Groundwater flow modelling in the central zone of Hanoi, Vietnam

in the Holocene aquifers located in the modelled area (corresponding tests located on Fig. 8) Pumping test K (m/s) TD7k 3 E-04 CD10-1 2 E-04 54e 1 E-04 44c 2 E-04 T37 2 E-04 VC 6 E-04 Hydrogeology Journal DOI 10.1007/s10040-008-0423-x Method Conceptual model The sedimentological heterogeneity of the studied area discussed in the introduction, as well as the awaited occurrence of significant vertical flow components (inter- actions between aquifers, drawdown caused by pumping wells), require a three-dimensional simulation of the groundwater flows. The lateral boundary of the study area is divided up into four sections (Fig. 4). Geometrically, it corresponds to the following boundaries and boundary conditions (in a clockwise direction) starting from north. The Red River boundary from north to east, corresponding to a prescribed piezometric head (Dirichlet condition). The corresponding water levels are those of the Red River, which are measured monthly at three stations (Fig. 3). The location of these stations leads to two possibilities for defining the Red River boundary condition. The first one considers the measurements given by stations PSH2 and PSH4. The observed values provided by the SD-THcat station are transferred to an intermediate point, equidistant from the two others. The variation of the water levels between two consecutive measuring points is considered as linear. The second way of defining the Red River boundary condition takes only into account the results given by the PSH2 and PSH4 measuring stations. The possible justification of this choice mainly comes from the location of the SD-THcat Table 2 Interpreted storage coefficient (S) values for the pumping tests carried out in depth-averaged conditions in the Holocene aquifers located in the modelled area (corresponding tests located on Fig. 8) Pumping test S (-) 54e 1.0 E-01 TD7k 1.2 E-01 CD10-1 3 E-02 44c 3 E-02 VC 1.7 E-01 Table 3 Interpreted hydraulic conductivity (K) values for the pu- mping tests carried out in depth-averaged conditions in the Pleis- tocene aquifer located in the modelled area (corresponding tests located on Fig. 8) Pumping test K (m/s) CD17 5 E-04 CD15 7 E-04 10aNSL 5 E-04 TD13 4 E-04 TD7 6 E-04 LY9 8 E-04 MD10 4 E-04 TD4 7 E-04 TD8 7 E-04 18aYP-TD 3 E-04 54TD 3 E-04 H36YP 6 E-04 H42YP 8 E-04 TDCD9 8 E-04 TDCD13 7 E-04 TDCD17 3 E-04 H31 5 E-04 CD10 4 E-04 CD12 7 E-04 813 3 E-04 46TD 2 E-04 50TD 3 E-04 48TD 2 E-04 TD3 5 E-04 5DT 4 E-04 LY6A 6 E-04 45TD 3 E-04 44c 2 E-04 Table 4 Interpreted storage coefficients (S) for the pumping tests carried out in depth-averaged conditions in the Pleistocene aquifer covered by Holocene sediments Pumping test S (-) 1 1 E-03 2 2 E-01 3 3 E-04 4 3 E-02 5 3 E-03 6 3 E-03 7 4 E-05 8 6 E-02 9 2 E-02 10 2 E-02 11 4 E-04 12 4 E-03 13 7 E-02 14 5 E-02 15 2 E-02 16 9 E-03 17 7 E-02 18 4 E-05 19 3 E-03 The number of the pumping test is indicative. The tests have been carried out throughout the province of Hanoi Table 5 Interpreted storage coefficients (S) for the pumping tests carried out in depth-averaged conditions in the outcropping Pleistocene aquifer Pumping test S (-) 1 2 E-01 2 3 E-03 3 1 E-03 4 2 E-01 5 2 E-01 6 2 E-01 7 2 E-01 8 2 E-01 9 2 E-01 10 2 E-01 11 2 E-01 12 2 E-01 13 2 E-01 14 2 E-01 15 2 E-01 16 6 E-02 17 1 E-02 The number of the pumping test is indicative. The tests have been carried out throughout the province of Hanoi Hydrogeology Journal DOI 10.1007/s10040-008-0423-x station, close to the Duong River providing a measure- ment which could significantly differ from actual water levels in the Red River. For this second possibility, the measurements at PSH2 are directly allocated to the northwestern extremity of the Red River boundary. The observed values at PSH4 are “corrected” as a function of the mean gradient in the Red River before being imposed on the southeastern extremity of the boundary. On the south boundary, a prescribed head (Dirichlet condition) is defined in every point of the Pleistocene and Holocene aquifer deposits cut by this boundary. The prescribed heads are provided by the piezometric time series from the P37, P36, P39, P38, Q64, P12, P8, Q63 and P9 observation wells, located at each extremity of the segments forming the south boundary. A prescribed impervious boundary (Neumann condition) is chosen, on the other hand, where the south boundary cuts less permeable silty clayey sediments. On the west boundary-south section, a prescribed piezometric head is chosen and defined with the help of the piezometric chronicles related to the P9 observation well. Because the geometry of the south section of this west boundary is designed in a way to approach an equipotential line close to the Mai Dich pumping field (Fig. 5), the groundwater level imposed is the same in every point of this section. The west boundary-north section is oriented perpen- dicularly to the Red River and to expected equipotential lines related to the Mai Dich pumping drawdown cone. A