FRIEND: Flow Regimes from International Experimental and Network Data (Proceedings of the Braunschweig
Conference, October 1993). IAHS Publ. no. 2 2 1 , 1994.
Studying storage behaviour using an operational
recession method
S. DEMUTH & P. SCHREffiER
Department of Hydrology, University of Freiburg, Werderring 4, D-79085
Freiburg, Germany
Abstract This paper presents the application of an operational recession
method developed in the FRIEND project in which a simple linear
exponential model has been adopted to describe baseflow recession. The
variability of recession behaviour in space and time has been investigated
on different geological and pedological conditions in the southwest of
Germany. Comparisons of the seasonal variation in recession behaviour
indicates a steeper recession in summer compared with the winter. This
is due to evaporation losses in summer and the influence of a snow melt
component affecting recharge conditions. Since the summer recession
behaviour for different data periods was not significantly different, the
operational method can be considered to be robust. Finally, the model
parameters were linked to geology and a classification according to
chronological geological units showed only small variations.
INTRODUCTION
In the last decades the hydrological behaviour of flow regimes have changed due to
human impact and climate variability. As a result, numerous droughts occurred in
Western Europe. In the FRIEND project a model has been developed to describe baseflow due to dry weather conditions. The model has first been applied and tested on a
Small Research Basin data set covering Western Europe (Demuth, 1989). In the current
study the model has been modified and its robustness will be tested on 30 catchments in
the southwest of Germany.
The information about storage behaviour of an aquifer can be obtained by recession
analysis (Knisel, 1963; Weyer & Karrenberg, 1970; Einsele, 1978; Pereira & Keller,
1982; Gustard et al., 1989; Tallaksen, 1991; Demuth, 1994). The mathematical
description of flow in an aquifer is usually based on the Depuit Boussinesq equation.
This differential equation can be solved by a simple exponential or an hyperbolic
function. Maillet (1905) first described the depletion of river flow by a simple
exponential model with the starting point and the depletion constant as parameters.
Later, detailed investigations followed based on an exponential approach including
additional reservoirs (Barnes, 1939). Kunkel (1962) and Singh & Stall (1971) for
example, applied parallel reservoir models with different initial discharges and different
depletion constants. Applying recession analysis to several parallel reservoirs in a
catchment has the advantage of producing better fits than using a single exponential
model. However, it is difficult to identify the parameters in a multiple exponential model
in an objective way. There are, for example, several ways of defining initial discharges
and depletion constants (Reed & Warne, 1985; Zecharias & Brutsaert, 1988; Tallaksen,
1991; Demuth, 1994).
52
S. Demuth & P. Schreiber
The study area is situated in the southern part of the Federal Republic of Germany.
The data for the various investigations were extracted from the European Water Archive
with 207 gauging stations in total for the whole country. From these stations 30
catchments were selected to investigate the model behaviour in more detail. They are
mostly located in the mountainous areas of the southern Black Forest, the Allgâuer and
Bavarian Alpine foreland, the Bavarian Forest and the "Fichtelgebirge'7 Franconian
Forest. In addition, about 100 stations with 20 years of record have been extracted to
describe the variation of the parameters of the master recession curve due to different
geological conditions.
THE OPERATIONAL RECESSION METHOD
The falling limb of the hydrograph represents the diminishing discharge from storage
in the absence of further rainfall. The parameter characterizing the recession curve can
be obtained by fitting an equation. When comparing catchments, the hyperbolic or the
simple exponential function are preferable, since each has only one parameter (Toebes
& Strang, 1964). In this study it is intended to compare baseflow recession from stations
situated mainly in the county of Baden Wuerttemberg (southwest Germany) and therefore a simple exponential model was chosen. The baseflow recession can be expressed
mathematically by a simple exponential equation of the form:
Q, = QQ.exp(-at)
(1)
where:
Qt discharge after timer [m3 s"1],
<2o initial discharge at start of period at time t0 [m3 s"1], and
a depletion coefficient [day"1].
