Improved Relationships for Peak Discharge Estimation at High Return Periods Using Geomorphological Characteristics: Case Study at Sultanate of Oman

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Improved Relationships for Peak Discharge Estimation at High Return Periods Using Geomorphological Characteristics: Case Study at Sultanate of Oman

Ayman G. Awadallap*, Samar A.H. Ali2 and Nabil A. Awadallap

1 Civil Engineering Dept., Faculty of Engineering, Fayoum University, Egypt

2 Ministry of Water Resources and Irrigation, Egypt.

Abstract Flash flooding can occur, even in hyper-arid regions, due to relatively short, intense burst of rainfall such as during a thunderstorm. Even though flash floods are localized, they present a significant hazard because of their unpredictability and commonly very short duration. To estimate peak discharges of flash floods, morphometric analysis is used to understand the nature of the hydrological processes in a basin, in order to develop a relationship that enables estimation of peak discharge values, in terms of morphometric parameters. The study is conducted using 28 flow gauging stations, in the northern region of Sultanate of Oman, in two steps. The first step is the extraction of morphometric parameters from available Digital Elevation Models. The second step is to develop relationships to estimate peak discharges, at different return periods, using linear and nonlinear regression methods. The best obtained relationship is a nonlinear one in terms of the total number of streams across all orders, the relative relief ratio, and the effective rainfall, with a coefficient of determination ranging from 0.979 to 0.997 and mean percentage absolute errors from 26% to 45%, for examined return periods.

Keywords Flood, Morphometric Parameters, Peak discharge, Regression, Arid Region, Oman.

  1. INTRODUCTION

    Flash floods in arid regions have benefits and harms. The immediate impacts of flash flooding include loss of human life, damage to property, damage to power transmission and sometimes power generation, destruction of crops and loss of livestock. This triggered attention to many factors that affect floods such as topography, nature of the soil, and vegetated cover percentage to produce relationships to calculate the peak flow discharges at different return periods. Some of those relationships were expressed in terms of morphometric parameters, which result from the morphometric analysis of the drainage basins.

    Several studies have explored the use of geomorphological characteristics. Developed relationships cover all climatic conditions. However, the current literature review focusses mainly on approaches to estimate flash floods and/or those developed in arid and semi-arid regions. Angillieri [1] studied the geomorphological characteristics of a basin with a stream order of 5 and a parallel dendritic pattern. The drainage density was found to be the parameter that affects floods patterns most. Bhatt and Ahmed [2] utilized GIS to extract the morphometric parameters to assess which of them influence flooding hazards the most. The main identified parameters include the

    ruggedness number () and the relief ratio (), the stream frequency (), the mean bifurcation ratio ( ), and the drainage density (). Six large basins were selected in Saudi

    Arabia by Shi [3] to assess flood hazards. The morphometric

    basins parameters of the six basins and their related 203 sub- basins were combined to develop a relationship that predicts peak discharge values at different return periods provided.

    In Oman, which is the study area of the current research, Al- Rawas [4] considered parameters like the drainage density, the relief ratio, the basin relief, the form factor, and the total basin area. He has also shown that it is possible to improve predictions of peak flow discharges by introducing other factors such as the extent of urbanization and the percentage of the vegetated cover area, which resulted in a significant improvement of peak discharges estimation, especially at high return periods. The developed equation was in terms of basin relief, relief ratio, total basin area, and the vegetated cover. The Ministry of Transport & Communications [5], Directorate of Roads and Land Transport, Sultanate of Oman, proposed an equation for northern Oman to predict the peak discharges at various return periods in terms of the catchment area, the slope of the maximum stream length within the basin, the estimated rainfall depth at the same return period, the runoff to rainfall ratio which was calculated based on the Soil Conservation Service SCS curve number model.

    Morphometric analysis was also used for prioritization of sub-watersheds [6], extracting basin parameters using remote sensing [7,8,9,10,11], understand Paleo fluvial systems in the Kuwait [12], geo-hydrological studies [13], extract hydrologic indices [14], comparison between manual and automated delineation of basins [15], drainage basin asymmetry analysis [16], and many other applications.

