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Journal of Arid Land
Journal of Arid Land  2021, Vol. 13 Issue (8): 801-813    DOI: 10.1007/s40333-021-0102-5     CSTR: 32276.14.s40333-021-0102-5
    
Mathematical and statistical modeling of morphometric and planar parameters of barchans in Pashoeyeh Erg in the west of Lut Desert, Iran
Hossein GHAZANFARPOUR1, Mohsen POURKHOSRAVANI1,*(), Sayed H MOUSAVI2, Ali MEHRABI3
1 Department of Geography and Urban Planning, Shahid Bahonar University of Kerman, Kerman 7618965984, Iran
2 Department of Geography and Ecotourism, Faculty of Natural Resources and Geosciences, University of Kashan, Kashan 8731753153, Iran
3 Department of Geography and Urban Planning, Shahid Bahonar University of Kerman, Kerman 7618965984, Iran
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Abstract  

Barchan dunes are among the most common accumulative phenomena made by wind erosion, which are usually formed in regions where the prevailing wind direction is almost constant throughout the year and there is not enough sand to completely cover the land surface. Barchans are among the most common windy landscapes in Pashoueyeh Erg in the west of Lut Desert, Iran. This study aims to elaborate on morphological properties of barchans in this region using mathematical and statistical models. The results of these methods are very important in investigating barchan shapes and identifying their behavior. Barchan shapes were mathematically modeled by simulating them in the coordinate system through nonlinear parabolic equations, so that two separate equations were calculated for barchan windward and slip-face parabolas. The type and intensity of relationships between barchan morphology and mathematical parameters were determined by the statistical modeling. The results indicated that the existing relationships followed the power correlation with the maximum coefficient of determination and minimum error of estimate. Combining the above two methods is a powerful basis for stimulating barchans in virtual and laboratory environments. The most important result of this study is to convert the mathematical and statistical models of barchan morphology to each other. Focal length is one of the most important parameters of barchan parabolas, suggesting different states of barchans in comparison with each other. As the barchan's focal length decreases, its opening becomes narrower, and the divergence of the barchan's horns reduces. Barchans with longer focal length have greater width, dimensions, and volume. In general, identifying and estimating the morphometric and planar parameters of barchans is effective in how they move, how much they move, and how they behave in the environment. These cases play an important role in the management of desert areas.

Key words： barchan dunes      desert      parabolic equations      statistical model      wind erosion      Pashoueyeh Erg      Lut Desert     
Received: 21 November 2020      Published: 10 August 2021
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GHAZANFARPOUR Hossein
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MOUSAVI Sayed H
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Hossein GHAZANFARPOUR, Mohsen POURKHOSRAVANI, Sayed H MOUSAVI, Ali MEHRABI. Mathematical and statistical modeling of morphometric and planar parameters of barchans in Pashoeyeh Erg in the west of Lut Desert, Iran. Journal of Arid Land, 2021, 13(8): 801-813.

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http://jal.xjegi.com/10.1007/s40333-021-0102-5     OR     http://jal.xjegi.com/Y2021/V13/I8/801

Month Precipitation (mm) Temperature (°C) Humidity (%)
Jan 6.40 13.70 36.90
