Water in the unsaturated zone
Proceedings of the Wageningen Symposium
L'eau dans la zone non saturée
Actes du Symposium de Wageningen
Volume I edited by/édité par P . E . Rijtema & H . Wassink
A contribution to the International Hydrological Decade U n e contribution à la Décennie hydrologique internationale
IASH/AIHS - Unesco
U n e s c o - I A S H joint publications / Coéditions U n e s c o - A I H S
1. Use of analog and digital computers in hydrology. Proceedings of the Tucson Symposium I Utili- sation des calculatrices analogiques et des ordinateurs en hydrologie. A ctes du Symposium de Tucson.
2. Water in the unsaturated zone. Proceedings of the Wageningen Symposium / L'eau dans la zone non saturée. Actes du Symposium de Wageningen.
3. Floods and their computation. Proceedings of the Leningrad Symposium / Les crues et leur évaluation. Actes du Symposium de Leningrad.
Published by Unesco / Publié par l'Unesco
4. Representative and experimental basins. Guide to international practices. (Will also appear in Russian and Spanish.)
4. Les bassins représentatifs et expérimentaux. Un guide des pratiques internationales. (Paraîtra également en russe et en espagnol.)
5. Discharge of selected rivers of the world, vol. 1 / Débits des principaux cours d'eau du monde, vol. 1.
Publié en 1969 par l'Association internationale d'hydrologie scientifique, Braamstraat 61, Gentbrugge, et par l'Unesco, place de Fontenoy, 75 Paris-7e
Printed by Ceuterick, Louvain, Belgium
T h e responsibility for the choice and presentation of facts and for opinions and views expressed lies with the authors.
T h e designations employed and the presentation of the material d o not imply the expression of any opinion whatsoever on the part of Unesco concerning the legal status of any country or territory or of its authorities, or concerning the delimitations of the frontiers of any country or territory.
L a responsabilité du choix et de la présentation des faits exposés, c o m m e celle des opinions et avis exprimés, incombe aux auteurs.
Les dénominations employées et la présentation des divers éléments n'impliquent de la part de l'Unesco aucune prise de position à l'égard du statut juridique de l'un quelconque des pays et territoires en cause, de son régime politique ou du tracé de ses frontières.
© 1969 Unesco/IASH Printed in Belgium S C . 6 8 / X X . 2 / A F
Preface
The International Hydrological Decade ( 1 H D ) 1965-1975 was launched by the thir- teenth session of the General Conference of Unesco to promote international co-operation in research and studies and the training of specialists and technicians in scientific hydrol- ogy. Its purpose is to enable all countries to m a k e a fuller assessment of their water resources and a m o r e rational use of them as m a n ' s demands for water constantly increase in face of developments in population, industry and agriculture. In 1968 National Committees for the Decade had been formed in 100 of Unesco's 125 M e m b e r States to carry out national activities and to contribute to regional and international activities within the programme of the Decade. The implementation of the programme is supervised by a Co-ordinating Council, composed of twenty-one M e m b e r States selected by the General Conference of Unesco, which studies proposals for developments of the pro- g r a m m e , recommends projects of interest to all or a large number of countries, assists in the development of national and regional projects and co-ordinates international co- operation.
Promotion of collaboration in developing hydrological research techniques, diffusing hydrological data and planning hydrological installations is a major feature of the pro- g r a m m e of the I H D which encompasses all aspects of hydrological studies and research.
Hydrological investigations are encouraged at the national, regional and international level to strengthen and to improve the use of natural resources from a local and a global perspective. The programme provides a means for countries well advanced in hydrolog- ical research to exchange scientific views and for developing countries to benefit from this exchange of information in elaborating research projects and in implementing recent developments in the planning of hydrological installations.
A s part of Unesco's contribution to the achievement of the objectives of the I H D the General Conference authorized the Director-General to collect, exchange and disseminate information concerning research on scientific hydrology and to facilitate contacts between research workers in this field. T o this end Unesco has initiated two collections of publica- tions, "Studies and Reports in Hydrology" and "Technical Papers in Hydrology".
