Download The effects of climate changes on aquifer storage

Hydrological Sciences -Journal- des Sciences Hydrologiques, 40,5, October 1995
615
The effects of climate changes on aquifer
storage and river baseflow
D. M. COOPER, W. B. WILKINSON &
N. W. ARNELL
Institute of Hydrology, Maclean Building, Crowmarsh Gifford, Wallingford,
Oxfordshire OX10 8BB, UK
Abstract The effects of changes in climate on aquifer storage and
groundwater flow to rivers have been investigated using an idealized
representation of the aquifer/river system. The generalized aquifer/river
model can incorporate spatial variability in aquifer transmissivity and is
applied with parameters characteristic of Chalk and Triassic sandstone
aquifers in the United Kingdom, and is also applicable to other aquifers
elsewhere. The model is run using historical time series of recharge,
estimated from observed rainfall and potential evaporation data, and
with climate inputs perturbed according to a number of climate change
scenarios. Simulations of baseflow suggest large proportional reductions
at low flows from Chalk under high evaporation change scenarios.
Simulated baseflow from the slower responding Triassic sandstone
aquifer shows more uniform and less severe reductions. The change in
hydrological regime is less extreme for the low evaporation change
scenario, but remains significant for the Chalk aquifer.
Effets des modifications climatiques sur la capacité de stockage
des aquifères et le débit de base des rivières
Résumé En utilisant une représentation simplifiée du système
aquifère/rivière, nous avons examiné les effets des modifications climatiques sur la capacité de stockage des aquifères et le débit d'eau souterraine drainé par les rivières. Le modèle aquifère/rivière généralisé
peut intégrer la variabilité spatiale de la transmissivité de l'aquifère et a
été appliqué avec des paramètres caractéristiques du Royaume-Uni, mais
il est applicable à d'autres aquifères n'importe où ailleurs. Le modèle est
exécuté en utilisant une chronique historique de recharge, estimée à partir
de la pluie observée et des données d'évaporation potentielle, et avec des
intrants climatiques perturbés selon un certain nombre de scénarios de
modification climatique. Pour les scénarios où 1'evaporation est
importante, les simulations du débit de base suggèrent que pour l'aquifère
de la craie il y aura une réduction des étiages relativement importantes.
Les débits de base simulés pour l'aquifère du grès triasique, qui répond
plus lentement, montrent des réductions plus uniformes et moins sévères.
Pour les scénarios où l'évaporation est modeste, la modification du
régime hydrologique est moins drastique, mais reste significative en ce
qui concerne l'aquifère de la craie.
INTRODUCTION
Over the past decade there have been many studies examining the potential
effects of global warming on river flows and surface water resources (Arnell,
Open for discussion until I April 1996
616
D. M. Cooper et al.
1994), but very little work has been done on implications for groundwater
resources.
Wilkinson & Cooper (1993) simulated changes in recharge, baseflow and
storage in aquifers having fast, intermediate and slow response characteristics,
identified in the United Kingdom with the Limestone, Triassic sandstone and
Chalk aquifers. In an idealized dimensionless analysis, recharge was assumed
to follow a regular simplified distribution over the period of the year
corresponding to winter in the United Kingdom and the aquifer properties were
taken to be constant throughout aquifer width.
This paper describes further simulations of baseflow and groundwater
storage, using sequences of measured rainfall data to generate recharge
estimates and a groundwater flow model which accounts for variability over
space in aquifer properties. The rainfall sequences are chosen as representative
of those falling in regions of Chalk and Triassic sandstone, the principal
aquifers in the United Kingdom. Use of these data gives a more realistic
estimate of the effects of climate change on baseflows from the two aquifer
types. The method is generally applicable in situations where one-dimensional
saturated flow from a catchment divide to a river gives a good approximation
to groundwater movement.
METHODOLOGY
Assessing the effects of climate change on hydrological systems
Most climate change impact assessments follow a linear approach, feeding
climatic inputs into a system model and comparing system performance with
and without changes in the inputs (Carter et al., 1992). The present study uses
an idealized model of the aquifer/river system, with input climatic series based
on observed climate data and perturbed according to climate change scenarios.