Feb 9.90 17.30 33.80
Mar 8.50 23.60 26.80
Apr 1.50 29.90 23.30
May 1.20 30.10 17.40
Jun 0.20 40.10 12.80
Jul 0.00 41.20 12.00
Aug 0.00 39.20 12.30
Sept 0.00 35.40 13.30
Oct 0.00 29.80 15.20
Nov 1.20 21.10 24.60
Dec 3.30 14.90 31.70
Table 1 Monthly average of climatic parameters in the study area (2003-2019)
Sample barchan Length (m) Width (m) Perimeter (m) Area (×103 m²) Height (m) Volume (×103 m³)
Barchan 1 270.25 290.13 605.45 8.81 3.10 4.55
Barchan 2 156.51 185.95 649.96 19.66 3.50 11.47
Barchan 3 220.45 235.25 555.18 8.76 2.60 3.80
Barchan 4 737.88 1100.02 4632.54 190.54 9.00 285.69
Barchan 5 154.69 153.37 613.25 15.22 3.30 8.37
Barchan 6 570.35 840.85 3800.25 173.76 8.20 237.37
Barchan 7 177.56 164.13 631.61 18.35 3.30 10.09
Barchan 8 350.15 355.32 900.52 28.71 4.80 22.96
Barchan 9 674.54 946.72 3912.14 173.89 8.60 249.15
Barchan 10 450.55 600.35 3580.65 13.65 7.40 16.83
Barchan 11 180.71 193.63 746.80 17.99 3.00 8.99
Barchan 12 196.63 196.87 710.21 25.98 3.30 14.28
Barchan 13 100.85 110.45 430.65 8.60 2.50 3.58
Barchan 14 735.97 879.93 3824.34 138.15 8.10 186.43
Barchan 15 150.22 160.85 600.95 17.56 2.80 8.19
Barchan 16 110.86 120.82 440.21 8.61 2.60 3.73
Barchan 17 155.21 168.48 593.51 17.53 2.60 7.60
Barchan 18 190.35 210.68 780.45 25.39 3.20 13.54
Barchan 19 790.19 776.33 3349.39 134.97 7.60 170.89
Barchan 20 125.64 115.93 476.11 7.75 2.00 2.59
Barchan 21 125.15 140.35 514.91 10.98 2.00 3.66
Barchan 22 210.23 220.56 540.24 8.71 2.70 3.92
Barchan 23 300.25 308.55 860.45 28.66 4.50 21.48
Barchan 24 183.13 196.32 720.93 24.71 2.50 10.29
Barchan 25 815.94 722.44 3250.63 119.11 7.00 138.90
Barchan 26 159.91 155.87 602.39 15.38 3.30 8.46
Barchan 27 161.91 158.87 605.39 15.38 3.50 8.97
Barchan 28 160.52 190.95 651.96 19.67 3.70 12.12
Barchan 29 198.95 209.66 782.51 28.54 4.10 19.50
Barchan 30 699.91 1111.12 4644.49 189.99 8.90 281.71
Barchan 31 149.98 150.95 609.97 15.20 3.50 8.87
Barchan 32 210.81 212.53 789.28 28.55 4.00 19.03
Barchan 33 180.25 168.52 638.12 18.36 3.70 11.32
Barchan 34 200.15 215.65 790.15 27.19 4.00 18.12
Barchan 35 595.55 895.75 3850.88 173.80 7.80 225.85
Barchan 36 150.12 165.58 570.65 14.76 3.50 8.61
Barchan 37 195.15 211.51 783.34 27.18 3.60 16.30
Barchan 38 170.75 183.63 735.85 18.18 3.10 9.39
Barchan 39 180.75 181.88 690.95 25.86 3.00 12.93
Barchan 40 600.85 750.25 3725.95 13.80 7.80 17.93
Barchan 41 140.47 159.91 560.54 14.64 3.00 7.32
Barchan 42 120.52 130.65 450.53 8.76 2.80 4.09
Barchan 43 150.25 170.35 605.57 17.66 3.20 9.41
Barchan 44 90.46 100.85 420.45 8.59 2.20 3.15
Barchan 45 180.95 200.93 775.25 25.37 3.10 13.11
Barchan 46 183.91 203.02 768.23 25.36 3.00 12.68
Barchan 47 750.65 736.55 3295.95 135.13 7.50 168.84
Barchan 48 120.85 110.95 460.76 7.69 2.40 3.08
Barchan 49 130.15 150.21 525.15 11.06 2.30 4.24
Barchan 50 170.45 180.54 620.95 24.61 2.20 9.02
Table 2 Morphometric and planar parameters of barchans in the study area
Fig. 1 A schematic representation of barchan's morphometric and planar parameters (Hesp ans Hastings, 1998; Sauermann et al., 2000; Daniell and Hughe, 2007). Lo, length of the windward side; Ls, length of the slip-face; La, length of the right horn; Lb, length of the left horn; Wa, width of the right side; Wb, width of the left side. The yellow color indicates the windward side, the orange color indicates the slip-face of the barchan, and the gray color indicates the barchan.
Fig. 2 Image of a barchan with its parabolas and components in the coordinate system. In this image, O is the origin of the coordinate system, F is the coordinates of the focus, S is the coordinates of the parabola's vertex, p is the distance between the focus and vertex, and G is the directrix of the parabola.
