EARTH SCIENCE FRONTIERS Volume 16, Issue 6, November 2009 Online English edition of the Chinese language journal Cite this article as: Earth Science Frontiers, 2009, 16(6): 276–281.
RESEARCH PAPER
The Estimation of Aquifer Parameters Using Tidal Effect in a Coastal Aquifer: A Case Study in Beihai Peninsula XIA Yuqiang1,2, LI Hailong1,3, 1 School of Environmental Studies; (MOE) Biogeology and Environmental Geology Lab, China University of Geosciences (Wuhan), Wuhan 430074, China 2 Department of Civil and Environmental Engineering; Environmental Hydrology and Hydraulics Laboratory (EHH), Temple University, Philadelphia PA19122, USA 3 School of Water Resources and Environment, China University of Geosciences (Beijing), Beijing 100083, China
Abstract: How to estimate aquifer parameters, or to confirm the extending length of the aquifer under the sea or the existence of the aquifer submarine outlet-capping, via the analysis for the observed data of water-level dynamic condition in observation well, has attracted much attention from hydrogeologists. Based on the well acquaintance with the hydrogeological conditions in the Beihai Peninsula, Guangxi Autonomous Region, China, the first confined aquifer in this area can be conceptualized into a vertical three-layered nonstationary flow model with the aquifer submarine outlet-capping and the leakage through the aquifer’s roof. The analytical solution to this model is applied to analyze the tidal and piezometer data in a coastal aquifer of the Beihai Peninsula in this article. The aquifer parameters are estimated using least-squares objective function with novel penalty functions incorporating known information. The solution prediction closely fits with the observation very well. Key Words: coastal multilayered aquifer system; submarine outlet-capping; tidal effect; least-squares penalty method; aquifer parameter estimation
1
Introduction
In coastal aquifers, the groundwater level (hydraulic head or water table) in coastal aquifer fluctuates with time in response to the water-level fluctuations of the tidal water body (sea or river or lagoon)[1], which is referred to as tidal effects. The research of the tide-derived groundwater flow in the coastal aquifer system plays an important and active role in solving various coastal hydrogeological, engineering geology, ecological and environmental problems related to tidal dynamics. Many previous studies indicate that the tidal effect would provide a convenient, economic, and reliable way to identify coastal hydrogeological conditions in a large scale[2–4]. In addition, tidal groundwater-level fluctuations in different distances from the coastline vary with different aquifer configurations[5–12]. How to estimate aquifer parameters
including the extending length of the confined aquifer under the sea and how to identify the existence of aquifer’s submarine outlet-capping, via the analysis of the tidal effect data from observation wells in coastal areas, are important and interesting tasks of hydrogeologists. The tidal and piezometer data in a coastal aquifer in the Beihai Peninsula, Guangxi Autonomous Region, China are used as a case study in this article. Based on the well acquaint with the hydrogeological conditions, this area can be conceptualized into a multilayer system with a shallow unconfined aquifer, a leaky confined aquifer, and a semipermeable layer between them. Based on Li and Jiao[9] and Li et al.[12], Xia et al.[13,14] derived an analytical solution for this aquifer system and discussed the influences of the model parameters on head fluctuations, respectively. In this article, the aquifer parameters in the study area are estimated
Received date: 10-Mar-2009; Accepted date: 15-Sep-2009.
