20:
95:. Satellite imagery often shows trails of cloud, or of enhanced brightness of cloud, behind ocean-going ships due to this effect. The decrease in global mean absorption of solar radiation due to increases in CCN concentrations exerts a cooling influence on climate; the global average magnitude of this effect over the industrial era is estimated as between −0.3 and −1.8 W/m.
480:
368:
700:
619:
192:
747:
264:
130:
550:
398:
215:
776:
648:
576:
796:
523:
503:
284:
235:
103:
Assume a uniform cloud that extends infinitely in the horizontal plane, also assume that the particle size distribution peaks near an average value of
409:
299:
656:
584:
141:
27:
916:
889:
1035:
1025:
924:
Rosenfeld, D. (2006). "Aerosol-Cloud
Interactions Control of Earth Radiation and Latent Heat Release Budgets".
62:
711:
962:
39:
1030:
92:
752:
This illustrates the Twomey Effect mathematically, that is, for a constant liquid water content,
240:
106:
1040:
528:
376:
1045:
977:
933:
904:
868:
200:
8:
755:
627:
555:
43:
981:
937:
908:
872:
1003:
949:
781:
508:
488:
403:
Taking our assumptions into account we can combine the previous two equations to yield
269:
220:
1007:
953:
880:
58:
61:) by such particles, as distinguished from direct effects (forcing) due to enhanced
993:
985:
941:
912:
876:
855:
Hartmann, Dennis L. Global
Physical Climatology. Amsterdam: Elsevier, 2016. Print.
807:
50:
817:
287:
73:
998:
989:
945:
1019:
84:
77:
19:
88:
475:{\displaystyle \tau ={\frac {3}{2}}{\frac {h\,LWC}{\rho _{L}{\bar {r}}}}}
23:
46:
16:
Effect concerning the increase of solar radiation reflected by clouds
26:
can be seen as lines in these clouds over the
Atlantic Ocean on the
822:
859:
Twomey, S. (December 1974). "Pollution and the planetary albedo".
812:
69:
890:"The Influence of Pollution on the Shortwave Albedo of Clouds"
363:{\displaystyle LWC={\frac {4}{3}}\pi {\bar {r}}^{3}\rho _{L}N}
54:
917:
10.1175/1520-0469(1977)034<1149:TIOPOT>2.0.CO;2
76:
of CCN can lead to formation of more cloud droplets with a
65:
or absorbing radiation by such particles not in clouds.
293:
The formula for the liquid water content of a cloud is
784:
758:
714:
659:
630:
587:
558:
531:
511:
491:
412:
379:
302:
272:
243:
223:
203:
144:
109:
695:{\displaystyle {\bar {r}}^{3}\propto {\frac {1}{N}}}
778:, increasing the number density of cloud droplets,
790:
770:
741:
694:
642:
614:{\displaystyle \tau \propto {\frac {1}{\bar {r}}}}
613:
570:
544:
517:
497:
474:
392:
362:
278:
258:
229:
209:
186:
124:
87:of the cloud, which results in an increase in the
158:
1017:
135:The formula for the optical depth of a cloud is
187:{\displaystyle \tau =2\pi \;\!h{\bar {r}}^{2}N}
578:constant, from the last equation we can write
923:
83:The increase in number density increases the
798:, increases the optical depth of the cloud.
72:particles that serve as CCN. Increasing the
960:
887:
858:
157:
997:
435:
18:
963:"Aerosol Effects on Clouds and Climate"
1018:
742:{\displaystyle \tau \propto N^{1/3}}
13:
266:is the average particle size, and
30:, an example of the Twomey effect.
14:
1057:
485:To derive the effect of changing
57:. This is an indirect effect (or
841:IPCC 4th Assessment Report, 2005
68:Cloud droplets normally form on
848:
28:East Coast of the United States
835:
667:
604:
463:
335:
250:
169:
116:
1:
828:
98:
49:, may increase the amount of
881:10.1016/0004-6981(74)90004-3
7:
801:
10:
1062:
624:and from the equation for
259:{\displaystyle {\bar {r}}}
125:{\displaystyle {\bar {r}}}
990:10.1007/s11214-006-9051-8
946:10.1007/s11214-006-9053-6
545:{\displaystyle \rho _{L}}
400:is the density of water.
