Abstract
Hydrographic operations to investigate the riverbed form throughout the entire length of a river are costly and time-consuming. This has made scholars use a wide range of alternative methods to address the issue. In the present study, however, a new framework using Artificial Intelligence (AI) based models is introduced to identify the thalweg of rivers, which provides an accurate estimate of a river thalweg via linking coordinates of their left and right banks. In this regard, we trained and tested the performance of two AI-based models, including Artificial Neural Network (ANN) and Adaptive Neuro-Fuzzy Inference System (ANFIS) models. The database of two rivers, namely the Qinhe River in China and the Gaz River in Iran was used to help evaluate the developed model. Outcomes of the two investigated case studies demonstrated that the values of the statistical error estimators, including the Root Mean Square Error (RMSE) of the ANFIS model were less than those of the ANN model. As a result, the ANFIS model can lead to more accurate results than the ANN model, and it is suitable for cases with less available data. Moreover, comparing the results from the developed models with those of the River Channel Morphology Model (RCMM) showed that AI-based models outdo numerical approaches in the identification of the thalweg of rivers. All in all, it is inferred that the proposed approach not only helps us achieve an accurate geometry of rivers but reduces the side costs and can be used as an effective alternative to field operations. The applicability of the proposed models to different river systems is also discussed as a potential direction for future research.
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All authors contributed to the study’s conception and design. Material preparation, data collection, and analysis were performed by Zohre Aghamolaei and Masoud-Reza Hesami Kermani. Zohre Aghamolaei: Writing - original draft. Masoud Reza Hesami Kermani: Writing - original draft, Project administration.
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Appendix
Appendix
Case study I:
Left | Talweg | Right | ||||||
|---|---|---|---|---|---|---|---|---|
x | y | z | X | Y | Z | X | Y | Z |
238607.47 | 3878357.49 | 824.23 | 238794.24 | 3878324.99 | 801.10 | 238954.52 | 3878297.10 | 834.39 |
238591.26 | 3878365.05 | 823.81 | 238802.93 | 3878359.96 | 805.34 | 238946.04 | 3878335.94 | 834.99 |
238575.04 | 3878372.61 | 824.00 | 238810.18 | 3878395.26 | 811.82 | 238928.31 | 3878372.47 | 837.59 |
238558.83 | 3878380.18 | 824.20 | 238815.96 | 3878430.82 | 822.03 | 238910.57 | 3878409.00 | 840.91 |
238542.62 | 3878387.74 | 824.79 | 238820.26 | 3878466.60 | 830.83 | 238892.83 | 3878445.53 | 841.80 |
238526.41 | 3878395.30 | 826.04 | 238823.08 | 3878502.52 | 836.73 | 238875.10 | 3878482.06 | 844.03 |
238510.19 | 3878402.86 | 826.64 | 238824.41 | 3878538.53 | 840.60 | 238863.97 | 3878521.07 | 843.98 |
238493.98 | 3878410.43 | 826.67 | 238824.25 | 3878574.56 | 842.98 | 238853.43 | 3878560.28 | 846.80 |
238477.77 | 3878417.99 | 826.48 | 238822.60 | 3878610.56 | 844.76 | 238842.88 | 3878599.50 | 849.88 |
238461.56 | 3878425.55 | 824.58 | 238819.46 | 3878646.46 | 841.70 | 238840.69 | 3878639.86 | 849.37 |
238445.34 | 3878433.11 | 822.69 | 238814.84 | 3878682.19 | 835.63 | 238840.27 | 3878680.47 | 843.39 |
238429.13 | 3878440.67 | 822.93 | 238808.74 | 3878717.71 | 831.82 | 238839.85 | 3878721.08 | 837.03 |
238412.92 | 3878448.24 | 823.58 | 238801.19 | 3878752.94 | 828.32 | 238839.43 | 3878761.69 | 831.91 |
238396.71 | 3878455.80 | 824.43 | 238792.18 | 3878787.83 | 823.13 | 238840.73 | 3878802.27 | 830.24 |
238380.49 | 3878463.36 | 825.51 | 238781.73 | 3878822.31 | 819.69 | 238829.53 | 3878840.23 | 830.97 |
238364.28 | 3878470.92 | 826.53 | 238769.87 | 3878856.34 | 819.67 | 238812.24 | 3878876.98 | 833.84 |
