1
CHAPTER ONE
INTRODUCTION
1-1
General
Water is the most abundant substance on earth, the principal constituent of all
living things, and major force constantly shaping the surface of the earth. It is also a
key factor in air-conditioning the earth for human existence and in influencing the
progress civilization.
Precipitation is the only source for the fresh water on earth. For that, the
study of precipitation is the basis of the hydrologic studies and systems where the
“design storm” is defined for use in the design of hydrologic systems. Usually the
design storm serves as the system input and the resulting rates of flow through the
system are calculated using rainfall – runoff relationship, and flow routing
procedures.
1-2
INTENSITY-DURATION-FREQUENCY RELATONSHIPS
One of the first steps in many hydrologic design project is the determination
of the rainfall event or event to be used. The most common approach is to use a
design storm or event that involves a relationship between rainfall intensity (or
depth), duration, and the frequency or return period appropriate for the facility and
site location. In many cases, the hydrologist has standard intensity-durationfrequency (IDF) curves available for the site and does not have to perform this
analysis. However, it is worthwhile to understand the procedure used to develop the
relationship. Usually, the information is presented as a graph, with duration plotted
on the horizontal axis, intensity on the vertical axis, and a series of curves, one for
each design return period.
2
1-3
Objective of the study
The main objective of this study is the development of rainfall intensity
equation used as a design storm in Riyadh region. This equation development is
based on intensity-duration-frequency (IDF) curves for the region.
1-4
Methodology
This study will be carried on through different steps, which include: -
A- Collecting data of rain for all available weather meteorological
stations within the vicinity of Riyadh and the surrounding regions,
which should includes records for the density of rain fall for different
durations (10 min, 20 min, 30 min, 60 min, 2 hours, and 24 hours).
B- Analyzing the data of rainfall and storms to obtain IDF curves using
different processes such as: Gumble and Log person type III methods.
Also, the curves for rainfall intensity for all methods durations “IDF
Curves” for different recurrence periods: 2 years, 5 years, 10 years, 25
years, 50 years, and 100 years will be conducted.
C- Developing an equation for rainfall intensity based on “IDF curves” is
then carried out, using any appropriate analysis such as regression, to
define different parameters of the equation.
1-5
Project layout
This study is presented in this project in five chapters.
General introduction in chapter I, while in chapter II, the theoretical
background of the analysis to obtain rainfall equation is given. Chapter III presents
the data available about study area and rainfall data. In chapter IV, the analysis and
procedure for developing the required equation is presented. Summary and
conclusion of this study are given in chapter V.
3
CHAPTER TWO
THEORITICAL BACKGROUND
When local rainfall data is available, IDF curves can be developed using
frequency analysis. Commonly used distributions for rainfall frequency analysis are
the Extreme Value Type I or Gumble distribution and Log Person Type III. For each
duration selected, the annual maximum rainfall depths are extracted from historical
rainfall records, and then frequency analysis is applied to the annual data. Data
should be long enough but in some situations, only a few years of data that available
and less than 20 years can be used with less accuracy.
2-1
Gumble Method
Using extreme-value theory (EV1) which shows that in a series of extreme
values P1, P2 ……. Pn where the samples are of equal size and P is an exponentially
distributed variable (for example, the maximum precipitation observed in a year’s
gauge readings), then the cumulative probability P that any of the X values will be
less than a particular value x (of return period T) approaches the value [Wilson,
1990].
P(X ≤ x) = e e
y
(2.1)
where e is the natural logarithm base and

 1 
y  In  In1  
 T 

That is, P is the probability of non-occurrence of an event X in T years, or
(2.2)
4
T=
1
1 P
Note that this argument refers to Gumbel’s method. (This should not be
confused with the normal usage of Tr = 1/P where P= probability of occurrence.)
The event X, of return period T years, is now defined as PT, where:
PT = Pav + KT S
(2.3)
where
Pav = average of all values of "annual precipitation" PT
S = standard deviation of the series, or
(P  Pav ) 2
S
n 1
(2.4)
where
n = number of years of record = number of PT values
and
KT = -
6
0.5772  y
π
(2.5)
5
2-2
Log Person Type III Method
Person derived a measure of skewness based on (mean – mode) relationship
and developed a family of curves to describe degree of skewness. One of these, the
Pearson Type III distribution, when used together with the logarithm of the variant P
is found to allow many annual flood series to plot as straight lines.
A skew coefficient (G), given by [Fetter, 1994]
n
G
* 3
n  (P *  Pav
)
i 1
(2.6)
(n  1)(n  2)s 3
where
P* = log P
n = number of events
S = standard deviation on value of P*
*
Pav
= mean of all values of P*
Accordingly, to compute precipitation PT* for a particular return period from an
annual series the following steps are required:
a) Transform all (n) values of P in the series to their logarithms (base 10)
or
P* = log P
for m = 1, 2 …n
b) Find the mean of all values of P*:
*
Pav
P*