Corresponding author. E-mail:
[email protected] Foundation item: Supported by the National Natural Science Foundation of China (No. 40672167) and the Program of Introducing Talents of Discipline to University “111 project” (No. B08030). Copyright © 2009, China University of Geosciences (Beijing) and Peking University, Published by Elsevier B.V. All rights reserved. DOI: 10.1016/S1872-5791(08)60121-9
XIA Yuqiang et al. / Earth Science Frontiers, 2009, 16(6): 276–281
using least-squares penalty method with the analytical solution of Xia et al.[14]
2
Geological background
The study area is located near North Gulf in the Beihai Peninsula, Guangxi Autonomous Region, China (Fig. 1). No great river are found around this area, the terrain is gently inclined into the sea. From shallow to deep, this area can be conceptualized into a multilayer system with unconsolidated sand and clay unconfined aquifer, coarse sands with gravel confined aquifers (three aquifers), clay soil and slime semipermeable layers between them, and basal sand-shale and granite impermeable bottom. Confined aquifers and semipermeable layers show a superimposed distribution and extend under the sea[15–17]. This system was studied by Li and Chen[18,19] who assumed that the roof and bottom of the first confining layer is impermeable. According to the characteristics of coastal sediments and submarine geomorphy in the North Gulf, fine sand, mealy sand, silt, clay, and organic oddments may gradually deposit under the sea in an anoxia environment. Furthermore, coarse sand sediments with brown silt deposits show a wide-exposure in present coastal zone off limits. The distributed depth of the coarse sand sediments is equivalent to the locality between the first confined aquifer and the unconfined aquifer[18,19]. Considering geologic history and tectonic movement, Li and Chen[18] pointed out that the coarse sand sediments would be the subcrop of the first confined aquifer and not covered by upper alluvial sediments, which is referred to as the “outlet-capping” hereafter[12]. Borehole data in this area indicate that the unconfined aquifer is thin and influenced largely by seasonal climate change. The third confined aquifer only distributes in the south of the study area. Compared with other two confined aquifers (first and second), the quantity of the water in the third confined aquifer is small. So the first and second confined aquifers are the main water-yielding strata for Beihai City. A simplified geological section through A–$ƍ in Fig. 1 is
Fig. 1
Location of borehole Kd4 in the Beihai Peninsula (modified Li and Chen[19])
Fig. 2
(a) Generalized geologic section plan of the borehole Kd4
through A–$ƍ in Fig. 1 (modified from Ref.[16]) and (b) schematic cross-section of the first confined aquifer system
shown in Fig. 2a. Based on the above-mentioned analysis, the first confined aquifer will be used to explore the tide-derived groundwater head fluctuation in the study area.
3
Conceptual model and solution
Considering the first confined aquifer system (Fig. 2a), we assume that the unconfined aquifer terminates vertically at the coastline, whereas the confined aquifer and the semipermeable layer extend under the sea for a certain distance L with an outlet-capping. The bottom of the leaky confined aquifer is impermeable, and all the layers extend landward infinitely. The aquifer is horizontal, homogeneous, and of constant thickness. Let the x axis be perpendicular to the coastline, the intersection of the mean sea surface and the beach face be the origin of the axis, and be positive landward (Fig. 2b). Compared to the groundwater-head fluctuation in the confined aquifer, the water table fluctuations in the unconfined aquifer can be neglected because the specific yield of the unconfined aquifer, which is usually several orders of magnitude greater than the storativity of the confined aquifer, can damp effectively the watertable fluctuations[7,8]. Neglecting the elastic storage of the semipermeable layer and considering the leakage effects of the aquifer’s offshore roof and the submarine outlet-capping, Xia et al.[14] presented the analytical solution for this aquifer system (Fig. 2b). Due to the space limitation, here, we have shown the relationship of the
XIA Yuqiang et al. / Earth Science Frontiers, 2009, 16(6): 276–281
Table 1 Parameters and notations cited from Xia et al.[14] Parameter h(x,t)
Definition
Dimension
Hydraulic head of the confined aquifer
Expression
[L]
L
Extending roof length of the aquifer
[L]
S
Storativity of the confined aquifer
NA*
K
Hydraulic conductivity of the confined aquifer
[LT 1] ˉ
2 ˉ1
T
Transmissivity of the confined aquifer
[L T ]
K1
Vertical hydraulic conductivity of the semipermeable layer
[LT 1] ˉ
b1
Thickness of the semipermeable layer
[L]
K'
Hydraulic conductivity of the submarine outlet-capping
[LT 1]
m
Thickness of the submarine outlet-capping
[L]
Compressibility of the confined aquifer’s skeleton
[M 1LT2]
ȕ
Compressibility of pore water in the confined aquifer
[M 1LT2]
Ϊ
Porosity of the aquifer
NA*
A
Tidal amplitude
[L]
t0
Tidal period
[T]
Ȧ
Tidal angular velocity
[T 1]
Le
Tidal loading efficiency
NA*
Le =
LS
Specific leakage of the semipermeable layer
[T 1]
LS = K1/ b1
a
Tidal wave propagation parameter of the confined aquifer
[L 1]
a
u
Dimensionless leakage of the semipermeable layer
NA*
u = LS /ȦS= K1/( b1ȦS)
ı
Leakance of the submarine outlet-capping
NA*
ı = K'/ amK
p
Intermediate variable
NA*
p
q
Intermediate variable
NA*
q
D
ˉ
ˉ ˉ
ˉ
Ȧ = 2ʌ/ t0
ˉ
ˉ
D /( D + T
ȕ)
ȦS 2T
1u
2
ʌS Tt 0
u 2
1 u u
NA* means the corresponding parameters or notations are dimensionless.
