1817:
1091:
68:
It is a statistical measurement typically based on historic data over an extended period, and is used usually for risk analysis. Examples include deciding whether a project should be allowed to go forward in a zone of a certain risk or designing structures to withstand events with a certain return
172:
to predict the magnitude of such an (unobserved) event. Even if the historic return interval is a lot less than 1000 years, if there are a number of less-severe events of a similar nature recorded, the use of such a model is likely to provide useful information to help estimate the future return
164:
That distinction is significant because there are few observations of rare events: for instance, if observations go back 400 years, the most extreme event (a 400-year event by the statistical definition) may later be classed, on longer observation, as a 200-year event (if a comparable event
161:: it is computed from a set of data (the observations), as distinct from the theoretical value in an idealized distribution. One does not actually know that a certain or greater magnitude happens with 1% probability, only that it has been observed exactly once in 100 years.
1538:
193:. That is disfavoured because each year does not represent an independent Bernoulli trial but is an arbitrary measure of time. This question is mainly academic as the results obtained will be similar under both the Poisson and binomial interpretations.
1686:
888:
1965:
359:
1827:
Return period is useful for risk analysis (such as natural, inherent, or hydrologic risk of failure). When dealing with structure design expectations, the return period is useful in calculating the riskiness of the structure.
1691:
727:
1308:
893:
1372:
1598:
572:
2026:
1401:
826:
1409:
1671:
1176:
2265:
181:
One would like to be able to interpret the return period in probabilistic models. The most logical interpretation for this is to take the return period as the counting rate in a
143:
The theoretical return period between occurrences is the inverse of the average frequency of occurrence. For example, a 10-year flood has a 1/10 = 0.1 or 10% chance of being
113:
1125:
150:
This does not mean that a 100-year flood will happen regularly every 100 years, or only once in 100 years. Despite the connotations of the name "return period". In any
880:
456:
1812:{\displaystyle {\begin{aligned}P(X=1)&={\binom {10}{1}}\times 0.01^{1}\times 0.99^{9}\\&\approx 10\times 0.01\times 0.914\\&\approx 0.0914\end{aligned}}}
1331:
1145:
1200:
1086:{\displaystyle {\begin{aligned}P(r;t)&={\frac {(\mu t)^{r}}{r!}}e^{-\mu t}\\P(r=1;t=10)&={\frac {(10/243)^{1}}{1!}}e^{-10/243}\approx 3.95\%\end{aligned}}}
776:
485:
750:
595:
422:
402:
382:
1848:
854:
215:
2258:
2496:
828:. This means, for example, that there is a 63.2% probability of a flood larger than the 50-year return flood to occur within any period of 50 year.
2864:
154:
100-year period, a 100-year event may occur once, twice, more, or not at all, and each outcome has a probability that can be computed as below.
69:
period. The following analysis assumes that the probability of the event occurring does not vary over time and is independent of past events.
2096:
2251:
185:
since it is the expectation value of the rate of occurrences. An alternative interpretation is to take it as the probability for a yearly
2148:
603:
3490:
1212:
3021:
3485:
1339:
577:
Consequently, the probability of exceedance (i.e. the probability of an event "stronger" than the event with return period
2112:
Peres, D. J.; Cancelliere, A. (2016-10-01). "Estimating return period of landslide triggering by Monte Carlo simulation".
2049:
1333:
is zero. Often that is a close approximation, in which case the probabilities yielded by this formula hold approximately.
3187:
3137:
3031:
1549:
3465:
2059:
1835:
event that exceeds design limits during the expected life of the structure is the complement of the probability that
2691:
493:
3475:
3427:
3310:
202:
1976:
1533:{\displaystyle {\frac {n!}{(n-r)!r!}}\mu ^{r}(1-\mu )^{n-r}\rightarrow e^{-\lambda }{\frac {\lambda ^{r}}{r!}}.}
3521:
3460:
3177:
3142:
2984:
2187:
1377:
168:
Further, one cannot determine the size of a 1000-year event based on such records alone but instead must use a
31:
781:
3470:
3162:
2927:
2054:
144:
1637:
3412:
3270:
2821:
2706:
1150:
3250:
3097:
3059:
2508:
2447:
2149:"Probability analysis of return period of daily maximum rainfall in annual data set of Ludhiana, Punjab"
1203:
190:
62:
3480:
3202:
3026:
2786:
2593:
2387:
2121:
206:
182:
80:
3516:
3376:
3371:
3172:
3016:
2638:
2491:
2412:
2319:
1104:
135:, in terms of the height of the surge, and similarly for other events. This is Weibull's Formula.
3526:
3511:
3402:
3315:
3280:
3132:
2648:
2553:
2457:
2349:
2282:
165:
immediately occurs) or a 500-year event (if no comparable event occurs for a further 100 years).
3122:
147:
in any one year and a 50-year flood has a 0.02 or 2% chance of being exceeded in any one year.
