parameters are calibrated given the infiltration rate calculated at the end of the first
step. For this step, a classical trial-and-error method is used [35]. The conductance
coefficient is automatically calibrated [35] using the horizontal permeability of the
aquifer near the river to calculate the conductance at each river cell [79].
The first step is crucial in our approach, since the second step is conditional to the
aquifer recharge estimated by the first step. Hydrosystem internal water fluxes
estimated by surface–subsurface-coupled models are highly sensitive to recharge
estimation [87], and subsurface parameters are highly sensitive to baseflow estimates
[88, 89], which are correlated with aquifer recharge [90, 91]. Taking into account
these crucial considerations, the core idea of our method is to add a baseflow
estimate to the classical measurements (total river discharge and groundwater levels)
that compose the multi-objective function to be minimised. Baseflow estimations
were calculated directly from observed discharge time series, distributed in 30 gauging stations across the Seine basin [45], with the one parameter recursive digital filter
first proposed by Lyne and Hollick [92] and later improved by Chapman
[93]. Hydrograph separation is based on the estimation of the recession parameter,
which is achieved by fitting the slope of logQ(t) after rainfall events [94].
River discharges are simulated properly by the CaWaQS model over
1993–2010 at various stations of the basin (Table 3). For instance, the Nash
Efficiency [95] at the Paris Austerlitz station reaches 0.9 [45].
4.2 Average Water Budget 1993–2010
The basin is submitted to an average annual precipitation rate of 812 mm a
À1 and
exhibits a large spatial variability according to both distance from the ocean and
elevation, ranging from 595 to 1,370 mm a
À1 (Fig. 4a).
The infiltration rate amounts to 111 mm a
À1 over the whole basin, corresponding
to 56% of the effective rainfall (Fig. 5). In coherence with the spatial distribution of
rainfall, a centripetal gradient is observed, ranging from 181 mm a
À1 on the eastern
Jurassic border to 82 mm a
À1 over the central part of the basin, where an aquifer
system is explicitly simulated (Fig. 4c). Groundwater withdrawals account for 14%
of the total aquifer system recharge, of which 21% is provided by infiltration from
rivers (Fig. 5).
Within the multilayer aquifer system, a dominant downward vertical flux from the
subsurface to the deep chalk aquifer is simulated, 44% of which is redistributed to
the alluvial deposits in the outer portions of the basin (Fig. 5). Supply from aquifers
to rivers appears to be the dominant flow direction along the modelled stream–
aquifer interface (Fig. 6); an exfiltration rate of 140 m
3 s
À1 from aquifers supplies the
river network, while 47 m
3 s
À1 infiltrates the other way around (Fig. 5). On average
the river network drains 10 L
À1 s
À1 km
À1 from the aquifer system [35, 45].
The proportion of the river network that is in a gaining configuration reaches 82%
and would rise to 97% if all water withdrawals in the aquifer system were stopped.
The surface–subsurface functioning is thus significantly altered by the
68
N. Flipo et al.
step. For this step, a classical trial-and-error method is used [35]. The conductance
coefficient is automatically calibrated [35] using the horizontal permeability of the
aquifer near the river to calculate the conductance at each river cell [79].
The first step is crucial in our approach, since the second step is conditional to the
aquifer recharge estimated by the first step. Hydrosystem internal water fluxes
estimated by surface–subsurface-coupled models are highly sensitive to recharge
estimation [87], and subsurface parameters are highly sensitive to baseflow estimates
[88, 89], which are correlated with aquifer recharge [90, 91]. Taking into account
these crucial considerations, the core idea of our method is to add a baseflow
estimate to the classical measurements (total river discharge and groundwater levels)
that compose the multi-objective function to be minimised. Baseflow estimations
were calculated directly from observed discharge time series, distributed in 30 gauging stations across the Seine basin [45], with the one parameter recursive digital filter
first proposed by Lyne and Hollick [92] and later improved by Chapman
[93]. Hydrograph separation is based on the estimation of the recession parameter,
which is achieved by fitting the slope of logQ(t) after rainfall events [94].
River discharges are simulated properly by the CaWaQS model over
1993–2010 at various stations of the basin (Table 3). For instance, the Nash
Efficiency [95] at the Paris Austerlitz station reaches 0.9 [45].
4.2 Average Water Budget 1993–2010
The basin is submitted to an average annual precipitation rate of 812 mm a
À1 and
exhibits a large spatial variability according to both distance from the ocean and
elevation, ranging from 595 to 1,370 mm a
À1 (Fig. 4a).
The infiltration rate amounts to 111 mm a
À1 over the whole basin, corresponding
to 56% of the effective rainfall (Fig. 5). In coherence with the spatial distribution of
rainfall, a centripetal gradient is observed, ranging from 181 mm a
À1 on the eastern
Jurassic border to 82 mm a
À1 over the central part of the basin, where an aquifer
system is explicitly simulated (Fig. 4c). Groundwater withdrawals account for 14%
of the total aquifer system recharge, of which 21% is provided by infiltration from
rivers (Fig. 5).
Within the multilayer aquifer system, a dominant downward vertical flux from the
subsurface to the deep chalk aquifer is simulated, 44% of which is redistributed to
the alluvial deposits in the outer portions of the basin (Fig. 5). Supply from aquifers
to rivers appears to be the dominant flow direction along the modelled stream–
aquifer interface (Fig. 6); an exfiltration rate of 140 m
3 s
À1 from aquifers supplies the
river network, while 47 m
3 s
À1 infiltrates the other way around (Fig. 5). On average
the river network drains 10 L
À1 s
À1 km
À1 from the aquifer system [35, 45].
The proportion of the river network that is in a gaining configuration reaches 82%
and would rise to 97% if all water withdrawals in the aquifer system were stopped.
The surface–subsurface functioning is thus significantly altered by the
68
N. Flipo et al.