model parameters only in Table 1 and have illustrated the basic parameters in Fig. 2b.
4 Data analyses and aquifer parameter estimation Borehole Kd4 screened in the aquifer is 375 m (x0) far from the northern coastline of Beihai Peninsula (Fig. 1). The confined aquifer has an average thickness of b = 15.26 m, and the thickness of semipermeable layer is b1 = 4.84 m[18,19]. The main sea tides are the diurnal tide with a period of 24.83 h and semidiurnal tide with half period of the diurnal one. The tidal data in the sea and groundwater-head fluctuation in the borehole Kd4 during October 9 and 11, 1985 are available in Li and Chen [19] as illustrated in Fig. 3. The sea tide and the groundwater-head fluctuation in the borehole Kd4 can be approximated by the superposition of the diurnal (Ȧ1= 0.253 hí1) and semidiurnal (Ȧ2 = 0.506 hí1) components[12], respectively, i.e., H sea (t ) M sea Asea ,1 cos(Z1 t T sea ,1) Asea , 2 cos(Z 2 t T sea , 2) (1a) H Kd 4 (t )
M Kd 4 AKd 4䋬1 cos(Z1 t T Kd 4䋬1 ) AKd 4䋬2 cos(Z 2 t T Kd 4䋬2 )
(1b)
where M, A, Ȧ, and ș are the mean water-level [L], amplitude [L], angular frequency [Tí1], and the phase shift [radian] of the water-level fluctuations, respectively; the subscript i = 1, 2
represents the diurnal and semidiurnal components, respectively. Their values are estimated using the least-squares fitting to the observed data and listed in Table 2. The fitting curves are shown in Fig. 3. Based on the assumption introduced by Li et al.[12] and the superposition principle, assume that the mechanism causing the difference between the mean water-level of the sea tide and groundwater head in the confined aquifer can be separated from the tidal effect, and that the diurnal and semidiurnal components of the groundwater-head fluctuations in the borehole Kd4 expressed in Eq.(1b) are caused by the diurnal and semidiurnal components of the sea tide specified by Eq. (1a), respectively. Then, by linking the equation (13) of Xia et al.[14] and (1b), the tide-induced groundwater-head fluctuation at Kd4 can be written as follows hKd 4 ( x0 , t ; aL, Le , u , ax0 , V ) 2
¦ ASea , j C j e
j 1
pa j x0
cos(Z j t qa j x0 M j T Sea , j )
(2)
In view of equations (20) and (21) of Xia et al.[14] and equation (2), we obtain C ( a j L, Le , u , V j ) exp( pa j x0 ) AKd 4, j Asea , j , j 1, 2 (3a) M ( a j L , Le , u , V j ) qa j x 0
T Kd 4 , j T sea, j , j
1, 2
(3b)
Five parameters aL, Le, u, ax0 and ı are contained in equation (2). In theory, if any parameter value among the five
XIA Yuqiang et al. / Earth Science Frontiers, 2009, 16(6): 276–281
Table 2 Fitting results of observed tidal level and groundwater head at Kd4 Fitting terms
*
RLS (m2 )
M (m)
A1 (m)
șң ҏ(radian)
A2 (m)
ҏș2 ҏ(radian)
Least-squares fitting of tidal level
2.568
1.686
í0.018
0.271
1.016
0.214
Least-squares head fitting at groundwater head Kd4
2.205
0.759
í0.002
0.167
1.472
0.089
*RLS, Residual of Least Squares, namely, the sum of the squares of the differences between the observed data and theoretical prediction.
