Interpretation of recession flow

Journal of Hydrology, 46 (1980) 89--101 © Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands

89

[3] INTERPRETATION OF RECESSION FLOW

M,G. ANDERSON and T.P. BURT* Department of Geography, University of Bristol, Bristol (Great Britain) Department of Geography, Huddersfield Polytechnic, Huddersfield HD 1 3DH (Great Britain) (Received December 4, 1978; revised and accepted July 5, 1979)

ABSTRACT Anderson, M.G. and Burt, T.P., 1980. Interpretation of recession flow. J. Hydrol., 46: 89--101. Various attempts at interpreting recession flow using graphical techniques are reviewed. Data derived from a laboratory slope drainage experiment and from an instrumented catchment are plotted using the same graphical presentations. These data are also interpreted using predictions based upon Darcy's law. It is shown that graphical techniques may falsely interpret the factors controlling recession and the need for field prediction of recession flow is stressed.

INTRODUCTION

T h e individual c o m p o n e n t s o f r u n o f f - - o v e r l a n d flow, t h r o u g h f l o w and g r o u n d w a t e r f l o w - - e a c h a p p e a r to possess distinct recession characteristics, a n d it was suggested b y Barnes ( 1 9 3 9 ) t h a t it was possible t o distinguish b e t w e e n t h e m using graphical analysis. Barnes m a i n t a i n e d t h a t f o r a n y t y p e o f flow, recession was g o v e r n e d b y the e q u a t i o n : Qt = Qokt

(1)

w h e r e Q0 = initial discharge at the s t a r t o f recession; Qt = discharge a f t e r t i m e t; and k = a c o n s t a n t k n o w n as the d e p l e t i o n factor. T h e f o r m o f eq. 1 is rarely used n o w a d a y s being r e p l a c e d b y t h e algebraicly e q u i v a l e n t f o r m : Q = Qo e x p ( - t / c )

(2)

In f a c t , k is n o r m a l l y used instead o f c, b u t to avoid c o n f u s i o n , t h e t w o are k e p t distinct in this case. In eq. 2, c has the d i m e n s i o n s o f t i m e and m u s t be e x p r e s s e d in a p p r o p r i a t e units, k is related t o c b y the f o l l o w i n g e q u a t i o n : k = exp(-1/c) *To whom correspondence should be addressed.

(3)

90

where i implies one unit of time. k is thus a dimensionless quality but its value does depend on the unit of time which is adopted. In Barnes' examples, the unit of time adopted was one day. Fig. 1 shows that the recessions examined by Barnes fell into distinct units, each defined by a straight line when plotted on semilogarithmic graph paper. The time since the storm rainfall determined the process "label" given to each recession line. By applying eq. 1 to each line, Barnes was thus able to provide a numerical value of h for each of his recession processes. Barnes found values of k of 0.329 for surface {overland) flow, 0.694 for subsurface stormflow (throughflow) and 0.980 for baseflow. ,, ',~

Overland

flow

4,000 3,000 =

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20 Jul

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Fig. 1. Data used by Barnes (1939) to define the components of recession flow.

The identification of recession components using semilogarithmic plots has become a common analysis technique in hydrology. Todd (1959) notes that the constant factor k is dependent on catchment characteristics and implies that variability between catchments will be reflected in the nature

91 of the recession flows produced. Bleasdale et al. (1963) identified the same three types of recession as noted by Barnes for streams in northwest England and for the Essex Stour. Ineson and Downing (1964} t o o k the analysis a stage further by subdividing the baseflow component. They recognised that the summer recession curve for many British rivers is not a simple straight line, but rather a composite curve. After June, the straight line recession of the early summer is replaced by a curved relationship. This is interpreted by Ineson and Downing as the result of a combination of two flow types originating from different parts of the catchment (Fig. 2). Discharge from areas close to the stream is assumed to dominate recession from February to June whilst drainage of aquifers further away from the stream controls recession thereafter. Addition of the two recession curves is responsible for the curved nature of the seasonal recession plot. 0

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MAR

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Fig. 2. An interpretation of groundwater recession during the summer for British rivers (from Ineson and Downing, 1964).

