Water Resources Research

Flash flood dynamics and composition in a semiarid mountain watershed

Authors


Abstract

[1] Flash flood hydrographs were examined using water stable isotopes (deuterium and oxygen) and a plug-flow lumped catchment model to assess the origin and routing processes of flood water in a semiarid basin in southwestern United States. Precipitation and stream water were sampled during storm and flood conditions at high and low elevations. Isotope mixing relationships readily determined the predominance of three sources for the representative summer monsoon events: high elevation precipitation from two major subbasins and base flow. Each flood progressed through a series of source water contributions, as indicated by several segments of linear mixing between these end-members. We developed a plug-flow lumped catchment model to test possible governing processes for specific watershed and forcing conditions. Results suggest two main findings: First, these flood events were generated primarily from event water runoff in high elevations that mixed at the flood bore with pre-event base flow resident in the stream. The power, speed, and turbulence of the flood bore cause it to mix with, ride atop and push the resident in-stream water in the front of the rising limb. Second, the timing and volume of flood waves from subbasins are identified by their combined isotopic signature at the basin outlet; this approach may provide an effective mesoscale constraint for rainfall-runoff models.

1. Introduction

[2] Flash floods are hazardous, short-lived, and difficult to predict. For these reasons, data on their composition and dynamics are sparse and challenging to obtain even with automated methods. They can be generated by high intensity rainfall, slow-moving storm systems, and even rapid snowmelt [Merz and Bloschl, 2003]. The danger associated with these natural occurrences can be magnified by anthropogenic activities. In particular, land-use change by deforestation and urbanization in large areas of prior flood-mitigating vegetation has increased the potential for damaging floods [Larsen et al., 2001]. Flash floods cause significant damage worldwide and their financial toll grows annually due to increasing population and infrastructure costs in close proximity to flood-prone areas [Gruntfest and Handmer, 2001; Pielke et al., 2002]. Further, they play an important role in the long-term geomorphology, hydrology, and ecology of streams and rivers [Baker et al., 1988].

[3] Several approaches have been employed for flood modeling, as reviewed by Beven [2005]. The appropriate degree of complexity for a particular model application depends on the scale of interest and information available [Sivapalan et al., 2003]. Downward modeling, an approach that focuses on the holistic behavior of a system, has gained popularity for examining appropriate complexity and for identifying the dominant modes of response to a system [Sivapalan and Young, 2005]. This approach offers promise for identifying the main hydrological processes important in different climates, landscapes, and scales which could then be applied in models for ungaged basins [Sivapalan et al., 2003].

[4] Isotope hydrograph separations (IHS) have also been used to illuminate hydrograph generation processes for several decades and the results in the literature can be summarized for several representative climate and hydrological conditions. In high-rainfall, response-dominated catchments, that have high quickflow/precipitation ratios, the tendency to observe large volumes of pre-event water in the hydrograph depends strongly on the precipitation intensity, which affects the degree of saturation overland flow [Bonell et al., 1999]. For example, steep, humid catchments studied in northeast Queensland, with 10-minute maximum rainfall intensities (I10) near 80 mm h−1, showed a dominance of event water in the hydrographs, with hydrometric data supporting saturation overland flow as the dominant mechanism [Bonell et al., 1999]. In contrast, in the shallow soil, steep slopes of the Maimai catchment in New Zealand, with 99% of rainfall intensities <9 mm h−1, McDonnell [1989] demonstrated the importance of macropore flow for delivering a large volume of pre-event water to hydrograph peaks through old water displacement. In the snowmelt dominated spring floods of the Rockies and Sierra Nevada Ranges in the Western USA, several researchers have shown the significant contribution from “old” water [Huth et al., 2004; Liu et al., 2004; Rademacher et al., 2005]. These examples are in contrast to monsoonal flash floods in low-elevation, low-relief semiarid ephemeral washes that are entirely event water [Ingraham et al., 1999].

[5] A less-explored category in this research is semiarid mountainous locations that combine conditions from these different groupings. These areas have well-wetted subhumid conditions in the high elevations that transition to ephemeral streams in the semiarid lower elevations. They also have a wide range of soil depths, from rock outcrops to areas of considerable storage capacity (several meters deep). It is not obvious a priori whether the flash floods generated by high-intensity storms in this environment will reflect the more humid conditions of the high elevations and have a pre-event dominated composition, or reflect the semiarid climate of the lower elevations and have an event dominated composition. In addition to climate, study scale will also dictate which hydrological processes dominate the stream composition. The majority of IHS studies are done at a scale <10 km2 [Buttle, 2005] where hillslope processes are observable, as opposed to larger scales where rapid transport in the channel network dominates.

[6] The Santa Catalina Mountains of southern Arizona provide an opportunity to explore the main processes involved in flood generation and routing at the mesoscale (∼100 km2) in a semiarid mountainous region. For this basin, the majority of rain events sampled for this study fell at high elevations where the majority of soils are thin and underlain by largely impermeable gneiss. Rilling and overland flow are visible at high elevations during rain events, and flash floods result with sharp rising limbs (base flow to peak conditions quicker than the 15-minute resolution of the stream gage). A conceptual model for flow contributions and pathways was developed based on preliminary findings from field observations. This model proposes that, for monsoon events with mainly high elevation precipitation, overland flow dominates the stream water composition near the headwaters and generates flood waves, and that these waves compress and mix with resident stream base flow as they coalesce and move down the canyon. To test this, the objectives of this paper are (1) to use isotopes to identify the relative source water contributions to a flash flood, (2) to develop a simple plug-flow lumped catchment model and apply it to data from two example storm events, and (3) to demonstrate how this information can indicate the timing of flood contributions from individual canyons in the studied basin and (4) explore flood bore dynamics. Finally, we consider how information obtained from this isotopic approach to studying flash floods could be further explored for application in downward modeling.