3381:
3220:
3212:
3152:
3112:
3001:
2816:
2578:
2568:
2354:
2168:
2092:
427:
169:
859:
3295:
3197:
3102:
2701:
2696:
2613:
2442:
2314:
2160:
2129:
2084:
2214:
2028:
is the expression for the probability of the occurrence of the event in question in a year;
1316:
1130:
3300:
3260:
3255:
3046:
2859:
2746:
2741:
2525:
2462:
2432:
2397:
2392:
2359:
2324:
2295:
1185:
186:
1960:{\displaystyle {\overline {R}}=1-\left(1-{1 \over T}\right)^{n}=1-(1-P(X\geq x_{T}))^{n}}
755:
464:
2125:
3361:
3245:
3225:
3107:
3092:
2979:
2964:
2959:
2919:
2899:
2811:
2653:
2643:
2633:
2598:
2530:
2515:
2422:
2344:
2304:
2044:
735:
580:
407:
387:
367:
3505:
3442:
3437:
3422:
3407:
3356:
3351:
3117:
3082:
2996:
2991:
2751:
2623:
2583:
2329:
2309:
752:, the probability of exceedance within an interval equal to the return period (i.e.
354:{\displaystyle P(r;t)={(\mu t)^{r} \over r!}e^{-\mu t}={(t/T)^{r} \over r!}e^{-t/T}}
3432:
3182:
3167:
3157:
3006:
2937:
2806:
2771:
2686:
2628:
2503:
2402:
2364:
2339:
2164:
839:
17:
2133:
461:
The probability of no-occurrence can be obtained simply considering the case for
3341:
3265:
2969:
2932:
2879:
2603:
2588:
2563:
2437:
1313:
This is valid only if the probability of more than one occurrence per unit time
132:
3447:
3127:
3011:
2951:
2909:
2781:
2618:
2486:
2427:
2417:
2334:
2243:
50:
2172:
3417:
3366:
3336:
3305:
3235:
3147:
2904:
2791:
2776:
2716:
2663:
2658:
2558:
2481:
2471:
2369:
2237:
Water
Resources Engineering, 2005 Edition, John Wiley & Sons, Inc, 2005.
2079:
ASCE, Task
Committee on Hydrology Handbook of Management Group D of (1996).
158:
58:
2088:
3087:
3054:
2731:
2573:
2540:
49:, is an average time or an estimated average time between events such as
3397:
3346:
2874:
2869:
2851:
2831:
2736:
2673:
2608:
2545:
3192:
3064:
2889:
2884:
2836:
2826:
2796:
2721:
2476:
2407:
2379:
2278:
131:
For floods, the event may be measured in terms of m/s or height; for
127:
is the rank of observed occurrences when arranged in descending order
1622:
is the number of recorded occurrences of the event being considered
3290:
3275:
3230:
2974:
2947:
2894:
2761:
2756:
2726:
2711:
2520:
2290:
2274:
2192:
National
Engineering Handbook, Part 654: Stream Restoration Design
54:
882:) then the probability of exactly one occurrence in ten years is
3320:
3285:
2841:
2801:
2766:
384:
is the number of occurrences the probability is calculated for,
2247:
2116:. Flash floods, hydro-geomorphic response and risk management.
3240:
2681:
722:{\displaystyle P(t>0;t)=1-P(t=0;t)=1-e^{-\mu t}=1-e^{-t/T}}
597:
to occur at least once within the time period of interest) is
1303:{\displaystyle P(X=r)={n \choose r}\mu ^{r}(1-\mu )^{n-r}.}
778:) is independent from the return period and it is equal to
2186:
National
Resources Conservation Service (August 2007).
1631:
Given that the return period of an event is 100 years,
1367:{\displaystyle n\rightarrow \infty ,\mu \rightarrow 0}
862:
842:
1979:
1851:
1689:
1640:
1552:
1412:
1380:
1342:
1319:
1215:
1188:
1153:
1133:
1107:
891:
784:
758:
738:
606:
583:
496:
467:
430:
410:
390:
370:
218:
139:
Return period as the reciprocal of expected frequency
83:
3390:
3329:
3211:
3073:
3045:
2946:
2918:
2850:
2672:
2539:
2456:
2378:
2289:
2194:. Washington, D.C.: U.S. Department of Agriculture
2020:
1959:
1811:
1665:
1592:
1532:
1395:
1366:
1325:
1302:
1194:
1170:
1139:
1119:
1085:
874:
848:
820:
770:
744:
721:
589:
566:
479:
450:
416:
396:
376:
353:
107:
1735:
1722:
1593:{\displaystyle \mu ={\frac {1}{T}}={m \over n+1}}
1253:
1240:
2259:
1842:The equation for assessing this parameter is
1676:So the probability that such an event occurs
157:Also, the estimated return period below is a
8:
567:{\displaystyle P(r=0;t)=e^{-\mu t}=e^{-t/T}}
732:Note that for any event with return period
2266:
2252:
2244:
2021:{\displaystyle {1 \over T}=P(X\geq x_{T})}
2009:
1980:
1978:
1951:
1938:
1898:
1883:
1852:
1850:
1839:events occur which exceed design limits.
1761:
1748:
1734:
1721:
1719:
1690:
1688:
1647:
1639:
1572:
1559:
1551:
1511:
1505:
1496:
1477:
1455:
1413:
1411:
1396:{\displaystyle n\mu \rightarrow \lambda }
1379:
1341:
1318:
1285:
1263:
1252:
1239:
1237:
1214:
1187:
1163:
1152:
1132:
1106:
1060:
1053:
1032:
1020:
1011:
958:
937:
921:
892:
890:
861:
841:
783:
757:
737:
709:
702:
677:
605:
582:
554:
547:
528:
495:
466:
440:
429:
409:
389:
369:
341:
334:
313:
301:
292:
277:
256:
240:
217:
87:
82:
2147:Kumar, Rajneesh; Bhardwaj, Anil (2015).
