PRECIPITATION AND ITS MEASUREMENT

CHAPTAR-2

MEASUREMENT OF PRECIPITATION Ch. Karamat Ali (C.E) Department of Civil Engineering University of Lahore

PRECIPITATION AND ITS MEASUREMENTS

Precipitation 

Precipitation is the general term used for all forms of moisture emanating from the clouds and falling to the ground. This following of moisture is termed as precipitation.



The essential requirements for precipitation to occur are; 1.

Some mechanism is required “to cool the air sufficiently” to cause condensation and droplet growth.

2.

Condensation nuclei are also necessary for formation of droplets. They are usually present in the atmosphere in adequate quantities.

3.

High cooling is essential for significant amount of precipitation. This is achieved by lifting of air. Thus a “meteorological phenomenon of lifting of air masses is

essential to result precipitation”.

PRECIPITATION AND ITS MEASUREMENTS

Types of Precipitation 

Precipitation is often classified according responsible for lifting of air as under:i)

Cyclonic Precipitation

ii)

Convective Precipitation

to

the

factors

iii) Orographic Precipitation

i. Cyclonic Precipitation Cyclonic precipitation results from “lifting of air masses converging into low pressure area of cyclone”. It is further classified as tropical and extra-tropical. Tropical Cyclone results into heavy rain falls and floods, whereas in extra-tropical, the rain fall is lower and of longer duration. Continued…

PRECIPITATION AND ITS MEASUREMENTS

ii. Convective Precipitation 

Convective precipitation is caused by natural rising of warmer lighter air in colder, denser surroundings, at high altitude. The difference in temperature may result from unequal heating at the surface, unequal cooling at the top of the air layer, or mechanical lifting when air is forced to pass over a denser colder air masses.



Convective precipitation is spotty and its intensity may vary form light showers to cloud bursts.

iii. Orographic Precipitation 

Orographic precipitation is due to the lifting of warm moisture laden air mass due to topographic barriers (such as mountains).



Precipitation is heavier on wind word slops and lighter on the leeward slop and the over all rainfall is general low.

PRECIPITATION AND ITS MEASUREMENTS

Forms of Precipitation Drizzle : When the size of water droplets is under 0.5 mm, and its intensity is < 0.01 mm per hour.

Rain

:

When the size of the drops is more than 0.5 mm. The upper size of water drop is generally 6.25 mm, as drops greater than this tend to break up as they fall through the air.

Glaze :

When the drizzle or rain freezes as it comes in contact with cold objects, it is known as glaze.

Snow

: It is precipitation in the form of ice crystal resulting from sublimation of water vapors directly to ice.

Hail

: Hail is lumps or bulbs of ice over 5 mm diameter formed by alternate freezing or melting as they are carried up and down in highly turbulent air currents.

PRECIPITATION AND ITS MEASUREMENTS

Measurement of Rain Fall 

Rainfall is the main source of water, used for irrigation. Therefore, a knowledge of its amount, character, seasons or periods is important for designing, improvement and maintenance of irrigation works”.



The amount of precipitation is defined as “the depth of water

which falls on a level surface”, and is measured by raingauge. The following are the main types of Rain-gauges:1.

Non-Automatic Rain-Gauges: This is also known as nonrecording rain-gauge. Symon’s Rain-Gauge is the instrument general used for rainfall measurements.

2.

Automatic Rain-Gauge: These are integrating type recording rain-gauges and are of three types; i) Weighing bucket rain-gauge ii) Tipping bucket rain-gauge iii) Float type rain-gauge

PRECIPITATION AND ITS MEASUREMENTS

Non-Recording Rain-Gauges (Symon’s Rain-Gauge) 

It consists of cylindrical vessel 127 mm (or 5”) in diameter with a base enlarged to 210 mm (or 8”) diameter. The top section is connected to a funnel provide with circular brass rim exactly 127 mm (5 inch) internal diameter.



The funnel shank is inserted in the neck of a receiving bottle which is 75 to 100 mm (3 to 4”) diameter. A receiving bottle of rain-gauge has a capacity of about 75 to 100 mm of rainfall and as during a heavy rainfall this quantity is frequently exceeded, the rain

should be measured 3 or 4 times in a day on day of heavy rainfall lest the receiver fill should overflow. 

A cylindrical graduated measuring device is furnished with each instrument, which reads to 0.2 mm. the rainfall should be estimated to the nearest 01. mm.



The rain collected in the bottle is measured through provided graduated cylinder.

