Return Period for the Maximum Daily Rainfall in Eastern Highlands of

Jordan Valley.

1EMAD AKAWWI *, 2METRI MDANAT

1Faculty of Engineering, Al-Balqa Applied University, Al-Salt, 19117, JORDAN;

2School of management and logistic sciences, German Jordanian University, Madaba, JORDAN

Abstract- Daily rainfall data for the last 30 years was used in the study area. Various available plotting position

formulae were employed to evaluate different return periods. Different statistical analyses of maximum daily

rainfall were undertaken. The best-fit curves were the Gumbel and Log-Pearson type III (3LP). As a result, the Xt

for the Log-Pearson type III and the Gumbel plotting position, which has the lowest RMSE as the best fit values

for the return periods.

Key-words: -Jordan, Mean, Rainfall, Return Level, Return Period, Standard Deviation, Statistical.

Received: June 23, 2021. Revised: March 17, 2022. Accepted: April 14, 2022. Published: May 10, 2022.

1. Introduction

Water scarcity occurs at the time of the demand of

surface and subsurface freshwater more than the

supply in any specific area due to a physician shortage

in storage water, inappropriate infrastructures to a

depot, distribute and access water [1]. Natural and

Human processing affects practically all sections of the

hydrological cycle. Human activities like to cut trees

and clear the forest, afforestation, and agriculture have

uncomfortable influences on the hydrological cycle,

including evapotranspiration, groundwater level,

surface sea level, and water flow regimes. Human

activities influence cloud formation [2]. Observational

studies and climate projections provide plenteous proof

that water resources vulnerable and have the prospect

to be powerfully wedged by global climate change,

with wide-ranging outcomes for ecosystems and

human beings' societies [3].

Changes in surface and groundwater resources are

especially relevant in locations where water

availability is an abbreviate factor for social and

economic development. As one of the Mediterranean

regions, the Middle East is a “hot-spot” region in terms

of water shortage and climate changes. Generally, as

most of the Middle East countries, Jordan depends

entirely on precipitation for its renewable water

resources. Most of the researchers in the water

management define that 83% of Jordan has low-

rainfall areas in which 90% of annual rainfall does not

reach 200 mm/year. The mean annual precipitation in

Jordan is estimated to be about 110 mm in 2009 2010

[4]). Haddadin et al.[5] discussed the water shortage in

Jordan and the significant elements of sustainable

water solutions. [6] studied the water condition in

Jordan by investigating a sample of a fifteen-year

record for water use. Decreasing in rainfall will lead to

a significant lack of surface runoff and groundwater

recharge processes in the Zarqa River Basin [7].

Referencing climate model analyses made by [8]

shows that the people at danger because of increasing

water scarcity with rising temperatures. The future

global climate change might influence public and

water demand in the industrial sector, yet as a

competitor with the need for water use for agricultural

irrigation [9]. Probabilistic distributions can be used in

the studies such as the management of water resources

and the reporting of practical factors about the

hydrologic cycle. Many researchers attempted to select

the best-fit model locations and estimate the desired

rainfall for different return periods. Annual maximum

daily precipitation for managing water resources was

used by several researchers to find the return periods

of rain. Prediction of rainfall using different

probability distributions for specific return periods was

studied by [10]. [11] have researched about analysis of

rainfall records to determine the characteristic of the

observed frequency distributions. [12] found that

Generalized Extreme Value, the distributions Pearson

type III and Log-Pearson type III, showed the most

significant number of best-fit results for the maximum

monthly rainfall. The statistical methods were used by

[13] estimated the missing rainfall data and compare

their results with the current methods.

The main question of this research is: what is the

best-fit probability distribution for the maximum daily

rainfall return period of the study area? This study’s

objectives are to apply the statistical analysis of the

rainfall for the last thirty-one years (1988-2018). The

main aim is to find the best-fit probability distribution

for the study area, which yields the maximum day

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annual rainfall for return periods of 2, 3, 5, 10, 15, 25,

50, and 100 years by using different plotting position

curves and the Probabilistic suitable distributions.

These results can give useful guidance for policy and

decision-making purposes.

