Discrimination of Five Network Types Based on The Lengths

Discrimination of Five Network Types Based on The Lengths Distribution of Tributary

Junction AnglesKichul Jung

Prashanth MarpuTaha B M J OuardaTaha B.M.J. Ouarda

Hosni Ghedira

Program of Water and Environmental Engineering, Masdar Institute of Science and Technology, Abu Dhabi, UAE

ContentsContents

1.Introduction2.Methodology3.Data Set4 Result4.Result5.Conclusion

1. Introduction (1)

• Drainage networks typically present distinctivecharacteristics when they develop under certain

Dendritic Rectangular

characteristics when they develop under certaintopographic or physiographical constraints.

• A dendritic network tends to be tree-like withbalanced branching among channels ofbalanced branching among channels ofdifferent sizes and tributaries which merge atacute angles [1], [2], [3].

• A rectangular network has channel sinuosityA rectangular network has channel sinuosityintroduced by a large number of right anglebends and tributaries that sometimes merge atnearly right angles [1], [3].

Trellis

• A trellis network appears lattice-like becausesmall channels tend to be numerous and shortcomparing to the large channels, and tributariesoften merge at nearly right angles [1] [3]often merge at nearly right angles [1], [3].

1. Introduction (2)

• A parallel network has straight channel courses, majorchannels similar to a parallel form and tributaries

Parallel channels similar to a parallel form, and tributariesmerging at very acute angles [1], [2], [3], [4].

• A pinnate network appears feather-like with a majorchannel that is very straight and oriented in a singlechannel that is very straight and oriented in a singledirection and many small tributaries joining the majorchannel at regular intervals and vary acute angles [1], [2],[3].

• Different features of networks have led to improvementof classification systems using quantitative methods.

• One classification system is to use measures derived

Pinnate

yfrom scaling invariance [5]: 1) the incremental drainageareas along channels 2) the irregularity of stream courses3) the angles formed by merging tributary junctions.

1. Introduction (3)

• Abrahams and Flint (1983) Phillips and Schumm (1987) Ichoku• Abrahams and Flint (1983), Phillips and Schumm (1987), Ichokuand Chorowicz (1994), and Mejia and Niemann all observeddifferences in the tributary junction angles for different networktypes [4], [6], [7].

• In this study, the angles are measured by considering any locationin the channel network that has a junction of two tributariesin the channel network that has a junction of two tributariesbetween the primary and the secondary tributaries.

• The tributary junction angle can influence the occurrence ofThe tributary junction angle can influence the occurrence ofdifferent drainage networks.

Objective

• The aim of this study is to propose a suitable methodology to identify rivernetworks which are not determined by using characteristics of alreadynetworks which are not determined by using characteristics of alreadyclassified networks based on the fractal analysis.

• 50 river networks in the USA are used for estimating the exponent of power-f i i i i ifi i f filaw or fractal dimension that aims to provide a classification system for five

network types.

• 10 Wadis in the northern regions of the UAE and Oman are analyzed toidentify the use of the new methodology to distinguish new networks.

• The exponent of the power-law can be an appropriate variable to determinechannel networks.channel networks.

• Then, the estimated values will be used for the regional frequency analysis toeasily characterize the physiographical property of drainage networks byconsidering the time of concentrations for each network typeconsidering the time of concentrations for each network type.

2. Methodology (1)

• The junction angles between the primary and theThe junction angles between the primary and thesecondary tributaries of channels is the keycharacteristic which can determine the drainagenetwork types.

• The junction angles are classified into threegroups in the following ranges: 0º - 60º, 30º -90º, 60º - 120º.

• These overlapping ranges are selected forcontinuity.

• The range between 0º and 120º is chosengbecause parallel and pinnate networks normallyhave acute junction angles.

2. Methodology (2)

Histogram of secondary lengths

2. Methodology (3)

For optimal bin size of histogram

The corresponding cumulative histogram in logarithmic scale

2.090

3. Data Set

• Digital Elevation Models (DEMs)Digital Elevation Models (DEMs)of 50 channel networks in the USAwere obtained from the NationalElevation Models (USGS) for five

k l ifi i id ifi d inetwork classification identified inprevious studies [5], [10], [11].

• DEMs for 10 wadis in the UAEd O l i d fand Oman were also acquired from

the Advanced Spaceborne ThermalEmission and ReflectionRadiometer (ASTER).( )

• The horizontal resolution for the DEMs is 1 arc-second, which generates approximately 30 mgrid cells with a linear dimension and basin size ranging from 11 km2 to 898 km2.

