## 1. Introduction

[2] The primary objective of the research described here is to use morphological parameters of step-pool sequences to model solute transport in stream segments for which tracer data are not available. We first review recent work on the formation and morphology of step-pool sequences, and then review modeling of solute transport processes, before describing the tracer and morphological data from several step-pool sequences in the Colorado Rocky Mountains, which we use to propose and test a morphologically based model of solute transport in step-pool streams.

[3] Step-pool systems have been widely studied during the past few years, resulting in a broad knowledge regarding mechanisms for sediment transport, energy dissipation, and geometrical patterns of self-organization. Such systems occur over a wide range of slopes above 0.02 m/m [*Chin*, 2003; *Wilcox and Wohl*, 2006; *Church and Zimmerman*, 2007], where other morphological configurations such as cascades can also be found [*Montgomery and Buffington*, 1997]. Step-pool sequences and cascades can be distinguished based on their hydraulic and bed-form characteristics, facilitating identification of each channel type from field observations. Moreover, these systems normally occur in the upper areas of a watershed and because of having high transport capacity, they play an important role moving sediments and nutrients downstream, as well as assimilating polluting solutes coming from point or nonpoint sources, such as those related to agricultural practices or waste water from mining [*Church and Zimmermann*, 2007; *Turowski et al*., 2009; *Chin*, 2002].

[4] Alluvial step-pool units consist of relatively immobile cobbles, boulders, or instream logs that span the channel width, forming a step followed by a scour pool containing finer sediment (Figure 1).

[5] The geometry of a step-pool unit is described via step length, *L _{s}*, and step height,

*H*, (Figure 1), which influence hydraulic flow regimes and sediment transport processes in step-pool sequences [

_{s}*Chin and Wohl*, 2005;

*Church and Zimmermann*, 2007;

*Comiti et al*., 2009].

*Abrahams et al*. [1995] found a strong relationship between

*L*,

_{s}*H*, and the channel reach slope,

_{s}*S*

_{0}(equation (1)), such that

*H*

_{s}/

*L*

_{s}/

*S*

_{0}remains almost constant over a wide range of slopes. More recently, however,

*Comiti et al*., [2005] and

*Church and Zimmerman*[2007] showed that for idealized step-pool arrangements, i.e., those sequences where steps control nearly all the drop in step-pool channels, step steepness increases with slope. This is expressed in equation (2), where

*k*=

*L*is a nearly constant parameter ranging between 6 and 8, which represents the scoured pool geometry.

_{s}/s*Comiti et al*. [2005] proposed an empirical equation (3) to explain relations among step-pool geometry features. This model was derived by combining data from natural step-pool units and scour holes downstream of grade-control structures, for which the ideal assumption underlying equation (2) is not necessarily satisfied, since the entire step-to-step drop can be influenced by the development of a tread downstream from the scoured hole [

*Church and Zimmerman*, 2007].

[6] In addition to studies highlighting the mutual adjustment between the geometrical features of step-pool units, other studies have examined the internal variability of these features within a reach. In contrast to the regular step spacing suggested by the step-unit geometry given by equations (1)-(3), *Curran and Wilcock* [2005] showed that the variability in step spacing along a step-pool channel can be represented through an exponential frequency distribution (equation (4)) for those cases where the most significant step-forming process is related to material that gets anchored against keystones or other mechanisms related to forced step-pool units. The proposed distribution for the step spacing *x* is described by the mean of the distribution, *β*, and a minimum possible value given for *x*_{0}, also called the exclusion zone, a region immediately downstream from a step where a second step cannot be formed. A more segregated approach was presented by *Myers and Swanson* [1997] for pool-riffle and step-pool sequences, where the pool length is represented with a Gamma distribution using a unique exclusion zone value, and the nonpool length downstream from the pool by a Poisson distribution.

[7] The planform variability within step-pool reaches has also received attention in several studies, particularly because it can strongly influence water quality assimilation and physical habitat identification. Bankfull width appears to be an especially useful parameter for describing planform variability, given its direct connection with flow regimes as well as being useful as scale factor when different stream reaches are compared. Besides bed-form variability, *Myers and Swanson* [1997] represented width variations along morphological units with a Gamma probability function. *Harman et al*. [2008] proposed a log-normal distribution to explain within-reach width variations, and they represented the reach-average hydraulic geometry parameters more reliably by using the geometric mean of width, depth, and velocity, rather than the arithmetic values. *Moody and Troutman* [2002] also found in-channel width variations that followed a marginal log-normal distribution, and they demonstrated the suitability of the approach across several orders of magnitude and different morphological stream types, including boulder and sand stream beds. In addition, they highlighted the concordance between the statistical behaviors for width and mean depth, and the corresponding hydraulic geometry equations derived from the data set used.