n
6
c) Compute the standard deviation of n values of P* using Eq (2.4).
d) Compute the skewness of the P* values from equation (2.6).
e) Calculate the precipitation PT from equation (2.3) then find PT* by anti-Log
of PT* .
where
K T is selected from Table (2.1) for the particular return period Tr and
skewnees G. Rainfall rate, it can be obtained by:
It 
PT*
Td
(2.7)
where Td is the selected rainfall duration.
2-3 Equation for IDF Curves
Intensity-duration-frequency curves have also been expressed as equations to
avoid having to read the design rainfall intensity from a graph. For example,
(Wenzel, 1982) provided coefficients for a number of cities in the United States for
an equation of the form:
I
c
e
Td  f
(2.8)
where I is the design rainfall intensity , Td is the rainfall duration, and c,e and f are
coefficients varying with location and return period Tr .
7
Table (2.1): Values of KT in the Pearson Type III distribution
Skew
Return period
coefficient
G
3.0
2.5
2.0
1.5
1.2
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
2
5
10
25
50
100
200
-0.667
-0.799
-0.990
-1.256
-1.449
-1.588
-1.660
-1.733
-1.806
-1.880
-1.955
-2.029
-2.104
-2.178
-2.253
-0.660
-0.77
-0.895
-1.018
-1.086
-1.128
-1.147
-1.166
-1.183
1.200
-1.216
-1.231
-1.245
-1.258
1.270
-0.396
-0.360
-0.307
-0.240
-0.195
-0.164
-0.148
-0.132
-0.116
-0.099
-0.083
-0.067
-0.050
-0.033
-0.017
1.180
1.250
1.303
1.333
1.340
1.340
1.339
1.336
1.333
1.328
1.323
1.317
1.309
1.301
1.292
2.003
2.012
1.996
1.951
1.910
1.877
1.859
1.839
1.819
1.797
1.774
1.750
1.726
1.700
1.673
3.152
3.048
2.912
2.743
2.626
2.542
2.498
2.453
2.407
2.359
2.311
2.261
2.211
2.159
2.106
4.051
3.845
3.605
3.330
3.149
3.023
2.957
2.891
2.824
2.755
2.686
2.615
2.544
2.472
2.400
0.0
-2.326
-1.282
0.000
1.282
1.645
2.054
2.326
-0.1
-0.2
-0.3
-0.4
-0.5
-0.6
-0.7
-0.8
-0.9
-1.0
-1.2
-1.5
-2.0
-2.5
-3.0
-2.400
-2.472
-2.544
-2.615
-2.686
-2.755
-2.824
-2.891
-2.957
-3.023
-3.149
-3.330
-3.605
-3.845
-4.051
-1.292
-1.301
-1.309
-1.317
-1.323
-1.328
-1.333
-1.336
-1.339
-1.340
-1.340
-1.333
-1.303
-1.250
-1.180
0.017
0.033
0.050
0.067
0.083
0.099
0.116
0.132
0.148
0.164
0.195
0.240
0.307
0.360
0.396
1.270
1.258
1.245
1.231
1.216
1.200
1.183
1.166
1.147
1.128
1.086
1.018
0.895
0.771
0.660
1.616
1.586
1.555
1.524
1.491
1.458
1.423
1.389
1.353
1.317
1.243
1.131
0.949
0.790
0.665
2.000
1.945
1.890
1.834
1.777
1.720
1.663
1.606
1.549
1.492
1.379
1.217
0.980
0.798
0.666
2.253
2.178
2.104
2.029
1.955
1.880
1.806
1.733
1.660
1.588
1.449
1.256
0.990
0.799
0.667
8
It is also possible to extend (2.8) to include the return period Tr using the equation
[Fetter, 1994]
cTrm
I
Td  f
(2.9)
cTrm
I e
Td  f
(2.10)
or
However, the suggested equation that will be used in this study is expressed in the
form:
cTrm
I e
Td
(2.11)
Which is similar to Eq. (2.10) but with omitting the factor f. In order to develop the
equation of rainfall for Riyadh area in the form of Eq. (2.11) it is required to
determine the coefficients c , m and e.
The method of substitution and logarithm transformation will be used to
obtain the above coefficients. The data of I, Td and Tr which are obtained from IDF
curves for Riyadh area is plugged in Eq. (2.11) to get the coefficients of the equation.
9
CHAPTER THREE
STUDY AREA AND AVAILABLE DATA
3-1
Description of the region of study
This study applied in Riyadh vicinity geographic location Riyadh city is
situated between latitude 38-42 north. It is located in the middle of Arabian
Peninsula. The height of Riyadh plateau is roughly 600m North West, 550m South
East above the mean sea level. This height is medium and do not share in the
occurrence of a vast gap in temperature or intensity of rainfall.
3-2
Data available
There is very rare or little rain in Riyadh which is usually stormy sudden rain.
It is mostly intensive, heavy rain during short periods of rainfall time. Data of
precipitation (rainfall) from various weather stations located in different sites in and
around Riyadh will be collected from different authorities. This data will be used in
preparing IDF curves and therefore in obtaining IDF equation for that site.
3-3
Data used to obtain IDF curves
To demonstrate the procedure to obtain IDF curves an available data of
precipitation for Riyadh area will be used. Table (3.1) shows that data of the extreme
values precipitation (mm) during period from year 1965 to 1993 for durations 10
min, 20 min, 30 min, 60 min, 2 hours and 24 hours. These data is obtained from the
Ministry of Agriculture and Water (MAW)
10
3-4
Verification by field data
To verify the procedure used to obtain IDF curves and the developed
equation, an available data of precipitation for AlKharj city (in Riyadh vicinity) was
used. Table (3.2) shows this data of the extreme values of precipitation (mm) during
the period from year 1973 to 1983 for durations 10 min, 20 min, 30 min, 60 min, 2
hours, and 24 hours.
11
Table3.1 Extreme precipitation depth (mm) for different durations in Riyadh area.
1965
10 min
-
20min
-
30 min
12
60 min
20
2 hr
20.5
24 hr
22
1966
-
-
2
3
7
1967
2
3
7
10
13
16.5
1968
7
7
11
14.5
17
19
1969
1
1.5
3.3
5
5.8
18.5
1970
2
2
2.2
-
4
4.5
1971
14
16.5
18.6
21
25
26
1972
5
6.5
10
13.5
13.6
17.8
1973
1
1.5
2.2
3.5
4
8.5
1975
5.5
-
-
-
-
31
1976
5
5.2
-
5.6
10.8
12.6
1977
10
11.6
11.8
-
-
11.8
1978
6.6
10.2
10.4
11.8
14.2
15.8
1979
4.7
5
5.2
6.8
8
13.4
1980
5.2
5.6
-
-
6.8
16.4
1981
7.8
7.8
7.8
7.8
7.8
7.8
1982
10.4
11
11
11
14
17.3
1983
3
5.6
8
10.4
11.4
14.6
1984
4
5
6.6
10.4
14
21.2
1985
3
3.8
5.4
9.4
16.8
27.6
1986
4.4
4.4
4.4
5.8
7
10.6
1988
1.6
1.6
2.4
3.6
4.8
14
1989
5.6
8
9.4
10.4
11.2
22
1993
4.4
6
7.4
9.4
11.2
17.6
12
Table3.2 Extreme precipitation depth (mm) for different durations in AlKharj area.
10 min
20min
30 min
60 min
2 hr
24 hr
1973
1.5
-
2
3
6.2
8.5
1974
6
6.5
-
6.7
-
9.5
1975
2
-
7
9.2
14.4
-
1976
8
14
-
19.6
25.2
-
1977
3.6
3.6
3.8
3.8
4.2
8.5
1978
2
2.6
3
3.8
4.4
5.2
1979
8
10.5
-
-
-
10.5
1980
1.4
2
2.6
3
5.2
5.8
1981
0.8
1
1.4
2.4
2.8
7.6
1982
10.6
12.2
13.4
16.6
17.4
18.4
1983
5.8
7
8.8
12.6
16.8
43.8
13
CHAPTER FOUR
IDF CURVES ANALYSIS AND EQUATION DEVELOPMENT
4-1
General
Storm designing can be obtained by developing an equation based on IDF
curves. However, the IDF curves are constructed using Gumble and Log Person III
methods with precipitation data for Riyadh area.
4-2
Application of Gumble distribution
Procedure to obtain IDF curves using Gumble distribution as mentioned in
chapter two was applied herein. The procedure starts by computation of different
statistical parameters such as the mean and standard deviation. An example of such
computations presented in Table (4.1). The rest of computations for other durations
are presented in Appendix A in Table (A1-A5). Computations of parameters KT
then PT and IT using equations mentioned in chapter two are presented in Tables
(4.2) and (4.3) for different durations.
The intensity duration frequency (IDF) curves are constructed by plotting the
obtained rainfall intensities versus rainfall duration for different return periods. These
curves are shown on Figure (4.1).
14
Table 4.1- Calculations of Statistical Parameters (Duration =10 min.) (Riyadh)
Gumble Method
Log Person Type III Method
P(mm)
(P- P * )^2
P * =Log P
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
2
7
1
2
14
5
1
5.5
5
10
6.6
4.7
5.2
7.8
10.4
3
4
3
4.4
1.6
5.6
4.4
26.4757
9.8939
3.4393
17.1848
9.8939
78.4030
0.0212
17.1848
0.1257
0.0212
23.5666
2.1157
0.1984
0.0030
7.0466
27.6102
4.6030
1.3121
4.6030
0.5557
12.5702
0.2066
0.3010
0.8451
0
0.3010
1.1461
0.6990
0.0
0.7404
0.6990
1.0
0.8195
0.6721
0.7160
0.8921
1.0170
0.4771
0.6021
0.4771
0.6435
0.2041
0.7482
0.6435
0.7839
0.1165
1.4076
0.7839
0.0016
0.2376
1.4076
0.1990
0.2376
0.0348
0.1346
0.2645
0.2213
0.0866
0.0287
0.5031
0.3415
0.5031
0.2948
0.9649
0.1921
0.2948
-0.6941
-0.0398
-1.6700
-0.6941
-0.0001
-0.1158
-1.6700
-0.0888
-0.1158
-0.0065
-0.0494
-0.1361
-0.1041
-0.0255
-0.0049
-0.3569
-0.1995
-0.3569
-0.1601
-0.9478
-0.0842
-0.1601