393:{\displaystyle \rho _{L}}
40:cloud condensation nuclei
38:describes how additional
888:Twomey, S. (July 1977).
792:
772:
743:
696:
644:
615:
572:
546:
519:
499:
476:
394:
364:
280:
260:
231:
217:is the optical depth,
211:
188:
126:
31:
1036:Atmospheric radiation
1026:Cloud and fog physics
793:
773:
744:
697:
645:
616:
573:
547:
520:
500:
477:
395:
365:
281:
261:
232:
212:
210:{\displaystyle \tau }
189:
127:
42:(CCN), possibly from
22:
961:Lohmann, U. (2006).
782:
756:
712:
657:
628:
585:
556:
529:
509:
489:
410:
377:
300:
270:
241:
237:is cloud thickness,
221:
201:
142:
107:
93:clouds appear whiter
982:2006SSRv..125..129L
938:2006SSRv..125..149R
909:1977JAtS...34.1149T
873:1974AtmEn...8.1251T
771:{\displaystyle LWC}
643:{\displaystyle LWC}
571:{\displaystyle LWC}
290:of cloud droplets.
999:20.500.11850/24256
788:
768:
739:
692:
640:
611:
568:
542:
515:
495:
472:
390:
360:
276:
256:
227:
207:
184:
122:
32:
818:Aerosols and soot
791:{\displaystyle N}
690:
670:
609:
607:
518:{\displaystyle h}
498:{\displaystyle N}
470:
466:
427:
338:
323:
279:{\displaystyle N}
253:
230:{\displaystyle h}
172:
119:
59:radiative forcing
1053:
1011:
1001:
967:
957:
920:
894:
884:
842:
839:
797:
795:
794:
789:
777:
775:
774:
769:
748:
746:
745:
740:
738:
737:
733:
701:
699:
698:
693:
691:
683:
678:
677:
672:
671:
663:
649:
647:
646:
641:
620:
618:
617:
612:
610:
608:
600:
595:
577:
575:
574:
569:
551:
549:
548:
543:
541:
540:
524:
522:
521:
516:
504:
502:
501:
496:
481:
479:
478:
473:
471:
469:
468:
467:
459:
456:
455:
445:
430:
428:
420:
399:
397:
396:
391:
389:
388:
369:
367:
366:
361:
356:
355:
346:
345:
340:
339:
331:
324:
316:
285:
283:
282:
277:
265:
263:
262:
257:
255:
254:
246:
236:
234:
233:
228:
216:
214:
213:
208:
193:
191:
190:
185:
180:
179:
174:
173:
165:
131:
129:
128:
123:
121:
120:
112:
1061:
1060:
1056:
1055:
1054:
1052:
1051:
1050:
1031:Climate forcing
1016:
1015:
1014:
976:(1–4): 129–37.
965:
932:(1–4): 149–57.
892:
867:(12): 1251–56.
851:
846:
845:
840:
836:
831:
808:Albrecht effect
804:
783:
780:
779:
757:
754:
753:
729:
725:
721:
713:
710:
709:
682:
673:
662:
661:
660:
658:
655:
654:
629:
626:
625:
599:
594:
586:
583:
582:
557:
554:
553:
536:
532:
530:
527:
526:
510:
507:
506:
490:
487:
486:
458:
457:
451:
447:
446:
431:
429:
419:
411:
408:
407:
384:
380:
378:
375:
374:
351:
347:
341:
330:
329:
328:
315:
301:
298:
297:
271:
268:
267:
245:
244:
242:
239:
238:
222:
219:
218:
202:
199:
198:
175:
164:
163:
162:
143:
140:
139:
111:
110:
108:
105:
104:
101:
51:solar radiation
17:
12:
11:
5:
1059:
1049:
1048:
1043:
1038:
1033:
1028:
1013:
1012:
958:
921:
903:(7): 1149–52.
