radar rainfall estimate experience in taiwan taichi chen wang,national central university goals:...
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Radar rainfall estimate experience in Taiwan
TaiChi Chen Wang ,National Central University
Goals:
Precipitation mechanisms in Taiwan area. Rainfall estimate from radar, disdrometer and raingauge network. Ground truth validation.
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Base data advantages CWB High density rain gauge network CWB S-Band Doppler radar network (since 2001) Difficulties Less rain gauge sites in mountain area Few gauges over ocean Terrain blocking of radar beams Heavy rain events often occur in mountain area
Z-R relations variability from QPESUMS
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QPESUMS : (2005)
CWBs solution to real time rainfall estimate
QC to radar and gauge data
Compensation for partial beam
Using gauge data to calibrate radar estimate
Rain map every 6-8 minutes
Good results in dense gauges area.
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TRMM/SCSMEX experience (1998)
Instruments: C-Pol radar, ARG Data processing: Attenuation effect in ZHH and ZDR ZDR bias KDP calculationRainfall estimate with polarimetric variables.
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Typhoon Nari (2001)
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Chart1
16.2771462.89
38.7883751.74
64.7517476.53
88.79711510.81
93.19511016.71
43.485095.68
28.8172469.21
24.7531886.55
22.4611906.07
20.0081765.85
&A
Page &P
Rain(2d)
Nt
mm/hr
Chart2
49.62216.2774.098
27.66438.7881.28
33.77864.7512.101
26.72788.7971.037
24.90493.1950.77
30.15643.481.251
47.24828.8173.906
48.75624.7534.201
46.89122.4613.761
44.09520.0083.174
&A
Page &P
lambda
Rain(2d)
m
lambda & mm/hr
m
Chart3
16.2770.1565
38.7880.1789
64.7510.1709
88.7970.1761
93.1950.1783
43.480.1632
28.8170.1603
24.7530.1614
22.4610.1585
20.0080.1552
&A
Page &P
Rain(2d)
D0
mm/hr
cm
Chart4
16.27740.1
38.78846.22
64.75147.63
88.79749.74
93.19550.17
43.4845.66
28.81742.7
24.75342.01
22.46141.5
20.00840.9
Rain(2d)
dBZ(2d)
mm/hr & dBZ
Chart5
16.277296.7661.2657
38.788251.2931.3916
64.751207.041.3441
88.797167.9621.4082
93.195161.0991.4283
43.48195.3451.3935
28.817269.8521.2717
24.753290.0561.2627
22.461279.6861.2764
20.008269.0351.297
&A
Page &P
Rain(2d)
A
b
Rain(2d) & A
b
Sheet1
mgammaN(D)log10 N(D)raintiprain2dmN(D)G-solLSFrainradnDrRnDcRG(D)RL(D)RnumberTlog10 NtnDiZnidBZG(D)ZL(D)ZABD0
2:064.09849.6221.48E+1010.1702617154152:0616.2774.09816.37616.40715.44416.40520.3416.3816.4115.441462.893.165211671210239.0340.110241.968478.98296.7661.26570.1565
2:121.2827.6644.09E+066.611723308342:1238.7881.2839.439.49540.28239.49554.0439.439.540.283751.743.574232733641867.4446.2241871.9940645.18251.2931.39160.1789
2:182.10133.7789.46E+077.9758911364592:1864.7512.10165.95166.17867.97466.176107.3765.9566.1867.977476.533.873700080357974.5547.6357983.5648312.93207.041.34410.1709
2:241.03726.7275.10E+066.7075701761792:2488.7971.03789.09489.48190.36889.48164.6289.0989.4890.3711510.814.061105885494128.0549.7494136.9874800.68167.9621.40820.1761
2:300.7724.9042.31E+066.3636119799802:3093.1950.7792.40792.75598.00592.755180.4892.4192.7598.0111016.714.0420519174104001.2950.17104008.7394063.27161.0991.42830.1783
2:361.25130.1567.06E+066.8488047011372:3643.481.25142.86842.95644.14542.956100.4142.8742.9644.155095.683.707202147236853.1745.6636857.2437068.02195.3451.39350.1632
2:423.90647.2481.16E+1010.0644579892272:4228.8173.90627.85327.90925.75927.90637.5327.8527.9125.762469.213.392558027118604.9942.718610.0715260.41269.8521.27170.1603
2:484.20148.7562.20E+1010.3424226808222:4824.7534.20123.7723.81722.22623.81432.623.7723.8222.231886.553.2756683215883.2742.0115887.9513092.21290.0561.26270.1614
2:543.76146.8916.55E+099.8162413202:5422.4613.76121.57721.6220.7621.61829.4821.5821.6220.761906.073.28013884614137.7141.514141.4312507.79279.6861.27640.1585
3:003.17444.0951.23E+099.0899051114173:0020.0083.17419.0319.05217.90519.05124.8619.0319.0517.911765.853.246953809712299.840.912302.5211486.06269.0351.2970.1552
Rain(2d)dBZmlambdaD0
2:1238.78846.221.2827.6640.1789
2:1864.75147.632.10133.7780.1709
2:2488.79749.741.03726.7270.1761
2:3043.4845.661.25130.1560.1632
Rain(2d)dBZmlambdaD0
2:2488.79749.741.0371.0370.1761
2:3093.19550.170.7724.9040.1783
D0Ab