zero-flux condition can thus reasonably be chosen for this section. This Neumann condition is interrupted at the P21a well (located on the boundary), where a Dirichlet condition is imposed. The lower boundary of the model corresponds to the basis of the Quaternary sediments. A null flux (Neumann condition) is imposed in every point because the underlying Tertiary shales (Jusseret et al., as previously given, “The stratigraphical architecture of the Quaternary deposits as support for hydrogeological mod- elling of the central area of Hanoi (Vietnam)”, unpub- lished report, 2008) are expected to have a very low permeability. The upper boundary condition will be discussed later, together with the conceptual choices related to the source and sink terms. The combination of the sedimentological data (Jusseret et al., as previously given, “The stratigraphical architec- ture of the Quaternary deposits as support for hydro- geological modelling of the central area of Hanoi (Vietnam)”, unpublished report, 2008) and the results of pumping tests are particularly useful to estimate the parameter values and spatial distribution of hydrogeolog- ical units (see Fogg et al. 1998; Foreman and Sharp 1981 and McCloskey and Finnemore 1996 for similar approaches). Table 6 Mean rates pumped in the Pleistocene aquifer by the well fields located in the modelled area. The main fields (see Fig. 5) are indicated in capitals. All rates refer to a date after 2000 Pumping fields Mean pumping rates (m3/day) CAO DINH 29,997 Don Thuy 7,700 LONG YEN 36,756 MAI DICH 15,800 NGOC HA 44,410 NGO SI LIEN 49,368 YEN PHU 87,488 Thuy Loi 500 Van Don 5,200 Phuc Tan 3,000 Lang Bac 10,000 Khuong Trung 7,075 TOTAL 297,294 Fig. 4 Location of the four boundaries of the modelled area Fig. 5 Location of the main pumping fields situated in the modelled area (circles represent wells) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x Three different types of geological materials charac- terize the Quaternary sediments: gravels, sands and silts-clays (Jusseret et al., as previously given, “The stratigraphical architecture of the Quaternary deposits as support for hydrogeological modelling of the central area of Hanoi (Vietnam)”, unpublished report, 2008). The hydrogeological properties of these materials are known on the basis of pumping tests interpretation. The corresponding tests have been carried out with wells screened throughout the entire thickness of the considered aquifer. The data related to hydraulic conductivities and storage coefficients were therefore measured in depth- averaged conditions. Consequently, all the materials making up an aquifer have been brought together to define a “mean material” which could be described as gravely sands (or sandy gravels), referring to the marked dominance of gravels and sands in Pleistocene and Holocene aquifer units. Values of the storage coefficient and effective porosity are determined, following the same assumption, for all the Holocene aquifers on the one hand, and the Pleistocene aquifer on the other hand. The silty clayey layer found within the Pleistocene deposits, at an altitude close to −50 m (Jusseret et al., as previously given, “The strati- graphical architecture of the Quaternary deposits as support for hydrogeological modelling of the central area of Hanoi (Vietnam)”, unpublished report, 2008) is also included in this “mean material”, so that the Pleistocene aquifer is considered as a unique gravely sandy layer. This hypothesis could also be supported by the discontinuous character of the “−50 m” silty clayey layer. It is however necessary to model explicitly the basal Holocene less permeable unit, because of the different piezometric heads observed in the Pleistocene and in the Holocene aquifers (when this layer is observed). Figure 6, adapted from Jusseret et al. (Jusseret et al., as previously given, “The stratigraphical architecture of the Quaternary deposits as support for hydrogeological modelling of the central area of Hanoi (Vietnam)”, unpublished report, 2008), represents, for example, one of the cross-sections showing the nature and spatial distribution of the sedimentary units explicitly included in the hydrogeolog- ical model. The corresponding cross-section is located in Fig. 7 (number 2). As this model aims to simulate groundwater flow at the regional scale, the possible anisotropy of the parameters is neglected. Thu and Fredlund (2000) have however demonstrated the simplis- tic character of this assumption when considering land subsidence processes. On the basis of hydraulic conductivity (K) values from pumping tests (Table 1; Fig. 8) interpreted in depth- averaged conditions, an equivalent hydraulic conductivity value of about 1 E-04 m/s is found for the gravely sandy Holocene deposits. This latter value thus corresponds to an equivalent homogeneous material chosen for the Holocene channel gravels and sands. Concerning the storage coefficient (S), data gathered (Table 2) provide an equivalent storage coefficient of the Fig. 6 Illustration