2. Study Area

The study area located to the eastern part of the Jordan

Valley as shown in the map (figure 1). These

Governorates shows significant differences in

elevations above mean sea level. Heights can go from

less than zero below mean sea level to more than 1240

Figure 1. Shows the map of drainage of the study area

(the study area represents by rectangle in Jordan Map

to the right).

The study area is characterized by a hot summer

(June – September). The temperature starts rising from

the beginning of May and increasing to a peak in the

month of august at 42ºC. The winter season is starting

with November and ending in March. The coldest

month is January with a minimum temperature of 0 ºC

and may reach to -5 at night in several days.

3. Methods and Materials

3.1. Data Management

The precipitation data and the temperature

collected from the meteorological department and the

water and irrigation Ministry for a hydraulic cycle for

the period (between 1988 and 2018). This work was

based on an extensive and comprehensive database of

meteorological data (rainfall and temperature). All data

were input and analyzed statistically by using

Microsoft (Excel).

3.2. Analysis of Annual Rainfall Data

The annual rainfall data obtained from the

meteorological department and irrigation and water

ministry for the last 30 years (1988 – 2018) were

analyzed and standardized.

The histograms and other plots were created for

the rainfall data. The statistical parameters as the

arithmetic mean (average), standard deviation,

coefficient of variation, and co-efficient of skewness of

annual rainfall were calculated by using the formulas

listed in Table 1.

The annual precipitation data is analyzed over the

study area regarding the statistical parameters. The

best fit distribution method is determined using various

plotting positions and probabilistic distribution

methods, as listed in Table 1.

Table 1. The Statistical Parameters that were used in this

study.

Name

abbreviatio

Rules

Information

Mean

(Average)

µ, XAvr

∑Xi/n

Xi: the

rainfall

intensity

(mm), n is

number of

the sample,

i= 1,2,…,n

Standard

Deviation

[∑(Xi - µ)2

/(n-1)]1/2

X is the

rainfall

amount, n is

the sample

length, and

i=1,2,….,n

Co-efficient

of Variation

( σ/ µ) x

100%

µ is the

mean, and σ

is standard

deviation

Co-efficient

of Skewness

1/ σ3 *

[N/N2-

3N+2]*[∑(X

i- µ)3]

σ is standard

deviation, N

number of

years, µ is

mean, and

i=1,2,…,n

Several Probabilistic distributions with its parameter estimation are used in this

study, as shown in table-1, and they are explained in the following sections. The

(1)

(2)

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variable X represents observed data, while x represents any possible value of that data

and is used to create the distribution functions, as shown in the next sections. Fx(x)

is the value of the distribution function for the point

where x corresponds to X’s observed data value.

3.3.1. Normal Distribution

The normal distribution is applied in a maximum

daily annual rainfall and runoff analysis [14]. The two

moments, average (µ) and variance (σ2), are the main

parameters of the normal distribution. The probability

density function (pdf), f(x) and cumulative distribution

function (cdf) and F(x) for a standard random variable

x are created by using the following formulas:

(3)

(4)

3.3.2. Two Parameters Log-Normal Distribution

(LN2)

The (pdf) and (cdf) of the 2-parameter Log-

normal distribution are expressed as the following

rules:

(5)

(6)

The range of the random variable is x > 0. The

logarithm of the x variable, y = ln(x), is well-described

by a normal distribution. By using the method of

moment estimators, the parameters are created as the

following formulas:

Are the commonly used parameters of the Log-

Normal distribution. Here, σY is the standard deviation,

and µY is the mean for this distribution.

3.3.3. Log-Pearson Type III

Log-Pearson Type III is one of the gamma family

distribution. This distribution describes a random

variable X, whose logarithm follows the Pearson type

III distribution. The pdf and cdf of log-Pearson type III

were calculated by using the following formulas:

(7)

(8)

The parameters scale “ᾳ,” shape “β” and location

“ᶓ” is estimated by using the method of moment

estimators as the following:

(9)

(10)

(11)

3.4. Goodness-of-fit Tests

These tests are used for evaluating the validity of

a specified or assumed probabilistic model. This test

can be applied by using several methods as plot

method, numerical method, and formal normality test.