1.25
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log10 R vs log10Z log10Z+ : Do < 0.125 cm : 0.125< Do < 0.150 cm. : 0.150 0.175 cm
Chart1
16.2771462.89
38.7883751.74
64.7517476.53
88.79711510.81
93.19511016.71
43.485095.68
28.8172469.21
24.7531886.55
22.4611906.07
20.0081765.85
&A
Page &P
Rain(2d)
Nt
mm/hr
Chart2
49.62216.2774.098
27.66438.7881.28
33.77864.7512.101
26.72788.7971.037
24.90493.1950.77
30.15643.481.251
47.24828.8173.906
48.75624.7534.201
46.89122.4613.761
44.09520.0083.174
&A
Page &P
lambda
Rain(2d)
m
lambda & mm/hr
m
Chart3
16.2770.1565
38.7880.1789
64.7510.1709
88.7970.1761
93.1950.1783
43.480.1632
28.8170.1603
24.7530.1614
22.4610.1585
20.0080.1552
&A
Page &P
Rain(2d)
D0
mm/hr
cm
Chart4
16.27740.1
38.78846.22
64.75147.63
88.79749.74
93.19550.17
43.4845.66
28.81742.7
24.75342.01
22.46141.5
20.00840.9
Rain(2d)
dBZ(2d)
mm/hr & dBZ
Chart5
16.277296.7661.2657
38.788251.2931.3916
64.751207.041.3441
88.797167.9621.4082
93.195161.0991.4283
43.48195.3451.3935
28.817269.8521.2717
24.753290.0561.2627
22.461279.6861.2764
20.008269.0351.297
&A
Page &P
Rain(2d)
A
b
Rain(2d) & A
b
Sheet1
mgammaN(D)log10 N(D)raintiprain2dmN(D)G-solLSFrainradnDrRnDcRG(D)RL(D)RnumberTlog10 NtnDiZnidBZG(D)ZL(D)ZABD0
2:064.09849.6221.48E+1010.1702617154152:0616.2774.09816.37616.40715.44416.40520.3416.3816.4115.441462.893.165211671210239.0340.110241.968478.98296.7661.26570.1565
2:121.2827.6644.09E+066.611723308342:1238.7881.2839.439.49540.28239.49554.0439.439.540.283751.743.574232733641867.4446.2241871.9940645.18251.2931.39160.1789
2:182.10133.7789.46E+077.9758911364592:1864.7512.10165.95166.17867.97466.176107.3765.9566.1867.977476.533.873700080357974.5547.6357983.5648312.93207.041.34410.1709
2:241.03726.7275.10E+066.7075701761792:2488.7971.03789.09489.48190.36889.48164.6289.0989.4890.3711510.814.061105885494128.0549.7494136.9874800.68167.9621.40820.1761
2:300.7724.9042.31E+066.3636119799802:3093.1950.7792.40792.75598.00592.755180.4892.4192.7598.0111016.714.0420519174104001.2950.17104008.7394063.27161.0991.42830.1783
2:361.25130.1567.06E+066.8488047011372:3643.481.25142.86842.95644.14542.956100.4142.8742.9644.155095.683.707202147236853.1745.6636857.2437068.02195.3451.39350.1632
2:423.90647.2481.16E+1010.0644579892272:4228.8173.90627.85327.90925.75927.90637.5327.8527.9125.762469.213.392558027118604.9942.718610.0715260.41269.8521.27170.1603
2:484.20148.7562.20E+1010.3424226808222:4824.7534.20123.7723.81722.22623.81432.623.7723.8222.231886.553.2756683215883.2742.0115887.9513092.21290.0561.26270.1614
2:543.76146.8916.55E+099.8162413202:5422.4613.76121.57721.6220.7621.61829.4821.5821.6220.761906.073.28013884614137.7141.514141.4312507.79279.6861.27640.1585
3:003.17444.0951.23E+099.0899051114173:0020.0083.17419.0319.05217.90519.05124.8619.0319.0517.911765.853.246953809712299.840.912302.5211486.06269.0351.2970.1552
Rain(2d)dBZmlambdaD0
2:1238.78846.221.03727.6640.1789
2:3043.4845.661.25130.1560.1632
Rain(2d)dBZmlambdaD0
2:2488.79749.741.0371.0370.1761
2:3093.19550.170.7724.9040.1783
D0Ab
1.25 < D0 < 1.52571.3
1.5 < D0 < 1.752691.29
D0 > 1.752941.35
Sheet3
No.RggammadBZAbgmlmggammalgammagn0ln0d0
593.225.3350.05185.151.41240.9792025.3319.793.32E+062.03E+050.18355
488.827.349.56191.751.39251.2662027.318.557.78E+068.72E+040.18079
364.7534.9947.38232.351.32782.4375034.9924.031.96E+086.51E+050.17454
643.4830.0845.51214.371.38731.3466030.0821.37.59E+061.37E+050.1668
238.7927.9646.1277.271.38071.4506027.9618.225.39E+064.83E+040.18315
728.8247.9542.41286.581.26544.1102047.9531.131.75E+105.21E+060.16227
824.7549.8841.7307.41.25494.4716049.8832.314.00E+109.12E+060.16323
922.4647.8241.25298.781.26824.0179047.8232.041.13E+106.59E+060.16078
1020.0144.3240.66286.261.29213.30751.012544.3228.921.50E+091.65E+060.15742
116.2851.0639.77314.361.25664.4114051.0631.663.06E+104.40E+060.15826
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Radar reflectivity underestimate
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: 1600 ~ 1700 ( UTC )Z (+3 dBZ ) with modified Z-R xRadar
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Drop size distribution and Z-R variability from two years (2001-2003)2D-video disrometer data
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The narrow Do distribution for heavy rainfall rate (> 65mm/hr) happened in typhoon and Mei-Yu cases.
