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# Terrestrial water load and groundwater fluctuation in the Bengal Basin

## Abstract

Groundwater-level fluctuations represent hydraulic responses to changes in groundwater storage due to aquifer recharge and drainage as well as to changes in stress that include water mass loading and unloading above the aquifer surface. The latter ‘poroelastic’ response of confined aquifers is a well-established phenomenon which has been demonstrated in diverse hydrogeological environments but is frequently ignored in assessments of groundwater resources. Here we present high-frequency groundwater measurements over a twelve-month period from the tropical, fluvio-deltaic Bengal Aquifer System (BAS), the largest aquifer in south Asia. The groundwater level fluctuations are dominated by the aquifer poroelastic response to changes in terrestrial water loading by processes acting over periods ranging from hours to months; the effects of groundwater flow are subordinate. Our measurements represent the first direct, quantitative identification of loading effects on groundwater levels in the BAS. Our analysis highlights the potential limitations of hydrogeological analyses which ignore loading effects in this environment. We also demonstrate the potential for employing poroelastic responses in the BAS and across other tropical fluvio-deltaic regions as a direct, in-situ measure of changes in terrestrial water storage to complement analyses from the Gravity and Climate Experiment (GRACE) mission but at much higher resolution.

## Introduction

Regional monitoring by the Gravity and Climate Recovery Experiment (GRACE) satellite mission1 has prompted concerns over the sustainability of deep groundwater pumping2, including across mega-delta regions of Asia3 where groundwater meets the needs of over 300 million people. The largest and most densely populated floodplain region is the Bengal Basin, which is the focus of intensive water use4, subject to substantial hydrological seasonality5 and highly vulnerable to climate change6. Here, the Rivers Ganges, Brahmaputra and Meghna (GBM) have a combined annual discharge at their confluence of 1350 km3, second only to the River Amazon. The GBM floodplains present the second largest seasonal gravity anomaly observed by the GRACE satellites5, driven by variations in terrestrial water storage (ΔTWS), the sum of changes in surface water runoff and storage, soil water and groundwater storage. The uppermost few hundred metres of the Holocene-Pleistocene GBM floodplain sediments constitute the Bengal Aquifer System7 (BAS), the source of domestic and irrigation water to over 100 million people8. ‘Deep groundwater’ in BAS, greater than 150 m below the floodplain surface, supplies Dhaka as well as many provincial and coastal towns and rural water supply schemes8 where it is developed as an alternative to shallow, arsenic-contaminated groundwater9. Human dependency on groundwater resources, exposure of groundwater to increasing climatic and anthropogenic stresses, and geogenic constraints on water quality are features of the BAS which are common to other major Asian mega-deltas9. The intensity of groundwater abstraction from the BAS has prompted concern7 over its sustainability, and focussed attention on the variability of seasonal amplitudes and secular trends in TWS, and especially of groundwater as a component of TWS. Controversy over interpretations of GRACE satellite gravity data across the Bengal Basin centres on assessments of secular groundwater depletion3, 10 which range from 1 to 4 km3/year; the disparity is partly associated with the choice of scaling factor applied to address amplitude damping that occurs during GRACE processing11, and partly with the use of global hydrological models which introduce substantial uncertainty12. In situ observations offer a valuable and necessary constraint on interpretations of changes in TWS12, 13, but despite extensive programmes of shallow water-table monitoring across the Bengal Basin4, 14, deeper levels of BAS remain largely unmonitored7. Management of the deep groundwater resource in BAS, as elsewhere across south Asia, lacks a sound empirical basis.

