Skip to main content

Advertisement

SpringerLink
Log in

Improvements in a simple harmonic analysis of groundwater time series based on error analysis on simulated data of specified lengths

  • Article
  • Published:
Paddy and Water Environment Aims and scope Submit manuscript

Abstract

Tidal response method is an efficient technique for investigating hydraulic properties of an aquifer in insular and coastal areas of highly permeable geological settings. The present study extends a simple and straightforward harmonic-analysis technique recently introduced as part of a tidal response method applied to a freshwater-lens aquifer. This simple analysis technique was examined with artificially synthesized time series composed of multiple realistic tidal components. The analysis outputs of major diurnal and semidiurnal components are sufficiently accurate if the analyzed time-series length is appropriately restricted. Limitations of the simple harmonic analysis in the applicable time-series length arise from tidal-component interference that occurs in analyses over a finite length. Definitively recommended simple harmonic-analysis technique with appropriate combinations of time-series lengths and extractable tidal components are convenient for investigating hydraulic properties of an aquifer, such as on a remote island where the freshwater lens is the only freshwater resource.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Abd-Elhamid HF, Javadi AA (2011) Impact of sea level rise and over-pumping on seawater intrusion in coastal aquifers. J Water Clim Change 2(1):19–28

    Article  Google Scholar 

  • Aichi M, Shiokari M, Tokunaga T (2011) A new analytical solution of water table response to tidal fluctuations and its application to estimate aquifer properties at the Niijima Island, Japan (in Japanese with English abstract). J Groundw Hydrol 53(3):249–265

    Article  Google Scholar 

  • Alcolea A, Castro E, Barbieri M, Carrera J, Bea S (2007) Inverse modeling of coastal aquifers using tidal response and hydraulic tests. Ground Water 45(6):711–722

    Article  CAS  PubMed  Google Scholar 

  • Aubrey DG, Speer PE (1985) A study of non-linear tidal propagation in shallow inlet/estuarine systems Part I: observations. Estuar Coast Shelf Sci 21(2):185–205

    Article  Google Scholar 

  • Azuma R, Hiraishi T, Nakano S (2011) Groundwater responses to tidal and meteo-hydrological forcing in a coastal sand-dune area (in Japanese with English abstract). J Jpn Soc Civil Eng Ser B2 67(2):I_1066–I_1070

    Google Scholar 

  • Baharuddin MFT, Taib S, Hashim R, Abidin MHZ, Rahman NI (2013) Assessment of seawater intrusion to the agricultural sustainability at the coastal area of Carey Island, Selangor, Malaysia. Arab J Geosci 6(10):3909–3928

    Article  Google Scholar 

  • Bailey RT, Jenson JW (2014) Effects of marine overwash for atoll aquifers: environmental and human factors. Ground Water 52(5):694–704

    Article  CAS  PubMed  Google Scholar 

  • Bailey RT, Jenson JW, Olsen AE (2009) Numerical modeling of atoll island hydrogeology. Ground Water 47(2):184–196

    Article  CAS  PubMed  Google Scholar 

  • Bailey RT, Jenson JW, Olsen AE (2010) Estimating the ground water resources of atoll islands. Water 2(1):1–27

    Article  Google Scholar 

  • British Columbia Ministry of Environment (2010) Guide to Conducting Well Pumping Tests. Water Stewardship Information Series

  • Carol ES, Kruse EE, Pousa JL, Roig AR (2009) Determination of heterogeneities in the hydraulic properties of a phreatic aquifer from tidal level fluctuations: a case in Argentina. Hydrogeol J 17(7):1727–1732

    Article  Google Scholar 

  • Carr PA (1971) Use of harmonic analysis to study tidal fluctuations in aquifers near the sea. Water Resour Res 7(3):632–643

    Article  Google Scholar 

  • Carr PA, Van der Kamp GS (1969) Determining aquifer characteristics by the tidal method. Water Resour Res 5(5):1023–1031

    Article  Google Scholar 

  • Cartwright DE, Tayler RJ (1971) New computations of the tide-generating potential. Geophys J R Astron Soc 23(1):45–73

    Article  Google Scholar 

  • Cartwright N, Nielsen P, Li L (2004) Experimental observations of watertable waves in an unconfined aquifer with a sloping boundary. Adv Water Resour 27(10):991–1004