    The current research aims to investigate relationships between peak discharges and a large set of morphometric parameters, to identify the most influencing to be used in an arid region. Furthermore, to allow benefits in an operational context, these relationships have to produce accurate discharges and to show a robust behavior across return periods. The paper is organized as follows: After this introduction, the next two sections present the case study and the available data followed by the methodology. The results and discussion come next and finally the research conclusions and recommendations for future research.

  2. CASE STUDY AND AVAILABLE DATA

    The study focusses on the northern region facing the Arabian Gulf of Sultanate of Oman, which occupies the southeastern part of the Arabian Peninsula. The area of Oman

    is close to 309 500 2 with most of it being an arid zone,

    subject to many flash floods that occurred in the years 1987,

    1989, 1997, 2002, 2003, 2005, 2007, 2010, 2015 and 2020. The

    Mean Annual Rainfall () is 51 mm for the entire country, ranging from less than 20 mm in its deserts to over 350 mm in

    its rugged mountains. The study area consists of 10 basins monitored by 28 streamflow gauging stations (Figure 1).

    The streamflow and rainfall frequency analysis results are obtained from the hydrology section report, issued by the Ministry of Transport and Communications [5], Directorate of roads and Land Transport, Oman, in the framework of the elaboration of the Highway Design Manual. Table S1 (in the supplementary material) summarizes the frequency analysis results of the flow gauging stations and the areal average of the daily rainfall depths at the same return periods.

    1. Basins identification and preprocessing

      Using 30-m DEM, whose source was the Shuttle Radar Topography Mission (SRTM) version 3 Plus [17], ten major basins are identified englobing all flow gauging stations. The extraction of the morphometric parameters of 28 drainage basins is created via ARC Hydro extension in ArcMap 10.4. These morphometric parameters are subdivided into four categories: drainage network, geometry, drainage texture, and basin relief parameters. Every category contains a group of parameters that describe the characteristics of the drainage basins.

    2. Calculation of morphometric parameters

      1. Drainage network parameters

        In this category, the Stream Order (), is determined based on the top-down Strahler method [18]. The Stream Number

        () defined as the number of streams in each order, the Total Numbers of Streams across all orders ( ), and the Stream Length (), which is the total length of individual stream

        segments of each order, are alsocalculated [19]. Finally, the

        Bifurcation Ratio () is calculated, as per Equation (1) [20].

        =

        +1

      2. Geometry parameters

        (1)

        Geometry parameters include the areal and linear

        characteristics, such as the total surface area (), the total basin perimeter (), and the basin length (), defined as the

        maximum dimension of the basin in the direction of the main

        drainage channel [21]. It encompasses also the form parameters that describe the shape of the basin, such as the

        Form Factor ( ) [22], the Elongation Ratio () [21], defined

        by equations 2 and 3, respectively.

        =

        2

        (2)

        =

        (3)

        where is the diameter of the circle with the same area as

        that of the basin.

      3. Drainage texture parameters

        These parameters include the Drainage density (), defined as the ratio between the summation of all streams

        length in a drainage basin to the area of the same drainage

        basin [23], the Stream frequency (), which is the ratio between the number of streams in one basin to the basin area,

        and the Constant of channel maintenance (), which is the

        inverse of the drainage density [21].

        =

        (4)

        Fig. 1. Study area and location of available flow gauging stations.

  3. METHODOLOGY

    The methodology of this study consists of two stages: (i) Preparing input data through Basins identification and

    =

    =

    1

    (5)

    (6)

    preprocessing then the extraction of morphometric parameters

    from the digital elevation model (DEM) and through determining the effective rainfall; (ii) developing an equation to estimate the peak discharges at different return periods using linear and nonlinear regression analyses.

      1. Basin relief parameters

    These parameters include the Total Basin Relief (), which is the difference between the maximum height of the basin and

    the height of the outlet for the same basin, the Relief Ratio

    (), which is the ratio of the total basin relief to the basin length, the Relative Relief Ratio (), which is the ratio between the total basin relief () and total basin perimeter ()

    [24], to finally obtain the value of the Ruggedness Number

    (), which is the product of by [25].

