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KL-parameterization of atmospheric aerosol size distribution

KL para meterization of atmospheric aerosol size distribution. KL-parameterization of atmospheric aerosol size distribution. 1. Assimilation of information 2. KL-model of size distribution 3. Test data 4. Test results. Hannes.Tammet@ut.ee University of Tartu, Institute of Physics

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KL-parameterization of atmospheric aerosol size distribution

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  1. KL parameterization of atmospheric aerosol size distribution KL-parameterization of atmospheric aerosol size distribution 1. Assimilation of information2. KL-model of size distribution3. Test data4. Test results Hannes.Tammet@ut.eeUniversity of Tartu, Institute of Physics with participation of Marko Vana Acknowledgements to Markku Kulmala and staff of Hyytiälä station

  2. A well forgotten model,references: Tammet, H.F. (1988) Sravnenie model'nykh raspredeleniï aérozol'nykh chastits po razmeram (in Russian). Acta Comm. Univ. Tartu824, 92–108. Translation of the previous paper: Tammet, H. (1992) Comparison of model distributions of aerosol particle sizes. Acta Comm. Univ. Tartu947, 136–149, http://ael.physic.ut.ee/tammet/kl1992.pdf Tammet, H. (1988) Models of size spectrum of tropospheric aerosol. In Atmospheric Aerosols and Nucleation. Lecture Notes in Physics, Springer-Verlag, Vienna, 309, pp. 75–78, http://www.springerlink.com/content/p7l948j8m356605k

  3. An example: two parameterizations

  4. Lost information: Assimilation of information Correlated parameters a ja b Spread ~S2 Spread ~S1

  5. Theory: correlationcoefficient 2D lost information: Equivalent error amplification: nD lost information: Equivalent error amplification: correlationmatrix

  6. KL-model of size distribution • Modification from 1988/92 to 2012: • radius replaced by diameter, • natural logarithm replaced by decimal logarithm.

  7. 3 variants of K

  8. 3 variants of L

  9. 3 variants of b

  10. 3 variants of dx

  11. Analytic properties

  12. Test data: origin and preparation • Hyytiälä aerosol measurements downloaded by Marko Vana • Three full years of 2008, 2009 ja 2010 • 1107 files dmYYMMDD.sum 40-columns d = 3…983 nm • 1051 files apsYYYYMMDD.sum 54-columns d = 523…19810 nm • Time step 10 minutes, a file contains header and ja 144 lines of data. • Some files contained broken lines or negative values of dn/dlgd, such files were rejected. Further, only these days were used where both DM and APS-files are present. • Preparative operations: • DM & APS–files were joined using new logarithm-homogeneous fraction structure containing 62 fractions from 3 to 19110 nm (method – interpolation). Where both DM and APS data present the average was calculated using weights (d – 500) / 500 for APS and (1000 – d) / 500 for DMPS. • All diurnal files were merged into a single 3-year file while the time of an interval center was interpolated to sharp minute 5, 15, 25 …(using neighbors with deviation < 10.8 minutes).

  13. Test data The file of 10-minute records Hyytiala08-10aerosol.xl contains 62 data columns and 141367 data lines that is 89.6 % of the maximum 157824 10-minute intervals in the 3 years. The 10-minute data are pretty noisy. Next, the data were convereted to hourly averages. Only these hours were included that contain at least 3 measurements. The file of hourly averages Hyytiala08-10aerosol-h.xlcontains one header line (incl. diameters) and 23517 data lines that cover 89.4% of possible 26304 hours. The 71 columns are: time DOY, 62 values of dn/dlgd, total number concentration, time parameters: year, month, day, hour, year quarter, day quarter, day-of-week.

  14. Test data

  15. Test data

  16. Test data

  17. Filtered test data Some strange irregularities: • the interval 10…..165 nm contains dn/dlgd < 10 cm-3, • the interval 190…3000 nm contains dn/dlgd < 0.001 cm-3. Such hours were excluded from the final KL test data. The file of filtered hourly averages Hyytiala08-10aerosol-hf.xl(h = hours, f = filtered) contains 21682 hours that is 82.5% of possible maximum.

