Elsevier

Environmental Modelling & Software

Volume 18, Issues 8–9, October–November 2003, Pages 683-692
Environmental Modelling & Software

Modelling stream recession flows

https://doi.org/10.1016/S1364-8152(03)00070-7Get rights and content

Abstract

The curvature in semilog plots of hydrograph recessions has been explained previously by the assumption of a power relationship between groundwater storage and its outflow to the stream, with no recharge occurring during the recession period. The current work uses an alternative hypothesis of a linear groundwater system with a continuing inflow from the vadose zone. This leads to the development of recession equations with time-varying inputs of various forms. Comparison of these and the ‘no recharge’ models, using data from 22 Australian benchmark catchments, leads to the conclusion that significant recharge does continue through recession periods, and should be accounted for in conceptual models of the rainfall-runoff process. While the initial value of the recharge is closely related to the stream flow, the time constants for all the models vary widely between events, which led to the development of master recession curves. The recession equation of the IHACRES model, which takes the form of the sum of two exponential functions, was found to provide a very good fit to the data. Evaporation and seepage losses can be incorporated in the recession equation, and the magnitude of the losses can be quantified.

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 isQt=Qoe−t/τ=Qoktwhere 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 byQ=S/τ=aSwhere 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 formQ=aSnwhere n would be expected to lie between 1 and 2.

This results (Chapman, 1999) in a recession equation of the formQt=Qo[1+(n−1)t/τo]−n/(n−1)where 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 asqt=Qo[fqe−t/τq+(1−fq)e−t/τS]where 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 isdSdt=R−Q.If the storage is linear, combining (6) and (2) givesτdQdt+Q=Rfor which the general solution is Qt=Qoe-t/τ+e-t/ττotRet/τdt.

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 R

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 R̄ 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

References (26)

  • T.G Chapman

    A comparison of algorithms for stream flow recession and baseflow separation

    Hydrol Proc

    (1999)
  • F.H.S Chiew et al.

    Australian data for rainfall-runoff modelling and the calibration of models against streamflow data recorded over different time periods

    Civil Engineering Transactions

    (1993)
  • F.H.S Chiew et al.

    Complete Set of Daily Rainfall, Potential Evapotranspiration and Streamflow Data for Twenty Eight Unregulated Australian Catchments

    (1993)
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