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Disdrometer network (2004)Radar reflectivity under estimate due to partial beam
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What do we learn from the disdrometer and radar observation?
The classical DSD and Z-R relation variability.
Heavy rain in typhoon has unique DSD. The under estimate reflectivity from terrain blocking.
Careful calibration with disdrometer and raingauges can provide more correct radar rainfall estimate.
Will Polarimetric radar help to provide better rainfall estimate?
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National Central University, Central Weather Bureau, Water Resources Agency and National Science Council help to upgrade the NCU Doppler radar to a dualPolarimetric system. (2004)
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Beam pattern calibration
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In northern Taiwan, two Doppler radars, one polarimetric radar , a few disdrometers and raingauge network.
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A rainband under the influence of typhoon Nanmadol (2004, Dec.)
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10logKDP/No
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2004/12/04 01: 19 to 11:49 NCU radar Si-DuShiDingNangangNan-Gang J-W disdrometerShi-Ding rain gaugeSi-Du raingauge
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51.0mm/hr 12401:1952.2mm/hr KDPZDR
Chart1
-9999
-9999
-9999
-9999
0.699
2.009
2.603
2.625
2.588
2.624
2.863
2.728
2.305
1.944
1.724
1.204
0.477
-9999
-9999
-9999
D(mm)
log(N(D))
Sheet1
0.33.5513.693.3363.7113.5443.6523.5113.4683.4933.5953.2723.4533.5033.4983.3123.213.153.193.4313.4773.4850.36-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
1719330.43.6393.6953.733.6793.6913.7153.6443.5633.5843.5993.5153.5333.5313.493.4663.4393.3483.3333.4213.5063.5280.46-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
0.53.6743.6733.9653.6323.7653.7333.7083.6023.6213.5763.6523.5623.5233.4583.5443.5673.4563.4043.3883.5013.5310.55-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-999900-9999-9999-99990-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990.47700-99990-9999-9999-9999-99990.3010-99990.3010.477-9999-9999-9999-99990-9999-9999-9999-9999-99990.4770-9999-99990-99990-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-999900-99990-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-999900-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
0.63.6753.6344.0983.5743.7933.7223.733.6063.6233.5363.7233.5593.4953.4113.5763.6323.5073.4313.343.4743.5090.66-99990.6020.6020.60200.77810.3010.3010.3010.6990.778-99990.8450.4770.30100000.4770.301-99990.4770.3010.4770-99990.3010.3010.47700.4770.3010.3010.3010.602000.7780.3010.4770.4770.477-99990.301-99990.4770.6990.301000.7780.84500.9031.04100.301-9999-9999-999900.6020.301-9999-9999-9999-999900.6990.6020.69900.6021.04110.9540.3010.6990.6991.1460.9031.0790.7780.8450.4771.1761.1141.0411.0791.0791.1761.2040.8450.90310.3010.8450.6990.3010.6990.6990.60200.6020.8450.6990.8451000.9030.6020.4770.47701.1140.6020.9030.6990.6990.4770.6990.6990.4770.477-99990.3010.3010.47700.301000.602-99990.6990.4770.6020.3010.4770.3010.3010.6020.4770-99990.3010.301-999900.301-999900.4770.95400.60200-9999-99990.3010-9999-9999-9999-99990.4770