PRECIPITATION AND ITS MEASUREMENTS Symon’s Rain-Gauge

PRECIPITATION AND ITS MEASUREMENTS

Automatic Rain Gauges i) Weighing Bucket Type Rain-Gauge 

Self recording gauges are used to determine rates of rainfall over periods of time. The most common type of self-recording rain gauge is the “weighing bucket type”, as shown in Figure.



The rainfall from the receiver (30 cm) flows to the bucket through the funnel.



The weight of the bucket is recorded by the mechanism of a pen, chart and a clock-work revolving drum.



This



This type has the advantage of measuring any type of precipitation like snow as it is based on weight.

graph of accumulated rainfall against the lapsed period i.e. (mass curve of the rainfall). mechanism

of

the

instrument

give

the

PRECIPITATION AND ITS MEASUREMENTS

Weighing Bucket Type Rain-Gauge (Figure)

PRECIPITATION AND ITS MEASUREMENTS

PRECIPITATION AND ITS MEASUREMENTS

Mass Curve

PRECIPITATION AND ITS MEASUREMENTS

Automatic Rain Gauges ii) Tipping Bucket Type Rain-Gauge 

The tipping bucket type rain-gauge consists of 30 cm diameter sharp edge receiver as shown in the figure. At the end of the receiver is provided a funnel and allied mechanism.



A pair of tipping buckets are pivoted under the funnel in such a way that when one bucket receives 0.25 mm (0.01 inch) of precipitation “it tips, discharging its contents into a reservoir bringing the other bucket under the funnel”.



The tipping operation is fitted with an electronic recording device to compute the intensity of rainfall over time.

PRECIPITATION AND ITS MEASUREMENTS

Tipping Bucket Type Rain-Gauge (Figure)

PRECIPITATION AND ITS MEASUREMENTS

Automatic Rain Gauges iii) Float Type Automatic Rain-Gauge 

The working of a float type rain-gauge is similar to the weighing bucket type gauge. A funnel receives the rain water which is collected in a rectangular container.



A float is provided at the bottom of the container. The float is raised as the water level rises in the container, its movement is transmitted and being recorded by a pen moving on a clock-work recording drum.



When the water level in the container rises so that the float touches the top, the siphon comes into operation, and releases the water; thus all the water in the box is drained out.

PRECIPITATION AND ITS MEASUREMENTS

Float Type Automatic Rain-Gauge

PRECIPITATION AND ITS MEASUREMENTS Float Type Automatic Rain-Gauge (Graph)

PRECIPITATION AND ITS MEASUREMENTS

Site Selection for Gauging Station i.

The site where a rain-gauge is set up should be an open place.

ii.

The distance between the Rain-gauge and the nearest object should be at least twice the height of the object. In no case should it be nearer to the obstruction than 30 metres.

iii.

The gauge should be placed on the level ground not upon a slop.

iv.

In the hill area, if suitable level area is not available then it should be placed on the top of the hill.

v.

Site should be best shielded from high wind.

vi.

A fence, if erected to protect the gauge from cattle etc. should not be less than twice its height.

PRECIPITATION AND ITS MEASUREMENTS Advantages and Disadvantages of Recording Rain-Gauges Following are the “advantages of recording type rain-gauge” over the non-recording type: 

The rainfall is “recorded automatically” and therefore, there is no necessity of any attendant.



The recording rain-gauge also gives the “intensity of rainfall at any time” while the non-recording gauge gives the “total rainfall in any particular interval of time”.



As no attendant is required such rain-gauge can be installed in far-off places also.



Possibility of human error is obviated.

Disadvantages.



It is costly comparing to non-recording gauge.



Fault may develop in electrical or mechanical mechanism or recording the rainfall.

PRECIPITATION AND ITS MEASUREMENTS

Sources of Errors in Recording the Measurements i.

The most serious error is the “deficiency of measurements due to wind”. Vertical acceleration of air forced upwards over a gauge gives and upward acceleration to precipitation about to enter the gauge and “results in deficient catch”.

ii.

Inclination of gauge may “cause lesser collection”. A 10% inclination gives about 15% low catch.

iii.

Tipping of the buckets may be affected due to rusting or accumulation of dirt at the pivot.

iv.

Mistakes in reading the scale of the gauge.

v.

Dents in the collector rim may change its receiving area.

vi.

Funnel and inside surface require about 2.5 mm of rain to get moistened when the gauge is initially dry. This may amount to the extent of 25 mm per year in some areas.