The Chalk and Triassic sandstone cover an extensive area of lowland
England, where they are a major water supply source. Rainfall records to
provide recharge estimates are taken from two locations, the Lambourn
catchment in southern England and the Teme catchment in the English
Midlands representing the respective aquifers. Figure 1 shows the Chalk and
Triassic sandstone aquifers within the United Kingdom, together with the
locations of the two study sites for which data were prepared. Although the
Teme catchment does not include Triassic sandstone outcrops, its rainfall
distribution is typical of those in Triassic sandstone areas.
The aquifer/river model
The idealized aquifer/river system described by Wilkinson & Cooper (1993)
was derived from Oakes & Wilkinson's (1972) schematic representation shown
Effects of climate changes on aquifer storage
617
Fig. 1 The Chalk and Triassic sandstone aquifer outcrops in the United
Kingdom, and the location of the Teme and Lambourn catchments.
in Fig. 2. They used a simple finite difference solution to the groundwater flow
equations to simulate changes in head and boundary fluxes in the aquifer. The
equations were written in terms of dimensionless variables using the assumption
of constant transmissivity, as described in Annex 1 of Wilkinson & Cooper
(1993). Some modifications to this basic model are presented here, with the
intention of providing a rather more realistic, though still idealized,
representation of groundwater processes.
In Wilkinson & Cooper (1993), a scaled transmissivity Ta = T/(SL2)
having units of time"1 was used in the dimensionless analysis, with T the
transmissivity, S the storage coefficient and L the aquifer width. For the
Triassic sandstone aquifer, setting Tto 90 m2 day"1, S to 0.1 and L to 3000 m
gave Ta = 0.0001 day"1. The assumption of constant transmissivity over the
width of the aquifer is believed reasonable for the Triassic sandstone
(Brassington & Walthall, 1985) and has been retained here, with the same
values of Ta used in the dimensionless analysis.
In contrast, the transmissivity of the Chalk in the United Kingdom is
known to be significantly higher nearer rivers than at catchment divides. Birtles
& Morel (1979), for example, found transmissivities between 100 and 5000
m2 day"1 in a Chalk catchment in southern England. This feature can be
approximated in a groundwater model using a function which allows variation
618
D, M. Cooper et al.
$mn
Fig. 2 Schematic aquifer
about the mean transmissivity. The modified dimensionless analysis for a
particular choice of function is shown in the Annex. For the approximation
chosen, the variation is allowed to depend on two parameters: c, the ratio of
the range of transmissivity to the mean transmissivity; and b influencing the
shape of the curve which describes the change in transmissivity between its
maximum value at the river and its minimum at the catchment divide.
Examples of the generated variation in transmissivity are shown in Fig. 3(a)
and (b). In practice, a good estimate of the value of c is likely to be available,
while b may be chosen as some reasonable value based on expert knowledge.
The parameter b is not fundamental, and may be replaced by other shape
parameters if a different pattern of change in transmissivity is thought to be
more realistic.
The effect on simulated baseflow of the variability introduced by using
these two parameters is shown in Fig. 4 for a Chalk type aquifer. For
comparison, three simulated baseflow curves for fixed transmissivity are
shown. The parameter Ta is expressed as Tav in those cases where variable
transmissivity is used. Ta (or Tav) is the mean scaled transmissivity Tmem/(SL2)
where S is the storage coefficient and L is the aquifer width. In the case of
variable transmissivity the maximum and minimum values at the river and
catchment divide are set to 100 and 1000 m2 day-1. Using the mean value of
550 m2 day"1 (compared with Wilkinson & Cooper's (1993) value of
405 m2 day"1), a storage coefficient of 0.015 and aquifer width 3000 m give a
value for Ta (or Tav) of 0.004. In computing these variable transmissivities,
b is set to 8, and c is [1000 - 100]/[0.5 x (1000 + 100)] = 18/11. The
extreme values of scaled transmissivity at the river and catchment divide, 0.007
and 0.0007, correspond to two of the fixed values of Ta selected for
619
Effects of climate changes on aquifer storage
0.0
0.0
River
0.1
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7
0.7
0.8
0.8
0.9
0.9
1.0
1.0
Catchment
Divide
Fig. 3 Shape of transmissivity curve (a) as a function of the shape
parameter b; and (b) as a function of the range parameter c, for b = 8.