821:{\displaystyle 1-\exp(-1)\approx 63.2\%}
2865:International scale of river difficulty
2153:Indian Journal of Agricultural Research
2071:
2034:is the expected life of the structure.
2219:UK Centre for Ecology & Hydrology
1666:{\displaystyle p={1 \over 100}=0.01.}
1178:), the probability of a given number
30:For the satellite return period, see
27:Estimated recurrence time of an event
7:
1171:{\displaystyle \tau =1{\text{year}}}
836:If the return period of occurrence
1726:
1349:
1244:
1076:
815:
25:
3022:Flooded grasslands and savannas
2165:10.5958/0976-058X.2015.00023.2
2015:
1996:
1948:
1944:
1925:
1913:
1709:
1697:
1489:
1474:
1461:
1436:
1424:
1387:
1358:
1346:
1282:
1269:
1231:
1219:
1029:
1014:
1001:
977:
934:
924:
911:
899:
806:
797:
661:
643:
628:
610:
518:
500:
310:
295:
253:
243:
234:
222:
108:{\displaystyle ={n+1 \over m}}
1:
2188:"Chapter 5: Stream Hydrology"
2134:10.1016/j.jhydrol.2016.03.036
2050:Cumulative frequency analysis
1616:is number of years on record.
1182:of events of a return period
1120:{\displaystyle n\times \tau }
404:the time period of interest,
3188:Universal Soil Loss Equation
3138:Hydrological transport model
3032:Storm Water Management Model
1857:
2215:"Flood Estimation Handbook"
1680:in 10 successive years is:
3543:
2692:Antecedent drainage stream
2081:Hydrology Handbook | Books
121:number of years on record;
73:Estimating a return period
29:
3456:
3428:River valley civilization
3311:Riparian-zone restoration
424:is the return period and
203:probability mass function
177:Probability distributions
3491:Countries without rivers
3466:Rivers by discharge rate
3178:Runoff model (reservoir)
3143:Infiltration (hydrology)
2213:Anonymous (2014-11-07).
875:{\textstyle \mu =0.0041}
451:{\displaystyle \mu =1/T}
32:Satellite revisit period
3163:River Continuum Concept
2928:Agricultural wastewater
2055:Frequency of exceedance
3486:River name etymologies
3413:Hydraulic civilization
3271:Floodplain restoration
3047:Point source pollution
2822:Sedimentary structures
2022:
1961:
1813:
1667:
1594:
1534:
1397:
1368:
1327:
1304:
1196:
1172:
1141:
1121:
1087:
876:
850:
822:
772:
746:
723:
591:
568:
481:
458:is the counting rate.
452:
418:
398:
378:
355:
109:
3098:Discharge (hydrology)
3060:Industrial wastewater
2541:Sedimentary processes
2089:10.1061/9780784401385
2023:
1962:
1814:
1668:
1595:
1535:
1398:
1369:
1328:
1326:{\displaystyle \tau }
1305:
1204:binomial distribution
1197:
1173:
1142:
1140:{\displaystyle \tau }
1122:
1101:In a given period of
1088:
877:
851:
823:
773:
747:
724:
592:
569:
482:
453:
419:
399:
379:
356:
191:binomial distribution
110:
63:river discharge flows
3203:Volumetric flow rate
2787:Riffle-pool sequence
2114:Journal of Hydrology
1977:
1849:
1687:
1638:
1550:
1410:
1378:
1340:
1317:
1213:
1195:{\displaystyle \mu }
1186:
1151:
1131:
1105:
889:
860:
840:
782:
756:
736:
604:
581:
494:
465:
428:
408:
388:
368:
216:
207:Poisson distribution
183:Poisson distribution
81:
77:Recurrence interval
3377:Whitewater kayaking
3372:Whitewater canoeing
3173:Runoff curve number
3017:Flood pulse concept
2126:2016JHyd..541..256P
1831:The probability of
1374:in such a way that
771:{\displaystyle t=T}
480:{\displaystyle r=0}
43:recurrence interval
18:Recurrence interval
3403:Aquatic toxicology
3316:Stream restoration
3281:Infiltration basin
3133:Hydrological model
2649:Sediment transport
2472:Estavelle/Inversac
2350:Subterranean river
2018:
1957:
1809:
1807:
1663:
1610:is return interval
1590:
1530:
1393:
1364:
1323:
1300:
1192:
1168:
1137:
1117:
1083:
1081:
872:
846:
818:
768:
742:
719:
587:
564:
477:
448:
414:
394:
374:
351:
105:
41:, also known as a
3499:
3498:
3476:Whitewater rivers
3382:Whitewater slalom