PRECIPITATION AND ITS MEASUREMENTS Example The chart fixed to an automatic float type Rain Gauge gives the result as shown in the table below;

PRECIPITATION AND ITS MEASUREMENTS Example The chart fixed to an automatic float type Rain Gauge gives the result as shown in the table below; Find 1. 2. 3. 4. 5.

Hourly Precipitation Daily Precipitation Time when the pointer reverted Period of no Precipitation Maximum Intensity of Precipitation

PRECIPITATION AND ITS MEASUREMENT

Computation of Average Rainfall Over a Basin Average Rainfall intensity is measured over a catchment by following commonly used method; 

Arithmetic Mean Method.



Thiessen polygon method



Isohyetal method



Weighted Length Method

Continued…. 23

PRECIPITATION AND ITS MEASUREMENT

Arithmetic Mean Method 

This is the simplest method of computing the average rain fall over a basin.



The average rainfall is obtained by “dividing the sum of depths recorded at different rain gauge stations of the basin” by the number of rain gauge stations.

Pm = (P1+P2+P3+…..+Pn) / n = 1/n ∑

n i=l

Pi

Merits and Demerits 1. 2. 3.

4.

5. 6.

It is one of the simplest methods. It is used to determine the approximate rainfall. If the rainfall is uniformly distributed over the whole catchment, method gives better results. If the number of rain gauge stations are more and variation of the individual record is not far from the mean; method is taken to be accurate. In hilly terrains, this method can yield fairly satisfactory results To install maximum number of rain gauge stations in the catchment, 24 for better results, is costly and not always possible.

• Example: Rainfall of five Rain Gauges is shown below. Calculate the Average Rainfall. Stations

Precipitation in mm

1 2 3 4 5 6

15.6 20.4 13.8 10.5 17.1 22.3

Total = 99.7 mm

Average Precipitation

∑P = 99.7 mm Pav = 99.7/6 = 16.62 mm Ans

PRECIPITATION AND ITS MEASUREMENT

Thiessen Polygon Method 

This is the weighted mean method.



The rain fall is never “uniform” over the entire area of the basin or catchments, “but-varies in intensity and duration from place to place”.



The rain fall recorded by each rain gauge station is weighted according to the area, it represents.



This method is more suitable under the following conditions. i.

For areas of moderate size ranging from say 750 sq km to 3000 sq km.

ii.

When the rain gauge stations are few compared to the size of the basin. Continued…. 26

PRECIPITATION AND ITS MEASUREMENT Thiessen Polygon Method (Figure-I)

27

PRECIPITATION AND ITS MEASUREMENT

Thiessen Polygon Method Procedure 

Join the adjacent rain gauge stations A,B,C,D,E etc. of the area dividing the entire area in a series of triangles as sown in figure.



Draw the perpendicular bisector of each of these lines, as shown by firm lines in figure.



The area enclosed by these perpendicular bisectors is served by respective rain gauges. Thus these perpendicular bisectors form a series of polygons around the Rain-gauge stations and containing one and only one Rain-gauge station in each polygon.



The entire area within any polygon is nearer to the Rain-gauge station contained there in than any other.



Find the area of each polygon and multiply it with the rainfall of the respective Rain-gauge. Continued…. 28

PRECIPITATION AND ITS MEASUREMENT

Thiessen Polygon Method The Calculations 

If P1, P2, P3, P4, P5, and P6 are the rainfalls in station and A1,A2,A3,A4,A5 and A6 are the areas respectively then average rainfall of the catchment is; Pav = (P1A1+P2A2+P3A3+P4A4+P5A5+P6A6+…+PnAn) A1+A2+A3+A4+A5+A6 +…+An

P=

n (∑ i=l

PiA1 )/ A

29

PRECIPITATION AND ITS MEASUREMENT Merits and demerits i.

Results are accurate than arithmetical mean method.

ii.

The greatest limitation of the method is its flexibility. A new Thiessen polygon diagram is to be drawn every time for the catchment if there is a change in the gauge network.

iii.

This method simply assumes linear variation of precipitation between stations and assigns each segment of area to the nearest station.

iv.

If gauging stations are few compared to the size of area, Thiessen polygon method should be used.

v.

Station weights remain constants when the same number of stations are used.

vi.

If catchment area is large and rain gauging stations are also quite large in number, it is then adoptable to computer computation. Continued…. 30

PRECIPITATION AND ITS MEASUREMENT

Thiessen Polygon Method • Example: The map of a river basin is shown in the figure 1. Rainfall observation of the available rain gauge stations are noted on the map itself. Draw the Network of Thiessen Polygon and find out the Average Rainfall.

