152:, and can cause serious performance issues with radar systems. What one person considers to be unwanted clutter, another may consider to be a wanted target. However, targets usually refer to point scatterers and clutter to extended scatterers (covering many range, angle, and Doppler cells). The clutter may fill a volume (such as rain) or be confined to a surface (like land). A knowledge of the volume or surface area illuminated is required to estimated the echo per unit volume, η, or echo per unit surface area, σ° (the
1736:
level to a height of 1750 metres. There could be rain at ground level but the top of the beam could be above cloud level. In the part of the beam containing rain the rainfall rate will not be constant. One would need to know how the rain was distributed to make any accurate assessment of the clutter and the signal to clutter ratio. All that can be expected from the equation is an estimate to the nearest 5 or 10 dB.
3804:
25:
122:
1754:
269:
2654:
3675:
1761:
For a target close to the Earth's surface such that the earth and target are in the same range resolution cell one of two conditions are possible. The most common case is when the beam intersects the surface at such an angle that the area illuminated at any one time is only a fraction of the surface
1569:
The implication is that when the radar is noise limited the variation of signal to noise ratio is an inverse fourth power. Halving the distance will cause the signal to noise ratio to increase (improve) by a factor of 16. When the radar is volume clutter limited, however, the variation is an inverse
3789:
The general significant problem is that the backscatter coefficient cannot in general be calculated and must be measured. The problem is the validity of measurements taken in one location under one set of conditions being used for a different location under different conditions. Various empirical
1735:
A problem with volume clutter, e.g. rain, is that the volume illuminated may not be completely filled, in which case the fraction filled must be known, and the scatterers may not be uniformly distributed. Consider a beam 10° in elevation. At a range of 10 km the beam could cover from ground
1744:
The surface clutter return depends upon the nature of the surface, its roughness, the grazing angle (angle the beam makes with the surface), the frequency and the polarisation. The reflected signal is the phasor sum of a large number of individual returns from a variety of sources, some of them
260:. The total signal competing with the target return is thus clutter plus noise. In practice there is often either no clutter or clutter dominates and the noise can be ignored. In the first case, the radar is said to be noise-limited, while in the second it is clutter-limited.
1121:
2466:
2293:
1745:
capable of movement (leaves, rain drops, ripples) and some of them stationary (pylons, buildings, tree trunks). Individual samples of clutter vary from one resolution cell to another (spatial variation) and vary with time for a given cell (temporal variation).
2756:
819:
3777:
3471:
3187:
2454:
3460:
3308:
1718:
1564:
2769:
There are a number of problems in calculating the signal to clutter ratio. The clutter in the main beam is extended over a range of grazing angles and the backscatter coefficient depends upon grazing angle. Clutter will appear in the
1350:
If the
Clutter Return Power is greater than the System Noise Power then the Radar is clutter limited and the Signal to Clutter Ratio must be equal to or greater than the Minimum Signal to Noise Ratio for the target to be detectable.
3021:
2141:
1345:
1455:
635:
542:
1770:
For the pulse length limited case the area illuminated depends upon the azimuth width of the beam and the length of the pulse, measured along the surface. The illuminated patch has a width in azimuth of
1962:
1187:
1622:
1245:
2909:
2649:{\displaystyle \ {\frac {S}{C}}={\frac {1}{1300}}{\frac {R^{3}}{P_{t}G^{2}\lambda ^{2}}}{\frac {1}{\tau \theta \sec \psi \sigma ^{o}}}{\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}\sigma }
2029:
2846:
964:
640:
The clutter is assumed to be a large number of independent scatterers that fill the cell containing the target uniformly. The clutter return from the volume is calculated as for the normal
2172:
307:
and that the scatterers are uniformly distributed through the volume. The clutter volume illuminated by a pulse can be calculated from the beam widths and the pulse duration, Figure 1. If
2666:
674:
1871:
3684:
3670:{\displaystyle \ {\frac {S}{C}}={\frac {4^{4}R^{2}}{P_{t}G^{2}\lambda ^{2}}}(180/\theta ^{o})^{2}{\frac {1}{\sigma ^{o}}}{\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}\sigma }
1815:
3052:
946:
A correction must be made to allow for the fact that the illumination of the clutter is not uniform across the beamwidth. In practice the beam shape will approximate to a
2761:
In the case of surface clutter the signal to clutter now varies inversely with R. Halving the distance only causes a doubling of the ratio (a factor of two improvement).
2352:
2324:
400:
3340:
3332:
2344:
428:
3199:
1633:
914:
881:
852:
666:
352:
329:
1466:
3045:
2165:
940:
372:
298:
2920:
2040:
1256:
1364:
4002:
553:
4109:
439:
1723:
Clearly narrow beamwidths and short pulses are required to reduce the effect of clutter by reducing the volume of the clutter cell. If
240:). This clutter type is especially bothersome since it appears to move and behave like common targets of interest, such as aircraft or
1727:
is used then the appropriate pulse duration to be used in the calculation is that of the compressed pulse, not the transmitted pulse.
