Groundwater Head Fluctuations Research Articles

Groundwater level fluctuation caused by tide and groundwater pumping in coastal multi-layer aquifer system

This paper considered the groundwater head fluctuation induced by tide and pumping in the coastal multi-layered aquifer system. The multi-layered aquifer system comprises an unconfined aquifer, an upper confined aquifer, and a lower confined aquifer. An aquiclude exists between each two aquifers. All the layers terminate at the coastline. The new analytical solutions describing groundwater head variation in the coastal multi-confined aquifer system are derived. Superposition principle and image methods are used for the derivation of the analytical solutions. Analytical solutions of different situations of without considering pumping, of without considering tidal effect, and of N-layered confined aquifers are also derived. The impacts of the parameters of the initial phase shift of tide, pumping rate, position of the pumping well, storage coefficient, and transmissivity on the groundwater head fluctuation are discussed. The analytical solutions are applied with application examples in fitting field observations and parameter estimations. The estimated values of the hydraulic conductivities in the upper and lower confined aquifers are within the range of the values obtained from the field experiments. The fitted results of the analytical solutions capture the main characteristics of groundwater head fluctuation affected by the tide and groundwater pumping. The study of groundwater head fluctuation in the coastal zone is helpful to understand the mechanism of seawater intrusion under the influence of tide and groundwater pumping.

Loading effect of phreatic level variations induced by river tide on groundwater head fluctuations in tidal river aquifer systems

The unconfined groundwater level variations caused by the river tide can impact the fluctuation of the groundwater head in the underlying confined aquifer by loading effect. In this study, we proposed a mathematical model and provided an analytical solution for a confined aquifer system considering the loading effect when the aquifer system is eroded by the tidal river to varying extents. The results demonstrated that the loading effect tends to amplify the amplitude of the tide-induced head fluctuation while reduce its phase shift in the confined aquifer. These effects are more significant with a larger tidal loading efficiency, a wider tidal river, and a smaller tidal propagation parameter of the unconfined aquifer. The analytical solution was validated by the observed groundwater level fluctuations from a groundwater level monitoring well near a tidal river in the Peral River Delta of China, and provided reliable estimations of aquifer parameters in the region.

수치해석 접근법에 따른 지하수 공간분포 예측

This study applied the MODFLOW model using finite difference method and the NNRK model combining neural network and residual kriging for spatial groundwater level prediction in Jeju Island, South Korea. For the MODFLOW model, the differences between observed and predicted groundwater levels were 0.014-4.327 m and the relative errors were 0.50-50.82 %. For the NNRK model, the differences between observed and predicted groundwater levels were 0.022-6.185 m and the relative errors were 0.66-49.35 %. Based on MSRE, IDW model, which is a non-spatial statistical model, showed better spatial prediction results than SK and OK models, whereas RK and NNRK models outperformed the IDW model. The MODFLOW model showed relatively better results than the NNRK model in dense areas considering recharge and geological structure although the MODFLOW and NNRK models produced similar results. Furthermore, the MODFLOW model was found to effectively reflect groundwater flow by strata and temporal groundwater head fluctuations due to pumping compared to the NNRK model.

Analytical Study on the Tidal Wave Propagation Coupled with Vertical Leakage from a Vertically Heterogeneous Aquitard in a Coastal Leaky Aquifer System

Abstract Analytical studies on the tidal wave propagation in a coastal leaky aquifer commonly assume that the low-permeability aquitard is homogeneous. The aquitard is, however, vertically heterogeneous in nature due to varying soil types along the burial depth as can be frequently seen from borehole logs. In this study, an innovative analytical model is developed to explore the vertical heterogeneity in aquitard hydraulic conductivity (K) and specific storage (Ss) on the tidal wave propagation coupling with vertical leakage from the aquitard. The novelty behind the newly derived analytical solution is attributed to the fact that the aquitard along the burial depth can be divided into any number of homogeneous zones, each of which is associated with distinct K and Ss values, so that arbitrary vertical heterogeneity pattern of aquitard K and Ss can be captured. Theoretical analysis results reveal that an interlayer within the aquitard with a smaller K can significantly enhance the amplitude and phase shift of periodic groundwater head fluctuations in the leaky aquifer, while a larger Ss of the interlayer will weaken the amplitude and phase shift provided a relatively small aquitard K. Buried locations of the interlayer also implement nonnegligible effects on the tidal wave propagation. For the scenario of exponentially decaying aquitard K and Ss, which is commonly encountered for a thick aquitard, a larger decay exponent results in smaller amplitude and phase shift. This analytical study highlights the importance of vertical aquitard heterogeneity on tidal wave propagation in a coastal leaky aquifer system.