    Article  Google Scholar 

  • Chapuis RP, Bélanger C, Chenaf D (2006) Pumping test in a confined aquifer under tidal influence. Ground Water 44(2):300–305

    Article  CAS  PubMed  Google Scholar 

  • Chattopadhyay PB, Singh VS (2013) Hydrochemical evidences: vulnerability of atoll aquifers in Western Indian Ocean to climate change. Glob Planet Change 106:123–140

    Article  Google Scholar 

  • Chattopadhyay PB, Vedanti N, Singh VS (2015) A conceptual numerical model to simulate aquifer parameters. Water Resour Manag 29(3):771–784

    Article  Google Scholar 

  • Chikamori K, Agemori C, Matsuda S (1972) The determination of the transmissibility of coastal aquifer (in Japanese with English abstract). Trans Jpn Soc Irrig Drain Reclam Eng 42:13–20

    Google Scholar 

  • Chui TFM, Terry JP (2013) Influence of sea-level rise on freshwater lenses of different atoll island sizes and lens resilience to storm-induced salinization. J Hydrol 502:18–26

    Article  Google Scholar 

  • Cordier E, Lézé J, Join J-L (2013) Natural tidal processes modified by the existence of fringing reef on La Reunion Island (Western Indian Ocean): impact on the relative sea level variations. Cont Shelf Res 55(1):119–128

    Article  Google Scholar 

  • Dillon P (1997) Groundwater pollution by sanitation on tropical islands. Technical Documents in Hydrology, IHP-V Project 6-1, UNESCO, Paris

  • Doodson AT (1921) The harmonic development of the tide-generating potential. Proc R Soc Lond Ser A 100(704):305–329

    Article  Google Scholar 

  • Drogue C, Razack M, Krivic P (1984) Survey of a coastal karstic aquifer by analysis of the effect of the sea-tide: example of the Kras of Slovenia, Yugoslavia. Environ Geol Water Sci 6(2):103–109

    Article  Google Scholar 

  • Duncan D (2012) Freshwater under threat/Pacific Islands/vulnerability assessment of freshwater resources to environmental change. United Nations Environment Programme (UNEP)

  • Emery WJ, Thomson RE (2001) Data analysis methods in physical oceanography, second and revised edition. Elsevier, Amsterdam

    Google Scholar 

  • Erskine AD (1991) The effect of tidal fluctuation on a coastal aquifer in the UK. Ground Water 29(4):556–562

    Article  Google Scholar 

  • Fakir Y, Razack M (2003) Hydrodynamic characterization of a Sahelian coastal aquifer using the ocean tide effect (Dridrate Aquifer, Morocco). Hydrol Sci J 48(3):441–454

    Article  Google Scholar 

  • Ferris JG (1951) Cyclic fluctuations of water level as a basis for determining aquifer transmissibility. Int Assoc Sci Hydrol Publ 33:148–155

    Google Scholar 

  • Fetter CW Jr (1972) Position of the saline water interface beneath oceanic islands. Water Resour Res 8(5):1307–1314

    Article  Google Scholar 

  • Feynman RP, Leighton RB, Sands M (2010) Harmonics. In: The Feynman lectures on physics, new millennium edition (3rd printing), vol I. Basic Books, New York, pp 50–1, 50–10

  • Foreman MGG, Henry RF (1989) The harmonic analysis of tidal model time series. Adv Water Resour 12(3):109–120

    Article  Google Scholar 

  • Gregg DO (1966) An analysis of ground-water fluctuations caused by ocean tides in Glynn County, Georgia. Ground Water 4(3):24–32

    Article  Google Scholar 

  • Guo H, Jiao JJ, Li H (2010) Groundwater response to tidal fluctuation in a two-zone aquifer. J Hydrol 381(3–4):364–371

    Article  Google Scholar 

  • Ishida S, Tsuchihara T, Imaizumi M (2006) Fluctuation of NO3-N in groundwater of the reservoir of the Sunagawa Subsurface Dam, Miyako Island, Japan. Paddy Water Environ 4(2):101–110

    Article  Google Scholar 

  • Ishida S, Tsuchihara T, Yoshimoto S, Imaizumi M (2011) Sustainable use of groundwater with underground dams. Jpn Agric Res Quart 45(1):51–61