2. Site Description

[7] The Sabino Creek watershed, located northeast of Tucson, Arizona, is on the south-facing slope of the Santa Catalina Mountains (Figure 1). This range is part of a northwest trending series of metamorphic blocks in the southeast portion of the Basin and Range region. The bedrock is predominantly gneiss, with steep and rugged terrain covered by thin soils, ranging from less than 0.25 m for the majority of the watershed to more than 1.5 m deep in some areas of the high elevations [DuBois, 1959; Whittaker et al., 1968]. The total area of the watershed is 91 km2 with elevations ranging from 823 m at the base of the mountains to 2,789 m at the summit of Mount Lemmon, the highest peak in the range. Sabino Creek is the primary stream in the watershed. It is perennial in the upper reaches where the areas with thicker soil depths enable groundwater storage capacity. At the basin outlet, the Sabino Creek registers flow at the gage an average of 294 days per year with a mean flow of 0.41 m3 s−1 (LSC1, Figure 1; USGS Stream Gage ID 94840010 [Fisk et al., 2006]). The watershed comprises two major subbasins in its higher elevations, the Upper Sabino Creek and the Palisade Creek subbasins, with areas of 45.1 and 22.2 km2, respectively. The highest peaks in each of these are Mount Lemmon, elevation 2789 m, and Mount Bigelow, elevation 2606 m, respectively. The confluence of the Sabino and Palisade creeks is at an elevation of 1100 m (near MSC1 in Figure 1); after this point there is only one other significant tributary, Rattlesnake Canyon, just before the outlet of the watershed (near LSC1 in Figure 1).

Figure 1.

Sabino Creek watershed is in the Santa Catalina Mountains northeast of Tucson, Arizona. There are two major subbasins in the higher elevations: Upper Sabino Creek and Palisade Creek. Precipitation was sampled at Mount Lemmon (MLP2), Mount Bigelow (BTP1), and Lower Sabino (LSP1). Stream sampling locations along the upper, middle, and lower Sabino Creek are marked as USC1, USC2, MSC1, and LSC1, respectively.

[8] The watershed is located near the eastern limit of the Sonoran desert, within a semiarid climate. The vegetation varies from southwestern desert shrub at low elevations, to broadleaf woodland chaparral between 1300 and 2200 m, and mixed coniferous forest at the highest elevations [Whittaker and Niering, 1965]. The average annual precipitation is 0.3 m at the base and 0.8 m near the summit [Guardiola-Claramonte, 2005]. The precipitation falls predominantly during two distinct seasons: a summer monsoon season (usually July through September) and a winter season (with the majority of precipitation occurring between December and March), separated by typically dry periods. Similar to the annual averages, monsoon precipitation within the Sabino Creek Watershed varies linearly from maximum values at high elevations to approximately half of the maximum value at the lowest elevations, based on data collected during six monsoon seasons prior to and following this study.

[9] Southern Arizona lies within the influence of the North American Monsoon [Adams and Comrie, 1997]. It is characterized by localized afternoon convective storms of high rainfall intensity and short duration. For our study site and study period (2003–2004), the average duration is usually a few hours and the average I10 is 73 mm h−1 [Desilets et al., 2007]. This produces a sharply peaked flash flood; flow at LSC1 returns to less than 1 m3 s−1 within a couple of days. The flow has been observed to dry completely when there are several weeks between storms. Winter precipitation in Sabino Creek watershed often are Pacific ocean frontal storms that are longer duration (a few days) and have lower rainfall intensity (average I10 = 13 mm h−1 [Desilets et al., 2007]). These frequently result in snow at high elevations, much of which, during the study period, melted within days or weeks after the storm passed.

[10] A wildfire persisted in the Santa Catalina Mountains for two months in the summer of 2003. In the Sabino Creek Watershed, more than 65 km2 were burned, of which approximately 10% were high burn severity, predominantly in the higher elevation woodland chaparral and coniferous vegetation zones [Guardiola-Claramonte, 2005]. Our study period begins one year after the wildfire and the flow patterns we observe may be influenced by common effects of wildfire such as increased overland flow, decreased canopy interception and evapotranspiration, and possible flow through burned root holes.

3. Model Description

[11] Based on field observations and the hydrogeology of the basin, flood formation is hypothesized to develop from predominantly event water runoff that mixes dispersively at the flood bore with resident stream water. The following is a simple formalization of these processes in a lumped catchment plug-flow mixing model. It is designed to test this hypothesis for a semiarid basin with a few major subbasins. The model is intentionally minimal in its input requirements to be applicable to basins without extensive hydrometric data available; instead, geochemistry is employed as an integrating parameter to discern the first order controls on flood water composition.

[12] Figure 2 shows a diagram to summarize the main components of the model. In its essence, the model is a linear mixing of flow and isotope values in two or more stream hydrographs below the confluence of the streams. The water balance is established by the hydrographs above the confluence. If hydrographs are not available, they can be approximated by a lognormal distribution as described below. The chemistry in each hydrograph is defined based on the hypothesis of plug flow in the stream channel with mixing at the front of the flood wave. At this interface there is mixing between two isotopically distinct waters: (1) flood water, assumed to be event water and (2) the resident pre-event base flow in the channel. The advection-dispersion equation is used to describe the step pulse change from one end-member composition to the other and back again.

Figure 2.

Diagram for model setup. Flow with time at points A and B are described by a normalized lognormal distribution (top right) where Qi,tot, Qi,ev, and Qi,bf represent total, event flow, and base flow in subbasin i. The relative flows (QA/QB) are set to match the rain volumes in the respective subbasins. The water composition is defined by the volume fractions (VFi) multiplied by the relative composition from the advective dispersion equation (middle right). This output is fitted to the observed data; adjustable parameters are the dispersion coefficients and the time lag between the onset of event water and the return to base flow. (bottom right) The event flood bore pushing and mixing with the resident stream base flow.