238348.07 | 3878478.48 | 827.18 | 238756.61 | 3878889.84 | 820.36 | 238794.96 | 3878913.73 | 838.47 |
238331.85 | 3878486.05 | 827.83 | 238741.98 | 3878922.77 | 821.73 | 238777.68 | 3878950.48 | 842.58 |
238315.64 | 3878493.61 | 827.03 | 238726.00 | 3878955.07 | 825.47 | 238758.63 | 3878986.10 | 850.55 |
238299.43 | 3878501.17 | 825.75 | 238704.56 | 3878983.83 | 828.33 | 238732.70 | 3879017.36 | 850.62 |
238281.57 | 3878512.31 | 824.14 | 238670.82 | 3879018.47 | 831.33 | 238693.46 | 3879051.44 | 852.56 |
238264.40 | 3878524.47 | 822.34 | 238632.37 | 3879047.82 | 832.54 | 238651.97 | 3879083.20 | 854.59 |
238247.36 | 3878536.83 | 820.96 | 238590.06 | 3879071.25 | 826.39 | 238610.48 | 3879114.96 | 849.58 |
238230.33 | 3878549.18 | 821.63 | 238544.79 | 3879088.25 | 824.52 | 238563.14 | 3879136.52 | 838.86 |
238213.29 | 3878561.54 | 819.38 | 238497.52 | 3879098.47 | 822.85 | 238514.79 | 3879156.33 | 837.01 |
238196.25 | 3878573.90 | 821.34 | 238449.26 | 3879101.68 | 823.55 | 238466.34 | 3879175.88 | 842.96 |
238179.21 | 3878586.25 | 823.77 | 238401.05 | 3879097.82 | 824.95 | 238417.18 | 3879193.56 | 853.34 |
238162.17 | 3878598.61 | 824.83 | 238353.92 | 3879086.97 | 823.85 | 238367.99 | 3879211.16 | 861.32 |
238145.14 | 3878610.96 | 824.28 | 238308.88 | 3879069.36 | 824.04 | 238317.02 | 3879222.65 | 857.35 |
238128.10 | 3878623.32 | 823.08 | 238266.88 | 3879045.37 | 829.22 | 238266.00 | 3879233.45 | 851.22 |
238111.06 | 3878635.68 | 821.66 | 238228.84 | 3879015.51 | 829.32 | 238213.90 | 3879229.61 | 844.74 |
238094.02 | 3878648.03 | 821.09 | 238193.73 | 3878982.23 | 827.29 | 238162.90 | 3879219.25 | 837.94 |
238076.98 | 3878660.39 | 821.07 | 238156.93 | 3878950.78 | 824.65 | 238112.80 | 3879204.57 | 837.40 |
238059.95 | 3878672.74 | 821.26 | 238119.37 | 3878920.25 | 822.00 | 238063.99 | 3879185.93 | 835.66 |
238039.72 | 3878675.23 | 820.07 | 238081.07 | 3878890.66 | 821.10 | 238015.18 | 3879167.30 | 835.38 |
238018.67 | 3878675.16 | 819.14 | 238042.05 | 3878862.02 | 820.62 | 237966.66 | 3879147.95 | 836.37 |
237997.63 | 3878675.10 | 818.60 | 238002.33 | 3878834.34 | 820.78 | 237918.51 | 3879127.65 | 836.08 |
237976.58 | 3878675.03 | 818.14 | 237961.95 | 3878807.66 | 821.93 | 237870.37 | 3879107.35 | 830.96 |
237955.53 | 3878674.96 | 817.59 | 237920.92 | 3878781.97 | 821.43 | 237822.22 | 3879087.06 | 825.83 |
237923.82 | 3878674.87 | 818.10 | 237894.31 | 3878766.06 | 821.09 | 237806.35 | 3879086.11 | 825.03 |
237892.90 | 3878669.26 | 819.40 | 237867.21 | 3878750.99 | 820.12 | 237790.48 | 3879085.16 | 824.48 |
237862.42 | 3878660.48 | 819.57 | 237839.90 | 3878736.31 | 822.96 | 237774.61 | 3879084.21 | 825.34 |
237831.95 | 3878651.69 | 819.04 | 237812.58 | 3878721.62 | 821.44 | 237758.74 | 3879083.26 | 826.19 |
237801.48 | 3878642.91 | 821.33 | 237785.27 | 3878706.94 | 821.00 | 237742.88 | 3879082.30 | 826.12 |
237771.01 | 3878634.12 | 822.15 | 237757.96 | 3878692.25 | 821.55 | 237727.01 | 3879081.35 | 825.90 |
237740.54 | 3878625.34 | 821.66 | 237730.65 | 3878677.57 | 821.37 | 237711.14 | 3879080.40 | 825.53 |
237710.07 | 3878616.55 | 820.28 | 237703.34 | 3878662.89 | 819.11 | 237695.27 | 3879079.45 | 824.33 |
237679.01 | 3878610.16 | 819.38 | 237676.03 | 3878648.20 | 817.55 | 237679.66 | 3879081.18 | 823.02 |
237647.91 | 3878603.99 | 818.52 | 237648.10 | 3878634.77 | 819.78 | 237664.28 | 3879085.22 | 822.33 |
237616.80 | 3878597.81 | 818.82 | 237619.20 | 3878623.55 | 820.24 | 237648.91 | 3879089.26 | 821.70 |
237585.70 | 3878591.63 | 819.16 | 237589.62 | 3878614.26 | 820.62 | 237633.53 | 3879093.30 | 821.48 |
237554.59 | 3878585.46 | 819.15 | 237559.49 | 3878606.96 | 820.43 | 237618.16 | 3879097.34 | 822.18 |
237523.49 | 3878579.28 | 819.36 | 237528.94 | 3878601.66 | 819.99 | 237602.78 | 3879101.38 | 823.03 |
237492.38 | 3878573.10 | 818.38 | 237498.11 | 3878598.39 | 819.20 | 237587.40 | 3879105.42 | 825.43 |