At two sites in southern Bangladesh (Fig. 1, and Supplementary Information) we recorded absolute groundwater pressure and atmospheric pressure at hourly intervals over one year in three closely-spaced boreholes screened at depths between 65 m and 250 m. For construction and completion details of the boreholes see Methods. At Gabura the boreholes GbPZ67, GbPZ116 and GbPZ212 (the numbers indicate the depth to the top of the screen in metres) are situated a few tens of metres from a tidal channel within the GBM delta; shallow groundwater is saline8 and groundwater pumping is insignificant. The Laksmipur boreholes LkPZ91, LkPZ152 and LkPZ244 are situated on the Lower Meghna floodplain, 10 km east of the River Meghna and 8 km from Laksmipur municipal boreholes which pump from 270–300 m depth. From the in-situ measurements at both sites we derived an hourly record of equivalent fresh water head at the depth of each borehole screen after correcting raw data for atmospheric pressure and salinity-density effects (see Methods). Environmental head15 has been proposed for use when vertical groundwater flux is sought and vertical variations in groundwater density occur. Following a recent critical analysis16, we used fresh water head to compare the temporal variation of groundwater head at specified depths in borehole water columns of constant density, where vertical flow components are not sought.

## Results

### Groundwater hydrographs at a coastal site

The Gabura hydrographs (Fig. 1) demonstrate distinctive periodic oscillations containing the principal solar-lunar tidal frequencies17 O1, K1, N2, M2 and S2 and the minor components18 MN4 and M4 (Fig. 2). The oscillations are close to synchronous at all three depths of measurement and amplitudes increase between GbPZ67 and GbPZ116; a summary of amplitudes for specific frequencies is given in Table 1. Subsurface hydraulic responses to a surface sinusoidal hydraulic impulse would dissipate exponentially with depth19 according to T, the period of the impulse, and D, the vertical hydraulic diffusivity (vertical hydraulic conductivity, K v , divided by specific storage, S s ) of the sediments. For the BAS, a value of 1.5 × 10−4 m2/s for D derived from K v and S s determined by inverse modelling20, suggests that hydraulic penetration of the diurnal tidal signal would be less than 10 m; the spring-neap tidal signal should not penetrate beyond a few tens of metres. Therefore we interpret the undamped periodic oscillations at up to 212 m depth as the fluid pressure changes in this coastal, confined and unconsolidated aquifer due to mechanical loading and unloading of the aquifer by tidal water movements above the aquifer surface, commensurate with analytical treatments21,22,23.

## Discussion

### Poroelastic effects in the Bengal Aquifer System

At both the coastal and the inland sites, over the annual duration of measurements, the data indicate groundwater heads responding dominantly to mechanical loading and unloading due to changes in terrestrial water storage above the aquifer surface by tidal and hydrological processes acting over periods ranging from hours to months and determined by poroelasticity; the effects of groundwater flow are subordinate. Poroelastic responses in the BAS have indeed been predicted25. They are favoured by the low topographic relief which restricts gravitational groundwater flow26, the low vertical hydraulic conductivity which further constrains depth of groundwater circulation20, 27, and the pronounced sediment compressibility5 reflected in high S s . Heavy monsoon rainfall and deep surface water flooding10 provide a large water load. Hydraulic diffusivity, D, controls the relative importance of poroelastic effects as compared to transient groundwater flow on the hydraulic heads of an aquifer. The vertical hydraulic diffusivity of BAS is low because the many silt-clay layers distributed throughout the fluvio-deltaic sediments20, 27 impose a low value of K v , and the sediment compressibility, hence Ss, is high5.

We focus on the short-term groundwater pressure transients up to annual time periods because these are the transients that are definitive of the poroelastic response. Projection of secular trends requires a multi-year record, therefore no assessment of potentially longer-term trends linked to groundwater abstraction has been made. The hydrographs have likely not captured the start of the 2013 monsoon season, so any assessment of longer-term trends might be highly misleading. From the strong groundwater pressure responses to mechanical loading, associated poroelastic deformation of the aquifer would be expected, the nature and scale of deformation depending on the drainage condition28. No actual measurements of aquifer deformation are available for BAS, although a clear seasonal deflection of the ground surface across Bangladesh with an amplitude of approximately 0.06 m has been observed and associated with larger-scale, deep crustal deformation by monsoon water loading across the entire Bengal Basin5.

