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A Solution to Small Sample Bias in Flood EstimationMetler, William 06 May 1972 (has links)
From the Proceedings of the 1972 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - May 5-6, 1972, Prescott, Arizona / In order to design culverts and bridges, it is necessary to compute an estimate of the design flood. Regionalization of flows by regression analysis is currently the method advocated by the U.S. Geological Survey to provide an estimate of the culvert and bridge design floods. In the regression analysis a set of simultaneous equations is solved for the regression coefficients which will be used to compute a design flood prediction for a construction site. The dependent variables in the set of simultaneous equations are the historical estimates of the design flood computed from the historical records of gaged sites in a region. If a log normal distribution of the annual peak flows is assumed, then the historical estimate of the design flood for site i may be computed by the normal as log Q(d,i) = x(i) + k(d)s(i). However because of the relatively small samples of peak flows commonly used in this problem, this paper shows that the historical estimate should be computed by to log Q(d,i) = X(i) + t(d,n-1) √((n+1)/n) s(i) where t(d,n-1) is obtained from tables of the Student's t. This t-estimate when used as input to the regression analysis provides a more realistic prediction in light of the small sample size, than the estimate yielded by the normal.
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Role of Modern Methods of Data Analysis for Interpretation of Hydrologic Data in ArizonaKisiel, Chester C., Duckstein, Lucien, Fogel, Martin M. 06 May 1972 (has links)
From the Proceedings of the 1972 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - May 5-6, 1972, Prescott, Arizona / Mathematical models, requiring substantial data, of hydrologic and water resources systems are under intensive investigation. The processes of data analysis and model building are interrelated so that models may be used to forecast for scientific reasons or decision making. Examples are drawn from research on modeling aquifers, watersheds, streamflow and precipitation in Arizona. Classes of problems include model choice, parameter estimates, initial condition, input identification, forecasting, valuation, control, presence of multiple objectives, and uncertainty. Classes of data analysis include correlation methods, system identification, stationarity, independence or randomness, seasonality, event based approach, fitting of probability distributions, and analysis for runs, range and crossing levels. Time series, event based and regression methods are reviewed. The issues discussed are applied to tree-ring analyses, streamflow gaging stations, and digital modeling of small watersheds and the Tucson aquifers.
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Geomorphic Features Affecting Transmission Loss PotentialWallace, D. E., Lane, L. J. 15 April 1978 (has links)
From the Proceedings of the 1978 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 14-15, 1978, Flagstaff, Arizona / Water yield studies and flood control surveys often necessitate estimating transmission losses from ungaged watersheds. There is an immediate need for an economical method that provides the required accuracy. Analysis of relations between stream order, drainage area, and volume of channel alluvium existing in the various orders is one means of estimating loss potential. Data needed for the stream order survey are taken from aerial photos. Stream order is analyzed using stereophoto maps. Stream lengths taken from the maps are combined with average channel width and depth data (determined by prior surveys) to estimate volumes of alluvium involved. The volume of channel alluvium in a drainage network is directly related to the stream order number of its channels. Thus, a volume of alluvium within a drainage network (with a known transmission loss potential) may be estimated by knowing the order of each length of channel and the drainage areas involved. In analyzing drainage areas of 56-mi² or less, 70 to 75 percent of the total drainage network length is contained within first and second order channels; yet, these constitute less than 10 percent of the total transmission loss potential of the areas. Analysis of stream order and drainage area versus volume of alluvium relations allows preliminary estimates of transmission loss potential to be made for ungaged areas.
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