237461.28 | 3878566.93 | 817.23 | 237467.13 | 3878597.16 | 817.30 | 237572.03 | 3879109.46 | 827.76 |
237430.25 | 3878570.56 | 817.92 | 237436.14 | 3878597.99 | 816.44 | 237556.65 | 3879113.51 | 828.62 |
237399.24 | 3878577.21 | 819.23 | 237405.27 | 3878600.86 | 817.22 | 237541.27 | 3879117.55 | 827.55 |
237368.23 | 3878583.87 | 819.99 | 237374.65 | 3878605.76 | 817.84 | 237525.90 | 3879121.59 | 826.06 |
237332.64 | 3878591.16 | 820.11 | 237338.48 | 3878614.29 | 818.56 | 237509.81 | 3879125.81 | 824.10 |
237297.04 | 3878598.46 | 819.35 | 237303.10 | 3878625.66 | 819.00 | 237493.72 | 3879130.04 | 822.12 |
237262.88 | 3878610.23 | 818.78 | 237268.73 | 3878639.80 | 818.28 | 237477.64 | 3879134.27 | 821.35 |
237229.73 | 3878625.11 | 818.64 | 237235.59 | 3878656.61 | 818.44 | 237461.55 | 3879138.50 | 821.46 |
237196.58 | 3878640.00 | 821.03 | 237209.04 | 3878679.89 | 819.84 | 237445.46 | 3879142.73 | 821.28 |
237163.43 | 3878654.88 | 823.81 | 237199.14 | 3878715.72 | 820.62 | 237429.37 | 3879146.95 | 821.27 |
237130.28 | 3878669.77 | 825.22 | 237190.98 | 3878751.98 | 822.19 | 237413.29 | 3879151.18 | 821.38 |
237097.13 | 3878684.65 | 826.16 | 237184.61 | 3878788.60 | 820.98 | 237399.20 | 3879158.70 | 821.27 |
237064.32 | 3878700.15 | 831.14 | 237180.01 | 3878825.48 | 818.52 | 237388.02 | 3879171.02 | 821.30 |
237034.21 | 3878720.50 | 827.97 | 237177.22 | 3878862.55 | 812.35 | 237376.84 | 3879183.34 | 821.11 |
237004.10 | 3878740.84 | 826.10 | 237176.40 | 3878899.69 | 804.77 | 237365.66 | 3879195.65 | 821.18 |
236973.99 | 3878761.19 | 825.95 | 237180.03 | 3878936.68 | 802.28 | 237354.48 | 3879207.97 | 821.47 |
236943.88 | 3878781.54 | 825.94 | 237181.33 | 3878973.83 | 803.50 | 237343.30 | 3879220.29 | 822.13 |
236913.78 | 3878801.88 | 825.38 | 237180.30 | 3879010.98 | 809.14 | 237332.12 | 3879232.60 | 822.95 |
236883.67 | 3878822.23 | 826.40 | 237176.96 | 3879048.00 | 812.83 | 237320.94 | 3879244.92 | 823.31 |
236853.56 | 3878842.57 | 829.38 | 237171.30 | 3879084.73 | 815.18 | 237309.76 | 3879257.24 | 823.66 |
236824.95 | 3878864.82 | 830.15 | 237163.35 | 3879121.04 | 817.76 | 237298.58 | 3879269.55 | 824.01 |
236798.09 | 3878889.30 | 827.93 | 237141.86 | 3879148.46 | 819.68 | 237289.07 | 3879283.11 | 824.10 |
236771.23 | 3878913.78 | 825.69 | 237111.77 | 3879170.27 | 822.40 | 237280.53 | 3879297.38 | 824.78 |
236756.40 | 3878927.30 | 825.39 | 237101.09 | 3879178.52 | 823.61 | 237275.60 | 3879305.63 | 825.47 |
236741.56 | 3878940.81 | 824.82 | 237090.55 | 3879186.95 | 825.21 | 237270.67 | 3879313.88 | 825.56 |
236726.73 | 3878954.33 | 824.92 | 237080.15 | 3879195.55 | 826.80 | 237265.74 | 3879322.13 | 825.57 |
236711.89 | 3878967.85 | 824.84 | 237069.90 | 3879204.32 | 828.37 | 237260.80 | 3879330.37 | 825.70 |
236697.06 | 3878981.37 | 824.55 | 237059.79 | 3879213.25 | 828.82 | 237255.87 | 3879338.62 | 825.22 |
236682.22 | 3878994.89 | 824.40 | 237049.83 | 3879222.35 | 827.84 | 237250.94 | 3879346.87 | 825.73 |
236667.39 | 3879008.41 | 824.89 | 237040.02 | 3879231.62 | 826.86 | 237246.00 | 3879355.12 | 826.15 |
236652.56 | 3879021.93 | 825.38 | 237030.36 | 3879241.04 | 825.86 | 237241.07 | 3879363.37 | 825.29 |
236637.72 | 3879035.44 | 824.02 | 237020.86 | 3879250.63 | 824.66 | 237236.14 | 3879371.61 | 824.71 |
236622.89 | 3879048.96 | 822.32 | 237011.52 | 3879260.36 | 823.64 | 237231.20 | 3879379.86 | 824.28 |
236608.05 | 3879062.48 | 820.90 | 237002.34 | 3879270.25 | 822.64 | 237226.27 | 3879388.11 | 823.85 |
236593.22 | 3879076.00 | 821.36 | 236993.32 | 3879280.29 | 821.64 | 237221.34 | 3879396.36 | 823.42 |
236578.39 | 3879089.52 | 821.80 | 236984.47 | 3879290.48 | 820.80 | 237216.40 | 3879404.61 | 822.83 |
236563.55 | 3879103.04 | 821.72 | 236975.79 | 3879300.81 | 820.04 | 237211.47 | 3879412.85 | 822.81 |
236550.11 | 3879117.74 | 820.98 | 236967.28 | 3879311.28 | 819.27 | 237206.54 | 3879421.10 | 823.03 |