T h e collection, "Studies and Reports in Hydrology", is aimed at recording data collected and the main results of hydrological studies undertaken within the framework of the Decade as well as providing information o n research techniques. Also included in the collection will be proceedings of symposia. Thus, the collection will comprise the compila- tion of data, discussion of hydrological research techniques and findings, and guidance material for future scientific investigations. It is hoped that the volumes will furnish material of both practical and theoretical interest to hydrologists and governments parti- cipating in the I H D and respond to the needs of technicians and scientists concerned with problems of water in all countries.
Unesco and the I A S H have together undertaken the implementation of several important projects of the I H D of interest to both Organizations, and in this spirit a n u m b e r of joint U n e s c o - I A S H publications are envisaged.
Préface
L a Décennie hydrologique internationale ( D H I ) 1965-1975 a été ouverte par la Conférence générale de l'Unesco à sa treizième session pour favoriser la coopération internationale en matière de recherches et d'études et la formation de spécialistes et de techniciens de l'hydrologie scientifique. Son but est de permettre à tous les pays d'évaluer plus complè- tement leurs ressources en eau et de les exploiter plus rationnellement, les besoins en eau augmentant constamment par suite de l'expansion démographique, industrielle et agricole. E n 1968, des comités nationaux pour la Décennie ont été constitués dans 100 des 125 États m e m b r e s de l'Unesco en vue de mener à bien les activités nationales et de participer aux activités régionales et internationales dans le cadre d u programme de la Décennie. C e p r o g r a m m e est exécuté sous la direction d ' u n Conseil de coordination composé de vingt et u n États membres désignés par la Conférence générale de l'Unesco, qui étudie les propositions d'extension d u programme, r e c o m m a n d e l'adoption de projets intéressant tous les pays ou u n grand nombre d'entre eux, aide à la mise sur pied de projets nationaux et régionaux et coordonne la coopération à l'échelon international.
L e programme de la D H I , qui porte sur tous les aspects des études et des recherches hydrologiques, vise essentiellement à développer la collaboration dans les domaines de la mise au point de techniques de recherches hydrologiques, de la diffusion des données hydrologiques et de l'organisation des installations hydrologiques. Il encourage les en- quêtes nationales, régionales et internationales visant à accroître et à améliorer l'utilisation des ressources naturelles, dans une perspective locale et générale. Il offre la possibilité aux pays avancés en matière de recherches hydrologiques d'échanger des idées, et aux pays en voie de développement de profiter de ces échanges d'informations pour l'élabo- ration de leurs projets de recherches et pour la planification de leurs installations hydrolo- giques selon les derniers progrès réalisés.
Pour permettre à l'Unesco de contribuer au succès de la D H I , la Conférence générale a autorisé le Directeur général à rassembler, échanger et diffuser des renseignements sur les recherches d'hydrologie scientifique et à faciliter les contacts entre chercheurs de ce domaine. A cette fin, l'Unesco publie deux nouvelles collections : «Études et rapports d'hydrologie» et «Documents techniques d'hydrologie».
L a collection «Études et rapports d'hydrologie» a pour but de présenter les données recueillies et les principaux résultats des études hydrologiques effectuées dans le cadre de la Décennie, et de fournir des renseignements sur les techniques de recherche. O n y trou- vera aussi les Actes de colloques. Cette collection comprendra donc des données, l'exposé de techniques de recherches hydrologiques et des résultats de ces recherches, et u n e documentation pour des travaux scientifiques futurs. O n espère que ces volumes fourni- ront aux hydrologues et aux gouvernements qui participent à la D H I des matériaux d ' u n intérêt tant pratique que théorique et qu'ils répondront aux besoins des techniciens et des h o m m e s de science qui s'occupent, dans tous les pays, des problèmes de l'eau.
L ' U n e s c o et l ' A I H S ont entrepris de réaliser conjointement plusieurs projets impor- tants de la D H I qui les intéressent l'une et l'autre; dans cette perspective, elles ont prévu un certain nombre de publications U n e s c o - A I H S .