0.73.6533.5834.1623.513.7893.6913.7213.5853.6013.4843.7483.5333.4513.3553.5743.6533.5183.4263.2833.4313.4710.770.6990.9031.3011.3010.7781.0791.0791.20411.3011.2041.11410.7781.0410.7780.8450.9031.04110.9540.8450.8450.77811.0410.9541.0790.77811.0410.8451.0410.9030.9031.1141.25511.4311.0410.9030.69910.7781.0410.3010.77810.7781.04111.0791.0791.3421.4621.6330.7781.1141.0790.301-999900.7780.8450.903-9999-9999-9999-99991.0791.381.6230.8450.4771.3421.5311.4311.1461.25511.5311.7321.581.5681.5441.3981.3621.5681.7321.7631.581.5051.7161.7241.5191.6131.5441.4621.381.3981.2041.4151.4911.3011.4311.3221.3221.2551.4311.5681.4311.0791.3221.231.2551.231.4771.5681.3421.5311.3621.4311.0791.3421.1761.20411.1760.9031.0790.9541.380.9541.20411.4151.1140.9541.1141.2041.3620.77811.0791.1461.0790.9540.7780.8450.6990.9540.4770.3010.8450.6020.9031.4770.9030.90310.6020.6020.8451.1460.8450.3010.69900.7780.7780.477
0.83.6133.5234.1753.443.7623.6453.6913.5473.5623.4233.7393.4923.3963.2913.5493.6423.5013.3983.2193.3773.420.912.0092.12.092.141.9592.2072.2232.0862.0722.212.2651.9541.941.8061.9031.8811.9191.8131.9961.9592.0831.8391.9191.8752.1462.2152.1961.9641.8451.8692.1432.0532.0531.9642.142.3012.3072.2992.2862.2972.232.192.2721.7322.1171.6721.692.0131.7851.691.581.7241.9542.0041.8811.6430.6991.4151.3010-99991.1461.6131.6330.9540.301-9999-99990.4772.1992.2942.1731.3011.3981.9032.2941.9821.7481.3421.7322.1462.3842.3692.4712.3582.3712.3672.5282.4332.5762.482.4912.6052.5682.4232.5652.3892.52.2282.2282.1672.252.3582.4082.42.4872.4612.252.3752.3892.2072.0832.382.3752.2922.3012.4962.5292.2672.5172.3652.1792.0532.142.2232.1041.9682.2171.9492.0612.1492.142.12.2552.212.2042.1672.1672.0832.0332.2551.8862.0331.9191.9441.8691.8921.7081.741.691.8451.7081.8261.7321.8261.7322.0831.821.741.8811.821.7561.9141.8861.255-99991.1761.2791.1141.230.602
0.93.563.4564.1493.3663.7183.5883.6453.4953.5093.3563.7053.4373.3343.2223.5053.6073.4633.3523.153.3143.361.122.6032.7622.7922.7242.6742.8022.6952.652.8182.8462.8652.2762.3442.2012.3422.4152.4012.2652.6032.4032.522.352.4812.5052.5552.782.6612.5262.7232.632.6982.6642.7542.6482.9312.9222.9442.782.872.8182.8222.7942.6552.4072.3282.0722.0972.4771.9441.9341.7561.9821.4910.9031.1141.11401.0790.477-9999-99991.0412.0171.1460-9999-9999-99991.742.962.7362.1270.6021.742.2552.431.7781.4151.7852.2072.2622.3712.4072.6512.8162.8982.8182.8182.7392.8742.7932.9983.0062.8972.7192.9262.7862.8042.5012.6772.5562.6332.9012.8032.7582.9592.9162.6032.6252.6962.7542.6372.8592.8922.9872.8432.9342.8222.7822.8322.7662.652.4622.6642.6122.4772.3732.5712.42.5252.5662.6962.5712.7492.8122.6382.5512.4132.4422.4382.6022.312.5212.3262.4232.3032.3182.2652.2532.1882.3712.4362.3782.1372.2332.1372.232.0722.1672.2812.2862.0971.8861.7991.230-99990.301-99990.301-9999
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4.6-0.673-0.172-3.548-0.032-1.017-0.447-0.958-0.787-0.745-0.26-2-0.725-0.44-0.314-1.292-1.946-1.76-1.342-0.375-0.478-0.519
4.7-0.807-0.28-3.812-0.129-1.171-0.572-1.107-0.922-0.879-0.368-2.191-0.856-0.553-0.417-1.448-2.131-1.932-1.494-0.478-0.592-0.638
4.8-0.94-0.387-4.077-0.227-1.325-0.698-1.255-1.058-1.013-0.475-2.383-0.986-0.668-0.521-1.605-2.317-2.105-1.647-0.581-0.707-0.757
4.9-1.074-0.496-4.343-0.324-1.479-0.823-1.405-1.194-1.148-0.582-2.575-1.118-0.782-0.625-1.762-2.504-2.279-1.799-0.684-0.823-0.876
5-1.209-0.604-4.61-0.422-1.634-0.949-1.554-1.33-1.283-0.69-2.768-1.249-0.897-0.729-1.919-2.691-2.454-1.953-0.788-0.938-0.995
5.1-1.343-0.712-4.878-0.52-1.79-1.076-1.704-1.467-1.419-0.798-2.962-1.381-1.012-0.833-2.077-2.879-2.628-2.107-0.892-1.054-1.114
5.2-1.478-0.821-5.147-0.618-1.945-1.202-1.855-1.604-1.555-0.906-3.156-1.513-1.127-0.938-2.235-3.067-2.804-2.261-0.996-1.17-1.234
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0.53.3513.5323.4843.7413.3043.4763.5583.5093.2383.5063.5243.3693.5653.6023.5870.55-9999
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0.73.4473.5793.5053.9433.3493.4673.6333.5443.1923.5023.6243.343.6343.6293.6670.771.301
0.83.4393.5583.4773.9573.3273.433.623.523.1443.4673.6163.2983.6183.6033.6540.912.14
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13.353.463.3733.8743.2283.3183.5273.4193.0213.3553.5283.183.5253.53.5631.332.818