236539.22 | 3879134.59 | 820.25 | 236958.95 | 3879321.89 | 818.49 | 237201.61 | 3879429.35 | 823.25 |
236528.33 | 3879151.45 | 820.58 | 236950.79 | 3879332.64 | 817.83 | 237196.67 | 3879437.60 | 823.46 |
236517.44 | 3879168.31 | 820.90 | 236942.80 | 3879343.52 | 817.67 | 237191.74 | 3879445.85 | 823.51 |
236508.43 | 3879185.85 | 821.63 | 236935.00 | 3879354.53 | 817.36 | 237186.81 | 3879454.09 | 823.30 |
236498.28 | 3879266.27 | 821.23 | 236881.97 | 3879441.80 | 817.82 | 237142.55 | 3879533.61 | 822.40 |
236488.14 | 3879346.69 | 821.90 | 236840.20 | 3879534.98 | 816.35 | 237142.55 | 3879625.36 | 818.61 |
236477.99 | 3879427.11 | 822.59 | 236810.33 | 3879632.64 | 820.78 | 237142.43 | 3879717.10 | 826.62 |
236467.85 | 3879507.53 | 823.00 | 236792.84 | 3879733.25 | 819.39 | 237134.65 | 3879807.80 | 826.66 |
236457.70 | 3879587.95 | 824.74 | 236787.98 | 3879835.26 | 819.43 | 237104.64 | 3879894.50 | 824.00 |
236447.55 | 3879668.37 | 819.28 | 236795.84 | 3879937.07 | 819.85 | 237074.64 | 3879981.20 | 820.13 |
236443.84 | 3879749.32 | 815.33 | 236816.30 | 3880037.12 | 823.10 | 237044.63 | 3880067.90 | 825.16 |
236440.53 | 3879830.31 | 823.90 | 236849.03 | 3880133.86 | 821.11 | 237014.62 | 3880154.60 | 824.49 |
236437.22 | 3879911.30 | 824.47 | 236861.82 | 3880234.23 | 815.90 | 236987.30 | 3880242.17 | 816.60 |
236433.90 | 3879992.29 | 819.77 | 236867.49 | 3880336.26 | 830.57 | 236961.15 | 3880330.11 | 824.15 |
236430.59 | 3880073.28 | 813.44 | 236873.95 | 3880438.17 | 837.13 | 236935.01 | 3880418.05 | 829.97 |
236420.57 | 3880153.12 | 817.91 | 236840.62 | 3880533.06 | 827.55 | 236908.86 | 3880505.99 | 827.90 |
236396.78 | 3880230.60 | 817.30 | 236758.50 | 3880591.11 | 814.17 | 236875.72 | 3880590.77 | 834.95 |
236372.98 | 3880308.09 | 819.45 | 236657.93 | 3880590.86 | 818.88 | 236826.87 | 3880668.43 | 827.37 |
236349.18 | 3880385.57 | 826.33 | 236564.28 | 3880550.92 | 825.70 | 236778.02 | 3880746.08 | 833.31 |
236312.03 | 3880457.54 | 827.75 | 236463.19 | 3880539.14 | 821.00 | 236728.87 | 3880823.54 | 831.76 |
236274.20 | 3880529.23 | 820.84 | 236363.34 | 3880558.84 | 824.41 | 236674.79 | 3880897.65 | 835.14 |
236236.37 | 3880600.92 | 820.39 | 236274.29 | 3880608.12 | 823.53 | 236620.71 | 3880971.77 | 836.65 |
236184.88 | 3880662.49 | 822.60 | 236204.57 | 3880682.26 | 823.44 | 236566.63 | 3881045.88 | 830.64 |
Cas study II:
Left | Talweg | Right | ||||||
|---|---|---|---|---|---|---|---|---|
x | y | z | x | y | z | x | y | z |
513069.80 | 2924874.00 | 6.61 | 513092.00 | 2924909.00 | 1.97 | 513107.10 | 2924929.00 | 5.73 |
513062.69 | 2924878.00 | 6.70 | 513086.31 | 2924911.00 | 2.02 | 513102.05 | 2924931.00 | 5.72 |
513052.58 | 2924883.00 | 6.82 | 513080.47 | 2924913.00 | 2.08 | 513097.20 | 2924932.00 | 5.72 |
513045.00 | 2924887.00 | 6.91 | 513074.84 | 2924914.00 | 2.13 | 513089.98 | 2924934.00 | 5.71 |
513040.50 | 2924892.00 | 7.04 | 513070.00 | 2924916.00 | 2.18 | 513083.80 | 2924936.00 | 5.70 |
513035.60 | 2924897.00 | 7.18 | 513064.31 | 2924917.00 | 1.93 | 513077.14 | 2924938.00 | 5.69 |
513032.68 | 2924900.00 | 7.22 | 513057.90 | 2924919.00 | 1.66 | 513070.50 | 2924939.00 | 5.68 |
513028.79 | 2924905.00 | 7.26 | 513051.65 | 2924923.00 | 2.08 | 513065.25 | 2924944.00 | 5.69 |
513025.80 | 2924908.00 | 7.30 | 513046.52 | 2924926.00 | 2.41 | 513059.50 | 2924949.00 | 5.69 |
513022.25 | 2924912.00 | 7.24 | 513041.70 | 2924929.00 | 2.73 | 513052.84 | 2924954.00 | 5.70 |
513016.70 | 2924917.00 | 7.15 | 513037.10 | 2924932.00 | 3.03 | 513047.30 | 2924959.00 | 5.70 |
513012.95 | 2924921.00 | 7.01 | 513032.26 | 2924935.00 | 2.54 | 513041.10 | 2924964.00 | 5.71 |
513008.71 | 2924926.00 | 6.86 | 513027.99 | 2924938.00 | 2.11 | 513035.90 | 2924969.00 | 5.71 |
513002.30 | 2924933.00 | 6.64 | 513020.50 | 2924943.00 | 1.35 | 513030.06 | 2924974.00 | 5.72 |
512998.58 | 2924936.00 | 6.65 | 513013.89 | 2924949.00 | 2.41 | 513024.00 | 2924979.00 | 5.72 |