The division of bank and basin storage components has also been used by Kunkle (1962) in order to explain recession flow characteristics. Kunkle extended the semilogarithmic plotting technique by constructing from the groundwater recession line a base flow duration curve, using the Searcy (1959) method. This effectively involves construction of a cumulative frequency curve, plotted against the logarithm of discharge, thereby expressing the percentage of time a given flow was equalled or exceeded during the year. Fig. 3 shows a baseflow duration curve for the Huron River, Michigan, and indicates the division of bank and basin storage which Kunkle used to explain the plot. Kunkle then proceeded to analyse similar curves for

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0"51 2 5 10 2'0 ' 4'0 ' 6'07'0 8'0 9'0 9'5 9'89'9 99"9 99"99 PERCENT OF TIME INDICATED DISCHARGE WAS EQUALED OR EXCEEDED

Fig. 3. An interpretation Kunkle, 1962).

for recession flow based on basin and bank storage (from

different sections of the Huron River, relating differences in the form of each curve to variations in local geology and surficial deposits. A different method of graphical analysis for recession flow has been employed by Hewlett and Hibbert (1963). They used a double-logarithmic plot of discharge against time to describe the decline in outflow from a model slope over 114 days following saturation of the soil on the slope (Fig. 4). The plot shows an apparent break in the character of the recession after just over a day's drainage. Thereafter the recession occurred at a much

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discharge recession from a draining slope (from Hewlett and

93

accelerated rate. This apparent change in drainage characteristics was interpreted by Hewlett and Hibbert as marking the cessation of saturated flow from the soil, with sustained flow being maintained thereafter by unsaturated flow mechanisms. These three basic types of analysis are all characterised by the same approach, namely inference of a variety of processes operating in a catchment based upon an interpretation of a graphical plot of the flow recession curve. Particular emphasis is thus placed by all three analyses on apparent breaks of slope in the plots produced. This paper seeks to show firstly, that false conclusions may be reached if such graphical methods are not supported by field evidence and secondly, that such data transformations must be treated cautiously since breaks of slope may prove apparent rather than real. GRAPHICAL PRESENTATIONS OF FIELD AND LABORATORY SLOPE RECESSION CURVES

Recession flows have been analysed for both field and laboratory situations. The field-derived recession was observed at Bicknoller Combe, Somerset, England, during the drought period of 1976. The instrumentation installed at Bicknoller has been fully described elsewhere (Anderson and Butt, 1977a). Following a storm of 25 mm on March 21, 1976, and the ensuing delayed peak in stream discharge caused by throughflow processes, on March 25, there followed a continuous recession in streamflow which lasted until the last day of August. The few small storms which did produce storm runoff during this period had no apparent effect on the baseflow recession. Over the five-month period, discharge fell from 11.04 to 0.17 1 s-~. The laboratory recession flow curve was produced from slope drainage experiments. Several designs of slope and different soil types have been used (Anderson and Burt, 1977b, 1978a), but in all cases the form of the recession curve produced was identical. Following complete saturation of the slope, drainage was allowed to proceed until discharge ceased. The recession curves produced were plotted graphically using the techniques described previously {Figs. 5--7). Also plotted on those figures is a recession curve with an arbitrary maximum discharge of 20 units with a discharge reduction of 2% per unit time thereafter (i.e. a constant rate of recession). Fig. 5 shows the recession curves as produced by the classical hydrologist's semilogarithmic plot. The laboratory slope drainage and the simulated recession both plot as straight lines, which implies that the laboratory slope outflow discharge also declines at a constant rate. The field recession is curvilinear, however, and is thus reminiscent of the recession flows discussed by Ineson and Downing. Following their example, it would appear reasonable to fit straight lines to the upper and lower portions of the curve. This then allows the conclusion to be drawn (following Ineson and Downing's argument) that up to 30 days bank storage dominates the recession, between 30 and 60 days both bank and basin storage contribute sig-

94

loo ATRSLOPE

FIELD RECESSION

01

2'0 4'0 6'0 8'0 1~)0 120 TIME FROM START OF DRAINAGE (days •,

140 160 rams • &)

1~}0

Fig. 5. Three recession curves plotted on semilogarithmic graph paper.

nificantly to streamflow, and thereafter the flow is dominated by basin storage. Thus, the data presented on Fig. 5 leads to the conclusion that the laboratory slope drainage is controlled by a single process, whereas the field situation to be dependent on two types of runoff. It is possible to fit eq. 1 to the straight lines presented on Fig. 5 but in order to be comparable with Barnes values of k, the laboratory slope curve must be replotted with the time axis in days rather than hours. After replotting, the calculated k-value for the laboratory slope recession was 0.52, whereas the two k-values for the field recession were 0.90 and 0.994. According to Barnes, the laboratory recession should be provided by subsurface stormflow whereas both recession curves for Bicknoller would be produced by groundwater. Fig. 6 shows the three recession curves plotted on logarithmic probability paper, thus replicating the base flow duration curves of Kunkle. This m e t h o d of graphical analysis would imply a change in flow process for all three recessions at low discharges. The laboratory slope and the simulated recession curves both accord to constant rates of recession (Fig. 5) so that the

