Effect of sampling density and design on estimation of streambed attributes

Underlying questions that are central to field studies of the groundwater–surface water interaction are the extent of error in means and spatial distributions of streambed attributes such as groundwater seepage rate or solute flux, and the relation of this error to the number and location of point measurements. To investigate these questions, spatially intensive point measurements of five streambed attributes were made in two 63-m long stream reaches in the North Carolina Coastal Plain: hydraulic conductivity (K), hydraulic head gradient between groundwater and stream water (J), nitrate concentration in streambed groundwater (C), and groundwater seepage (v=KJ) and nitrate flux (f=vC) through the streambed. In all, 10 datasets (2 reaches, 5 attributes), each with 54 closely-spaced point values, were created (540-point values in all). For each dataset, subsets of 8- to 40-point values were selected from the 54 available to evaluate the effects of sampling density (the number of point values per reach, or per m2 of streambed) and sampling design (the relative number of point values from the right side, left side, and center of the channel) on the mean and the spatial field of the streambed attribute. Specifically, we evaluated the following as a function of sampling density and sampling design: (1) the likelihood of error in the reach-average value of each streambed attribute, (2) the average magnitude of error and distribution of error in the reach-average value of each attribute, (3) the magnitude of error in the prediction of point values of each attribute, and (4) the geometry of interpolated surfaces of two attributes (K and f). In all cases, “error” in a value or interpolated surface based on a subset of points was taken as a deviation from the corresponding result based on the full dataset of 54 points. The probability (p) that error did not occur increased with sampling density for each sampling design and attribute in both reaches, though the effect of “diminishing returns” was evident for sampling densities greater than ∼24 points per reach (roughly 0.05–0.06 points per m2 of streambed). Relative to sampling density, sampling design had little effect on values of p. Average error in streambed attributes was generally small (⩽10%) and less than the 95% confidence limits about the reach-average values of the attributes. The ability to estimate unknown point values by interpolation among other point values was poor using both 12- and 36-point subsets,