113.2
247.0345
13.6439
9.0402
-7.6802
Pave 
 P  113.2  5.1455
n
22
( P  Pave ) 2
1
 247.0345
S
n 1
21
 11.764
2
*
*
( P * - Pav
)^2 ( P * - Pav
)^3
Year

Pave 
2
S*
 P *  13.6439  1.1864
n
22
( P *  P *ave ) 2
1
 9.0402
n 1
21

 0.4305
 S  0.6561
 S  3.43
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.424
3
15
Table 4.2- Calculations Using Gumble Method (Durations =10, 20, 30 min.)
(Riyadh)
10 min,
Pav=5.15,S=3.43
Tr
30 min,
Pav=7.81,S=14.2
IT
KT
PT
PT*
IT
KT
27.56
-0.17
5.50
16.46
-0.17
7.10
14.20
7.57
45.40
0.75
8.96
26.89
0.75
10.88
21.77
1.35
9.54
57.21
1.35
11.26
33.79
1.35
13.39
26.77
25
2.12
12.02
72.14
2.12
14.17
42.51
2.12
16.55
33.10
50
2.69
13.87
83.21
2.69
16.33
48.98
2.69
18.90
37.79
100
3.22
15.70
94.20
3.22
18.47
55.40
3.22
21.22
42.45
(Year)
KT
PT
2
-0.17
4.59
5
0.75
10
PT*
20 min,
Pav=6.13,S=7.34
Table 4.3- Calculations Using Gumble Method (Durations =1, 2, 24 hrs.)
(Riyadh)
Tr
60 min,
Pav=9.59,S=5.03
24 hr,
Pav=16.4,S=6.55
IT
KT
PT
PT*
IT
KT
8.77
-0.17
10.16
5.08
-0.17
15.32
0.64
13.21
13.2
0.75
15.17
7.58
0.75
21.11
0.88
1.35
16.15
16.15
1.35
18.49
9.24
1.35
24.94
1.04
25
2.12
19.87
19.87
2.12
22.68
11.34
2.12
29.78
1.24
50
2.69
22.63
22.63
2.69
25.79
12.90
2.69
33.37
1.39
100
3.23
25.36
25.36
3.23
28.88
14.44
3.23
36.94
1.54
(Year)
KT
PT
2
-0.17
8.79
5
0.75
10
PT*
120 min,
Pav=11.1,S=5.67
16
17
4-3
IDF curves using Log Person III
The same procedure to obtain IDF curves will be applied using Log Person Type
III method. Statistical parameters for this method were obtained and displayed in Table
(4.1), and Tables (A1-A5) in Appendix A. Values of computed rainfall intensity using
Log Person Type III are presented in Tables (4.4) and (4.5)for different durations.
Parameters G and KT used for developing IDF curves for this method are presented in
Table (4.6).IDF curves and generated are plotted as shown in Figure (4.2).
4-4
Generating IDF curves for AlKharj
The same procedure was applied to data obtained from AlKharj area in
order to obtain IDF curves. The results and Tables of those computations are
presented in Appendix B.
However, the IDF curves are shown on Figure (4.3) and (4.5) for Gumble and
Log Person Type III, respectively.
4-5
Development of Rainfall Intensity-Duration Equation
The procedure used to obtain an equation that computes the rainfall intensity for
certain duration (with fixed return period), or the rainfall- intensity-duration equation,
uses the available IDF curves results with any logarithm transformation.
The procedure is performed by defining the relation between I, Td and Tr in Eq. (2.11)
in a liner manner.
If Eq. (2.11) rearranged as:
I
where
K
Tde
K= c Tr m
(4.1)
(4.2)
Then, taking logarithms of both sides rearranged equation to obtain:
Log I = Log K – e Log Td
(4.3)
18
Table 4-4- Log Person III Results (Durations =10, 20, 30 min.) (Riyadh)
10 min
Tr
(Year
)
KT
PT
2
-2.73
-0.22
5
-1.33
10
PT*
20 min
30 min
IT
KT
PT
PT*
IT
KT
PT
PT*
IT
0.60
3.62
-2.66
-0.86
0.82
2.46
-3.07
0.00
0.01
0.01
0.21
1.63
9.78
-1.32
0.31
2.04
6.13
-1.3
0.47
4.65
9.30
0.08
0.65
4.42
26.54
0.08
0.72
5.30
15.90
0.18
0.87
8.74
17.48
25
1.21
0.99
9.80
58.78
1.22
1.06
11.58
34.74
1.10
1.12
11.21
22.42
50
1.47
1.07
11.82
70.91
1.50
1.15
14.04
42.11
1.27
1.17
11.66
23.32
100
1.74
1.17
14.32
85.91
1.80
1.24
17.17
51.50
1.42
1.20
12.07
24.13
Table 4-5- Log Person III Results (Durations =1, 2, 24 hrs.) (Riyadh)
60 min
Tr
120 min
24hr
(Year)
KT
PT
PT*
IT
KT
PT
PT*
IT
KT
PT
PT*
IT
2
-2.81
0.20
1.95
1.95
-2.66
0.33
3.28
1.64
-2.93
0.59
5.93
0.25
5
-1.13
0.58
5.76
5.76
-1.32
0.66
6.58
3.29
-1.34
0.91
9.10
0.38
10
0.11
0.95
9.47
9.47
0.08
1.00
10.03
5.01
0.14
1.20
12.04
0.50
25
1.19
1.22
12.23
12.23
1.22
1.29
12.86
6.43
1.15
1.41
14.05
0.59
50
1.43
1.29
12.85
12.85
1.50
1.36
13.55
6.78
1.37
1.45
14.48
0.60
100
1.67
1.35
13.48
13.48
1.8
1.43
14.28
7.14
1.57
1.49
14.88
0.62
19
Table 4-6- Log Person III Parameters (Riyadh)
10 min
20 min
30 min
60 min
120 min
24 min
Log Pav
1.1864
1.3392
1.5712
1.7488
1.3392
2.2579
Log S2
0.4305
0.515
0.0720
0.7924
0.9064
1.261
Log S
0.6561
0.7175
0.2685
0.8902
0.9520
1.123
Log G
-1.424
-1.349
-1.1234
-1.226
-1.1856
-1.1217
-2.729
-1.326
0.083
1.206
1.471
1.742
-2.658
-1.321
0.077
1.222
1.504
1.799
-3.07
-1.34
0.183
1.102
1.271
1.422
-2.814
-1.133
0.114
1.185
1.428
1.671
-2.657
-1.321
0.077
1.222
1.504
1.8
-2.933
-1.338
0.142
1.154
1.366
1.57
 2 yr
5 yr