885:
861:Atmos. Environ
856:
852:
850:
847:
844:
843:
833:
832:
830:
827:
826:
825:
820:
815:
810:
803:
800:
787:
767:
764:
761:
750:
749:
736:
732:
728:
724:
720:
717:
703:
702:
689:
686:
681:
676:
669:
666:
639:
636:
633:
622:
621:
606:
603:
598:
593:
590:
567:
564:
561:
539:
535:
514:
505:while keeping
494:
483:
482:
465:
462:
454:
450:
444:
441:
438:
434:
426:
423:
418:
415:
387:
383:
371:
370:
359:
354:
350:
344:
337:
334:
327:
322:
319:
314:
311:
308:
305:
288:number density
275:
252:
249:
226:
206:
195:
194:
183:
178:
171:
168:
161:
156:
153:
150:
147:
118:
115:
100:
97:
74:number density
15:
9:
6:
4:
3:
2:
1058:
1047:
1044:
1042:
1041:Air pollution
1039:
1037:
1034:
1032:
1029:
1027:
1024:
1023:
1021:
1009:
1005:
1000:
995:
991:
987:
983:
979:
975:
971:
970:Space Sci Rev
964:
959:
955:
951:
947:
943:
939:
935:
931:
927:
926:Space Sci Rev
922:
918:
914:
910:
906:
902:
898:
897:J. Atmos. Sci
891:
886:
882:
878:
874:
870:
866:
862:
857:
854:
853:
838:
834:
824:
821:
819:
816:
814:
811:
809:
806:
805:
799:
785:
765:
762:
759:
734:
730:
726:
722:
718:
715:
708:
707:
706:
687:
684:
679:
674:
664:
653:
652:
651:
650:we can write
637:
634:
631:
601:
596:
591:
588:
581:
580:
579:
565:
562:
559:
537:
533:
512:
492:
460:
452:
448:
442:
439:
436:
432:
424:
421:
416:
413:
406:
405:
404:
401:
385:
381:
357:
352:
348:
342:
332:
325:
320:
317:
312:
309:
306:
303:
296:
295:
294:
291:
289:
273:
247:
224:
204:
181:
176:
166:
159:
154:
151:
148:
145:
138:
137:
136:
133:
113:
96:
94:
90:
86:
85:optical depth
81:
79:
75:
71:
66:
64:
60:
56:
53:reflected by
52:
48:
45:
44:anthropogenic
41:
37:
36:Twomey effect
29:
25:
21:
1046:Particulates
973:
969:
929:
925:
900:
896:
864:
860:
849:Bibliography
837:
751:
704:
623:
484:
402:
372:
292:
196:
134:
102:
89:cloud albedo
82:
78:smaller size
67:
35:
33:
24:Ship tracks
1020:Categories
829:References
705:therefore
99:Derivation
63:scattering
1008:121796083
954:122885098
719:∝
716:τ
680:∝
668:¯
605:¯
592:∝
589:τ
534:ρ
464:¯
449:ρ
414:τ
382:ρ
349:ρ
336:¯
326:π
251:¯
205:τ
170:¯
155:π
146:τ
117:¯
47:pollution
823:Contrail
802:See also
978:Bibcode
934:Bibcode
905:Bibcode
869:Bibcode
813:Sulfate
286:is the
91:making
70:aerosol
1006:
952:
373:where
197:where
55:clouds
1004:S2CID
966:(PDF)
950:S2CID
893:(PDF)
552:and
34:The
994:hdl
986:doi
974:125
942:doi
930:125
913:doi
877:doi
1022::
1002:.
992:.
984:.
972:.
968:.
948:.
940:.
928:.
911:.
901:34
899:.
895:.
875:.
863:.
525:,
132:.
80:.
1010:.
996::
988::
980::
956:.
944::
936::
919:.
915::
907::
883:.
879::
871::
865:8
786:N
766:C
763:W
760:L
735:3
731:/
727:1
723:N
688:N
685:1
675:3
665:r
638:C
635:W
632:L
602:r
597:1
566:C
563:W
560:L
538:L
513:h
493:N
461:r
453:L
443:C
440:W
437:L
433:h
425:2
422:3
417:=
386:L
358:N
353:L
343:3
333:r
321:3
318:4
313:=
310:C
307:W
304:L
274:N
248:r
225:h
182:N
177:2
167:r
160:h
152:2
149:=
114:r
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