DANIELLA P.
SABAC BSABE 2B March 31, 2021
LWE 221 - HYDROMETEOROLOGY
LESSON 3 – Precipitation: Spatial Distribution
Exercise 2 – Application
Answer the following problems and write in your journal.
1. Explain briefly the following relationships relating to the precipitation over a
basin:
a. Depth-Area Relationship
For a rainfall of a given duration, the average depth decreases with the area
in an exponential fashion given by
b. Maximum Depth-Area-Duration Curves
The development of relationship, between maximum depth-area-duration for a
region is known as DAD analysis and forms an important aspect of hydro-
meteorological study. First, the severe most rainstorms that have occurred in the
region under study are considered. The maximum depth-area curve for a given
duration D is prepared by assuming the area distribution of rainfall for smaller
duration to be similar to the total storm. Preparation of DAD curves involves
considerable computational effort and requires meteorological and topographical
information of the region. Detailed data on severe most storms in the past are
needed. DAD curves are essential to develop design storms for use in computing
the design flood in the hydrological design of major structures such as dams.
c. Intensity Duration Frequency Relationship
The rainfall Intensity-Duration-Frequency (IDF) relationship is one of the most
commonly used tools in water resources engineering, either for planning, designing
and operating of water resource projects, or for various engineering projects
against floods. These curves have been generated from a 31-year recorded rainfall
data. Maximum intensities occur at shout duration large variations with return
period, Furthermore, it also notices; at long duration there is no much difference in
intensities with return period.
2. What is meant by Probable Maximum Precipitation (PMP) over a basin?
Explain how PMP is estimated.
Probable maximum precipitation (PMP) is a theoretical concept that is widely
used by hydrologists to arrive at estimates for probable maximum flood (PMF) that find
use in planning, design and risk assessment of high-hazard hydrological structures
such as flood control dams upstream of populated areas. The PMP represents the
greatest depth of precipitation for a given duration that is meteorologically possible for
a watershed or an area at a particular time of year, with no allowance made for long-
term climatic trends. Various methods are in use for estimation of PMP over a target
location corresponding to different durations. Moisture maximization method and
Hershfield method are two widely used methods. The former method maximizes the
observed storms assuming that the atmospheric moisture would rise up to a very high
value estimated based on the maximum daily dew point temperature. On the other
hand, the latter method is a statistical method based on a general frequency equation
given by Chow. The present study provides one-day PMP estimates and PMP maps
for Mahanadi river basin based on the aforementioned methods. There is a need for
such estimates and maps, as the river basin is prone to frequent floods. Utility of the
constructed PMP maps in computing PMP for various catchments in the river basin is
demonstrated. The PMP estimates can eventually be used to arrive at PMF estimates
for those catchments. (Chavan & Srinivas, 2015)
PMP is used in the design of major hydraulic structures such as spillways in
large dams. There appears to be a physical upper limit to the amount of precipitation
that can occur over a given area in a given time
PMP – It is the greatest or the extreme rainfall for a given duration that is
physically possible over a raingauge station or a basin. It is that rainfall over a basin
which would produce a flood with no risk of being exceeded. PMP can be statistically
estimated as PMP=
are the mean of the annual maximum rainfall series, a
frequency factor (that depends on the statistical distribution of the series, number of
years of record, and the return period) and the standard deviation of the series
respectively. K~ 15
3. A catchment area has seven rain gauge stations. In a year the annual rainfall
recorded by the gauges are as follows:
For a 5% error in the estimation of mean rainfall, calculate the minimum
number of additional stations required to be established in the catchment.
𝑮𝑰𝑽𝑬𝑵:
𝑚=7
𝑀𝑒𝑎𝑛 𝑎𝑛𝑛𝑢𝑎𝑙 𝑟𝑎𝑖𝑛𝑓𝑎𝑙𝑙 (𝑃̅) = 130.43 𝑐𝑚
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐷𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝜎𝑚−1 ) = 22.6 𝑐𝑚
𝜀 = 5%
(calculated beforehand through calculator)
(a) Coefficient of variation (c) Minimum number of additional
stations with e = 5%
100 × 𝜎𝑚−1
𝐶𝑣 =
𝑃̅ 𝐶𝑣 2
𝑁=( )
100 × 22.56 𝜀
𝐶𝑣 =
130.43 17.297 2
𝑁=( )
𝐶𝑣 = 17.297 % 5%
𝑁 = 11.96 ≈ 12 𝑟𝑎𝑖𝑛 𝑔𝑎𝑢𝑔𝑒 𝑠𝑡𝑎𝑡𝑖𝑜𝑛𝑠
(b) Standard error in the estimation
of the mean
𝐶𝑣
𝜀𝑒𝑥 =
√𝑚
17.297
𝜀𝑒𝑥 =
√7
𝜀𝑒𝑥 = 6.54 %
Hence, the minimum number of rain gauges is 12. Therefore, the number of
additional rain gauge required is (12 – 7) = 5.