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Fig. 6. B a s e f l o w duration curves for the three recession curves.

identification of a break in flow type on Fig. 6 would appear spurious, a result of the plotting technique rather than a real division. The field recession curve did show an apparent change of process on Fig. 5 with basin storage taken to provide the streamflow below discharges of 0.3 1 s -1. The baseflow duration curve (Fig. 6) also apparently identifies a change in process but at a discharge of 0.2 1 s -1. Such a break cannot be identified on Fig. 5. Also the discharges of 0.3 and 0.2 1 s-~ were separated by 60 days, so it seems unlikely that the two plots are identifying the same change in flow conditions. The fact that the baseflow duration curve identifies an apparent change in flow conditions on what are known to be constant recession rates, and that on the field curve, a break is also identified in the middle of a period of constant recession, implies that the shape of the curves produced on Fig. 6 results from the graphical technique itself and is n o t from any real change in flow process. However, it may be that processes can alter

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Fig. 7. Double-logarithmicplots for the threerecessioncurves. without producing a change in the rate of recession, so that the lack of a break of slope on the semilogarithmic plot may n o t necessarily be significant. Fig. 7 shows the three recession curves plotted on double logarithmic paper, thereby following the method of Hewlett and Hibbert. All three recession curves produce apparent breaks of slope when presented in this method, a break which is taken by Hewlett and Hibbert to represent the cessation of saturated soil moisture flow, leaving unsaturated flow to provide the outflow discharge. The laboratory slope and simulated recession curves both represent constant rates of recession, so that the break in slope on Fig. 7 would appear to be apparent rather than marking a real change in process. On the other hand, it may be that processes can change without causing a change in the rate of recession (i.e. without producing a break in slope on the semilogarithmic plot). Thus Hewlett and Hibbert's method of analysis apparently identifies a change in process which is n o t shown on the semilogarithmic plot, and the question must be asked as to which graphical method is providing a realistic description of the physical processes involved. As fax as the field recession is concerned, the double-logarithmic plot again identifies a change in flow characteristics, in this case at 4 1 s-1, whereas the semilogarithmic analysis identified a break below 1 1 s -1. Again the problem arises as to which plot, if either, provides a true indication of a change in recession flow.

97 PREDICTION OF RECESSION FLOW

The occurrence of a change of slope on the plots described above has been interpreted (by the hydrologists who first suggested the use of such techniques) as indicating a change of flow process. Some d o u b t concerning such interpretation is initially suggested by the simulated recession curve; though representing a regular recession of 2% per unit time, nevertheless there is a clear break of slope on the plots suggested by Kunkle (1962), and by Hewlett and Hibbert (1963}. It would seem likely that a regular decline in discharge would represent the influence of a single process, and that if the flow type were to change, this would probably produce a change in the rate of recession. In order to examine the interpretations of recession flow gained from Figs. 5--7, an attempt has been made to predict outflow discharge for both the field and the laboratory recession.

(a) The laboratory slope recession The laboratory slope drainage experiments have been fully described elsewhere (Anderson and Burt, 1977b) so only a brief description is necessary here. The slope model was saturated and then allowed to drain, outflow discharge being measured, and tensiometers and piezometers being used to ascertain the dimensions of the saturated wedge during drainage. The saturated hydraulic conductivity of the soil was tested in a permeameter (Burt, 1978a) and the unsaturated hydraulic conductivity--soil water potential relationship was derived from a soil column drainage test (Watson, 1966). Table I shows the observed discharge during drainage together with discharge predictions based on Darcy's (1856} law. It should be noted that TABLE I A comparison b e t w e e n observed and predicted discharge for the l a b o r a t o r y slope during drainage

Time Saturated Water table (rain.) cross-sectional slope area (dimensionless) (cm :)

Observed Predicted discharge discharge (cm 3 rain.-') using water table data (cm s min.-' )

Predicted discharge including saturated area above water table (cm s min. -1 )

1 12 24 40 65 90

53.00 32.00 25.00 17.50 10.00 6.00

60.60 38.35 27.82 14.62 11.75 9.71

22.41 19.04 16.24 13.50 10.72 7.77

0.55 0.40 0.33 0.20 0.20 0.20

F r o m A n d e r s o n and Burt (1977b).

