Modelling stream recession flows
Introduction
After surface runoff from a catchment into a stream has ceased, the recession part of the streamflow hydrograph is regarded as resulting from groundwater discharging into the stream. The equation most used for this period iswhere Qo, Qt are the flows at times 0 and t, τ is the turnover time of the groundwater storage, and k is the recession constant for the selected time units. The first form has a long history (Boussinesq, 1877, Horton, 1933, Maillet, 1905), while the second was popularised by Barnes (1939).
Eq. (1) results from a linear storage, in which the groundwater storage S is related to the stream flow Q bywhere a=1/τ.
While this equation would be expected from an aquifer in which there is little variation in flow depth, in unconfined flow situations a two-dimensional hydraulic analysis (Chapman, 1963, Werner and Sundquist, 1951) suggests a non-linear relationship (Coutagne, 1948) of the formwhere n would be expected to lie between 1 and 2.
This results (Chapman, 1999) in a recession equation of the formwhere τo=So/Qo is now the turnover time at time 0.
Wittenberg (1994) fitted this equation to 21 streams in Germany and China, and obtained values of n ranging from 1.1 to 9.1, but stated that a value of 2.5 was ‘typical’. Chapman (1999) obtained mean values of n from 1.6 to 3.2 for 11 benchmark catchments in eastern Australia, and suggested that the high values might be attributed to horizontal convergence of the groundwater flow paths.
Both these approaches are based on the assumption that no significant groundwater recharge occurs during a recession period, that is, all recharge occurs during periods of surface runoff. This assumption is enshrined in many popular rainfall-runoff models, such as MODHYDROLOG (Chiew et al., 1993) and AWBM (Boughton, 1993).
It is the main purpose of this paper to question whether this assumption is valid, as consideration of soil physics would suggest that the duration of recharge would be considerably longer than that of surface runoff. Wu et al. (1996) emphasised the critical importance of water-table depth in determining the lag between rainfall and groundwater recharge. With shallow water-tables, recharge events correspond closely with individual rainfall events. As the depth to groundwater increases, correspondence tends to be with groups of rainfall events, and trends towards a single annual process. With a very deep water-table, variations in water-table depth become imperceptible.
Even at a depth of only 1.5 m, deep drainage has been estimated as occurring continuously over 4–6 weeks under wheat and lupin crops in a deep sandy soil at Moora, WA (Anderson et al., 1998).
Similar conclusions can be drawn from considering percolation from the base of deep lysimeters. Fig. 1 shows a typical percolation hydrograph for a lysimeter 2.4 m deep at Coshocton, Ohio (Chapman and Malone, 2002). It will be noted that the peaks in percolation correspond to very high rainfalls or groups of rainfall events, and that the percolation continues at a rate of about 1 mm/day for periods of over 50 days.
It is therefore apparent that streamflow recession equations should take account of recharge continuing through some or all of the recession period, and such equations are developed in the next section. These conceptual equations, and those based on the ‘no recharge’ assumption, will be compared with the equation derived from the systems approach in the linear module of the IHACRES model (Jakeman and Hornberger, 1993), which can be expressed aswhere τq, τs are the time constants for quick and slow flow respectively, and fq is the fraction of quick flow in the stream flow at time 0.
Section snippets
Recessions with recharge
Assuming the groundwater behaves as a storage of volume S with time-varying input of recharge R and output of streamflow Q, the water balance equation isIf the storage is linear, combining (6) and (2) givesfor which the general solution is
This solution will now be evaluated in terms of three different assumptions about the time variation of R.
Model 1: It is assumed that variation in R is sufficiently small that it can be replaced by its mean value
Data and calculations
The data used in this study were the stream flow records in the data set of Australian catchments prepared by Chiew and McMahon (1993a). The locations of the gauging stations are shown in Fig. 2, and details of the catchments are given in Table 1.
Flows for the 24-h period up to midnight were used for the Queensland catchments, and up to 9 a.m. for the other stations. Daily flows in ML were converted to an equivalent depth in mm over each catchment. Recession periods were identified as sections
Comparison of models
The models have been compared in two ways. Table 2 gives the number of events in which each model gave the best fit to the data. In Table 3, a score based on ranks has been used, with a score of 5 for the best fitting model and a zero score for the worst. Both tables show that each model can on occasions provide the best fit to the data, but in general the models based on the ‘no recharge’ assumption (, ) perform less well than those which assume a continuing recharge (, , ). There does not
Relations between parameters
For models 1, 2 and 3, there is a strong relationship (Fig. 4) between the stream flow Qo at the start of a recession and the fitted value of recharge Ro, which presumably reflects variations in the height of the water-table.