of the spatial distribution of the sedimentary and hydrogeological units included in the groundwater flow model (cross- section number 2, see Fig. 7 for location) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x Holocene aquifers in the order of magnitude of 1 E-02 to 1 E-01 (−) showing that these aquifers are or become unconfined when and where pumping tests were per- formed. In deeper zones (permanently saturated), the definition of the storativity is closer to that defined for a confined aquifer. Smaller storativity values have therefore to be defined. If a value of 1 E–08 Pa–1 is given for the volumic compressibility (α), a storage coefficient in the order of magnitude of 1 E-04 to 1 E-03 (−) is obtained. The latter values are acceptable for a nearly incompress- ible aquifer whose thickness varies from a few to tens of meters. A similar procedure is adopted for the Pleistocene aquifer parameters (Table 3, Fig. 8). An averaged equivalent value of K is found close to that obtained for the Holocene units, i.e. order of magnitude of K around 1 E-04 to 1 E-03 m/s. The value of the storage coefficient defined for the Pleistocene aquifer covered by a Holocene sedimentary layer is between 1 E-05 and 1 E-01 (−) (Table 4). The calibration of the transient-state model on measured piezometric head time series will provide additional information. The variability from 1 E-05 to 1 E-01 is certainly a consequence of the semi-confined character of the Pleistocene aquifer covered by Holocene deposits. Table 5 (outcropping Pleistocene aquifer) shows a set of values which could be related to the effective porosity (ne) values of sandy gravely sediments. In outcrop areas, where the aquifer is unconfined, a storativity value in the order of magnitude of 1 E-02 to 1 E-01 (−) is thus admitted in the zone of intermittent saturation. At greater depths, where the intermittent saturation is not observed, the storage coefficient is, as for Holocene aquifers, characterized by values between 1 E-05 and 1 E-03 (−). For the silty clayey layers, a conventional range of values have been chosen. Hydraulic conductivity values on the one hand have been defined between 1 E-05 and 1 E-09 m/s, depending on the proportion of coarse elements (silts) compared to clays (Fetter 2001). A storage coefficient corresponding to the value adopted for the confined aquifer multiplied by 5 has, on the other hand, been chosen. This choice takes into account the important total porosity (up to 50%) and volumic compressibility (α) of these materials. Two main recharge sources of the aquifers can be distinguished: rainfall and the Red River. The unknown rates of recharge through surface-water bodies (smaller rivers, lakes) are here conceptually included in the effective rainfall term. This term is approximated by subtracting the potential evapotranspira- tion from the raw rainfall data at disposal. In Hanoi, the thickness of the unsaturated zone generally reaches a few meters, possibly more where a Holocene aquifer is not recorded. Consequently, it is Fig. 7 Location of cross-sections (numbers 1–11) in the Hanoi area (modelled area is light grey). Section 2 is shown in Fig. 6 Hydrogeology Journal DOI 10.1007/s10040-008-0423-x acceptable to suppose that the recharge flow rates related to rainfall (between April and September, i.e. the rainy season) undergo an annual “smoothing” that is accentuat- ed by the presence of many small surface-water bodies. Three potential scenarios, principally differing in the spatial distribution of the infiltration rates, are tested in the model. The first scenario considers no infiltration related to rainfall. This scenario, undoubtedly far from the reality, will force the model to exaggerate the importance of the recharge from the Red River. The second scenario simulates infiltration only where superficial Holocene and Pleistocene gravely sandy deposits are occurring, and in West Lake and White Silk Lake (Fig. 9). The hydraulic conductivity values related to the lacustrine sediments are considered as equal to those of the gravely sandy sediments. With this scenario, infiltration through the superficial silty clayey deposits is conceptually chosen to be zero, with hydraulic conductivity of the order of magnitude of 1 E-09 m/s. The third and last infiltration scenario considers an infiltration distributed over the whole study area. In this scenario, the hydraulic conduc- tivity value of the superficial silty clayey sediments is therefore chosen with a maximum value of 1 E-05 m/s. The groundwater recharge through the Red River is included in the boundary conditions of the model. Secondary rivers and lakes are represented as gravely sandy “windows”, opened on Holocene aquifers and through which water from rainfall is infiltrating. The only (known) groundwater sink term in Hanoi is represented by the public and private pumping wells. Nowadays, ten main pumping fields exist in Hanoi. Six of them are located in the modelled area: Cao Dinh, Long Yen, Mai Dich, Ngoc Ha, Ngo Si Lien and Yen