10 yr
K T 25 yr

50 yr

100 yr
20
21
22
23
Now if Log I is plotted versus Log Td then a decreasing straight line should be
obtained. The abscissa of the line equals (Log K) while slope of the line is the factor e.
So, the idea to determine Equation (2.11) coefficients is to plot the obtained rainfallduration values from (IDF) curves using their logarithm values .The procedure is
presented herein step by step.
4-5-1 Procedure of developing the parameters of the equation :
The procedure of developing the parameters (Riyadh area) can be illustrated in
the following steps:
a) Computation the logarithm of intensity (Log I) versus the logarithm of
duration (Log Td ). Table (4.7) presents the computed values of logarithms I and
Td for Gumble method.
b) Plotting the values of (Log I) versus (Log Td ) for different return periods.
These plots are in Figure (4.5) (a, b) for Gumble and Log Person III
respectively.
c) From Figure (4.5), values of coefficient (e) are obtained where:
e = slope of the lines for each return period Tr .
Then
eav 
e
, where n=6 or number of return periods Tr .
n
d) Also from Figure (4.5), the values of (Log K) for each return period are
determined. The value of (Log K) is equal to the intersect of the plotted line with
Y-axis (Log I). Value of factor (e) and (Log K) are displayed in Tables (4.8) and
(4.9) for Gumble and Log Person III respectively.
Now, from Eq. (4.2), after taking logarithm of both sides, then:
Log K = Log C+ m Log Tr
(4.4)
24
Table 4-7- calculations Using Gumble Method
For Tr =2 years
Td
For Tr =5 years
For Tr =10 years
(min)
Log Td
I
Log I
Log
I
Log I
Log Td
I
Log
I
10
1
27.56
1.44
1
45.40
1.66
1
57.21
1.76
20
1.30
16.46
1.22
1.30
26.89
1.43
1.30
33.79
1.53
30
1.48
14.20
1.15
1.48
21.77
1.34
1.48
26.77
1.43
60
1.78
8.77
0.94
1.78
13.21
1.12
1.78
16.15
1.21
120
2.08
5.01
0.71
2.08
7.58
0.88
2.08
9.24
0.97
1440
3.16
0.64
-0.20
3.16
0.88
-0.06
3.16
1.04
0.02
For Tr =25 years
Td
For Tr =50 years
For Tr =100 years
(min)
Log Td
I
Log I
Log Td
I
Log I
Log Td
I
Log I
10
1
72.14
1.86
1
83.21
1.92
1
94.20
1.97
20
1.30
42.51
1.62
1.30
48.98
1.69
1.30
55.40
1.74
30
1.48
33.10
1.52
1.478
37.79
1.58
1.48
42.45
1.63
60
1.78
19.87
1.30
1.78
22.63
1.36
1.78
25.36
1.40
120
2.08
11.334
1.06
2.08
12.90
1.11
2.08
14.44
1.16
1440
3.16
1.24
0.09
3.16
1.39
0.14
3.16
1.54
0.187
25
Table 4-8-value of (e) and (Log K) for Gumble method
Tr
LOG Tr
K
LOG K
e
2
0.301
181.4
2.26
0.73
5
0.7
478.6
2.68
0.91
10
1
315.2
2.50
0.73
25
1.4
562.3
2.75
0.84
50
1.7
446.7
2.65
0.70
100
2
955.0
2.98
0.90
Average=0.80
Table 4-9-value of (e) and (Log K) for Log Person III method
Tr
LOG Tr
K
LOG K
e
2
0.301
26.3
1.42
0.64
5
0.7
234.4
2.37
0.90
10
1
371.5
2.57
0.91
25
1.4
1223.3
3.01
0.97
50
1.7
691.3
2.84
0.97
100
2
812.3
2.91
1.0
Average=0.89
26
27
e) Plotting (Log K) versus (Log Tr ) from Tables (4.8) and (4.9) for Gumble
and Log Person III respectively to find the coefficients (m) and (c) of the
equation. This Plot is displayed in Fig. (4.6).The coefficient (c) of the
equation is equivalent to the anti-log of the intersect of the plotted line with
Y-axis (Log K), while coefficient (m) is equal to the slope of the line.
f) Substituting the values of c, m and e in the equation
cTrm
I e
Td
(4.5)
The factors of the equation are displayed in Table (4.10)
Then the rainfall equation based on Gumble method is:
I
131.3 T
0.44
(4.6)
0.80
Td
and the equation based on Log Person III method is :
I
112.2 T
0..46
0.89
Td
(4.7)
Then Eqs (4.6) and (4.7) can be combined and averaged to get one
equation that describes design rainfall intensity in Riyadh area as function of
duration and return period. This equation to following form:
I
121.8 T
0.45
0.85
Td
28
29
Table 4-10-values of equation coefficients
Parameters
Gumble
Log Person III
c
131.3
112.2
m
0.44
0..46
e
0.80
0.89
30
4-6
Verification of the developed equation
4-6-1 Rainfall Rates
In order to verify the realistic of the obtained equations (4.6) and (4.7), these
equations were applied to AlKharj data for Gumble and Log Person methods. Rainfall
intensity values which are obtained using equation (4.6) for Gumble and (4.7) for Log
Person III are tabulated in Tables (4.11) and (4.12) respectively.
4-6-2 Comparison of Results
In order to verify that the parameters of the developed equations are reasonable
and have been correctly, comparison of rainfall rates that obtained using IDF methods
for Riyadh ( Tables 4.2 - 4.5) and for AlKharj (Tables B1-B5) will be compared with
rainfall rates obtained using Eqs. (4.6) and (4.7) .For illustration, the result of
comparison is displayed on Tables (4.13) and (4.14) for Gumble and Log Person III,
respectively. Then, for each return period ( Tr ) the correlation can be evaluated by
plotting the rainfall intensity from the historical data (ICst) with the rainfall
intensity from the equation (Ieq) both Gumble and Log Person III methods. An
example of this correlation are shown on Figures (4.7) and (4.8) for Gumble and
Log Person III in Riyadh area, respectively. Other Figures for other return
periods are shown in Appendix C.
31
Table 4-11-Rinfall rates using Eq. (4.6)-Gumble
Td
(min)
Tr =2 yrs Tr =5 yrs
Tr =10
yrs
Tr =25
yrs
Tr =50
yrs
Tr =100
yrs
10
28.230
42.249
57.314
