Approaches to estimate uncertainty in longitudinal channel water balances Noah M. Schmadel ⇑ , Bethany T. Neilson, David K. Stevens Utah Water Research Laboratory, Civil and Environmental Engineering, Utah State University, 8200 Old Main Hill, Logan, UT 84322-8200, United States article info Article history: Received 3 February 2010 Received in revised form 21 August 2010 Accepted 17 September 2010 This manuscript was handled by Andras Bardossy, Editor-in-Chief, with the assistance of Vazken Andréassian, Associate Editor Keywords: Rating curve Dilution gauging Channel water balance First-order error analysis summary 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 instan- taneous 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 per- formed. 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. Ó 2010 Elsevier B.V. All rights reserved. 1. Introduction Groundwater exchange within stream networks is widely rec- ognized as affecting biogeochemical processes, aquatic ecology, and water quality in and near streams (Baxter et al., 2003; Bencala, 1983; Cey et al., 1998; Covino and McGlynn, 2007) because of its role in heat (Constantz, 1998) and solute transport (Harvey et al., 1996). Previous studies regarding stream water–groundwater interactions have used various methods to directly estimate groundwater exchange (Cey et al., 1998; Covino and McGlynn, 2007; Harvey et al., 2003) and have used model parameterization to indirectly estimate groundwater exchange while including other physical transport processes (e.g., hyporheic exchange) (Runkel, 1998; Wagner and Harvey, 1997). These interactions are often poorly understood because they are challenging to accurately pre- dict and measure (Winter et al., 1998). This is apparent due to com- plex surface–subsurface exchange flow paths and residence times (Harvey et al., 2003). These exchanges range from centimeters to hundreds of meters and minutes to years (Harvey et al., 1996), which makes locations, quantities, and distributions difficult to anticipate. Winter et al. (1998) describe stream water–groundwater in such systems as being a single continuously interconnected resource. Often, groundwater exchange (defined as stream gains and losses) within a study reach can be spatially variable and dynamic (Covino and McGlynn, 2007; Payn et al., 2009). Techniques typically used to estimate various scales of stream water–groundwater exchange include point stream gauging with velocity–area techniques (Rantz, 1982), rating curve predictions from stage data (Kennedy, 1983; Ruehl et al., 2006), stream tracer techniques (Harvey and Wagner, 2000; Payn et al., 2009; Ruehl et al., 2006), stream temperature surveys (Becker et al., 2004; Constantz, 1998; Constantz et al., 2002; Keery et al., 2007), hydro- metric measurements (Baxter et al., 2003; Cey et al., 1998; Covino and McGlynn, 2007; Landon et al., 2001), and isotopic tracers with hydrograph separation (Cey et al., 1998). The results of these types of studies support heat and solute transport modeling applications and can provide parameter estimates that more completely describe physical transport processes (e.g., transient storage) and information regarding flow path residence times (Bencala and Walters, 1983; Choi et al., 2000; Harvey et al., 2005; Harvey and Wagner, 2000). Direct measurement of groundwater exchanges commonly use rating curve estimates and tracer dilution gauging. Rating curves are based on correlations between discharge observations, fre- quently measured using the velocity–area method, and stage data. High-frequency time series of discharge estimates are then gener- ated from continuous stage data. Errors in rating curve predictions 0022-1694/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.jhydrol.2010.09.011 ⇑ Corresponding author. Tel.: +1 435 797 0748. E-mail address: n.schma@aggiemail.usu.edu (N.M. Schmadel). Journal of Hydrology 394 (2010) 357–369 Contents lists available at ScienceDirect Journal of Hydrology journal homepage: www.elsevier.com/locate/jhydrol