3213:River engineering
3113:Groundwater model
3074:River measurement
3002:Flood forecasting
2817:Sedimentary basin
2674:Fluvial landforms
2579:Bed material load
2355:River bifurcation
2098:978-0-7844-0138-5
1988:
1891:
1860:
1733:
1655:
1588:
1567:
1525:
1449:
1251:
1166:
1047:
952:
745:{\displaystyle T}
590:{\displaystyle T}
487:. The formula is
417:{\displaystyle T}
397:{\displaystyle t}
377:{\displaystyle r}
328:
271:
170:statistical model
103:
16:(Redirected from
3534:
3461:Rivers by length
3296:River morphology
3198:Wetted perimeter
3103:Drainage density
2614:Headward erosion
2443:Perennial stream
2315:Blackwater river
2268:
2261:
2254:
2245:
2238:
2235:
2229:
2228:
2226:
2225:
2210:
2204:
2203:
2201:
2199:
2183:
2177:
2176:
2144:
2138:
2137:
2109:
2103:
2102:
2076:
2027:
2025:
2024:
2019:
2014:
2013:
1989:
1981:
1966:
1964:
1963:
1958:
1956:
1955:
1943:
1942:
1903:
1902:
1897:
1893:
1892:
1884:
1861:
1853:
1818:
1816:
1815:
1810:
1808:
1795:
1770:
1766:
1765:
1753:
1752:
1740:
1739:
1738:
1725:
1672:
1670:
1669:
1664:
1656:
1648:
1599:
1597:
1596:
1591:
1589:
1587:
1573:
1568:
1560:
1539:
1537:
1536:
1531:
1526:
1524:
1516:
1515:
1506:
1504:
1503:
1488:
1487:
1460:
1459:
1450:
1448:
1422:
1414:
1402:
1400:
1399:
1394:
1373:
1371:
1370:
1365:
1332:
1330:
1329:
1324:
1309:
1307:
1306:
1301:
1296:
1295:
1268:
1267:
1258:
1257:
1256:
1243:
1202:is given by the
1201:
1199:
1198:
1193:
1177:
1175:
1174:
1169:
1167:
1164:
1146:
1144:
1143:
1138:
1127:for a unit time
1126:
1124:
1123:
1118:
1092:
1090:
1089:
1084:
1082:
1069:
1068:
1064:
1048:
1046:
1038:
1037:
1036:
1024:
1012:
969:
968:
953:
951:
943:
942:
941:
922:
881:
879:
878:
873:
855:
853:
852:
847:
827:
825:
824:
819:
777:
775:
774:
769:
751:
749:
748:
743:
728:
726:
725:
720:
718:
717:
713:
688:
687:
596:
594:
593:
588:
573:
571:
570:
565:
563:
562:
558:
539:
538:
486:
484:
483:
478:
457:
455:
454:
449:
444:
423:
421:
420:
415:
403:
401:
400:
395:
383:
381:
380:
375:
360:
358:
357:
352:
350:
349:
345:
329:
327:
319:
318:
317:
305:
293:
288:
287:
272:
270:
262:
261:
260:
241:
114:
112:
111:
106:
104:
99:
88:
21:
3542:
3541:
3537:
3536:
3535:
3533:
3532:
3531:
3522:Time in science
3502:
3501:
3500:
3495:
3471:Drainage basins
3452:
3386:
3325:
3301:Retention basin
3261:Erosion control
3256:Detention basin
3207:
3123:Hjulström curve
3075:
3069:
3041:
2985:Non-water flood
2942:
2914:
2860:Helicoidal flow
2846:
2747:Fluvial terrace
2742:Floating island
2668:
2543:
2535:
2526:Rhythmic spring
2460:
2452:
2433:Stream gradient
2374:
2360:River ecosystem
2325:Channel pattern
2293:
2285:
2272:
2242:
2241:
2236:
2232:
2223:
2221:
2212:
2211:
2207:
2197:
2195:
2185:
2184:
2180:
2146:
2145:
2141:
2111:
2110:
2106:
2099:
2078:
2077:
2073:
2068:
2041:
2005:
1975:
1974:
1947:
1934:
1876:
1872:
1871:
1847:
1846:
1825:
1806:
1805:
1793:
1792:
1768:
1767:
1757:
1744:
1720:
1712:
1685:
1684:
1636:
1635:
1629:
1577:
1548:
1547:
1517:
1507:
1492:
1473:
1451:
1423:
1415:
1408:
1407:
1376:
1375:
1338:
1337:
1315:
1314:
1281:
1259:
1238:
1211:
1210:
1184:
1183:
1149:
1148:
1129:
1128:
1103:
1102:
1099:
1080:
1079:
1049:
1039:
1028:
1013:
1004:
971:
970:
954:
944:
933:
923:
914:
887:
886:
858:
857:
838:
837:
834:
780:
779:
754:
753:
734:
733:
698:
673:
602:
601:
579:
578:
543:
524:
492:
491:
463:
462:
426:
425:
406:
405:
386:
385:
366:
365:
330:
320:
309:
294:
273:
263:
252:
242:
214:
213:
199:
187:Bernoulli trial
179:
141:
89:
79:
78:
75:
47:repeat interval
35:
28:
23:
22:
15:
12:
11:
5:
3540:
3538:
3530:
3529:
3524:
3519:
3514:
3504:
3503:
3497:
3496:
3494:
3493:
3488:
3483:
3478:
3473:
3468:
3463:
3457:
3454:
3453:
3451:
3450:
3445:
3440:
3435:
3430:
3425:
3420:
3415:
3410:
3405:
3400:
3394:
3392:
3388:
3387:
3385:
3384:
3379:
3374:
3369:
3364:
3362:Stone skipping
3359:
3354:
3349:
3344:
3339:
3333:
3331:
3327:
3326:
3324:
3323:
3318:
3313:
3308:
3303:
3298:
3293:
3288:
3283:
3278:
3273:
3268:
3263:
3258:
3253:
3248:
3246:Drop structure
3243:
3238:
3233:
3228:
3226:Balancing lake
3223:
3217:
3215:
3209:
3208:
3206:
3205:
3200:
3195:
3190:
3185:
3180:
3175:
3170:
3165:
3160:
3155:
3153:Playfair's law
3150:
3145:
3140:
3135:
3130:
3125:
3120:
3115:
3110:
3108:Exner equation
3105:
3100:
3095:
3093:Bradshaw model
3090:
3085:
3079:
3077:
3071:
3070:
3068:
3067:
3062:
3057:
3051:
3049:
3043:
3042:
3040:
3039:
3034:
3029:
3024:
3019:
3014:
3009:
3004:
2999:
2994:
2989:
2988:
2987:
2982:
2980:Urban flooding
2972:
2967:
2965:Crevasse splay
2962:
2960:100-year flood
2956:
2954:
2944:
2943:
2941:
2940:
2935:
2930:
2924:
2922:
2920:Surface runoff
2916:
2915:
2913:
2912:
2907:
2902:
2900:Stream capture
2897:
2892:
2887:
2882:
2877:
2872:
2867:
2862:
2856:
2854:
2848:
2847:
2845:
2844:
2839:
2834:
2829:
2824:
2819:
2814:
2812:Rock-cut basin
2809:
2804:
2799:
2794:
2789:
2784:
2779:
2774:
2769:
2764:
2759:
2754:
2749:
2744:
2739:
2734:
2729:
2724:
2719:
2714:
2709:
2704:
2699:
2694:
2689:
2684:
2678:
2676:
2670:
2669:
2667:
2666:
2661:
2656:
2654:Suspended load
2651:
2646:
2644:Secondary flow
2641:
2636:
2634:Retrogradation
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2599:Dissolved load
2596:
2591:
2586:
2581:
2576:
2571:
2566:
2561:
2556:
2550:
2548:
2537:
2536:
2534:
2533:
2531:Spring horizon
2528:
2523:
2518:
2516:Mineral spring
2513:
2512:
2511:
2501:
2500:
2499:
2497:list in the US
2494:
2484:
2479:
2474:
2468:
2466:
2454:
2453:
2451:
2450:
2445:
2440:
2435:
2430:
2425:
2423:Stream channel
2420:
2415:
2410:
2405:
2400:
2395:
2390:
2384:
2382:
2376:
2375:
2373:
2372:
2367:
2362:
2357:
2352:
2347:
2345:Drainage basin
2342:
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2305:Alluvial river
2301:
2299:
2287:
2286:
2273:
2271:
2270:
2263:
2256:
2248:
2240:
2239:
2230:
2205:
2178:
2139:
2104:
2097:
2070:
2069:
2067:
2064:
2063:
2062:
2060:Residence time
2057:
2052:
2047:
2045:100-year flood
2040:
2037:
2036:
2035:
2029:
2017:
2012:
2008:
2004:
2001:
1998:
1995:
1992:
1987:
1984:
1968:
1967:
1954:
1950:
1946:
1941:
1937:
1933:
1930:
1927:
1924:
1921:
1918:
1915:
1912:
1909:
1906:
1901:
1896:
1890:
1887:
1882:
1879:
1875:
1870:
1867:
1864:
1859:
1856:
1824:
1821:
1820:
1819:
1804:
1801:
1798:
1796:
1794:
1791:
1788:
1785:
1782:
1779:
1776:
1773:
1771:
1769:
1764:
1760:
1756:
1751:
1747:
1743:
1737:
1732:
1729:
1724:
1718:
1715:
1713:
1711:
1708:
1705:
1702:
1699:
1696:
1693:
1692:
1674:
1673:
1662:
1659:
1654:
1651:
1646:
1643:
1628:
1625:
1624:
1623:
1617:
1611:
1601:
1600:
1586:
1583:
1580:
1576:
1571:
1566:
1563:
1558:
1555:
1541:
1540:
1529:
1523:
1520:
1514:
1510:
1502:
1499:
1495:
1491:
1486:
1483:
1480:
1476:
1472:
1469:
1466:
1463:
1458:
1454:
1447:
1444:
1441:
1438:
1435:
1432:
1429:
1426:
1421:
1418:
1392:
1389:
1386:
1383:
1363:
1360:
1357:
1354:
1351:
1348:
1345:
1322:
1311:
1310:
1299:
1294:
1291:
1288:
1284:
1280:
1277:
1274:
1271:
1266:
1262:
1255:
1250:
1247:
1242:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1191:
1162:
1159:
1156:
1136:
1116:
1113:
1110:
1098:
1095:
1094:
1093:
1078:
1075:
1072:
1067:
1063:
1059:
1056:
1052:
1045:
1042:
1035:
1031:
1027:
1023:
1019:
1016:
1010:
1007:
1005:
1003:
1000:
997:
994:
991:
988:
985:
982:
979:
976:
973:
972:
967:
964:
961:
957:
950:
947:
940:
936:
932:
929:
926:
920:
917:
915:
913:
910:
907:
904:
901:
898:
895:
894:
871:
868:
865:
856:is 243 years (
849:{\textstyle T}
845:
833:
830:
817:
814:
811:
808:
805:
802:
799:
796:
793:
790:
787:
767:
