stations with respect to a set of
axes at point M are given below. Estimate the annual rainfall at point M by using the
USNWS method.

[Hint: In the US National Weather Service (USNWS) method, the weightage to the stations
are inversely proportional to the square of the distance of the station from the station M. If
the co-ordinate of any station is (x, y) then D 2 = x 2 + y 2 and weightage
  
12. The data from an isohyetal map of a 24-hour storm is given below. Assuming that the
storm centre had an area of 25 km2, obtain the Depth-Area curve of this store. Using the
depth-area curve, estimate the average depth of rainfall over an area of 2400 sq. km. It can
be assumed that the storm centre is located at the centre of the area.