Analyzing Hydraulic Conductivity Sampling Schemes in an Idealized Meandering Stream Model

Hydraulic conductivity (K) is an important parameter affecting the flow of water through sediments under streams, which can vary by orders of magnitude within a stream reach. Measuring heterogeneous K distributions in the field is limited by time and resources. This study investigates hypothetical sampling practices within a modeling framework on a highly idealized meandering stream. We generated three sets of 100 hydraulic conductivity grids containing two sands with connectivity values of 0.02, 0.08, and 0.32. We investigated systems with twice as much fast (K=0.1 cm/s) sand as slow sand (K=0.01 cm/s) and the reverse ratio on the same grids. The K values did not vary with depth. For these 600 cases, we calculated the homogenous K value, Keq, that would yield the same flux into the sediments as the corresponding heterogeneous grid. We then investigated sampling schemes with six weighted probability distributions derived from the homogenous case: uniform, flow-paths, velocity, in-stream, flux-in, and flux-out. For each grid, we selected locations from these distributions and compared the arithmetic, geometric, and harmonic means of these lists to the corresponding Keq using the root-mean-square deviation. We found that arithmetic averaging of samples outperformed geometric or harmonic means for all sampling schemes. Of the sampling schemes, flux-in (sampling inside the stream in an inward flux-weighted manner) yielded the least error and flux-out yielded the most error. All three sampling schemes outside of the stream yielded very similar results. Grids with lower connectivity values (fewer and larger clusters) showed the most sensitivity to the choice of sampling scheme, and thus improved the most with the flux-insampling. We also explored the relationship between the number of samples taken and the resulting error. Increasing the number of sampling points reduced error for the arithmetic mean with diminishing returns, but did not substantially reduce error associated with geometric and harmonic means.