Fourier analysis17, 29 of the time series of tidal and atmospheric signals and groundwater heads provides detail of the periodic loads on the BAS (Fig. 2, Table 1). At Gabura, groundwater responses to the solar-lunar tidal components are undamped and in-phase to the depth of GbPZ212, critical evidence for the dominantly mechanical response of the aquifer at these depths to periodic tidal loading at the surface. At Laksmipur, groundwater responses to the diurnal and semi-diurnal atmospheric frequencies are likewise largely undamped to the depth of LkPZ244; they enable a direct evaluation of barometric efficiency from the relative amplitudes of the atmospheric signals and their groundwater responses. At Laksmipur the main lunar semi-diurnal (M2) component of the earth tide is also evident, at an increasing amplitude with depth, while at Gabura any earth tide response is masked by the dominant tidal load responses at the frequencies common17 to all ocean and earth tides.

### Geological weighing lysimetry in the Bengal Basin

Observations of groundwater levels responding to changes in near-surface water mass, equivalent to those reported here, have been made in diverse geological and hydrological environments worldwide and underlie the concept of ‘geological weighing lysimeters’34,35,36,37,38,39. The approach employs the equation governing one-dimensional, transient groundwater pressure $$(\frac{\partial p}{\partial t})$$ in permeable, elastically compressible sediments under purely vertical strain35:

$$\frac{\partial p}{\partial t}=D\frac{{\partial }^{2}p}{\partial {z}^{2}}+C\frac{\partial {\sigma }_{T}}{\partial t}$$
(1)

where the first term on the right describes flow-induced changes, and the second term describes the effect of changes in vertical stress, or mass loading. D is the sediment hydraulic diffusivity (hydraulic conductivity divided by specific storage); C is the sediment loading efficiency (dimensionless), which has a value between 0 and 1 according to the distribution of surface load between the confined water and the solid matrix; and σ T is the total vertical stress applied as a mechanical load on the formation. Conventional hydrogeological analysis neglects the second term on the right of Eq. (1), effectively uncoupling the flow field from the stress field on the premise that poroelastic effects are normally secondary to hydraulic effects. Where groundwater flow is negligible, however, groundwater pressure responds instantaneously to addition or subtraction of mechanical load19, as governed by:

$$\frac{\partial p}{\partial t}=C\frac{\partial {\sigma }_{T}}{\partial t}$$
(2)

Groundwater head response to tidal loading at Gabura potentially provides an empirical means for a direct measure of loading efficiency C, the proportional change in groundwater pressure relative to change in total vertical stress, and hence the possibility of applying geological weighing lysimetry in the Bengal Basin. However the actual tidal signal at Gabura, where the coastline is densely dissected by tidal channels, is unknown and likely considerably different to the Chittagong tide. Therefore we determined C indirectly through its relationship21 with barometric efficiency, B, where:

$$B+C=1$$
(3)

Determination of B requires that influences on groundwater head other than atmospheric pressure can be estimated and subtracted from the measurements, or are minor in comparison to the atmospheric effects, or are absent17. At Gabura, barometric effects are obscured by the tidal responses which are more than two orders of magnitude greater than the atmospheric signal (Fig. 2). However at Laksmipur, during undisturbed periods of dry-season recession (Fig. 3), the trend of groundwater head decline can be determined and subtracted to reveal the inverse relationship between atmospheric pressure and groundwater pressure (Fig. 4). Barometric efficiency determined by linear regression of this relationship17 is 0.31 ± 0.02 (LkPZ91), 0.16 ± 0.03 (LkPZ152) and 0.21 ± 0.03 (LkPZ244), giving values for loading efficiency, C, from Eq. (3) as 0.69 ± 0.02 (LkPZ91), 0.84 ± 0.03 (LkPZ152) and 0.79 ± 0.03 (LkPZ244); ranges are ± twice the standard error in each case (Table 2). The mean value of C by this method is 0.77. The Fourier method17, 29 applied to the solar diurnal, S1, and semi-diurnal, S2, atmospheric frequency components and groundwater responses (Fig. 2, Table 1) indicates values for B of 0.19-0.16 (LkPZ91), 0.16-0.13 (LkPZ152) and 0.13-0.21 (LkPZ244). The mean values for loading efficiency, C, from Eq. (3) by the Fourier method are 0.82 (LkPZ91), 0.85 (LkPZ152) and 0.83 (LkPZ244). The two approaches illustrate the variability in C for BAS and yield values consistent with measurements of loading efficiency at geological weighing lysimeter sites elsewhere34, 36, 37

but uncertainty remains in the evaluated range between 0.67 and 0.87. There is no consistent trend with depth.