[13] If a flow gage at the point of interest, just upstream of the confluence, is not available, a hydrograph shape can be represented as a normalized lognormal distribution

equation image

where y(t) is the height of the volumetric flow hydrograph and t is time. The mean (μ) and standard deviation (σ) are adjusted to match the shape of other available hydrographs in the respective subbasins. Higher precipitation intensity will typically yield a steeper hydrograph, and therefore a lower σ and μ. Similarly, along the length of the stream and within the contributing area of the storm, as the drainage area increases, the hydrograph volume will increase and width will broaden (lower σ). The peaks of the generalized hydrographs are scaled to match relative volumes of precipitation in each subbasin for a given event so that the volumetric flow rate (Q) is defined as

equation image

where f is the fraction of total rain volume and i denotes an individual subbasin.

[14] The isotope values of the water in each subbasin hydrograph is calculated as a plug flow of event water with mixing between event and pre-event water at the front and tail end of the hydrograph as given by the advection-dispersion equation (ADE) [Ogata and Banks, 1961],

equation image

where C is the isotope value, DL the coefficient of longitudinal hydrodynamic dispersion, vx is the average velocity in the x-direction, defined by the celerity of the flood wave, and t is the time of input of a particular isotope value. The solution for a continuous injection is

equation image

where the dimensionless forms of composition and time are defined as

equation image
equation image

and the Peclet number (Pe) as

equation image

Isotope values are varied between two end-members for each subbasin: (1) event water as determined from rain sampling and (2) resident base flow as determined from stream sampling. The relative composition (CR) represents the fraction of water with the breakthrough end-member.

[15] This ADE solution is applied at two points in the hydrograph: (1) at the flood bore where it interfaces between flood event water and pre-event base flow and (2) at the point in the recession where the event water begins to be replaced by base flow, isotopically.

equation image

where ΔtR represents the time between the initial transition to event water and the later transition back to base flow, and the Peclet numbers are specified for the flood rising limb (Pe,f) and recession (Pe,r). The Peclet numbers vary because of the two different velocities occurring at these two stages of the hydrograph, vf and vr. Although vf is readily determined as the flood wave celerity from stream gage data, vr cannot be determined independently of the isotope data and therefore is lumped with the dispersion coefficient as a fitting parameter. Additive mixing of the water from each channel determine the water volume and isotope values below the confluence of the subbasin streams according to

equation image
equation image

where n is the total number of subbasins considered and C(t)mix is the resultant isotopic value.

[16] Ideally, the minimum known parameters for application of the model are the isotopic value of the precipitation end-member, hydrograph shape, flood wave celerity, and stream length for each of the individual subbasins. The adjustable parameters for fitting the model results to stream isotopic data are the dispersion coefficients and time between the initial transition to event water and the later transition back to base flow. The model is optimized by minimizing the root mean squared error (RMSE) between determined and observed values.

4. Method

[17] To test our conceptual model and characterize the response of the system to monsoon storms, precipitation and stream water samples were collected throughout five events during the monsoon seasons in 2003 and 2004. In the streams, grab samples were collected in glass bottles with Polyseal® caps. The main sampling site was along the Lower Sabino Creek (LSC1, Figure 1) at the base of the watershed (elevation 829 m) at a United States Geological Survey flow gage (ID 94840010). This gage resides at Sabino Dam, a reservoir built in the 1930s, which has since filled with sediment [Kurupakorn, 1973]. This feature minimizes scour-fill challenges typical of other gaging stations on alluvial channels. The gage measures stream height with a pressure transducer every 15 minutes with 0.3 cm precision. Due to the flashy nature of most monsoon flood events during the study period, the gage often jumped from a zero value (i.e., if there was flow it was below minimum gage measurement level) to the maximum registered flow for the hydrograph within the 15-minute period. Water samples were collected prior to the flood wave, during the peak, and then spaced along the falling limb at increasing time intervals (Figure 3). For one event, samples were also collected in the Upper Sabino Creek (USC2, 2376 m) near the top of the watershed (Figure 1).

Figure 3.

Precipitation and stream data for the 13 August 2004 (left) and 23 July 2004 events. The precipitation bars represent data binned into 10-minute increments; stream gage discharge measurements are in 15-minute increments. Stream sampling times are marked as solid circles on the hydrographs. The inset at the bottom right shows the fitting of a lognormal curve (dashed line) to the flood hydrograph at USC1 (solid line) for the 23 July event.

[18] Precipitation samples were collected with a funnel into HDPE bottles that were prepared with mineral oil to prevent evaporation. There was one station at low elevation (LSP1, 800 m), and two at high elevations (MLP2, 2750 m; BTP1, 2583 m). Bottles were typically exchanged following every storm event in order to isolate and characterize the total precipitation from each event at the sampled location. This is a direct measure of the integrated isotope value and is equivalent to a volume-weighted mean isotope value calculated from sequential samples taken throughout the storm event. For one of the events, multiple precipitation samples were collected during the course of the storm at the MLP2 station. Precipitation amounts were determined from four tipping bucket rain gages operated by Pima County Flood Control District (http://alert.dot.pima.gov/scripts/pima.pl) which measure rainfall in 1 mm increments. The Pima County site identifiers for the gages located near the BTP1, MLP2, and LSC1 sites are WT2150, ML1090, and SD2160 respectively. Pima County operates an additional rain (MG2290) and stream gage (MG2293) in the Upper Sabino Creek watershed (USC1) located at the site of a discontinued USGS stream gage (ID#09483300). Stream gage MG2293 records the stage for every 6 cm stage fluctuation. Due to inaccessibility, rain gages are not representative across the Sabino Creek watershed. Therefore radar images from the National Weather Service (1.4-km resolution) were qualitatively used to observe the location, extent, and tracking of the storm cells.