85.775
116.362
157.857
20
16.214
24.265
32.919
49.265
66.832
90.665
30
11.723
17.543
23.80
35.617
48.319
65.549
60
6.733
10.076
13.670
20.457
27.752
37.648
120
3.867
5.787
7.851
11.749
15.939
21.623
1440 (24 hr)
0.530
0.793
1.075
1.609
2.1833
2.962
Table 4-12-Rinfall rates using Eq. (4.7)-Log Person III
Td
Tr =2
(min)
yrs
10
3.32
20
Tr =5
yrs
Tr =10
yrs
Tr =25
yrs
Tr =50
yrs
Tr =100
yrs
7.567
14.12
32.209
60.105
112.159
1.78
4.055
7.567
17.261
32.209
60.105
30
1.23
2.815
5.253
11.983
22.361
41.728
60
0.661
1.509
2.815
6.422
11.983
22.361
120
0.354
0.808
1.509
3.441
6.422
11.983
1440 (24 hr)
0.038
0.086
0.161
0.368
0.686
1.280
32
Table4-13-Rainfall rate (mm/hr)-for Gumble method
Tr =2 years
Td
(min)
I historical
Riyadh
AlKharj
10
27.56
23.70
20
16.46
30
Tr =5years
Ieq
I historical
Riyadh
AlKharj
28.23
45.40
42.04
17.38
16.21
26.89
14.20
9.08
11.72
60
8.77
7.01
120
5.01
1440
0.638
Ieq
I historical
Ieq
Riyadh
AlKharj
42.25
57.21
54.18
57.31
30.39
24.27
33.79
39.00
32.92
21.77
16.72
17.54
26.77
21.78
23.80
6.73
13.21
12.72
10.08
16.15
16.45
13.67
4.69
3.87
7.58
8.32
5.79
9.24
10.72
7.85
0.46
0.53
0.879
0.92
0.79
1.04
1.23
1.08
Tr =25 years
Td
Tr =10 years
I historical
Tr =50years
Ieq
(min) Riyadh AlKharj
I historical
Tr =100 years
Ieq
Riyadh AlKharj
I historical
Ieq
Riyadh AlKharj
10
72.14
69.52
85.78
83.21
80.91
116.36
94..20
92.20
157.86
20
42.51
49.88
49.27
48.98
59.98
66.83
55.40
65.96
90.67
30
33.20
28.17
35.62
37.79
32.91
48.32
42.45
37.62
65.55
60
19.87
21.28
20.46
22.63
24.82
27.75
25.36
28.34
37.65
120
11.34
13.75
11.75
12.90
16.00
15.92
14.44
18.24
21.62
1440
1.24
1.62
1.61
1.39
1.91
2.183
1.54
2.19
2.96
33
Table4-14-Rainfall rate (mm/hr)-for Log Person III method
Tr =2 years
Td
(min)
I historical
Riyadh
AlKharj
10
3.62
2.35
20
2.46
30
Tr =5years
Ieq
I historical
Riyadh
AlKharj
3.32
9.78
6.50
2.83
1.78
6.13
0.01
2.47
1.23
60
1.95
2.05
120
1.64
1440
0.25
Ieq
I historical
Ieq
Riyadh
AlKharj
7.57
26.54
20.60
14.12
4.70
4.06
15.90
12.61
7.57
9.30
3.58
2.82
17.48
7.94
5.25
0.66
5.76
2.38
1.51
9.48
4.64
2.82
2.00
0.35
3.29
1.25
0.81
5.01
2.95
1.51
0.09
0.04
0.38
0.12
0.09
0.50
0.30
0.16
Tr =25 years
Td
Tr =10 years
I historical
Tr =50years
Ieq
(min) Riyadh AlKharj
I historical
Tr =100 years
Ieq
Riyadh AlKharj
I historical
Ieq
Riyadh AlKharj
10
58.78
59.36
32.21
70.91
78.70
60.11
85.91
107.13
112.16
20
34.74
54.88
17.26
42.11
91.79
32.21
51.50
172.70
60.11
30
22.42
30.42
11.98
23.13
49.91
22.36
24.13
92.81
41.73
60
12.23
23.19
6.42
12.85
45.36
11.98
13.48
108.91
22.36
120
6.43
21.20
3.44
6.78
47.53
6.42
7.14
135.82
11.98
1440
0.59
2.60
0.37
0.60
6.32
0.69
0.62
20.06
1.28
34
35
36
CHAPTER FIVE
SUMMARY AND CONCLUSION
5-1
Summary
In this project, an attempt has been made to develop an equation for design
rainfall rate as a function of duration and return period, in Riyadh area.
The development of the equation was based on the construction of intensityduration-frequency (IDF) curves. These curves were obtained for Riyadh area, from
a historical annual rainfall data, using Gumble and Log Person III methods.
Comparison between values of rainfall rates obtained by the developed equation and
the actual historical data were preformed in order to check and verify the accuracy of
the equation.
5-2
Conclusion
Based on results obtained, some conclusions can be drawn from this study as
follows:
a)
It is recommended to use IDF curves for developing an equation for
design rainfall rate in any area.
b)
IDF curves based on Gumble method is better to be used than Log
Person III in order to develop design rainfall equation because the
37
correlation between historical and compute rainfall rates for Gumble
is better than the correlation for Log Person Type III.
c)
It is better to obtain historical rainfall data for at least 20 years when
IDF curves are constructed.
d)
Comparison of results showed that the obtained equation estimates
rainfall intensity for Riyadh area better than AlKharj city.
38
. REFERENCES
1)
Fetter, C.W, Applied Hydrology, Prentice Hall, Englewood
Cliffs, N.J., 1994, pp. 300-312.
2)
Linsley, R.K., Kohler, M.A., and Paulhus, J.L., Hydrology for
Engineering, McGraw-Hill Book Co. Ltd., UK, 1988, pp. 345354.
3)
Froehlich, D.C. (1993), "Short-duration-rainfall intensity
equations for drainage design", J. Irrig. and Drain. Engrg. ,
119(5), pp. 814-828.
4)
Wilson, E.M., Engineering Hydrology, 4th Edition, Agency,
London, 1990, pp. 105-111.
39
40
Table A1- Calculations of Statistical Parameters (Duration =20 min.)- Riyadh
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
3
7
1.5
2
16.5
6.5
1.5
5.2
11.6
10.2
5
5.6
7.8
11
5.6
5
3.8
4.4
1.6
8
6
9
49
2.25
4
272.25
42.25
2.25
27.040
134.56
104.04
25
31.36
60.84
121
31.36
25
14.44
19.36
2.56
64
36
0.4771
0.8451
0.1761
0.3010
1.2175
0.8129
0.1761
0.7160
1.0645
1.0086
0.6990
0.7482
0.8921
1.0414
0.7482
0.6990
0.5798
0.6435
0.2041
0.9031
0.7782
0.7432
0.2441
1.3528
1.0778
0.0148
0.2770
1.3528
0.3884
0.0755
0.1093
0.4099
0.3493
0.1999
0.0887
0.3493
0.4099
0.5767
0.4841
1.2884
0.1902
0.3148
-0.6407
-0.1206
-1.5735
-1.1190
-0.0018
-0.1458
-1.5735
-0.2420
-0.0207
-0.0361
-0.2624
-0.2064
-0.0894
-0.0264
-0.2064
-0.2624
-0.4380
-0.3368
-1.4625
-0.0829
-0.1766
128.8
1077.56
14.7313
10.2970
-9.0242