47.55 29.38 20.88 10.42 7.80 4.00

98 the suction--moisture curve for the soil indicated that the slope soil desaturated at a tension of 0.6 cm. This meant that the water table was slightly higher than that predicted by the piezometer data. However, whether the "piezometer" or the "corrected" water table measurements are used, both predictions for discharge are very close to the observed. This clearly suggests that the outflow discharge is provided at all times by saturated flow, and is n o t related to unsaturated flow in the latter part of drainage, a result which would have been inferred had Hewlett and Hibbert's interpretation of Fig. 7 been used. The insignificance of unsaturated flow is confirmed by calculations of unsaturated flow in the slope. For example, after 40 min., the predicted unsaturated flow is 0.53 cm 3 min. -1 compared to the observed discharge of 17.50 cm 3 min. -1. Thus at all stages of recession, outflow discharge from the laboratory slope is produced by saturated flow (drainage from the saturated wedge). There is no significant discharge contribution from unsaturated flow during the latter stages of drainage, so that the break of slope on Fig. 7 would appear to be spurious. Similarly, the constancy of process involved puts d o u b t on the change of process which would be inferred if Kunkle's interpretation of the Fig. 6 plot is to be followed.

(b) The field recession Streamflow at Bicknoller Combe is produced entirely by throughflow, except for overland flow occurring during rainstorms. The field recession curve is therefore concerned only with subsurface flow processes since the peak discharge prior to the recession was produced by a delayed throughflow pulse (Anderson and Butt, 1977a). In addition, most of the streamflow originates from hillslope hollows, little being produced on the spurs except during exceptionally saturated conditions (Anderson and Burt, 1978b, c). In order to predict the recession flow for Bicknoller Combe, an attempt has been made to predict flow in one hillslope hollow, with the assumption that this hollow provides a model for catchment drainage as a whole. Unfortunately, in this case there is no observed discharge to compare with the predicted hollow discharge since the hollow outflow occurs over a 50-m channel length and it was not therefore possible to measure the throughflow; the use of throughflow troughs did not provide a meaningful sample of total hollow flow (Burt, 1978b). Predictions of hollow discharge were again based on Darcy's law: the dimensions of the saturated wedge were provided by an automatic tensiometer system (Anderson and Burt, 1977a; Burt, 1978c); the saturated hydraulic conductivity for the field soil was measured using both field and laboratory tests, whilst the unsaturated conductivity---soil water potential relationship was found by running a soil column drainage test in the field. Table II shows predicted hollow discharge for four occasions during the 1976 summer recession [full details of the predictions are provided in Burt (1978b)]. At all stages of drainage saturated flow is the dominant process, which again suggests that Hewlett and Hibbert's interpretation of

99 TABLE II Stream and hollow discharge at Bicknoller Combe during the summer recession of 1976 Date

Stream discharge (1 s-1 )

27.3.76 15.4.76 4.6.76 28.9.76

7.17 1.16 0.294 0.170

Total hollow discharge (1 s-1 )

0.902 0.626 0.150 0.085

Saturated flow in hollow

Percentage unsaturated flow in hollow

(l s')

Unsaturated flow in hollow (l s-')

0.828 0.585 0.134 0.0756

0.0722 0.0414 0.0160 0.0094

8.0 6.5 11.9 11.0

From Burt (1978b). L_

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- -

Stream w i t h weir site

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• Tensiometer site C o n t o u r interval 3m ( d a t u m - n o t c h of weir A)

2"/.3 Date and limit of Saturation Wedge, summer 1976

Fig. 8. The continued existence of saturated conditions in the instrumented hollow at Bicknoller Combe during the summer of 1976.

Figs. 4 a n d 7 is i n c o r r e c t . T h e f a c t t h a t s a t u r a t e d t h r o u g h f l o w r e m a i n s d o m i n a n t a t all stages o f d r a i n a g e is s u p p o r t e d b y Fig. 8 w h i c h s h o w s t h a t a saturated wedge continued to exist in the hollow throughout the summer

