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12 TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS Complex discharge ratings If variable backwater or highly unsteady flow exists at a gaging station, the discharge rating cannot be described by stage alone. Variable backwater may be caused by a tribu- tary stream that enters the control reach down- stream from the gage, by manipulation of gates at a dam, or by flow of water into and from overbank storage created by natural constric- tions in the stream channel. The discharge un- der these conditions is a function of both stage and the slope of the energy gradient, which is approximated by the slope of the water sur- face between two stage gages. Stage-faIl-dis- charge ratings are usually determined empir, ically from observations of (1) discharge, (2) stage at the base gage, and (3) the fall of the water surface between the base gage and an auxiliary stage gage downstream. The general procedures used in developing these ratings are described in book 3, chapter A9, of this series, by Carter and Davidian:' If the flow is very unsteady, as in a tidal reach, the acceleration head governs the energy slope. Under this condition unsteady-flow equa- tions must be used to describe the variation of discharge with time. This method is described by Davidian.' .\ special type of unsteady flow is ,treated nuder the headiul! "lTniformly pro~ressive flow" in Cartel' and Davidian.' For such flow the stag-e and rate of change of stage obsen'ed at a single gage al'e used to establish the e:!is- "harge rating. (omputation and Preparation of Discharge Records _\ ('ont inuous record of flow at a gaging sta' tion is "omputed from records of stage and the e:!i,.:harl-'" mting for t.he station. The type of stage rl'core:!er used at the station determines whether the computations are done manually or r. ("nrh'r, It. W.. lllld Da\idilln. Jlll"ob. Dlflchargc rntlngs at ~agill~ :-:tatlou,,: u.~. Gt'ol. :-:Ur\"C;\' Tf'chnlqlU'S Watl'r- Hl'SlIlll'('l'l'< 11\\'.. hHnk ::, chnp. .\!., unllub. dllta. ., Da\'leUall, .Jllcob. CllmlHttatiOJl of discharge in tidal rl'lll'IIt',,: l"$. G('()], Surv!:')' 1'p("hniques \Vllter-Rf'llOUrCl:'S In\".. ullpub.llata. by an electronic computer. In either system the en~ineer must study the data and prepare what is termed a station analysisbefore computllJtions a re performed. I Station analysis A station analysis, which documents the re- sult of the study of the data, is prepared for e.a"h station at the end of each water year. The study inc1ue:!es the foIlowin~items: 1. A review of field surveys of gage datum and a determination of the datum corrections if , any, to be applied to gage readings taken during the year. 2. c\ review of discharge-measurement notes. :t An analysis of the discharge rating and the determination of the rating (or shifts) ap- plicable during each period of the year. 4. The preparation of tables which express the e:!ischarge rating. Manual computations If stage is recorded at the station on a strip- chart recorder, all computations are performed manually in the following order: 1. Determination and application of gage- height and time correetions to the gage- height chart. 2. Computation of the mean gage height for each day, or for shotter periods if the range in discharge during the day is large. Sub- division is necessary because of curvature in the discharge rating. 3. Computation of discharge for each period from mean values of stage and the dis- charge rating, including any shift correc- tions. 4. Computation of peak values of gage height ane:! discharge. ;), Listing of the values of mean daily gage heights and e:!ischarge and momentary peaks. H. Computation of mean flow for each month ane:! the year in cubic feet, pel' secone:! ane:! in inches. 7. RedE'\Y llnd t'ompal'ison of the record of dis- charge with that of nearby streams.