512993.31 | 2924941.00 | 6.68 | 513007.70 | 2924955.00 | 3.40 | 513019.97 | 2924982.00 | 5.72 |
512989.30 | 2924944.00 | 6.70 | 513000.99 | 2924962.00 | 2.61 | 513015.70 | 2924986.00 | 5.72 |
512983.97 | 2924948.00 | 6.67 | 512994.90 | 2924968.00 | 1.89 | 513011.64 | 2924989.00 | 5.73 |
512978.24 | 2924953.00 | 6.63 | 512992.19 | 2924971.00 | 1.86 | 513008.13 | 2924992.00 | 5.74 |
512973.10 | 2924957.00 | 6.59 | 512987.51 | 2924972.00 | 2.28 | 513006.90 | 2924993.00 | 5.74 |
512969.19 | 2924960.00 | 6.60 | 512986.27 | 2924976.00 | 1.79 | 513003.80 | 2924996.00 | 5.75 |
512966.01 | 2924963.00 | 6.60 | 512983.40 | 2924979.00 | 1.75 | 512999.79 | 2924999.00 | 5.72 |
512963.19 | 2924965.00 | 6.60 | 512980.99 | 2924983.00 | 1.91 | 512996.99 | 2925002.00 | 5.71 |
512960.36 | 2924967.00 | 6.60 | 512979.10 | 2924986.00 | 2.03 | 512993.19 | 2925005.00 | 5.69 |
512957.27 | 2924970.00 | 6.61 | 512973.01 | 2924989.00 | 1.95 | 512988.20 | 2925009.00 | 5.66 |
512954.40 | 2924972.00 | 6.61 | 512967.30 | 2924991.00 | 1.88 | 512985.01 | 2925012.00 | 5.64 |
512950.38 | 2924975.00 | 6.61 | 512962.82 | 2924994.00 | 1.87 | 512979.95 | 2925016.00 | 5.61 |
512947.99 | 2924977.00 | 6.61 | 512958.70 | 2924996.00 | 1.86 | 512974.50 | 2925021.00 | 5.58 |
512943.78 | 2924981.00 | 6.62 | 512954.00 | 2924999.00 | 1.94 | 512968.94 | 2925026.00 | 5.60 |
512940.20 | 2924984.00 | 6.62 | 512952.33 | 2925004.00 | 1.72 | 512965.94 | 2925028.00 | 5.61 |
512936.00 | 2924987.00 | 6.58 | 512950.40 | 2925010.00 | 1.47 | 512962.90 | 2925031.00 | 5.61 |
512930.35 | 2924992.00 | 6.53 | 512944.60 | 2925012.00 | 1.65 | 512960.40 | 2925033.00 | 5.62 |
512927.51 | 2924994.00 | 6.51 | 512939.77 | 2925014.00 | 1.78 | 512956.79 | 2925036.00 | 5.64 |
512924.60 | 2924996.00 | 6.48 | 512935.40 | 2925016.00 | 1.89 | 512952.40 | 2925040.00 | 5.65 |
512920.41 | 2924999.00 | 6.44 | 512930.70 | 2925018.00 | 2.01 | 512950.24 | 2925042.00 | 5.66 |
512916.12 | 2925002.00 | 6.41 | 512932.10 | 2925023.00 | 1.98 | 512947.99 | 2925044.00 | 5.67 |
512912.50 | 2925005.00 | 6.37 | 512928.90 | 2925027.00 | 1.88 | 512945.17 | 2925046.00 | 5.68 |
512908.42 | 2925008.00 | 6.35 | 512926.52 | 2925030.00 | 1.81 | 512942.51 | 2925048.00 | 5.69 |
512905.10 | 2925011.00 | 6.33 | 512924.42 | 2925032.00 | 1.74 | 512941.24 | 2925049.00 | 5.70 |
512902.34 | 2925013.00 | 6.33 | 512922.60 | 2925034.00 | 1.68 | 512937.10 | 2925053.00 | 5.71 |
512899.81 | 2925015.00 | 6.33 | 512919.34 | 2925037.00 | 1.70 | 512935.46 | 2925056.00 | 5.70 |
512896.70 | 2925017.00 | 6.33 | 512916.90 | 2925040.00 | 1.71 | 512934.17 | 2925058.00 | 5.70 |
512893.20 | 2925019.00 | 6.32 | 512912.50 | 2925043.00 | 1.70 | 512932.69 | 2925060.00 | 5.69 |
512889.65 | 2925024.00 | 6.30 | 512907.90 | 2925047.00 | 1.68 | 512931.01 | 2925063.00 | 5.68 |
512887.30 | 2925027.00 | 6.29 | 512904.01 | 2925050.00 | 1.68 | 512929.20 | 2925066.00 | 5.67 |
512883.79 | 2925031.00 | 6.29 | 512901.75 | 2925051.00 | 1.68 | 512926.68 | 2925070.00 | 5.65 |
512880.70 | 2925035.00 | 6.30 | 512898.75 | 2925053.00 | 1.68 | 512923.55 | 2925075.00 | 5.63 |
512878.33 | 2925038.00 | 6.30 | 512895.20 | 2925056.00 | 1.68 | 512920.39 | 2925080.00 | 5.61 |
512875.40 | 2925042.00 | 6.32 | 512890.66 | 2925059.00 | 1.78 | 512917.90 | 2925084.00 | 5.60 |
512872.17 | 2925046.00 | 6.31 | 512886.20 | 2925061.00 | 1.88 | 512915.48 | 2925088.00 | 5.58 |
512868.71 | 2925050.00 | 6.30 | 512883.53 | 2925065.00 | 2.04 | 512913.70 | 2925091.00 | 5.57 |
512865.90 | 2925054.00 | 6.29 | 512880.50 | 2925069.00 | 2.22 | 512911.62 | 2925095.00 | 5.55 |
512862.24 | 2925059.00 | 6.26 | 512875.15 | 2925071.00 | 2.11 | 512908.87 | 2925099.00 | 5.52 |
512860.20 | 2925066.00 | 6.00 | 512868.90 | 2925073.00 | 1.97 | 512906.70 | 2925103.00 | 5.50 |
512853.57 | 2925069.00 | 6.21 | 512865.53 | 2925077.00 | 2.44 | 512903.89 | 2925108.00 | 5.50 |
