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Mathematical Models and Their Applications to Isotope Studies in Groundwater Hydrology

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Mathematical Models and Their Applications to Isotope Studies in Groundwater Hydrology IAEA-TECDOC-777 Mathematical models and their applications to isotope studies in groundwater hydrology Proceedings of a final Research Co-ordination Meeting held Vienna,in June1-4 1993 INTERNATIONAL ATOMIC ENERGY AGENCY The IAEA does not normally maintain stocks of reports in this series. However, microfiche copies of these reports can be obtained from ClearinghousS I N I e International Atomic Energy Agency Wagramerstrasse 5 P.O. Box 100 A-1400 Vienna, Austria Orders shoul accompaniee db prepaymeny db f Austriao t n Schillings 100, fore for e chequa th f mth IAEf m o n i o n i r eAo microfiche service coupons which may be ordered separately from the INIS Clearinghouse. The originating Section of this document in the IAEA was: Isotope Hydrology Section International Atomic Energy Agency Wagramerstrasse 5 0 10 P.Ox Bo . A-1400 Vienna, Austria MATHEMATICAL MODEL THEID SAN R APPLICATIONO ST ISOTOPE STUDIE GROUNDWATESN I R HYDROLOGY IAEA, VIENNA, 1994 IAEA-TECDOC-777 ISSN 1011-4289 Printed by the IAEA in Austria December 1994 FOREWORD During the last few decades, the use of tracer techniques in dealing with a variety of hydrological and hydrogeological problems have proved their value in improving the assessment, developmen d managemenan t f wateo t r resources n thiI . s regarde th , methodologies based on observations of temporal and spatial variations of naturally occurring isotopes, often referre 'environmentas a o dt l isotope techniques' widele ar , y employen a s da integra e routinl th par f o te investigations relate o variout d s hydrological systemsd an , particularl regionan yi l ground water aquifers. A substantial amoun f o isotopt r ecollectefa dat o d s publisheaan d d from hydrogeological applications of natural isotopes, however, is often used for qualitative inferences to be made of the system under study, and unproved understanding of processes dynamicd an f wateso r circulation e nee r improveTh .dfo d methodologie r quantitativfo s e evaluations to be made from isotope data as regards the relevant physical parameters of the system has been recognized and a co-ordinated research programme (CRP) was initiated by the IAEA for this purpose in 1990. The main objective of the CRP during 1990-1993 was to intensify co-ordinated international efforts into appraisal of existing models and development of further mathematical formulations as a basis for quantitative interpretation of isotope data in groundwater hydrology. This publication is the result of the CRP and compiles papers summarizing the results and findings of the work undertaken by the participating institutes. Both theoretical aspects of mathematical modelling approache theid san r application isotopo st e dat actuan ao l field result coverede sar . YurtseverY . Mr , Divisio Physicaf no Chemicad an l l Sciences IAEe th s A wa office, r in charge of designing and implementing the CRP. It is expected that the information provided will be useful guidance material to scientists involved in research/development of isotope applications in hydrology, as well as to engineers and professionals involved in field applications of environmental isotopes in groundwater systems. EDITORIAL NOTE In preparing this document for press, staff of the IAEA have made up the pages from the original manuscripts submittedas authors.the viewsby The expressed necessarilynot do reflect those of the governments of the nominating Member States or of the nominating organizations. Throughout the text names of Member States are retained as they were when the text was compiled. The use of particular designations of countries or territories does not imply any judgement by publisher,the legalthe IAEA,to the status as of such countries territories,or of their authoritiesand institutions or of the delimitation of their boundaries. The mention of names of specific companies productsor (whether indicatednot or registered)as does not imply any intention to infringe proprietary rights, nor should it be construed as an endorsement or recommendation on the part of the IAEA. The authors responsibleare havingfor obtained necessarythe permission IAEAthe to for reproduce, translate materialuse or from sources already protected copyrights.by CONTENTS SUMMARY OF THE CO-ORDINATED RESEARCH PROGRAMME ......... 7 calibration O validatiod nan f mathematicano l modelinterpretatioe th r sfo f no environmental tracer data in aquifers ............................ 11 ZuberA. approacw Atranspore ne th o ht t problem ..........................3 4 . N. Limic, T. Legovic Ellam: An effective tool for modelling sharp fronts in quantitative isotopic hydrology ......................................7 6 . Herrera/ Assessmen f groundwateo t r fluxe transmissivitied an s environmentay sb l tracers: Summar f theoryyo , applicatio sensitivitd nan y analysis ................3 9 . EM. Adar Fluid flosolutd wan e transpor fracturen i t d media .....................3 12 . Moreno,L. NeretnieksI. Synthesis of geochemical, isotopic and groundwater modelling analysis to explain regional flow in a coastal aquifer of southern Oahu, Hawaii ........ 