Transcript 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 responsible for lifting of air as under: according to the factors i) Cyclonic Precipitation ii) Convective Precipitation iii) Orographic Precipitation i. Cyclonic Precipitation Cyclonic precipitation results from converging into low pressure area of “lifting of air masses 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 irrigation for works”.
designing, improvement and maintenance of
The amount of precipitation is defined as
which falls on a level “the depth of water surface”, and is measured by rain gauge
. The following are the main types of
Rain-gauges
: 1.
2.
Non-Automatic Rain-Gauges: recording rain-gauge.
This is also known as non Symon’s Rain-Gauge is the instrument general used for rainfall measurements.
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 mechanism of the instrument give the
graph of accumulated rainfall against the lapsed period i.e. (mass curve of the rainfall)
.
This type has the advantage of measuring any type of precipitation like snow as it is based on weight.
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.
iii.
iv.
v.
vi.
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.
The gauge should be placed on the level ground not upon a slop.
In the hill area, if suitable level area is not available then it should be placed on the top of the hill.
Site should be best shielded from high wind.
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.
ii.
iii.
iv.
v.
vi.
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”.
Inclination of gauge may “cause lesser collection”. A 10% inclination gives about 15% low catch.
Tipping of the buckets may be affected due to rusting or accumulation of dirt at the pivot.
Mistakes in reading the scale of the gauge.
Dents in the collector rim may change its receiving area.
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.
P m = (P 1 +P 2 +P 3 + …..+P n ) / n = 1/n ∑ n i=l P i 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, for better results, is costly and not always possible.
24
•
Example:
Rainfall of five Rain Gauges is shown below. Calculate the Average Rainfall.
Stations
1 2 3 4 5 6
Precipitation in mm
15.6
20.4
13.8
10.5
17.1
22.3
Average Precipitation
∑P = 99.7 mm P av = 99.7/6 = 16.62 mm Ans
Total = 99.7 mm
PRECIPITATION AND ITS MEASUREMENT
Thiessen Polygon Method
This is the weighted mean method.
The rain fall is never basin or catchments, from place to place ”.
“uniform” over the entire area of the “but-varies in intensity and duration
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 P 1 , P 2 , P 3 , P 4 , P 5 , and P 6 are the rainfalls in station and A1,A2,A3,A4,A5 and A6 are the areas respectively then average rainfall of the catchment is; P av = (P 1 A 1 +P 2 A 2 +P 3 A 3 +P 4 A 4 +P 5 A 5 +P 6 A 6 + …+P n A n ) A 1 +A 2 +A 3 +A 4 +A 5 +A 6 + …+A n
P = ( ∑
n i=l
P
i
A
1
)/ A
29
PRECIPITATION AND ITS MEASUREMENT Merits and demerits i.
Results are accurate than arithmetical mean method.
ii.
iii.
iv.
v.
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.
This method precipitation simply between assumes stations linear and segment of area to the nearest station.
variation assigns of each If gauging stations are few compared to the size of area, Thiessen polygon method should be used.
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
J K L A B C D E F G H I
Area of Thiessen Polygon (A) cm2
112.25
53.50
120.0
62.5
119.0
144.0
72.0
130.0
62.5
85.0
110.0
40.0
∑A=1110.75
•
Average Precipitation: =
∑AP ∑A = 76428.75
1110.75
= 68.8 cm Precipitation in cm (P)
62.5
70.7
67.5
85.0
77.5
80.0
82.5
55.0
52.5
67.5
60.0
57.5
Ans Product A X P
7020.0
3745.0
8100.0
5312.5
9922.5
11520.0
5940.0
6950.0
3281.25
5737.5
6600.0
2300.0
∑AP=26428.75
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.
iii.
For large areas over 5000 square km.
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 P 1 , P 2 , …… P n between the successive isohyets A 1 , A 2 , …… P n-1 and areas Average precipitation is then calculated as; P av = A 1 [P 1 +P 2 /2]+A 2 [P 2 +P 3 /2]+ ….+A n-1 [P n-1 +P n /2] A 1 +A 2 +A 3 +A 4 + ….+A n-1 P = A 1 [P 1 +P 2 /2]+A 2 [P 2 +P 3 /2]+ ….+A n-1 [P n-1 +P n /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 1 2 3 4 5 6 7 30 _ 40 40 _ 50 50 _ 60 60 _ 70 70 _ 80 80 _ 90 90 _ 100 Mean Value of Rainfall ‘P’ (cm) 35.0
45.0
55.0
65.0
75.0
85.0
95.0
Area ‘A’ 32.0
162.0
155.0
92.0
228.0
120.0
65.0
∑A=854
P av = ∑Pm ∑A = 55790 854 = 65.33 cmAns
Product ∑P av X A 1120.0
7290.0
8525.0
5980.0
17100.0
10200.0
5575.0
55700.0
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. In consistency 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 P A , P B and P C are precipitation of the nearby station and P x estimated the precipitation of missing station then is the
41
P x = P A +P B +P C /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 N A , N B and N C , differs from that of the N X of station X with missing data from previous record by more than 10%.