3843:
108:
3882:
The tradeoff for doing this is that adding fill pulses will degrade the performance, due to wasted transmitter power and a longer
303:
First find the magnitude of the clutter return. Assume that the clutter fills the cell containing the target, that scatterers are
3821:
42:
1883:
3825:
46:
1132:
89:
331:
is the time duration of the transmitted pulse then the pulse returning from a target is equivalent to a physical extent of
1579:
1202:
153:
61:
1116:{\displaystyle \ C={\frac {P_{t}G_{t}A_{r}}{2\log 2(4\pi )^{2}R^{4}}}{\frac {\pi }{4}}(R\theta )(R\phi )(c\tau /2)\eta }
145:
2857:
2288:{\displaystyle \ C={\frac {c}{2^{7}\pi ^{3}}}{\frac {P_{t}G^{2}\lambda ^{2}}{R^{3}}}\tau \theta \sec \psi \sigma ^{o}}
1973:
2788:
68:
3864:
164:
Clutter may be caused by man-made objects such as buildings and — intentionally — by radar countermeasures such as
3814:
35:
2751:{\displaystyle \ {\frac {S}{C}}=4\times 10^{-7}{\frac {\cos \psi }{R\tau \theta }}{\frac {\sigma }{\sigma ^{o}}}}
814:{\displaystyle \ C={\frac {P_{t}G_{t}A_{r}}{(4\pi )^{2}R^{4}}}{\frac {\pi }{4}}(R\theta )(R\phi )(c\tau /2)\eta }
354:, as is the return from any individual element of the clutter. The azimuth and elevation beamwidths, at a range
304:
3863:
systems. Clutter folding becomes a problem when the range extent of the clutter (seen by the radar) exceeds the
75:
3772:{\displaystyle \ {\frac {S}{C}}=5.25\times 10^{4}{\frac {1}{\theta ^{o2}R^{2}}}{\frac {\sigma }{\sigma ^{o}}}}
1126:
A number of simplifying substitutions can be made. The receiving antenna aperture is related to its gain by:
3790:
formulae and graphs exist which enable an estimate to be made but the results need to be used with caution.
1827:
181:
1250:
The same antenna is generally used both for transmission and reception thus the received clutter power is:
277:
217:
165:
57:
3868:
3182:{\displaystyle \ C={\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}\pi R^{2}(\theta /2)^{2}\sigma ^{o}}
2774:, which again will involve a range of grazing angles and may even involve clutter of a different nature.
4104:
3905:"Detection of Ground Clutter for Dual-Polarization Weather Radar Using a Novel 3D Discriminant Function"
1777:
237:
2771:
4024:
3961:
3916:
188:
trails. Radar clutter can also be caused by other atmospheric phenomena, such as disturbances in the
2449:{\displaystyle \ C=1300{\frac {P_{t}G^{2}\lambda ^{2}}{R^{3}}}\tau \theta ^{o}\sec \psi \sigma ^{o}}
4099:
645:
221:
3883:
2302:
1570:
square law and halving the distance will cause the signal to clutter to improve by only 4 times.
220:
to detect targets. Clutter may also originate from multipath echoes from valid targets caused by
3455:{\displaystyle \ C={\frac {P_{t}G^{2}\lambda ^{2}}{4^{4}R^{2}}}(\theta ^{o}/180)^{2}\sigma ^{o}}
3950:"Detection of Ground Clutter from Weather Radar Using a Dual-Polarization and Dual-Scan Method"
377:
252:
Electromagnetic signals processed by a radar receiver consist of three main components: useful
3303:{\displaystyle \ C={\frac {P_{t}G^{2}\lambda ^{2}}{4^{4}\pi ^{2}R^{2}}}\theta ^{2}\sigma ^{o}}
1724:
1713:{\displaystyle \ {\frac {S}{C}}={\frac {16(\log 2)\sigma }{\pi R^{2}\theta \phi c\tau \eta }}}
951:
193:
3317:
2329:
405:
4077:
3969:
3924:
3879:
of the radar, increasing the range over which clutter suppression is applied by the system.
3781:
As in the case of Volume
Clutter the Signal to clutter ratio follows an inverse square law.
1559:{\displaystyle \ {\frac {S}{C}}={\frac {1024(\log 2)G\sigma }{(4\pi )^{3}R^{2}c\tau \eta }}}
917:
225:
213:
201:
126:
2460:
The expression for the target return remains unchanged thus the signal to clutter ratio is
892:
859:
830:
651:
337:
314:
82:
4037:
2782:
The calculation is similar to the previous examples, in this case the illuminated area is
241:
3993:
3965:
3920:
3871:, and the clutter "folds" back in range. The solution to this problem is usually to add
3945:
3876:
3030:
2150:
925:
357:
283:
141:
4093:
947:
430:
respectively if the illuminated cell is assumed to have an elliptical cross section.
209:
197:
169:
136:
is the unwanted return (echoes) in electronic systems, particularly in reference to
1193:
884:
3016:{\displaystyle \ C={\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}A\sigma ^{o}}
2136:{\displaystyle \ C={\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}A\sigma ^{o}}
280:
are examples of volume clutter. For example, suppose an airborne target, at range
958:
the
Gaussian approximation of the antenna. The corrected back scattered power is
3803:
300:, is within a rainstorm. What is the effect on the detectability of the target?
24:
4059:
4028:
121:
4073:
3929:
3904:
3872:
1753:
1340:{\displaystyle \ C={\frac {P_{t}G\lambda ^{2}}{1024(\log 2)R^{2}}}c\tau \eta }
955:
233:
205:
189:
177:
173:
149:
1450:{\displaystyle \ S={\frac {P_{t}G^{2}\lambda ^{2}}{(4\pi )^{3}R^{4}}}\sigma }
4036:(Technical report). RADC Technical Reports. Vol. 1980. Rome, New York:
668:, and the clutter cell volume as derived above. The clutter return is then
630:{\displaystyle \ V_{m}\approx {\frac {\pi }{4}}(R\theta )(R\phi )(c\tau /2)}
268:
185:
4081:
1757:
Figure 2. Illustration of high- and low-angle surface-clutter illumination
3974:
3949:
3828: in this section. Unsourced material may be challenged and removed.