    Article  Google Scholar 

  • Jacob CE (1950) Flow of groundwater. In: Rouse H (ed) Engineering hydraulics. Willey, Chapman & Hall, Limited, New York, London, pp 321–386

    Google Scholar 

  • Jha MK, Kamii Y, Chikamori K (2003) On the estimation of phreatic aquifer parameters by the tidal response technique. Water Resour Manag 17(1):69–88

    Article  Google Scholar 

  • Jha MK, Namgial D, Kamii Y, Peiffer S (2008) Hydraulic parameters of coastal aquifer systems by direct methods and an extended tide-aquifer interaction technique. Water Resour Manag 22(12):1899–1923

    Article  Google Scholar 

  • Joseph A, Balachandran KK, Mehra P, Prabhudesai RG, Kumar V, Agarvadekar Y, Revichandran C, Dabholkar N (2009) Amplified Msf tides at Kochi backwaters on the southwest coast of India. Curr Sci 97(6):776–784

    Google Scholar 

  • Ketabchi H, Mahmoodzadeh D, Ataie-Ashtiani B, Werner AD, Simmons CT (2014) Sea-level rise impact on fresh groundwater lenses in two-layer small islands. Hydrol Process 28(21):5938–5953

    Article  Google Scholar 

  • Kobayashi T, Koda K (eds) (2012) Development of survey method for freshwater lens in Marshall Islands. JIRCAS Working Report 77

  • Koda K, Kobayashi T, Ishida S, Yoshimoto S (2013) Estimation of hydraulic parameters in the freshwater lens aquifer in Laura Island (in Japanese). Water Land Environ Eng 81(7):541–545

    Google Scholar 

  • Kudryavtsev SM (2004) Improved harmonic development of the Earth tide-generating potential. J Geod 77:829–838

    Article  Google Scholar 

  • Kvale EP (2006) The origin of neap-spring tidal cycles. Mar Geol 235(1–4):5–18

    Article  Google Scholar 

  • Li H, Jiao JJ, Tang Z (2006) Semi-numerical simulation of groundwater flow induced by periodic forcing with a case-study at an island aquifer. J Hydrol 327(3–4):438–446

    Article  Google Scholar 

  • Liu Y, Shang S-H, Mao X-M (2012) Tidal effects on groundwater dynamics in coastal aquifer under different beach slopes. J Hydrodyn Ser B 24(1):97–106

    Article  Google Scholar 

  • Marone E, Raicich F, Mosetti R (2013) Harmonic tidal analysis methods on time and frequency domains: similarities and differences for the Gulf of Trieste, Italy, and Paranaguá Bay, Brazil. Bollettino di Geofisica Teorica ed Applicata 54(2):183–204

    Google Scholar 

  • Martin JB, Gulley J, Spellman P (2012) Tidal pumping of water between Bahamian blue holes, aquifers, and the ocean. J Hydrol 416–417:28–38

    Article  Google Scholar 

  • Millham NP, Howes BL (1995) A comparison of methods to determine K in a shallow coastal aquifer. Ground Water 33(1):49–57

    Article  CAS  Google Scholar 

  • Mondal NC, Singh VS, Sarwade DV, Nandakumar MV (2009) Appraisal of groundwater resources in an island condition. J Earth Syst Sci 118(3):217–229

    Article  CAS  Google Scholar 

  • Morgan LK, Werner AD (2014) Seawater intrusion vulnerability indicators for freshwater lenses in strip islands. J Hydrol 508(16):322–327

    Article  Google Scholar 

  • Nawa N, Miyazaki K (2009) The analysis of saltwater intrusion through Komesu underground dam and water quality management for salinity. Paddy Water Environ 7(2):71–82

    Article  Google Scholar 

  • Ni JC, Cheng W-C, Gec L (2013) A simple data reduction method for pumping tests with tidal, partial penetration, and storage effects. Soils Found 53(6):894–902

    Article  Google Scholar 

  • Nielsen P (1990) Tidal dynamics of the water table in beaches. Water Resour Res 26(9):2127–2134

    Google Scholar 

  • Pandit A, Ei-Khazen CC, Sivaramapillai SP (1991) Estimation of hydraulic conductivity values in a coastal aquifer. Ground Water 29(2):175–180

    Article  Google Scholar 

  • Parker BB (2007) Tidal analysis and prediction. NOAA Special Publication NOS CO-OPS 3, Silver Spring, Maryland