Pave 
 P  128.8  6.133
n
21
( P  Pave ) 2
1
S  n  1  20 1077.56
 53.878
2
Pave 
2
S*
 P *  14.7313  1.3392
n
21
( P *  P *ave ) 2
1
10.2970

n 1
20

 0.515
 S  0.7175
 S  7.340
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.349
3
41
Table A2- Calculations of Statistical Parameters (Duration =30 min.)-Riyadh
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
12
7
11
3.3
2.2
18.6
10
2.2
11.8
10.4
5.2
7.8
11
8
6.6
5.4
4.4
2.4
9.4
7.4
64
169
81
278.89
316.84
1.96
100
316.84
67.24
92.16
219.04
148.84
81
144
179.56
213.16
243.36
309.76
112.36
158.76
1.0792
0.8451
1.0414
0.5185
0.3424
1.2695
1.0
0.3424
1.0719
1.0170
0.7160
0.8921
1.0414
0.9031
0.8195
0.7324
0.6435
0.3802
0.9731
0.8692
0.0441
0.0006
0.0296
0.1230
0.2775
0.1602
0.0171
0.2775
0.0411
0.0218
0.0235
0.0005
0.0296
0.0011
0.0025
0.0187
0.0510
0.2391
0.0108
0.0
0.0093
0.0
0.0051
-0.0431
-0.1462
0.0641
0.0022
-0.1462
0.0083
0.0032
-0.0036
0.0
0.0051
0.0
-0.0001
-0.0026
-0.0115
-0.1169
0.0011
0.0
156.1
3297.77
16.4980
1.3695
-0.3717

Pave 
 P  156.1  7.805
n
20
( P  Pave ) 2
1
 3297.77 
S
n 1
19
 173.567
2

Pave 
2
S*
 P *  16.4980  1.5712
n
20
( P *  P *ave ) 2
1
 1.3695
n 1
19

 0.0720
 S  0.2685
 S  14.174
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.1234
3
42
Table A3- Calculations of Statistical Parameters (Duration =60 min.) -Riyadh
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
20
2
10
14.5
5
21
13.5
3.5
5.6
11.8
6.8
7.8
11
10.4
10.4
9.4
5.8
3.6
10.4
9.4
108.2640
57.6840
0.1640
24.0590
21.1140
130.0740
15.2490
37.1490
15.96
4.8620
7.8120
3.2220
1.9740
0.6480
0.6480
0.0380
14.4020
35.94
0.6480
0.0380
1.3010
0.3010
1.0
1.1614
0.6990
1.3222
1.1303
0.5441
0.7482
1.0719
0.8325
0.8921
1.0414
1.0170
1.0170
0.9731
0.7634
0.5563
1.0170
0.9731
0.2005
2.0960
0.5607
0.3451
1.1021
0.1820
0.3825
1.4513
1.0012
0.4582
0.8395
0.7339
0.5004
0.5355
0.5355
0.6016
0.9709
1.4220
0.5355
0.6016
-0.0898
-3.0344
-0.4198
-0.2027
-1.1570
-0.0776
-0.2027
-1.1570
-1.0018
-0.3101
-0.7693
-0.6287
-0.3540
-0.3918
-0.3918
-0.4667
-0.9567
-1.6957
-0.3918
-0.4667
191.9
479.9495
18.3622
15.0558
-14.7913

Pave 
 P  191.9  9.595
n
20
( P  Pave ) 2
1
S  n  1  19 479.9495
 25.2605
2
Pave 
2
S*
 P *  18.3622  1.7488
n
20
( P *  P *ave ) 2
1
 15.0558
n 1
19

 0.7924
 S  0.8902
 S  5.026
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.226
3
43
Table A4- Calculations of Statistical Parameters (Duration =120 min.) -Riyadh
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
20.5
3
13
17
5.8
4
25
13.6
4
10.8
14.2
8
6.8
7.8
14
11.4
14
16.8
7
4.8
11.2
11.2
88.6165
65.3893
3.6620
34.9711
27.9456
50.2165
193.5893
6.3184
50.2165
0.0820
9.6947
9.5256
18.3729
10.8002
8.4893
0.0984
8.4893
32.6456
16.6984
39.5184
0.0129
0.0129
1.3118
0.4771
1.1139
1.2304
0.7634
0.6021
1.3979
1.1335
0.6021
1.0334
1.1523
0.9031
0.8325
0.8921
1.1461
1.0569
1.1461
1.2253
0.8451
0.6812
1.0492
1.0492
0.3254
1.9742
0.5902
0.4247
1.2516
1.6387
0.2345
0.5604
1.6387
0.7204
0.5327
0.9586
1.1018
0.9802
0.5418
0.6811
0.5418
0.4315
1.0755
1.4422
0.6938
0.6938
-0.1856
-2.7738
-0.4534
-0.2768
-1.4002
-2.0977
-0.1135
-0.4196
-2.0977
-0.6114
-0.3888
-0.9385
-1.1565
-0.9705
-0.3988
-0.5621
-0.3988
-0.2834
-1.1154
-1.7320
-0.5779
-0.5779
243.9
675.3659
21.6449
19.0334
-19.5303