If P A , P B , P C are average storm precipitation of A, B and C in the year when average precipitation at X, i.e., P X is missing, then.
P X = 1/3 [N X / N A ] x P A + [N X /N B ] x P B + N X /N C x P C
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 2 nd 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
Prpt.
A
21
B
23
C
19
D
20
E
23
F
24
G
19
H
?
I
21
J
22
K
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
Example PRECIPITATION AND ITS MEASUREMENT
• • •
The average annual precipitation at five rain gauge stations in a catchment is as follows.
Station
Avg. PPt
P
2400
Q
2332
R
2431
S
2207
T
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
PPT
P
?
Q
2113
R
2200
S
2028
T
2095
PRECIPITATION AND ITS MEASUREMENT Solution Precipitation at P (in mm) = ¼ (2400X2113 + 2400 X 2200 + 2400 X 2028 + 2400 X 2095) 2332 2431 2207 2231 = ¼ (2174+2172+2205+2253) = 2201 mm
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.
ii.
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.
Shifting of rainfall station to a new position Error in observation from a certain year.
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, ( ∑P X ) and accumulated values
of average of group of base stations ∑P av
are calculated starting from latest record.
The values ∑P X are plot as ordinate date of rainfall for the entire period.
∑P a as abscissa for available
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; P
cx
= (P
x
) 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 Year 1950 1951 1952 1953 1954 1955 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.
Annual Rainfall of Station M (mm) 676 578 95 462 472 699 Average Annual Rainfall of the group (mm) 780 660 110 520 540 800 Year 1965 1966 1967 1968 1969 1970 Annual Rainfall of Station M (mm) 1244 999 573 596 375 635 Average Annual Rainfall of the group (mm) 1400 1140 650 646 350 590 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 1956 1957 1958 1959 1960 1961 1962 1963 1964 479 431 493 503 415 531 504 828 679 540 490 560 575 480 600 580 950 770 1971 1972 1973 1974 1975 1976 1977 1978 1979 Annual Rainfall of Station M (mm) 497 386 438 568 356 685 825 426 612 Average Annual Rainfall of the group (mm) 490 400 390 570 377 653 787 410 588
YEAR 1979 1978 1977 1976 1975 1974 1973 1972 1971 1970 1969 1968 1967 1966 1965 1964 CALCULATION OF DOUBLE MASS CURVE P m (mm) 612 426 825 685 356 568 438 386 497 635 375 596 573 999 1244 679 ∑P m (mm) 612 1038 1863 2548 2904 3472 3910 4296 4793 5428 5803 6399 6972 7971 9215 9894 P av (mm) 588 410 787 653 377 570 390 400 490 590 350 646 650 1140 1400 770 P av (mm) 588 998 1785 2438 2815 3385 3775 4175 4665 5255 5605 6251 6901 8041 9441 10211 Adjusted values of P m (mm) 689.92
671.95
1171.51
1458.82
796.25
Finalized values of P m (mm) 612 426 825 685 356 568 438 386 497 635 375 699 672 1172 1459 796 Continued….
YEAR 1963 1962 1961 1960 1959 1958 1957 1956 1955 1954 1953 1952 1951 1950 CALCULATION OF DOUBLE MASS CURVE P m (mm) 828 504 531 415 503 493 431 479 699 472 462 95 578 676 ∑P m (mm) 10722 11226 11757 12172 12675 13168 13599 14078 14777 15249 15711 15806 16384 17060 P av (mm) 950 5801 600 480 575 560 490 540 800 540 520 110 660 780 P av (mm) 11161 11741 12341 12821 13396 13956 14446 14986 15786 16326 16846 16956 17616 18396 Adjusted values of P m (mm) 970.98
591.03
622.70
486.66
589.86
578.13
505.43
561.72
819.71
553.51
541.78
111.41
677.81
792.73
Total of P m = Mean of P m = Finalized values of P m (mm) 971 591 623 487 590 578 505 562 820 554 542 111 678 793 19004 mm 633.5 mm
CALCULATION OF DOUBLE MASS CURVE