1.13.2793.393.3033.7923.1583.2473.4573.3492.9473.2843.4573.1083.4553.433.4921.512.758
1.23.1953.313.2233.6893.0783.1683.3753.2692.8693.2063.3723.0293.3733.353.411.672.777
1.33.0993.223.1363.5682.9893.0833.2823.1812.7853.123.2762.9453.2813.2633.3161.912.963
1.42.9943.1233.0433.4322.8922.9923.183.0852.6983.0293.172.8563.1813.1683.2142.262.635
1.52.883.022.9433.2832.7892.8973.0712.9842.6072.9343.0552.7643.0733.0683.1042.582.033
1.62.7592.912.8393.1232.682.7982.9562.8772.5132.8342.9332.6672.9592.9632.9872.871.146
1.72.6322.7962.7312.9532.5662.6952.8342.7652.4162.732.8052.5682.8392.8532.8653.20.954
1.82.4992.6772.6182.7752.4482.5892.7072.652.3172.6232.672.4662.7142.7392.7373.54-9999
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2.21.9222.1662.1381.991.9412.142.1592.1541.9012.1692.0872.0352.1752.2522.1845.37-9999
2.31.7682.0312.0111.781.8062.0232.0142.0231.7942.051.9321.9232.0322.1232.037
2.41.6121.8941.8821.5641.671.9041.8651.891.6851.931.7731.8091.8871.9931.887
2.51.4521.7541.7521.3451.5311.7831.7151.7541.5741.8071.6121.6941.7391.861.735
2.61.291.6121.621.1211.391.661.5611.6171.4631.6831.4481.5771.5881.7261.58
2.71.1251.4691.4860.8941.2481.5371.4061.4781.3511.5581.2811.461.4361.591.423
2.80.9591.3231.350.6631.1031.4121.2481.3381.2371.4321.1131.3411.2811.4521.264
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3.20.2720.7260.795-0.2910.5110.9020.6010.7610.7760.9140.4180.8570.6460.8880.61
3.30.0960.5740.654-0.5360.3590.7720.4350.6140.6590.7830.240.7340.4830.7440.442
3.4-0.0810.420.511-0.7830.2060.6410.2680.4650.5410.650.060.6110.3190.5980.273
3.5-0.260.2650.367-1.0330.0530.5090.10.3160.4230.517-0.1210.4860.1540.4520.103
3.6-0.440.1090.223-1.284-0.1020.377-0.070.1650.3040.382-0.3030.361-0.0120.305-0.068
3.7-0.622-0.0480.078-1.538-0.2580.244-0.2410.0140.1850.247-0.4870.235-0.1790.157-0.241
3.8-0.804-0.205-0.069-1.793-0.4140.11-0.413-0.1380.0650.112-0.6720.109-0.3480.008-0.415
3.9-0.988-0.364-0.216-2.05-0.572-0.024-0.586-0.291-0.055-0.025-0.858-0.018-0.517-0.141-0.589
4-1.173-0.524-0.363-2.309-0.73-0.159-0.759-0.445-0.176-0.161-1.045-0.145-0.687-0.291-0.765
4.1-1.358-0.684-0.512-2.569-0.889-0.295-0.934-0.6-0.297-0.299-1.233-0.273-0.859-0.443-0.942
4.2-1.545-0.845-0.661-2.831-1.049-0.431-1.11-0.755-0.419-0.437-1.422-0.401-1.031-0.594-1.119
4.3-1.733-1.007-0.81-3.094-1.21-0.567-1.286-0.911-0.541-0.576-1.612-0.53-1.204-0.747-1.298
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4.6-2.301-1.497-1.263-3.892-1.696-0.98-1.82-1.383-0.909-0.994-2.187-0.919-1.727-1.207-1.838
4.7-2.492-1.661-1.415-4.16-1.859-1.118-2-1.541-1.033-1.135-2.381-1.049-1.903-1.362-2.019
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0.93.633.1553.2923.0413.5333.2673.2083.1773.0453.0662.9523.3883.7483.0444.083.1943.433.8073.5523.3961.122.865
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1.72.6522.4732.5512.3662.7452.5742.4672.472.352.2362.2162.522.612.3582.5382.5082.6142.6882.7012.6273.20.477
1.82.4742.3682.4262.2652.6082.4652.3422.3552.242.0892.0932.3642.42.2512.2572.4022.472.4832.5492.4963.540
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2.41.2631.6911.5981.6141.6921.7511.5141.6041.5221.1021.2791.3150.9761.5570.351.7131.5051.0841.5271.616
2.51.0441.5721.451.51.5281.6251.3661.4711.3950.9241.1331.1250.7171.4350.0041.5911.3310.831.3421.458
2.60.821.4511.31.3851.361.4971.2161.3351.2670.7420.9850.9320.4531.311-0.3491.4681.1540.5711.1541.298
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2.80.3621.2060.9931.1521.0171.2370.9091.061.0050.3710.6830.537-0.0881.059-1.0711.2180.7920.040.7690.97
2.90.1281.0820.8361.0330.8431.1050.7520.920.8720.1820.5290.335-0.3640.932-1.441.0920.607-0.2310.5720.803
3-0.110.9570.6780.9140.6660.9720.5940.7780.738-0.010.3740.13-0.6430.803-1.8140.9640.42-0.5060.3730.634
