Bootstrapping techniques employing random subsampling were used with the AFINCH (Analysis of Flows In Networks of CHannels) model to gain insights into the effects of variation in streamflow-gaging-network size and composition on the accuracy and precision of streamflow estimates at ungaged locations in the 0405 (Southeast Lake Michigan) hydrologic subregion. AFINCH uses stepwise-regression techniques to estimate monthly water yields from catchments based on geospatial-climate and land-cover data in combination with available streamflow and water-use data. Calculations are performed on a hydrologic-subregion scale for each catchment and stream reach contained in a National Hydrography Dataset Plus (NHDPlus) subregion. Water yields from contributing catchments are multiplied by catchment areas and resulting flow values are accumulated to compute streamflows in stream reaches which are referred to as flow lines. AFINCH imposes constraints on water yields to ensure that observed streamflows are conserved at gaged locations.  

Data from the 0405 hydrologic subregion (referred to as Southeast Lake Michigan) were used for the analyses. Daily streamflow data were measured in the subregion for 1 or more years at a total of 75 streamflow-gaging stations during the analysis period which spanned water years 1971–2003. The number of streamflow gages in operation each year during the analysis period ranged from 42 to 56 and averaged 47. Six sets (one set for each censoring level), each composed of 30 random subsets of the 75 streamflow gages, were created by censoring (removing) approximately 10, 20, 30, 40, 50, and 75 percent of the streamflow gages (the actual percentage of operating streamflow gages censored for each set varied from year to year, and within the year from subset to subset, but averaged approximately the indicated percentages).

Streamflow estimates for six flow lines each were aggregated by censoring level, and results were analyzed to assess (a) how the size and composition of the streamflow-gaging network affected the average apparent errors and variability of the estimated flows and (b) whether results for certain months were more variable than for others. The six flow lines were categorized into one of three types depending upon their network topology and position relative to operating streamflow-gaging stations.    

Statistical analysis of the model results indicates that (1) less precise (that is, more variable) estimates resulted from smaller streamflow-gaging networks as compared to larger streamflow-gaging networks, (2) precision of AFINCH flow estimates at an ungaged flow line is improved by operation of one or more streamflow gages upstream and (or) downstream in the enclosing basin, (3) no consistent seasonal trend in estimate variability was evident, and (4) flow lines from ungaged basins appeared to exhibit the smallest absolute apparent percent errors (APEs) and smallest changes in average APE as a function of increasing censoring level. The counterintuitive results described in item (4) above likely reflect both the nature of the base-streamflow estimate from which the errors were computed and insensitivity in the average model-derived estimates to changes in the streamflow-gaging-network size and composition. Another analysis demonstrated that errors for flow lines in ungaged basins have the potential to be much larger than indicated by their APEs if measured relative to their true (but unknown) flows.    

 “Missing gage” analyses, based on examination of censoring subset results where the streamflow gage of interest was omitted from the calibration data set, were done to better understand the true error characteristics for ungaged flow lines as a function of network size. Results examined for 2 water years indicated that the probability of computing a monthly streamflow estimate within 10 percent of the true value with AFINCH decreased from greater than 0.9 at about a 10-percent network-censoring level to less than 0.6 as the censoring level approached 75 percent. In addition, estimates for typically dry months tended to be characterized by larger percent errors than typically wetter months.