?o
Scaled distance (xj)
^,
350
150
200
250
o
Nov
Oct
Time In Days
Fig. 4 Effect on baseflow of using fixed and variable transmissivity for an
idealized Chalk aquifer.
620
D. M. Cooper et al.
comparison in Fig. 4. The recharge used in the simulations shown in Fig. 4 is
the cosine function used by Wilkinson & Cooper (1993).
With the selected representation of variable transmissivity, the simulated
baseflow response to autumn rainfall is more rapid than with transmissivity
fixed at the same mean value. This is due to rapid drainage from the region of
high transmissivity nearer the river. Simulated summer flows are sustained by
the region of lower transmissivity further from the river, but are lower than
those for the fixed mean transmissivity simulation. Note that the percentage
difference at low flows is greater than at high flows although the absolute
difference in flow is less.
Introducing variable transmissivity to the model in the manner suggested
also gives a quite different simulated distribution of stored water in the aquifer
from that found assuming a fixed transmissivity with the same arithmetic mean.
This is demonstrated in Fig. 5(a) and (b) for high and low baseflow conditions.
The simulated effect of high conductivity near the river is to give a relatively
low water table, and a lower storage volume over the whole width of the
catchment.
!a)
Tav = Ta = .004 / day
Fixed transmissivity (Ta)
Variable transmissivity (Tav)-
Tav = Ta = .004 / day
Fixed transmissivity (Ta)
Variable transmissivity (Tav) •-
0.0
River
0.1
0.2
0.3
0.4
0.5
0.6
Scaled distance
0.7
0.8
0.9
1.0
Catchment
divide
Fig. 5 Water table comparison under (a) high baseflow and (b) low
baseflow conditions using fixed and variable transmissivity for an idealized
Chalk aquifer.
Effects of climate changes on aquifer storage
621
Baseline input data
Wilkinson & Cooper (1993) used a cosine function with a periodicity of six
months, peaking on 1 February, to represent the seasonal distribution of aquifer
recharge. The current study used daily time series representative of Chalk and
Triassic sandstone aquifers derived from observed climate data and a simple
soil moisture accounting model.
Thirty-year daily rainfall and potential evaporation sequences for the
baseline period 1951 to 1980 were derived (Arnell & Reynard, 1993) for the
Lambourn (representing Chalk), and the Teme (representing Triassic sandstone)
(Fig. 1). The potential evaporation data were taken from the MORECS data
base (Thompson et al., 1983), extended back to 1951 by regression against
temperature data.
Daily recharge was estimated using a soil moisture accounting model
which assumes a variation in soil moisture capacity across the catchment
(Moore, 1985; Arnell & Reynard, 1993). The soil moisture model parameters
were based on calibrations with observed river flow data for the Lambourn and
Teme catchments. Any rainfall beyond that needed to replenish soil moisture
deficits is assumed either to recharge the underlying aquifer or to generate
surface flow, and it is further assumed for the current study that the ratio of
these volumes remains constant throughout the year. There is also no explicit
allowance for the attenuating effect of the unsaturated zone.
Thirty-year sequences of daily recharge estimates were generated for the
Lambourn and Teme, and estimated average daily recharge calculated to provide
a realistic sequence of daily recharges through the year. Despite this averaging,
the sequence remained highly variable on a daily scale, and was smoothed using
a 60-day weighted moving average. This preserves the seasonal pattern of
recharge while eliminating day to day variability and can be seen as simulating
the averaging effect of water transmission through the unsaturated zone. While
valuable in highlighting the major seasonal variation in the recharge data and
simulated baseflow, this smoothing is not essential to modelling. Running the
model with unsmoothed data simply gives a simulated baseflow response
showing greater daily variability about the main underlying seasonal trend. Note
that the model given by equation (3) in the Annex remains linear since the
variability of transmissivity is independent of head. Thus smoothing, which is
itself a linear operation, has no distorting effect on model behaviour, in the sense
that the smoothing operation may be carried out either before or after running
the model with an identical final result. However, in computing baseflow
duration curves, the thirty-year recharge sequence was used unsmoothed to
ensure that the correct distribution of individual daily data was preserved.