3.1-0.3490.8310.5190.7940.4870.8380.4350.6350.602-0.2040.217-0.076-0.9270.673-2.1920.8350.231-0.7840.1720.463
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4.8-4.731-1.42-2.367-1.338-2.755-1.569-2.452-1.932-1.823-3.73-2.616-3.843-6.101-1.648-9.096-1.467-3.207-5.864-3.491-2.635
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5.1-5.546-1.831-2.9-1.727-3.356-2.01-2.985-2.405-2.268-4.384-3.139-4.543-7.064-2.073-10.38-1.889-3.845-6.81-4.171-3.208
5.2-5.819-1.969-3.079-1.858-3.558-2.158-3.163-2.563-2.418-4.604-3.315-4.778-7.388-2.216-10.811-2.03-4.059-7.127-4.4-3.4
5.3-6.094-2.108-3.259-1.988-3.76-2.307-3.343-2.722-2.567-4.824-3.491-5.013-7.712-2.359-11.244-2.172-4.273-7.446-4.629-3.593
5.4-6.369-2.246-3.438-2.119-3.963-2.455-3.523-2.881-2.717-5.045-3.667-5.25-8.038-2.502-11.678-2.314-4.489-7.766-4.858-3.786
D(mm)
log(N(D))
D(mm)
log(N(D))
Chart2
3.5513.693.3363.7113.5443.6523.5113.4683.4933.5953.2723.4533.5033.4983.3123.213.153.193.4313.4773.485
3.6393.6953.733.6793.6913.7153.6443.5633.5843.5993.5153.5333.5313.493.4663.4393.3483.3333.4213.5063.528
3.6743.6733.9653.6323.7653.7333.7083.6023.6213.5763.6523.5623.5233.4583.5443.5673.4563.4043.3883.5013.531
3.6753.6344.0983.5743.7933.7223.733.6063.6233.5363.7233.5593.4953.4113.5763.6323.5073.4313.343.4743.509
3.6533.5834.1623.513.7893.6913.7213.5853.6013.4843.7483.5333.4513.3553.5743.6533.5183.4263.2833.4313.471
3.6133.5234.1753.443.7623.6453.6913.5473.5623.4233.7393.4923.3963.2913.5493.6423.5013.3983.2193.3773.42
3.563.4564.1493.3663.7183.5883.6453.4953.5093.3563.7053.4373.3343.2223.5053.6073.4633.3523.153.3143.36
3.4963.3844.0933.293.6593.5223.5853.4323.4463.2843.6513.3733.2643.1483.4463.5523.4073.2933.0763.2453.292
3.4253.3084.0113.213.5893.4493.5153.3613.3753.2083.583.3013.1893.0713.3763.4813.3373.2232.9983.1713.218
3.3463.2283.9093.1293.5093.3713.4353.2823.2963.1283.4963.2233.112.9913.2973.3983.2553.1442.9183.0913.139
3.2623.1453.793.0463.4223.2873.3493.1983.2113.0453.43.1393.0272.9083.2093.3043.1643.0572.8353.0083.056
3.1723.063.6562.9623.3283.1993.2563.1083.1222.963.2953.052.9412.8233.1143.2013.0652.9632.752.9222.969
3.0792.9733.512.8763.2283.1083.1583.0143.0282.8723.1812.9572.8522.7363.0133.0892.9582.8642.6642.8332.879
2.9812.8833.3522.7893.1233.0133.0552.9152.932.7833.062.8612.7612.6482.9082.9712.8452.762.5762.7422.787
2.8812.7923.1852.7023.0142.9162.9482.8142.8292.6922.9332.7612.6682.5582.7972.8472.7272.6512.4862.6482.692
2.7772.73.0092.6132.92.8162.8382.712.7252.62.82.6592.5732.4672.6832.7172.6042.5392.3952.5532.595
2.6712.6062.8262.5242.7842.7142.7242.6032.6192.5072.6622.5542.4762.3752.5652.5822.4772.4232.3042.4562.496
2.5632.5112.6352.4342.6642.612.6072.4932.512.4122.522.4482.3782.2822.4432.4432.3462.3042.2112.3572.396
2.4522.4152.4392.3432.5412.5042.4882.3812.3992.3162.3732.3392.2782.1892.3192.3012.2112.1822.1172.2572.294
2.342.3182.2372.2522.4162.3972.3662.2682.2862.2192.2232.2282.1782.0942.1922.1542.0732.0582.0232.1562.19
2.2262.222.032.162.2882.2882.2422.1522.1712.1222.0692.1162.0761.9982.0632.0051.9331.9321.9282.0542.086
2.112.1211.8182.0682.1592.1782.1162.0352.0552.0231.9122.0021.9731.9021.9321.8521.7891.8031.8321.9511.98
1.9932.0221.6021.9752.0272.0671.9881.9171.9371.9241.7531.8871.8691.8061.7981.6971.6441.6721.7351.8461.873
1.8741.9221.3821.8821.8941.9541.8581.7971.8181.8241.5911.7711.7651.7081.6631.541.4961.541.6391.7411.765
1.7551.8211.1581.7891.7581.8411.7271.6761.6981.7241.4261.6531.661.611.5261.381.3461.4061.5411.6351.657
1.6341.720.9311.6951.6221.7261.5951.5531.5771.6231.2591.5351.5541.5121.3871.2181.1941.2711.4431.5291.547
1.5121.6180.7011.6011.4841.6111.4611.431.4541.5221.0911.4151.4471.4131.2471.0531.041.1341.3451.4211.437
1.3891.5150.4681.5061.3441.4941.3261.3051.331.420.921.2941.3391.3141.1060.8880.8850.9961.2461.3131.326