Applying the Laksmipur boreholes as geological weighing lysimeters34 (see Methods) we evaluated seasonal inundation over the 2013 monsoon period, ΔTWSm (Table 2). In an infinite, uniform half-space, 90% of the terrestrial water loading signal derives from a ‘sensing area’ of radius approximately ten times the borehole depth35, i.e. 3 km2 (LkPZ91), 10 km2 (LkPZ152) and 20 km2 (LkPZ244). We determined ΔTWSm directly from the accumulation of groundwater head (as equivalent fresh water head) recorded between the start (h1) and end (h2) of the rising limbs of the groundwater hydrographs and accounting for loading efficiency, C, where:

$${{\rm{\Delta }}\mathrm{TWS}}_{{\rm{m}}}=({{\rm{h}}}_{2}\mbox{--}{{\rm{h}}}_{1})/C$$
(4)

By this analysis, using the estimates of C from evaluation of B by linear regression and Fourier analysis, seasonal inundation during the 2013 monsoon period averaged 0.90 m effective water depth, ranging from 1.15 m (LkPZ91) to 0.71 m (LkPZ244) and possibly underestimating the full seasonal inundation if, as noted, the hydrographs have not captured the start of the monsoon. As the integrated seasonal accumulation of water mass, ΔTWSm is the same variable as measured by GRACE at a scale1 of approximately 105 km2, assessments of which range from 0.49 to 0.75 m per monsoon season across the GBM floodplains over the period 2003–20075, 10 and 0.51 m for 2013 (Supplementary Information). Differences potentially arising from the large contrast in observation scale highlight possible within-basin variability of ΔTWS. Discrepancy may additionally be due to amplitude damping that occurs during GRACE processing11, for which no ground-truth basis for a scaling correction currently exists.

To further explore the hydro-mechanical BAS response to ΔTWS, we assembled characteristics of the aquifer in a numerical model of coupled vertical strain and groundwater flow in one-dimension (see Methods). A value of C = 0.75 was chosen as representative for the BAS, approximately central to the range of determined values. The significance of uncertainty in C was explored by applying the minimum (C = 0.67) and maximum (C = 0.87) values of the determined range. The simulations reproduce the characteristic features of the Gabura and Laksmipur hydrographs (Fig. 5, and Supplementary Information). Results are consistent with conclusions of hydrograph analysis that the deep groundwater head variations monitored over a twelve month period are inexplicable without reference to poroelasticity. The purely hydraulic response, when C = 0 (Fig. 5b and e), is significantly overprinted by poroelastic effects at all values of C within the determined range when vertical hydraulic diffusivity values representative of BAS are applied (Fig. 5c and f, and Supplementary Information). The modelled hydrograph peaks are synchronous with the surface water loading signal, and the poroelastic effect becomes increasingly dominant with depth (Fig. 5d and g). In the tidal scenario, the shorter period of the spring/neap tidal signal compared to monsoonal forcing leads to shallower penetration of the hydraulic response, so the poroelastic influence is more uniformly dominant throughout the stratigraphic column. Modelling therefore confirms that ignoring poroelastic effects on hydraulic head would lead to false conclusions in respect of aquifer replenishment and depletion.

The depth at which poroelastic effects become important can vary greatly from one location to another, depending largely on the permeability structure of the overlying formations. Poroelastic dominance has been recorded at 40 m (New Zealand34) and 52 m (South Carolina, USA36). The model results (Fig. 5 and Supplementary Information) suggest that poroelastic effects in BAS may become significant at depths much shallower than reported here for Gabura and Laksmipur. In the monsoon scenarios with C = 0.75, poroelasticity imposes a relative difference exceeding 25% of the purely hydraulic response at depths as shallow as 25 m (Fig. 5d), thus affecting water levels over approximately half the hydrological year including the monsoon season (when groundwater levels are higher than otherwise) and the dry season (when groundwater levels are lower than otherwise). Boreholes used for groundwater level monitoring by the Bangladesh Water Development Board range from less than 5 m to 77 m depth (median 30 m, n = 1035)4; 76% (n = 790) are deeper than 25 m and are therefore vulnerable to significant poroelastic disturbance where confined conditions pertain.