Analytical study for wave-induced submarine groundwater discharge in subtidal zone

Both tide and wave are significant coastal driving forces of submarine groundwater discharge (SGD). The hydrodynamic process of tidal SGD is well studied while wave induced part is still challenging to quantify. In this paper, an analytical study was performed to investigate wave-induced SGD in a subtidal aquifer extending horizontally infinitely with impermeable horizontal bottom. The loading effect of seawater weight overlying the seabed was taken into account. The analytical solution was validated by two-dimensional numerical simulations with modeling domains of finite horizontal extension length. Sensitivity analyses of the analytical solution showed that the amplitude of groundwater head fluctuations generally decayed exponentially with the aquifer thickness, and the decay rate decreased with increasing loading efficiency. Loading effect can decrease the head gradients between seawater and porewater. Wave-induced SGD generally increased with the aquifer’s thickness, permeability, wavenumber, wave period, and decreased with the loading efficiency and specific storage of the aquifer. The analytical and simulated results may provide guidance for assessing the wave-induced SGD and shed light on modeling the biogeochemistry process in wave dominated porous seabed environment.

A generalized analytical solution of groundwater head response to dual tide in a multi‐layered island leaky aquifer system

AbstractThe hydraulic properties of coastal aquifer systems are relevant to various hydrogeological, hydro‐ecological and engineering problems. This study presents an analytical solution for predicting groundwater head fluctuations induced by dual‐tide in multi‐layered island aquifer systems, consisting of an unconfined aquifer on the top and any number of leaky aquifers below. The solution was derived via the methods of matrix differential calculus and separation of variables. It is more general than any existing analytical solutions for the tidal pressure propagation since the new solution can consider multi‐layered aquifer systems along with the effects of leakage and aquifer length. Using this solution, we illustrated potential errors that may occur due to neglecting one or more vital factors affecting groundwater fluctuations. Besides, we articulated the groundwater response to the dual‐tide in complex coastal aquifers. Considering that some thin semipermeable layers may be ignored in practical field investigation, we also demonstrated the effects due to simplification of aquifer layers. The results showed that with the increase in the number of overlapped leaky layers, the tidal propagation in the bottom part of multi‐layered aquifer system approaches that in a single confined aquifer with the same transmissivity and storage.

Numerical groundwater modelling for studying surface water-groundwater interaction and impact of reduced draft on groundwater resources in central Ganga basin.

Water resources in India's Indo-Gangetic plains are over-exploited and vulnerable to impacts of climate change. The unequal spatial and temporal variation of meteorological, hydrological and hydrogeological parameters has created additional challenges for field engineers and policy planners. The groundwater and surface water are extensively utilized in the middle Gangetic plain for agriculture. The primary purpose of this study is to understand the discharge and recharge processes of groundwater system using trend analysis, and surface water and groundwater interaction using groundwater modelling. A comprehensive hydrological, and hydrogeological data analysis was carried out and a numerical groundwater model was developed for Bhojpur district, Bihar, India covering 2395 km2 geographical area, located in central Ganga basin. The groundwater level data analyses for the year 2018 revealed that depth to water level varies from 3.0 to 9.0 meter below ground level (m bgl) in the study area. The M-K test showed no significant declining trend in the groundwater level in the study area. The groundwater modelling results revealed that groundwater head is higher in the southern part of the district and the groundwater flow direction is from south-west to north-east. The groundwater head fluctuation between the monsoon and the summer seasons was observed to be 2 m, it is also witnessed that groundwater is contributing more to rivers in the monsoon season in comparison with other seasons. Impact of reduction in pumping on groundwater heads was also investigated, considering a 10% reduction in groundwater withdrawal. The results indicated an overall head rise of 2 m in the southern part and 0.2-0.5 m in the middle and northern part of the district.