In model 1, the calibrated value of ranges from a minimum of 0.01 mm/day for catchments 25 and 26 to a maximum of 3.1 mm/day for catchment 2, with an overall average of 0.4 mm/day. Expressed as a proportion of the stream flow at time 0 (Qo), the values range from 0.11 to
The evaporation loss model (model 4)
The only catchment in which the loss effect was evident over a duration suitable for model fitting was the Canning River (25) in the period from October of each year. Fig. 7 shows that model 4 fits the data in this period very well, even when there is evidence of some minor ‘freshes’ in the stream flow. The average value of E for 12 such periods is 0.0025 mm/day, which is 23% of the average flow at the start of the period. Taking the potential evaporation at this time of year to be 5 mm/day,
Application of master recession curves
Except in streams fed by groundwater through a long dry season, such as the Jardine, most recession curves have a duration of less than 20 days. For the sites with at least 10 recession events of duration greater than 10 days, the mean durations ranged from 11.5 to 16.7 days, with an overall mean for all stations of 14.2 days.
Under these conditions, the curvature in the semilog plot of stream flow against time is not well defined, and there are attractions in the concept of constructing a
Discussion
The observation that semilog plots of hydrograph recessions are generally concave upwards is reinforced by the low scores of Eq. (1), the straight line solution. While the nonlinear groundwater storage puts curvature into the model, the shape of the curve does not match the data, as well as the sum of two exponential recessions (Eq. (5)) or the models which assume continuing recharge (, , ).
The differences between the quick flow time constants determined from the recessions and those obtained
Conclusions
This study supports the conclusion that groundwater recharge continues, at a constant or slowly declining rate, through periods of base flow. This suggests that conceptual models of the rainfall-runoff process should provide for rapid accessions to groundwater during periods when the soil store is saturated, followed by a continuing recharge until the next event. The initial value of this recharge is closely related to the stream flow at the start of the recession, with a value of 25% of that
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2017, Journal for Nature ConservationRegional low-flow frequency analysis with a recession parameter from a non-linear reservoir model
2015, Journal of HydrologyCitation Excerpt :In studies where recession parameters were used to estimate low-flow statistics, a linear reservoir model is always assumed. This approximation is used for convenience, but a non-linear relation is more accurate in general (Brutsaert and Nieber, 1977; Whittenberg, 1994; Chapman, 2003). In this study, we propose to use a recession parameter assuming the non-linear reservoir model in a regional model along with other physiographical and meteorological characteristics for the estimation of low-flow quantiles.
Recession analysis across scales: The impact of both random and nonrandom spatial variability on aggregated hydrologic response
2015, Journal of HydrologyCitation Excerpt :However, the influence of the intersection of the random and nonrandom small-scale variability on aggregating hydrologic processes across spatial scales remains poorly understood. The recession process, an important part of hydrologic response, has been widely used to provide insight into hydrologic understanding and modeling (e.g., Hall, 1968; Zecharias and Brutsaert, 1988; Vogel and Kroll, 1992; Troch et al., 1993, 2013; Tallaksen, 1995; Szilagyi et al., 1998; Furey and Gupta, 2000; Smakhtin, 2001; Chapman, 2003; Rupp and Selker, 2006a; Brutsaert, 2008; Kirchner, 2009; Shaw et al., 2013). Among these applications, recession analyses across spatial scales have been used to understand the role of the variability of landscape characteristics in the upscaling of hydrologic processes.
A hydraulic mixing-cell method to quantify the groundwater component of streamflow within spatially distributed fully integrated surface water-groundwater flow models
2011, Environmental Modelling and SoftwareCitation Excerpt :The groundwater component of streamflow cannot be measured easily in the field (Hattermann et al., 2004; McCallum et al., 2010) and therefore is usually quantified using indirect methods. Indirect methods can involve the use of environmental and conservative tracers for separation of the hydrograph (McGlynn and McDonnell, 2003; McGuire and McDonnell, 2006), and recession analysis based on conceptual storage–discharge relationships for the catchment (Chapman, 2003; Eckhardt, 2008). However, as pointed out by Hewlett and Troendle (1975), ‘the accurate prediction of the hydrograph implies adequate modelling of the sources, flowpaths and residence time of water’.