𝐹𝑖𝑛𝑎𝑙 𝐴𝑛𝑠𝑤𝑒𝑟 𝑖𝑠 5 𝑟𝑎𝑖𝑛 𝑔𝑎𝑢𝑔𝑒𝑠.
4. 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.
𝑮𝒊𝒗𝒆𝒏: 𝒂𝟏 = 𝟗𝟐; 𝒂𝟐 = 𝟏𝟐𝟖; 𝒂𝟑 = 𝟏𝟐𝟎; 𝒂𝟒 = 𝟏𝟕𝟓; 𝒂𝟓 = 𝟖𝟓
𝑷𝟏 = 𝟏𝟓; 𝑷𝟐 = 𝟏𝟐; 𝑷𝟑 = 𝟗; 𝑷𝟒 = 𝟔; 𝑷𝟓 = 𝟑; 𝑷𝟔 = 𝟏
𝑨 = 𝟔𝟎𝟎 𝒌𝒎𝟐
𝑷 𝟏 + 𝑷𝟐 𝑷𝟐 + 𝑷 𝟑 𝑷𝟑 + 𝑷𝟒 𝑷𝒏−𝟏 + 𝑷𝒏
𝒂𝟏 ( ) + 𝒂𝟐 ( ) + 𝒂𝟑 ( ) + 𝒂𝒏 ( )
̅=
𝑷 𝟐 𝟐 𝟐 𝟐
𝑨
𝑷 + 𝑷 𝑷 + 𝑷 𝑷 + 𝑷 𝑷 + 𝑷 𝑷 + 𝑷
𝒂𝟏 ( 𝟏 𝟐 𝟐 ) + 𝒂𝟐 ( 𝟐 𝟐 𝟑 ) + 𝒂𝟑 ( 𝟑 𝟐 𝟒 ) + 𝒂𝟒 ( 𝟒 𝟐 𝟓 ) + 𝒂𝟓 ( 𝟓 𝟐 𝟔 )
̅=
𝑷
𝑨
𝟏𝟓 + 𝟏𝟐 𝟏𝟐 + 𝟗 𝟗+ 𝟔 𝟔+ 𝟑 𝟑+ 𝟏
𝟗𝟐 ( ) + 𝟏𝟐𝟖 ( ) + 𝟏𝟐𝟎 ( ) + 𝟏𝟕𝟓 ( ) + 𝟖𝟓 (
= 𝟐 𝟐 𝟐 𝟐 𝟐 )
𝟔𝟎𝟎
𝟏𝟐𝟒𝟐 + 𝟏𝟑𝟒𝟒 + 𝟗𝟎𝟎 + 𝟕𝟖𝟕. 𝟓 + 𝟏𝟕𝟎
=
𝟔𝟎𝟎
𝟒𝟒𝟒𝟑. 𝟓
=
𝟔𝟎𝟎
= 𝟕. 𝟒𝟎𝟓𝟖𝟑𝟑𝟑𝟑
̅ = 𝟕. 𝟒𝟏 𝒄𝒎
𝑷
5. Following are the data of a storm as recorded in a self-recording rain gauge
at a station:
(a) Plot the hyetograph of the storm.
Intensity
Time from the ∆𝑷 𝒊𝒏 𝒕𝒊𝒎𝒆 ∆𝑷
Cumulative rainfall
beginning of storm ∆𝒕 = 𝟏𝟎 𝒎𝒊𝒏𝒔 𝒊= × 𝟔𝟎
(mm) ∆𝒕
(mins) (cm)
(mm/hr)
10 19 19 114
20 41 32 192
30 48 7 42
40 68 20 120
50 91 23 138
60 124 33 198
70 152 28 168
80 160 8 48
90 166 6 36
Table 1. Hyetograph data
Hyetograph
INTENSITY (mm/hr)
TIME FROM THE BEGINNING OF STORM (mins)
Figure 1. Hyetograph Graph
(b) Plot the maximum intensity-duration curve of the storm.
Incremental Depth of Rainfall (mm) in various Duration
∆𝑡 = 10 ∆𝑡 = 20 ∆𝑡 = 30 ∆𝑡 = 40 ∆𝑡 = 50 ∆𝑡 = 60 ∆𝑡 = 70 ∆𝑡 = 80 ∆𝑡 = 90
19 41 48 68 91 124 152 160 166
22 29 49 72 105 133 141 147
7 27 50 83 111 119 125
20 43 76 104 112 118
23 56 84 92 98
33 61 69 75
28 36 42
8 14
6
Table 2. Incremental Depth of Rainfall (mm) in various Duration
Maximum Intensity-Duration Data
Duration (mins) Maximum Depth (mins) Maximum Intensity (mm/hr)
10 33 198
20 61 183
30 84 168
40 104 156
50 112 134.4
60 119 133
70 141 130
80 160 120
90 166 110.7
Table 3. Maximum Intensity-Duration Data
Maximum Intensity-Duration Curve
MAXIMUM INTENSITY DURATION (mm/hr)
DURATION (mins)
Figure 2. Maximum Intensity-Duration Curve Graph
CALCULATIONS