    Google Scholar 

  • Presley TK (2005) Effects of the 1998 drought on the freshwater lens in the Laura area, Majuro Atoll, Republic of the Marshall Islands. USGS scientific investigations report 2005–5098

  • Raubenheimer B, Guza RT, Elgar S (1999) Tidal water table fluctuations in a sandy ocean beach. Water Resour Res 35(8):2313–2320

    Article  Google Scholar 

  • Razack M, Drogue C, Romariz C, Almeida C (1980) Ocean tide effect study on a coastal carbonate aquifer (Miocene of Algarve, Portugal) (in French with English abstract). J Hydrol 45(1–2):57–69

    Article  Google Scholar 

  • Robinson IS, Warren L, Longbottom JF (1983) Sea-level fluctuations in the Fleet, an English tidal lagoon. Estuar Coast Shelf Sci 16(6):651–668

    Article  Google Scholar 

  • Rotzoll K, El-Kadi AI, Gingerich SB (2008) Analysis of an unconfined aquifer subject to asynchronous dual-tide propagation. Ground Water 46(2):239–250

    Article  CAS  PubMed  Google Scholar 

  • Sánchez Úbeda JP, Calvache Quesada ML, López Chicano M, Duque C, Martín Rosales W (2013) Tidal influence on measured head of the discharge zone of the Motril-Salobreña Coastal Aquifer (Granada) (in Spanish with English abstract). Geogaceta 53:121–124

    Google Scholar 

  • Schmorak S, Mercado A (1969) Upconing of fresh water-sea water interface below pumping wells, field study. Water Resour Res 5(6):1290–1311

    Article  CAS  Google Scholar 

  • Schultz G, Ruppel C (2002) Constraints on hydraulic parameters and implications for groundwater flux across the upland-estuary interface. J Hydrol 260(1–4):255–269

    Article  Google Scholar 

  • Schureman P (1940) Manual of harmonic analysis and prediction of tides. U.S. Government Printing Office, Washington, DC, U.S. Department of Commerce Coast and Geodetic Survey Special Publication No. 98 Revised (1940) edition (reprinted 1958 with corrections)

  • Sekiguchi H, Azuma R, Sambodho K (2007) Field observations of unconfined groundwater dynamics in a nourished sand beach (in Japanese with English abstract). Proc Coast Eng JSCE 54:721–725

    Article  Google Scholar 

  • Shih DC-F (1999) Inverse solution of hydraulic diffusivity determined by water level fluctuation. J Am Water Resour Assoc 35(1):37–47

    Article  Google Scholar 

  • Shih DC-F, Lin G-F (2004) Application of spectral analysis to determine hydraulic diffusivity of a sandy aquifer (Pingtung County, Taiwan). Hydrol Process 18(9):1655–1669

    Article  Google Scholar 

  • Shirahata K, Ishida S, Yoshimoto S, Tsuchihara T (2014) New simple method for estimating hydraulic properties of a freshwater-lens aquifer by analysis of tidal groundwater fluctuations (in Japanese with English summary). Tech Rep Natl Inst Rural Eng 215:141–154

    Google Scholar 

  • Shoji J, Momii K, Fujino K, Kunitake M (1999) Analysis of seawater intrusion into a Ryukyu Limestone coastal aquifer using an immiscible approach—development and conservation of groundwater resources on a small island (I) (in Japanese with English abstract). Trans Jpn Soc Irrig Drain Reclam Eng 201:59–66

    Google Scholar 

  • Smith AJ (1999) Application of a tidal method for estimating aquifer diffusivity: Swan River, Western Australia. CSIRO Land and Water Technical Report 13/99

  • Smith AJ, Hick WP (2001) Hydrogeology and aquifer tidal propagation in Cockburn Sound, Western Australia. CSIRO Land and Water Technical Report 6/01

  • Spennemann DHR (1996) Nontraditional settlement patterns and typhoon hazard on contemporary Majuro Atoll, Republic of the Marshall Islands. Environ Manag 20(3):337–348

    Article  CAS  Google Scholar 

  • Tamura Y (1987) A harmonic development of the tide-generating potential. Bulletin d’Informations Marées Terrestres 99:6813–6855

    Google Scholar 

  • Trefry MG (1999) Periodic forcing in composite aquifers. Adv Water Resour 22(6):645–656