By convention, the baseflow recession constant exp(-a) is replaced by K. An
alternative to the recession constant is the half-life t05 which is the time taken by the
streamflow to fall to half its initial value. The half-life has an advantage of having a
physical meaning. Before the recession parameters were calculated the recession limbs
were selected according to defined selection criteria. To characterize the mean storage
behaviour of an aquifer, many baseflow recession limbs have to be examined. In
addition, a comparison of single recession events between different river catchments is
not convenient. The current operational recession model scans through the hydrograph
of time series data extracting only suitable recession limbs and then calculates a master
baseflow recession curve for any given river catchment. By simply averaging the
depletion coefficient "a" and the initial discharge Q0 from each recession limb, a master
baseflow recession curve could be constructed for each catchment. The number of
analysed recession limbs varied considerably (between 4 and 163 segments). The
computations were carried out separately for the different seasons. The flow chart of the
recession program is shown in Fig. 1.
THE EFFECT OF SEASON AND TIME ON THE MODEL PARAMETERS
The effect of the season on the recession curve has been described by several authors
Studying storage behaviour using an operational recession method
53
Calculating mean flow
of whole period MQ
Select seasonr
Summer = May to September
January to April and
Winter
October to September
one day time step
t = t + 1
Q(ti) < MQ ?
yes
Qltj) > Q ( t 2 ) >Q(t 3 ) and
0(t„>t3) * 6(t n + 1 )
Q(tn)
Q(tn+2)
or:
Q(tn)
n+2
S^
Ï
Q( n+2)
fc
Q(tn+1)
and
Q < t n + 1 ) and
Q ( t n + 1 ) and
Q(tn)
?
jryes
Q(tr
i) = (QlO+Qtt,, >))/2
tyes
Regression:
y = a In Q(t)
Qo
t = t end
Arithmetic Mean of
Q Q and «-values over
unique length of
depletion curves
Arithmetic mean over
all Q Q - and «-values
Fig. 1 Operational baseflow recession programme.
(Croft, 1948; Knisel, 1963; Singh & Stall, 1971; Ferderer, 1973; Gripp, 1977; Ando
et al., 1986). The climatic conditions in southern Germany, with temperatures near 0°C
in winter and the frequent change of freezing and melting often disturbs the real baseflow from aquifers. The comparison of summer and winter recessions shows higher
mean half-lives (steeper recession curves) in summer. The differences in half-lives
between the summer and winter season is, in general, 5 days. The catchments with
greater differences are situated in the mountainous areas of the Bavarian Alps which are
influenced by melting and freezing. Therefore, in this study, the summer recession was
considered in more detail.
To examine the influence of the time of record on the depletion coefficient and the
half-life of the baseflow master recession curve, the time series of the hydrograph from
1940 to 1970 has been split up into decades. For each decade the model parameters
S. Demuth & P. Schreiber
54
(half-life) were calculated and analysed. The individual mean runoff for the selected
decades was not significantly different from the mean runoff of the entire record from
1940 to 1979.
Figure 2 illustrates the deviations of the mean half-lives for the individual decades
from 1940-1949, 1950-1959,1960-1969 and from 1970-1979 from the mean half-lives
computed for the entire record. The deviations are generally small in magnitude. For
some stations, for example Gutach 1960-1969, the differences in the half-lives for the
individual decades (summer seasons) are less than two days, and as such do not appear
in the figures.
In the summer seasons, 22 catchments (about 75% of the total) have deviations in
T940-49
Wertach
SS3
1950-59
Geitnach
1960-69
Osterach
gffl
1970-79
Grower Regen
Wei^er Main
Fig. 2 Deviations of the mean half-lives for individual decades with mean half-lives for
the whole of the period (summer seasons).
Studying storage behaviour using an operational recession method
55
half-lives from the long-term period (1940-1979) of less than four days. Four catchments
(12.5%) show deviations in half-lives between 4-6 days. A further four catchments
(12.5%) show deviations of more than 6 days. Significant differences in the average
half-lives for the summer seasons can be identified for the stations: Ramsauer Ache
(Alps), Isar (Alps), Ellbach (Alps), Ammer (Alps), GroBe Vils, Baunach, Reiche
Ebrach, and Pfinz (Black Forest).