Figures 6(a) and 6(b) compare the idealized recharge sequence used by
Wilkinson & Cooper (1993) with the recharge sequences used in the current
study. The estimated recharge periods for both aquifer types are longer than the
idealized recharge period, which was originally intended to represent recharge
in a region of eastern England which is drier than the two selected study sites.
622
D. M. Cooper et al.
(a)
Recharge period
6 months
—5 months
4 months
o
3
present climate
future climate (low e) future climate (high e) -
T3
12
m 1
(b)
Recharge period
6 months
—
5 months
4 months
o
4-
Kl
•—
E 2
-tpresent climate
future climate (low e)
future climate (high e)
Q
-s 2
o
Jan
150
200
250
300
350
Dec
Time in days from start of recharge period
Fig. 6 Idealized recharge compared with recharge derived from soil
moisture model: (a) Chalk aquifer; and (b) Triassic sandstone aquifer with
present and future climate scenarios.
Climate change scenarios
Two climate change scenarios were used, both based on scenarios produced by
the Climate Change Impacts Review Group (CCIRG, 1991). Table 1 summarizes the scenarios used (Arnell & Reynard, 1993).
The two potential evaporation scenarios make different assumptions about
changes in the meteorological variables affecting evaporation (Arnell &
Reynard, 1993). PE1 was calculated by applying the Penman-Monteith
potential evaporation equation with temperature increased according to Table 1
and the other meteorological variables — humidity, wind speed and radiation
- held constant. PE2 was calculated by assuming changes in these other components at the extreme end of the realistic range, as shown in Table 2.
The scenarios were applied to the 1951 to 1980 daily baseline data to
calculate 30-year rainfall and potential evaporation sequences representative of
average conditions around the year 2050.
Effects of climate changes on aquifer storage
CM
oo m ON
Q
CM " * CM NO
w
OH
CM Tf 00 O
a
CM O CO oo
T3
CD
ON
ON
ON
ON
9
o
u
e
a
o
«a
e
o
a
«n
o
CN
o
;>>
«O
o
o
o
a
S
o
a,
c
a
CO
a
o
6S
c
'3
—i CM
w w
1
a
«
o
43
On OH
&
3
Jm
hum
radi atio
eed
^-'
—
u *
C3 as,
ta ra
o
>D u>
<
3
pi
3
"3 JÏ
c
*-t
a
•3 13
Li
o .§* •a •a
O.
a a
S 1> S 2
o S o o
H 0* CU PH
1
fM]
rt
J J
T3
C
£
623
624
D. M. Cooper et al.
RESULTS
Changes in recharge
The three (one present, two future) annual series of smoothed daily recharge
estimates for the Chalk and Triassic sandstone aquifers are shown in Fig. 6(a)
and (b), expressed in dimensionless form. Assuming that the proportion of
excess rainfall going to recharge remains constant, the percentage change in the
volume of recharge is given in Table 3.
Table 3 Percentage change in annual rainfall, potential evaporation and
recharge
Rainfall
Potential evaporation, PE1
Potential evaporation, PE2
Recharge (rain + PE1)
Recharge (rain + PE2)
Chalk
Triassic sandstone
4
9
29
-2
-21
4
9
30
2
-13
Note that under the "low" évapotranspiration scenario (PE1) annual
recharge is similar to present, but increased rainfall in winter gives increased
winter recharge. Under the other scenario, with higher potential evaporation,
recharge is reduced throughout the year, particularly in autumn: the effect of
the extra winter rainfall is offset by the shorter winter recharge season caused
by longer-lasting soil moisture deficits.