4. Result (1)

2.043 1.989

• One example of this analysis isshown in the figure based onangles for three groups of ranges:

1.754

0º - 60º, 30º - 90º, 60º - 120º(Dendritic: Buffalo Creek, WV)

• The estimated values are 2.043,1.989, and 1.754, respectively.

• The analysis has been conductedfor ten networks identified fromfor ten networks identified fromeach network classification.

4. Result (2)

Network TypesExponent of Power‐ Law

(angle: 0º ‐ 60º)Exponent of Power‐ Law


(angle: 60º ‐ 120º)

Dendritic Networks 2 066 1 845 1 741

Table 1. The mean of the power-law for 50 basins

Dendritic Networks 2.066 1.845 1.741

Rectangular Networks 3.183 2.506 2.201

Trellis Networks 2.775 2.401 1.989

Parallel Networks 1.964 2.236 2.846

Pinnate Networks 1.738 1.888 2.019

Network TypesExponent of Power‐ Law



(angle: 60º ‐ 120º)




Table 2. The standard deviation of the power-law for 50 basins

• It was observed that networks of same type have similar values for the estimated exponent ofthe power-law based on fractal dimensions among each network type.


Pinnate Networks 0.184 0.194 0.136

• Parallel networks indicate the higher value of standard deviation compared to other drainagenetworks. This might be because sub-parallel networks exist among parallel networks analyzed[4].

Thursday, October 18, 2012

4. Result (3)

Network Types Exponent of Power- Law (angle: 0º - 60º)

Exponent of Power- Law (angle: 30º - 90º)


Table 1. The mean of the power-law for 50 basins in the USA for each network type





Pinnate Networks 1 738 1 888 2 019Pinnate Networks 1.738 1.888 2.019

Network Types Exponent of Power- Law (angle: 0º - 60º)




Table 2. The mean of the power-law for 10 wadisin the UAE and Oman

• Wadis in the UAE and Oman seem to have similar values of the exponent of the power-law torectangular networks.

• These Wadis were also identified as rectangular networks by using measures derived fromscaling invariance.

5. Conclusion (1)

• This study presents an alternative methodology to identify they p gy ydrainage network types by using the distribution of lengths ofthe secondary tributaries in different angle ranges based onfractal analysis.fractal analysis.

• The analysis revealed that the estimated values of the fractaldimensions are similar for channel networks of the same typeb i ifi l diff h l f h h kbut are significantly different to the values of the other networktypes.

• The exponents of the power-law for wadis tend to be similar toThe exponents of the power law for wadis tend to be similar torectangular networks.

5. Conclusion (2)

• In the future research, the estimated exponent will be used as anew variable of physiographical characteristics for the regionalfrequency analysis which allows us to transfer informationfrequency analysis which allows us to transfer informationfrom gauged sites to ungauged sites by estimating the time ofconcentration for five river networks.

Thi t b i i bl d id th• This exponent can be a more precise variable and provide theeasier way to determine the physiographical property becausethe exponent directly indicates the drainage network’scharacteristic that aims to distinguish network types.

References

[1] Zernitz, E. R. (1932). The Journal of Geology 40(6), pp. 498-521.

[2] Parvis M (1950) Photogrammetric Engineering 16 pp 375 409[2] Parvis, M. (1950). Photogrammetric Engineering 16, pp. 375-409.

[3] Howard, A. D. (1967). American Association of Petroleum Geologists Bulletin 51 (11), pp. 2246-2259.

[4] Pilli L F d S A S h (1987) G l 15 813 816[4] Pillips, L. F., and S. A. Schumm (1987). Geology, 15, pp. 813-816

[5] Mejia, A. I., and J. D. Niemann (2008). Journal of Geophysical Research 113(F2), F02015.

[6] Abrahams, A. D., and J. J. Flint (1983). Geol. Soc. Am. Bull., 94, pp. 80-91

[7] Ichoku, C., and J. Chorowicz (1994). Water Resour. Res., 30, pp. 161-174

[8] Gloaguen, R., P. R. Marpu, and I. Niemeyer (2007). Nonlinear Processes in Geophysics 14, pp. 131-138.

[9] Shimazaki, H., and S. Shinomoto (2007). Neural Computation 19(6), pp. 1503-1527.

[10] Jung, K., J.D. Niemann, and X. Huang (2011). Geomorphology 132(3-4), pp. 260-271.

[11] Jung, K., and T.B.M.J. Ouarda (2012). Journal of Geophysical Research, Proceedings.

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Discrimination of Five Network Types Based on The Lengths