Vulnerability of water resources under a changing climate and human activity in the lower Great Lakes region

AbstractGlobally, the number of people experiencing water stress is expected to increase by millions by the end of the century. The Great Lakes region, representing 20% of the world's surface freshwater, is not immune to stresses on water supply due to uncertainties on the impacts of climate and land use change. It is imperative for researchers and policy makers to assess the changing state of water resources, even if the region is water rich. This research developed the integrated surface water‐groundwater GSFLOW model and investigated the effects of climate change and anthropogenic activities on water resources in the lower Great Lakes region of Western New York. To capture a range of scenarios, two climate emission pathways and three land development projections were used, specifically RCP 4.5, RCP 8.5, increased urbanization by 50%, decreased urbanization by 50%, and current land cover, respectively. Model outputs of surface water and groundwater discharge into the Great Lakes and groundwater storage for mid‐ and late century were compared to historical to determine the direction and amplitude of changes. Both surface water and groundwater systems show no statistically significant changes under RCP 4.5 but substantial and worrisome losses with RCP 8.5 by mid‐century and end of century. Under RCP 8.5, streamflow decreased by 22% for mid‐century and 42% for late century. Adjusting impervious surfaces revealed complex land use effects, resulting in spatially varying groundwater head fluctuations. For instance, increasing impervious surfaces lowered groundwater levels from 0.5 to 3.8 m under Buffalo, the largest city in the model domain, due to reduced recharge in surrounding suburban areas. Ultimately, results of this study highlight the necessity of integrated modelling in assessing temporal changes to water resources. This research has implications for other water‐rich areas, which may not be immune to effects of climate change and human activities.

Multiple Wavelet Coherence to Evaluate Local Multivariate Relationships in a Groundwater System.

Groundwater level fluctuations are affected by surface properties due to complex correlations of groundwater-surface water interaction and/or other surface processes, which are usually hard to be accurately quantified. Previous studies have assessed the relationship between groundwater level fluctuations and specific controlling factors. However, few studies have been conducted to explore the impact of the combination of multiple factors on the groundwater system. Hence, this paper tries to explore the localized and scale-specific multivariate relationships between the groundwater level and controlling factors (such as hydrologic and meteorological factors) using bivariate wavelet coherence and multiple wavelet coherence. The groundwater level fluctuations of two wells in areas covered by different plant densities (i.e., the riparian zone of the Colorado River, USA) are analyzed. Main findings include three parts. First, barometric pressure and river stage are the best factors to interpret the groundwater level fluctuations at small scales (<1day) and large scales (>1day) at the well of low-density plants stand, respectively. Second, at the well of high-density plants stand, the best predictors to control the groundwater level fluctuations include barometric pressure (<1day), the combination of barometric pressure and temperature (1-7 days), temperature (7-30 days), and the combination of barometric pressure, temperature, and river stage (>30 days). The best predictor of groundwater head fluctuations depends on the variance of the vegetation coverage and hydrological processes. Third, these results provide a suite of factors to explain the groundwater level variations, which is an important topic in water-resource prediction and management.

Identification of hydrogeological evolution using hydrogeology-seismology analysis of groundwater head fluctuation related to the 1999 MW = 7.5 Chi-Chi earthquake

At 1:47 a.m. on September 21, 1999, the Mw 7.5 Chi-Chi earthquake struck Taiwan. The purpose of this study is to (1) apply multiple spatiotemporal-frequency analysis to filter the post-seismic change in groundwater head to explore the implicit drawdown associated with excess pore-water pressure release and effective stress relief during post-seismic evolution and (2) establish a stochastic experimental optimization model for identifying the hydrogeological evolution. The approaches used for post-seismic drawdown filtration include multi-rank principal components decomposition, multi-frequent wavelet transforms decomposition, and multi-level wavelet de-noising. This study especially evaluates the following advanced post-seismic evolving parameters: (1) harmonic average leaking/injecting rate, (2) distance between the acting position and monitoring well, (3) storage coefficient under effective stress relief and formation compression, and (4) transmissivity for excess-pore-water pressure release. This study applies the integrated methodology on 179 monitoring wells in the Chou-Shui River alluvial fan. Results show that the overlying principal components PCs and low-level wavelet de-noising can filter additional sources/sinks, in which the extracted drawdown from PC1+PC3 was related to the excess pore-water pressure relaxation process, that from PC2+PC5+PC6+PC7 and high-frequency wavelet de-noised detail cD2 related to the earth tidal fluctuation effect, and that from PC4+PC9 and cD3 related to the barometric effect. According to the Riemann integral and an objective function value duration curve, calculated occurrence probability from the stochastic optimization for SC2, the storage coefficient was reduced from pre-seismic pumping test value 0.00107, post-seismic 27th hour evolving value 0.000826 to post-seismic pumping test value 0.000578 in 2004, and the transmissivity increased from pre-seismic test value 92.4 m2/h, post-seismic 27th hour evolving value 98.6 m2/h to post-seismic test value 147.6 m2/h. The results demonstrate that the SC2 and GH3 zones suffer from crustal compression and the permeability was increased to dissipate excess pore-water pressure and effective stress.