Changes in baseflow and storage
The equilibrium scaled baseflow estimates derived from the present day and
two climate change scenario series, and the percentage change, are shown in
Fig. 7(a) and (b) using the aquifer properties defined above for the Chalk and
Triassic sandstone. The scaling is such that the baseflow estimates are
qx = qlL, where q is the unsealed baseflow defined in the Annex. Note that qx
is only scaled by aquifer length, so Figs 7(a) and 7(b) are directly comparable
for a given aquifer length. The corresponding changes in scaled storage are
shown in Figs 8(a) and 8(b), with storage vx = vS/'L and v as defined in the
Annex. Since S is different for the two aquifers, Figs 8(a) and 8(b) are not
directly comparable.
Figures 7 and 8 show that under the low evaporation PE1 scenario there
is a simulated reduction of up to 15% in baseflow and 10% in storage for the
Chalk aquifer, these values occurring during autumn. Under this scenario,
baseflow and storage are little different from the present day in the Triassic
Effects of climate changes on aquifer storage
(a)
625
Tav = .004 / day
j^^"
~~~<i;;^.
future climate (high e)
>
% §>
_>> £ -20
'5 =o
Ta = .0001 /day
present climate
—
future climate flow e) —
future climate (high e)
(b)
future climate (low e) future climate (high e) -
-60
0
50
100
150
200
250
300
350
Jan
Time In Days
Dec
Fig. 7 Estimated scaled baseflow: (a) Chalk; and (b) Triassic sandstone:
present and future climate scenarios.
sandstone. For the high evaporation PE2 scenario, the Triassic sandstone
aquifer shows a very uniform simulated reduction in baseflow and storage of
around 12% over the year. The simulated baseflow in the Chalk aquifer
remains low longer into the autumn under the climate change scenario, as well
as being lower than under the present climate at all times. This combination of
general effects leads to simulated baseflow reductions of up to 52 % during the
critical period in the early autumn before the main winter recharge begins. This
is also a feature of storage in the Chalk aquifer, where there is a reduction of
up to 45% slightly later in the year.
Another way to represent the effect of climate change on the 30-year
daily sequences of baseflow estimates is through baseflow duration curves, as
shown in Fig. 9(a) and (b). In interpreting these curves, it is important to
recognize that at high flows the river response is likely to be significantly
influenced by a surface or shallow subsurface response: it is only at low flows
that the baseflow duration curves provide a good indication of river flows. In
accord with other evidence presented, the results suggest little change in
baseflow under the low evaporation PE1 scenario for the Triassic aquifer.
D. M. Cooper et al.
626
(a)
Ta = .0001 / day
?
Ë
> 0.04
P^
V,
«"-20-
-60
Tav = .004 / day
present ciimate
—
future climate (low c)
future climate (Iii^'
(b)
future climate (Sow e) future climate (high e) -
-60
0
50
100
150
200
250
300
350
Jan
Time In Days
Dec
Fig. 8 Estimated scaled storage: (a) Chalk; and (b) Triassic sandstone:
present and future climate scenarios.
Under this scenario, the Chalk aquifer shows baseflow reductions of up to 15%
in the 80 to 95% exceedance probability range. In both aquifers there are
notable changes under high evaporation PE2 conditions. For the Triassic
sandstone aquifer, the percentage reduction in baseflow for any exceedance
probability is about 15%. However, because of the rather limited annual range
of baseflow contributions from this aquifer, the baseflow currently exceeded
95% of the time (Q95) would, under the PE2 scenario, be exceeded only 50%
of the time. For the Chalk aquifer, baseflow with a given exceedance
probability is reduced by up to 40%, high values being reached for moderately
high exceedance probabilities. There is, however, less change in the proportion
of time a given baseflow is exceeded because of the greater overall variability
of baseflow contribution for this type of aquifer.
Simulated baseflows with very low exceedance probability occurred
mainly in 1976, when a dry summer followed a dry winter, over which there
was no simulated recharge since rainfall was insufficient to satisfy the simulated
soil moisture deficit. For this particular year, it happened that the realizations
of baseflow for the Chalk aquifer under the present climate and low evap-
Effects of climate changes on aquifer storage
627
1 day flow
0,005
—Î
I
0.002 —~—
o.ooi
I
•
•
——
s
_______
<-
0. i
--—
!.
-
f
•—
-j-..__——~-~—
-——— - - — — — - J —
. — . - ] - - -
5.10.