  18. KL-parameterization of atmospheric aerosol size distribution TESTRESULTS

  19. 3-year average: KL4 & KL5 from 10 to 3000 nm

  20. What is KL5?

  21. 3-year average: KL4 & KL5 from 3 to 10000 nm KL4: K = 3.18 L = 0.97 b = 4240 dx = 117 std = 0.152 KL5: K = 3.05 L = 1.01 b = 4980 dx = 98 c = 0.45 std = 0.138

  22. Method of fitting • Given: a table of function measured _dn/dlgd (d) • Task: choose 5 parameters K L b dx c • Special case of KL4  c = 0. • The fitting deviation in typical diagrams is • Δ = lg (fitted_dn/dlgd) – lg (measured_dn/dlgd). • Measure of visual quality: std (Δ) • Policy: • choose b so that average (Δ) = 0 • choose other parameters so that std (Δ)  min. • An arbitrary technique of minimization can be used

  23. Fitting of test data Mean standard deviation between approximation and measurements of lg (dn/dlgd)KL4  0.192 KL5  0.144 Standard deviation of mean distribution approximation were: KL4  0.097 KL5  0.032

  24. Examples: 10% of KL4 9500) 2009-04-14-12 KL4: 0.109 3.681 0.265 1149 267 KL5: 0.106 3.616 0.229 1073 266 0.119

  25. Examples: 10% of KL4 12752) 2009-09-30-05 KL4 0.109 2.006 2.226 6407 18 KL5 0.094 2.000 2.446 6557 18 0.236

  26. Examples: 10% of KL4 11805) 2009-08-19-07 KL4 0.109 3.026 2.051 7109 70 KL5 0.108 2.924 2.33 7878 62 0.443

  27. Examples: 50% of KL4 11714) 2009-08-11-10 KL4 0.189 3.16 1.785 7544 114 KL5 0.095 2.795 2.353 9634 81 0.973

  28. Examples: 50% of KL4 11844) 2009-08-20-23 KL4 0.189 3.05 2.383 11169 55 KL5 0.189 3.044 2.403 11216 55 0.033

  29. Examples: 50% of KL4 11915) 2009-08-24-04 KL4 0.189 3.102 2.526 4226 95 KL5 0.102 2.855 2.982 4724 76 0.879

  30. Examples: 90% of KL4 18557) 2010-08-11-13 KL4 0.278 3.19 0.361 2101 163 KL5 0.172 2.663 0.745 3737 96 1.312

  31. Examples: 90% of KL4 18549) 2010-08-11-05 KL4 0.222 3.235 1.197 1472 154 KL5 0.182 2.615 1.954 2418 85 1.335

  32. Examples: 90% of KL4 19310) 2010-09-14-12 KL4 0.278 2.895 1.179 1293 104 KL5 0.120 2.523 2.127 2389 62 1.409

  33. Analysis: KL4 Correlation matrix K L b dx 1.000 -0.251 -0.207 0.717 -0.251 1.000 0.594 -0.567 -0.207 0.594 1.000 -0.446 0.717 -0.567 -0.446 1.000 Det 0.191055, loss 0.36 digits, erroramplification 1.23 Eigenvectors 0.449 0.666 -0.198 -0.561 -0.504 0.427 -0.668 0.340 -0.460 0.539 0.704 0.022 0.575 0.286 0.132 0.754 Eigenvalues 2.413 0.978 0.410 0.197

  34. Analysis: KL5 Correlation matrix K L b dx c 1.000 -0.286 -0.152 0.730 -0.393 -0.286 1.000 0.589 -0.546 0.215 -0.152 0.589 1.000 -0.373 0.071 0.730 -0.546 -0.373 1.000 -0.336 -0.393 0.215 0.071 -0.336 1.000 Det 0.167549, loss 0.39 digits, erroramplification 1.25 Eigenvectors 0.470 0.432 -0.422 -0.220 0.602 -0.473 0.418 -0.154 -0.699 -0.295 -0.377 0.619 -0.161 0.669 -0.017 0.553 0.125 -0.354 0.090 -0.737 -0.324 -0.487 -0.803 0.076 0.068 Eigenvalues 2.540 1.159 0.701 0.392 0.207

  35. Properties of KL: • graphic, • simple interpretation, • minimum loss of information, • analytic integrals available. Conclusion: it works outx

  36. 2009 THANKYOU, KL

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