Phu (Fig. 5). The shift from the 1990s to the 2000s would have been accompanied by a linear rise of the pumping rates, from 430,000 to 473,780 m3/day (RIGMR 2006; data- base); these rates are moreover exclusively related to the Pleistocene aquifer. Available pumping rate data (Table 6) are referring to an unknown period, but definitely after 2000 (V.T. Tam, MONRE, personal communication, 2006). Because of this uncertainty, the pumping rate data given in Table 6 are hypothetically reported to the month of December 2004. For the same reason, the linear rise previously mentioned (from 430,000 to 473,780 m3/day) is considered as representative of the modelled period (January 1995–December 2004). Monthly pumping rates from January 1995 onwards are calculated on the basis of this ratio and of the pumping rates of December 2004 (Table 6). Within each pumping field, the total pumping rate is equally shared out among the wells. The depths of the well screens are only known for the nine wells belonging to one particular pumping field (Khuong Trung, located to the south and outside of the modelled area): the mean depth of the bottom of the screen is around –50 m, while the top of the screen is around −30 m. These values are adopted for each well in the modelled area. Fig. 8 Pumping tests carried out inside and close to the modelled area Hydrogeology Journal DOI 10.1007/s10040-008-0423-x The database of RIGMR (2006) also identifies private pumping wells inside the urban zone of Hanoi, which broadly corresponds to the study area. These private withdrawals are, in Hanoi, an important sink term as they represent more than one third of the rates officially pumped—close to 120,000 m3/day according to the database of RIGMR (2006). The great number of private pumping wells south of the Red River, as well as the small values of the individual pumping rates leads to conceptu- alize this solicitation as a negative flux uniformly spread over the modelled area. The evolution of this sink term between 1995 and 2004 is defined following the same process as that adopted for public pumping wells (linear variation). The pumping rate for January 1995 has been chosen as null, a hypothesis which could be acceptable if one supposes that the appearance and growth of the private companies’ water needs have followed the recent economic development of Hanoi. December 2004 saw a pumping rate of 120,000 m3/s, following the same logic as that adopted for the evolution of the public pumping rates. The hypotheses concerning the ways of defining the Red River boundary condition and the recharge by precipitation have been combined to obtain the two groups of three conceptual models, detailed below. 1. Models with a Red River boundary condition imposed by the measurements at three stations (group 1): without infiltration (model 1.1); with infiltration through superficial gravely sandy deposits only, with minimized hydraulic conductivity of the silty clayey deposits belonging to the first layer (model 1.2); with infiltration through the whole surface of the model, with maximized hydraulic conductivity of the silty clayey deposits belonging to the first layer (model 1.3) 2. Models with a Red River boundary condition imposed by the measurements at two stations (group 2): without infiltration (model 2.1); with infiltration through super- ficial gravely sandy deposits only, with minimized hydraulic conductivity of the silty clayey deposits belonging to the first layer (model 2.2); with infiltration through the whole surface of the model, with maxi- mized hydraulic conductivity of the silty clayey deposits belonging to the first layer (model 2.3). Data input Using the MODFLOW 2000 calculation code, the constructed mesh includes 102,405 cells equally spread over five layers. Cell dimensions are horizontally fixed to 55 m (west–east axis) and 57 m (north–south axis), without any refinement areas. This choice results from the uncertainty related to the pumping rates, which does not justify the need for obtaining more accurate results in some specific stressed areas. Besides the upper and lower boundaries of the mesh, built on the basis of core data, the elevation of the five layers of cells are as follows: 2 m amsl (base of layer 1, top of layer 2), −8 m amsl (base of layer 2, top of layer 3), −18 m amsl (base of layer 3, top of layer 4), −23 m amsl (base of layer 4, top of layer 5). Figure 10 illustrates the spatial distribution of the parameters related to the five layers of the mesh. Fig. 11 shows an example of the application of this distribution to one of the cross-sections, located on Fig. 7 (cross-section number 2).The groundwater level measurements as given by the P37, P36, P39, P38, Q64, P12, P8, Q63, P9 and P21 wells are exploited to define boundary conditions of the model. The data related to the observation wells located in the modelled zone (11 for the Pleistocene aquifer, 5 for the Holocene aquifers, see Fig. 3) are used for the calibration of the model. Results The six conceptual models presented above