In this study, the Plot methods and the root mean

square error (RMSE) was used to evaluate the best

model.

3.4.1. Root Mean Square Error (RMSE)

This method indicates that the smallest RMSE

value is the best-fit model. It measures the difference

between estimates and observed values. It can be

calculated using the following formula:

(12)

xi is the observed value, and X is the estimated

number.

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3.4.2. Graphical Test

It is the most suitable test for determining the

best-fit model. The Q-Q plot of observed and

estimated values is used. Several plotting positions

were used for specific distributions to calculate the

plotting position of the non-exceedance probability, as

mentioned in table 2. Most of the plotting position

formula that was used here have the following

formula:

(13)

n is the rank of the observed value X (X(i) is

ascending order), n = 1, 2, . . ., N. N is the total

number of observations.

Gumble plotting position, which gives unbiased

quintiles; Gringorten’s plotting position (a = 0.44);

Cunnane’s plotting position (a = 0.4) [15]. The

observed data, X(i), against the estimated values, x(F)

(the quantile function), are plotted to create the Q-Q

plot, with F identify by the p i:n for the specific

distribution.

3.5. Return Period (T)

The main important target of frequency analysis is

to find the return period. If the variable (x) equal to or

greater than an event of magnitude xt, occurs once in T

years, then the probability of occurrence P (X ≥ x) in

the given year of the X (Variable) is:

(14)

(15)

The rainfall amounts related to the 50- or 100-

year return periods cannot be directly estimated from a

data set. They can be generated from the 98th and 99th

percentiles for the 50 years and the 100 years return

period, respectively, of a fitted distribution [16].

4. Results and Discussions

The methodology motioned in the previous

sections was developed to the 31 years observational

data in which lists the maximum daily rainfall in

millimeters (mm) was gotten from irrigation and water

ministry and department of Meteorology.

The distribution of annual precipitation all over

Jordan was summarized in figure-2 the study area of

Ajlun governorate located within the range of yearly

rainfall capacity of 700 to 900 mm/year.

Figure 2. the annual precipitation all over

Jordan, Ajlun and Al-Salt governorates

located within the range of 700 – 900 mm/Y.

4.1. Statistical Analysis

The histogram of the annual rainfall distributions

for the 31 years (figure-4) shows that the total

precipitation in the last decade (2009-2018) for about

4949 mm, while the total rainfall for the decade (1999

– 2008) was 4809 mm and for a decade (1989 – 1998)

was about 5849 mm. This information for the total

rainfall shows that the total rainfall in the decade (1999

– 2008) and decade (2009 – 2018) decreased by about

17% compared to the decade (1989-1998). On the

other hand, the total rainfall is almost the same for the

decades (1999 – 2008) and (2009 – 2018). The

maximum daily rain was between 26 mm and 131 mm.

Figure 3. Annual rainfall (Lift) and the

Maximum Day Annual Rainfall (Right)

distributed for the period of 31 years (1988-

2018).

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The results of the statistical parameters are

calculated and listed in table- 2.

Table 2. Plotting Position Methods and

Probabilistic Distribution Methods.

Plotting

Position

Method

Value of

Probabilistic Distribution

Method

Gumbel

1/(1+n)

Normal Distribution

Gringorten

(r – 0.44)/

(n + 0.12)

Log-Normal Distribution

Cunnane

(r – 0.4)/

(n + 0.2)

Log-Pearson Type III

Weibull

r / (n+1)

“r is the rank of the

rainfall, n is the total

number of observations

(years)”

4.2. Probability Plotting Position Modules

4.2.1. Gumble plotting Position

Gumble plotting position was plotted in figure-4,

then the residual and RMSE were estimated from this

curve.

The return period “T” 3, 5, 10, 15, 25, 50, and 100

years and the return periods values “xt” results

obtained from Gumble plotting position are

summarized in table 6.

Figure 4. Gumble Plotting Position of

rainfall distribution: The vertical axis

represents the maximum rainfall (mm/day)

and the horizontal axis is the quintiles of the

percent point.