    Article  Google Scholar 

  • Trefry MG, Bekele E (2004) Structural characterization of an island aquifer via tidal methods. Water Resour Res 40(1):W01505

    Article  Google Scholar 

  • Trefry MG, Jhonston CD (1998) Pumping test analysis for a tidally forced aquifer. Ground Water 36(3):427–433

    Article  CAS  Google Scholar 

  • Underwood MR, Peterson FL, Voss CI (1992) Groundwater lens dynamics of atoll islands. Water Resour Res 28(11):2889–2902

    Article  Google Scholar 

  • Urish DW (1980) Asymmetric variation of Ghyben-Herzberg lens. J Hydraul Division Proc Am Soc Civil Eng 106(7):1149–1158

    Google Scholar 

  • Van der Velde M, Green SR, Vanclooster M, Clothier BE (2007) Sustainable development in small island developing states: agricultural intensification, economic development, and freshwater resources management on the coral atoll of Tongatapu. Ecol Econ 61(2–3):456–468

    Article  Google Scholar 

  • White I, Falkland T (2010) Management of freshwater lenses on small Pacific islands. Hydrogeol J 18(1):227–246

    Article  CAS  Google Scholar 

  • Xia Y, Li H (2009) The estimation of aquifer parameters using tidal effect in a coastal aquifer: a case study in Beihai Peninsula. Earth Sci Front 16(6):276–281

    Article  Google Scholar 

  • Yamada S, Yonahara N, Sobue H (2009) The Quaternary coral reef complex deposits (Ryukyu Group) and hydrogeologic features on Tarama-jima, Okinawa Prefecture, Japan (in Japanese). Abstracts of the 116th annual meeting of the geological society of Japan:83

  • Yoshimoto S, Tsuchihara T, Ishida S, Masumoto T, Imaizumi M (2011) Groundwater flow and transport and potential sources of groundwater nitrates in the Ryukyu Limestone as a mixed flow aquifer in Okinawa Island, Japan. Paddy Water Environ 9(4):367–384

    Article  Google Scholar 

  • Yoshimoto S, Tsuchihara T, Ishida S, Imaizumi M (2013) Development of a numerical model for nitrates in groundwater in the reservoir area of the Komesu subsurface dam, Okinawa, Japan. Environ Earth Sci 70(5):2061–2077

    Article  CAS  Google Scholar 

  • Zhou X (2008) Determination of aquifer parameters based on measurements of tidal effects on a coastal aquifer near Beihai, China. Hydrol Process 22(16):3176–3180

    Article  Google Scholar 

  • Zhou Q, Bear J, Bensabat J (2005) Saltwater upconing and decay beneath a well pumping above an interface zone. Transp Porous Media 61(3):337–363

    Article  CAS  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for useful suggestions that greatly helped to improve the original manuscript. This work was supported by a research project (Development of Mitigation and Adaptation Technologies as Countermeasures against Global Warming Affects in Agriculture, Forestry and Fisheries, 91150) funded by Ministry of Agriculture, Forestry and Fisheries of Japan and in part by JSPS KAKENHI Grant Number 26660194.

Funding

This study was supported by a project sponsor Ministry of Agriculture, Forestry and Fisheries of Japan: “Development of Mitigation and Adaptation Technologies as Countermeasures against Global Warming Affects in Agriculture, Forestry and Fisheries (91150),” and in part by JSPS KAKENHI Grant Number 26660194.

Author information

Authors and Affiliations

  1. National Institute for Rural Engineering, National Agriculture and Food Research Organization, 2-1-6 Kannondai, Tsukuba, Ibaraki, 305-8609, Japan

    Katsushi Shirahata, Shuhei Yoshimoto, Takeo Tsuchihara & Satoshi Ishida

Authors
  1. Katsushi Shirahata
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shuhei Yoshimoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Takeo Tsuchihara
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Satoshi Ishida
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Katsushi Shirahata.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shirahata, K., Yoshimoto, S., Tsuchihara, T. et al. Improvements in a simple harmonic analysis of groundwater time series based on error analysis on simulated data of specified lengths. Paddy Water Environ 15, 19–36 (2017). https://doi.org/10.1007/s10333-016-0525-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10333-016-0525-3

Keywords

Search

Navigation