512850.40 | 2925073.00 | 6.21 | 512862.30 | 2925081.00 | 2.88 | 512901.45 | 2925112.00 | 5.51 |
512846.98 | 2925078.00 | 6.20 | 512858.87 | 2925085.00 | 2.69 | 512899.40 | 2925115.00 | 5.51 |
512844.80 | 2925081.00 | 6.20 | 512855.34 | 2925089.00 | 2.49 | 512897.68 | 2925118.00 | 5.51 |
512841.29 | 2925086.00 | 6.19 | 512852.70 | 2925092.00 | 2.34 | 512894.75 | 2925123.00 | 5.52 |
512837.17 | 2925092.00 | 6.18 | 512849.58 | 2925096.00 | 2.20 | 512891.80 | 2925128.00 | 5.52 |
512833.90 | 2925097.00 | 6.18 | 512846.15 | 2925100.00 | 2.04 | 512890.40 | 2925130.00 | 5.52 |
512830.03 | 2925102.00 | 6.17 | 512843.30 | 2925104.00 | 1.91 | 512888.69 | 2925136.00 | 5.50 |
512826.10 | 2925108.00 | 6.15 | 512839.96 | 2925108.00 | 2.12 | 512886.80 | 2925142.00 | 5.48 |
512823.44 | 2925114.00 | 6.12 | 512836.00 | 2925113.00 | 2.38 | 512884.90 | 2925149.00 | 5.46 |
512821.50 | 2925119.00 | 6.10 | 512831.50 | 2925118.00 | 1.73 | 512882.69 | 2925156.00 | 5.45 |
512817.22 | 2925129.00 | 5.65 | 512828.60 | 2925126.00 | 1.94 | 512880.90 | 2925162.00 | 5.43 |
512814.50 | 2925136.00 | 5.37 | 512825.60 | 2925134.00 | 2.08 | 512878.96 | 2925168.00 | 5.42 |
512812.19 | 2925142.00 | 4.81 | 512825.60 | 2925142.00 | 1.94 | 512877.96 | 2925172.00 | 5.42 |
512809.90 | 2925147.00 | 4.25 | 512825.60 | 2925148.00 | 1.82 | 512876.70 | 2925176.00 | 5.41 |
512807.30 | 2925156.00 | 3.93 | 512825.60 | 2925159.00 | 1.63 | 512875.78 | 2925179.00 | 5.41 |
512804.35 | 2925164.00 | 4.02 | 512821.60 | 2925167.00 | 1.67 | 512874.52 | 2925184.00 | 5.40 |
512802.69 | 2925168.00 | 4.07 | 512819.84 | 2925171.00 | 1.69 | 512873.20 | 2925189.00 | 5.39 |
512800.80 | 2925173.00 | 4.13 | 512817.50 | 2925176.00 | 1.71 | 512871.40 | 2925195.00 | 5.38 |
512800.30 | 2925181.00 | 4.29 | 512815.50 | 2925186.00 | 2.10 | 512870.99 | 2925198.00 | 5.38 |
512798.65 | 2925187.00 | 4.45 | 512813.81 | 2925193.00 | 2.41 | 512870.47 | 2925202.00 | 5.37 |
512797.11 | 2925193.00 | 4.61 | 512812.70 | 2925198.00 | 2.61 | 512869.70 | 2925207.00 | 5.37 |
512795.70 | 2925198.00 | 4.75 | 512812.09 | 2925201.00 | 2.52 | 512869.47 | 2925208.73 | 5.37 |
512794.45 | 2925203.00 | 4.89 | 512810.70 | 2925207.00 | 2.30 | 512869.08 | 2925212.00 | 5.36 |
512792.90 | 2925209.00 | 5.07 | 512809.95 | 2925215.00 | 2.51 | 512868.60 | 2925216.00 | 5.36 |
512791.91 | 2925213.00 | 5.19 | 512809.30 | 2925221.00 | 2.69 | 512867.90 | 2925221.00 | 5.36 |
512790.79 | 2925218.00 | 5.32 | 512808.61 | 2925228.00 | 2.56 | 512867.10 | 2925226.00 | 5.35 |
512789.90 | 2925222.00 | 5.42 | 512807.94 | 2925234.00 | 2.42 | 512866.46 | 2925231.00 | 5.37 |
512788.52 | 2925228.00 | 5.50 | 512807.40 | 2925239.00 | 2.31 | 512866.11 | 2925234.00 | 5.38 |
512787.18 | 2925233.00 | 5.58 | 512806.77 | 2925245.00 | 2.02 | 512865.70 | 2925237.00 | 5.39 |
512785.85 | 2925238.00 | 5.65 | 512806.20 | 2925251.00 | 1.75 | 512868.30 | 2925241.00 | 5.39 |
512784.74 | 2925243.00 | 5.72 | 512805.80 | 2925255.00 | 1.58 | 512871.00 | 2925246.00 | 5.39 |
512783.70 | 2925247.00 | 5.78 | 512805.80 | 2925261.00 | 1.77 | 512873.19 | 2925250.00 | 5.35 |
512782.25 | 2925253.00 | 5.82 | 512805.80 | 2925267.00 | 1.95 | 512875.20 | 2925254.00 | 5.32 |
512780.80 | 2925259.00 | 5.85 | 512805.80 | 2925271.00 | 2.08 | 512877.81 | 2925259.00 | 5.28 |
512779.23 | 2925266.00 | 5.89 | 512805.80 | 2925275.00 | 2.18 | 512880.54 | 2925264.00 | 5.23 |
512777.63 | 2925272.00 | 5.94 | 512805.50 | 2925277.00 | 2.29 | 512882.80 | 2925268.00 | 5.19 |
512776.10 | 2925279.00 | 5.97 | 512804.20 | 2925285.00 | 1.83 | 512885.90 | 2925273.00 | 5.15 |
512779.30 | 2925290.00 | 5.98 | 512803.30 | 2925291.00 | 1.84 | 512888.07 | 2925277.00 | 5.11 |
512781.01 | 2925296.00 | 5.98 | 512803.67 | 2925296.00 | 1.82 | 512890.00 | 2925280.00 | 5.08 |
512782.69 | 2925302.00 | 5.99 | 512804.00 | 2925300.00 | 1.80 | 512891.51 | 2925283.00 | 5.06 |