1.2651.4120.2321.4121.2031.3771.1891.181.2061.3170.7471.1731.2311.2150.9630.720.7280.8561.1471.2051.214
1.141.309-0.0071.3171.0621.261.0521.0531.081.2140.5731.0511.1231.1150.8190.5510.570.7161.0471.0951.102
1.0151.205-0.2481.2220.9191.1410.9130.9260.9541.1110.3970.9281.0141.0140.6740.380.410.5740.9470.9860.989
0.8891.101-0.4911.1260.7741.0220.7740.7980.8271.0070.220.8040.9040.9140.5270.2080.2490.4320.8470.8750.876
0.7620.997-0.7361.0310.6290.9020.6340.6690.6990.9030.0410.680.7940.8130.380.0340.0870.2880.7470.7650.762
0.6340.892-0.9840.9350.4840.7820.4920.540.5710.799-0.1390.5540.6840.7120.232-0.141-0.0760.1430.6460.6540.647
0.5060.787-1.2330.8390.3370.6610.350.410.4420.694-0.3210.4290.5730.610.083-0.317-0.24-0.0020.5450.5420.532
0.3770.681-1.4840.7430.1890.540.2080.2790.3120.589-0.5030.3020.4620.508-0.067-0.494-0.406-0.1480.4440.430.417
0.2470.576-1.7370.6470.0410.4180.0640.1470.1820.484-0.6870.1760.350.406-0.218-0.672-0.572-0.2950.3420.3180.301
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D(mm)
log(N(D)
Sheet1
0.33.5513.693.3363.7113.5443.6523.5113.4683.4933.5953.2723.4533.5033.4983.3123.213.153.193.4313.4773.4850.36-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
1719330.43.6393.6953.733.6793.6913.7153.6443.5633.5843.5993.5153.5333.5313.493.4663.4393.3483.3333.4213.5063.5280.46-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
0.53.6743.6733.9653.6323.7653.7333.7083.6023.6213.5763.6523.5623.5233.4583.5443.5673.4563.4043.3883.5013.5310.55-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-999900-9999-9999-99990-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990.47700-99990-9999-9999-9999-99990.3010-99990.3010.477-9999-9999-9999-99990-9999-9999-9999-9999-99990.4770-9999-99990-99990-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-999900-99990-9999-9999-9999-99990-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-9999-99990-9999-9999-9999-9999-999900-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999-9999
0.63.6753.6344.0983.5743.7933.7223.733.6063.6233.5363.7233.5593.4953.4113.5763.6323.5073.4313.343.4743.5090.66-99990.6020.6020.60200.77810.3010.3010.3010.6990.778-99990.8450.4770.30100000.4770.301-99990.4770.3010.4770-99990.3010.3010.47700.4770.3010.3010.3010.602000.7780.3010.4770.4770.477-99990.301-99990.4770.6990.301000.7780.84500.9031.04100.301-9999-9999-999900.6020.301-9999-9999-9999-999900.6990.6020.69900.6021.04110.9540.3010.6990.6991.1460.9031.0790.7780.8450.4771.1761.1141.0411.0791.0791.1761.2040.8450.90310.3010.8450.6990.3010.6990.6990.60200.6020.8450.6990.8451000.9030.6020.4770.47701.1140.6020.9030.6990.6990.4770.6990.6990.4770.477-99990.3010.3010.47700.301000.602-99990.6990.4770.6020.3010.4770.3010.3010.6020.4770-99990.3010.301-999900.301-999900.4770.95400.60200-9999-99990.3010-9999-9999-9999-99990.4770
0.73.6533.5834.1623.513.7893.6913.7213.5853.6013.4843.7483.5333.4513.3553.5743.6533.5183.4263.2833.4313.4710.770.6990.9031.3011.3010.7781.0791.0791.20411.3011.2041.11410.7781.0410.7780.8450.9031.04110.9540.8450.8450.77811.0410.9541.0790.77811.0410.8451.0410.9030.9031.1141.25511.4311.0410.9030.69910.7781.0410.3010.77810.7781.04111.0791.0791.3421.4621.6330.7781.1141.0790.301-999900.7780.8450.903-9999-9999-9999-99991.0791.381.6230.8450.4771.3421.5311.4311.1461.25511.5311.7321.581.5681.5441.3981.3621.5681.7321.7631.581.5051.7161.7241.5191.6131.5441.4621.381.3981.2041.4151.4911.3011.4311.3221.3221.2551.4311.5681.4311.0791.3221.231.2551.231.4771.5681.3421.5311.3621.4311.0791.3421.1761.20411.1760.9031.0790.9541.380.9541.20411.4151.1140.9541.1141.2041.3620.77811.0791.1461.0790.9540.7780.8450.6990.9540.4770.3010.8450.6020.9031.4770.9030.90310.6020.6020.8451.1460.8450.3010.69900.7780.7780.477