Table des matières
Volume I
Foreword/Avant-propos 13 List of Participants/Liste des participants 15
Chapter I General lectures
Three-phase Domain in Hydrology C. H. M . van Bavel 23 Discussion
Hydrophysical Properties and Moisture Regime in Unsaturated Zone
A. A. Rode 33 Discussion
Role of Vegetation in Soil Water Problems H . L . Penman 49 Discussion
Chapter II Determination of soil moisture
Comparative Study of Water Balance in Aerated Zones with Radioactive Methods and Weighable Lysimeter
M . de Boodt, P. Moerman, and J. de Boever 63 Measuring Soil Moisture in the Brenig Catchment Area; Problems of Using
Neutron Scatter Equipment in Peaty Areas J. A. Cole and M.J. Green 74 Instrument for Measuring Soil Moisture by Neutron Scattering T. Milanov 88 Changes in Moisture Content of Topsoil Measured with a Neutron Moisture
Gauge E. Danfors 96 Determination of Soil Moisture with Neutron Method in Finland / . Virta 105
Neutron Moisture Meter for Saline Soils
L.I. Beskin, V.A. Emelyanou, and B . M . Kondratyev 109 Measurement of Soil Moisture from Temperature Gradient
T. Foldi and L. Szónyi 113 S o m e Methods for the Determination of Soil Moisture and Balance Measuring
/ . Vasa 119 Polish Isotope Apparatus for Research on Soil Moisture H . Filipkowska 124
Nuclear Techniques in Hydrological Investigations in the Unsaturated Z o n e
E. Halevy 131 Discussion
Calibration and Evaluation of W i d e Range Method for Measuring Moisture
Stress in Field Soil Samples L.S. McQueen and R.F. Miller 147 Hydraulic and Pressure Head Measurements with Strain G a u g e Pressure
Transducers A. Klute and D . B . Peters 156 Direct Measurement of Moisture Potential: A N e w Technique
A. J. Peck and R. M . Rabbidge 165 Discussion
Chapter IV Determination of capillary conductivity and diffusivity
Water Transport in Soils by Evaporation and Infiltration D . A. Rose 171 Capillary Conductivity Data, Estimated by A Simple Method G.P. Wind 181 Diffusivity Determination by a N e w Outflow Method A.J. Peck 191 Study on Pressure M e m b r a n e Properties in Relation to Capillary Conductivity
Measurements E. Vetterlein 203 Soil Water Diffusivity and Water Content Distribution during Outflow Experi-
ments
J.M. Davidson, J. W. Biggar, D . R . Nielsen, A. W. Warrick, and D.K. Cassel 214 A n Infiltration Method for the Determination of the Capillary Conductivity of
Undisturbed Soil Cores J. Wesseling and K.E. Wit 223 Determination of Capillary Conductivity and Diffusivity of Soil in situ
R. Kotizsch 235 Determination of the Coefficients of Water Migration through Soils
R.J. Bally 245 Validity of Point Dilution Method E. Gaspar and M . Oncescu 256
Divergences entre valeurs expérimentales et théorie de la diffusivité capillaire
L. Sine and A. Bentz 263 Vérification de la loi de Darcy généralisée et détermination de la conductivité
capillaire à partir d'une infiltration horizontale G. Vachaud 277 Discussion
Chapter V Relation between soil characteristics and soil properties
Hydrological Constants of Pampean Soils: Brown and Black Prairie
/ . / . Burgos and W. C. Corsi 295 Relation between Lithological Properties and Shape of the Desorption Curve
W . C . Visser 305 The Microhydrologic Characterization of Soils D . E . Elrick 311
Effects of Salts and Organic Materials on the Hydraulic Conductivity of Soils
Chen Tsen-tuo 317 Soil Moisture Pressure in S o m e Climatic Zones L.I. Sudnitsin 323
A n Empirical Mathematical Expression for the Desorption Curve W. C. Visser 329 Étude spectrophotométrique en infrarouge du comportement des sols argileux
humectés L. Arcan 336
Analysis of S o m e Factors Affecting Water Vapour Diffusion in Soils
M . Kutilek 350 Moisture Content and Hydrophility as Related to Water Capillary Rise in Soils
S.A. Wladitchensky 360 Determination of Pore Size by Air Bubbling Pressure Method W. P. Stakman 366
Relation between Particle Size, Pore Size, and Hydraulic Conductivity of Sand
Separates W. P. Stakman 373 Discussion
Chapter V I Infiltration and redistribution of soil moisture following precipitation and its influence o n groundwater flow
Redistribution of Moisture after Infiltration in Dry Soils. Influence of Gravity