147 C.I. Voss, W.W. Wood Calibration and verification of a regional groundwater flow model by comparing simulate measured dan d environmental isotope concentrations: An applicatio Alnare th o nt p aquifer syste southwestermn i n Sweden ........9 17 . G. Barmen Applicatio f hydrogeochemicano l modellin validatior gfo f nhydrologio e flow modellin Tucsoe th n gi n basin aquifer, Arizona, United State f Americso a ....9 20 . R.M. Kalin, A. Long Cyclic mode r seasonafo l l recharg dischargd ean grounf eo sprind dan g water Valdae inth y experimental basin (humid zone) using environmental isotope data .................................5 25 . V.l. Ferronskij, V.V. Romanov, L.S. Vlasova, G.P. Kolesov, S.A. Zavileiskij, V.T. Dubinchuk List of Participants ........................................ 283 SUMMARY OF THE CO-ORDINATED RESEARCH PROGRAMME INTRODUCTIO BACKGROUND NAN D Environmental isotope methods in water sciences have already reached a stage of routine applicatio a wid o t ne spectru f hydrologicamo l problems encountere n watei d r resources assessment, developmen managementd an t fielde Th . , often referre 'isotops a o dt e hydrology' presentls i , recognizeya d scientific disciplin methodologied ean developer fa o ss d employee ar integran a s da l part f investigationo f wateso r resources. presentt A environmentae ,th l isotope data collected from field applications, particularly for regional ground water systems, is often employed for improved understanding of the various processes involve occurrencee th n di , sourc flod ewan dynamic groundwatere th f so . Neemora r d'informatioe fo th efficien f o e us t n content isotope th f o ' e dat estimatinr afo g e relevanth t physical parameter e hydrologicath f o s l system through formulatiod an n developmen f appropriato t e mathematical model r isotopfo s e transpor n hydrologicai t l systems is recognized. This has been the main motivation for the IAEA to initiate and implemen a Co-ordinatet d Research Programme (CRP n Mathematicao ) l Modelr fo s Quantitative Evaluatio f Isotopo n e Dat n Hydrologyi a e programm Th e .mai th nd ha e objective of co-ordinating joint efforts of interested national institutions in development of modelling formulations for isotope transport processes in hydrological systems and verifying their applicability. The scope and modality of carrying out the CRP was initially designed at a consultants meeting organize IAEAe th y db fro 8 Decemberm4- ,topice 198th n 9,o during whice hth present state-of-the-art in available model formulations was reviewed and further research needs were delineated. Subsequently topie IAEe th th ,c n A o durin initiateP CR g e 1990dth . A total of ten institutions took part in the CRP. The first co-ordination meeting of the programm hels Viennn edwa i a from 18-22 November, 199 whico 1t l chiehal f scientific investigators contracts/agreemente (CSIth f o ) s attended revieo t , progrese wth s madd ean plan further required work. The second (final) co-ordination meeting was also held in Vienna (1-4 June 1993), during whic overale hth l achievements were reviewee th detain di d an l programme was concluded. The final manuscripts prepared by each participating institute on resulte th f theiso r work were also presente discussed dan t thida s final meeting finae Th .l manuscript compilee sar d into this technical document. SCOP ACHIEVEMENTD EAN S Considering that model formulations for different hydrological subsystems (i.e. surface waters, unsaturated zone moisture transport, saturated groundwater flotranspord wan r fo t different media, etc.) would need different approaches due to different nature of transport processes s limite wa e subjec th o saturate,P t d CR t e mattedth flof o rgroundwaten wi r systems, wher naturae eth l isotope mose ar s t frequently employed generae Th . l modelling formulations include aredP withi:CR e scope th nth f eo Linear lumped parameter models, Stochastic model r fracturesfo d media transport, Distributed parameter numerical models of flow and transport with geochemical coupling, Compartmental modelling approach, Numerical solution algorithm transporr sfo t modelling. The scope of the programme included all above theoretically possible types of formulations, and work undertaken by the participating institutions was related to one or several aspects of these formulations. The work undertaken was both related to theoretical considerations of development of conceptual models and relevant mathematical formulations as o theit wel s ra l applicatio o actuant l field dat o assest a s their applicabilit d datan ya requirements. Results of the work undertaken and detailed discussions led to the following conclusions overvien a e capabilities a th f wo contributiond an s f differeno s t mathematical modelling approaches in isotope data evaluations for groundwater systems. Lumped parameter models, which are based on tracer input-output concentration relationships, have been developed usesufficientle b practicn dn i ca interpretatior d efo yan n of environmental tracer data.
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