[19] All samples were analyzed for δD and δ18O at the Laboratory of Isotope Geochemistry at the University of Arizona using a Finnegan Delta-S Mass Spectrometer according to the methods outlined in the works of Craig [1957] and Gehre et al. [1996]. The precision was reported as 0.9 and 0.08‰ (1σ) for δD and δ18O, respectively.

5. Results

[20] Several monsoon storm and flash flood events were sampled in the Upper and Lower Sabino Creek watershed. Analysis of two example events, the best sampled with the most distinct end-members, demonstrates how isotopes can be used to observe the routing of water along the major surface water flow paths. One of these events occurred on 13 August 2004 (Figure 3). Precipitation totals at Mount Lemmon (MLP2), Mount Bigelow (BTP1), Upper Sabino Creek (USC1), and Lower Sabino Creek (LSC1) were 47, 27, 48, and 0.5 mm, respectively. For this storm, the three high elevation gages recorded nearly an order of magnitude more rain than the low elevation gage. Also, the majority of rain fell within one hour generating rapid runoff at high elevations and a sharp-peaked hydrograph at the Lower Sabino Creek stream gage. Radar images document two separate storm cells that developed on the northwest and southeast sides of the high elevation portions of the watershed. These cells eventually coalesced and moved off the mountain to the northwest.

[21] Several samples were collected to characterize the event. Three precipitation samples were collected at MLP2 over the course of the storm. At BTP1, a single sample captured the full integrated mean isotope value of the entire precipitation event. Four stream samples were collected during peak flow at high elevation in the Upper Sabino Creek (USC2). At the lower site (Lower Sabino Creek, LSC1), three samples were taken of the base flow in the two hours before the flood peak, and thirteen samples were taken throughout the hydrograph. The mean isotope signatures at Mount Lemmon and Mount Bigelow differ by approximately 1.5‰ for δ18O and 10‰ for δD. The Mount Lemmon precipitation that was collected through time shows a typical rainout pattern of decreasing stable isotope values as the storm progressed (Figure 4). This pattern is controlled by the oxygen and hydrogen isotopic fractionation factors between liquid water and water vapor at the condensation temperature in the air mass. As the rain falls from the air mass the remaining oxygen and hydrogen isotopes in the air mass of the storm become more negative for as long as condensation and precipitation continue to occur.

Figure 4.

Isotope results for the high elevation precipitation and the Upper Sabino Creek (USC2) during the flood event on 13 August 2004. The arrow indicates the time progression of the Mount Lemmon precipitation and Upper Sabino Creek samples. For reference, the local [Wright, 2001] (dashed) and global [Rozanski et al., 1993] (solid) meteoric water lines are included. The solid circle and error bars represent the average and standard deviation of the base flow isotope value in the Upper Sabino Creek for 38 samples collected between 1993 and 2007.

[22] The Lower Sabino Creek hydrograph samples show mixing between three isotopically-labeled end-members (Figure 5): (1) base flow water immediately prior to the flood wave, (2) precipitation at BTP1 which represents water in the Palisade Creek subbasin, and (3) precipitation at MLP2 which represents water from the Upper Sabino Creek subbasin. Isotopically, the flood water proceeds through three mixing segments between the end-members. First, during the rising limb of the hydrograph, a pre-event pulse progresses linearly toward water from Palisade Creek subbasin. Next, water from Upper Sabino Creek subbasin contributes to the mixture and becomes dominant. Finally, at the tail of the hydrograph, the water returns to its pre-event isotopic signature. The stream values never reach 100% of either precipitation end-member isotopically, though they come much closer to the MLP2 end-member. In general, there is a strong base flow component, even when the mixing is primarily between the two event waters.

Figure 5.

Isotope results (left) and hydrograph separation (right) for storm events on 13 August 2004 (top) and 23 July 2004 (bottom). The numbered segments in the left figures correspond to those in the right. The isotopic value for precipitation at Mount Lemmon on 23 July 2004 was estimated based on a rainout calculation relative to the measured value from Mount Bigelow.

[23] Another event, near the beginning of Monsoon season on 23 July 2004, produced a similarly shaped hydrograph (Figure 3b) but had drier pre-event wetness conditions and a distinct pattern of isotopic values at the basin outlet (Figure 5). The precipitation totals for MLP2, BTP1, USC1, and LSC1 were 49, 49, 66, and 23 mm, respectively. For this storm, rain depths at the higher elevations were more than double that recorded at the lower elevation. This contrasts with the August event with nearly an order of magnitude difference between elevations with the low elevation barely registering precipitation. A bulk precipitation sample was collected at BTP1. At the LSC1 sampling site, one sample was taken of the base flow 25 minutes prior to the flood peak arrival, and eighteen samples were collected throughout the hydrograph. No precipitation samples were obtained from MLP2 for this event. However, a value for this site was estimated using the available data and assuming rainout was the main mechanism for rainfall variability between the two sites. The rainfall amount data time series supports a rainout mechanism: the first moment of the rainfall at Mount Lemmon lags that at Mount Bigelow by 14 minutes. Also, radar images confirm the storm movement from the southeast. For the isotopic calculation, a rainout slope of 9.0 was selected based on temperature data at the BTP1 sampling site during the event (10°C) and the fractionation factors determined by Majoube [1971]. A best fit line was determined using this slope and the isotope values of the rain at Mount Bigelow and the stream samples influenced by this rain value, which have a matching slope. The value for the precipitation at the MLP2 location was determined as the intersection of this line with a best fit line through the base flow value and the stream samples influenced by the mixing between the base flow and storm water (Figure 5). The estimated value for MLP2 is (δD, δ18O) = (−53, −8‰).

[24] Base flow at the basin outlet transitioned from no-flow to a very low flow (<0.1 m3 s−1) following precipitation in the low elevations; the low flow persisted for approximately two hours until the onset of the flash flood (50 m3 s−1). Although the Sabino Creek was originally dry at the outlet, it was not dry in the higher elevations, though it is unknown precisely what length of stream had water. In this case, the low elevation rain increased stream connectivity and enabled the small amount of flow, which we sampled for the base flow end-member. The isotopic rain value (δD, δ18O) = (−38, −4.4‰) collected at the low elevation site (LSC1) was much more enriched than the first stream water sample (δD, δ18O) = (−46, −6.3‰), and this signature probably had some influence on the base flow value.