were first successively tested in order to define the most adapted hypotheses related to the modelled area and considered period (1995–2004). The objective function (F) here exploited corresponds to a RMS (root mean square) error, calculated on the basis of observed (measured) and calculated piezometric heads. A trial-and-error procedure was chosen for minimizing F. Because of the construction of six models, hydraulic conductivity represents the only parameter likely to be modified by the manual calibration. K is not allowed to vary within a same aquifer unit, i.e. Holocene or Pleistocene. Where silty clayey sediments are concerned, Fig. 9 Map of the modelled area, illustrating the spatial distribu- tion of the infiltration related to precipitation, as defined in the second conceptual model of recharge (P precipitation, PET potential evapotranspiration) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x K receives an identical value in a given layer of the mesh but can vary from one layer to another. Steady-state conditions The calibrated and validated values of K, obtained in steady-state conditions and shared by the six conceptual models, are summarized in Table 7. The calibration process was carried out on the basis of the data of January 1995, while validation was envisaged on the basis of the data related to the months of July 1995, January 2000, July 2000, January 2004 and July 2004. These steady- state calibration and validation processes led to the selection of the most efficient model (model 1.2) for Fig. 10 Spatial distribution of the hydrogeological parameters in the five layers of the constructed model Fig. 11 a Cross-section number 2 in the modelled domain. b Spatial discretization of cross-section number 2 in the modelled domain. See Fig. 7 for location Hydrogeology Journal DOI 10.1007/s10040-008-0423-x simulating groundwater flows during the selected periods, inside the 63-km2 study area. As a consequence, it could also be determined that (1) the Red River boundary was more accurately defined by using the measures given by three stations rather than two and, more importantly, that (2) among the given hypotheses, the infiltration process could be best conceptualized as occurring through superficial gravely sandy deposits with a minimized hydraulic conductivity (1 E-09 m/s) of the silty clayey deposits belonging to the first layer. The application field of these conclusions, of course, does not go beyond the boundaries of the modelled area. These final observations however have good chances to be applicable to periods different to those used for the calibration and validation processes. This statement can be justified by the fact that the proposed simulation is based on physical (mathematical description of the groundwater flows in saturated conditions) and sedimen- tological principles which guarantee the reliability of the model used for predictive purposes. The sensitivity analysis carried out in steady-state conditions, on the basis of model 1.2 running with the data related to January 1995, led to the following conclusions (Figs. 12, 13 and 14): & The calculated results for the Pleistocene aquifer are not very sensitive to an increase of K. & A variation of K of the silts and clays separating the Pleistocene and Holocene aquifers strongly modifies the calculated results for the Holocene aquifers. & The model is generally more sensitive to the variation of the parameters when comparing the results calcu- lated for the Holocene aquifers to those calculated for the Pleistocene aquifer. & The RMS errors seem to constrain Ksilts-clays to an order of magnitude of 1 E-08 m/s and Kgravels-sands (regardless which aquifer unit) to a value superior or equal to 1 E-04 m/s (because of the sharp rise of the RMS error when considering lower values). The latter parameter can however be augmented by three orders of magnitude without significantly modifying the quality of the calculated results. The sensitivity of the model when considering the Holocene aquifers has probably to be related to the spatial distribution of these units. The latter is indeed more constraining than that of the Pleistocene aquifer, forming a continuous unit, not laterally interrupted by less permeable deposits. Moreover, the calibrated set of hydraulic conductivities does not always correspond to the minimal error calculated by the model (Fig. 14). This observation can be justified by the fact that the choice of the parameters has been made on the basis of the results calculated for six periods (validation process), while the sensitivity analysis has only been carried out on the basis of the January 1995 data. Concerning Fig. 12, the absence of value for a K/Kcalibrated of 0.1 is explained by a calculated error too high for being represented. Table 7 Calibrated and validated values of K (steady-state conditions) Material K (m/s) Gravels-sands (Holocene) 5 E-04 Gravels-sands (Pleistocene) 9 E-04 Silts-clays (layer 2) 4 E-08 Silts-clays (layers 3 and 4) 1.9 E-08 1 10 100 1000 10000 