• Solution: The Thiessen Polygon are drawn as explained earlier and are shown in Figure-I. The area of each polygon has measured by planimeter and is shown in following table. The Map of the area is drawn into a scale of (1 cm=320 m) and the results are tabulated as below.

Stations

Area of Thiessen Polygon (A) cm2

Precipitation in cm (P)

Product AXP

A B C D E F G H I J K L

112.25 53.50 120.0 62.5 119.0 144.0 72.0 130.0 62.5 85.0 110.0 40.0

62.5 70.7 67.5 85.0 77.5 80.0 82.5 55.0 52.5 67.5 60.0 57.5

7020.0 3745.0 8100.0 5312.5 9922.5 11520.0 5940.0 6950.0 3281.25 5737.5 6600.0 2300.0

∑A=1110.75 • Average Precipitation:

=

∑AP=26428.75

∑AP

∑A = 76428.75 1110.75 = 68.8 cm

Ans

PRECIPITATION AND ITS MEASUREMENT

 Isohyetal Method 

“An isohyets is a line joining places of equal rainfall intensities on the rain fall map of a basin”.



An Isohyetal map showing contours of “equal rainfall” presents a more accurate picture of the rain fall distribution over the basin.



This method is more suited under the following conditions. i.

For hilly and rugged areas.

ii.

For large areas over 5000 square km.

iii.

For areas where the net-work of rain gauge stations with in the storm area is sufficiently dense, Isohyetal method gives more accurate distribution of rainfall. Continued…. 33

PRECIPITATION AND ITS MEASUREMENT Isohyetal Method (Figure-II)

34

PRECIPITATION AND ITS MEASUREMENT Procedure    

From the rain fall data prepare the isohyetal map as shown in figure. Measure the areas between two successive isohyets with the help of a planmeter. Multiply each area by the mean rainfall between the isohyets. Calculate the average rainfall by the following equation

The Calculation 

Let the isohyets represent the rainfall P1, P2,…… Pn and areas between the successive isohyets A1, A2,…… Pn-1 Average precipitation is then calculated as; Pav = A1[P1+P2/2]+A2[P2+P3/2]+….+An-1[Pn-1+Pn/2] A1+A2+A3+A4+….+An-1

P = A1[P1+P2/2]+A2[P2+P3/2]+….+An-1[Pn-1+Pn/2] A Continued….

35

PRECIPITATION AND ITS MEASUREMENT Merits and demerits i.

ii.

iii. iv.

v.

The isohyetal method permits the use and interpretation of all available data and is well adapted to display and discussions. If the analyst has the knowledge of orographic effect, he can use it in constructing the isohyetal map. Also he must have knowledge of storm morphology. Then the final map prepared by the experienced analyst should represent a more realistic precipitation pattern than just obtained from gauged data. In the hilly and rugged basin, this method is most suitable. In sufficient dense network of rainfall stations within storm area, this method may give reasonable accurate indication of rainfall distribution. Overall impression may be concluded that the isohyetal method is superior to the other two methods. 36

PRECIPITATION AND ITS MEASUREMENT Isohyetal Method • Example: Isohyets of different rainfall are shown in Figure-II. The rainfall and areas of adjacent Isohyets are also given in the figure. Find out the Average Rainfall of basin.

Solution: i) Draw the Isohyets on the basis of Rainfall intensity catchment. ii) Find out the area through planimeter between the two Isohyets. iii) Find out the average of two Isohyets of particular area.

iv) Then multiply the area with the mean Isohyets v) Find out the accumulative area and the product of each area and Isohyets. vi) Then the calculate the mean rainfall as under;

S. No.

Values of isohyets bounding the strip cm

Mean Value of Rainfall ‘P’ (cm)

Area ‘A’