764:
761:
741:
730:
729:
716:
712:
708:
705:
701:
697:
694:
691:
686:
683:
680:
676:
672:
669:
666:
663:
660:
657:
654:
651:
648:
645:
642:
639:
636:
633:
630:
627:
624:
621:
618:
615:
612:
609:
586:
575:
574:
561:
557:
553:
550:
546:
542:
537:
534:
531:
527:
523:
520:
517:
514:
511:
508:
505:
502:
499:
476:
473:
470:
447:
443:
439:
436:
433:
413:
393:
373:
362:
361:
348:
344:
340:
337:
333:
326:
323:
316:
312:
308:
304:
300:
297:
291:
286:
283:
280:
276:
269:
266:
259:
255:
251:
248:
245:
239:
236:
233:
230:
227:
224:
221:
198:
195:
178:
175:
140:
137:
129:
128:
122:
102:
98:
95:
92:
86:
74:
71:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3539:
3528:
3525:
3523:
3520:
3518:
3515:
3513:
3510:
3509:
3507:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3467:
3464:
3462:
3459:
3458:
3455:
3449:
3446:
3444:
3443:Surface water
3441:
3439:
3438:Sacred waters
3436:
3434:
3431:
3429:
3426:
3424:
3423:Riparian zone
3421:
3419:
3416:
3414:
3411:
3409:
3408:Body of water
3406:
3404:
3401:
3399:
3396:
3395:
3393:
3389:
3383:
3380:
3378:
3375:
3373:
3370:
3368:
3365:
3363:
3360:
3358:
3357:Riverboarding
3355:
3353:
3352:River surfing
3350:
3348:
3345:
3343:
3340:
3338:
3335:
3334:
3332:
3328:
3322:
3319:
3317:
3314:
3312:
3309:
3307:
3304:
3302:
3299:
3297:
3294:
3292:
3289:
3287:
3284:
3282:
3279:
3277:
3274:
3272:
3269:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3232:
3229:
3227:
3224:
3222:
3219:
3218:
3216:
3214:
3210:
3204:
3201:
3199:
3196:
3194:
3191:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3169:
3166:
3164:
3161:
3159:
3156:
3154:
3151:
3149:
3146:
3144:
3141:
3139:
3136:
3134:
3131:
3129:
3126:
3124:
3121:
3119:
3116:
3114:
3111:
3109:
3106:
3104:
3101:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3080:
3078:
3076:and modelling
3072:
3066:
3063:
3061:
3058:
3056:
3053:
3052:
3050:
3048:
3044:
3038:
3037:Return period
3035:
3033:
3030:
3028:
3025:
3023:
3020:
3018:
3015:
3013:
3010:
3008:
3005:
3003:
3000:
2998:
2997:Flood control
2995:
2993:
2992:Flood barrier
2990:
2986:
2983:
2981:
2978:
2977:
2976:
2973:
2971:
2968:
2966:
2963:
2961:
2958:
2957:
2955:
2953:
2949:
2945:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2921:
2917:
2911:
2908:
2906:
2903:
2901:
2898:
2896:
2893:
2891:
2888:
2886:
2883:
2881:
2878:
2876:
2873:
2871:
2868:
2866:
2863:
2861:
2858:
2857:
2855:
2853:
2849:
2843:
2840:
2838:
2835:
2833:
2830:
2828:
2825:
2823:
2820:
2818:
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2793:
2790:
2788:
2785:
2783:
2780:
2778:
2775:
2773:
2770:
2768:
2765:
2763:
2760:
2758:
2755:
2753:
2750:
2748:
2745:
2743:
2740:
2738:
2735:
2733:
2730:
2728:
2725:
2723:
2720:
2718:
2715:
2713:
2710:
2708:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2688:
2685:
2683:
2680:
2679:
2677:
2675:
2671:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2640:
2637:
2635:
2632:
2630:
2627:
2625:
2624:Palaeochannel
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2595:
2592:
2590:
2587:
2585:
2584:Granular flow
2582:
2580:
2577:
2575:
2572:
2570:
2567:
2565:
2562:
2560:
2557:
2555:
2552:
2551:
2549:
2547:
2542:
2538:
2532:
2529:
2527:
2524:
2522:
2519:
2517:
2514:
2510:
2507:
2506:
2505:
2502:
2498:
2495:
2493:
2490:
2489:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2469:
2467:
2464:
2459:
2455:
2449:
2446:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2419:
2416:
2414:
2411:
2409:
2406:
2404:
2401:
2399:
2396:
2394:
2391:
2389:
2386:
2385:
2383:
2381:
2377:
2371:
2368:
2366:
2363:
2361:
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2333:
2331:
2330:Channel types
2328:
2326:
2323:
2321:
2318:
2316:
2313:
2311:
2310:Braided river
2308:
2306:
2303:
2302:
2300:
2297:
2292:
2288:
2284:
2280:
2276:
2269:
2264:
2262:
2257:
2255:
2250:
2249:
2246:
2234:
2231:
2220:
2216:
2209:
2206:
2193:
2189:
2182:
2179:
2174:
2170:
2166:
2162:
2158:
2154:
2150:
2143:
2140:
2135:
2131:
2127:
2123:
2119:
2115:
2108:
2105:
2100:
2094:
2090:
2086:
2082:
2075:
2072:
2065:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2042:
2038:
2033:
2030:
2010:
2006:
2002:
1999:
1993:
1990:
1985:
1982:
1973:
1972:
1971:
1952:
1939:
1935:
1931:
1928:
1922:
1919:
1916:
1910:
1907:
1904:
1899:
1894:
1888:
1885:
1880:
1877:
1873:
1868:
1865:
1862:
1854:
1845:
1844:
1843:
1840:
1838:
1834:
1829:
1823:Risk analysis
1822:
1802:
1799:
1797:
1789:
1786:
1783:
1780:
1777:
1774:
1772:
1762:
1758:
1754:
1749:
1745:
1741:
1730:
1727:
1716:
1714:
1706:
1703:
1700:
1694:
1683:
1682:
1681:
1679:
1660:
1657:
1652:
1649:
1644:
1641:
1634:
1633:
1632:
1626:
1621:
1618:
1615:
1612:
1609:
1606:
1605:
1604:
1584:
1581:
1578:
1574:
1569:
1564:
1561:
1556:
1553:
1546:
1545:
1544:
1527:
1521:
1518:
1512:
1508:
1500:
1497:
1493:
1484:
1481:
1478:
1470:
1467:
1464:
1456:
1452:
1445:
1442:
1439:
1433:
1430:
1427:
1419:
1416:
1406:
1405:
1404:
1390:
1384:
1381:
1361:
1355:
1352:
1343:
1334:
1320:
1297:
1292:
1289:
1286:
1278:
1275:
1272:
1264:
1260:
1248:
1245:
1234:
1228:
1225:
1222:
1216:
1209:
1208:
1207:
1205:
1189:
1181:
1160:
1157:
1154:
1134:
1114:
1111:
1108:
1096:
1073:
1070:
1065:
1061:
1057:
1054:
1050:
1043:
1040:
1033:
1025:
1021:
1017:
1008:
1006:
998:
995:
992:
989:
986:
983:
980:
974:
965:
962:
959:
955:
948:
945:
938:
930:
927:
918:
916:
908:
905:
902:
896:
885:
884:
883:
869:
866:
863:
843:
831:
829:
812:
809:
803:
800:
794:
791:
788:
785:
765:
762:
759:
739:
714:
710:
706:
703:
699:
695:
692:
689:
684:
681:
678:
674:
670:
667:
664:
658:
655:
652:
649:
646:
640:
637:
634:
631:
625:
622:
619:
616:
613:
607:
600:
599:
598:
584:
559:
555:
551:
548:
544:
540:
535:
532:
529:
525:
521:
515:
512:
509:
506:
503:
497:
490:
489:
488:
474:
471:
468:
459:
445:
441:
437:
434:
431:
411:
391:
371:
346:
342:
338:
335:
331:
324:
321:
314:
306:
302:
298:
289:
284:
281:
278:
274:
267:
264:
257:
249:
246:
237:
231:
228:
225:
219:
212:
211:
210:
208:
204:
196:
194:
192:
188:
184:
176:
174:
171:
166:
162:
160:
155:
153:
148:
146:
138:
136:
134:
126:
123:
120:
117:
116:
115:
100:
96:
93:
90:
84:
72:
70:
66:
64:
60:
56:
52:
48:
44:
40:
39:return period
33:
19:
3481:Flash floods
3433:River cruise
3330:River sports
3183:Stream gauge
3168:Rouse number
3158:Relief ratio
3036:
3007:Flood-meadow
2938:Urban runoff
2852:Fluvial flow
2837:River valley
2807:River island
2772:Meander scar
2687:Alluvial fan
2629:Progradation
2504:Karst spring
2448:Winterbourne
2403:Chalk stream
2365:River source
2340:Distributary
2233:
2222:. Retrieved
2218:
2208:
2196:. Retrieved
2191:
2181:
2156:
2152:
2142:
2117:
2113:
2107:
2080:
2074:
2031:
1969:
1841:
1836:
1833:at least one
1832:
1830:
1826:
1678:exactly once
1677:
1675:
1630:
1619:
1613:
1607:
1602:
1542:
1335:
1312:
1206:as follows.
1179:
1100:
835:
731:
576:
460:
363:
200:
180:
167:
163:
156:
151:
149:
142:
133:storm surges
130:
124:
118:
76:
67:
46:
42:
38:
36:
3342:Fly fishing
3266:Fish ladder
3251:Daylighting
2970:Flash flood
2933:First flush
2880:Plunge pool
2604:Downcutting
2589:Debris flow
2564:Aggradation
2438:Stream pool
2120:: 256–271.
51:earthquakes
3517:Seismology
3506:Categories
3448:Wild river
3128:Hydrograph
3118:Hack's law
3083:Baer's law
3027:Inundation
3012:Floodplain
2952:stormwater
2910:Whitewater
2782:Oxbow lake
2619:Knickpoint
2594:Deposition
2487:Hot spring
2428:Streamflow
2418:Stream bed
2335:Confluence
2224:2019-12-21
2198:7 February
2159:(2): 160.
2066:References
173:interval.
65:to occur.
