Download - sand bed calculation.ppt
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The Stream Restoration ToolboxThe Stream Restoration Toolbox consists of current basic research cast into the form of tools that can be used by practitioners. The details of a tool are presented through a PowerPoint presentation, augmented by embedded Excel spreadsheets or other commonly available applications. The toolbox is a vehicle for bringing research findings into practice. While many tools are being developed by NCED Researchers, the opportunity to contribute a tool to the Toolbox is open to the community. For more information on how to contribute please contact Jeff Marr at [email protected].
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Statement of liability and usageThis tool is provided free of charge. Use this tool at your own risk. In offering this tool, the following entities and persons do not accept any responsibility or liability for the tools use by third parties: The National Center for Earth-surface Dynamics; The universities and institutions associated with the National Center for Earth-surface dynamics; andThe authors of this tool. Users of this tool assume all responsibility for the tool results and application thereof. The readers of the information provided by the Web site assume all risks from using the information provided herein. None of the above-mentioned entities and persons assume liability or responsibility for damage or injury to persons or property arising from any use of the tool, information, ideas or instruction contained in the information provided to you.
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Title Page Tool Title: The calculator for topographic characteristics and sediment transport from sand bed surveysTool Author: Brandon McElroyAuthor e-mail: [email protected]
Version: 1.1Associated files:1) SandBedCalc.ppt (this file)2) SandBedCalc.xls
Date: May, 2006
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Outline of this DocumentLimitationsBed material load only, not total loadRequires high data integrity, accurate surveyingMinimum data standards MotivationA.TheoreticApplied
Schematic Overview
Introduction to Tool
Theory Behind ToolCharacteristic Height & LengthSediment Flux from Mass ConservationTranslation and Characteristic Velocity
Using the Tool
VIIReferences
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-Estimates of bed geometry and sediment transport produced with this tool are only snapshots of very dynamic systems and are onlyvalid for the transport conditions under which bed was surveyed
-Estimates of sediment flux produced with this tool are inherently limitedby the quality of topographic data used to produce them
-Minimum data standards for reliable tool accuracy-Ten or more characteristic dune lengths in total survey-Many tens of elevation measurements per characteristic dune length-Survey locations repeated within a very small fractionof characteristic dune lengthWarnings on tool limitations
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THEORETIC -Characterizing bed topography and sediment transport in sandy systemsis essential for elucidating underlying processes their relations
-Using remote sensing methods, e.g. acoustic doppler, avoids effects of interfering with systems while collecting data, e.g. sediment traps
APPLIED -Rates of sediment delivery to deltas are a fundamental part of theiroverall sediment budgets