  4. RESULTS AND DISCUSSION

    A. Morphometric characteristics of the 28 drainage basins

    =

    ()

    (7)

    We present hereafter the major morphometric

    characteristics of the 28 drainage basins. Starting by the

    = () (8)

    = × (9)

    1. Calculating the effective rainfall depth

      The effective rainfall, which is also used as a predictor of peak discharges, is calculated using the well-acknowledged Soil Conservation Service Curve Number (SCS-CN) [26].

      2

      drainage networks characteristics, five basins are of second-

      order, twelve basins are of third-order, nine basins are of fourth order, and two basins area of fifth-order. On the other hand, the values of bifurcation ratios range between 2 and 7 and higher bifurcation ratio values are observed at lower stream orders in the mountains, while lower bifurcation ratio values are observed at higher stream orders where the area is characterized as flat. As for the average bifurcation ratio values, the

      = ( 0.2)

      + 0.8

      (10)

      maximum value is 6 for station No. 5, while the minimum value

      is 2.56 for station No. 1.

      Where is the effective rainfall depth (mm) corresponding to the rainfall depths at return period , is the rainfall depth (mm) at return period , is the potential storage of the soil (mm), which takes into account the , calculated as follows:

      1000

      = ( 10) × 25.4 (11)

      The relies on determining the hydrologic soil group and

      the land cover. Hydrologic Soil Groups are obtained from the

      Global Hydrologic Soil Groups (HYSOGs250m) dataset and hence the areal averages of the Curve Number for each basin are determined assuming a desert shrub cover of poor condition [27].

    2. Developing relationships to estimate peak discharge using morphometric parameters

    Relationships are developed to estimate peak discharges at various return periods equation. Linear and nonlinear regression equations are tested. The nonlinear equation is of the form:

    = 1 × 2 × × (12)

    where:

    is the peak discharge at return period n.

    1, 2, , are input variables.

    , , , are the regression coefficients.

    A stepwise regression method is used, via the Statistical

    Package for Social Sciences (SPSS) software [28], to select the most influential morphometric variables affecting the discharges. Beside the verification of the statistical significance of the regression coefficients to be included and the overall significance of the developed relationships, three performance criteria are calculated to assess the goodness of

    fit: 2 (the adjusted coefficient of determination), the Mean Absolute Percentage Error () and the Roof Mean Square Error () defined as follows:

    As for the geometrical and the drainage texture characteristics, two of the studied basins are circular, while the remaining basins are elongated with the possibility of low peak discharges. It is also found that the drainage densities are relatively low, ranging from 0.53 to 0.30, with an average value of 0.40. Investigating the stream frequencies, it is found that the frequency values are also low, where the maximum value is

    0.10 and the minimum is 0.05 with an average value of 0.08. On the other hand, the constant channel maintenance values are high, which reflects strong control of lithology, where the range is between 3.36 and 1.89 with an average value of 2.55.

    The drainage texture values are less than 2, which indicates that the surface of the basins is very coarse. As for the infiltration number values, they range from 0.05 to 0.02 with an average value of 0.03. The lengths of overland flow range from

    1.68 km to 0.95 km. These high values indicate decreased values of drainage density and surface runoff with weak development of the drainage density.

    For the relief characteristics, the maximum ruggedness number is 0.98 and the minimum number is 0.18 while the average is equal to 0.56, where these weak values express that the study region has weak dissection and erosion.

    B. Developing relationships to estimate peak discharge

    To develop an equation to estimate peak discharges at 2, 5, 10, 25, 50 and 100-year return periods, linear regression is first explored. The application of the linear regression with a constant term shows that the most influential variables are the area, the rainfall depths at the 100-year return period, the effective rainfall depths corresponding to the rainfall depths at the 100-year return period, and the total lengths of streams orders. By verifying the parameters coefficients resulting from the linear regression analysis, it is noticed that the coefficient of the intercept is not statistically significant. Deleting the

    = 100

    1

    | |

    (13)

    intercept term from the regression equation, the most influential

    = 1

    ||

    parameters are the number of stream order 4, the length of

    stream order 1, the length of stream order 4, the total surface

    Where:

    =

    1

    ( )2

    =1

    (14)

    area, the rainfall depths at 100-year return period, and the effective rainfall depths corresponding to the rainfall depths at 100-year return period. The linear equation for the 100-year

    , is the observed peak dscharge;

    is the estimated peak discharge;

    is the average value for the observed series; and

    is the number of data points.

    return period can be written as follows.