In 23 catchments the average half-lives for the decade 1970-1979 are higher than the
overall average of the 40-year period (Table 1). Higher half-lives are detected, if the
catchment drains through narrow cavities in the subsoil, and, if at the same time, other
factors such as evaporation play a minor role. The comparison of deviations in half-lives
of the different decades with the period of record, shows that the decade from 1970-1979
was on average relatively dry. Therefore, this decade reflects in general the real master
recession curve. For the decades from 1950-1959 and 1960-1969 the same number of
catchments fall approximately below the average half-life as above it. The recession
behaviour of these decades differs only to a minor extent from the recession behaviour
for the entire period. The decade from 1940-1949 contrasts with the decade from 19701979 and shows for the summer seasons lower average half-lives than the long-term
average. Here 66% of catchments show average half-lives below the half-life of the
overall period and 33 % of catchments lie above.
The investigation of the effects of the different decades on the half-life of the baseflow master recession curve showed that master recession curves do not regularly differ
between individual decades. Just for the summer seasons, deviations of less than four
days can be found in nearly 75 % of the catchments. Thus, it can generally be concluded
that the method to determine the master recession curve for the summer seasons is
relatively robust towards the selected decade and provides constant values.
Table 1 Number of average decade half-lives, which are higher or lower than the 40-year average of the
half-lives.
Summer seasons:
lower than t05
higher than t05
1940-1949
1950-1959
1960-1969
1970-1979
19
10
17
13
12
17
7
23
EFFECT OF GEOLOGY ON MODEL PARAMETERS
The storage capacity of a catchment depends in particular on geology and soils. In
general, catchments with a high storage capacity show shallow recession curves resulting
in low depletion coefficients and long half-lives. Catchments with low retention capacity
will give steep recession curves with high depletion coefficients and shorter half-lives.
Weyer (1972), Einsele (1978) and Toussaint (1981) studied the relationship between
geology and the parameters of the master recession curve. Weyer computed the depletion coefficient for different springs in the Rhenanian slate mountains (Schiefergebirge).
The calculations were based on measurements of spring capacities from August to
September in 1959 by applying a linear exponential model. The determined depletion
56
S. Demuth & P. Schreiber
coefficients vary between 0.00334 and 0.02055 day 1 (corresponding half-lives between
27 and 207 days). Toussaint analysed the dry weather year 1976 for 114 Hessian river
catchments. He assigned these catchments to hydrogeological defined regions. For siltstone he determined half-lives less than 7 days, for crystalline bed-rock the values lay
between 5 and 7 days and for effusive rock between 6 and 9 days. For sandstone he
computed half-lives of about 10 days and for carbonate rocks of about 15 days. Einsele
summarized the research work of several authors whose studies were not only carried
out for seasons in single years, but also considered two or more dry weather years. The
half-lives found by Einsele occur in a wide range. The values for sand and gravel lie
between 35 and 150 days, for sandstone between 9 and 120 days and for karst limestone
as well as for the dolomite formation between 9 and 120 days.
In this paper the results of a detailed study of the relationship between geology and
the depletion coefficient will be presented, based on 98 river catchments situated mainly
in southern Germany. The computation of the recession constant was carried out
according to the introduced model for a time period with a minimum of 20 years. To
determine the influence of geology on the recession constant, an assignment and
chronological-geological classification of the recession constants was constructed. The
result of this calculation for the summer seasons is summarized in Table 2.
Mean half-lives up to 35 days (a < 0.0198 day"1) exist for Keuper (Ammer) and
Coquina (Leutasch). Both catchments are situated in the Bavarian Alps. Average halflives less than 10 days (a = -0.1386 day"1) were derived in the crystalline of the Black
Forest, in the Tertiary of the Alpine foreland and on the Swabian Alb and Franconian
Alb. The Devonian of the Rhenanian "Slate mountains" and Fichtelgebirge also show
average half-lives less than 10 days. All these catchments have aquifers on fissured
rocks, showing relatively high coefficients of conductivity (between 10"5 to 10"7 m s"1)
resulting in quick depletion.