-Understanding effects of sediment loads on ecosystems requiresinformation on sediment fluxes
-Characterizations of channels for restoration necessitate transport ratesto evaluate the stability of a reachMotivation
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Tool OverviewInput: 2 or more bed surveysCalculation based on mass conservationOutput: Characteristic Values ofDune HeightDune LengthBed Translation VelocityBed Deformation RateBed Material Sediment Flux
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Introduction to the toolUnder most conditions, sand bedded rivers transport sediment through through the propagation of topographic forms. Each sediment grain moves intermittently such that the bed topography is continually being recreated. In many sandy systems, there is very little sediment suspended into the flow and transported very large distances, but in some instances that style of transport can play a significant role. This tool does not specifically address that case, rather it is focused on the sediment that is an active part of the bed. A low altitude aerial photograph of the N. Loup River, Nebraska. The clarity of the water is indicative of the absence of suspended sediment. The complex bed topography can be seen as contrasts in color intensity. (from D. Mohrig)
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Theory behind toolThis profile comes from the photo in the previous slide and depicts well the complexity of the bed topography. The salient features can, however, be straightforwardly characterized by statistical measures of height and length. That is achieved by calculating the variability of elevations for profile subsets of many different lengths. It is called the roughness function.(1)R = roughness function [m]L = profile subset length [m]N = number of profile subsets of length L = bed elevation [m]L = mean bed elevation of subset [m]i = index of measurements [/]
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Theory behind toolThe roughness plot has 2 distinct regimes. One in which R is nearly constant and another in which the slope of R is nearly constant. The value of R at large lengths is the saturation height. The mid point of the transition to constant slopes at lower R occurs at the saturation length. The saturation height and length are related proportionally to a characteristic height and length, respectively, by factors near 1.Plot of roughness function for profile in previous slideSaturation Height = 3.8cmSaturation Length = 190cm
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Theory behind toolIn the plot above, the 2 profiles were taken at the same location about half an hour apart, and the gray profile retains much of the form of the black profile. Specifically the bed has been acted upon in a way that gives the appearance that it has been both translated in the direction of sediment transport and that it has been deformed from its initial configuration. That behavior can be understood within the context of the conservation of mass of the bed sediment, i.e. Exners equation:-- Initial Profile-- Subsequent Profile
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Theory behind toolExners Equationqs= sediment flux [m2/s]x = position along profile [m]Cb= sediment concentration in bed [/] = bed elevation [m]t = time [s]By using the chain rule in the right-hand side an equation that can be directly integrated is obtained. Vc is a characteristic velocity.This is the equation implemented in the accompanying Excel file tocalculate sediment transport.(2)
