Laserfiche WebLink
<br />2-03 <br /> <br />2-03. <br /> <br />PROBABILITI INPERERCE <br /> <br />a. ICnowledge that a certain set of conditions can result <br />in various sets of data because of r&Jldom Vli.riations is used to <br />infer that lllIY particular set of data could have resulted from <br />various sets of hydrologic ccnditions. . 'l'heproblem in making <br />probability estimates is essentially to determine the set of <br />conditions that most likely generated the semple of data that <br />has been recorded. This set of conditions is represented by <br />a "parent population" which consists of all of the hydrologic <br />events that would be generated if the record continues indefi- <br />nitely III1d controlling conditions do not change. <br /> <br />E.. In probability analysis, there are two basicapp:i-oaches <br />to estimating or inferring the parent population from sample data. <br />First, data can be arranged in the order of magnitude to form a <br />frequency arrq, illustrated on exhibit 1, and a graph of. magni- <br />tude versus observed frequency plotted, as shown onexbibit 2. <br />A smooth curve drawn through the plotted data would represent an <br />estimate of the parent population frCllll which the proba,bilities <br />of future events can be determined.. 'l'he second basic approach is <br />to derive from the data general statistics representing the <br />average magnitude of floods, the variability from that averllile, <br />and any other pertinent statistics relating frequency to magnituie <br />as indicated by the data. . <br /> <br />2-04. <br /> <br />CUMULATIVE FRE~Y CURV!S <br /> <br />A cumulative frequency curve, or siDiply frequency curve, <br />suc a us ra e on ,re es the magnitude of <br />an event to the frequency with which that magnitude is exceeded <br />as events occur at rlll1dom. For example, if 25 floods at a loca- <br />tion exceed 10,000 c.f.s. in 100 years, on the average, then the <br />value of 10,000 c.f .s. on the cumulative frequency curve will <br />corres:pond to an exceedence probability of 0.25 in lllIY 1 ;rear <br />or an exceedence frequency of 25 times per 100 years, 250 times <br />per thousand years, etc., or simply 25 percent. While a single <br />frequency curve can represent the frequency of peak discharges <br />at a given location, the frequency of flood volumes would be repre- <br />sented by an entirely different curve, or by more then one curve <br />U vo11lllles for various durations are concerned.. Frequency curves <br />can also be used to represent the frequency of reservoir stages, <br />river stages, precipitation, III1d many oiher phenomena. <br /> <br /> <br />E.. Frequency curves are most cOlmlOnly used in flood control <br />benefits studies for the purpose of evaluating the economic effect <br /> <br />- 5 - <br />