[25] As in the August event, the isotope values in the Lower Sabino Creek samples show nearly linear mixing between three end-members; however, the shape of the mixing lines differ significantly (Figure 5). This dissimilarity indicates a divergence in the order of the flood water contributions from the end-member subbasins. The relative timing of the flood waves at the basin outlet, a direct result of the wave celerity, depends on the volumetric flow rate, which is generally higher in the Upper Sabino Creek subbasin due to its larger aerial extent, and on the relative timing and depths of rainfall. For this event, rainfall in the Upper Sabino and Mount Lemmon gages was more sustained compared to that at Mount Bigelow (Figure 3). The pattern of isotopic data in the hydrograph suggests that water from the Upper Sabino Creek subbasin arrives first, followed by a distinct contribution from Palisade Creek subbasin, after which the data retraces itself back to Upper Sabino Creek water and finally back to pre-event water. Also, there is much less contribution from base flow throughout, and though the water eventually evolves toward the pre-event conditions, it does not reach that value by the last sample collected three days after flood peak.

6. Discussion

6.1. Model Application

[26] The lumped catchment plug-flow model is applied to this study area to test the underlying hypotheses for processes contributing to flow in semiarid catchments, with the intent to characterize dominant processes that can be applied in other similar semiarid settings. The model structure reflects the geometry of Sabino Creek watershed with two high elevation subbasins (Upper Sabino Creek and Palisade Creek). The event water end-member for each subbasin is from the bulk samples collected at the MLP2 and BTP1 sites. A single mean isotope value for precipitation at Mount Lemmon was used while the additional temporal data was incorporated into sensitivity analysis. Because the traveltime distribution from the hillslopes to the channels is unknown, and spatial variability is averaged, adding this to the model would require an arbitrary routing mechanism which would add a model parameter unsupported by data. As an alternative, our model proposes that the high elevation rainfall averages during the development of the flood bore in the channel network. Specifically, although rain is distributed over the subwatershed, we assume the isotope value that falls in a subbasin is quickly organized into a well-mixed flood bore with composition equal to the depth-averaged value observed in precipitation samples. The base flow end-member is taken as the average of isotope values from the samples collected immediately before the arrival of the flood wave. Based on the catchment geometry and the isotopic end-members for a particular rain event, the model simulates the isotopic composition of the flood water, which can be compared with the isotopic composition of samples collected through time at LSC1. The model is designed to predict water isotope values beneath the confluence of the selected subbasins. Due to the inaccessibility of this point in the Sabino Creek watershed, flow data is unavailable from this area and samples were collected farther downstream (LSC1). For flow data, we fitted lognormal parameters (μ, σ) to hydrographs at USC1 and LSC1 and used these as constraints for the modeled hydrographs above the confluence.

[27] The model in this form is applied to the two storm events described above, with parameters of the advection-dispersion equation calculated for the details of each event. The average velocity (vx) is taken as the celerity of the flood wave as determined from the traveltime of the peak between the stream gage at high elevation and that at the basin outlet (Figure 1), approximately 10 km h−1 for both events. Due to the limited availability of flow data, this value is applied for both subbasins. The length (L) of the stream for each subbasin is from the streams' origins to their confluence, 15 and 8 km for the Upper Sabino Creek and Palisade Creek subbasins, respectively. The longitudinal dispersion is defined in general terms as DL = σ2/2t where σ2 is the variance of the spreading. For Sabino Creek, we have no a priori information on this value, and optimized it as a fitting parameter in the model (equations (7), (8), and (10)). From this, we determined values near 5 km2 h−1 for the rising limb of our events, which yields a Peclet number (Pe = vxL/DL) of 30. This value is lower than expected, indicating a large amount of dispersive spreading. We hypothesize that as the flood bore advances it flows atop the slower moving base flow more quickly than the base flow is incorporated by the turbulent front (Figure 2, bottom right). This behavior has been observed during field sampling. In addition, because our model assumes mixing just below the confluence but our sampling point is further downstream, the additional mixing along this stream length (between MSC1 and LSC1) may contribute to the lower Peclet number. In general, the mixing between the event and pre-event water at the flood bore–base flow interface will increase downstream as the wave celerity decreases and has additional time for mixing. The second optimized parameter in our model was the time between the initiation of the event and the initiation of return to base flow (Δtr, equations (8) and (10)). This was determined from the timing of the transitions between the isotope event and base flow end-members to be approximately 13 h for the events evaluated.

[28] An analysis was performed to assess the sensitivity of the model parameters to temporal isotopic variability in the precipitation and uncertainty in the base flow data. Values were selected based on the observed temporal range of a storm event at MLP1 (±3, ±0.3 per mil in δD, δ18O) and the rainout slope (9.0). The results were much more sensitive to the Mount Lemmon precipitation isotopic values than the Mount Bigelow. For the Mount Lemmon end-member, a perturbation of 10% of the maximum temporal range (±0.3, ±0.03 per mil) resulted in a 13% difference in DL and 4.5% difference in Δtr. For the Mount Bigelow end-member, even perturbing to the maximum observed in the temporal range resulted in only a 5.3% difference in DL and a 2% difference in Δtr. This dissimilarity in sensitivity could be explained by the much larger volume of water coming from the subbasin represented by the Mount Lemmon precipitation. For the base flow, sensitivity was tested along the slope of the evaporation curve (5.3). The results were similar to those for the Mount Lemmon precipitation sample. For a ±0.7 per mil deviation (δD), there was 16 and 8% difference in DL and Δtr, respectively. In general, in the sensitivity analyses, we have found the parameter values to be somewhat sensitive (up to 70% deviation using the most extreme end-members), but consistency in the isotopic patterns that support our proposed flow mechanism.

