ASCE 50-08/51-08

Abstract

This standard guideline outlines a procedure to optimize the fitting and goodness-of-fit testing of a probability density function (pdf) to a sample of saturated hydraulic conductivity (<em>K</em>) measurements. The procedure assumes a uniform scale of observation (similar measuring device) and statistically homogeneous and independent hydraulic conductivity measurements. Two pdfs are recommended for fitting purposes when such a sample of saturated hydraulic conductivity measurements is available. The first is the lognormal pdf, recommended when logarithmically transformed <em>K</em> data have coefficient of skew (<em>C_sY</em>) in the range -0.05 less than or&#160;equal to &#160;<em>C_sY&#160;</em>&#160;less than or equal to 0.05. The second is the (threeparameter) log-gamma pdf, recommended when logarithmically transformed <em>K</em> data have coefficient of skew <em>C</em>_<em>sY</em> greater than 0.05. Testing the goodness-of-fit to <em>K</em> data achieved by the lognormal or the log-gamma pdfs is performed with the chi-squared method. <br><strong>PURPOSE</strong> <br>Saturated hydraulic conductivity measurements made at different locations in an aquifer exhibit substantial variability. Those measurements can be treated using the laws of probability to obtain a proper description of the characteristics of saturated hydraulic conductivity that goes beyond the calculation of its average, standard deviation, or other indicators of central tendency and asymmetry. The fitting of saturated hydraulic conductivity with a proper pdf is a necessary step&#8212;after its measurement in the field or in the laboratory&#8212;to arrive at a complete description of its probabilistic characteristics. Analysts can then use the fitted pdf in a variety of analyses and design modes that provide a wider range of options than those available when saturated hydraulic conductivity is treated deterministically, i.e., as a nonrandom entity.