Paddy and Water Environment

, Volume 15, Issue 1, pp 19–36 | Cite as

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

  • Katsushi Shirahata
  • Shuhei Yoshimoto
  • Takeo Tsuchihara
  • Satoshi Ishida


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.


Groundwater Tidal response Harmonic analysis Artificial time series Time-series length Simple and straightforward 



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.


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.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


  1. 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):19–28CrossRefGoogle Scholar
  2. 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):249–265CrossRefGoogle Scholar
  3. 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):711–722CrossRefPubMedGoogle Scholar
  4. 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):185–205CrossRefGoogle Scholar
  5. 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_1070Google Scholar
  6. 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):3909–3928CrossRefGoogle Scholar
  7. Bailey RT, Jenson JW (2014) Effects of marine overwash for atoll aquifers: environmental and human factors. Ground Water 52(5):694–704CrossRefPubMedGoogle Scholar
  8. Bailey RT, Jenson JW, Olsen AE (2009) Numerical modeling of atoll island hydrogeology. Ground Water 47(2):184–196CrossRefPubMedGoogle Scholar
  9. Bailey RT, Jenson JW, Olsen AE (2010) Estimating the ground water resources of atoll islands. Water 2(1):1–27CrossRefGoogle Scholar
  10. British Columbia Ministry of Environment (2010) Guide to Conducting Well Pumping Tests. Water Stewardship Information SeriesGoogle Scholar
  11. 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):1727–1732CrossRefGoogle Scholar
  12. Carr PA (1971) Use of harmonic analysis to study tidal fluctuations in aquifers near the sea. Water Resour Res 7(3):632–643CrossRefGoogle Scholar
  13. Carr PA, Van der Kamp GS (1969) Determining aquifer characteristics by the tidal method. Water Resour Res 5(5):1023–1031CrossRefGoogle Scholar
  14. Cartwright DE, Tayler RJ (1971) New computations of the tide-generating potential. Geophys J R Astron Soc 23(1):45–73CrossRefGoogle Scholar
  15. 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):991–1004CrossRefGoogle Scholar
  16. Chapuis RP, Bélanger C, Chenaf D (2006) Pumping test in a confined aquifer under tidal influence. Ground Water 44(2):300–305CrossRefPubMedGoogle Scholar
  17. Chattopadhyay PB, Singh VS (2013) Hydrochemical evidences: vulnerability of atoll aquifers in Western Indian Ocean to climate change. Glob Planet Change 106:123–140CrossRefGoogle Scholar
  18. Chattopadhyay PB, Vedanti N, Singh VS (2015) A conceptual numerical model to simulate aquifer parameters. Water Resour Manag 29(3):771–784CrossRefGoogle Scholar
  19. 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 42:13–20Google Scholar
  20. 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 502:18–26CrossRefGoogle Scholar
  21. 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):119–128CrossRefGoogle Scholar
  22. Dillon P (1997) Groundwater pollution by sanitation on tropical islands. Technical Documents in Hydrology, IHP-V Project 6-1, UNESCO, ParisGoogle Scholar
  23. Doodson AT (1921) The harmonic development of the tide-generating potential. Proc R Soc Lond Ser A 100(704):305–329CrossRefGoogle Scholar
  24. 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):103–109CrossRefGoogle Scholar
  25. Duncan D (2012) Freshwater under threat/Pacific Islands/vulnerability assessment of freshwater resources to environmental change. United Nations Environment Programme (UNEP)Google Scholar
  26. Emery WJ, Thomson RE (2001) Data analysis methods in physical oceanography, second and revised edition. Elsevier, AmsterdamGoogle Scholar
  27. Erskine AD (1991) The effect of tidal fluctuation on a coastal aquifer in the UK. Ground Water 29(4):556–562CrossRefGoogle Scholar
  28. 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):441–454CrossRefGoogle Scholar