[29] The two events presented were selected as instructive because several end-members were sampled and the spatial variability in the precipitation end-members for the high elevation subbasins (Δ(δ18O, δD) = 1.5, 10‰) allows for straightforward identification of the water at the basin outlet. The variability is exploited by setting the average rain isotope value from each location as an independent end-member to track the input signature of water in each respective subbasin. In support of this approach, we compared the high elevation precipitation at Mount Lemmon with the high elevation Upper Sabino Creek water and found the data match closely (Figure 4). The similarity between the stream and rainfall isotope values suggests a large and rapid influence of event water in the high elevation runoff. In this case, the surface runoff from each subbasin should be distinguishable and isotopically similar to the precipitation, and may be used to estimate the timing and quantities of the contributing source water to the hydrograph at the Lower Sabino Creek outlet.

[30] Sampling flash floods at the basin scale is inherently complicated and better resolution is always desired. In this case, precipitation across a large area in the high elevations is represented by just two sampling locations and the local length scale of variability is unknown, though currently being measured in ongoing studies. In support of our approach, the difference between the two subbasin isotope values is large relative to the measurement precision, the high elevation stream values closely matches the precipitation, and, in the July event where there are two hydrograph peaks, the transition in the isotope data matches the flow transition. If the flood water were dominated by a wider range of isotope values due to spatial variability we would expect to see more deviation in the basin outlet results. However, additional studies will be beneficial to determine the importance of variability relative to the proposed mechanisms.

[31] The model captures the shape and progression of the isotope values at the basin outlet for both events (Figure 6) in spite of differences between their respective precipitation amounts, pre-event wetness conditions, end-member isotope values, and resultant outflow isotope pattern. For the event on 13 August 2004, there is, first, linear mixing between the pre-event base flow and event water from the Palisade Creek subbasin. This is consistent with an interpretation of mixing between the resident stream water at the flood bore with the overland and rapid throughflow of the Palisade Creek subbasin event water. When the second flood wave arrives from the Upper Sabino Creek subbasin it too is advancing a pre-event pulse, though it only includes water that was resident in the higher elevation stream; the water initially present in the lower stream was already displaced by the first flood wave. The isotope data moves along a curved path representing the mixing of all three end-members which progresses toward a dominance of the event water from the Upper Sabino subbasin. As the runoff recedes there is a return to the original pre-event base flow conditions. For the 23 July event, the model pattern closely matches the measured isotope results where the Upper Sabino Creek subbasin water arrives first, followed by a distinct contribution from Palisade Creek subbasin, after which the data retraces itself back to Upper Sabino Creek water and finally back to pre-event water. This supports the hypothesis that the flood bore mixes with resident stream water and pushes it to the front of the hydrograph, a behavior also observed by Nolan and Hill [1990]. Further, it illustrates how the efficient combination of isotope data combined with volume at a few locations in this type of watershed can be a practical tool for water district managers.

Figure 6.

Simulated (solid line) and measured isotope results for storm event on (left) 13 August 2004 and (right) 23 July 2004.

[32] These model results can be contrasted with what would be expected from conceptual models that emphasize alternative end-members or processes. Other possible end-members considered include low elevation precipitation, an elevation-averaged precipitation value which is based on isotope elevation gradient from low and high elevation samples, the previous event precipitation, high elevation base flow, and the previous event runoff. Each of these end-members were individually considered in the model for several events, but consistently yielded a different pattern than that observed at the basin outlet and a higher RMSE. In contrast, the high elevation and base flow end-members yielded a close relationship between the modeled and hydrograph values for several storm events. For example, low elevation precipitation and high elevation base flow are significantly enriched and depleted, respectively, compared to the initial base flow values and the pattern during the hydrograph peak and recession (see Figures 3 and 4). Specifically, when alternative end-members were fit to the data, the RMSE of deuterium ranged from 2.0 to 5.0 for the best combinations compared to 0.95 for the chosen end-members.

[33] Alternative processes for delivering pre-event water to the stream would also yield a different isotopic pattern. In particular, if the majority of the pre-event water were from groundwater storage, whether incorporated by rapid water table development and macropore flow or by throughflow, that end-member would be isotopically lighter than observed (Figure 4). The explanation for this requires a brief discussion of the nature of the pre-event base flow, where it comes from and how it persists in time. The high elevations of the Santa Catalinas are the only portion of the mountain block that has thicker (>1.5 m) soil in some areas with sufficient storage capacity to enable nearly perennial flow. Flow in the low elevations is largely fed from the higher elevation drainage. This is reflected in the isotope data. Base flow samples collected at high elevations (USC2) for over three years show that the isotope value for this water maintains a consistently negative value near −65‰ δD, −9‰ δ18O (Figure 4), indicating a relatively large and well-mixed groundwater reservoir. The low elevation base flow isotope value generally falls along an evaporation line (slope ∼5) from the high elevation value, with the exact location along this evaporation line depending on the amount of time since a previous rain event. If the high elevation groundwater was rapidly transported to the stream during a flood event we would expect to see a large contribution from this end-member in the flood peak. In contrast, for the 13 August event, the isotope values of the peak flood water moves immediately from the preflood base flow value toward the isotopically heavier value of the Palisade Creek subbasin, rather than in the negative direction that would represent high elevation groundwater (Figures 3 and 4). This understanding of base flow in the Sabino Creek Watershed also explains why the volume of the pre-event base flow is larger in the tail of the hydrograph than prior to the storm event. This component comes from drainage of the high elevation soil reservoir, which has just increased its flow due to infiltration of high elevation precipitation.