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Theory behind tool(3)Traditionally, equation 2 has been evaluated for geometrically regular bed topography, as above, leading to the bedload equation. (Eq. 3; Simons, et al., 1971) Further, the constant of integration, qs0 had been assumed zero both for convenience and because is was argued to represent an otherwise negligibly small amount of transport via suspension.
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Theory behind toolThis shows the same profiles as before separated by half an hour, but here the subsequent profile has been shifted backward by the translation length, the mean distance of bed propagation. It can be quickly seen that certain parts of the bed changed faster than others. (see red arrows) The deformation is then measured by the amount of non-overlapping area. The two equations below distinguish the parts of the total sediment flux, the translative flux and the deformative flux. Their sum is exactly equation 2.
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Theory behind toolcross-correlation functionTo determine the translation length, the evolved profile is cross-correlated with the initial profile. The resulting correlation function has a maximum at the translation length. The characteristic velocity, Vc is then the length divided by the time between surveyed profiles.
Chart1
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Shift Distance [m]
Correlation value [/]
Cross-correlation plot
Example
Height0.1125063528
Length2.91
Velocity
Deformation Rate
Bed Material Flux
Time10:3511:03
[hr]019
PositionDepthDepth
[m][m][m]
0-0.0270.0050.0641042153
0.02-0.0320.0140.0768113971
0.04-0.0310.0230.0900580645
0.06-0.0320.0240.1036609365
0.08-0.0350.0290.1175186906
0.1-0.0370.0370.1317785822
0.12-0.0360.040.146560847
0.14-0.0330.0370.1616128547
0.16-0.0290.0380.176730159
0.18-0.0250.0390.1921433248
0.2-0.0160.0370.2078257831
0.22-0.0120.0330.2235298568
0.24-0.010.0340.2393375045
0.26-0.0120.040.2555770109
0.28-0.0110.0440.2722150521
0.3-0.0080.0440.2886927787
0.32-0.0050.0430.3048435717
0.34-0.0010.0450.3210416485
0.360.0030.0430.3374680384
0.3800.0370.3537597821
0.4-0.0110.0330.369599853
0.42-0.0130.0370.3850418394
0.44-0.010.0440.4001424818
0.46-0.0050.0480.4147720876
0.48-0.0090.0510.4289428154
0.5-0.010.0480.4428037218
0.52-0.0060.0460.4561530626
0.540.0010.0410.4686373351
0.560.0080.0380.48007551
0.580.0110.0360.4907256216
0.60.0140.0360.5007200646
0.620.0180.040.5099926417
0.640.0230.0450.5184861621
0.660.0180.0450.5262843855
0.680.0110.0370.5335219581
0.70.0070.0310.5400953061
0.720.0050.0280.5460593686
0.740.0040.0310.5515911222
0.7600.0340.5569531044
0.7800.0330.5620124703
0.80.0070.0340.566571979
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0.860.0250.0360.5782501754
0.880.0280.0310.5816298408
0.90.0290.0260.5846060179
0.920.030.0240.5869211225
0.940.0320.0230.5884594219
0.960.0340.0220.5891691292
0.980.030.020.5890578997
10.030.0190.5881527528
1.020.0270.0190.5864032524
1.040.0250.0130.5841516432
1.060.0250.0030.58153077
1.080.026-0.0070.5782740425
1.10.027-0.0110.5738712458
1.120.024-0.0180.5681989918
1.140.021-0.020.5615747575
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1.20.02-0.0240.5358140963
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1.240.02-0.0350.5143630152