    100 = 448.724 0.0151 0.0414 + 5.43

    8.14100 + 14.95100 (15)

    where: 100 is the peak discharge at 100-year return period, 4 is the stream number of 4th stream order, 1 is the length of streams of the 1st order, 4 is the length of streams of the 4th

    order, is the Area, 100 is the rainfall depths at the 100-year

    100

    To obtain an improved relationship, the nonlinear option is

    return period and

    is the effective rainfall depths

    explored and is transformed to the linear form using natural

    corresponding to the rainfall depths at the 100-year return

    period. This equation produces a of 347.4 m3/s, a

    logarithms. The obtained relationship is described by equation

    16.

    of 40.78% (which is rather high) with an adjusted 2 of 0.95.

    Tables I to III provide the results of the analysis, while Figure

    2 presents a plot of the predicted vs. the observed 100.

    Relationships for other return periods are also explored;

    however, for 2-year and 5-year return periods, no satisfactory equation, with statistically significant coefficients, is found.

    Fig. 2. Predicted vs. Observed 100 using linear regression TABLE I.

    Model

    Adjusted

    Std-Error of the Estimate

    6

    0.975

    0.951

    0.938

    391.7322402

    TABLE II. MODEL SUMMARY FOR LINEAR REGRESSION WITHOUT INTERCEPT TERM

    ln 100 = 1.022 ln + 0.594 ln + 0.868 ln 100 (16) where 100 is the Peak discharge at the 100-year return period, is the total numbers of streams across all orders, Rp is the Relative Relief Ratio and 100 is the effective rainfall

    depths corresponding to the rainfall depths at the 100-year

    return period.

    The obtained relationship is simpler, yet it produces a lower

    (compared to the linear equation with a larger number of variables) of 32.37% (calculated in the original scale of

    variables), a of 335m3/s, with an adjusted 2 of 0.995.

    Tables IV to VI provide the full results of the analysis

    (calculated in the natural logarithm scale), while Figure 3

    presents a plot of the predicted vs. the observed 100. Relationships for all return periods are also explored. All

    coefficients are found statistically significant.

    TABLE V. MODEL SUMMARY FOR LINEAR REGRESSION OF NATURAL LOGARITHMS OF VARIABLES

    Model

    Adjusted

    Std-Error of the Estimate

    1

    0.996

    0.995

    0.994

    0.4025221

    TABLE VI. ANOVA TABLE FOR SECOND SCENARIO LINEAR REGRESSION OF NATURAL LOGARITHMS OF VARIABLES

    Model

    Sum of Squares

    Df

    Mean Square

    F

    Sig.

    1

    Regression

    1279.617

    3

    426.539

    2632.565609

    0.000

    Residual

    4.051

    25

    0.162

    Total

    1283.667

    28

    TABLE III. ANOVA TABLE FOR SECOND SCENARIO LINEAR WITHOUT INTERCEPT TERM

    Model

    Sum of Squares

    Df

    Mean Square

    F

    Sig.

    6

    Regression

    66144088.756

    6

    11024014.793

    71.839

    0.000

    Residual

    3375991.257

    22

    153454.148

    Total

    69520080.013d

    28

    TABLE VII. COEFFICIENTS TABLE FOR LINEAR REGRESSION OF NATURAL LOGARITHMS OF VARIABLES

    Model

    Unstandardized Coefficients

    Standardized Coefficients

    t

    sig.

    B

    Std. Error

    Beta

    6

    ln

    1.022

    0.081

    0.485

    12.593

    0.000

    ln

    0.594

    0.201

    0.40

    2.960

    0.007

    100

    ln

    0.868

    0.063

    0.530

    13.839

    0.000

    TABLE IV.