Pave 
 P  243.9  11.086
n
22
( P  Pave )
1
 675.3659 
n 1
21
 32.160
S
2

2
Pave 
2
S*
 P *  21.644  1.3392
n
22
( P *  P *ave ) 2
1
 19.0334
n 1
21

 0.9064
 S  0.9520
n
 S  5.671
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.1856
3
44
Table A5- Calculations of Statistical Parameters (Duration = 24 hr.) -Riyadh
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1965
1966
1967
1968
1969
1970
1971
1972
1973
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1988
1989
1993
22
7
16.5
19
18.5
4.5
26
17.8
8.5
31
12.6
11.8
15.8
13.4
16.4
7.8
17.3
14.6
21.2
27.6
10.6
14
22
17.6
31.4067
88.2817
0.0109
6.7817
4.4275
141.5109
92.240
1.9717
62.3442
213.2817
14.4084
21.1217
0.3550
8.9750
0.0
73.8884
0.8175
3.2250
23.0800
125.5334
33.5917
5.74
31.4067
1.450
1.3424
0.8451
1.2175
1.2788
1.2672
0.6532
1.4150
1.2504
0.9294
1.4914
1.1004
1.0719
1.1987
1.1271
1.2148
0.8921
1.2380
1.1644
1.3263
1.4409
1.0253
1.1461
1.3424
1.2455
0.8382
1.9961
1.0826
0.9588
0.9816
2.5752
0.7106
1.0151
1.7650
0.5876
1.3400
1.4067
1.1221
1.2788
1.0881
1.8655
1.0402
1.1959
0.8679
0.6675
1.5194
1.2361
0.8382
1.0250
-0.7674
-2.8202
-1.1264
-0.9389
-0.9726
-4.1324
-0.5990
-1.0227
-2.3448
-0.4505
-1.5511
-1.6685
-1.1886
-1.4461
-1.1349
-2.5480
-1.0609
-1.3079
-0.8085
-0.5454
-1.8729
-1.3743
-0.7674
-1.0378
393.5
985.8496
28.2243
29.0022
-33.4872

Pave 
 P  393.5  16.396
n
24
( P  Pave ) 2
1
985.8496

S
n 1
23
 42.863
2

 P *  28.2243  2.2579
Pave 
2
S*
n
24
( P *  P *ave ) 2
1
29.0022

n 1
23

 1.261
 S  1.123
 S  6.547
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.1217
3
45
46
Table B1- Calculations Using Gumble Method (Duration =10, 20, 30 min.)-AlKharj
Tr
10 min,
Pav=4.52,S=3.34
20 min,
Pav=6.60,S=5.22
30 min,
Pav=5.25,S=4.48
(Year)
KT
PT
IT
KT
PT
IT
KT
PT
IT
2
-0.17
3.95
23.70
-0.17
5.79
17.38
-0.17
4.54
9.08
5
0.75
7.01
42.04
0.75
10.13
30.39
0.75
8.36
16.72
10
1.35
9.03
54.18
1.35
12.99
38.99
1.35
10.89
21.78
25
2.12
11.59
69.52
2.12
16.63
49.88
2.12
14.09
28.17
50
2.69
13.48
80.91
2.69
19.32
57.98
2.69
16.46
32.91
100
3.23
15.37
92.20
3.23
21.99
65.96
3.23
18.81
37.62
Table B2- Calculations Using Gumble Method (Duration =1, 2, 24 hrs.) -AlKharj
Tr
60 min,
Pav=8.07,S=7.27
120 min,
Pav=10.7,S=10.30
24 hr,
Pav=13.1,S=15.2
(Year)
KT
PT
IT
KT
PT
IT
KT
PT
IT
2
-0.17
7.01
7.01
-0.17
9.39
4.69
-0.17
11.02
0.46
5
0.75
12.72
12.72
0.75
16.64
8.32
0.75
22.14
0.92
10
1.35
16.50
16.50
1.35
21.44
10.72
1.35
29.51
1.23
25
2.12
21.28
21.28
2.12
27.50
13.75
2.12
38.81
1.62
50
2.69
24.82
24.82
2.69
32.0
16.0
2.69
45.72
1.91
100
3.23
28.34
28.34
3.23
36.47
18.24
3.23
52.57
2.190
47
Table B3- Log Person III Results (Duration =10, 20, 30 min.) -AlKharj
10 min
20 min
30 min
Tr
(Year)
KT
PT
PT*
IT
KT
PT
PT*
IT
2
-2.48
-0.41
0.39
2.35
-1.66
-0.03
0.94
2.83
5
-1.30
0.03
1.08
6.50
-1.15
0.19
1.56
10
0.04
0.54
3.44
20.60
-0.15
0.62
25
1.26
0.99
9.89
59.36
1.34
50
1.58
1.12
13.12
78.70
100
1.94
1.25
17.85
107.1
KT
PT
PT*
IT
-1.52
0.09
1.24
2.47
4.70
-1.09
0.25
1.79
3.58
4.20
12.61
-0.19
0.60
3.97
7.94
1.26
18.29
54.88
1.34
1.18
15.21
30.42
1.86
1.49
30.60
91.79
1.90
1.40
24.96
49.91
2.50
1.76
57.57
172.7
2.61
1.67
46.41
92.81
TableB4- Log Person III Results (Duration =1, 2,24hrs.)-AlKharj
60 min
120 min
24hr
Tr
(Year)
KT
PT
PT*
IT
KT
PT
PT*
IT
KT
PT
PT*
IT
2
-1.09
0.31
2.05
2.05
-1.14
0.30
2.01
1.00
-1.14
0.34
2.18
0.09
5
-0.94
0.38
2.38
2.38
-0.96
0.40
2.50
1.25
-0.96
0.44
2.77
0.12
10
-0.28
0.67
4.64
4.64
-0.27
0.77
5.91
2.95
-0.27
0.85
7.15
0.30
25
1.31
1.37
23.19
23.19
1.32
1.62
42.40
21.20
1.32
1.80
62.45
2.60
50
1.98
1.66
45.34
45.34
1.97
1.98
95.06
47.53
1.98
2.18
151.7
5
6.32
100
2.85
2.04
108.9
108.9
2.82
2.43
271.7
135.8
2.82
2.68
481.5
20.06
48
TableB5 - Log Person III Parameters-AlKharj
10 min
20 min
30 min
60 min
120 min
24 min
Log Pav
0.5233
0.6871
0.671
0.790
0.9164
1.014
Log S 2
0.1405
0.1845
0.1457
0.1918
0.290
0.351
Log S
0.375
0.4296
0.3817
0.4379
0.5386
0.5923
Log G
-0.21
0.90
1.16
1.811
1.72
1.72
 2 yr
5 yr

10 yr
K T 25 yr

50 yr

100 yr
-2.479
-1.3018
0.0347
1.2567
1.5829
1.9395
-1.66
-1.147
-0.148
1.339
1.859
2.498
-1.5168
-1.0944
-0.1888
1.340
1.9034
2.6092
-1.091
-0.9415
-0.2817
1.3134
1.9790
2.8481
-1.139
-0.9639
-0.2695
1.3198
1.9708
2.8174
-1.139
-0.9639
-0.2695
1.3198
1.9708
2.8174
49
Table B6- Calculations of Statistical Parameters (Duration =10 min.) -AlKharj
Gumble Method
Log Person Type III Method
*
*
( P* -
( P* -
*
Pav
)^2
*
Pav
)^3
Year
P(mm)
(P- P )^2
P =log P
1973
1.5
9.1094
0.1761
0.1206
-0.042
1974
6
2.1958
0.7782
0.0649
0.0165
1975
2
6.3412
0.3010
0.0494
-0.011
1976
8
12.1231
0.9031
0.1442
0.0548
1977
3.6
0.8431
0.5563
0.0011
3.5816
1978
2
6.3412
0.3010
0.0494
-0.011
1979
8
12.1231
0.9031
0.1442
0.0548
1980
1.4
9.7231
0.1461
0.1423
-0.054
1981
0.8
13.825
-0.097
0.3847
-0.2386
1982
10.6
36.989
1.0253
0.2519
0.1265
1983
5.8
1.6431
0.7634
0.0576
0.0138

