Examining individual recession events instead of a data cloud: Using a modified interpretation of dQ/dt–Q streamflow recession in glaciated watersheds to better inform models of low flow

Summary

To examine stream recession rates, hydrologists have plotted the rate of change in discharge (dQ/dt) versus the mean discharge (Q). Such plots typically result in a large cloud of data points where the slope of the lower bound of the cloud is often used to infer aquifer hydraulic properties as informed by certain interpretations of the Boussinesq Equation. For seven watersheds in New York State, USA ranging from 100 km² to 6415 km², we distinguish data points in the dQ/dt–Q plot belonging to individual recession events instead of looking at the entire data cloud. The recession curve of individual events consistently shifts upward during the summer and late fall (relative to spring and late fall curves) and much of the scatter in the data cloud appears to be due to seasonal variations in recession. We speculate that these seasonal variations in recession rate may be due to variations in watershed evapotranspiration (ET). Additionally, most individual recession events have slopes of approximately two when plotted as log dQ/dt versus log Q. Application of the Boussinesq Equation to watershed-scale recession date predicts slopes shifting from 3 to 3/2 as recession progresses, thus the observed slope of two casts doubt on whether it is appropriate to apply hydraulic aquifer theory to these types of watersheds to infer aquifer properties or predict low flows. As a further validation of the hydrologic information content of individual recession curves, the individual recession curves from time periods with minimal ET (early spring and late fall) were used to establish storage–discharge functions for two of the smaller watersheds. With these storage–discharge functions, a simple hydrologic model could reasonably simulate time series with minimal calibration (Nash–Sutcliffe R² of 0.71 and 0.67 on log transformed discharge). Overall, this paper suggests that the analysis of individual event recession curves (particularly when compared among watersheds and seasons) can be a valuable tool for gaining insights into hydrological processes at the scale of large watersheds and can justify alternatives to current low flow models.

Introduction

Climate change is anticipated to increase evapotranspiration and lead to longer arrival times between rainfall events (Allen and Ingram, 2002). Consequently, summer streamflows will also presumably decrease in many locales, such as the northeastern US (Hayhoe et al., 2007). However, there are a limited number of tools to assess changes in low streamflow in a nonstationary climate. Statistical regression models have been used to relate watershed characteristics (such as area, mean rainfall, and baseflow properties) to a measure of low-flow such as the 7-day, 10-year return period discharge (e.g. Brandes et al., 2005, Vogel and Kroll, 1992), but such models inherently assume stationarity among the many factors not explicitly used as explanatory variables. Computational models (from simple bucket models to complicated spatially distributed models) are often used to simulate hydrologic time series, but there is general acknowledgment that these models are often applied with limited interest in replicating low-flows (Smakhtin, 2001, Fenicia et al., 2006). This bias against predicting low-flows in part comes from the frequent use of model goodness-of-fit criteria that much more heavily weight accurate prediction of high flows than low flows (Khan, 1989), thus discouraging careful consideration and characterization of the processes dictating low flows. Relative to the error in modeling high flows (which can be three orders of magnitude larger than low flows), low flows are often modeled sufficiently by assuming they originate from a subsurface linear reservoir or a slight variant.

The idea of a subsurface reservoir that behaves in accord with a low-order power function is backed by recession flow analyses that assess the rate of change in discharge (dQ/dt) between rainfall events in proportion to the discharge (Q). This method was first proposed by Brutsaert and Nieber (1977) to avoid picking the exact time at which recession begins. Herein, we will refer to it as the dQ/dt–Q method of recession analysis. As initially demonstrated by Brutsaert and Nieber (1977) and repeated many times in the literature (see examples in Mendoza et al., 2003, Brutsaert and Lopez, 1998, Eng and Brutsaert, 1999), plotting paired values of the rate of change in discharge at a given discharge typically results in a cloud of data points where the lower envelope in log–log space has a slope often deemed to be either 1 or 1.5 over the range of moderate and low flows and 3 for higher flows. A slope of 1 is equivalent to an exponential decline in discharge with time. A slope of 1.5 results from solving the Boussinesq Equation with the assumption that the water surface retains a curvilinear shape throughout the entire drainage process, representative of an aquifer that has been draining for a long-time. A slope of 3 results from solving the Boussinesq Equation with a boundary condition that assumes that the furthest extent of the aquifer remains infinitely distant from the channel, representative of an aquifer that has been draining for a short-time. Brutsaert and Nieber’s (1977) linkage of dQ/dt–Q curves to solutions of the Boussinesq Equation attempted to infer watershed-scale aquifer properties (such as effective porosity and hydraulic conductivity) from measurements of streamflow recession.

Thus, most investigations employing the Brutsaert–Nieber approach to recession analysis tend to focus on the role aquifer properties play in recession. However, dQ/dt–Q curves are not always interpreted strictly in terms of hydraulic aquifer theory. For instance, dQ/dt–Q curves are sometimes analyzed by fitting a best-fit line through the data cloud (e.g. Vogel and Kroll, 1992, Lyon et al., 2009, Kirchner, 2009, Krakauer and Temimi, 2011) instead of fitting lines along the bounds of the cloud in adherence with the Brutsaert–Nieber approach to recession analysis. Additionally, several recent papers have shifted the focus of recession analysis to processes other than just the outflow from a saturated groundwater aquifer. Harman et al. (2009) demonstrated that recession curves with slopes between 1 and 3 can be generated by watershed models constructed from unit hydrographs with no basis in the fundamental equations of groundwater hydraulics. Clark et al. (2009) assessed whether different combinations of parallel linear reservoirs representative of broad catchment features other than just aquifer characteristics could be used to model recession curves. Kirchner (2009) demonstrated that recession curves can be used to construct a storage–discharge relationship that can be used to simulate the full range of streamflow (not just baseflows) when applied in conjunction with precipitation and evapotranspiration (ET) measurements. These recent papers have suggested that recession data could be reassessed more broadly, outside the lens of the hydraulic aquifer theory.