6.2. Pre-Event Water in Mountainous Semiarid Flash Floods

[34] Our formalized conceptual model has been shown to predict isotope values for two different storm conditions in the watershed, but it includes strict assumptions about the nature of the pre-event water. Namely, the model assumes that all of the pre-event water was originally stored in the stream. Therefore as a further test of these assumptions, we verify whether there is sufficient storage in the stream to account for all of the observed pre-event water by comparing the volume of pre-event water as determined from isotope hydrograph separation (IHS) with a volume estimate of base flow resident in the stream based on stream length and gage height dimensions.

[35] Our former analysis has been independent of IHS, and its introduction here requires a brief statement of caution. Past researchers have shown that the commonly made assumptions of constant spatial and temporal end-members can be invalid in small basins [Buttle, 2005]. In the case of the two storm events studied, we do observe spatial and temporal variability. At the basin-scale there appears to be adequate averaging of event water in the channel network to allow for the identification of a few dominant end-members; however, the variability is expected to introduce error into the volume calculations which is difficult to quantify without higher resolution sampling. As an alternative, we calculated the sensitivity of the IHS results to the temporal variations in the precipitation end-members. We found a range of 1.0 to 5.7% difference in the volume fractions and 3.0 to 16.7% difference in the component volumes using combined end-member deviations of ±10% of the maximum observed temporal variability. For the extreme end-members, the range of differences in volumes increased to 4.2 to 43.4%. Errors reported below were calculated using the ±10% end-member deviation. Also, measurements of stream volume from limited cross section and gage height data can have significant error. Therefore the volumes presented are estimates calculated for the exercise of comparing order of magnitude quantities.

[36] For the 13 August event, the volume of pre-event water between points 1 and 2 (Figure 5) was calculated to be 11,500 ± 1700 m3 using IHS. Assuming the conditions of our conceptual model, this volume is attributed to the water in the streams in Palisade Creek subbasin all the way to the larger basin outlet. Similarly, for the hydrograph segment between 2 and 3 (Figure 5), the volume determined from IHS is 19,500 ± 2900 m3. This represents water in the streams of the Upper Sabino Creek subbasin. The total volume, 31,000 ± 4600 m3, yields an equivalent cross-sectional area of 0.4 m2 water surface all the way along the channel. In applying IHS to this data set we assign the base flow isotope value to the full length of the stream, ignoring evaporation and other potential influences. As described in the previous section, the base flow in the stream originates from high elevations and exhibits an evaporated signature in the downstream direction. The linear distribution of the isotopic signature along the stream at any point in time is complicated by the presence of numerous deep pools in the bedrock beneath the stream, variable flow rates, and time since the previous rain. The variation is therefore unknown, but expected to largely fall along the evaporation line established separately by four sampled points along the entire stream length (USC1, USC2, MSC1, LSC1). Therefore by assuming the value from the basin outlet, we may be underestimating the amount of pre-event water in the flood peak. However, if we look at the 13 August event, if the high elevation stream contribution (Upper Sabino base flow, Figure 4) were significant then we would expect to see the isotope data in the hydrograph at the basin outlet move in the direction of that end-member. Since it does not may mean that the evaporated signature develops early in the high elevations. Further, this possible underestimating would be less important for storm events that closely follow a previous event (on the order of days rather than weeks) because the evaporated profile has less time to redevelop after being modified by the precipitation, and the base flow is more uniform throughout.

[37] For comparison with the values determined from IHS, the volume of water resident in the stream prior to the flood event was estimated. To do this, gage height data collected immediately prior to the flood wave were used from three locations (Figure 1): Upper Sabino Creek (USC1), confluence of the Sabino and Palisade streams (MSC1), and Lower Sabino Creek (LSC1). For the confluence location, the gage was not available until after the studied storm events, so data from an event similar in precipitation depth and duration were used. The value for the cross-sectional area used for the upper and lower stream lengths was the average of the confluence and high elevation, and confluence and low elevation gages, respectively. This approach yielded a volume of water residing in the combined Palisade and Lower Sabino Creek subbasins, which represents the hydrograph segment from 1 to 2 (Figure 5), of 18,000 m3. For the Upper Sabino Creek subbasin (represented by the segment between points 2 to 3; Figure 5) the volume was 10,500 m3. These values can be considered a conservative estimate in that they do not consider water stored in the abundant pools found in the basin. Based on these estimates, the total resident stream water from both approaches is approximately 30,000 m3. The similarity of this result from independent methods provides additional support for our hypothesis that resident stream water is an important component of a flash flood peak and influences flood bore dynamics.

[38] Based on the model results and above analysis we propose that, when delineating water sources for flash floods at the basin scale, a source of water must be considered that may not be significant for less flashy hydrographs or smaller watersheds: the resident in-stream water. The relative importance of this pre-event source likely reflects the rapid timescales (on the order of hours) involved. For Sabino Creek watershed, the time between peak rain and peak runoff at high elevation (for an 8 km2 catchment) can be as short as 25 minutes and the same peak arrives at the basin outlet in less than 2 h (23 July event). The turbulent flood bore readily incorporates the resident stream water so that what would have taken days to travel from top to bottom under typical base flow conditions now does so along with the rest of the flood in hours, thus compressing its timing and making it a significant component of the peak. In addition, basin size likely plays an important role in the observed results. Although a consistent relationship has not been developed between basin scale and event water [Buttle, 2005], our results suggest the importance of the flood bore for producing a pre-event component in the flood peak. At the ∼100 km2 scale, the flood bore has time to develop in the channel network and advance atop and mix with the resident stream water; this process would not be expected at the hillslope scale. Another important factor for generating the behavior we observe in these two storms is the location of the rainfall and the size of the catchment area at the sampling points. As is common for monsoon storms in the Santa Catalina Mountains, the majority of the rainfall for the two studied events occurred at high elevations. In this case, the basin size and stream length in the Sabino Creek Watershed is sufficient to allow for the organization of the flood water into a distinct bore before arriving at the low elevation sampling point. If the rain were to fall in the lower or middle elevations of the basin it is not certain whether this behavior would be observed.