The maximum daily annual rainfall forms an

approximately straight line depicting an excellent

distribution to the model used [17]. The scale

parameter is estimated by the slope of the trend line (α

=18.4) and the location parameter (μ = 44.16). The

fitted function R2 = 0.96 indicates a proper adjustment

of the distributed points. After extracting the location

and the scale parameters of the Gumble distribution,

the estimating of the extreme rainfall of the Area was

possible.

4.2.2. Cunnane Plotting Position

Fitted function R2 = 0.95 for this plotting, shows a

pretty adjustment of the distributed points. After

determining the location (μ= 44.11) and scale

parameters (α= 18.61) of the Cunnane plotting (Figure-

5), estimating the extreme rainfall by using this plot, it

was possible.

Figure 5. The Cunnane Plotting Position extreme

value distribution of rainfall.

4.2.3. Weibull Plotting Position

The maximum daily rainfall (points on the graph) form

a nearly straight line depicting a valid distribution to

the model used. The scale parameter is estimated (α

=19.93) and the location parameter (μ= 43.8). The

fitted function R2 = 0.94 shows a proper adjustment of

the distributed points. After that, the extreme rainfall

was estimated at the area by using Weibull plotting

Position (Figure-6).

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Figure 6. The Weibull Plotting Position

extreme value distribution of rainfall.

4.2.4. Gringorten Plotting Position

The annual maximum rainfall forms a nearly

straight line depicting a perfect distribution to the

model used where the proper function (R2= 0.96) is

shown in figure 7. The scale parameter is estimated (α

=18.33) and the location parameter (μ= 44.768). By

using these parameters, the extreme rainfall was

expected of the area.

Figure 7. The Gringorten Plotting Position

extreme value distribution of rainfall.

4.3. Goodness-of-fit Test

The results of the RSME values are listed in table

3. The values of the RMSE show that the lowest value

is 5.57 for Gumble Plotting Position. R2 is the best fit

with 95.8, which is the best value among all plotting

positions. Therefore, the Gumble is the best plotting

position curve for area.

Table 3. the values of the statistical parameters.

Description

Symbol

Value

Mean (Average)

µ, XAvr

54.6

Standard Deviation

23.3

Co-efficient of Variation

0.43

Co-efficient of Skewed

SSkewedSkewness

1.69

Kurtosis of Distribution

3.3

The results of the Q-Q plots among the four

plotting position and normal-log distribution (figure-

8), the plots among the four plotting position and

normal distribution (figure-9) and the plot among the

four plotting position and the log-Pearson type III

distribution (figure-10) show that the best-fit graphs

are the log-Pearson type III. The best fit was the

graphs between log-Pearson type III and the Gumle

plotting position.

Figure 8. Log- Normal Distribution, with

Griguton, Gunna, Weibull and Gumble

plotting Positions.

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Figure 9. Normal Distribution, with

Griguton, Gunna, Weibull and Gumble

plotting Positions.

Figure 10. Log-Pearson TypeIII

Distribution, with Griguton, Gunna, Weibull

and Gumble plotting Positions.

4.4. Return Periods “T” and Return Level “Xt”

The results of the return periods (T) and return

level (Xt) for the four plotting position graphs and the

average of the four plotting positions are listed in

table-4, and the results and the average of (T) and (Xt)

for the three probability distributions are listed on

table-5.

Table 4. the results of RSME for all the plotting

positions.

Plotting Position

RSME

Gumble

95.81

5.57

Gunnane

95.45

9.68

Weibull

93.9

6.01

Grington

95.6

6.1

Table 5. The results of return periods (T) and

return level (Xt) for the four different

plotting positions.

As a result, the return level (Xt) for the log-

Pearson type III and the Gumble plotting position

which has the lowest RMSE as the best fit values

which are return periods of 3, 5, 10, 20, 25, 50, and

100 years have a return level (Xt) 62.2, 74.8, 90.5,

99.4, 110.4, 125.1 and 139.8 mm respectively as a

maximum daily rainfall in the year. Due to high slope

of the study area most of the rain and the surface water

drains toward the Jordan Valley at the west of the

study area. By estimating the catchment area of the

Jordan Valley, we expect that the Jordan Valley will be

flooded if the daily rain is more than 90 mm/day.