## Conclusions

Our findings expose the magnitude of the poroelastic effects of terrestrial water loading on the largest fluvio-deltaic aquifer system in south Asia. They challenge the validity of the traditional philosophy of borehole water level measurement as a means to monitor groundwater storage and recharge in BAS10, 31, 32 and possibly other extensive fluvio-deltaic aquifers of the Asian mega-deltas. More generally, they challenge the application of uncoupled, solely hydraulic treatments of transient groundwater conditions in these regions33. Strategies for management and monitoring of groundwater resources in the fluvio-deltaic aquifers of south Asia should consider a broader, coupled hydro-mechanical approach which acknowledges poroelasticity.

Applying determinations of loading efficiency at Laksmipur, we have made the first direct, in-situ determination of ΔTWS in a tropical fluvio-deltaic environment. Results complement GRACE determinations made across much larger spatial scales and at lower temporal resolution. We propose that multiple nests of deep boreholes across the GBM floodplains could be used to establish the scale of within-basin variability of ΔTWS and to allow a direct calibration25 of the magnitude of scaling factors applied in GRACE assessments.

## Methods

### Determination of equivalent fresh water head

We recorded absolute groundwater pressure in three boreholes at each of two sites in southern Bangladesh (Table 3) using ‘In-Situ Rugged Troll 100’ piezoresistors suspended at a known depth approximately 10 m below the static water level and set to record at hourly intervals. The boreholes were drilled by direct-circulation rotary drilling, and completed with PVC casing and a 10 m length of screen at the base, the annular space between casing and borehole wall being sealed with a bentonite and clay mixture to ensure isolation of the head measurement interval. We installed a barometric recorder in the air-filled section of one piezometer at each site to record atmospheric pressure. We evaluated groundwater density at each piezometer from electrical conductivity, a proxy for total dissolved solid content, and temperature measured in the discharge line of a submersible pump. Three well volumes were flushed prior to making measurements. We took the ratio of dissolved solids concentration in mg/L to electrical conductivity in μS/cm as 0.65 and determined density as function of temperature and concentration following standard relationships40.

To determine equivalent fresh water head at each piezometer screen, first we subtracted barometric pressure from in-situ measurements of absolute groundwater pressure to obtain gauge pressure, p w . Then we computed equivalent fresh water head, h f (m, relative to local datum), taking account of the piezoresistor depth and the groundwater density:

$${h}_{f}=({\rm{e}}-{{\rm{z}}}_{1})+({p}_{w}+{p}_{t})/({1000}^{\ast }{\rm{g}})$$
(5)
$${p}_{t}=({{\rm{z}}}_{1}\mbox{--}{{\rm{z}}}_{2}){\rho }_{f}\cdot {\rm{g}}$$
(6)

where:

e is elevation of the piezometer reference measurement point relative to local datum (m);

z1 is depth of the piezometer open section, below the piezometer reference point (m);

p w is gauge pressure at the piezoresistor (Pa);

p t is pressure at the piezometer screen due to fluid below the piezoresistor (Pa);

z2 is depth of the piezoresistor, below the piezometer reference point (m);

ρ f is groundwater density (kg/m3);

g is acceleration due to gravity.

Frequency analysis of the atmospheric, tidal and groundwater time series was implemented using the Fast Fourier Transform (FFT) algorithm in the R programming language41 (version 3.0.1). FFT was performed after the hourly time series data were detrended using a 25-point (i.e. 25-hour) moving average in order to remove the lower frequency components.