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1.280.024-0.0410.4887824828
1.30.027-0.0490.4741843996
1.320.028-0.0530.4585411193
1.340.028-0.0540.4419458587
1.360.027-0.0510.4245742432
1.380.035-0.0490.4065690249
1.40.045-0.0470.3880585454
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1.440.052-0.0340.3497140907
1.460.057-0.0280.329734211
1.480.059-0.0250.3091518008
1.50.055-0.0260.2878038434
1.520.051-0.030.2653386375
1.540.044-0.0260.2418439959
1.560.037-0.0210.2178571525
1.580.031-0.0190.1938653556
1.60.028-0.020.17000145
1.620.028-0.0220.146223556
1.640.025-0.0160.1226757764
1.660.022-0.0120.0994819497
1.680.019-0.0130.0764664506
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1.740.0230.0020.0088794461
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1.860.030.013-0.108581153
1.880.0260.016-0.1247634685
1.90.0220.02-0.1400379351
1.920.0220.026-0.1542636022
1.940.0170.027-0.1674368671
1.960.010.025-0.1798729552
1.9800.027-0.1917398365
2-0.0110.031-0.2027249875
2.02-0.0210.036-0.2125582154
2.04-0.0240.037-0.2213624577
2.06-0.0250.037-0.2291854488
2.08-0.0260.035-0.2357637504
2.1-0.0270.036-0.2408343743
2.12-0.0310.037-0.2444054266
2.14-0.0370.034-0.2469839694
2.16-0.0420.028-0.248933863
2.18-0.0480.024-0.2502870802
2.2-0.0570.023-0.2509022198
2.22-0.070.026-0.25062257
2.24-0.0810.031-0.2495197318
2.26-0.090.031-0.2475910033
2.28-0.0940.033-0.2449651766
2.3-0.0970.035-0.2415747034
2.32-0.10.039-0.2373858096
2.34-0.10.04-0.2325092744
2.36-0.0970.041-0.2270810949
2.38-0.0980.044-0.2210720002
2.4-0.1030.042-0.2144455142
2.42-0.10.038-0.2074817372
2.44-0.0940.037-0.2003378314
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27.080.0210.024
27.10.0230.031
27.120.0240.03
27.140.0230.031
27.160.0210.027
27.180.0190.027
27.20.0170.023
27.220.0180.027
27.240.0170.025
27.260.0170.022
27.280.0160.019
27.30.0120.021
27.320.010.024
27.340.0090.024
27.360.0080.025
27.380.0060.024
27.40.0050.022
27.420.0080.02
27.440.0090.017
27.460.0060.012
27.480.0040.01
27.50.0010.014
27.5200.018
27.540.0030.017
27.560.0060.019
27.580.0090.024
27.60.0140.029
27.620.020.027
27.640.0230.023
27.660.0260.022
27.680.0280.022
27.70.0310.024
27.720.0320.027
27.740.0320.032
27.760.0350.037
27.780.0350.04
27.80.0340.04
27.820.0340.04
27.840.0340.041
27.860.0360.036
27.880.0350.03
27.90.0360.027
27.920.0390.028
27.940.0420.032
27.960.0440.034
27.980.0410.035
280.040.036
28.020.0420.04
28.040.0460.046
28.060.0470.048
28.080.0470.048
28.10.0480.05
28.120.0480.053
28.140.0440.053
28.160.0420.049
28.180.0410.044
28.20.0420.045
28.220.0390.047
28.240.0360.047
28.260.0340.045
28.280.0340.045
28.30.0350.043
28.320.0360.041
28.340.0370.039
28.360.0370.04
28.380.0350.039
28.40.0350.035
28.420.0370.03
28.440.0370.033
28.460.0380.037
28.480.040.036
28.50.040.031
28.520.0390.03
28.540.0380.033
28.560.0380.033
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28.60.0340.035
28.620.0310.035
28.640.0320.034
28.660.0290.039
28.680.0240.044
28.70.020.046
28.720.0170.047
28.740.0130.048
28.760.0110.051
28.780.0120.051
28.80.0130.049
28.820.0130.049
28.840.0120.052
28.860.0110.054
28.880.0070.053
28.90.0060.048
28.920.0090.048
28.940.0120.051
28.960.0130.053
28.980.0160.051
290.020.047
29.020.020.046
29.040.0180.041
29.060.0180.035
29.080.0210.03
29.10.0250.029
29.120.0280.03
29.140.0310.03
29.160.0360.03
29.180.040.03
29.20.040.031
29.220.040.03
29.240.0410.031
29.260.0430.034
29.280.0440.037
29.30.0440.037
29.320.0430.033
29.340.0440.032
29.360.0440.034