0.83.6133.5234.1753.443.7623.6453.6913.5473.5623.4233.7393.4923.3963.2913.5493.6423.5013.3983.2193.3773.420.912.0092.12.092.141.9592.2072.2232.0862.0722.212.2651.9541.941.8061.9031.8811.9191.8131.9961.9592.0831.8391.9191.8752.1462.2152.1961.9641.8451.8692.1432.0532.0531.9642.142.3012.3072.2992.2862.2972.232.192.2721.7322.1171.6721.692.0131.7851.691.581.7241.9542.0041.8811.6430.6991.4151.3010-99991.1461.6131.6330.9540.301-9999-99990.4772.1992.2942.1731.3011.3981.9032.2941.9821.7481.3421.7322.1462.3842.3692.4712.3582.3712.3672.5282.4332.5762.482.4912.6052.5682.4232.5652.3892.52.2282.2282.1672.252.3582.4082.42.4872.4612.252.3752.3892.2072.0832.382.3752.2922.3012.4962.5292.2672.5172.3652.1792.0532.142.2232.1041.9682.2171.9492.0612.1492.142.12.2552.212.2042.1672.1672.0832.0332.2551.8862.0331.9191.9441.8691.8921.7081.741.691.8451.7081.8261.7321.8261.7322.0831.821.741.8811.821.7561.9141.8861.255-99991.1761.2791.1141.230.602
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2.42.112.1211.8182.0682.1592.1782.1162.0352.0552.0231.9122.0021.9731.9021.9321.8521.7891.8031.8321.9511.98
2.51.9932.0221.6021.9752.0272.0671.9881.9171.9371.9241.7531.8871.8691.8061.7981.6971.6441.6721.7351.8461.873
2.61.8741.9221.3821.8821.8941.9541.8581.7971.8181.8241.5911.7711.7651.7081.6631.541.4961.541.6391.7411.765
2.71.7551.8211.1581.7891.7581.8411.7271.6761.6981.7241.4261.6531.661.611.5261.381.3461.4061.5411.6351.657
2.81.6341.720.9311.6951.6221.7261.5951.5531.5771.6231.2591.5351.5541.5121.3871.2181.1941.2711.4431.5291.547
2.91.5121.6180.7011.6011.4841.6111.4611.431.4541.5221.0911.4151.4471.4131.2471.0531.041.1341.3451.4211.437
31.3891.5150.4681.5061.3441.4941.3261.3051.331.420.921.2941.3391.3141.1060.8880.8850.9961.2461.3131.326
3.11.2651.4120.2321.4121.2031.3771.1891.181.2061.3170.7471.1731.2311.2150.9630.720.7280.8561.1471.2051.214
3.21.141.309-0.0071.3171.0621.261.0521.0531.081.2140.5731.0511.1231.1150.8190.5510.570.7161.0471.0951.102
3.31.0151.205-0.2481.2220.9191.1410.9130.9260.9541.1110.3970.9281.0141.0140.6740.380.410.5740.9470.9860.989
3.40.8891.101-0.4911.1260.7741.0220.7740.7980.8271.0070.220.8040.9040.9140.5270.2080.2490.4320.8470.8750.876
3.50.7620.997-0.7361.0310.6290.9020.6340.6690.6990.9030.0410.680.7940.8130.380.0340.0870.2880.7470.7650.762
3.60.6340.892-0.9840.9350.4840.7820.4920.540.5710.799-0.1390.5540.6840.7120.232-0.141-0.0760.1430.6460.6540.647
3.70.5060.787-1.2330.8390.3370.6610.350.410.4420.694-0.3210.4290.5730.610.083-0.317-0.24-0.0020.5450.5420.532
3.80.3770.681-1.4840.7430.1890.540.2080.2790.3120.589-0.5030.3020.4620.508-0.067-0.494-0.406-0.1480.4440.430.417
3.90.2470.576-1.7370.6470.0410.4180.0640.1470.1820.484-0.6870.1760.350.406-0.218-0.672-0.572-0.2950.3420.3180.301
40.1170.47-1.9910.55-0.1090.295-0.080.0160.0510.378-0.8720.0480.2380.304-0.369-0.851-0.739-0.4430.240.2050.185
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4.8-4.731-1.42-2.367-1.338-2.755-1.569-2.452-1.932-1.823-3.73-2.616-3.843-6.101-1.648-9.096-1.467-3.207-5.864-3.491-2.635
4.9-5.001-1.557-2.545-1.468-2.955-1.716-2.629-2.089-1.971-3.947-2.79-4.076-6.421-1.79-9.522-1.607-3.419-6.178-3.717-2.825
5-5.273-1.694-2.722-1.597-3.155-1.863-2.806-2.247-2.12-4.165-2.964-4.309-6.742-1.931-9.95-1.748-3.631-6.494-3.944-3.016
5.1-5.546-1.831-2.9-1.727-3.356-2.01-2.985-2.405-2.268-4.384-3.139-4.543-7.064-2.073-10.38-1.889-3.845-6.81-4.171-3.208
5.2-5.819-1.969-3.079-1.858-3.558-2.158-3.163-2.563-2.418-4.604-3.315-4.778-7.388-2.216-10.811-2.03-4.059-7.127-4.4-3.4
5.3-6.094-2.108-3.259-1.988-3.76-2.307-3.343-2.722-2.567-4.824-3.491-5.013-7.712-2.359-11.244-2.172-4.273-7.446-4.629-3.593
5.4-6.369-2.246-3.438-2.119-3.963-2.455-3.523-2.881-2.717-5.045-3.667-5.25-8.038-2.502-11.678-2.314-4.489-7.766-4.858-3.786
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D(mm)
log(N(D))
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0