Figure 3 demonstrates that most half-lives are between 10 and 20 days. An exception
is Coquina, which is the only chronological-geological group value above 30 days and
thus stands out of the scheme. However, this could be due to a small sample of only two
river catchments. Again when comparing the mean half-lives of each group only
Coquina stands out of the scheme. (The average was computed using the depletion
coefficients and not the half-lives.) The other chronological-geological groups have
Table 2 Mean range of half-lives of different chronological-geological groups (98 catchments).
Geology
Plutonic rocks
Metamorphic rocks
Devonian
Carboniferous
New Red Sandstone
Coquina
Keuper
Jurassic
Cretaceous
Tertiary
Quaternary
Half-lives (days)
from
to
mean
9
8
8
9
7
31
5
8
8
6
8
18
19
20
18
26
35
35
30
31
21
24
13
11
11
12
14
33
14
13
13
10
13
57
Studying storage behaviour using an operatiotial recession method
O GEO \
Plutonic rocks
\
O;
Metamorphic rocks
\
Oj O C
\
Carboniferous
oi
<aémto
Q
o oo
o !
....
o c p o çOOO
Red Sandstone
|0K» 0
|o
Coquina
Jurassic rocks
Cretaceous
Tertiary
Quaternary
©
! OCffiffip «S ;
;
iO O
o
o I
poo
bo
oi
o
o-
Keuper
|
©
O ! O
Oi
o «BO
CD OD0( DOO p
10
15
O
20
Mean h a l f - l i v e s
i
i
j
25
30
35
40
[d]
Fig. 3 Relationship between mean half-lives and chronological-geological groups.
mean values between 10 and 15 days (a = 0.0462-0.0693 day*1). The range should
make it possible to differentiate between chronological-geological groups. Plutonic,
Metamorphic, Devonian, Carboniferous and Tertiary rocks show mean half-life ranges
of about 10 days. Quaternary and Jurassic rocks have a mid-position with ranges from
15 to 22 days. Above them lie the ranges of Cretaceous rocks with 23 days, and Keuper
with 30 days.
A comparison between the average half-lives presented by Weyer and the values
derived in this study is not possible, because Weyer's values are based on single
measurements. Although Toussaint considered only short-term investigations, the
requirements for a comparison are given. He used comparable starting values to select
the master recession curves and computed the parameters with an exponential model.
The average depletion coefficients of the dry weather year 1976 vary only slightly from
the long-term mean depletion coefficients. The results of Toussaint's differentiation,
according to geology, show a different pattern. He also could not find a significant
difference for the depletion coefficients on different rock types. The half-lives published
by Einsele were all higher. The very wide ranges in half-lives could not be proved
although the study is based on a larger sample size. On the contrary, the results of this
study showed that deviations of the storage-term over many years reduce the ranges.
58
S. Demuth & P. Schreiber
SUMMARY
The computation of the master recession curve was based on an exponential model often
applied in hydrology. The parameters of the baseflow recession curve were calculated
for each catchment by fitting a simple linear regression model to the log-transformed
flow data. Investigating the influence of different threshold values of the baseflow
master recession curve did not indicate the participation of a fast component (direct
runoff). The selection of the average long-termflowas a threshold was considered satisfactory. The examination of the effect of different decades on the recession half-life
showed that the master recession curves do not regularly differ for the single decades.
Nearly 75% of the catchments had, for the summer seasons, deviations of less than 4
days compared to the entire period from 1940 to 1979. Thus, it can generally be concluded that the method to determine the master recession curve for the summer seasons
is relatively robust towards the selected decade and therefore provides constant values.
Many authors established great inconsistencies in the storage behaviour due to
different geological units, which could not be proved in this study. The investigations
outlined in this paper showed that inconsistencies in the storage term over a long period
resulted in small ranges. Fissured rocks showed a smaller range of half-lives than
alluvium (porous aquifers). A clear criterion to differentiate geology using mean
depletion coefficients could not be developed.
Acknowledgements The research presented in this paper was carried out as a part of the
German contribution to the FRIEND (Flow Regimes from International Experimental
and Network Data) project. Support was given by the National Committee of the Federal
Republic of Germany for the International Hydrological Programme (IHP). The authors
would like to thank the members of the FRIEND Low Flow Group for their many
valuable discussions.