[8] Despite the recent advances in understanding step-pool systems at spatial scales comparable to their morphological unit size, several questions remain unsolved with respect to solute transport processes, which have received less attention in terms of the linkages with channel morphology features and their spatial variability throughout a stream network. Those aspects become further relevant in the context of environmental management, especially for water quality modeling, to support environmental discharge estimation and stream restoration.

[9] Transient Storage (TS) models have been widely applied at the reach scale to assess solute transport mechanisms [*Lees et al*., 1998; *Runkel and Broshears*, 1991; *Lees et al*., 2000; *Camacho and González*, 2008], hyporheic exchange rates [*Harvey et al*., 1996; *Choi et al*., 2000; *Kazezyılmaz-Alhan and Medina*, 2006], linkages between channel geometry and hydraulic patterns [*Richardson and Carling*, 2006; *Smith et al*., 2006; *Wondzell*, 2006], and quantification of habitat abundance [*Lancaster and Hildrew*, 1993; *Lancaster et al*., 1996]. These types of models describe the lumped dispersion processes within a reach by including equivalent stagnant or dead zones that account not only for surface transient storage but also for storage in the hyporheic zone.

[10] The TS model [*Bencala and Walters*, 1983] and the Aggregated Dead Zone (ADZ) model [*Beer and Young*, 1983] have provided a basis for important research in solute transport, as well as for engineering applications in the last two decades.

[11] For the ADZ framework, the transport process within a reach is conceptualized to occur within two regions. The solute first enters a completely active zone, where pure advection takes place for a time span, *τ*. The solute is then transported and enters a completely stirred ADZ, where dispersion takes place during a remaining hydraulic residence time given by *T _{r}* (Figure 2). The mean passage time of the solute along the stream reach is then given by

*t*= τ +

_{m}*T*. The mass-balance equation for the ADZ model under steady-flow conditions is given by equation (5), where

_{r}*C*denotes the known input concentration at the upstream edge of the reach and

_{u}*C*(

*t*) the downstream output concentration [

*Lees et al*., 2000].

[12] An important assumption of the ADZ model is that only a fraction of the total water volume within the reach is completely stirred: this proportion is identified as the dispersive fraction, DF, as shown in equation (6). It is worth noting that DF can be expressed in terms of either the ratio of the well-mixed volume, *V*, to the total reach volume, *V*_{TOTAL}, or, under steady-flow conditions and discharge *Q*, the ratio between the corresponding resident times for both volumes. DF can vary from 0, which represents a completely advective system, to 1, representing an ideal dispersive system.

[13] An initial finding regarding DF was that it is nearly constant for a wide range of discharges [*Wallis et al*., 1989]. This assumption continues to be used to support some ADZ applications, especially in flat regions because the assumption implies only measuring or estimating the mean travel time along the reach of interest. Nevertheless, *González* [2008] found that DF could vary up to 22% within the same reach in mountain streams under different flow conditions. Hence, the dispersion process along a mountain stream reach should not be assessed by carrying out a single or a few tracer experiments. Besides, economic limitations typically make DF, *t _{m}*, or τ, infeasible to obtain by tracer measurements throughout an entire mountainous region or watershed.

[14] Because of the good performance reported for the ADZ approach for modeling solute transport, as well as the fact that the model is known for having physically based and measurable parameters and for being parsimonious (two parameters), we adopt it to explore scaling patterns of solute transport processes in step-pool sequences. The more recent knowledge available for such systems allows us to explore a morphologically based representation of the model with the hope that it can be used to support solute transport applications in ungaged regions, as well as habitat abundance assessment and distributed hydrologic modeling.

[15] In the subsequent sections, we first describe the ADZ model framework and how it was used to obtain solute transport parameters for nine step-pool reaches during high, intermediate, and low flows. We then derived morphological features for those reaches using detailed topographic data and applying an objective method. Next, transport parameters and morphological parameters are combined base on dimensionless forms for discharge, travel times, and features of morphological step-pool-run units, providing evidences to support the invariance of the solute movement mechanisms. Finally, we present a morphologic-based extension for the ADZ model that we test with the available data.