  29. Ferris JG (1951) Cyclic fluctuations of water level as a basis for determining aquifer transmissibility. Int Assoc Sci Hydrol Publ 33:148–155Google Scholar
  30. Fetter CW Jr (1972) Position of the saline water interface beneath oceanic islands. Water Resour Res 8(5):1307–1314CrossRefGoogle Scholar
  31. 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, 50–10Google Scholar
  32. Foreman MGG, Henry RF (1989) The harmonic analysis of tidal model time series. Adv Water Resour 12(3):109–120CrossRefGoogle Scholar
  33. Gregg DO (1966) An analysis of ground-water fluctuations caused by ocean tides in Glynn County, Georgia. Ground Water 4(3):24–32CrossRefGoogle Scholar
  34. Guo H, Jiao JJ, Li H (2010) Groundwater response to tidal fluctuation in a two-zone aquifer. J Hydrol 381(3–4):364–371CrossRefGoogle Scholar
  35. 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):101–110CrossRefGoogle Scholar
  36. Ishida S, Tsuchihara T, Yoshimoto S, Imaizumi M (2011) Sustainable use of groundwater with underground dams. Jpn Agric Res Quart 45(1):51–61CrossRefGoogle Scholar
  37. Jacob CE (1950) Flow of groundwater. In: Rouse H (ed) Engineering hydraulics. Willey, Chapman & Hall, Limited, New York, London, pp 321–386Google Scholar
  38. Jha MK, Kamii Y, Chikamori K (2003) On the estimation of phreatic aquifer parameters by the tidal response technique. Water Resour Manag 17(1):69–88CrossRefGoogle Scholar
  39. 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):1899–1923CrossRefGoogle Scholar
  40. 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):776–784Google Scholar
  41. 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):5938–5953CrossRefGoogle Scholar
  42. Kobayashi T, Koda K (eds) (2012) Development of survey method for freshwater lens in Marshall Islands. JIRCAS Working Report 77Google Scholar
  43. 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):541–545Google Scholar
  44. Kudryavtsev SM (2004) Improved harmonic development of the Earth tide-generating potential. J Geod 77:829–838CrossRefGoogle Scholar
  45. Kvale EP (2006) The origin of neap-spring tidal cycles. Mar Geol 235(1–4):5–18CrossRefGoogle Scholar
  46. 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):438–446CrossRefGoogle Scholar
  47. 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):97–106CrossRefGoogle Scholar
  48. 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):183–204Google Scholar
  49. Martin JB, Gulley J, Spellman P (2012) Tidal pumping of water between Bahamian blue holes, aquifers, and the ocean. J Hydrol 416–417:28–38CrossRefGoogle Scholar
  50. Millham NP, Howes BL (1995) A comparison of methods to determine K in a shallow coastal aquifer. Ground Water 33(1):49–57CrossRefGoogle Scholar
  51. Mondal NC, Singh VS, Sarwade DV, Nandakumar MV (2009) Appraisal of groundwater resources in an island condition. J Earth Syst Sci 118(3):217–229CrossRefGoogle Scholar
  52. Morgan LK, Werner AD (2014) Seawater intrusion vulnerability indicators for freshwater lenses in strip islands. J Hydrol 508(16):322–327CrossRefGoogle Scholar
  53. 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):71–82CrossRefGoogle Scholar
  54. 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):894–902CrossRefGoogle Scholar
  55. Nielsen P (1990) Tidal dynamics of the water table in beaches. Water Resour Res 26(9):2127–2134Google Scholar
  56. Pandit A, Ei-Khazen CC, Sivaramapillai SP (1991) Estimation of hydraulic conductivity values in a coastal aquifer. Ground Water 29(2):175–180CrossRefGoogle Scholar
  57. Parker BB (2007) Tidal analysis and prediction. NOAA Special Publication NOS CO-OPS 3, Silver Spring, MarylandGoogle Scholar
  58. 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 2005–5098Google Scholar
  59. Raubenheimer B, Guza RT, Elgar S (1999) Tidal water table fluctuations in a sandy ocean beach. Water Resour Res 35(8):2313–2320CrossRefGoogle Scholar
  60. 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):57–69CrossRefGoogle Scholar