20. 30.
—
.-......-.-
50.
70. 80.
90.
-
95.
—
.__
99.
99-9
A
0.1
1.
5.
10.
20. 30.
50.
70. 80.
90.
95.
99.
99.9
% of time discharge exceeded
A
A
Rain+PE2
©
©
Rain+PEl
Q
H
Baseline
Fig. 9 Baseflow duration curves: (a) Chalk; and (b) Triassic sandstone:
present and future scenarios.
oration change scenario baseflow were almost identical. This explains the
convergence of the baseflow duration curves in these two cases at very low
exceedance probabilities.
For both aquifer types there is a major change to the flow regime, with
substantial reductions in the magnitude of low river flows. These would almost
certainly have amenity and water supply implications.
628
D. M. Cooper et al.
Transient change in groundwater storage between 1980 and 2050
The transient change in storage at the year's end following gradual climate
change is shown in Fig 10. It is assumed that the daily rainfall and evaporation
figures change linearly between their mean values over the 70-year period of
climate change from 1980 to 2050. There is little lag in the response of aquifer
storage to the simulated changing recharge over the period. Assuming no
climate change beyond 2050, an equilibrium storage is achieved immediately
for the Chalk aquifer. However, it takes 30 years for the Triassic sandstone to
reach an equilibrium storage. In their earlier paper, Wilkinson & Cooper
(1993) considered an equivalent change in annual recharge over a 30-year
rather than a 70-year period, and in this case there was a delay of around 40
years in the achievement of equilibrium storage for a Triassic sandstone
aquifer. Under the slower climate change scenario, therefore, the response of
the Triassic sandstone aquifer is somewhat less delayed, but it remains true that
equilibrium is not maintained.
E = time of attainment of equilibrium
'£
-
c
E
"E
Triassic Sow e
\
Triassic high e
j
Chalk
low e
Chalk
high e
\
E
.
2
4
7
E
\
10
,
1
20
40
I
1
70 100
L_
200
Years (log scale)
Fig. 10 Evolution of aquifer storage following 70 years' climate change,
showing times to equilibrium (3 sig. figs).
CONCLUSIONS
This paper has investigated the effects of global warming on groundwater
recharge, storage and river basefiow, using an idealized representation of the
aquifer/river system and parameters typical of fast and slow response aquifers
in a temperate climate in western Europe. The main conclusions are:
(a)
Low evaporation climate change scenarios are likely to give little change
in recharge of the Triassic sandstone aquifer, and small but significant
changes for the Chalk aquifer. Under high evaporation change scenarios
there are significant reductions in recharge for both aquifers.
Effects of climate changes on aquifer storage
629
(b)
For the Triassic sandstone aquifer, both storage and river baseflow are
little affected by the scenario with a relatively modest increase in
evaporation. This scenario does, however, give reductions in baseflow
and storage of up to 15% and 10% respectively in autumn for the Chalk
aquifer. Under a high evaporation scenario the timing of maximum
baseflow and storage is not significantly changed in the Chalk aquifer,
but minimum values occur two to four weeks later in the autumn, with
reductions of around 55% and 40% from their present climate values.
For the Triassic sandstone aquifer, baseflow and storage are uniformly
reduced by around 12% from present-day values.
(c)
Under the high evaporation scenario, simulated baseflow with a given
exceedance probability is reduced by up to 40% in the Chalk aquifer,
and by around 15% for the Triassic sandstone aquifer. This reduction in
low river flows has serious potential implications for users abstracting
water directly from the river, aquatic ecosystems and the amenity value
of the river environment.
(d) Assuming a 70-year transient change in climate under a high evaporation
scenario, the Chalk aquifer responds quickly enough to maintain
equilibrium, while the Triassic sandstone aquifer is unable to maintain
equilibrium and does not regain a steady state until 30 years after the end
of the climate change period.
The idealized aquifer/river system model can readily be applied to other
aquifers and in other climatic regimes, given appropriate values of model
parameters, and provides a valuable tool for water resources impact
assessment.