A. Feodoroff 385 Infiltration in Terms of Soil Moisture, Rain Intensity and Depth of Rainfall
K. Sdgi 390 Infiltration Rate as Related to Hydraulic Conductivity, Moisture Deficit and
Other Properties A. Canarache, E. Moloc, and R. Dumitriu 392 Movement of Water in Sandy Soils after Ploughing at a Depth of 50 c m H. Rid 401
Nature of Minimal Water Retentive Capacity A. A. Rode 407 Étude d'une rédistribution après l'arrêt d'une infiltration horizontale
G. Vachaud 416 Discussion
Chapter VII T h e mathematics of unsaturated flow
A Theoretical Analysis and Numerical Solutions of Unsaturated Flow in Soil
H . Kobayashi 429 Numerical Analysis of Ponded Rainfall Infiltration / . Rubin 440
Analysis of Infiltration into Stratified Soil Columns
F.D. Whisler and A. Klute 451 A Linearization Technique for the Study of Infiltration J.R. Philip 471
Solutions of the Non-Linear Diffusion Equation with a Gravity Term in
Hydrology S. Irmay 478 S o m e Numerical Methods for Solving Problems of Non-Steady Seepage in
N o n - H o m o g e n e o u s Anisotropic Soils L. N. Burejev and Z. M . Burejeva 500 Absorption and Infiltration in T w o - and Three-Dimensional Systems
J.R. Philip 503 Discussion
Foreword
T h e study of water in the unsaturated zone is a d o m a i n that has been particularly devel- oped by specialists w h o are concerned with soil science. It must not be forgotten, however, that soil moisture constitutes one of the elements of the hydrological cycle and as such has a place in the field of hydrological studies. T h e Wageningen Symposium had the merit of gathering together all those w h o are interested in this unsaturated zone and whose points of view, without being fundamentally different, illustrated the necessity of a confrontation. This was accomplished on a very large scale at Wageningen. It is n o cause for astonishment, then, that the programme of this meeting w a s very wide and that the n u m b e r of papers presented far exceeded that generally achieved at hydrological colloquia on a specific and limited subject.
Three general lectures provided a broad scientific introduction before the following points were taken u p :
Determination of soil moisture.
Determination of soil moisture potential.
Determination of capillary conductivity and diffusivity.
Relation between soil characteristics and soil properties.
Infiltration and redistribution of soil moisture following precipitation and its influence on groundwater flow.
The mathematics of unsaturated flow.
Energy relations in water transport and supply of water by capillary rise.
Evaporation from bare soils and accumulation of salts.
Extraction of soil moisture by plants.
Influence of temperature on the transport of water.
Rate of recharge of groundwater and its influence o n groundwater flow.
Effect of the capillary fringe on groundwater flow.
Storage capacity.
It would seem that nothing escaped the authors' attention, particularly the relations between soil moisture and precipitation and temperature o n one hand and with the aquifer on the other.
T h e Wageningen Symposium was organized by Unesco with the co-operation of F A O , I A S H and the International Society of Soil Science.
A s is currently the custom for the symposia of the International Hydrological Decade, the two volumes of the papers presented at Wageningen form a combined U n e s c o / I A S H publication.
Avant-propos
L'étude de l'eau dans la zone non saturée est u n domaine qui a particulièrement été développé par les spécialistes s'occupant de la science du sol. Il ne faut cependant pas oublier que l'humidité du sol constitue un des éléments du cycle hydrologique et, c o m m e telle, fait partie du c h a m p d'études des hydrologues. L e Symposium de Wageningen eut le mérite de rassembler tous ceux qui s'intéressent à cette zone non saturée et dont les points de vue, sans être foncièrement différents, montraient la nécessité d'une confron- tation. Celle-ci s'est opérée sur une très vaste échelle à Wageningen. Il ne faut donc pas s'étonner si le programme de cette réunion fut très étendu et si le nombre des c o m m u n i - cations présentées dépassa de loin ce qui est généralement atteint dans les colloques hydrologiques à sujet précis et limité.