  61. Robinson IS, Warren L, Longbottom JF (1983) Sea-level fluctuations in the Fleet, an English tidal lagoon. Estuar Coast Shelf Sci 16(6):651–668CrossRefGoogle Scholar
  62. Rotzoll K, El-Kadi AI, Gingerich SB (2008) Analysis of an unconfined aquifer subject to asynchronous dual-tide propagation. Ground Water 46(2):239–250CrossRefPubMedGoogle Scholar
  63. 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 53:121–124Google Scholar
  64. Schmorak S, Mercado A (1969) Upconing of fresh water-sea water interface below pumping wells, field study. Water Resour Res 5(6):1290–1311CrossRefGoogle Scholar
  65. Schultz G, Ruppel C (2002) Constraints on hydraulic parameters and implications for groundwater flux across the upland-estuary interface. J Hydrol 260(1–4):255–269CrossRefGoogle Scholar
  66. 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)Google Scholar
  67. 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 54:721–725CrossRefGoogle Scholar
  68. Shih DC-F (1999) Inverse solution of hydraulic diffusivity determined by water level fluctuation. J Am Water Resour Assoc 35(1):37–47CrossRefGoogle Scholar
  69. 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):1655–1669CrossRefGoogle Scholar
  70. 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 215:141–154Google Scholar
  71. 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 201:59–66Google Scholar
  72. Smith AJ (1999) Application of a tidal method for estimating aquifer diffusivity: Swan River, Western Australia. CSIRO Land and Water Technical Report 13/99Google Scholar
  73. Smith AJ, Hick WP (2001) Hydrogeology and aquifer tidal propagation in Cockburn Sound, Western Australia. CSIRO Land and Water Technical Report 6/01Google Scholar
  74. Spennemann DHR (1996) Nontraditional settlement patterns and typhoon hazard on contemporary Majuro Atoll, Republic of the Marshall Islands. Environ Manag 20(3):337–348CrossRefGoogle Scholar
  75. Tamura Y (1987) A harmonic development of the tide-generating potential. Bulletin d’Informations Marées Terrestres 99:6813–6855Google Scholar
  76. Trefry MG (1999) Periodic forcing in composite aquifers. Adv Water Resour 22(6):645–656CrossRefGoogle Scholar
  77. Trefry MG, Bekele E (2004) Structural characterization of an island aquifer via tidal methods. Water Resour Res 40(1):W01505CrossRefGoogle Scholar
  78. Trefry MG, Jhonston CD (1998) Pumping test analysis for a tidally forced aquifer. Ground Water 36(3):427–433CrossRefGoogle Scholar
  79. Underwood MR, Peterson FL, Voss CI (1992) Groundwater lens dynamics of atoll islands. Water Resour Res 28(11):2889–2902CrossRefGoogle Scholar
  80. Urish DW (1980) Asymmetric variation of Ghyben-Herzberg lens. J Hydraul Division Proc Am Soc Civil Eng 106(7):1149–1158Google Scholar
  81. 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):456–468CrossRefGoogle Scholar
  82. White I, Falkland T (2010) Management of freshwater lenses on small Pacific islands. Hydrogeol J 18(1):227–246CrossRefGoogle Scholar
  83. 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):276–281CrossRefGoogle Scholar
  84. 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:83Google Scholar
  85. 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):367–384CrossRefGoogle Scholar
  86. 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):2061–2077CrossRefGoogle Scholar
  87. Zhou X (2008) Determination of aquifer parameters based on measurements of tidal effects on a coastal aquifer near Beihai, China. Hydrol Process 22(16):3176–3180CrossRefGoogle Scholar
  88. Zhou Q, Bear J, Bensabat J (2005) Saltwater upconing and decay beneath a well pumping above an interface zone. Transp Porous Media 61(3):337–363CrossRefGoogle Scholar

Copyright information

© The International Society of Paddy and Water Environment Engineering and Springer Japan 2016

Authors and Affiliations

  • Katsushi Shirahata
    • 1
  • Shuhei Yoshimoto
    • 1
  • Takeo Tsuchihara
    • 1
  • Satoshi Ishida
    • 1
  1. 1.National Institute for Rural EngineeringNational Agriculture and Food Research OrganizationTsukubaJapan

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