29.380.0430.038
29.40.0410.041
29.420.0420.041
29.440.0410.039
29.460.0370.035
29.480.0340.029
29.50.0290.018
29.520.0240.004
29.540.02-0.003
29.560.016-0.002
29.580.0150.002
29.60.0140.003
29.620.0120.006
29.640.0070.01
29.6600.014
29.68-0.0080.011
29.7-0.0130.007
29.72-0.0180.002
29.74-0.0220.007
29.76-0.0240.018
29.78-0.0240.03
29.8-0.0250.031
29.82-0.0270.029
29.84-0.0270.03
29.86-0.0250.034
29.88-0.0250.037
29.9-0.0280.036
29.92-0.0330.032
29.94-0.0330.029
29.96-0.0330.033
29.98-0.0320.038
30-0.0310.044
30.02-0.030.044
30.04-0.030.042
30.06-0.0290.038
30.08-0.0270.036
30.1-0.0260.038
30.12-0.0250.04
30.14-0.0210.043
30.16-0.0130.047
30.18-0.0090.047
30.2-0.0090.044
30.22-0.010.041
30.24-0.0080.048
30.26-0.0040.048
30.28-0.0040.046
30.3-0.0040.043
30.32-0.0020.044
30.340.0020.045
30.360.0040.045
30.380.0020.044
30.40.0040.044
30.420.0070.041
30.440.0110.044
30.460.0130.044
30.480.0130.049
30.50.0130.052
30.520.0110.054
30.540.0090.051
30.560.0060.047
30.580.0050.048
30.60.0070.044
30.620.0080.045
30.640.0090.042
30.660.010.043
30.680.0130.046
30.70.0140.049
30.720.0130.051
30.740.0140.049
30.760.0140.043
30.780.0120.043
30.80.0070.038
30.820.0030.034
30.84-0.0020.025
30.86-0.0070.019
30.88-0.0110.012
30.9-0.0110.008
30.92-0.0140.006
30.94-0.0170.005
30.96-0.020
30.98-0.0240
Example
Shift Distance [m]
Correlation value [/]
Cross-correlation plot
DataInput
0.1125063528
2.91
Time10:4010:59
[hr]
PositionDepthDepth
[m][m][m]
0-0.0530.02
0.02-0.0550.019
0.04-0.0530.024
0.06-0.0470.026
0.08-0.040.027
0.1-0.0410.029
0.12-0.0410.033
0.14-0.0390.042
0.16-0.0350.045
0.18-0.0340.042
0.2-0.0370.037
0.22-0.0380.036
0.24-0.0380.035
0.26-0.0380.031
0.28-0.0460.024
0.3-0.0440.02
0.32-0.0360.017
0.34-0.0280.015
0.36-0.0250.014
0.38-0.0240.02
0.4-0.0290.025
0.42-0.0320.03
0.44-0.0320.032
0.46-0.0250.035
0.48-0.030.033
0.5-0.0430.028
0.52-0.0430.025
0.54-0.0360.02
0.56-0.0290.017
0.58-0.0240.016
0.6-0.0170.016
0.62-0.0060.011
0.64-0.0080.006
0.66-0.0110.009
0.68-0.0130.012
0.7-0.0160.007
0.72-0.0140.002
0.74-0.011-0.002
0.76-0.011-0.006
0.78-0.013-0.014
0.8-0.014-0.012
0.82-0.011-0.008
0.84-0.013-0.009
0.86-0.012-0.014
0.88-0.01-0.018
0.9-0.004-0.022
0.92-0.002-0.031
0.94-0.002-0.036
0.96-0.001-0.029
0.98-0.001-0.029
10.002-0.036
1.020.008-0.043
1.040.01-0.042
1.060.014-0.038
1.080.013-0.04
1.10.012-0.043
1.120.009-0.046
1.140.007-0.042
1.160.009-0.041
1.180.011-0.04
1.20.012-0.042
1.220.018-0.038
1.240.022-0.036
1.260.018-0.036
1.280.011-0.031
1.30.012-0.024
1.320.02-0.027
1.340.023-0.031
1.360.026-0.029
1.380.025-0.022
1.40.021-0.017
1.420.017-0.02
1.440.012-0.017
1.460.008-0.008
1.480.009-0.003
1.50.01-0.001
1.520.017-0.002
1.540.018-0.002
1.560.015-0.003
1.580.01-0.009
1.60.006-0.012
1.620.014-0.014
1.640.022-0.014
1.660.017-0.008
1.680.0130.005
1.70.0150.015
1.720.0220.018
1.740.0260.015
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1.780.0280.018
1.80.0260.02
1.820.0140.019
1.840.010.017
1.860.0090.019
1.880.0090.016
1.90.0040.015
1.920.0040.018
1.940.0090.022
1.960.0080.02
1.980.0040.02
20.0040.02
2.0200.021
2.04-0.0040.019
2.06-0.0080.016
2.08-0.0120.017
2.1-0.0160.017
2.12-0.0230.02
2.14-0.0260.021
2.16-0.0310.016
2.18-0.0360.016
2.2-0.0380.02
2.22-0.0430.021
2.24-0.0470.02
2.26-0.0550.022
2.28-0.0630.026
2.3-0.0780.025
2.32-0.0880.02
2.34-0.0940.02
2.36-0.0920.023
2.38-0.0910.019
2.4-0.0880.017
2.42-0.090.019
2.44-0.0950.021
2.46-0.0930.019
2.48-0.0840.014
2.5-0.0830.011
2.52-0.0860.007
2.54-0.0920.004
2.56-0.089-0.004