Monitoring groundwater heads and estimating recharge in multi-aquifer systems illustrated by an irrigated area in north-west Bangladesh

The impact of groundwater abstraction in multi-aquifer systems can be identified by monitoring variations of groundwater heads with depth and with time. Equally important are estimates of recharge to the groundwater system including contributions from irrigation. A case study from the Rajshahi Barind in Bangladesh illustrates the methodologies. Abstraction of groundwater from deep tubewells has resulted in substantial increases in agricultural production but also significant falls in groundwater heads in the aquifers. Monitoring of the groundwater heads at different depths and relating these to the lithology has indicated the formation of an additional water table in an intermediate aquifer; this leads to the conceptualisation of the aquifer system as two Units, Upper and Lower. Estimates of the potential recharge to the aquifer system are obtained from a daily soil water balance which is enhanced to include the representation of recharge from standing water in flooded ricefields. Detailed fieldwork, over a period of more than 2 years, includes daily records of groundwater heads, rainfall, temperature and hours of pumping for irrigation; information about the crops grown in the command area is also collected. Individual, but interconnected, conceptual and computational models for the two Units are developed. The outputs of the computational models show good agreement with measured groundwater head fluctuations. Using information from the computational models, the sustainability of the current abstraction patterns is considered.

Analytical Solution of Tidal Loading Effect in a Submarine Leaky Confined Aquifer System

Although there are many existing analytical studies of tidal groundwater level fluctuations in coastal aquifer systems, few of them focus on an offshore submarine aquifer. Here, we consider tidal groundwater head fluctuations in a submarine leaky confined aquifer overlain by a semipermeable seabed. Both the seabed and the confined aquifer are assumed to extend horizontally infinitely. A one-dimensional mathematical model is established to describe the problem, and the analytical solution is derived. The impacts of the tidal loading efficiency, hydraulic conductivity and elastic storage of the semipermeable layer and aquifer on the groundwater head fluctuations in the aquifer system are analyzed and discussed. Solution analyses indicated that tidal loading effects tend to enhance the amplitude of the tidal groundwater fluctuation in the confined aquifer system and to reduce the phase shift between the groundwater head and the sea tide fluctuations.

The Risk of Liquefaction Associated with Water Head Fluctuation in the Low-lying Area of Tokyo

In the wide area of the eastern part of Tokyo, the ground level is less than mean sea level. This area is more vulnerable to disasters than other areas. If large flood damage such as storm surge should occur in this area, the disaster would be a long-term catastrophe. On the coast of Tokyo Bay, countermeasures have been taken by tide embankments and floodgates. However, considering the damage scale when it occurs, an analysis in this area is very important. In this area, ground settlement occurred and groundwater head dropped because groundwater excessively withdrew by the industrial purpose during the period of economic growth. Currently, the groundwater head recovers and the ground settlement has been subsided. However, due to the groundwater head fluctuation, pore water pressure distribution had been different from hydrostatic pressure distribution. Therefore, in the analysis in this area, it is necessary to consider past groundwater head fluctuation. In this research, the ground settlement and the distribution of pore water pressure are simulated from groundwater level fluctuation over the past 100 years. Then, we conducted the seismic analysis by input the distribution of effective stress calculating from the simulated ground water pressure. The sites analyzed in this research are Tokyo Sea Life Park at the mouth of Arakawa River.

