• A Solution to Small Sample Bias in Flood Estimation

      Metler, William; Systems & Industrial Engineering, University of Arizona, Tucson, Arizona 85721 (Arizona-Nevada Academy of Science, 1972-05-06)
      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.
    • Water Disposition in Ephemeral Stream Channels

      Sammis, T. W.; Hydrology and Water Resources, University of Arizona (Arizona-Nevada Academy of Science, 1972-05-06)
      The contribution of flows from small watersheds to groundwater recharge is of interest. Water disposition depends on infiltration and evaporation characteristics. This study had the objective of developing an infiltration equation for estimating transmission losses during a flow event in an ephemeral stream near Tucson, Arizona, in the rocky mountain forest and range experiment station. Palo Verde, desert hackberry, cholla, marmontea and mesquite are the major bank species of the sandy channels. A climatic section consisting of a hydrothermograph recording rain gage and class a evaporation pan was installed. A water balance method was used to estimate evapotranspiration. A specially designed infiltrometer was used to simulate flow events. The data allowed the following conclusions: Philip's infiltration equation is an excellent mathematical model, initial moisture affects initial infiltration rate, the Philip coefficients are determinable by the infiltrometer constructed, soil moisture affects infiltration rates, and transpiration rates diminish linearly proportional to the ratio of available water to field capacity.