REFERENCES
Ando, Y., Takahasi, Y., Ito,T. & I t o , K. (1986) Regionalization of parameters by basin geology for use in a groundwater
runoff recession equation. In: Conjunctive Water Use (Proc. Budapest Symp., July 1986), 151-159. IAHS Publ. no.
156.
Barnes, B. F. (1939) The structure of discharge-recession curves. Trans. Am. Geophys. Un., Reports and Papers,
Hydrology.
Croft, J. F. (1948) Water loss by stream surface evaporation and transpiration by riparian vegetation. Trans. Am. Geophys.
Un. 29(2), 235-239.
Demuth, S. (1989) The application of the West German IHP recommendations for the analysis of data from small research
basins. In: FRIENDS in Hydrology (Proc. Bolkesja Symp., April 1989), 47-60. IAHS Publ. no. 187.
Demuth, S. (1993) Untersuchungenzum Niedrigwasser in West-Europa (Low flow Studies in Western Europe). Freiburger
Schriftenzur Hydrologie, Bd. 1 (in press).
Einsele, G. (1978) Neubildung und Abfluss von Grundwasser in verschiedenen geologisch definierten Landschaftstypen.
DVWK10, Hydrologie Fortbildungs-kurs, Vortrag 13, Karlsruhe.
Fédérer, C. A. (1973) Forest transpiration greatly speeds streamflow recession. Wat. Resour.Res.
9(6), 1599-1604.
Gripp, H. (1977) Recession — en tidsinvariant process? (Recession - a time variant process?). Varmet i Norden 10(2),
50-53.
Gustard, A., Roald, L. A., Demuth, S., Lumadjeng, H. S., Gross, R. & Arnell, R. (1989) Flow Regimefrom Experimental
and Network Data: vol. I, Hydrological Studies. Instituteof Hydrology, Wallingford, Oxfordshire, UK.
Knisel.W. G. (1963) Baseflow recession analysis for comparison of drainage basinsand geology./. Geophys. Res. 68 (12).
3649-3653.
Studying storage behaviour using an operational recession
method
59
Kunkel, G. R. (1962) The baseflow duration curve, a technique for the study of groundwater discharge from a drainage
basin./. Geophys. Res. 67, 1543-1554.
Maillet, E. (1905) Mécanique et physique du globe - Essais d'hydraulique souterraine et fluviale. Libraire Scientifique,
A. Herman, Paris.
Pereira, L. S. & Keller, H. M. (1982) Factors affecting recession parameters and flow components in eleven small Pre-Alp
basins. In: Hydrological Aspects ofAlpine and High Mountain Areas (Ptoc. Exeter Symp., July 1982), 233-242. IAHS
Publ. no. 138.
Reed, D. W. & Warne, D. W. (1985) Low flow forecasting» aid regulation of the river Wye. Report to Welsh Water South
Eastern Division.
Singh, K. P. & Stall, J. B. (197 l)Derivationofbaseflowrecessioncurves and parameters. Wat. Resour.Res. 7(2), 292-303.
Tallaksen, L. M. (1991) Recession rate and variability with special emphasis upon the influence of évapotranspiration.
Rapportserie: Hydrologi. Universitetet i Oslo, Rapport Nr. 25.
Toebes, C. & Strang, D. D. (1964) On recession curves. 1 - Recession equations. / . Hydrol. (NZ) 3(2), 2-15.
Weyer, K. U. & Karrenberg, H. (1970) Influence of fractured rocks on the recession curve in limited catchment areas in
hill country: A result of regional research and a first evaluation of runoff at hydrogeological experimental basins. J.
Hydrol. (NZ) 9(2), 177-191.
Weyer, K. U. (1972) Ermittlung der Grundwassermengen in den Festgesteinen der Mittel-gebirge aus Messungen des
Trockenwetterabfiusses. PhD Thesis, Universitat Bonn.
Zecharias, Y. B. & Brutsaert, W. (1988) Recession characteristics of groundwater outflow and baseflow from mountainous
watersheds. Wat. Resour. Res. 24(10), 1651-1658.