Generalized additive model estimation of no-flow fractions and L-moments to support flow-duration curve quantile estimation using selected probability distributions for bay and estuary restoration in the Gulf States

Censored and uncensored generalized additive models (GAMs) were developed using streamflow data from 941 U.S. Geological Survey streamflow-gaging stations (streamgages) to predict decadal statistics of daily streamflow for streams draining to the Gulf of Mexico. The modeled decadal statistics comprise no-flow fractions and L-moments of logarithms of nonzero streamflow for six decades (1950–2009). These statistics represent metrics of decadal flow-duration curves (dFDCs) derived from about 10 million daily mean streamflows. The L-moments comprise the mean, coefficient of L-variation, and the third through fifth L-moment ratios. The GAMs were fit to the statistics from 941 streamgages and 2,750 streamgage-decades by using watershed properties such as basin area and slope, decadal precipitation and temperature, and decadal values of flood storage and urban development percentages. The GAMs then estimated decadal statistics for 9,220 prediction locations (stream reaches) coincident with outlets of level-12 hydrologic unit codes. Both entire dataset (whole model) and leave-one-watershed-out model results are reported. No-flow fractions are censored data, and Tobit extensions to GAMs were used to model ephemeral streamflow conditions. Conversely, uncensored GAMs were used for estimation of the L-moments. The GAMs are shown, by coverage probabilities, to construct reliable 95-percent prediction limits. An example shows how no-flow fractions and L-moments may be used to approximate dFDCs by using selected probability distributions (mathematical formulas) including the asymmetric exponential power, generalized normal, and kappa distributions.