100000 1000000 0.001 0.01 0.1 1 10 100 1000 K/Kcalibrated (-) R M S er ro r ( m) Pleistocene Holocene Total Fig. 12 RMS errors calculated as a function of the variation of Kgravels-sands of the Pleistocene aquifer 0 1 2 3 4 5 6 K/Kcalibrated (-) Pleistocene Holocene Total 0.001 0.01 0.1 1 10 100 1000 R M S er ro r ( m) Fig. 13 RMS errors calculated as a function of the variation of Kgravels-sands of the Holocene aquifers Hydrogeology Journal DOI 10.1007/s10040-008-0423-x Transient-state conditions The specific storage (Ss) and effective porosity (ne) are the only parameters which have been modified in comparison with the calibration and validation processes in steady- state conditions. The initial conditions defined before starting the calibration in transient-state conditions are those calculated by model 1.2, running in steady-state conditions with the January 1995 data set. The piezomet- ric maps calculated for the Pleistocene and Holocene aquifers and used as initial conditions are presented on Figs. 15, 16 and 17 (layer 1 is the uppermost). Light grey areas indicate calculated piezometric heads higher than the topographic surface, while dark grey zones indicate dry (inactive) cells. Note on these three figures, the pumping- induced drawdown cone related to the Mai Dich and Ngoc Ha fields (Fig. 5), inducing the drainage of the cells above it and belonging to the first and second layers. As only the active cells are considered by the model when calculating further piezometry, these cells are not reactivated during later time steps. Considering the hydrogeological context encountered in Hanoi, with measured piezometric heads undergoing a nearly continuous lowering since 1995, this constraint does not create inconsistency. The modelling of the multi-annual trends can therefore be carried out starting from January 1995, which represents a “maxi- mum” during the simulated period. The calibration in transient-state conditions has been carried out on the basis of results comparison for the month of December in 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003 and 2004. Changing stresses and 0 1 2 3 4 5 6 0.001 0.01 0.1 1 10 100 1000 K/Kcalibrated (-) R M S er ro r ( m) Pleistocene Holocene Total Fig. 14 RMS errors calculated as a function of the variation of Ksilts-clays of the layers 2–4 Fig. 15 Piezometric head maps calculated in steady-state conditions (model 1.2) with the data related to January 1995 (layers 1 and 2). Water levels are given in metres relative to msl Hydrogeology Journal DOI 10.1007/s10040-008-0423-x boundary conditions are taken into account in the model. The calibrated values of the specific storage (Ss) and effective porosity (ne) are presented in Table 8. Figure 18 illustrates a selection (December of 1995, 2000 and 2004) of scatter plots built on the basis of calculated versus measured piezometric heads at the end of each year. Considering the conceptual hypotheses adopted, the calculated results can be considered as very satisfactory: the scatter points follow a clear linear trend and the difference between calculated and measured values is less than one meter at several observation wells. Comparisons between the evolutions of calculated and measured piezometric heads are illustrated on Fig. 19. Again, the piezometric trends are fairly well simulated (general decrease through time, up- and down-going evolution), Fig. 16 Piezometric head maps calculated in steady-state conditions (model 1.2) with the data related to January 1995 (layers 3 and 4). Water levels are given in metres relative to msl Fig. 17 Piezometric head map calculated in steady-state condi- tions (model 1.2) with the data related to January 1995 (layer 5, Pleistocene aquifer). Water levels are given in metres msl Table 8 Calibrated values of specific storage (Ss) and effective porosity (ne) in transient-state conditions, for the period between January 1995 and December 2004 Material ne (−) Ss (m–1) Gravels-sands (Pleistocene-Holocene) 3 E-01 2 E-04 Silts clays 1 E-03 3 E-01 Hydrogeology Journal DOI 10.1007/s10040-008-0423-x with the exception of the P47 (Holocene aquifer) and P17 (Pleistocene aquifer) observation wells. The former shows a trend not satisfactorily reproduced; the latter systemat- ically furnishes calculated values several meters below the observed ones (up to 7 m for December 2001). Validation was carried out by testing seasonal varia- tions (Fig. 20). The calculated trends are again well reproduced, except for the variations of the Pleistocene groundwater at P17 and of the Holocene aquifer at P35. The RMS error calculated for the whole aquifer units a -15.00 -10.00 -5.00 0.00 5.00 10.