229:
168:. Other causes include natural objects such as terrain features, sea,
537:{\displaystyle \ V_{m}=\pi R\tan(\theta /2)R\tan(\phi /2)(c\tau /2)}
3860:
1355:
648:
is replaced by the product of the volume backscatter coefficient,
641:
257:
253:
137:
120:
2765:
Problems in calculating clutter for the pulse length limited case
3995:
A Canadian
Perspective on High-Frequency Over-the-Horizon Radar
1460:
with a resulting expression for the signal to clutter ratio of
3797:
18:
954:. The correction factor is found by integrating across the
2326:
is the back scatter coefficient of the clutter. Converting
3867:
interval of the radar, and it no longer provides adequate
1957:{\displaystyle \ A=2R(c\tau /2)(\tan \theta /2)\sec \psi }
200:
events. This phenomenon is especially apparent near the
4074:
Clutter suppression using amplitude weighted waveforms
1731:
Problems in calculating signal to volume clutter ratio
1182:{\displaystyle \ A_{r}={\frac {G\lambda ^{2}}{4\pi }}}
3687:
3474:
3343:
3320:
3202:
3055:
3033:
2923:
2860:
2791:
2669:
2469:
2355:
2346:
to degrees and putting in the numerical values gives
2332:
2305:
2175:
2153:
2043:
1976:
1886:
1830:
1780:
1636:
1582:
1469:
1367:
1259:
1205:
1135:
967:
928:
895:
862:
833:
677:
654:
556:
442:
408:
380:
360:
340:
317:
286:
1762:
intersected by the beam as illustrated in Figure 2.
1617:{\displaystyle \ G={\frac {\pi ^{2}}{\theta \phi }}}
1240:{\displaystyle \ G={\frac {\pi ^{2}}{\theta \phi }}}
1877:The area illuminated by the radar is then given by
49:. Unsourced material may be challenged and removed.
3771:
3669:
3454:
3326:
3302:
3181:
3039:
3015:
2903:
2840:
2750:
2648:
2448:
2338:
2318:
2287:
2159:
2135:
2023:
1956:
1865:
1809:
1712:
1616:
1558:
1449:
1339:
1239:
1181:
1115:
934:
908:
875:
846:
813:
660:
629:
536:
422:
394:
366:
346:
323:
292:
2904:{\displaystyle \ A\approx \pi R^{2}\theta ^{2}/4}
4030:A model for high frequency radar auroral clutter
2024:{\displaystyle \ A=R(c\tau /2)\theta \sec \psi }
212:produces convection patterns in the ionospheric
4060:"Radar Clutter | SKYbrary Aviation Safety"
3859:is a term used in describing "clutter" seen by
3785:General problems in calculating surface clutter
2841:{\displaystyle \ A=\pi R^{2}\tan ^{2}\theta /2}
272:Figure 1. Illustration of illuminated Rain Cell
3987:
3985:
4001:(Technical report). Ottawa, Ontario, Canada:
3909:Journal of Atmospheric and Oceanic Technology
3903:Golbon-Haghighi, M.H.; Zhang G. (July 2019).
8:
1967:For 'small' beamwidths this approximates to
433:The volume of the illuminated cell is thus:
256:(e.g., echoes from aircraft), clutter, and
216:. Radar clutter can degrade the ability of
1358:the return from the target itself will be
3973:
3928:
3844:Learn how and when to remove this message
3761:
3752:
3743:
3730:
3720:
3714:
3691:
3686:
3655:
3645:
3624:
3614:
3604:
3597:
3589:
3580:
3574:
3564:
3555:
3540:
3530:
3520:
3508:
3498:
3491:
3478:
3473:
3466:The target return remains unchanged thus
3446:
3436:
3424:
3418:
3402:
3392:
3380:
3370:
3360:
3353:
3342:
3319:
3294:
3284:
3271:
3261:
3251:
3239:
3229:
3219:
3212:
3201:
3173:
3163:
3151:
3139:
3123:
3113:
3092:
3082:
3072:
3065:
3054:
3032:
3007:
2991:
2981:
2960:
2950:
2940:
2933:
2922:
2893:
2887:
2877:
2859:
2851:which for small beamwidths simplifies to
2830:
2818:
2808:
2790:
2740:
2731:
2705:
2696:
2673:
2668:
2634:
2624:
2603:
2593:
2583:
2576:
2567:
2542:
2533:
2523:
2513:
2502:
2496:
2486:
2473:
2468:
2440:
2421:
2406:
2395:
2385:
2375:
2368:
2354:
2331:
2310:
2304:
2279:
2252:
2241:
2231:
2221:
2214:
2205:
2195:
2185:
2174:
2152:
2127:
2111:
2101:
2080:
2070:
2060:
2053:
2042:
1998:
1975:
1934:
1911:
1885:
1843:
1829:
1821:The length measured along the surface is
1799:
1779:
1686:
1653:
1640:
1635:
1598:
1592:
1581:
1538:
1528:
1486:
1473:
1468:
1435:
1425:
1404:
1394:
1384:
1377:
1366:
1319:
1289:
1276:
1269:
1258:
1221:
1215:
1204:
1162:
1152:
1143:
1134:
1099:
1056:
1047:
1037:
1004:
994:
984:
977:
966:
927:
900:
894:
867:
861:
838:
832:
797:
754:
745:
735:
714:
704:
694:
687:
676:
653:
616:
573:
564:
555:
523:
503:
477:
450:
441:
412:
407:
384:
379:
359:
339:
316:
285:
109:Learn how and when to remove this message
3944:Golbon-Haghighi, M.H.; Zhang G.; Li Y.;
1752:
267:
4003:Defence Research and Development Canada
3895:
942:= distance from the radar to the target
3027:Substituting for the illuminated area
2147:Substituting for the illuminated area
1866:{\displaystyle \ (c\tau /2)\sec \psi }
248:Clutter-limited or noise-limited radar
4005:. p. 38. DRDC Ottawa TM 2006-285
1196:is related to the two beamwidths by:
547:For small angles this simplifies to:
140:. Such echoes are typically returned
7:
3826:adding citations to reliable sources
47:adding citations to reliable sources
3992:Riddolls, Ryan J (December 2006).