Parameter Minimum Maximum Difference Mean SD Skewness
Length (m) 110.87 815.94 705.07 310.64 263.21 1.250
Width (m) 115.93 1100.02 984.09 350.36 325.10 1.393
Perimeter (m) 440.20 4632.54 4192.34 1428.70 1426.79 1.355
Area (m2) 7747.12 191,000.00 183,000.00 51,723.00 60,823.68 1.407
Height (m) 2.00 9.00 7.00 4.27 2.33 1.166
Volume (m3) 2582.27 286,000.00 283,000.00 58,838.00 91,642.22 1.578
Table 3 Statistical characteristics of the studied barchans in the study area
Samples for modeling barchan parabolas Parabola p (m) Coordinates of the vertex Equation of the directrix Coordinates of the focus Parabola equation
Barchan 1 Windward side 15.45 0.00, 0.00 x= -15.45 15.45, 0.00 y2=61.798x
Slip-face 11.60 91.46, 0.00 x=79.86 103.07, 0.00 y2=46.42(x-91.46)
Barchan 2 Windward side 16.56 0.00, 0.00 x= -16.56 16.56, 0.00 y2=66.260x
Slip-face 22.84 129.11, 0.00 x=106.27 151.95, 0.00 y2=91.36(x-129.11)
Barchan 3 Windward side 19.59 0.00, 0.00 x= -19.59 19.59, 0.00 y2=78.350x
Slip-face 16.12 135.82, 0.00 x=119.69 151.94, 0.00 y2=64.48(x-135.82)
Barchan 4 Windward side 30.87 0.00, 0.00 x= -30.87 30.87, 0.00 y2=123.501x
Slip-face 42.15 295.19, 0.00 x=253.04 337.33, 0.00 y2=168.61(x -295.19)
Barchan 5 Windward side 18.12 0.00, 0.00 x= -18.12 18.12, 0.00 y2=72.470x
Slip-face 9.05 82.49, 0.00 x=73.44 91.54, 0.00 y2=36.20(x-82.49)
Barchan 6 Windward side 17.85 0.00, 0.00 x= -17.85 17.85, 0.00 y2=71.390x
Slip-face 23.43 107.12, 0.00 x=83.69 130.55, 0.00 y2=93.73(x-107.12)
Barchan 7 Windward side 16.74 0.00, 0.00 x= -16.74 16.74, 0.00 y2=66.980x
Slip-face 17.31 134.01, 0.00 x=116.71 151.32, 0.00 y2=69.23(x-134.012)
Barchan 8 Windward side 29.82 0.00, 0.00 x= -29.83 29.83, 0.00 y2=119.304x
Slip-face 42.86 291.33, 0.00 x=248.47 334.20, 0.00 y2=171.45(x-291.33)
Barchan 9 Windward side 16.80 0.00, 0.00 x= -16.80 16.80, 0.00 y2=67.208x
Slip-face 9.33 107.83, 0.00 x=98.49 117.17, 0.00 y2=37.34(x-107.83)
Barchan 10 Windward side 15.31 0.00, 0.00 x= -15.37 15.37, 0.00 y2=61.470x
Slip-face 21.97 110.12, 0.00 x=88.15 132.09, 0.00 y2=87.89(x-110.12)
Barchan 11 Windward side 23.44 0.00, 0.00 x= -23.44 23.44, 0.00 y2=93.750x
Slip-face 35.05 145.14, 0.00 x=110.08 180.19, 0.00 y2=140.21(x-145.14)
Barchan 12 Windward side 38.55 0.00, 0.00 x= -38.55 38.55, 0.00 y2=154.197x
Slip-face 51.55 237.40, 0.00 x=185.85 288.94, 0.00 y2=206.19(x-237.397)
Barchan 13 Windward side 12.11 0.00, 0.00 x= -12.11 12.11, 0.00 y2=48.440x
Slip-face 9.86 75.95, 0.00 x=66.08 85.81, 0.00 y2=39.45(x-75.95)
Barchan 14 Windward side 14.10 0.00, 0.00 x= -14.10 14.10, 0.00 y2=56.420x
Slip-face 17.73 114.15, 0.00 x=96.41 131.88, 0.00 y2=70.93(x-114.15)
Barchan 15 Windward side 21.50 0.00, 0.00 x= -21.50 21.50, 0.00 y2=85.990x
Slip-face 25.08 128.38, 0.00 x=103.30 153.45, 0.00 y2=100.31(x-128.38)
Barchan 16 Windward side 51.52 0.00, 0.00 x= -51.52 51.52, 0.00 y2=206.091x
Slip-face 64.75 195.17, 0.00 x=130.42 259.93, 0.00 y2=259.012(x-195.17)
Barchan 17 Windward side 12.39 0.00, 0.00 x= -12.39 12.39, 0.00 y2=49.560x
Slip-face 17.46 60.93, 0.00 x=43.47 78.40, 0.00 y2=69.85(x-60.93)
Barchan 18 Windward side 13.23 0.00, 0.00 x= -13.24 13.24, 0.00 y2=52.940x
Slip-face 8.69 83.08, 0.00 x=74.39 91.77, 0.00 y2=34.76(x-83.08)
Barchan 19 Windward side 19.09 0.00, 0.00 x= -19.09 19.09, 0.00 y2=76.370x
Slip-face 18.72 130.46, 0.00 x=111.74 149.18, 0.00 y2=74.88(x-130.46)
Barchan 20 Windward side 57.27 0.00, 0.00 x= -57.27 57.27, 0.00 y2=229.870x