59:landslides
3527:Durations
3512:Hydrology
3418:Limnology
3367:Triathlon
3337:Canyoning
3306:Revetment
3236:Check dam
3148:Main stem
2905:Waterfall
2792:Point bar
2777:Mouth bar
2717:Billabong
2664:Water gap
2659:Wash load
2639:Saltation
2559:Anabranch
2482:Holy well
2370:Tributary
2173:0367-8245
2003:≥
1932:≥
1920:−
1911:−
1881:−
1869:−
1858:¯
1800:≈
1787:×
1781:×
1775:≈
1755:×
1742:×
1554:μ
1509:λ
1501:λ
1498:−
1490:→
1482:−
1471:μ
1468:−
1453:μ
1431:−
1391:λ
1388:→
1385:μ
1359:→
1356:μ
1350:∞
1347:→
1321:τ
1290:−
1279:μ
1276:−
1261:μ
1190:μ
1155:τ
1135:τ
1115:τ
1112:×
1077:%
1071:≈
1055:−
963:μ
960:−
928:μ
864:μ
816:%
810:≈
801:−
795:
789:−
704:−
696:−
682:μ
679:−
671:−
638:−
549:−
533:μ
530:−
432:μ
336:−
282:μ
279:−
247:μ
159:statistic
3221:Aqueduct
3088:Baseflow
3055:Effluent
2732:Cut bank
2697:Avulsion
2574:Bed load
2554:Abrasion
2039:See also
1097:Binomial
145:exceeded
3398:Aquifer
3391:Related
3347:Rafting
2875:Meander
2870:Log jam
2832:Thalweg
2737:Estuary
2609:Erosion
2546:erosion
2458:Springs
2413:Current
2380:Streams
2320:Channel
2283:springs
2279:streams
2122:Bibcode
1627:Example
832:Example
205:of the
197:Poisson
189:in the
3193:WAFLEX
3065:Sewage
2948:Floods
2890:Riffle
2885:Rapids
2827:Strath
2797:Ravine
2722:Canyon
2477:Geyser
2408:Coulee
2393:Bourne
2388:Arroyo
2291:Rivers
2275:Rivers
2171:
2095:
1970:where
1803:0.0914
1603:where
1147:(e.g.
870:0.0041
364:where
55:floods
3291:Levee
3276:Flume
3231:Canal
2975:Flood
2895:Shoal
2762:Gully
2757:Gulch
2727:Chine
2712:Bayou
2569:Armor
2521:Ponor
2296:lists
1790:0.914
1661:0.01.
1543:Take
1403:then
152:given
61:, or
3321:Weir
3286:Leat
2950:and
2842:Wadi
2802:Rill
2767:Glen
2752:Gill
2702:Bank
2544:and
2509:list
2492:list
2463:list
2398:Burn
2281:and
2200:2023
2169:ISSN
2093:ISBN
1784:0.01
1759:0.99
1746:0.01
1165:year
1074:3.95
813:63.2
617:>
201:The
3241:Dam
2707:Bar
2682:Ait
2161:doi
2130:doi
2118:541
2085:doi
1653:100
1336:If
1066:243
1026:243
792:exp
209:is
45:or
3508::
2277:,
2217:.
2190:.
2167:.
2157:49
2155:.
2151:.
2128:.
2091:.
2083:.
1837:no
1778:10
1728:10
1058:10
1018:10
999:10
57:,
53:,
37:A
2465:)
2461:(
2298:)
2294:(
2267:e
2260:t
2253:v
2227:.
2202:.
2175:.
2163::
2136:.
2132::
2124::
2101:.
2087::
2032:n
2016:)
2011:T
2007:x
2000:X
1997:(
1994:P
1991:=
1986:T
1983:1
1953:n
1949:)
1945:)
1940:T
1936:x
1929:X
1926:(
1923:P
1917:1
1914:(
1908:1
1905:=
1900:n
1895:)
1889:T
1886:1
1878:1
1874:(
1866:1
1863:=
1855:R
1763:9
1750:1
1736:)
1731:1
1723:(
1717:=
1710:)
1707:1
1704:=
1701:X
1698:(
1695:P
1658:=
1650:1
1645:=
1642:p
1620:m
1614:n
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1585:1
1582:+
1579:n
1575:m
1570:=
1565:T
1562:1
1557:=
1528:.
1522:!
1519:r
1513:r
1494:e
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1465:1
1462:(
1457:r
1446:!
1443:r
1440:!
1437:)
1434:r
1428:n
1425:(
1420:!
1417:n
1382:n
1362:0
1353:,
1344:n
1298:.
1293:r
1287:n
1283:)
1273:1
1270:(
1265:r
1254:)
1249:r
1246:n
1241:(
1235:=
1232:)
1229:r
1226:=
1223:X
1220:(
1217:P
1180:r
1161:1
1158:=
1109:n
1062:/
1051:e
1044:!
1041:1
1034:1
1030:)
1022:/
1015:(
1009:=
1002:)
996:=
993:t
990:;
987:1
984:=
981:r
978:(
975:P
966:t
956:e
949:!
946:r
939:r
935:)
931:t
925:(
919:=
912:)
909:t
906:;
903:r
900:(
897:P
867:=
844:T
807:)
804:1
798:(
786:1
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763:=
760:t
740:T
715:T
711:/
707:t
700:e
693:1
690:=
685:t
675:e
668:1
665:=
662:)
659:t
656:;
653:0
650:=
647:t
644:(
641:P
635:1
632:=
629:)
626:t
623:;
620:0
614:t
611:(
608:P
585:T
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556:/
552:t
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516:t
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510:0
507:=
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501:(
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438:1
435:=
412:T
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307:T
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299:t
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265:r
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250:t
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238:=
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232:t
229:;
226:r
223:(
220:P
125:m
119:n
101:m
97:1
94:+
91:n
85:=
34:.
20:)
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