2.58-0.096-0.01
2.6-0.108-0.008
2.62-0.11-0.005
2.64-0.103-0.003
2.66-0.102-0.006
2.68-0.106-0.009
2.7-0.11-0.012
2.72-0.105-0.026
2.74-0.093-0.039
2.76-0.082-0.049
2.78-0.071-0.056
2.8-0.068-0.058
2.82-0.07-0.062
2.84-0.072-0.065
2.86-0.08-0.074
2.88-0.082-0.082
2.9-0.084-0.092
2.92-0.079-0.096
2.94-0.076-0.098
2.96-0.073-0.099
2.98-0.073-0.096
3-0.067-0.095
3.02-0.064-0.095
3.04-0.061-0.098
3.06-0.059-0.098
3.08-0.053-0.092
3.1-0.046-0.085
3.12-0.047-0.08
3.14-0.044-0.074
3.16-0.04-0.072
3.18-0.042-0.072
3.2-0.05-0.071
3.22-0.051-0.07
3.24-0.047-0.073
3.26-0.038-0.08
3.28-0.032-0.086
3.3-0.023-0.084
3.32-0.018-0.089
3.34-0.02-0.094
3.36-0.021-0.095
3.38-0.015-0.092
3.4-0.007-0.094
3.42-0.001-0.095
3.44-0.001-0.084
3.46-0.003-0.073
3.480-0.07
3.50.008-0.073
3.520.013-0.075
3.540.011-0.078
3.560.004-0.074
3.580.004-0.068
3.60.005-0.064
3.620.003-0.061
3.640.005-0.053
3.660.01-0.042
3.680.014-0.037
3.70.019-0.039
3.720.024-0.041
3.740.026-0.037
3.760.025-0.032
3.780.026-0.032
3.80.026-0.034
3.820.018-0.031
3.840.015-0.025
3.860.019-0.025
3.880.03-0.024
3.90.039-0.019
3.920.043-0.014
3.940.044-0.01
3.960.046-0.011
3.980.045-0.011
40.042-0.013
4.020.037-0.015
4.040.041-0.018
4.060.049-0.017
4.080.05-0.019
4.10.051-0.022
4.120.054-0.021
4.140.063-0.01
4.160.068-0.001
4.180.0740.002
4.20.0760.008
4.220.0730.014
4.240.070.02
4.260.0710.023
4.280.0690.03
4.30.0620.038
4.320.0580.035
4.340.0580.032
4.360.0550.033
4.380.0440.035
4.40.0390.033
4.420.0360.028
4.440.0340.025
4.460.0330.027
4.480.0320.027
4.50.0280.021
4.520.0290.019
4.540.0310.019
4.560.0340.021
4.580.030.021
4.60.0270.023
4.620.030.026
4.640.0290.022
4.660.0220.018
4.680.0160.021
4.70.0120.024
4.720.0080.022
4.74-0.0010.02
4.760.0010.022
4.780.0110.02
4.80.0190.013
4.820.0160.006
4.840.0170.003
4.860.022-0.001
4.880.025-0.008
4.90.02-0.012
4.920.015-0.006
4.940.0120.003
4.960.0070.005
4.980.001-0.001
5-0.004-0.001
5.02-0.0060.009
5.04-0.0110.017
5.06-0.0180.024
5.08-0.0260.025
5.1-0.0230.025
5.12-0.0190.02
5.14-0.0160.015
5.16-0.020.015
5.18-0.0250.015
5.2-0.0310.01
5.22-0.0420.01
5.24-0.0460.013
5.26-0.0530.016
5.28-0.060.015
5.3-0.0660.015
5.32-0.0620.019
5.34-0.0510.02
5.36-0.050.021
5.38-0.0480.022
5.4-0.0450.021
5.42-0.0380.021
5.44-0.0330.02
5.46-0.0350.021
5.48-0.0290.017
5.5-0.0270.012
5.52-0.020.009
5.54-0.0170.007
5.56-0.0140.01
5.58-0.0120.008
5.6-0.016-0.003
5.62-0.018-0.019
5.64-0.012-0.031
5.66-0.007-0.037
5.68-0.011-0.042
5.7-0.016-0.048
5.72-0.013-0.054
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60.033-0.049
6.020.032-0.046
6.040.031-0.041
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6.080.023-0.035
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6.120.023-0.035
6.140.024-0.038
6.160.026-0.043
6.180.03-0.047
6.20.035-0.043
6.220.033-0.035
6.240.029-0.032
6.260.028-0.029
6.280.03-0.019
6.30.032-0.008
6.320.0340
6.340.0380.005
6.360.040.011
6.380.0390.011
6.40.0380.008
6.420.0420.009
6.440.0470.013
6.460.0510.017
6.480.0520.021
6.50.0510.027
6.520.0490.03
6.540.0440.03
6.560.0390.033
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6.60.0370.047
6.620.0410.047
6.640.0440.047
6.660.040.048
6.680.0360.049
6.70.0330.045
6.720.0320.04
6.740.0290.042
6.760.0310.044
6.780.0370.045
6.80.0410.046
6.820.0390.05
6.840.0380.056
6.860.0360.059
6.880.0390.059
6.90.0410.061
6.920.0450.062
6.940.0460.061
6.960.0470.06
6.980.0540.059
70.060.058
7.020.0630.058
7.040.0620.056
7.060.060.058
7.080.0610.063
7.10.0630.069