512784.10 | 2925307.00 | 5.99 | 512804.28 | 2925303.00 | 1.77 | 512892.92 | 2925285.00 | 5.03 |
512785.96 | 2925313.00 | 6.02 | 512804.73 | 2925307.00 | 1.72 | 512893.80 | 2925287.00 | 5.01 |
512787.91 | 2925320.00 | 6.06 | 512805.20 | 2925312.00 | 1.67 | 512896.11 | 2925288.00 | 5.02 |
512789.70 | 2925326.00 | 6.09 | 512805.75 | 2925316.00 | 1.63 | 512898.74 | 2925290.00 | 5.02 |
512792.00 | 2925334.00 | 5.96 | 512806.30 | 2925321.00 | 1.58 | 512900.99 | 2925291.00 | 5.03 |
512797.33 | 2925340.00 | 5.95 | 512808.36 | 2925325.00 | 2.10 | 512903.07 | 2925292.00 | 5.03 |
512800.07 | 2925343.00 | 5.94 | 512809.95 | 2925327.00 | 2.50 | 512905.30 | 2925293.00 | 5.04 |
512803.42 | 2925346.00 | 5.94 | 512813.20 | 2925333.00 | 3.32 | 512907.28 | 2925294.00 | 5.04 |
512806.90 | 2925350.00 | 5.93 | 512816.20 | 2925338.00 | 2.71 | 512910.20 | 2925295.00 | 5.05 |
512811.86 | 2925355.00 | 5.95 | 512818.20 | 2925342.00 | 2.30 | 512912.11 | 2925296.00 | 5.05 |
512813.50 | 2925357.00 | 5.96 | 512820.10 | 2925345.00 | 1.92 | 512913.64 | 2925297.00 | 5.05 |
512815.94 | 2925359.00 | 5.97 | 512827.05 | 2925348.00 | 2.00 | 512916.05 | 2925298.00 | 5.04 |
512818.08 | 2925362.00 | 5.97 | 512832.80 | 2925350.00 | 2.07 | 512917.19 | 2925299.00 | 5.04 |
512821.20 | 2925365.00 | 5.98 | 512837.57 | 2925352.00 | 2.21 | 512919.90 | 2925300.00 | 5.04 |
512825.20 | 2925369.00 | 5.99 | 512843.70 | 2925354.00 | 2.39 | 512921.89 | 2925301.00 | 5.03 |
512827.17 | 2925371.00 | 6.00 | 512850.37 | 2925357.00 | 2.03 | 512923.81 | 2925302.00 | 5.03 |
512831.90 | 2925376.00 | 6.01 | 512854.70 | 2925359.00 | 1.79 | 512926.60 | 2925303.00 | 5.02 |
512836.37 | 2925381.00 | 6.01 | 512863.40 | 2925360.00 | 1.74 | 512930.03 | 2925304.00 | 5.01 |
512838.44 | 2925383.00 | 6.02 | 512867.71 | 2925360.00 | 1.79 | 512933.00 | 2925305.00 | 5.00 |
512841.50 | 2925386.00 | 6.02 | 512872.10 | 2925361.00 | 1.83 | 512935.82 | 2925306.32 | 4.99 |
512848.10 | 2925388.00 | 6.04 | 512882.50 | 2925358.00 | 1.92 | 512937.70 | 2925307.00 | 4.98 |
512854.30 | 2925390.00 | 6.03 | 512890.90 | 2925356.00 | 2.10 | 512940.98 | 2925308.00 | 4.97 |
512857.80 | 2925390.00 | 6.03 | 512892.90 | 2925355.00 | 2.14 | 512944.85 | 2925309.00 | 4.96 |
512866.90 | 2925391.00 | 6.00 | 512898.50 | 2925353.00 | 2.17 | 512947.70 | 2925310.00 | 4.95 |
512873.40 | 2925394.00 | 6.01 | 512903.10 | 2925352.00 | 2.14 | 512953.90 | 2925312.00 | 4.67 |
512881.05 | 2925396.00 | 6.00 | 512911.40 | 2925349.00 | 2.09 | 512958.00 | 2925313.00 | 4.49 |
512886.60 | 2925397.00 | 5.99 | 512913.30 | 2925348.00 | 2.02 | 512961.70 | 2925314.00 | 4.32 |
512891.00 | 2925398.00 | 6.00 | 512917.60 | 2925349.00 | 2.13 | 512968.35 | 2925316.00 | 3.95 |
512894.44 | 2925399.00 | 6.01 | 512922.60 | 2925351.00 | 2.14 | 512972.40 | 2925318.00 | 3.73 |
512898.20 | 2925400.00 | 6.02 | 512931.80 | 2925354.00 | 2.25 | 512975.82 | 2925319.00 | 3.54 |
512908.40 | 2925398.00 | 6.13 | 512941.10 | 2925351.00 | 2.40 | 512979.17 | 2925320.00 | 3.35 |
512920.14 | 2925396.00 | 6.10 | 512951.30 | 2925348.00 | 2.58 | 512983.45 | 2925321.00 | 3.11 |
512931.22 | 2925395.00 | 6.08 | 512964.20 | 2925343.00 | 2.69 | 512986.40 | 2925322.00 | 2.95 |
512937.30 | 2925394.00 | 6.07 | 512970.90 | 2925341.00 | 2.51 | 512988.61 | 2925323.00 | 2.91 |
512952.20 | 2925391.00 | 6.10 | 512979.70 | 2925338.00 | 2.36 | 512992.21 | 2925324.00 | 2.85 |
512966.90 | 2925389.00 | 6.16 | 512984.90 | 2925339.00 | 1.94 | 512995.50 | 2925325.00 | 2.79 |
512984.11 | 2925387.00 | 6.16 | 512990.00 | 2925340.00 | 1.70 | 512997.39 | 2925326.00 | 2.84 |
512988.10 | 2925386.00 | 6.16 | 512994.50 | 2925343.00 | 1.50 | 513000.48 | 2925327.00 | 2.93 |
512991.50 | 2925385.00 | 6.17 | 512998.90 | 2925346.00 | 1.32 | 513002.80 | 2925328.00 | 2.99 |
512999.48 | 2925388.00 | 6.15 | 513008.20 | 2925349.00 | 1.57 | 513008.10 | 2925329.00 | 3.13 |