Therefore, we expect that the Jordan Valley will be

flooded in the year 2021 and so on every 10 years. Due

to the lack of researches about the return periods for

the study area that makes a comparison between my

findings and previous results is too difficult.

5. Conclusions

This research has explained a probability

modeling of maximum daily rainfall in Ajlun, Jordan,

using different plotting positions and probability

distributions. The maximum daily rainfall study for

determining the best-fitted probability distributions

revealed that the best probability distributions for the

rainfall data set. The log-Pearson type-III and Gumbel

were the best fit for the maximum daily rain of the

study area. The maximum daily rainfall amounts

relating to return periods of 3 to 100 years are

Plotting

Positions

Return Periods (T) Years

Return Level- Xt (mm)

100

Gumble

62.

74.8

90.5

99.4

110.4

125.1

139.8

Gunna

60.

72.0

86.0

93.9

103.6

116.7

129.7

Weibull

61.

73.7

88.6

97.1

107.6

121.6

135.5

Gringuton

60.

71.8

85.7

93.5

103.2

116.1

129.0

Average

MAX.

Daily

rainfall

61.

73.1

87.7

106

119.9

133.5

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generated together with their uncertainties. Despite the

good results of our analysis in this research, the

estimations of the extreme return level values may

have uncertain validity. Due to the lowering of the

rainfall and the increase of the population in the study

area, the area will suffer from water scarcity soon. On

the other hand, we expect that the Jordan Valley will

be flooded in the winter season in the year 2021 and so

on every 10 years. Therefore the decision makers must

take in there consideration of these results. They have

to protect the farmers in the Jordan Valley from these

flooding by building embankments and small dams

along the Jordan Valley are on the drainage systems in

the mountains surroundings the Jordan Valley.

Acknowledgments

The author acknowledges Al-Balqa Applied University

for its supporting in this research for offering a

sabbatical leave.

References

[1] FAO. Coping with water scarcity - an action

framework for agriculture and food security. FAO

Water Report 38, Rome: Food and Agriculture

Organization of the United Nations, 2012.

[2] Krüger, O. and GraßI, H. The indirect aerosol

effect over Europe. Geophysical Research Letters

29(19), 1925: doi:10.1029/2001GL014081, 2002.

[3] Broska LH, Poganietz WR, Vogele S. Extreme

events defned—a conceptual discussion applying a

complex systems approach. Futures 115:102490, 2020

[4] World Bank Report, Climate Change Adaptation

and Natural Disasters Preparedness in the Coastal

Cities of North Africa, World Bank, Washington, DC,

pp. 34–35, http://hdl.handle.net/10986/18708, 2010

[5] Hadadin,N.; Qaqish, M.; Akawwi, E; and Bdour,

A. “Water shortage in Jordan - Sustainable solutions,”

Desalination, vol. 250, no. 1, pp. 197–202,

https://doi.org/10.1016/j.desal.2009.01.026, 2010.

[6] Al-ansari, N.; Alibrahiem, N.; Alsaman, M.; and

Knutsson, S. “Water Demand Management in Jordan,”

Engineering, vol. 6, no. January, pp. 19–26,

doi: 10.4236/eng.2014.61004, 2014.

[7] Abdulla, F.; Eshtawi, T.; Assaf, H. Assessment of

the impact of potential climate change on the water

balance of a semi-arid watershed. Water Resour.

Manag. 23, 2051–2068, doi: 10.1007/s11269-008-

9369-y, 2009.

[8] Parry, M., Arnell, N., McMichael, T., Nicholls, R.,

Martens, P., Kovats, S., Livermore, M., Rosenzweig,

C., Iglesias, A., and Fischer, G. Millions at risk:

defining critical climate change threats and targets.

Global Environmental Change 11: 181-183,

http://dx.doi.org/10.1016/S0959-3780(01)00011-5,

2001.