Slip-face 72.22 188.11, 0.00 x=115.89 260.33, 0.00 y2=288.88(x-188.108)
Table 4 Results of mathematical modeling of the studied barchans in the study area using parabolic equations
Sig. SE R2adj R2 r Type of
relationship		 Parameters
0.015 0.156 0.955 0.970 0.985 Power Focal length & width
0.024 0.311 0.929 0.952 0.976 Power Focal length & length
0.190 0.109 0.943 0.962 0.981 Power Focal length & height
00.22 0.247 0.935 0.957 0.978 Power Focal length & perimeter
0.006 0.148 0.983 0.989 0.994 Power Focal length & area
0.008 0.250 0.975 0.984 0.992 Power Focal length & volume
Table 5 Correlations between the focal length of the windward slope parabola and the morphometric and planar parameters of barchans in the study area
Fig. 3 Relationships between the focal length of windward slope parabola and the morphometric and planar parameters of barchans in the study area. (a), length; (b), width; (c), volume; (d), height; (e), perimeter; (f), area.
Sig. SE R2adj R2 r Type of relationship Parameters
0.107 0.497 0.695 0.797 0.893 Power Focal length & width
0.160 0.887 0.558 0.705 0.840 Power Focal length & length
0.144 0.288 0.599 0.732 0.856 Power Focal length & height
0.126 0.577 0.645 0.763 0.874 Power Focal length & perimeter
0.114 0.650 0.677 0.785 0.886 Power Focal length & area
0.122 0.934 0.657 0.772 0.878 Power Focal length & volume
Table 6 Correlations between the focal length of the slip-face parabola and the morphometric and planar parameters of barchans in the study area
Fig. 6 Relationships between the focal length of slip-face parabola and the morphometric and planar parameters of barchans in the study area. (a), length; (b), width; (c), volume; (d), height; (e), perimeter; (f), area.
Parameters Equation
parameter		 Unstandardized
coefficient		 SE t Sig. Equation
Focal length & width Constant 0.061 0.075 0.814 0.501 p=0.061W2.843
Power 2.834 0.410 6.917 0.020
Focal length & length Constant 0.247 0.210 1.176 0.361 p=0.247L2.317
Power 2.317 0.283 8.176 0.150
Focal length & height Constant 0.064 0.038 1.656 0.240 p=0.64H0.124
Power 1.431 0.201 7.109 0.019
Focal length & perimeter Constant 0.124 0.171 0.729 0.542 p=0.124P3.041
Power 3.041 0.457 6.647 0.022
Focal length & area Constant 0.658 0.542 1.214 0.349 p=0.658A3.650
Power 3.650 0.275 13.297 0.006
Focal length & volume Constant 0.007 0.010 0.718 0.547 p=0.007V5.081
Power 5.081 0.464 10.947 0.008
Table 7 Correlations between the focal length of the windward slope parabola and the morphometric and planar parameters of barchans in the study area
Parameters Equation
parameter		 Unstandardized
coefficient		 SE t Sig. Equation
Focal length & width Constant 3.507 5.592 0.627 0.595 p=3.507W1.457
Power 1.457 0.521 2.799 0.107
Focal length & length Constant 8.589 13.402 0.641 0.587 p=8.589L1.115
Power 1.115 0.509 2.189 0.160
Focal length & height Constant 0.543 0.501 1.084 0.392 p=0.543H0.705
Power 0.705 0.301 2.340 0.144
Focal length & perimeter Constant 10.600 19.605 0.541 0.643 p=10.600P1.533
Power 1.533 0.604 2.539 0.126
Focal length & area Constant 138.689 288.796 0.480 0.678 p=138.689A1.836
Power 1.836 0.680 2.700 0.114
Focal length & volume Constant 12.553 37.580 0.334 0.770 p=12553V2.541
Power 2.541 0.977 2.599 0.122
Table 8 Correlation coefficients between the focal length of the slip-face parabola and the morphometric and planar parameters of barchans in the study area
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