Transcript Probable Maximum Precipitation

An Introduction to
PRECIPITATION
Mrinmoy Majumder
www.baipatra.ws
Precipitation
Precipitation is any form by which condensation of atmospheric water
vapor is pulled down by gravity and deposited on the Earth's surface.
Precipitation is generally measured with either rain gauge or radars.
The data is represented by Mass curve and/or Hyetographs. The
arial distribution of precipitation is expressed by DAD curves. The
frequency of precipitation is expressed by Frequency Duration
Curves and/or PMP.
Different Forms of Precipitation
Raindrop : Common in tropical zones and lower elevation areas. Raindrops are
formed due to the condensation and coalescence process. Water droplets
above freezing temperature, due to turbulence in the air, collides with each
other to form larger droplets. When mass of the droplets become larger than the
resistance of air to gravity, those droplets fall to ground as raindrops.
Ice pellets : If sub-freezing layer is present in both below and above an above
freezing layer raindrops are converted to crystals of ice before reaching the
ground as the cold layer, below the warm re-freezes the raindrops into ice.
Hail : Hail forms in storm clouds when super cooled water droplets freeze on
contact with dust or dirt. The storm's updraft blows the hailstones to the upper
part of the cloud. The updraft dissipates and the hailstones fall down, back into
the updraft, and are lifted up again. The hailstone gains in ice layer and grows
increasingly larger with each ascent. Once a hailstone becomes too heavy to be
supported by the storm's updraft, it falls from the cloud.
Snowflakes : Snow crystals form when tiny super cooled cloud droplets (about
10 μm in diameter) freeze.
Drizzle : Rain-droplets of size less than 0.5 mm and rain intensity of less than
1mm/h is known as drizzle.
Glaze : When rain or drizzle touches ground at zero degree centigrade, glaze or
freezing rain is formed.
Causes of Precipitation or Weather System for Precipitation
Front : Front is the condition when two distinct mass of air meets with
each other and the warmer air moves up above the cold air.In the time of
ascending, the air is adiabatically cooled and creates cloud and
subsequent precipitation.
Cyclone : A large low pressure region is known as Cyclone.
Tropical – When the diameter of the low pressure region is 100200km,centre is 10-50km in diameter and if in the tropics, the cyclone is
known as Tropical Cyclone. Heavy rainfall and wind speed of 119km/hr
can be observed in the region. The intensity of the storm decreases with
the distance from the eye or center of the cyclone.
Extra-tropical – Cyclones that form outside the tropical zone and are
associated with a frontal system is called as Extra-tropical Cyclone. The
circulation of wind is counterclockwise in the northern hemisphere.
Though magnitude of precipitation and wind velocity is smaller than the
tropical cyclones. The intensity of the precipitation is low but the duration
and extent of the low pressure region is larger than the former.
Anticyclones : A region of low pressure with moderate wind speed and
clockwise wind circulation is called as Anti-Cyclone.
Convective Precipitation : Localized warming can form a warm air
mass surrounded by a cooler one. The warmer mass moves up and form
convective clouds and subsequent precipitation. Areal extent of such
precipitation is small.
Orographic Precipitation : The warm, moist air moves up in the
windward side of the mountain barriers and undergo cooling,
condensation and Orographic Precipitation. Leeward slopes of the
barrier faces lighter rainfall than the other side.
Measurement of Precipitation
Gauges
Radars
There are two type of gauges :
As amount of precipitation over a large area
can be measured with a good degree of
accuracy radars are now frequently used in
measurement of precipitation.
1.Recording
2. Non Recording
Recording gauges can be further classified
into:
When electro-magnetic signals of a radar
crosses with a drop of precipitation it can be
observed that :
a. Tipping Bucket
Pr = average echo-power
b. Weighing Bucket
= CZ/r2
c. Natural Syphon
where C = constant,
Z = radar echo factor = aIb
r = distance to target volume
I = rainfall intensity in mm/hr
A,b = coefficients, calibrated with the help of
observed gauge data of the same region.
d. Optical Type
Telemetry to send data of multiple gauge stations through a radio channel
and advent of optical rain gauges has improved the accuracy and
exclusivity of measurement.