100

of 1976, despite the extreme drought conditions prevailing. Since saturated throughflow remains dominant throughout recession, the breaks of slope noted on Figs. 5 and 6 must also be questioned. Such breaks of slope cannot be blindly interpreted as denoting the change from bank storage as the dominant runoff generator, unless there is clear field evidence to support the inference. In the case of the Bicknoller recession, such field evidence is lacking, and indeed no change of process was observed. In fact, the field recession on Fig. 5 is probably better interpreted as a single curve, rather than as two distinct lines, this curve being related to the combined changes in the slope and size of the saturated wedge. At Bicknoller, even at very low flow, runoff is provided by throughflow and no groundwater appears to be involved (which accords with the known impermeable condition of the Devonian Old Red Sandstone bedrock). It is interesting, however, that the k-values for the field recession in Fig. 5 are above 0.9, which would imply, if Barnes' conclusions are followed, that groundwater flow is involved. Thus for the field recession plot in Fig. 5, not only is the break of slope apparent rather than real, but the process label which would normally be applied to the k-exponent is also incorrect. Similarly the break of slope on Fig. 6 appears spurious so that comparisons with Kunkle's conclusions also would be irrelevant. It would seem therefore that inference from graphical plots of recession flow is open to question. The field plots on Figs. 5--7 show that a single flow process can produce clear y e t meaningless breaks of slope on some plots. One should be even more cautious a b o u t applying "labels" to the various lines produced on such plots: without supporting field evidence, the inferences drawn about which flow processes are operating may be quite false. CONCLUSIONS

It is concluded that the runoff processes generating recession flow cannot be inferred from graphical plotting techniques. Some graphical techniques produce breaks of slope, which could then be interpreted as indicating a change in flow characteristics, even though no change of flow process has actually occurred. On the other hand, the semilogarithmic plot (Fig. 5) did correctly predict a single recession line for the laboratory slope drainage, but did n o t provide a single straight line for the field recession, even though it too was generated by a single flow process. There would appear to be no substitute for actual observation of the flow processes involved, and any inference from graphical plots of recession flow must be treated with caution if unsupported by field evidence. The use of recession flow graphs may be very useful for low flow prediction purposes, but their use as indicators of the flow processes operating during recession is probably very limited.

101 REFERENCES Anderson, M.G. and Burt, T.P., 1977a. Automatic monitoring of soil moisture conditions in a hillslope spur and hollow. J. Hydrol., 33: 27--36. Anderson, M.G. and Burt, T.P., 1977b. A laboratory model to investigate the soil moisture conditions on a draining slope. J. Hydrol., 33: 383--390. Anderson, M.G. and Butt, T.P., 1978a. Experimental investigations concerning the topographic control of soil water movement on hillslopes. Z. Geomorphol., Neue Folge, Suppl. Band, 29: 52---63. Anderson, M.G. and Burt, T.P., 1978b. The role of topography in controlling throughflow generation. Earth Surf. Processes, 3: 331--344. Anderson, M.G. and Burt, T.P., 1978c. Toward more detailed field monitoring of variable source areas. Water Resour. Res., 14(6): 1123--1131. Barnes, B.S., 1939. The structure of discharge--recession curves. Trans. Am. Geophys. Union, 20: 721--725. Bleasdale, A., Boulton, A.G., Ineson, J. and Low, F., 1963. Study and assessment of water resources. I.C.E. Syrup. on Water Resources, pp. 121--136. Burt, T.P., 1978a. Three simple and low cost instruments for the measurement of soil moisture properties. Huddersfield Polytechnic, Dep. Geogr., Pap. No. 6, 24 pp. Burt, T.P., 1978b. Runoff processes in a small upland catchment with special reference to the role of hillslope hollows. Ph.D. Thesis, University of Bristol, Bristol. Burt, T.P., 1978c. An automatic fluid scanning switch tensiometer system. Br. Geomorphol. Res. Group, Tech. Bull., No. 21, 30 pp. Darcy, H., 1856. Les fontaines publiques de la ville de Dijon. Dalmont, Paris. Hewlett, J.D. and Hibbert, A.R., 1963. Moisture and energy considerations within a sloping soil mass during drainage. J. Geophys. Res., 64: 1081--1087. Ineson, J. and Downing, R.A., 1964. The groundwater component of river discharge and its relationship to hydrogeology. J. Inst. Water Eng., 18: 519--541. Kunkle, G.R., 1962. The baseflow duration curve, a technique for the study of groundwater discharge from a drainage basin. J. Geophys. Res., 67: 1543--1554. Searcy, J.K., 1959. Flow duration curves. In: Manual of Hydrology; Part II, Low Flow Techniques. U.S. Geol. Surv., Water-Supply Pap. 1542-A, 33 pp. Todd, D.K., 1959. Groundwater Hydrology. Wiley, New York, N.Y., 336 pp. Watson, K.K., 1966. An instantaneous profile method for determining the hydraulic conductivity of unsaturated porous materials. Water Resour. Res., 2 : 709--715.