1810:{\displaystyle \ 2R\tan \theta /2}
14:
3802:
2914:The clutter return is as before
23:
3813:needs additional citations for
950:which itself approximates to a
920:(area) of the receiving antenna
34:needs additional citations for
3642:
3632:
3571:
3549:
3433:
3411:
3160:
3145:
3110:
3100:
2978:
2968:
2621:
2611:
2098:
2088:
2006:
1989:
1942:
1922:
1919:
1902:
1851:
1834:
1671:
1659:
1525:
1515:
1504:
1492:
1422:
1412:
1312:
1300:
1107:
1090:
1087:
1078:
1075:
1066:
1034:
1024:
805:
788:
785:
776:
773:
764:
732:
722:
624:
607:
604:
595:
592:
583:
531:
514:
511:
497:
485:
471:
144:, sea, rain, animals/insects,
1:
154:radar backscatter coefficient
129:cluttering the radar display
4110:Radio frequency propagation
4040:. p. 9. RADC-TR-80-122
4038:Rome Air Development Center
3193:This can be simplified to:
2319:{\displaystyle \sigma ^{o}}
2034:The clutter return is then
887:of the transmitting antenna
854:= transmitter power (Watts)
180:, birds, turbulence in the
4126:
3865:pulse repetition frequency
311:is the speed of light and
204:, where the action of the
3930:10.1175/JTECH-D-18-0147.1
1766:Pulse length limited case
395:{\displaystyle \theta /2}
305:statistically independent
3327:{\displaystyle \theta }
2778:Beam width limited case
2339:{\displaystyle \theta }
423:{\displaystyle \phi /2}
182:atmospheric circulation
3773:
3671:
3456:
3328:
3304:
3183:
3041:
3017:
2905:
2842:
2752:
2650:
2450:
2340:
2320:
2289:
2161:
2137:
2025:
1958:
1867:
1811:
1758:
1714:
1618:
1560:
1451:
1341:
1241:
1183:
1117:
936:
910:
877:
848:
815:
662:
631:
538:
424:
396:
368:
348:
325:
294:
273:
230:ionospheric reflection
218:over-the-horizon radar
130:
3774:
3672:
3457:
3329:
3305:
3184:
3042:
3018:
2906:
2843:
2753:
2651:
2451:
2341:
2321:
2290:
2162:
2138:
2026:
1959:
1868:
1812:
1756:
1715:
1619:
1561:
1452:
1342:
1242:
1184:
1118:
937:
911:
909:{\displaystyle A_{r}}
878:
876:{\displaystyle G_{t}}
849:
847:{\displaystyle P_{t}}
816:
663:
661:{\displaystyle \eta }
632:
539:
425:
397:
369:
349:
347:{\displaystyle \tau }
326:
324:{\displaystyle \tau }
295:
276:Rain, hail, snow and
271:
238:anomalous propagation
124:
3975:10.3390/atmos7060083
3822:improve this article
3685:
3679:Which simplifies to
3472:
3341:
3318:
3200:
3053:
3031:
2921:
2858:
2789:
2667:
2467:
2353:
2330:
2303:
2173:
2151:
2041:
1974:
1884:
1828:
1778:
1634:
1580:
1467:
1365:
1257:
1203:
1133:
965:
926:
893:
860:
831:
675:
652:
554:
440:
406:
378:
358:
338:
315:
284:
58:"Clutter" radar
43:improve this article
4082:10.1049/cp:19971786
4072:V. Gregers-Hansen,
3966:2016Atmos...7...83G
3921:2019JAtOT..36.1285G
3869:clutter suppression
2660:This simplifies to
646:radar cross section
226:atmospheric ducting
3769:
3667:
3452:
3324:
3300:
3179:
3037:
3013:
2901:
2838:
2748:
2646:
2446:
2336:
2316:
2285:
2157:
2133:
2021:
1954:
1863:
1807:
1759:
1710:
1614:
1556:
1447:
1337:
1237:
1179:
1113:
932:
906:
873:
844:
811:
658:
627:
534:
420:
392:
364:
344:
321:
290:
274:
194:geomagnetic storms
131:
3854:
3853:
3846:
3767:
3750:
3699:
3690:
3662:
3595:
3547:
3486:
3477:
3409:
3346:
3278:
3205:
3130:
3058:
3040:{\displaystyle A}
2998:
2926:
2863:
2794:
2772:antenna sidelobes
2746:
2729:
2681:
2672:
2641:
2574:
2540:
2494:
2481:
2472:
2412:
2358:
2258:
2212:
2178:
2160:{\displaystyle A}
2118:
2046:
1979:
1889:
1833:
1783:
1725:pulse compression
1708:
1648:
1639:
1612:
1585:
1554:
1481:
1472:
1442:
1370:
1326:
1262:
1235:
1208:
1177:
1138:
1064:
1054:
970:
952:Gaussian function
935:{\displaystyle R}
762:
752:
680:
581:
559:
445:
367:{\displaystyle R}
293:{\displaystyle R}
222:ground reflection
202:geomagnetic poles
119:
118:
111:
93:
4117:
4084:
4070:
4064:
4063:
4056:
4050:
4049:
4047:
4045:
4035:
4021:
4015:
4014:
4012:
4010:
4000:
3989:
3980:
3979:
3977:
3941:
3935:
3934:
3932:
3915:(7): 1285–1296.