Non-Recording Gauge
Rainfall
This type of gauges do not give
continuous plot of rainfall against time
Collecting Funnel : Rainfall is
collected through the funnel
Metal Container : Funnel is
attached to the bottle with the
help of this clamp.
Measuring Cylinder : When the
collecting bottle overflows the water is
collected in the measuring cylinder to
measure rainfall
Collecting Bottle : The water
collected by the funnel is channeled
to this bucket. From where water is
taken to the measuring cylinder to
measure rainfall.
Retrieved from http://www.imdpune.gov.in/surface_instruments/workshop/Instruments/raingauge.html
Recording Gauges
This type of gauges do give
continuous plot of rainfall against time
A rain gauge (also known as a udometer or a pluviometer) is a
type of instrument used by meteorologists and hydrologists to gather
and measure the amount of liquid precipitation (as opposed to solid
precipitation that is measured by a snow gauge) over a set period of
time.A recording rain gauge can measure data continuously or for a
specific time duration. As mentioned earlier recording type raingauge
is further classified into tipping bucket,weighing bucket,syphon type
and optical type rain gauge.
The optimal number of rain gauge required for a catchment is
estimated by,
N = coefficient of variation of the rainfall data in the existing station /
allowable degree of error in the estimation of mean precipitation
If data is missing and the rainfall at different gauge station varies less
than 10% from the mean then the missing rainfall data of the station
which was unable to measure due to relocation or natural calamities
will be given by,
Test for Consistency of Record
Performed by double mass curve technique where
accumulated annual rainfall of a station is plotted against
accumulated annual rainfall average of a group of 5-10
station in a chronological manner. If the curve deviates
from the slope of itself the slope of the deviated curve is
divided from the slope of the original curve. The result is
multiplied with the annual precipitation of the station to
estimate the corrected precipitation which is used to
measure the deviation of consistency of the measured
rainfall data.
Summation of mean precipitation of the
number of neighboring station
neighboring stations /
But if rainfall of the adjacent station varies more than 10% then
normal ratio method is used :
The normal or annual precipitation for 30 years of the station whose
data was missing is divided by number of stations and the result is
multiplied by the summation of the ratio of precipitation and normal
precipitation of each neighborhood station.
Tipping Bucket Type
Clockwise driven chart : When
the buckets become full it tips
and the signal is channelized
through an electric pen for
marking in this chart
Electric Pen
Tipping Bucket : This bucket
can hold 0.2 mm of water. Once
full it tips sending a signal to the
Electric Pen for recording.
Weighing Bucket Type
Collecting Funnel: The funnel
is used for collecting rain water
Collecting Bucket: The bucket
is filled up by the collected rain
water.The weight of the bucket
and the water is recorded on a
clock work driven chart to
provide a continuous plot of
storm.
Natural-Syphon Type
Float Connected Pen
A float (not seen in the picture) is attached to this pen
which records the rising level in the scale.
Recording Scale
This scale records the rising of the float through the
pen.
Rain Water Collecting Funnel
Optical Type
• In optical raingauge a laser sensor and a
photo transducer sensor is attached below
the collecting bucket.
• When the bucket overflows excess water
falls into the laser.
• The water diffracts the optical ray which is
captured by the sensor and recorded to
measure the rainfall.
Data Representation
Mass Curve
Hyetograph
A graphical representation of accumulated
precipitation against time arranged in a
chronological manner.
Hyetograph is a curve which represents
precipitation intensity or incremental precipitation
against duration of the event.
Represents :
Represents :
Duration and Magnitude of Storm
Intensities at various time interval
Characteristic of storm floods
Total precipitation in a specific time duration
Mass curve
Hyetograph
Figure shows a comparative diagram of masscurve and hyetograph for rainfall.Retrieved from
http://tolstoy.newcastle.edu.au/R/e9/help/10/01/attachment.html
Contd.
Data Representation
Point/Station Rainfall
Mean Precipitation
The representation of precipitation per
hour/day/month for a specific gauge station is
know as point or station rainfall data.
The average precipitation of a catchment can be
estimated based on the data recorded by the
gauge stations present in that catchment. The
following methods are widely used :
Represents :
Moving average of the curve between
precipitation against duration time for three to
five consecutive time steps can represent the
trend of the variable in that station.
Arithmetic Mean
Thiessen Mean Method
Isohyetal Method
Arithmetic Mean
What ?