7.120.0640.073
7.140.0670.071
7.160.0680.072
7.180.0650.071
7.20.0640.067
7.220.0650.061
7.240.0650.057
7.260.0610.055
7.280.0620.047
7.30.0650.036
7.320.0660.027
7.340.0650.025
7.360.0650.022
7.380.0690.01
7.40.068-0.003
7.420.071-0.009
7.440.076-0.011
7.460.081-0.013
7.480.081-0.018
7.50.083-0.017
7.520.085-0.014
7.540.086-0.011
7.560.082-0.009
7.580.077-0.01
7.60.077-0.013
7.620.077-0.01
7.640.073-0.005
7.660.066-0.005
7.680.059-0.003
7.70.055-0.003
7.720.051-0.003
7.740.047-0.006
7.760.046-0.007
7.780.044-0.003
7.80.0420.001
7.820.0380.003
7.840.0320.005
7.860.0310.01
7.880.0290.016
7.90.0290.021
7.920.0270.021
7.940.0250.021
7.960.0230.023
7.980.020.024
80.0190.019
8.020.0180.015
8.040.0170.013
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8.10.0130.003
8.120.0070.008
8.140.0040.017
8.1600.025
8.18-0.0070.031
8.2-0.0160.034
8.22-0.0210.035
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8.28-0.0330.043
8.3-0.0450.05
8.32-0.0510.053
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8.36-0.0560.05
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8.4-0.0480.053
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8.44-0.0520.055
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8.48-0.0420.06
8.5-0.0360.064
8.52-0.0270.064
8.54-0.0170.057
8.56-0.0130.055
8.58-0.0090.056
8.6-0.0040.06
8.620.0010.061
8.640.0070.058
8.660.010.057
8.680.0140.057
8.70.0160.058
8.720.0150.056
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8.760.0040.049
8.780.0030.048
8.80.0040.045
8.820.0060.04
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8.90.0280.028
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90.0450.024
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9.10.0450.033
9.120.0520.033
9.140.0560.033
9.160.0570.033
9.180.0550.032
9.20.0520.027
9.220.0480.022
9.240.0420.02
9.260.0340.022
9.280.0270.021
9.30.0230.019
9.320.0170.013
9.340.0050.009
9.36-0.0080.006
9.38-0.010.006
9.4-0.0110.004
9.42-0.0130.003
9.44-0.0160.002
9.46-0.02-0.001
9.48-0.026-0.001
9.5-0.0310
9.52-0.033-0.002
9.54-0.0350
9.56-0.0360.003
9.58-0.0340.008
9.6-0.0320.008
9.62-0.0360.008
9.64-0.0410.014
9.66-0.0480.019
9.68-0.0510.022
9.7-0.0510.02
9.72-0.0480.022
9.74-0.0450.025
9.76-0.0430.025
9.78-0.0390.021
9.8-0.0370.02
9.82-0.0350.02
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9.86-0.0330.022
9.88-0.030.02
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9.92-0.0260.015
9.94-0.0250.018
9.96-0.0220.021
9.98-0.0170.021
10-0.0140.018
10.02-0.0110.014
10.04-0.0120.013
10.06-0.0070.013
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10.1-0.0060.012
10.1200.016
10.1400.021
10.16-0.0040.025
10.18-0.0070.029
10.2-0.0030.032
10.220.0030.033
10.24-0.0040.032
10.26-0.0050.033
10.280.0010.03
10.30.0090.024
10.320.0120.019
10.340.0130.019
10.360.0180.02
10.380.0220.014
10.40.0220.007
10.420.0250.002
10.440.027-0.001
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10.50.031-0.009
10.520.03-0.002
10.540.026-0.001
10.560.027-0.003
10.580.028-0.007
10.60.026-0.01
10.620.026-0.013
10.640.03-0.019
10.660.035-0.023
10.680.035-0.024
10.70.039-0.022
10.720.046-0.022
10.740.048-0.021
10.760.042-0.019
10.780.034-0.017
10.80.036-0.015
10.820.04-0.012
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10.860.033-0.007
10.880.029-0.004
10.90.03-0.003
10.920.032-0.007
10.940.03-0.009
10.960.031-0.009
10.980.033-0.007
110.036-0.01
11.020.039-0.012
11.040.038-0.011
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