513004.20 | 2925389.00 | 6.14 | 513017.54 | 2925352.00 | 1.97 | 513016.19 | 2925330.00 | 3.39 |
513011.91 | 2925391.00 | 6.15 | 513025.10 | 2925355.00 | 2.30 | 513021.70 | 2925331.00 | 3.57 |
513019.68 | 2925393.00 | 6.15 | 513033.30 | 2925359.00 | 2.81 | 513028.12 | 2925332.00 | 3.78 |
513025.80 | 2925395.00 | 6.16 | 513040.40 | 2925362.00 | 3.03 | 513031.70 | 2925332.00 | 3.90 |
513032.46 | 2925397.00 | 6.18 | 513046.30 | 2925364.00 | 3.21 | 513036.98 | 2925333.00 | 4.07 |
513039.78 | 2925399.00 | 6.20 | 513053.10 | 2925367.00 | 1.36 | 513041.29 | 2925333.00 | 4.21 |
513045.20 | 2925400.00 | 6.21 | 513057.80 | 2925370.00 | 1.51 | 513048.20 | 2925334.00 | 4.43 |
513053.37 | 2925402.00 | 6.21 | 513062.00 | 2925374.00 | 1.65 | 513055.40 | 2925335.00 | 4.67 |
513060.20 | 2925404.00 | 6.21 | 513070.90 | 2925380.00 | 1.94 | 513062.70 | 2925336.00 | 4.90 |
513067.62 | 2925407.00 | 6.19 | 513077.90 | 2925380.00 | 1.75 | 513069.39 | 2925337.00 | 5.01 |
513073.39 | 2925409.00 | 6.17 | 513084.80 | 2925380.00 | 1.97 | 513078.00 | 2925338.00 | 5.15 |
513077.00 | 2925410.00 | 6.16 | 513095.10 | 2925386.00 | 1.56 | 513085.06 | 2925339.00 | 5.17 |
513090.50 | 2925415.00 | 6.12 | 513101.30 | 2925389.00 | 1.51 | 513092.60 | 2925340.00 | 5.20 |
513097.80 | 2925417.00 | 6.04 | 513107.72 | 2925393.00 | 1.60 | 513107.60 | 2925342.00 | 5.10 |
513104.73 | 2925420.00 | 5.96 | 513112.90 | 2925397.00 | 1.67 | 513115.70 | 2925343.00 | 5.08 |
513110.89 | 2925422.00 | 5.89 | 513115.10 | 2925398.00 | 1.62 | 513129.80 | 2925344.00 | 5.06 |
513115.20 | 2925423.00 | 5.85 | 513121.10 | 2925401.00 | 1.96 | 513139.20 | 2925346.00 | 5.05 |
513120.80 | 2925425.00 | 5.76 | 513127.20 | 2925404.00 | 2.30 | 513142.34 | 2925346.00 | 5.05 |
513128.80 | 2925427.00 | 5.93 | 513134.20 | 2925401.00 | 2.32 | 513147.68 | 2925347.00 | 5.05 |
513134.60 | 2925429.00 | 6.05 | 513141.20 | 2925397.00 | 2.26 | 513153.54 | 2925348.00 | 5.04 |
513141.65 | 2925431.00 | 6.09 | 513149.90 | 2925401.00 | 2.50 | 513157.18 | 2925348.00 | 5.04 |
513151.68 | 2925433.00 | 6.14 | 513157.30 | 2925405.00 | 2.60 | 513161.30 | 2925349.00 | 5.04 |
513156.20 | 2925434.00 | 6.17 | 513162.96 | 2925407.00 | 2.08 | 513165.82 | 2925350.00 | 5.03 |
513163.69 | 2925436.00 | 6.13 | 513166.50 | 2925409.00 | 1.76 | 513170.16 | 2925350.00 | 5.03 |
513172.99 | 2925438.00 | 6.09 | 513175.00 | 2925406.00 | 1.62 | 513172.81 | 2925351.00 | 5.03 |
513178.00 | 2925439.00 | 6.07 | 513183.50 | 2925403.00 | 1.61 | 513176.10 | 2925351.00 | 5.02 |
513184.10 | 2925441.00 | 5.91 | 513189.90 | 2925403.00 | 1.54 | 513180.40 | 2925350.00 | 5.01 |
513190.63 | 2925441.00 | 5.82 | 513197.10 | 2925404.00 | 1.45 | 513184.37 | 2925349.00 | 4.99 |
513197.80 | 2925440.00 | 5.72 | 513205.70 | 2925404.00 | 1.38 | 513187.80 | 2925348.00 | 4.98 |
513211.50 | 2925439.00 | 5.81 | 513212.67 | 2925405.00 | 1.39 | 513194.90 | 2925347.00 | 4.96 |
513220.16 | 2925438.00 | 5.88 | 513217.40 | 2925406.00 | 1.40 | 513201.86 | 2925345.00 | 4.95 |
513228.30 | 2925438.00 | 5.93 | 513224.70 | 2925407.00 | 1.37 | 513208.06 | 2925344.00 | 4.94 |
513239.40 | 2925437.00 | 5.95 | 513230.90 | 2925408.00 | 1.34 | 513213.40 | 2925343.00 | 4.92 |
513245.97 | 2925437.00 | 5.93 | 513234.90 | 2925405.00 | 1.61 | 513217.79 | 2925342.00 | 4.91 |
513253.90 | 2925436.00 | 5.91 | 513241.20 | 2925400.00 | 1.65 | 513222.60 | 2925341.00 | 4.90 |
513258.57 | 2925434.00 | 5.93 | 513245.40 | 2925397.00 | 1.68 | 513226.34 | 2925340.00 | 4.90 |
513264.70 | 2925431.00 | 5.94 | 513250.84 | 2925396.00 | 1.56 | 513228.63 | 2925340.00 | 4.89 |
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Aghamolaei, Z., Hessami-Kermani, MR. Developing a New Artificial Intelligence Framework to Estimate the Thalweg of Rivers. Water Resour Manage 37, 5893–5917 (2023). https://doi.org/10.1007/s11269-023-03632-8
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DOI: https://doi.org/10.1007/s11269-023-03632-8