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 Calculated piezometric head (m amsl) O bs er ve d pi ez o m et ric h ea d (m am sl ) Pleistocene Hcalc=Hobs Hcalc=Hobs +/- 1 m Holocene b -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 Calculated piezometric head (m amsl) O bs er ve d pi ez o m et ric h ea d (m am sl ) Pleistocene Hcalc=Hobs Hcalc=Hobs +/- 1 m Holocene c -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 -20.00 -15.00 -10.00 -5.00 0.00 5.00 10.00 Calculated piezometric head (m amsl) O bs er ve d pi ez o m et ric h ea d (m am sl ) Pleistocene Hcalc=Hobs Hcalc=Hobs +/- 1 m Holocene Fig. 18 Scatter plots obtained after calibration in transient-state conditions (December of a 1995, b 2000, c 2004) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x (Holocene and Pleistocene), 1.6 m, demonstrates the very satisfactory quality of the model, in spite of the strong conceptual choices made.The constructed model shows a very weak sensitivity to the variation of the specific storage and effective porosity of the encountered materials (decrease of the RMS error by 5 cm when multiplying the specific storage by 100). The constructed model hence is not authorized to constrain the orders of magnitude of the specific storage and effective porosity for the equivalent materials defined in the study area. Interpretation of the results The calibration and validation of the constructed ground- water flow model answers the initially asked questions. According to the obtained values of the objective function, in steady- and transient-state conditions, the sedimentological model seems to be efficient to simulate the three-dimensional geometry of the layers and the heterogeneity influencing the three-dimensional ground- water flow in saturated conditions. The semi-annual piezometric variations observed between 1995 and 2004 P17 Holocene -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P47 Holocene 0.00 1.00 2.00 3.00 4.00 5.00 6.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P17 Pleistocene -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P47 Pleistocene 0.00 1.00 2.00 3.00 4.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P35 Pleistocene -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P43 Pleistocene -16.00 -14.00 -12.00 -10.00 -8.00 -6.00 -4.00 -2.00 0.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed Fig. 19 Comparison between the calculated and observed piezometric heads at the P43, P35, P17 and P47 observation wells (transient- state conditions, annual time step marked out for December of each year) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x are also well simulated, with the exception of the P17 (Pleistocene aquifer) and P35 (Holocene aquifers) obser- vation wells. 1. Following the conceptual hypothesis expressed through the Red River boundary condition with a prescribed piezometric head varying linearly between the three measuring stations, the flow rate entering the model through this boundary (January 1995, steady-state conditions) and calculated by MODLFOW is about 4.78 m3/s. This flow rate is very unequally shared out between the five modelled layers. In all, 93% of this flux is indeed entering layer 5, exclusively representing the Pleistocene aquifer. The infiltration from rainfall is between 0.9 m3/s (recharge through Pleistocene out- crops, lakes and watercourses) and 3.03 m3/s (maxi- mum infiltration, i.e. through the whole study area). The main recharge source of the groundwater in the modelled domain (in January 1995) is the Red River. Depending on the chosen conceptual model of re- P35 Holocene -2.00 -1.50 -1.00 -0.50 0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P47 Holocene 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P35 Pleistocene -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P17 Pleistocene -6.00 -4.00 -2.00 0.00 2.00 4.00 6.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P43 Pleistocene -14.00 -12.00 -10.00 -8.00 -6.00 -4.00 -2.00 0.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric h ea d (m am sl ) Calculated Observed P58 Pleistocene -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 Pi ez o m et ric he ad (m am sl ) Calculated Observed Fig. 20 Comparison between the calculated and observed piezometric heads at the P43, P35, P58, P17 and P47 observation wells (transient-state conditions, semi-annual time step marked out for June and December of each year) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x charge, the relative importance of the recharge from the Red River as compared to recharge from the rainfall is varying. The calibration in steady-state conditions shows a rainfall infiltration rate in January 1995 closer to 0.9 m3/s than 3.03 m3/s. Even with a maximum recharge by rainfall infiltration, the latter only repre- sents 63% of recharge from the Red River. 