Approaches to estimate uncertainty in longitudinal channel water balances

The effects of uncertainty in field measurements on estimated longitudinal channel water balances are a poorly understood aspect of hydrology. A mountain stream study reach in northern Utah with spatially variable groundwater exchange was used to explore a detailed uncertainty analysis approach to estimate the error in water balances. Net changes in stream flow were first estimated for both a 515 m and a 560 m reach using two discharge measurement methods: (1) rating curves and (2) dilution gauging with instantaneous tracer experiments. Errors in estimates were quantified using 95% joint confidence regions for rating curves and a first-order error analysis for dilution gauging. With the mean errors in rating curve predictions and dilution gauging estimated to be ±8.2% and ±8.4%, respectively, neither method was found to definitively detect net changes in stream flow at this scale. Using dilution gauging, net channel water balances were then estimated for a collection of 56–229 m sub-reaches within the two original study reaches. When considering the ±8.1% error (defined as 95% prediction intervals) in these estimates at this scale, significant net changes were observed in only half of the sub-reaches. Gross gains and losses that contribute to these net changes were estimated and a first-order error analysis was additionally performed. Half of the sub-reaches had significant gross gains and losses concurrently occurring that did not have significant net changes. The uncertainty analyses proved imperative to appropriately interpret results.