Product ∑P av X A

1 2 3 4 5 6 7

30 _ 40 40 _ 50 50 _ 60 60 _ 70 70 _ 80 80 _ 90 90 _ 100

35.0 45.0 55.0 65.0 75.0 85.0 95.0

32.0 162.0 155.0 92.0 228.0 120.0 65.0

1120.0 7290.0 8525.0 5980.0 17100.0 10200.0 5575.0

∑A=854

55700.0

Pav =

∑Pm ∑A = 55790 854

= 65.33 cmAns

PRECIPITATION AND ITS MEASUREMENT Example Find the “Average Precipitation” for the following given data by all the three methods; a) Arithmetic Mean

b) Polygon Method

PRECIPITATION AND ITS MEASUREMENT Example c) Isohyetal Method

PRECIPITATION AND ITS MEASUREMENT

Interpolation and Adjustment of Missing Data 

Some times Rainfall Data in 1 or 2 stations may be missed. Inconsistency of average rainfall may occur in catchment due to various reasons.  exposure of station may be changed with growth of trees and buildings. In such situation interpolation in the estimation in the average rainfall is required.  This interpolation a done by following methods depending upon causes of inconsistency. Arithmetic Mean Method 





In order to determine the missing data at a particular station, estimate this data, at lest three stations closed to the station of missing data. It is necessary that these three stations are evenly distributed around the station under consideration. If normal precipitation at each of these selected stations is with in 10% of that station with missing data then simple arithmetical mean of precipitation of those three stations will give the value of missing station. If PA, PB and PC are precipitation of the nearby station and Px is the estimated the precipitation of missing station then 41

P = P +P +P /3

PRECIPITATION AND ITS MEASUREMENT Interpolation and Adjustment of Missing Data

Normal Ratio Method 

This method is used for interpolation when the normal annual precipitation of, say, three nearby stations A, B and C NA, NB and NC, differs from that of the NX of station X with missing data from previous record by more than 10%.



If PA, PB, PC are average storm precipitation of A, B and C in the year when average precipitation at X, i.e., PX is missing, then. PX = 1/3 [NX/ NA] x PA + [NX/NB] x PB + NX/NC x PC

42

PRECIPITATION AND ITS MEASUREMENT Example: 

The normal annual rainfall at station A,B,C and D in a basin are 80.97, 67,59, 76.28 and 92.01 cm respectively. In the year 1975, the station D was inoperative and station A,B and C recorded annual precipitation of 91.11, 72,23 and 79.89 cm respectively. Estimate the rain fall at station D in that year.



Solution:



As the annual rainfall values vary more than 10 %, the Normal ratio method is adopted



PD = 92.01/3 X [91.11/80.79 + 72.23/67.59 + 79.89/76.28]



PD = 99.48 cm

43

PRECIPITATION AND ITS MEASUREMENT Example • In a catchment area, daily precipitation was observed by 11 rain gauge stations. On 2nd August 2005, the observations indicated that one gauge was out of order. The observation taken by 10 rain gauges are as follows • Estimate the missing data at ‘H’ Station

A

B

C

D

E

F

G

H

I

J

K

Prpt.

21

23

19

20

23

24

19

?

21

22

18

Solution • Since there is not much variation in the precipitation data, a simple arithmetic average of the precipitation observed at the 10 remaining stations was taken as under Precipitation at H = 21+23+19+20+23+24+19+21+22+18 = 210 = 21mm 10 10

PRECIPITATION AND ITS MEASUREMENT Example • The average annual precipitation at five rain gauge stations in a catchment is as follows. Station

P

Q

R

S

T

Avg. PPt

2400

2332

2431

2207

2231

• However the precipitation at station P was not available for the year 1996 because the rain gauge was out of order. The precipitation observed at the other stations in1996 was as follows. • Evaluate the precipitation at station ‘P’ during 1996. Station

P

Q

R

S

T

PPT

?

2113

2200

2028

2095

PRECIPITATION AND ITS MEASUREMENT Solution Precipitation at P (in mm) = ¼ (2400X2113 + 2400 X 2200 + 2400 X 2028 + 2400 X 2095) 2332

2431

= ¼ (2174+2172+2205+2253)

= 2201 mm

2207

2231

PRECIPITATION AND ITS MEASUREMENT Interpolation and Adjustment of Missing Data

Double Mass Curve 

A double mass curve shown in figure is drawn for a period of 29 years of a catchment to check the inconsistency of rainfall record of a station (say, X) and accordingly to adjust the incorrect results.



The cause of inconstancy may be; i. Shifting of rainfall station to a new position ii. Error in observation from a certain year. iii. Change in the vicinity of the station due to growth of trees, building, fencing, cutting of forest nearby changing the wind pattern, etc. iv. Rain gauge may be faulty from a certain period. v. Site of instrument may be changed or replaced without record. Continued…. 47

PRECIPITATION AND ITS MEASUREMENT

Procedure 

To draw this curve, a group of stations (say, 10) is taken as base station in the neighborhood of the problem station “X”.