2. The validation of the model in transient-state condi- tions with pumping conditions led to calculated piezometric maps related to the months of June (rainy season) and December (dry season) for the period 1995–2004. The regional groundwater flow trends are compared mostly within layer 5 (representing the biggest part of the modelled domain). As an example, Fig. 21 illustrates the piezometric maps calculated by MODFLOW for June and December 1999. The calculated groundwater levels are imposed (see bound- ary conditions) higher close to the Red River during the rainy than during the dry season. Around the Mai Dich pumping field, far from the Red River, the piezometry does not, on the other hand, strongly vary during the year. Regional groundwater flow trends are oriented orthogonally to the Red River boundary and converge to the pumping fields. The pumping drawdown cones are indeed more clearly detected during the dry season than during the rainy season. The effects of the Cao Dinh, Yen Phu and Long Yen pumping fields on the piezometry are not very marked, regardless of the period of the year. The proximity of the Red River indeed allows for recharge by the river, which compensates for the pumping, resulting in a nearly constant piezometry all year round. A piezometric dome (December) or a dividing line of the groundwater flows (June) is noted to the south-west of the Ngo Si Lien pumping field. This observation is justified by the absence of pumping fields in this area.As a conclusion, the regional flow trends are barely modified inside the modelled domain from rainy to dry season: only the seasonal increase of the radius of influence of the pumping fields combined with the general lowering of the piezometry close to the Red River during the dry season are observed. 3. The calculated and observed piezometric evolutions at the observation wells close to the Red River are generally very similar (Figs. 19 and 20). Regardless of the investigated aquifer unit, piezometric head ups and downs are faithfully reproduced, with a RMS error lower than 2 m: this tends to demonstrate that the Red Fig. 21 Piezometric head maps, comparing the regional groundwater flow directions during the months of June (rainy season) and December (dry season) 1999 (Pleistocene aquifer, layer 5) Hydrogeology Journal DOI 10.1007/s10040-008-0423-x River water level represents an equipotential line for the Holocene, as well as for the Pleistocene aquifers inside the modelled zone. Moreover, the heterogeneity defined for the hydrogeological units and the calibrated values of hydraulic conductivity (in the order of magnitude of 1 E-04 m/s for the aquifers and 1 E- 08 m/s for the silty clayey units) seem to be acceptable for reproducing realistic behaviour of the aquifers. This statement is of course true for the defined stresses and simulated period. Conclusions and perspectives The modelling of the groundwater flow in steady- and transient-state conditions, during the 1995–2004 period, has finally allowed for the definition of several important processes related to the regional dynamics of the shallow aquifers in Hanoi. First, the recharge process through precipitation in the modelled urban area essentially occurs through the main superficial water bodies (notably the West Lake and White Silk Lake, modelled as “windows” opened on the Holocene aquifers) and Pleistocene deposit outcrop areas. Second, values of hydraulic conductivity related to the modelled equivalent materials were estimat- ed: an order of magnitude of 1 E-08 m/s was obtained for the silty-clayey sediments. The hydraulic conductivity of the aquifers was, on the other hand, far less constrained, as its optimal value can be between 1 E-04 and 1 E-01 m/s. Third, orders of magnitude of specific storage and effective porosity could not be constrained, as the proposed model appears to be insensitive to the variation of these parameters. Fourth, the adopted conceptual hypotheses related to sedimentology, stresses and bound- ary conditions simulate the piezometric trends between 1995 and 2004 very satisfactorily, with time steps of 1 year or 6 months (RMS error lower than 2 m). Finally, the simulations in steady- and transient-state conditions have answered the initial questions about the importance of recharge through the Red River, and have confirmed the equilibrium state between Holocene and Pleistocene aquifers close to the Red River, and moderate variation in regional flow trends depending on the season (dry or rainy). The good quality of the results would also suggest that the sedimentological reconstruction as proposed by Jusseret et al. (Jusseret et al., as previously given, “The stratigraphical architecture of the Quaternary deposits as support for hydrogeological modelling of the central area of Hanoi (Vietnam)”, unpublished report, 2008), and accordingly the spatial distribution of the hydrogeological units, is not too far from the reality. As a general conclusion, the study carried out provides the essential basis for further studies dealing with modelling of solutes (e.g. Jussel et al. 1994a, b; Vorlicek et al. 2004) or coupled modelling of groundwater flow and land subsidence processes (e.g. Dassargues and Baeteman 1994; Dassargues et al. 1993; Dassargues and Zhang 1992; Xu and Van der Gun 1995). Acknowledgements S. Jusseret and A. Dassargues should like to express their gratitude to V.T. Tam and N.X. Khien (RIGMR) for their hospitality and welcome during the three weeks spent by the first author in Hanoi in February 2006. C. 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