3900:
3849:
3842:
3838:
3835:
3829:
3806:
3798:
3778:
3776:
3775:
3770:
3768:
3766:
3765:
3753:
3751:
3749:
3748:
3747:
3738:
3737:
3721:
3719:
3718:
3700:
3692:
3688:
3676:
3674:
3673:
3668:
3663:
3661:
3660:
3659:
3650:
3649:
3630:
3629:
3628:
3619:
3618:
3609:
3608:
3598:
3596:
3594:
3593:
3581:
3579:
3578:
3569:
3568:
3559:
3548:
3546:
3545:
3544:
3535:
3534:
3525:
3524:
3514:
3513:
3512:
3503:
3502:
3492:
3487:
3479:
3475:
3461:
3459:
3458:
3453:
3451:
3450:
3441:
3440:
3428:
3423:
3422:
3410:
3408:
3407:
3406:
3397:
3396:
3386:
3385:
3384:
3375:
3374:
3365:
3364:
3354:
3344:
3333:
3331:
3330:
3325:
3309:
3307:
3306:
3301:
3299:
3298:
3289:
3288:
3279:
3277:
3276:
3275:
3266:
3265:
3256:
3255:
3245:
3244:
3243:
3234:
3233:
3224:
3223:
3213:
3203:
3188:
3186:
3185:
3180:
3178:
3177:
3168:
3167:
3155:
3144:
3143:
3131:
3129:
3128:
3127:
3118:
3117:
3098:
3097:
3096:
3087:
3086:
3077:
3076:
3066:
3056:
3046:
3044:
3043:
3038:
3022:
3020:
3019:
3014:
3012:
3011:
2999:
2997:
2996:
2995:
2986:
2985:
2966:
2965:
2964:
2955:
2954:
2945:
2944:
2934:
2924:
2910:
2908:
2907:
2902:
2897:
2892:
2891:
2882:
2881:
2861:
2847:
2845:
2844:
2839:
2834:
2823:
2822:
2813:
2812:
2792:
2757:
2755:
2754:
2749:
2747:
2745:
2744:
2732:
2730:
2728:
2717:
2706:
2704:
2703:
2682:
2674:
2670:
2655:
2653:
2652:
2647:
2642:
2640:
2639:
2638:
2629:
2628:
2609:
2608:
2607:
2598:
2597:
2588:
2587:
2577:
2575:
2573:
2572:
2571:
2543:
2541:
2539:
2538:
2537:
2528:
2527:
2518:
2517:
2507:
2506:
2497:
2495:
2487:
2482:
2474:
2470:
2455:
2453:
2452:
2447:
2445:
2444:
2426:
2425:
2413:
2411:
2410:
2401:
2400:
2399:
2390:
2389:
2380:
2379:
2369:
2356:
2345:
2343:
2342:
2337:
2325:
2323:
2322:
2317:
2315:
2314:
2294:
2292:
2291:
2286:
2284:
2283:
2259:
2257:
2256:
2247:
2246:
2245:
2236:
2235:
2226:
2225:
2215:
2213:
2211:
2210:
2209:
2200:
2199:
2186:
2176:
2166:
2164:
2163:
2158:
2142:
2140:
2139:
2134:
2132:
2131:
2119:
2117:
2116:
2115:
2106:
2105:
2086:
2085:
2084:
2075:
2074:
2065:
2064:
2054:
2044:
2030:
2028:
2027:
2022:
2002:
1977:
1963:
1961:
1960:
1955:
1938:
1915:
1887:
1872:
1870:
1869:
1864:
1847:
1831:
1816:
1814:
1813:
1808:
1803:
1781:
1719:
1717:
1716:
1711:
1709:
1707:
1691:
1690:
1677:
1654:
1649:
1641:
1637:
1627:it follows that
1623:
1621:
1620:
1615:
1613:
1611:
1603:
1602:
1593:
1583:
1565:
1563:
1562:
1557:
1555:
1553:
1543:
1542:
1533:
1532:
1513:
1487:
1482:
1474:
1470:
1456:
1454:
1453:
1448:
1443:
1441:
1440:
1439:
1430:
1429:
1410:
1409:
1408:
1399:
1398:
1389:
1388:
1378:
1368:
1346:
1344:
1343:
1338:
1327:
1325:
1324:
1323:
1295:
1294:
1293:
1281:
1280:
1270:
1260:
1246:
1244:
1243:
1238:
1236:
1234:
1226:
1225:
1216:
1206:
1188:
1186:
1185:
1180:
1178:
1176:
1168:
1167:
1166:
1153:
1148:
1147:
1136:
1122:
1120:
1119:
1114:
1103:
1065:
1057:
1055:
1053:
1052:
1051:
1042:
1041:
1010:
1009:
1008:
999:
998:
989:
988:
978:
968:
941:
939:
938:
933:
915:
913:
912:
907:
905:
904:
882:
880:
879:
874:
872:
871:
853:
851:
850:
845:
843:
842:
820:
818:
817:
812:
801:
763:
755:
753:
751:
750:
749:
740:
739:
720:
719:
718:
709:
708:
699:
698:
688:
678:
667:
665:
664:
659:
636:
634:
633:
628:
620:
582:
574:
569:
568:
557:
543:
541:
540:
535:
527:
507:
481:
455:
454:
443:
429:
427:
426:
421:
416:
401:
399:
398:
393:
388:
373:
371:
370:
365:
353:
351:
350:
345:
330:
328:
327:
322:
299:
297:
296:
291:
242:weather balloons
148:and atmospheric
125:Different radar
114:
107:
103:
100:
94:
92:
51:
27:
19:
4125:
4124:
4120:
4119:
4118:
4116:
4115:
4114:
4090:
4089:
4088:
4087:
4071:
4067:
4058:
4057:
4053:
4043:
4041:
4033:
4023:
4022:
4018:
4008:
4006:
3998:
3991:
3990:
3983:
3943:
3942:
3938:
3902:
3901:
3897:
3892:
3857:Clutter folding
3850:
3839:
3833:
3830:
3819:
3807:
3796:
3794:Clutter folding
3787:
3757:
3739:
3726:
3725:
3710:
3683:
3682:
3651:
3641:
3631:
3620:
3610:
3600:
3599:
3585:
3570:
3560:
3536:
3526:
3516:
3515:
3504:
3494:
3493:
3470:
3469:
3442:
3432:
3414:
3398:
3388:
3387:
3376:
3366:
3356:
3355:
3339:
3338:
3316:
3315:
3290:
3280:
3267:
3257:
3247:
3246:
3235:
3225:
3215:
3214:
3198:
3197:
3169:
3159:
3135:
3119:
3109:
3099:
3088:
3078:
3068:
3067:
3051:
3050:
3029:
3028:
3003:
2987:
2977:
2967:
2956:
2946:
2936:
2935:
2919:
2918:
2883:
2873:
2856:
2855:
2814:
2804:
2787:
2786:
2780:
2767:
2736:
2718:
2707:
2692:
2665:
2664:
2630:
2620:
2610:
2599:
2589:
2579:
2578:
2563:
2547:
2529:
2519:
2509:
2508:
2498:
2465:
2464:
2436:
2417:
2402:
2391:
2381:
2371:
2370:
2351:
2350:
2328:
2327:
2306:
2301:
2300:
2275:
2248:
2237:
2227:
2217:
2216:
2201:
2191:
2190:
2171:
2170:
2149:
2148:
2123:
2107:
2097:
2087:
2076:
2066:
2056:
2055:
2039:
2038:
1972:
1971:
1882:
1881:
1826:
1825:
1776:
1775:
1768:
1751:
1742:
1740:Surface clutter
1733:
1682:
1678:
1655:
1632:
1631:
1604:
1594:
1578:
1577:
1534:
1524:
1514:
1488:
1465:
1464:
1431:
1421:
1411:
1400:
1390:
1380:
1379:
1363:
1362:
1315:
1296:
1285:
1272:
1271:
1255:
1254:
1227:
1217:
1201:
1200:
1169:
1158:
1154:
1139:
1131:
1130:
1043:
1033:
1011:
1000:
990:
980:
979:
963:
962:
924:
923:
896:
891:
890:
863:
858:
857:
834:
829:
828:
741:
731:
721:
710:
700:
690:
689:
673:
672:
650:
649:
560:
552:
551:
446:
438:
437:
404:
403:
376:
375:
356:
355:
336:
335:
313:
312:
282:
281:
266:
250:
208:on the earth’s
162:
115:
104:
98:
95:
52:
50:
40:
28:
17:
16:Unwanted echoes
12:
11:
5:
4123:
4121:
4113:
4112:
4107:
4102:
4092:
4091:
4086:
4085:
4065:
4051:
4027:(March 1980).
4016:
3981:
3936:
3894:
3893:
3891:
3888:
3877:coherent dwell
3852:
3851:
3810:
3808:
3801:
3795:
3792:
3786:
3783:
3764:
3760:
3756:
3746:
3742:
3736:
3733:
3729:
3724:
3717:
3713:
3709:
3706:
3703:
3698:
3695:
3666:
3658:
3654:
3648:
3644:
3640:
3637:
3634:
3627:
3623:
3617:
3613:
3607:
3603:
3592:
3588:
3584:
3577:
3573:
3567:
3563:
3558:
3554:
3551:
3543:
3539:
3533:
3529:
3523:
3519:
3511:
3507:
3501:
3497:
3490:
3485:
3482:
3464:
3463:
3449:
3445:
3439:
3435:
3431:
3427:
3421:
3417:
3413:
3405:
3401:
3395:
3391:
3383:
3379:
3373:
3369:
3363:
3359:
3352:
3349:
3323:
3312:
3311:
3297:
3293:
3287:
3283:
3274:
3270:
3264:
3260:
3254:
3250:
3242:
3238:
3232:
3228:
3222:
3218:
3211:
3208:
3191:
3190:
3176:
3172:
3166:
3162:
3158:
3154:
3150:
3147:
3142:
3138:
3134:
3126:
3122:
3116:
3112:
3108:
3105:
3102:
3095:
3091:
3085:
3081:
3075:
3071:
3064:
3061:
3036:
3025:
3024:
3010:
3006:
3002:
2994:
2990:
2984:
2980:
2976:
2973:
2970:
2963:
2959:
2953:
2949:
2943:
2939:
2932:
2929:
2912:
2911:
2900:
2896:
2890:
2886:
2880:
2876:
2872:
2869:
2866:
2849:
2848:
2837:
2833:
2829:
2826:
2821:
2817:
2811:
2807:
2803:
2800:
2797:
2779:
2776:
2766:
2763:
2759:
2758:
2743:
2739:
2735:
2727:
2724:
2721:
2716:
2713:
2710:
2702:
2699:
2695:
2691:
2688:
2685:
2680:
2677:
2658:
2657:
2645:
2637:
2633:
2627:
2623:
2619:
2616:
2613:
2606:
2602:
2596:
2592:
2586:
2582:
2570:
2566:
2562:
2559:
2556:
2553:
2550:
2546:
2536:
2532:
2526:
2522:
2516:
2512:
2505:
2501:
2493:
2490:
2485:
2480:
2477:
2458:
2457:
2443:
2439:
2435:
2432:
2429:
2424:
2420:
2416:
2409:
2405:
2398:
2394:
2388:
2384:
2378:
2374:
2367:
2364:
2361:
2335:
2313:
2309:
2297:
2296:
2282:
2278:
2274:
2271:
2268:
2265:
2262:
2255:
2251:
2244:
2240:
2234:
2230:
2224:
2220:
2208:
2204:
2198:
2194:
2189:
2184:
2181:
2156:
2145:
2144:
2130:
2126:
2122:
2114:
2110:
2104:
2100:
2096:
2093:
2090:
2083:
2079:
2073:
2069:
2063:
2059:
2052:
2049:
2032:
2031:
2020:
2017:
2014:
2011:
2008:
2005:
2001:
1997:
1994:
1991:
1988:
1985:
1982:
1965:
1964:
1953:
1950:
1947:
1944:
1941:
1937:
1933:
1930:
1927:
1924:
1921:
1918:
1914:
1910:
1907:
1904:
1901:
1898:
1895:
1892:
1875:
1874:
1862:
1859:
1856:
1853:
1850:
1846:
1842:
1839:
1836:
1819:
1818:
1806:
1802:
1798:
1795:
1792:
1789:
1786:
1767:
1764:
1750:
1747:
1741:
1738:
1732:
1729:
1721:
1720:
1706:
1703:
1700:
1697:
1694:
1689:
1685:
1681:
1676:
1673:
1670:
1667:
1664:
1661:
1658:
1652:
1647:
1644:
1625:
1624:
1610:
1607:
1601:
1597:
1591:
1588:
1567:
1566:
1552:
1549:
1546:
1541:
1537:
1531:
1527:
1523:
1520:
1517:
1512:
1509:
1506:
1503:
1500:
1497:
1494:
1491:
1485:
1480:
1477:
1458:
1457:
1446:
1438:
1434:
1428:
1424:
1420:
1417:
1414:
1407:
1403:
1397:
1393:
1387:
1383:
1376:
1373:
1356:radar equation
1348:
1347:
1336:
1333:
1330:
1322:
1318:
1314:
1311:
1308:
1305:
1302:
1299:
1292:
1288:
1284:
1279:
1275:
1268:
1265:
1248:
1247:
1233:
1230:
1224:
1220:
1214:
1211:
1190:
1189:
1175:
1172:
1165:
1161:
1157:
1151:
1146:
1142:
1124:
1123:
1112:
1109:
1106:
1102:
1098:
1095:
1092:
1089:
1086:
1083:
1080:
1077:
1074:
1071:
1068:
1063:
1060:
1050:
1046:
1040:
1036:
1032:
1029:
1026:
1023:
1020:
1017:
1014:
1007:
1003:
997:
993:
987:
983:
976:
973:
944:
943:
931:
921:
903:
899:
888:
870:
866:
855:
841:
837:
822:
821:
810:
807:
804:
800:
796:
793:
790:
787:
784:
781:
778:
775:
772:
769:
766:
761:
758:
748:
744:
738:
734:
730:
727:
724:
717:
713:
707:
703:
697:
693:
686:
683:
657:
642:radar equation
638:
637:
626:
623:
619:
615:
612:
609:
606:
603:
600:
597:
594:
591:
588:
585:
580:
577:
572:
567:
563:
545:
544:
533:
530:
526:
522:
519:
516:
513:
510:
506:
502:
499:
496:
493:
490:
487:
484:
480:
476:
473:
470:
467:
464:
461:
458:
453:
449:
419:
415:
411:
391:
387:
383:
363:
343:
320:
289:
265:
264:Volume clutter
262:
249:
246:
161:
158:
117:
116:
31:
29:
22:
15:
13:
10:
9:
6:
4:
3:
2:
4122:
4111:
4108:
4106:
4103:
4101:
4098:
4097:
4095:
4083:
4079:
4075:
4069:
4066:
4061:
4055:
4052:
4039:
4032:
4031:
4026:
4020:
4017:
4004:
3997:
3996:
3988:
3986:
3982:
3976:
3971:
3967:
3963:
3959:
3955:
3951:
3948:(June 2016).
3947:
3940:
3937:
3931:
3926:
3922:
3918:
3914:
3910:
3906:
3899:
3896:
3889:
3887:
3885:
3880:
3878:
3874:
3870:
3866:
3862:
3858:
3848:
3845:
3837:
3827:
3823:
3817:
3816:
3811:This section
3809:
3805:
3800:
3799:
3793:
3791:
3784:
3782:
3779:
3762:
3758:
3754:
3744:
3740:
3734:
3731:
3727:
3722:
3715:
3711:
3707:
3704:
3701:
3696:
3693:
3680:
3677:
3664:
3656:
3652:
3646:
3638:
3635:
3625:
3621:
3615:
3611:
3605:
3601:
3590:
3586:
3582:
3575:
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2018:
2015:
2012:
2009:
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1999:
1995:
1992:
1986:
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949:
948:sinc function
929:
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897:
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864:
856:
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211:
210:magnetosphere
207:
203:
199:
198:space weather
195:
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179:
175:
171:
170:precipitation
167:
159:
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113:
110:
102:
99:December 2016
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
4105:Radar theory
4068:
4054:
4042:. Retrieved
4029:
4019:
4007:. Retrieved
3994:
3957:
3953:
3946:Doviak R. J.
3939:
3912:
3908:
3898:
3881:
3856:
3855:
3840:
3834:January 2024
3831:
3820:Please help
3815:verification
3812:
3788:
3780:
3681:
3678:
3468:
3465:
3313:
3192:
3026:
2913:
2850:
2781:
2768:
2760:
2659:
2459:
2298:
2146:
2033:
1966:
1876:
1820:
1769:
1760:
1749:Beam filling
1743:
1734:
1722:
1626:
1572:
1568:
1459:
1353:
1349:
1249:
1194:antenna gain
1191:
1125:
945:
916:= effective
823:
639:
546:
432:
332:
308:
302:
275:
251:
163:
133:
132:
105:
96:
86:
79:
72:
65:
53:
41:Please help
36:verification
33:
3873:fill pulses
3334:to degrees
3314:Converting
178:dust storms
150:turbulences
142:from ground
4100:Atmosphere
4094:Categories
4044:2 December
4025:Elkins, TJ
4009:2 December
3954:Atmosphere
3890:References
3884:dwell time
956:beam width
234:refraction
206:solar wind
192:caused by
190:ionosphere
174:hail spike
69:newspapers
3960:(6): 83.