Statistical Analysis of Extreme Events in Precipitation, Stream Discharge, and Groundwater Head Fluctuation: Distribution, Memory, and Correlation

Hydrological extremes in the water cycle can significantly affect surface water engineering design, and represents the high-impact response of surface water and groundwater systems to climate change. Statistical analysis of these extreme events provides a convenient way to interpret the nature of, and interaction between, components of the water cycle. This study applies three probability density functions (PDFs), Gumbel, stable, and stretched Gaussian distributions, to capture the distribution of extremes and the full-time series of storm properties (storm duration, intensity, total precipitation, and inter-storm period), stream discharge, lake stage, and groundwater head values observed in the Lake Tuscaloosa watershed, Alabama, USA. To quantify the potentially non-stationary statistics of hydrological extremes, the time-scale local Hurst exponent (TSLHE) was also calculated for the time series data recording both the surface and subsurface hydrological processes. First, results showed that storm duration was most closely related to groundwater recharge compared to the other storm properties, while intensity also had a close relationship with recharge. These relationships were likely due to the effects of oversaturation and overland flow in extreme total precipitation storms. Second, the surface water and groundwater series were persistent according to the TSLHE values, because they were relatively slow evolving systems, while storm properties were anti-persistent since they were rapidly evolving in time. Third, the stretched Gaussian distribution was the most effective PDF to capture the distribution of surface and subsurface hydrological extremes, since this distribution can capture the broad transition from a Gaussian distribution to a power-law one.

Temporal Scaling Analytical Method to Identify Multi-Fractionality in Groundwater Head Fluctuations.

Natural dynamics such as groundwater head fluctuations may exhibit multi-fractionality, likely caused by multi-scale aquifer heterogeneity and other controlling factors, whose statistics requires efficient quantification methods. As a scaling exponent, the Hurst exponent can describe the temporal correlation or multifractal behavior in groundwater level fluctuation processes. However, the scaling behavior may change with time under natural conditions, likely due to the non-stationary evolution of internal and external conditions, which cannot be characterized by traditional methods using a single or several scaling exponents for the complex features of the overall process. This methods note quantifies the multi-fractionality using the timescale local Hurst exponent (TS-LHE) and then proposes a systematic statistical method to analyze groundwater head fluctuations. Time series of daily groundwater level fluctuations from three wells located in the lower Mississippi valley are analyzed, after removing the seasonal cycle, which leads to transient TS-LHE, implying multi-fractionality and multifractal-scaling behavior that changes with time and location. Therefore, the temporal scaling analysis proposed here may provide useful and quantitative information to understand the nature of dynamic hydrologic systems.

A global-scale two-layer transient groundwater model: Development and application to groundwater depletion

Groundwater is the world’s largest accessible source of freshwater to satisfy human water needs. Moreover, groundwater buffers variable precipitation rates over time, thereby effectively sustaining river flows in times of droughts and evaporation in areas with shallow water tables. In this study, building on previous work, we simulate groundwater head fluctuations and groundwater storage changes in both confined and unconfined aquifer systems using a global-scale high-resolution (5′) groundwater model by deriving new estimates of the distribution and thickness of confining layers. Inclusion of confined aquifer systems (estimated 6–20% of the total aquifer area) improves estimates of timing and amplitude of groundwater head fluctuations and changes groundwater flow paths and groundwater-surface water interaction rates. Groundwater flow paths within confining layers are shorter than paths in the underlying aquifer, while flows within the confined aquifer can get disconnected from the local drainage system due to the low conductivity of the confining layer. Lateral groundwater flows between basins are significant in the model, especially for areas with (partially) confined aquifers were long flow paths crossing catchment boundaries are simulated, thereby supporting water budgets of neighboring catchments or aquifer systems. The developed two-layer transient groundwater model is used to identify hot-spots of groundwater depletion. Global groundwater depletion is estimated as 7013 km3 (137 km3y−1) over 1960–2010, which is consistent with estimates of previous studies.