    COEFFICIENTS TABLE FOR LINEAR REGRESSION WITHOUT INTERCEPT TERM

    Model

    Unstandardized Coefficients

    Standardized Coefficients

    t

    sig.

    B

    Std. Error

    Beta

    6

    5.427

    1.103

    2.194

    4.921

    0.000

    100

    14.946

    2.875

    0.746

    5.198

    0.000

    100

    -8.143

    1.894

    -0.694

    -4.299

    0.000

    4

    -0.041

    0.012

    -0.345

    -3.333

    0.003

    4

    448.721

    168.938

    0.222

    2.656

    0.014

    1

    -0.015

    0.006

    -1.125

    -2.566

    0.018

    Fig. 3. Predicted vs. Observed 100 using nonlinear regression

    By applying the same nonlinear form, for of streams of the 50-, 25-, 10-, 5-, and 2-year return periods, the following

    equations (17 to 21) are obtained:

    50

    the rainfall depths at 100-year return period. As for the nonlinear regression analysis, the developed relationship is in terms of the total numbers of stream across all orders, the

    ln 50 = 1.046 ln + 0.581 ln + 0.852 ln ln 25 = 1.1 ln + 0.603 ln + 0.809 ln 25

    10

    (17)

    (18)

    relative relief ratio, and the effective rainfall depths

    corresponding to the rainfall depths at the 100-year return

    period. The linear equation produces a of 40.78% with

    ln 10 = 1.247 ln + 0.733 ln + 0.662 ln (19)

    5

    an adjusted 2 of 0.95 but the nonlinear equation (which has a

    ln 5 = 1.419 ln + 0.931 ln + 0.414 ln ln 2 = 1.409 ln + 0.837 ln + 0.128 ln 2

    (20)

    (21)

    fewer number of input variables) shows better performance and

    produces a of 32.37% with an adjusted 2 of 0.995.

    The for 50, 25, 10, 5 and 2 are 26.1%,

    27.83%, 37.31%, 44.44% and 45.13%, respectively with

    adjusted 2 of 0.997, 0.996, 0.993, 0.986 and 0.979,

    respectively. Figures 4 and 5 show plots between the relative

    errors for various return periods and the total No. of streams across all orders and the relative relief ratio values.

    Fig. 4. Relative errors for various return periods vs.

    Fig. 5. Relative errors for various return periods vs.

  5. CONCLUSIONS AND RECOMMENDATIONS

The aim of this research is to develop relationships that estimate peak flow discharge at various return periods. The study area is located in the northern region of the Sultanate of Oman, which consists of 10 basins monitored by 28 peak flow discharges stations. Morphometric parameters are extracted and analyzed to shed light on the basins underlying hydrologic processes and their eventual response to floods.

Using a stepwise regression approach, linear and nonlinear relationships are developed between selected morphometric parameters and peak discharges at various return periods. A linear equation is developed in terms of the length of streams for order 4, the number of streams for order 4, the length of streams for order 1, the area, the rainfall depths at 100-year return period, and the effective rainfall depths corresponding to

Recommendations for future research include to extend the

study to more gauged basins in arid regions, to relate the morphological parameters to the time of concentration of the basins calculated via calibration of the observed flows, and to extend the study to produce relationships to estimate average runoff values and not only peak discharges.

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Published by : http://www.ijert.org

International Journal of Engineering Research & Technology (IJERT)

ISSN: 2278-0181

Vol. 11 Issue 04, April-2022

TABLE S1. FREQUENCY ANALYSIS RESULTS OF THE STREAMFLOW AT THE GAUGING STATIONS IN NORTH OMAN

Return Periods (years) Return Periods (years)

2

5

10

25

50

100

2

5

10

25

50

100

Station ID

Rainfall (mm)

Flow (m3/sec)