The accumulated rainfall of station X, (∑PX) and accumulated values of average of group of base stations ∑Pav are calculated starting from latest record.



The values ∑PX are plot as ordinate ∑Pa as abscissa for available date of rainfall for the entire period.



In this plot a break in the slope will be been seen from the particular year. Which indicates the years of change in precipitation regime of station X.



The values at X beyond the period of change of regime the particular year are corrected as under;



The original slope of the mass curve of rainfall upto the change of years is extended by a dotted line as shown in the figure-III. 48

PRECIPITATION AND ITS MEASUREMENT 

The correction to the data of rainfall at X from 1982 to 1971 is the slope of the dotted line divided by the slope of the second mass curve of 1983 to 1971, i.e. (c/b) / (s/b) = c/s

Thus the corrected data at X is; 

Pcx = (Px) x c/s

All the inconsistent data of X from 1982 to 1979 are corrected by multiplying by c/s, the value of which is obtained from the plot measuring c and s as per scale

49

PRECIPITATION AND ITS MEASUREMENT Double Mass Curve (Figure-III)

50

ANNUAL RAINFALL DATA FOR STATION M AS WELL AS THE AVERAGE ANNUAL RAINFALL VALUES Example Annual rainfall data for station M as well as the average annual rainfall values for a group of ten neighboring stations located in a meteorologically homogeneous region are given below. Test the consistency of the annual rainfall data of station M and correct the record if there is any discrepancy. Estimate the mean annual precipitation at station M. Year

Annual Rainfall of Station M (mm)

Average Annual Rainfall of the group (mm)

Year

Annual Rainfall of Station M (mm)

Average Annual Rainfall of the group (mm)

1950

676

780

1965

1244

1400

1951

578

660

1966

999

1140

1952

95

110

1967

573

650

1953

462

520

1968

596

646

1954

472

540

1969

375

350

1955

699

800

1970

635

590 Continued….

ANNUAL RAINFALL DATA FOR STATION M AS WELL AS THE AVERAGE ANNUAL RAINFALL VALUES Year

Annual Rainfall of Station M (mm)

Average Annual Rainfall of the group (mm)

Year

Annual Rainfall of Station M (mm)

Average Annual Rainfall of the group (mm)

1956

479

540

1971

497

490

1957

431

490

1972

386

400

1958

493

560

1973

438

390

1959

503

575

1974

568

570

1960

415

480

1975

356

377

1961

531

600

1976

685

653

1962

504

580

1977

825

787

1963

828

950

1978

426

410

1964

679

770

1979

612

588

CALCULATION OF DOUBLE MASS CURVE YEAR

Pm (mm)

∑Pm (mm)

Pav (mm)

Pav (mm)

Adjusted values of Pm (mm)

Finalized values of Pm (mm)

1979

612

612

588

588

612

1978

426

1038

410

998

426

1977

825

1863

787

1785

825

1976

685

2548

653

2438

685

1975

356

2904

377

2815

356

1974

568

3472

570

3385

568

1973

438

3910

390

3775

438

1972

386

4296

400

4175

386

1971

497

4793

490

4665

497

1970

635

5428

590

5255

635

1969

375

5803

350

5605

375

1968

596

6399

646

6251

689.92

699

1967

573

6972

650

6901

671.95

672

1966

999

7971

1140

8041

1171.51

1172

1965

1244

9215

1400

9441

1458.82

1459

1964

679

9894

770

10211

796.25

796 Continued….

CALCULATION OF DOUBLE MASS CURVE YEAR

Pm (mm)

∑Pm (mm)

Pav (mm)

Pav (mm)

Adjusted values of Pm (mm)

Finalized values of Pm (mm)

1963

828

10722

950

11161

970.98

971

1962

504

11226

5801

11741

591.03

591

1961

531

11757

600

12341

622.70

623

1960

415

12172

480

12821

486.66

487

1959

503

12675

575

13396

589.86

590

1958

493

13168

560

13956

578.13

578

1957

431

13599

490

14446

505.43

505

1956

479

14078

540

14986

561.72

562

1955

699

14777

800

15786

819.71

820

1954

472

15249

540

16326

553.51

554

1953

462

15711

520

16846

541.78

542

1952

95

15806

110

16956

111.41

111

1951

578

16384

660

17616

677.81

678

1950

676

17060

780

18396

792.73

793

Total of Pm =

19004 mm

Mean of Pm=

633.5 mm

CALCULATION OF DOUBLE MASS CURVE