49.7
111.26
5.7567
1.4105
-0.0897
Pave 
 P  49.7  4.51818
n
11
( P  Pave ) 2
1

 111.2564 
S
n 1
10
 11.12564
2
Pave 
2
S*
 P *  5.7567  0.5233
n
11
( P *  P *ave ) 2
1
 (1.4105)
n 1
10

 0.1405
 S  0.375
n
 S  3.336
G
n P *  P * ave
i 1
n  1n  2s *3
 G  0.21
3
50
Table B7- Calculations of Statistical Parameters (Duration =20 min.) -AlKharj
Gumble Method
Log Person Type III Method
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
6.5
3.9276
0.8129
0.0839
0.0243
1976
14
89.905
1.1461
0.3879
0.2416
1977
3.6
0.8431
0.5563
0.0011
3.582
1978
2.6
3.6794
0.4150
0.0117
-0.0013
1979
10.5
35.7822
1.0212
0.2479
0.1234
1980
2
6.3412
0.3010
0.0494
-0.011
1981
1
12.378
0
0.2739
-0.1433
1982
12.2
59.010
1.0864
0.3170
0.1785
1983
7
6.1594
0.8451
0.1035
0.0333

59.2
218.026
6.1840
1.4762
0.4455
Year
1973
1974
1975
Pave 
 P  59.2  6.6
n
9
( P  Pave )
1
 218.026 
S
n 1
8
 27.25
2

2
Pave 
2
S*
 P *  6.1840  0.6871
n
( P *  P *ave ) 2 1
 1.4762 
n 1
8

 0.1845
 S  0.4296
n
 S  5.220
9
G
n P *  P * ave
i 1
n  1n  2s *3
 G  0.90
3
51
Table B8- Calculations of Statistical Parameters (Duration =30 min.) -AlKharj
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1973
2
6.3412
0.3010
0.0494
-0.011
7
6.1594
0.8451
0.1035
0.0333
1977
3.8
0.5158
0.5798
0.0032
0.0002
1978
3
2.3049
0.4771
0.0021
-9.873
1980
2.6
9.7231
0.1461
0.1423
-0.054
1981
1.4
78.887
1.1271
0.3645
0.2201
1982
13.4
18.334
0.9445
0.1774
0.0747
1983
8.8
18.334
0.9445
0.1774
0.0747

42
140.599
5.365
1.0198
0.3382
1974
1975
1976
1979
Pave 
 P  42  5.25
n
8
( P  Pave ) 2
1
 140.599 
S
n 1
7
 20.086
2

 S  4.482
Pave 
2
S*
 P *  5.365  0.671
n
8
( P *  P *ave ) 2 1
 1.0198
n 1
7

 0.1457
 S  0.3817
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.16
3
52
Table B9- Calculations of Statistical Parameters (Duration =60 min.) -AlKharj
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1973
3
2.3049
0.4771
0.0021
-9.873
1974
6.7
4.7603
0.8261
0.0916
0.0277
1975
9.2
21.919
0.9638
0.1940
0.0854
1976
19.6
227.46
1.2923
0.5912
0.4546
1977
3.8
0.5157
0.5798
0.0032
0.0002
1978
3.8
0.5157
0.5798
0.0032
0.0002
1980
3
2.3049
0.4771
0.0021
-9.873
1981
2.4
4.487
0.3802
0.0205
-0.0029
1982
16.6
145.97
1.2201
0.4855
0.3383
1983
12.6
65.316
1.1004
0.3330
0.1921

80.7
475.56
7.8967
1.7265
1.0954
1979
Pave 
S
2

 P  80.7  8.07
n
10
( P  Pave ) 2 1
 475.56
n 1
9
 52.84
Pave 
2
S*
 P *  7.8967  0.790
n
10
( P *  P *ave ) 2 1
 1.7265
n 1
9

 0.1918
 S  0.4379
 S  7.27
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.811
3
53
Table B10- Calculations of Statistical Parameters (Duration =120 min.) -AlKharj
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1973
6.2
2.8285
0.7924
0.0724
0.0195
1975
14.4
97.650
1.1584
0.4033
0.2560
1976
25.2
427.74
1.4014
0.7710
0.6769
1977
4.2
0.1012
0.6232
0.0099
0.0009
1978
4.4
0.0139
0.6435
0.0144
0.0017
1980
5.2
0.4649
0.7160
0.0371
0.0072
1981
2.8
2.9521
0.4472
0.0058
-0.0004
1982
17.4
165.94
1.2405
0.5144
0.3689
1983
16.8
150.84
1.2253
0.4928
0.3459

96.6
848.53
8.2479
2.3211
1.6767
1974
1979
Pave 
S
2

 P  96.6  10.73
n
9
( P  Pave ) 2 1
 848.53
n 1
8
 106.1
Pave 
2
S*
 P *  8.2479  0.9164
n
9
( P *  P *ave ) 2 1
 2.3211
n 1
8

 0.290
 S  0.5386
n
 S  10.30
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.72
3
54
Table B11- Calculations of Statistical Parameters (Duration = 24 hr.) -AlKharj
Gumble Method
Log Person Type III Method
Year
P(mm)
(P- P * )^2
P * =log P
*
( P * - Pav
)^2
*
( P * - Pav
)^3
1973
8.5
15.855
0.9294
0.1649
0.0669
1974
9.5
24.819
0.9777
0.2065
0.0938
1977
8.5
15.855
0.9294
0.1649
0.0669
1978
5.2
0.4649
0.7160
0.0371
0.0072
1979
10.5
35.782
1.0211
0.2479
0.1234
1980
5.8
1.6431
0.7634
0.0576
0.0138
1981
7.6
9.4976
0.8808
0.1278
0.0457
1982
18.4
192.70
1.2648
0.5497
0.4077
1983
43.8
1543.1
1.6415
1.2502
1.3979

117.8
1839.69
9.1243
2.8067
2.2234
1975
1976
Pave 
 P  117.8  13.1
n
9
( P  Pave ) 2 1
S  n  1  8 1839.69
 229.961
2
Pave 
2
S*
 P *  9.1243  1.014
n
9
( P *  P *ave ) 2 1
 2.8067 
n 1
8

 0.351
 S  0.5923
 S  15.164
n
G
n P *  P * ave
i 1
n  1n  2s *3
 G  1.72
3
55
56
57
58
59