Fig. 3 Observed sea level and hydraulic head data at Kd4 during Oct. 9 and 11, 1985 and their least-squares fittings
parameters is known, then the values of the other four parameters can be obtained by solving equation (2) because the values of AKd4,j, Asea,j, șKd4,j, and șsea,j are available and listed in Table 2. However, due to the complexities of the expressions of C (ajL, Le, u, ıj) and ij (ajL, Le, u, ıj) (see equations (3a) and (3b)), it is difficult to estimate the parameters by directly solving the equation (2). Least-squares method may be more convenient and efficient to estimate the parameters. According to the seabed isopleth depth map of the North Gulf, the extending roof length for the first confined aquifer was evaluated about 2000 m far from the north bank of the seabed[18], so it is reasonable to construct the following least-squares objective function
F
2000.0 º ª min aL ax0 »¼ a , aL , ı , u « 375.0 ¬
2
+
25
¦ [ hKd 4 ( x 0 , t j ; aL , Le , u , ax 0 , V ) j 1
* 2
Le 0.5
hj ]
(4)
minimizing equation (4), the value of the objective function F is 0.153 m2. Using the value of ax0 and x0 = 375 m, the confined aquifer’s tidal wave propagation parameter a can be estimated, and then, the extending roof length of the confined aquifer can be obtained from the value of aL, i.e. L = 1966 m. In addition, from the confined aquifer’s tidal wave propagation parameter defined in Xia et al.[14], one can yield S/T = t0a2/ʌ. If a and tidal period t0 were known, S/T would be estimated. According to the type of the confined aquifer, 3.6 m·hí1 is specified as the averaged value of K. In view of the average thickness of the confined aquifer, the value of transmissibility coefficient is estimated: if T = 54.9 m2·hí1, then S = 2.97 × 10í6. Following the definition of the semipermeable layer’s hydraulic conductivity (K1) in Xia et al.[14], its value is 2.96 × 10í5 m·hí1, which is close to the value (8.825 × 10í5 m·hí1) obtained by Li[20] with the numerical simulation of three-dimensional flow in this study area. The value of specific hydraulic conductivity (Kƍ = ıaKm) is also available. Estimated values of aquifer parameters are listed in Table 3. If the thickness of the outlet-capping ranges from 1 to 10 m, then the range of the hydraulic conductivity of the outlet-capping is 1.49 × 10–3–1.49 × 10í4 m·hí1, indicating a weak hydraulic connection between the seawater and the groundwater at the subcrop of the main aquifer. This result is coincident with the discussion and description about the sediments at the subcrop and on the seabed in sections 1.3.3 and 2.2 of Li and Chen[18]. Table 3 shows that the fitted value of dimensionless leakage (u) is 8.15, indicating that there is a certain quantitative leakage through the semipermeable layer, which is confirmed by the numerical simulation of three-dimensional flow[20]. Figure 3 shows the observed and predicted groundwaterhead fluctuations using the estimated parameters, the two
*
where h j (j=1,…,25) are the 25 observed groundwater-head data at the borehole Kd4, tj (h) is the j-th observation time of the head at Kd4 as shown in Fig. 3. A Fortran code was developed to solve numerically the least-squares problem (Eq. (4)), and an optimum estimate is made for model parameters using quasi-Newton iteration method and penalty function method. The advantages of the least-squares penalty function method used here include making the best use of observation data and improving the precision and reliability of the parameter estimation. Based on pumping tests in this area and given Le = 0.5, the parameter values are used for their initial value when minimizing equation (4): ax0 = 0.22, aL = 0.29, u = 6.0, and ı = 5.0. After
Table 3 Estimated aquifer parameters near Kd4 borehole Parameter –1
Estimated value
a (m )
8.27 × 10–5
L (m)
1966
Le
0.5
u
8.15
S/T (h·m–2)
5.41 × 10–8
S
2. 97 × 10–6
K1 (m·h )
2. 96 × 10–5
K' (m·h–1)
1.49 × 10–4
–1
*
2
F (m )
*F, value of the objective function (4).