When the variation of precipitation in various stations is small arithmetic mean is used to
estimate mean precipitation of the catchment.
Formula
If Pn is the precipitation recorded by nth gauge station in a specific duration of time and N be
the total number of stations available in the catchment, then arithmetic mean of precipitation is
given by,
Pm = (P1+P2+P3…Pn)/N
Thiessen Mean Method
What ?
When the variation of precipitation in various stations is larger than 10% Thiessen Mean method is
used as a method to estimate mean precipitation of the catchment.
Formula
If Pn is the precipitation recorded by nth gauge station in a specific duration of time and N be the total
number of stations available in the catchment and An is the surrounding area, created by the bisects of the
straight lines connecting the gauge stations, of the nth gauge station, then mean precipitation is given by,
Pm =
(A1P1+A2 P2+A3 P3…AnPn)/(A1+A2+A3…An)
Iso-hyetal Method
What ?
When the variation of precipitation in various stations is larger than 10% Iso-hyetal method is used as a
method to estimate mean precipitation of the catchment. Iso-hyetal lines join the stations or points
which have equal magnitude of precipitation.(Iso means equal and hyeto means rain,hence Isohyetal.
For example line joining equal temperature points, isotherm; equal cloud cover, isoneph; equal
humidity, isohume; equal pressure, isobar etc.
Formula
If Pn is the precipitation of the nth isohyet in a specific duration of time and N and An-1 is the inter-isohyet
area, then mean precipitation is given by,
Pm =
[{(A1(P1+P2)/2}+{A3(P2+P3)/2}..+{An-1(Pn-1+Pn)/2}]/Total Area of the Catchment
Isohyet method is more accurate than the Arithmetic mean and Thiessen Mean Method of estimating
precipitation within a catchment.
Depth Area Duration
•
Depth Area Duration curve is used to represent the relationship between precipitation
depth and area.
•
DAD curves is analyzed before the hydrological design of large hydraulic structures.
•
To develop DAD :
•
1.The severemost storm is first identified.
•
2.Then Isohyetal maps and mass curve of the storm is compiled.
•
3.From the mass curve the rainfall depth and from Isohyetal map,area of the storm is
estimated.
•
4.A curve is drawn showing depth of precipitation against area starting from the
center of the storm
•
From the curve it can be observed that for a given duration precipitation is inversely
proportional to area and for a given area, precipitation depth is proportional to
duration of rainfall.
Frequency of Precipitation
Probability of An Extreme Event is important and
essential for designing hydraulic structures for
extreme condition. In this regard Probability of
precipitation events are calculated and used in the
analysis often called as uncertainty or risk analysis.
•
Probability (P) of precipitation X cm of duration
Y hr occurring r times in n successive years will
be :
Plotting Position
(Weibull Formula)
A plot of precipitation magnitude with the
return period can be calculated with the
help of plotting position which is
calculated by,
P
Pr,n
= (m/(N+1))
(1)
= nCrPrq(n-r)
= {n!/(n-r)!r!}Prq(n-r)
•
(2)
Return period or recurrence interval is the
inverse of P.
(3)
If the event of precipitation within a time frame
is arranged in a descending order based on the
magnitude then m in Equation 3 will be the
order number and N will be the number of
years included in the time frame. Equation 3
varies for different regions and is an empirical
equation to estimate probability.
Frequency of Precipitation
Probable Maximum Precipitation (PMP)
Intensity-Duration-Frequency (IDF)
–
–
–
Intensity of precipitation decreases with
increase in duration
Increase in return period will make that
intensity of precipitation rarer
Relationship between precipitation
intensity(i), duration(D) of the
precipitation and return period(T) of the
same is represented as :
i = (KTx)/ (D+a)n
(4)
where x,K,a and n are constants which varies with
catchments
–
–
–
Probability of maximum possible
precipitation for a given catchment area
which can not be exceeded is known as
probable maximum precipitation
Used in designs of major hydraulic
structures like reservoir, dams, channels,
spillways etc.
According to statistical studies PMP can
be estimated as :
PMP = Pm + Kσ
(5)
where Pm is the mean precipitation,K is the frequency factor
which depends upon statistical distribution of the
precipitation time series,number of years of record and
return period.