REFERENCES
Arnell, N. W. (1994) Hydrology and climate change. In: The Rivers Handbook, ed. P. Calow & G. E.
Petts. Vol. 2, 173-185. Blackwell, Oxford, UK.
Arnell, N. W. & Reynard, N. S. (1993) Impact of climate change on river flow regimes in the United
Kingdom. Report to Department of the Environment. Institute of Hydrology, Wallingford, UK.
Birtles, A. B. & Morel, E. H. (1979) Calculation of aquifer parameters from sparse data. Wat. Resour.
Res., 15(4), 832-847.
Brassington, F. C. & Walthall, S. (1985) Field techniques using borehole packers in hydrogeological
investigations. Quart. J. Eng. Geol. 18, 181-193.
Carter, T. R., Parry, M. L., Nishioka, S. & Harasawa, H. (1992) Preliminary Guidelines for Assessing
Impacts of Climate Change. Intergovernmental Panel on Climate Change Working Group II.
Environmental Change Unit and Center for Global Environmental Research, University of Oxford,
Oxford, UK.
CCIRG (Climate Change Impacts Review Group) (1991) The Potential Effects of Climate Change in the
United Kingdom. HMSO, London, UK.
Moore, R. J. (1985) The probability-distributed principle and runoff production at point and basin scales.
Hydrol. Sci. J. 30, 263-297.
Oakes, D. B. & Wilkinson, W. B. (1972) Modelling of Groundwater and Surface Water Systems. I Theoretical Relationships Between Groundwater Abstraction and Base Flow. Water Resources
Board, Reading, UK.
Thompson, N., Barrie, I. A. & Ayles, M. (1981) The Meteorological Office Rainfall and Evaporation
Calculation System (MORECS). Hydrological Memorandum no. 45, Meteorological Office 8,
Bracknell, UK.
Wilkinson, W. B. & Cooper, D. M. (1993) The response of idealised aquifer/river systems to climate
change. Hydrol. Sci. J. 38(5), 379-390.
630
D. M. Cooper et al.
ANNEX
The aquifer/river model
The continuity equation and Darcy's Law in one dimension for spatially
variable transmissivity may be written:
,dh
S^l = ^ + r
dx
(1)
dh
q = T(x)
dx
where S is the storage coefficient (dimensionless), T(x) is transmissivity (l21"1)
and r is recharge (11"1).
Combining these equations gives:
, dh
dT(x) K, dh
™ . d2h
i— = — — x — + T(x)
+r
dt
dx
dx
dx2
The variable transmissivity is assumed to be expressible as:
(2)
T(x) = r mean (l + c x g(x;b))
where the maximum value of transmissivity, at the river, is r max , and the
minimum r min with Tmean = (r max + r min )/2. The parameter c is
(^max — ^min)^mean' m e range of transmissivities divided by the mean. The
function g(x;b), with shape parameter b, must be chosen as 0.5 at the river,
decreasing to - 0 . 5 at the catchment divide and with mean value zero. WithL
defined as aquifer length, then following transformation to dimensionless
variables:
x1 = xlL; hx = hSII; r = TaXt; rx = r/(TaXl);
g^x^b)
= g(x;b)
with Ta = Tmem/(SL2) and / = total annual recharge, equation (2) becomes:
dh,M
_i =
dh, r
d h,
cXg[(xl;b)-±+\lHcXg1(xi;b))\—±+r1
(3)
dr
dx,
i i . o
dx
x
n
Note that this reduces to the case for constant transmissivity when c is
zero. The boundary conditions for this equation are:
(h)x,
/
=0
dhx
=0
dxx
r > 0
(4)
r > 0
A suitable choice of function gi(xx;b) is:
gfcvb) =
1
l+e'm
l-e
-bl2
v
l-e
1+
b(xrl/2)
(5)
b(x,-l/2)
Effects of climate changes on aquifer storage
In recomputing untransformed baseflow and aquifer storage per
width of aquifer from the dimensionless equations, the relationships used
q = I.L.Ta[l +cxgx{xx;b)] x (dhl/dxl)x
h^dix^.I.LIS
(i2)
Received 14 October 1994; accepted 20 March 1995
(l2 t_1)