[9] Arnell., N.W. ‘Climate change and global water

resources: SRES emissions and socio-economic

scenarios’, Global Environmental Change 14: 31-52,

https://doi.org/10.1016/j.gloenvcha.2003.10.006, 2004

[10] Upadhaya and Singh, Estimation of consecutive

days maximum rainfall by various methods and their

comparison, Indian Journal of soil conservation 26 (2),

193-200, 1998.

[11] Omran, Z. A., Al-Bazzaz, S. T., & Ruddock, F.

Statistical Analysis of Rainfall Ecords of Some Iraqi

Eteorological Stations, Journal of Babylon

University/Engineering Sciences/ No. (1)/ Vol. (22):

2014.

[12] Ashraful Alam, Kazuo Emura, Craig Farnham and

Jihui Yuan, Best-Fit Probability Distributions and

Return Periods for Maximum Monthly Rainfall in

Bangladesh, Climate, 6(9),

https://doi.org/10.3390/cli6010009, 2018.

[13] Abdullah A. Abbas,, Nashaat A. Ali , Gamal

Abozeid , and Hassan I. Mohamed, COMPARISON

OF DIFFERENT METHODS FOR ESTIMATING

MISSING MONTHLY RAINFALL DATA, Twenty-

Second International Water Technology Conference,

IWTC22, Ismailia, 12-13 September 2019

[14] Markovic, R.D. Probability Functions of Best Fit

to Distributions of Annual Precipitation and Runoff;

Colorado State University Hydrology Paper No. 8;

Colorado State University: Fort Collins, CO,

USA,1965.

[15] Vogel, R.M.; Kroll, C.N. Low-Flow Frequency

Analysis Using Probability-Plot Correlation

Coefficients. J. Water Resour. Plan. Manag., 115, 338–

357, https://doi.org/10.1061/(ASCE)0733-

9496(1989)115:3(338) , 1989.

[16] Cunnane, C. Unbiased plotting positions—A

review. J. Hydrol. 37, 205–222,

https://doi.org/10.1016/0022-1694(78)90017-3, 1978.

[17] Wilks, D.S. Comparison of three-parameter

probability distributions for representing annual

extreme and partial duration precipitation series. Water

Resour. Res., 29, 3543–3549,

https://doi.org/10.1029/93WR01710, 1993.

[18] Chamber,J.; Cleveland, W.; Kleiner, B.; Tukey, P.

Graphical Methods for Data Analysis. Biomtric,

January 1983.

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Creative Commons Attribution License 4.0

(Attribution 4.0 International, CC BY 4.0)

This article is published under the terms of the Creative

Commons Attribution License 4.0

https://creativecommons.org/licenses/by/4.0/deed.en_US

Authors contributions:

The contribution of the first Author Emad was

collect data, writing and editing the manuscript.

The contribution of the second Author Metri was

read and editing the article.

Tables Capture

Table 1. The Statistical Parameters that were used in this study.

Table 2. Plotting Position Methods and Probabilistic Distribution Methods.

Table 3. the values of the statistical parameters.

Table 4. the results of RSME for all the plotting positions.

Table 5. The results of return periods (T) and return level (Xt) for the four different plotting positions.

Figures Capture

Figure 1. Shows the map of drainage of the study area (the study area represents by rectangle in Jordan Map to the

right).

Figure 2. the annual precipitation all over Jordan, Ajlun and Al-Salt governorates located within the range of 700 –

900 mm/Y.

Figure 3. Annual rainfall (Lift) and the Maximum Day Annual Rainfall (Right) distributed for the period of 31 years

(1988-2018).

Figure 4. Gumble Plotting Position of rainfall distribution: The vertical axis represents the maximum rainfall

(mm/day) and the horizontal axis is the quintiles of the percent point.

Figure 5. The Cunnane Plotting Position extreme value distribution of rainfall.

Figure 6. The Weibull Plotting Position extreme value distribution of rainfall.

Figure 7. The Gringorten Plotting Position extreme value distribution of rainfall.

Figure 8. Log- Normal Distribution, with Griguton, Gunna, Weibull and Gumble plotting Positions.

Figure 9. Normal Distribution, with Griguton, Gunna, Weibull and Gumble plotting Positions.

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