0.153
XIA Yuqiang et al. / Earth Science Frontiers, 2009, 16(6): 276–281
curves match closely. Namely, the hypotheses used in this article, i.e., considering the joint actions of the loading efficiency, semipermeable layer’s leakage, and the outlet-capping are more reasonable, compared with the assumptions used by predecessors who only considered the loading efficiency or combined actions of the loading efficiency and semipermeable layer’s leakage. In addition, compared with a lot of minimizing numerical tests, the fitted result of the optimum estimate for parameters shows that the minimizing process of the objective function using quasi-Newton iteration method and penalty function method is improved significantly.
[6]
5
[10] Li H L, Jiao J J. Analytical solutions of tidal groundwater flow
van der Kamp G.. Tidal fluctuations in a confined aquifer extending under the sea. Proc. Int. Geol. Congr. 24th, Section 11, 1972: 101–106.
[7]
Li H L, Jiao J J. Tide-induced groundwater fluctuation in a coastal leaky confined aquifer system extending under the sea. Water Resources Research, 2001, 37 (5): 1165–1171.
[8]
Jiao J J, Tang Z H. An analytical solution of groundwater response to tidal fluctuation in a leaky confined aquifer. Water Resources Research, 1999, 35 (3): 747–751.
[9]
Li H L, Jiao J J. Analytical studies of groundwater-head fluctuation in a coastal confined aquifer overlain by a semi-permeable layer with storage. Advances in Water Resources, 2001, 24 (5): 565–573.
Conclusions
in coastal two-aquifer system. Advances in Water Resources,
The tidal and piezometer data in a coastal aquifer in the Beihai Peninsula, Guangxi Autonomous Region, China are used to estimate the aquifer parameters based on least-squares penalty method with the analytical solution derived by Xia et al.[14]. The fitting result suggests that the model is suitable to describe the real aquifer, and the characteristics of the tidal wave propagation in the confined aquifer are well described. The results strongly indicated a weak-hydraulic outlet-capping covering the aquifer’s submarine outlet and a considerable leakage through the aquifer’s roof. In addition, the difficulty in the use of tidal data is the non-availability of applicable analysis method. In the future researches, analytical and numerical methods, hypothesis, and case study will be used to explore the relations between the observed tidal data and the hydrogeological conditions of coastal aquifer. The results will provide a theoretical guide and technical support for solving various coastal hydrogeological, engineering geological, ecological, and environmental problems related to tidal dynamics.
2002, 25 (4): 417–426. [11] Li H L, Jiao J J. Tidal groundwater level fluctuations in L-shaped leaky coastal aquifer system. Journal of Hydrology, 2002, 268: 234–243. [12] Li H L, Li G Y, Chen J M, et al. Tide-induced head fluctuations in a confined aquifer with sediment covering its outlet at the sea
floor.
Water
Resources
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2007,
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doi:10.1029/2005WR004724. [13] Xia Y Q, Li H L, Guo Q N, et al. Analytical study for tidal wave propagation in a coastal leaky confined aquifer system: Effect of the submarine silt-interface. In: The 34th Congress of International Association of Hydrogeology (IAH). Beijing, 2006. [14] Xia Y Q, Li H L, Boufadel M C, et al. Tidal wave propagation in a coastal aquifer: Effects of leakages through its submarine outlet-capping and offshore roof. Journal of Hydrology, 2007, 337: 249–257, doi:10.1016/j.jhydrol.2007.01.036. [15] Zhou X, Ju X M, Wang J P, et al. Characteristics of groundwater regimes in coastal aquifers. Groundwater, 1997, 19 (1): 15–18.
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