3759:σ
3755:σ
3728:θ
3708:×
3665:σ
3639:π
3622:λ
3587:σ
3562:θ
3538:λ
3444:σ
3416:θ
3378:λ
3322:θ
3292:σ
3282:θ
3259:π
3237:λ
3171:σ
3149:θ
3133:π
3107:π
3090:λ
3005:σ
2975:π
2958:λ
2885:θ
2871:π
2868:≈
2828:θ
2825:
2802:π
2738:σ
2734:σ
2726:θ
2723:τ
2715:ψ
2712:
2698:−
2690:×
2644:σ
2618:π
2601:λ
2565:σ
2561:ψ
2558:
2552:θ
2549:τ
2531:λ
2438:σ
2434:ψ
2431:
2419:θ
2415:τ
2393:λ
2334:θ
2308:σ
2277:σ
2273:ψ
2270:
2264:θ
2261:τ
2239:λ
2203:π
2125:σ
2095:π
2078:λ
2019:ψ
2016:
2010:θ
1996:τ
1952:ψ
1949:
1932:θ
1929:
1909:τ
1861:ψ
1858:
1841:τ
1797:θ
1794:
1705:η
1702:τ
1696:ϕ
1693:θ
1680:π
1675:σ
1666:
1609:ϕ
1606:θ
1596:π
1551:η
1548:τ
1522:π
1511:σ
1499:
1445:σ
1419:π
1402:λ
1354:From the
1335:η
1332:τ
1307:
1287:λ
1232:ϕ
1229:θ
1219:π
1174:π
1160:λ
1111:η
1097:τ
1085:ϕ
1073:θ
1059:π
1031:π
1019:
809:η
795:τ
783:ϕ
771:θ
757:π
729:π
656:η
614:τ
602:ϕ
590:θ
576:π
571:≈
521:τ
501:ϕ
495:
475:θ
469:
460:π
410:ϕ
382:θ
342:τ
319:τ
196:or other
127:artifacts
3875:to each
1192:and the
918:aperture
644:but the
3962:Bibcode
3917:Bibcode
236:(e.g.,
134:Clutter
83:scholar
4076:1997,
3689:
3476:
3345:
3204:
3057:
2925:
2862:
2793:
2671:
2471:
2357:
2299:where
2177:
2045:
1978:
1888:
1832:
1782:
1638:
1584:
1573:Since
1471:
1369:
1261:
1207:
1137:
969:
824:where
679:
558:
444:
374:, are
254:signal
214:plasma
186:meteor
184:, and
160:Causes
138:radars
85:
78:
71:
64:
56:
4034:(PDF)
3999:(PDF)
3861:radar
3462:Watts
3310:Watts
3189:Watts
3023:Watts
2656:Watts
2456:Watts
2295:Watts
2143:Watts
278:chaff
258:noise
166:chaff
146:chaff
90:JSTOR
76:books
4046:2023
4011:2023
3705:5.25
2492:1300
2366:1300
1490:1024
1298:1024
885:gain
402:and
62:news
4078:doi
3970:doi
3925:doi
3824:by
3553:180
3430:180
2816:tan
2709:cos
2555:sec
2428:sec
2267:sec
2013:sec
1946:sec
1926:tan
1855:sec
1791:tan
1663:log
1496:log
1304:log
1016:log
492:tan
466:tan
228:or
156:).
45:by
4096::
3984:^
3968:.
3956:.
3952:.
3923:.
3913:36
3911:.
3907:.
3886:.
3712:10
2694:10
1657:16
883:=
244:.
224:,
176:,
172:,
4080::
4062:.
4048:.
4013:.
3978:.
3972::
3964::
3958:7
3933:.
3927::
3919::
3847:)
3841:(
3836:)
3832:(
3818:.
3763:o
3745:2
3741:R
3735:2
3732:o
3723:1
3716:4
3702:=
3697:C
3694:S
3657:4
3653:R
3647:3
3643:)
3636:4
3633:(
3626:2
3616:2
3612:G
3606:t
3602:P
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3566:o
3557:/
3550:(
3542:2
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3489:=
3484:C
3481:S
3448:o
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3434:)
3426:/
3420:o
3412:(
3404:2
3400:R
3394:4
3390:4
3382:2
3372:2
3368:G
3362:t
3358:P
3351:=
3348:C
3296:o
3286:2
3273:2
3269:R
3263:2
3253:4
3249:4
3241:2
3231:2
3227:G
3221:t
3217:P
3210:=
3207:C
3175:o
3165:2
3161:)
3157:2
3153:/
3146:(
3141:2
3137:R
3125:4
3121:R
3115:3
3111:)
3104:4
3101:(
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3084:2
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3074:t
3070:P
3063:=
3060:C
3035:A
3009:o
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2993:4
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2983:3
2979:)
2972:4
2969:(
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2931:=
2928:C
2899:4
2895:/
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2879:2
2875:R
2865:A
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2832:/
2820:2
2810:2
2806:R
2799:=
2796:A
2742:o
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2684:=
2679:C
2676:S
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2615:4
2612:(
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2500:R
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2484:=
2479:C
2476:S
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2423:o
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2363:=
2360:C
2312:o
2281:o
2254:3
2250:R
2243:2
2233:2
2229:G
2223:t
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2207:3
2197:7
2193:2
2188:c
2183:=
2180:C
2155:A
2129:o
2121:A
2113:4
2109:R
2103:3
2099:)
2092:4
2089:(
2082:2
2072:2
2068:G
2062:t
2058:P
2051:=
2048:C
2007:)
2004:2
2000:/
1993:c
1990:(
1987:R
1984:=
1981:A
1943:)
1940:2
1936:/
1923:(
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1917:2
1913:/
1906:c
1903:(
1900:R
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1891:A
1873:.
1852:)
1849:2
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1838:c
1835:(
1817:.
1805:2
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1669:2
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1646:C
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1600:2
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1519:4
1516:(
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1505:)
1502:2
1493:(
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1479:C
1476:S
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1416:4
1413:(
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1375:=
1372:S
1329:c
1321:2
1317:R
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1310:2
1301:(
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1267:=
1264:C
1223:2
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1145:r
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1108:)
1105:2
1101:/
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1091:(
1088:)
1082:R
1079:(
1076:)
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996:t
992:G
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975:=
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902:r
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803:2
799:/
792:c
789:(
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777:(
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765:(
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685:=
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611:c
608:(
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599:R
596:(
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584:(
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515:(
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457:=
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390:2
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333:c
309:c
288:R
232:/
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