The basic approach we seek to take in this paper is to assess individual event recessions instead of the cloud of points. Of particular motivation in examining individual events is to deduce the reason for the cloud of points (i.e. Why don’t dQ/dt–Q recession curves more often collapse along a single line?). In applying the dQ/dt–Q recession method, there have only been several papers that have considered individual recession events. Szilagyi and Parlange (1998) illustrate the fit of short and long time solutions of the Boussinesq Equation to a single 6-day, wintertime recession event in Georgia, USA but do not analyze multiple events. Szilagyi et al. (2007) compared dQ/dt–Q curves for periods with and without ET as simulated by a 2-dimensional numerical ground water model applied a 20 m wide (from channel to upslope groundwater divide) sand aquifer. Rupp et al. (2009) used a 2-dimensional ground water model to, in part, evaluate the influence of vadose zone drainage time and aquifer drainage time on apparent stream recession characteristics. Rupp et al. (2009) found that for simulations where the vadose drainage time was short, individual recession curves on a dQ/dt–Q plot were visible. These dQ/dt–Q curves for different simulated events were approximately parallel but offset horizontally due to differences in initial aquifer storage conditions at the start of the recession period. In Rupp et al. (2009) no dQ/dt–Q curves from actual data were presented. However, Biswal and Marani (2011) did assess individual recession curves from actual data as they sought to relate properties of river network morphology to observed streamflow recession. For 67 US watersheds ranging from 10 to 8858 km², they consistently found individual dQ/dt–Q recession slopes of approximately 2 in basins with minimal anthropogenic disturbance. As in Rupp et al. (2009), the individual dQ/dt–Q curves observed by Biswal and Marani were approximately parallel and had horizontal offsets. However, no evaluation of internal hydrologic conditions for different curves was made because the object of the study was to assess scaling between measurable geomorpohological properties using the observed recession slopes. McMillan et al. (2011) displayed dQ/dt–Q curves color-coded by season for a single ∼1 km² catchment in New Zealand. Again, individual dQ/dt–Q curves were observed to be approximately parallel in slope and to shift horizontally with season due to a presumed change in the contributing subsurface reservoir. Despite these numerous suggestions of shifting of dQ/dt–Q curves in the literature, systematic patterns in shifting (particularly with season) have not yet been specifically evaluated for multiple watersheds.

In their original paper proposing the dQ/dt–Q recession method, Brutsaert and Nieber (1977) openly state that one looks at the lower bound to minimize the influence of “overland flow, interflow, and channel storage”. In the conclusions of the same paper, Brutsaert and Nieber (1977) also explicitly note that their analysis assumed ET was of minor influence and additional research would be needed to evaluate its role. Despite this early acknowledgment of the possibility of additional processes influencing apparent recession rates, there has only been limited work to identify which processes most strongly influence the cloud of points that arises from most dQ/dt–Q recession analyses. In particular there have been very few studies to examine the role of ET. The influence of ET was examined several times in older literature prior to use of the dQ/dt–Q method (e.g. Fédérer, 1973, Weisman, 1977). For example, in relating the recession constant of an exponential recession function to regional pan evaporation data, Weisman (1977) demonstrated the recession constants for certain time periods maintained a consistent relationship with concurrent pan evaporation rates. More recently, Szilagyi et al. (2007) presented dQ/dt–Q recession data by month (but not by event) and demonstrated larger dQ/dt values occur for a given Q during summer months. Additionally, the work of Kirchner (2009) and Teuling et al. (2010) has explicitly attempted to control for the influence of ET. In particular Kirchner (2009) and Teuling et al. (2010) used small watersheds (<10 km²) with short in-stream travel time so that night time recession curves would be representative of periods with minimal ET. In this paper, we explore the possibility of elucidating the influence of ET on stream recession in large watersheds (100 + km² to 1000 + km²) by considering the difference between individual recession curves (instead of the cloud of data points) watersheds with primarily deciduous vegetation in which ET strongly varies seasonally.

The three basic objectives of the paper are as follows:

• Present dQ/dt–Q for individual recession events for medium to large sized watersheds and compare the individual curves to that of a curve fit to the lower envelope of a cloud of dQ/dt–Q recession points not distinguished by event.

• Examine the relationship between season (used as proxy for ET) and the degree of shift in the recession curves for the individual events.

• Evaluate the hydrologic information contained in event recession curves by considering the ability to use recession curves from seasonal periods with minimal ET as a storage–discharge relationship in a simple hydrologic model.

Overall, the intent of this paper is to help further refine the application of the dQ/dt–Q recession method in light of a continued lack of consensus on how to interpret the cloud of data points (Brutsaert, 2005, p. 424).