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e ~ , .. e .. '. e (1) The reach is treated as a whole; subreach length equals reach length. Equal weight is given 10 the inflowing hydrograph values in determining their average. The time period over which averaging occurs is centered on the inflow value being routed; i.e., the one at a lag-time duration earlier than the time pertinent 10 the outflow hydrograph value. The constant time interval used to define the inflow hydrograph, the number of points used for averaging, and the lag time (outflow value time minus routed inflow value time, expressed as an integer number of time intervals) are chosen by trial and error for a best fit with observations. (2) The hope in using this method is that the storagelhydrograph relation that exists for the reach in the calibration event is reflected in the arithmetic param- eters determined, and that these will continue 10 be valid. for the subject event. The lack of any theoretical basis for this hope makes the method unreasonable rather than approximate. The term approximate suggests that there is some control over the amount of error. But, in princi- ple, the error in the computed subsidence for the subject event could be zero, plus or minus a hundred percent or more. Only if a series of calibration events lead to about the same parameter values in each case could one reason- ably suppose that a subject event in the same reach with about the same inflow hydrograph as the calibration events, calculated with those values of parameters, would yield an outflow hydrograph of about the same accuracy as the calibration events. In general, the method is not recommended. c. Successive average-lag method. In this technique (EM 1110-2-1408 19(0), also known as the Tatum Method, each ordinate of the outflow hydrograph for a subreach is the numerical average of the routed inflow value and the preceding ordinate in the hydrograph. The ordinates of the inflow hydrograph are separated by constant time intervals, Ll.t, a parameter of the method. Subreach length is defined as the distance traveled by the flood wave in a time interval Ll.l/2, taken as the lag time. The outflow hydrograph for a subreach constitutes the inflow hydrograph for the next subreach, for which the procedure is repeated. (I) Additional subreaches are introduced until the outflow for the subject reach bas been determined. The number of subreaches constitutes another parameter of the method. The parameter values are chosen for a best fit with calibration hydrographs. EM 1110-2.1416 15 Oct 93 (2) A physical interpretation of the Tatum Method exists; it corresponds to a linear Modified Puis technique in which subreach storage is directly proportional to subreach outflow with the constant of proportionality K = Ll.l!2. Nonetheless, the method, like Progressive Average- Lag, must be considered empirical, and is not generally recommended. d. Modified Puis. This approach is more rational than the average-lag methods, because it strives 10 solve the mass-conservation relationship (equation 5-2) by providing a second, storage versus flow, relation neces- sary 10 close the system. (I) The method is characterized by a far-reaching physical assumption which, unfortunately, is often not warranted in rivers. The required slorage versus flow relation stems from the assumption that there exists a unique relatinnship between storage in the reach and outflow from the reach. It is further assumed that this relationship can be found for the reach, either theoreti- cally or empirically from past events; and that, once determined, applies to the study event. The mathematical form of the relationship is not important, a graph or table of numbers will suffice. (2) An empirical relation can be found by measuring discharges as they vary with time during a calibration flood event at the inlet and outlet of the reach and apply- ing the volume-conservation principle, (Equation 5-2). To the extent that tributary flow is accounted for, the relationship is valid for the event for which the informa- tion was recorded. To the extent that the relationship will continue to be valid for another event, or a different inflow hydrograph, it can be successfully used 10 predict outflow hydrographs for that event (3) A storage-outflow relation can be easily devised for a channel which is so large that the water surface remains level during the event 10 be simulated (a reser- voir or "level pool") and if a discharge coefficient, the0- retical or empirical, is available for the outlet. This is the physical circumstance for which the basic assumption of the Modified Puis method is valid. (4) Hypothetical relationships between storage and outflow are sometimes derived for rivers from steady flow computations. Steady water surface profiles and, hence, water volumes, are computed in the reach for a sequence of discharges (outflows). The resulting table of 5-31