Hydraulic response of an unconfined-fractured two-aquifer system driven by dual tidal or stream fluctuations

Many islands consist of limestone sedimentary deposits that are better described as a two-aquifer system consisting of an unconfined aquifer (Quaternary sediments) above a fractured aquifer (fractured limestone) in which groundwater heads are closely regulated by tidal fluctuations on both sides of the islands (dual tides). Propagation of tidal signal, reflected in hydraulic head fluctuation in such a two-aquifer system is significantly different from that in a single aquifer system that is often assumed. The Laplace domain solution of the head fluctuation in such a two-aquifer system subjected to dual tides is obtained first and subsequently inverted to yield real-time solution. Unlike previous solutions, Fourier series with complex variables are avoided and Fourier sine transform is used instead. The solution takes into account an instantaneously drainable water table, hydraulic conductivity anisotropy and arbitrary time-dependent tidal fluctuations. The hydraulic connection of the underlying fractured aquifer and the overlying unconfined aquifer is explored in details. The presented solution can be used to evaluate the head fluctuations and the aquifer parameter estimation of the two-aquifer system underneath a strip-shape island subjected to dual tides. The results can be used to determine the optimum piezometer location to estimate hydraulic parameters of the two-aquifer system using groundwater head fluctuation data. Stream-aquifer interaction is similar to the tidal-aquifer interaction if the chemical difference of the salt water and fresh water is not a concern. The developed solution for tidal-aquifer interaction here can also be used to investigate the aquifer response to stream stage variations in river basin aquifers.

Understanding and quantifying focused, indirect groundwater recharge from ephemeral streams using water table fluctuations

AbstractUnderstanding and managing groundwater resources in drylands is a challenging task, but one that is globally important. The dominant process for dryland groundwater recharge is thought to be as focused, indirect recharge from ephemeral stream losses. However, there is a global paucity of data for understanding and quantifying this process and transferable techniques for quantifying groundwater recharge in such contexts are lacking. Here we develop a generalized conceptual model for understanding water table and groundwater head fluctuations due to recharge from episodic events within ephemeral streams. By accounting for the recession characteristics of a groundwater hydrograph, we present a simple but powerful new water table fluctuation approach to quantify focused, indirect recharge over both long term and event time scales. The technique is demonstrated using a new, and globally unparalleled, set of groundwater observations from an ephemeral stream catchment located in NSW, Australia. We find that, following episodic streamflow events down a predominantly dry channel system, groundwater head fluctuations are controlled by pressure redistribution operating at three time scales from vertical flow (days to weeks), transverse flow perpendicular to the stream (weeks to months), and longitudinal flow parallel to the stream (years to decades). In relative terms, indirect recharge decreases almost linearly away from the mountain front, both in discrete monitored events as well as in the long‐term average. In absolute terms, the estimated indirect recharge varies from 80 to 30 mm/a with the main uncertainty in these values stemming from uncertainty in the catchment‐scale hydraulic properties.

Groundwater Response to Tidal Fluctuation in an Inhomogeneous Coastal Aquifer-Aquitard System

This paper investigates tide-induced groundwater fluctuation and submarine groundwater discharge (SGD) in a leaky inhomogeneous coastal aquifer system with an upper unconfined aquifer, a lower confined aquifer, and an aquitard between them. The upper left aquifer is formed due to land reclamation. The SGD defined as the groundwater flow from land into the sea is controlled mainly by the hydraulic gradient between land and sea. An analytical expression is developed to discuss and assess the effect of inhomogeneity on the groundwater head fluctuation in the leaky aquifer system. Joint effects of aquifers’ parameters such as leakage and hydraulic diffusivity on the groundwater head fluctuation and SGD are investigated. The predicted results from the analytical expression indicate that the groundwater head fluctuation in both unconfined and confined aquifers is dependent on dimensionless leakages and increases with dimensionless hydraulic diffusivity.

Deriving hydrogeological parameters through time series analysis of groundwater head fluctuations around well fields

A method is presented by which time series analysis is applied to support groundwater system conceptualization and provide calibration targets for a steady groundwater model. The method is demonstrated for heads measured in the vicinity of a drinking-water well field. The estimated steady response to pumping was used to classify the monitoring wells as semi-confined or phreatic. Based on this conceptualization, the aquifer system was represented by two layers separated by a leaky bed, which represents the resistance to vertical flow of the layers. The model could be calibrated satisfactorily using the drawdowns estimated by time series analysis. This approach was more successful than deriving the aquifer parameters directly from the analytical well function of Hantush, which was successful for a limited number of monitoring wells only and required the a priori choice of the elevation of a confining layer which was not clear from bore logs. This study shows that time series analysis can lead to qualitative and quantitative insights regarding the local hydrogeology, providing complementary information to available bore logs to design a conceptual groundwater model. Time series analysis provides a cost-effective alternative to pumping tests when measured head fluctuations influenced by pumping wells are available.