[39] Several mechanisms have been identified in the literature for delivering pre-event water to a flood wave [e.g., Jones et al., 2006; McDonnell, 1990]. All of these contributors likely play some role in most systems, but the dominant source varies by climate, hydrogeology, basin size, and topography. For mountainous semiarid regions with intense storm forcing inputs in the high elevations, resident stream water is the main component of the pre-event water in the hydrograph.

6.3. Application to Downward Modeling of Basin-Scale Runoff Processes

[40] The scale of the data collected in this study is well suited for a downward modeling approach that emphasizes the larger basin-scale outcomes over the summation of the microscale, as advocated by Sivapalan and Young [2005]. There are a few main differences between the two examined storm events that illuminate the type of basin-scale information from this analysis that would be useful in runoff and flood routing models. Three examples are briefly explored below: soil wetness, bank storage, and flood peak timing.

[41] The 23 July event was the first major flood of the season, with dry pre-event soil conditions. In contrast, the week prior to the 13 August event there had been several days of low intensity rain. Repeated rain events and antecedent moisture conditions have been shown to affect the relative importance of different runoff generating mechanisms in semiarid watersheds [Dick et al., 1997; Lange et al., 2003]. In our data, this manifested itself as a difference in the volume of pre-event water. The 23 July event, with the lower volume of base flow in the stream under initial drier conditions, had much less pre-event water in both the initial peak and in the peak for the flood wave from the second subbasin. Because the pre-event water is an important component of the flood peak at the basin outlet, this information is critical for predicting peak height important for potential flood risk estimates. In particular, if several floods were examined in combination with measured soil conditions, a general basin-scale relationship could be established to predict the percentage of event water and the relative contributions of pre-event and storm water runoff, with the aim of quantifying the resultant peak height.

[42] The isotope pattern of the hydrograph stream samples in the 23 July event suggests that water moving into the stream banks for temporary storage and release could be a significant mechanism for governing the chemistry of the water during the hydrograph recession. We expect this process to be more strongly manifested in the data from events with drier prestorm conditions. In this case, as the peak flood waters encounter the dry stream banks in the lower elevations, infiltration occurs and then, just hours later when the flood has receded, the same water exfiltrates in the opposite order. This process has been observed in low-elevation high-order streams in semiarid regions and can be important for nutrient flushing [Huth, 2003]. The isotope data for the 23 July event progresses from pre-event water to mixtures with high-elevation precipitation from each subbasin, then retraces the opposite order during the hydrograph recession. With additional data on prestorm soil conditions, piezometric water content, and soil-water samples collected in transects into the stream banks throughout an event, it may be possible to form more precise conclusions about the conditions that control the significance of stream bank storage processes.

[43] The order of flood contributions from the two subbasins is also different between the two events. This order depends on the velocity of the flood wave, which is a function of the size of the storm event, the stream lengths, the spatial and temporal distribution of precipitation, and the antecedent soil moisture conditions. The Palisade Creek is 8400 m in length compared to the Upper Sabino Creek, which is 15,500 m to their confluence, but the contributing area for the Upper Sabino Creek is also twice the size of the Palisade Creek, generating a larger volume of water and therefore a higher velocity flood wave. For a basin in which precipitation is well gaged, this type of information for several events could yield integrated stream parameters for flood routing models. The isotope information is particularly important in this application because peak contributions from individual canyons can be identified based on isotope data even though flood waves have merged such that there is only one physical peak in the hydrograph.

7. Conclusions

[44] We investigated the hypothesis that runoff from high-elevation intense storm events in our mountainous semiarid basin is primarily event water from the high elevation precipitation that advances and mixes dispersively with resident stream water at the flood bore during flash flood flow. To test this we developed a simple plug-flow lumped catchment model. We identified the dominant end-members for this model based on isotopic information and used these values to simulate the isotope data time series of two monsoon storm flood events. We found good agreement between the data and simulated results for two dissimilar events, supporting the underlying process assumptions of the model for this type of setting in a monsoon season.

[45] Tracing the isotopically distinct precipitation end-members in the two major high elevation subbasins, we estimated the timing and quantity of peak flow from those subbasins. Because of the isotope data distinction, this was possible even when the hydrograph comprised a single physical peak. This information could be used as an additional mesoscale constraint in a runoff or flood routing model.

[46] Hydrograph separation analysis indicated a significant contribution of pre-event water in the flood peak. Although this has been seen in several other climates, it is generally not expected in semiarid terrain. Based on high elevation stream data and the model results, we attribute the majority of this pre-event water to base flow that was resident in the stream prior to the flood. A comparison of the IHS pre-event volume with an estimate of base flow stream volume indicates there is sufficient storage in the stream network to account for the pre-event water observed. For mountainous semiarid terrain, with mostly thin and dry soils, an intense convective storm will produce observable overland flow and a flash flood on the timescale of hours. Applying isotopic analysis can be useful for identifying the timing of the flood routing processes critical for flood hazard assessments. In this environment, the resident stream water must be considered as a significant pre-event end-member capable of contributing a substantial volume to the peak of a flash flood.

Acknowledgments

[47] This work was funded by NSF Small Grants for Exploratory Research EAR-0342831, Arizona University System Technology and Research Initiative Fund grant P04-21, and NSF Science and Technology Center for Semiarid Hydrology and Riparian Areas. The authors thank several colleagues in the Hydrology and Water Resources Department at the University of Arizona: Steve Lyon and Peter Troch for the streamflow data, Maite Guardiola-Claramonte for assistance with site maps, watershed variables, and laboratory and field work, and Karletta Chief for help with sampling and laboratory work. We also thank Erik Pytlak of the National Weather Service for help preparing and interpreting radar images. We appreciate the support of the Coronado National Forest for granting access to field sites. This manuscript benefited from the insightful comments of Robert H. Webb and two anonymous reviewers.

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