### Evaluating monsoon season accumulation of terrestrial water storage (TWSm)

Monsoon seasonal TWS accumulation was determined (Table 2) for the sensing area of each piezometer at the Laksmipur site from the difference in the equivalent fresh water head calculated at the time of maximum head, at 5.00 am on 30/9/2013 in all cases, and the minimum head at the onset of the monsoon evident at 11.00 am 4/6/2013 (LkPZ91), midday 4/6/2013 (LkPZ152), and midday 20/6/2013 (LkPZ244), using Eq. (4) after correction for barometric effects. Acknowledging uncertainty in the value of loading efficiency, C, the range of values obtained from evaluation of barometric efficiency, B, by linear regression and Fourier analysis was applied.

### Modelling coupled vertical strain and groundwater flow

We applied a numerical model to simulate the combined poroelastic and hydraulic response of the BAS aquifer using a generalised layered representation of the BAS hydrostratigraphy (Fig. 5) and an equivalent uniform representation (Supplementary Information). We used the generic finite-element code FlexPDE (pdesolutions.com) for this purpose, which has been tested in earlier modelling studies to simulate poroelastic effects42. Models were one-dimensional and solve a hydraulic head based version of Eq. (1). Values of vertical hydraulic conductivity, K v , and specific storage, S s , are consistent with the uniform BAS aquifer representation in a basin-scale numerical model20. A single value of loading efficiency, C, is applied (Fig. 5), making the model results indicative rather than representative of a specific site. The full range of determined values of C, including uncertainty, was applied in successive runs of the uniform aquifer representation (Supplementary Information). As a surface boundary condition, the hydraulic head is varied in accordance with an idealized monsoonal or spring/neap tidal loading scenario representing the changing depth of water at the surface. At the base the of the model domain no fluid flow is allowed. Models were run for a time-period of ten years at which point a dynamic steady state is reached and results were analysed.

### Data Availability

The datasets both generated and analysed during the current study are available from the corresponding author on reasonable request.

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## Acknowledgements

We are grateful to the Bangladesh Water Development Board (BWDB) for making available multi-level monitoring boreholes installed as part of the programme Establishment of Monitoring Network and Mathematical Model Study to Assess Salinity Intrusion in Groundwater in the Coastal Area of Bangladesh due to Climate Change funded by the Bangladesh Climate Change Trust Fund of the Government of Bangladesh. We also acknowledge the BWDB for providing daily rainfall measurements. We accessed tide height data for Chittagong, the closest tidal gauge station in the Bay of Bengal for which data were available covering the period of groundwater pressure recording, from the University of Hawaii Sea Level Center UHSLC (2014) http://uhslc.soest.hawaii.edu/. Kamrul Islam (formerly of BWDB, now at the Institute of Water Modelling, Dhaka) and Sukhen Goswami (formerly of Dhaka University, now at the Dhaka Water Supply & Sewerage Authority) assisted with the field installations, download of data and groundwater sampling. We acknowledge financial support from the UK Department for International Development (DfID) under the project Groundwater Resources in the Indo-Gangetic Basin (Grant 202125–108). Management and scientific oversight of the DfID project by Professor Alan MacDonald of the British Geological Survey is gratefully acknowledged. We thank Dr. Mark Cuthbert for constructive comments on a draft manuscript. The paper is published with the permission of the Executive Director of the British Geological Survey (NERC).

## Author information

Authors

### Contributions

W.G.B., R.G.T. and M.S. conceived the investigations and led the interpretation; A.Z. conceived preliminary investigations, and contributed experimental infrastructure and contextual data; R.G.T., M.S., A.Z., K.M.A. and D.J.L. installed the instrumentation; D.J.L. led the groundwater sampling and analysis; K.M.A. managed the data acquisition; M.S. led the data management; V.F.B. and W.G.B. designed the modelling scenarios; V.F.B. performed the modelling and contributed to the interpretation; W.G.B. drafted the manuscript; all authors reviewed the manuscript.

### Corresponding author

Correspondence to W. G. Burgess.

## Ethics declarations

### Competing Interests

The authors declare that they have no competing interests.

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Burgess, W.G., Shamsudduha, M., Taylor, R.G. et al. Terrestrial water load and groundwater fluctuation in the Bengal Basin. Sci Rep 7, 3872 (2017). https://doi.org/10.1038/s41598-017-04159-w

• Accepted:

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