Al Haju

25.5266

45.9267

61.7977

85.6321

106.8273

131.7804

63.1

149.3

223.1

340.9

450.3

581.9

Al Khawd

28.0086

45.0199

57.8313

77.3542

95.7721

119.5013

182.2

458.7

722.2

1,187.20

<>1,662.40

2,282.90

Al Qabil

25.5543

45.3459

60.4363

82.5873

102.0995

125.0799

257.1

466.9

601.3

766.2

885.1

1,000.30

Aswad

29.0159

51.4752

68.2597

92.1047

111.9861

133.8655

56.9

170.2

305.8

602.8

974.3

1,552.20

Az-Zahir 1

27.3975

45.6224

58.2137

74.7786

88.8173

105.6090

49.2

105.9

155.6

236.9

314

408.6

Bayda

28.9517

49.0594

64.3791

86.5181

105.2802

126.1991

53.9

136.7

218.9

369.9

530.3

746.6

Dasir

28.0344

44.0919

55.5522

71.8504

86.0520

102.9803

77.5

147.7

207.9

304.2

393.8

501.7

Fulayj

29.5455

48.7032

63.4086

85.3456

104.9945

128.3451

75.7

191.6

310.2

534.4

778.5

1,115.20

Ghuzayn

25.8687

42.4364

55.2441

74.2861

91.1553

110.8873

118.3

291.9

469.2

803.1

1,166.00

1,665.60

Hajir 1

22.2801

42.4666

59.6023

87.5287

114.5510

148.8266

21.6

69.2

128.9

265.9

444.7

733.2

Hajir 2

19.1242

39.0019

56.8761

87.3439

117.9233

157.6807

21.1

54.5

84.8

136.1

186.5

250.1

Hajir 3

21.0202

47.6535

74.0773

123.2076

176.4796

250.1670

50.55

112.18

159.26

226.99

283.96

346.88

Hammam

22.9344

44.2485

62.2564

91.5553

120.1050

156.7727

44.8

101.8

166.4

300.6

460.4

698.5

Hayl

28.7206

46.5384

59.6603

78.4386

94.4864

112.7616

300.6

578.8

792.3

1100.9

1361.5

1650.4

Houqain

31.9282

47.8533

58.1182

70.8629

80.1957

89.3757

145.91

326.14

453.22

623.19

756.45

895.08

Ibra

43.7961

67.5225

83.3288

103.9365

119.9982

136.8623

184.21

464.112

723.35

1169.03

1613.32

2181.05

Lihban

27.8773

42.6513

53.8911

70.6816

86.0750

104.8581

112.8

228.5

331.3

501.5

665.1

867.8

Maul

21.9370

46.8962

70.5411

113.0987

158.1655

219.5834

47.4

114.6

170.6

257.9

337.2

430.7

Mazara 1

25.4710

45.5658

61.3427

85.5396

107.7388

134.7869

483.6

1,192.90

1,878.50

3,104.90

4,374.40

6,050.10

Mulayinah

28.0036

46.5979

60.6756

80.9737

98.1891

117.4469

234.9

461.4

627

856.2

1,041.80

1,240.30

Mutarid

25.3417

44.5111

58.8649

79.7141

98.0799

119.8371

91.2

179.7

242.1

325.7

391.1

459.3

Qalhat

22.6451

37.3307

47.3589

60.3282

71.0200

83.4860

60.5

191.9

340.4

647.9

1,013.40

1,556.90

Riqqah

28.2156

45.8042

58.5863

76.4321

91.1606

107.2898

69.6

133.6

192.7

293.7

394.1

521.8

Sabakh

28.2540

48.0942

62.8274

83.6653

100.9762

119.9733

77.9

164.1

241.3

369.8

494.1

648.9

Sur

25.4959

44.8019

59.7473

79.8306

98.8334

125.1173

150.9

341.5

524.4

849.2

1,183.10

1,621.40

Yanbu

27.7224

45.4225

58.4640

76.8554

92.1386

108.9188

47.5

91.8

121.1

158.4

186.1

213.6

Al Bih Near Salhad

45.7548

74.2834

92.6443

116.1033

134.1467

152.9760

52.1

112.6

162.9

241.3

312.4

396.2

Khasab Near Khasab

27.8773

42.6513

53.8911

70.6816

86.0750

104.8581

81.8

191.9

296.5

480.9

668.9

913.9

IJERTV11IS040084

www.ijert.org

(This work is licensed under a Creative Commons Attribution 4.0 International License.)

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