Trois exposés généraux ont servi de large introduction scientifique avant que soient abordés les points suivants :
L a détermination de l'humidité du sol et celle du potentiel d'humidité du sol.
L a détermination de la perméabilité et de la diffusion capillaires.
L a relation entre les caractéristiques du sol et ses propriétés.
L'infiltration et la redistribution de l'humidité du sol à la suite des pluies et son influence sur la nappe aquifère.
Les mathématiques de l'écoulement n o n saturé.
Les relations énergétiques dans le mouvement de l'eau sous l'action de la capillarité.
L'évaporation des sols nus et l'accumulation des sels.
L'extraction de l'humidité du sol par les plantes.
L'influence de la température sur le mouvement de l'eau.
L e taux de recharge de la nappe et son influence sur le mouvement de la nappe.
L'influence de la zone capillaire sur le mouvement de la nappe.
L a capacité d'emmagasinement.
Il semble que rien n'ait échappé aux auteurs, notamment les rapports de l'humidité du sol avec les précipitations et la température, d'une part, avec la nappe aquifère, d'autre part.
Le Symposium de Wageningen fut organisé par l'Unesco avec la coopération de la F A O , de l ' A I H S et de l'Association internationale de la science du sol.
C o m m e il en est actuellement l'usage pour les colloques de la Décennie hydrologique internationale, les deux volumes contenant les communications de Wageningen sont une publication conjointe de l'Unesco et de l ' A I H S .
AFGHANISTAN
M O H A M M E D SAFI, A. M .
ARGENTINA
B U R G O S , J. Juan, Comité national pour la Décennie hydrologique, Université de Buenos Aires, Sarmiento 1371, Buenos Aires.
A U S T R A L I A
M A R T I N , G.J., 262 Bass Highway, Launceston, Tasmania.
P A S S I O U R A , J.B., c/o Oranjelaan 12, Wageningen, Netherlands.
PHILIP, J . R . , C . S . I . R . O . , Division of Plant Industry, P . O . Box 109, Canberra City A . C . T . S M I T H , S.T., Department of Agriculture, Jarrah Road, South Perth.
A U S T R I A
K A S T A N E K , F . , Hochschule für Bodenkultur, Institut fur Wasserbau, A 1180 Vienna, Gregor- Mendelstr. 33.
W I E D E R S T E I N , F . , Hydrographisches Zentralbüro im Bundesministerium für Land und Forst- wirtschaft, Marxergasse 2, 1030 Vienna III.
BELGIUM
B E N T Z , A . , Ministère de l'éducation nationale et de la culture, Améliorations foncières, Hydrau- lique, Topographie, Institut agronomique de l'État, Gembloux.
D E B O O D T , M . , Faculteit der Landbouwwetenschappen, Coupure Links 235, Gent.
V A N G A N S E , R . , Centre de recherches routières, 21 Drève des éleveurs, Sterrebeek.
Mm e G A S P A R , Ministère de l'éducation nationale et de la culture, Améliorations foncières, Hydraulique, Topographie, Institut agronomique de l'État, Gembloux.
H A R T M A N , R . , Faculteit Bodemkunde en Géologie, Rijkslandbouwhogeschool, Gent.
LEISTRA, M . , Faculteit Bodemkunde en Géologie, Rijkslandbouwhogeschool, Gent.
D E M E E S T E R , P . , Faculteit Bodemkunde en Géologie, Rijkslandbouwhogeschool, Gent.
S U V E E , G . , Rijksuniversiteit Gent, Faculteit der Wetenschappen, Observatorium, Josef Plateaustr.
22, Gent.
T I S O N , L . , Braamstraat 61, Gentbrugge.
V E R N E M M E N , G . , Rijksuniversiteit Gent, Faculteit der Wetenschappen, Observatorium, Josef Plateaustr. 22, Gent.
C A M E R O O N
M O T A Z E , A . , Direction du génie rural et de l'hydraulique agricole, boîte postale 236, Yaounde.
C A N A D A
E L R I C K , D . E . , Dept. of Soil Science, University of Guelph, Guelph, Ontario.
V A N S C H A I K , J., Canada Department of Agriculture, Research Branch, Research Station, Leth- bridge, Alberta.
CZECHOSLOVAKIA
B E N E T I N , J., C S A V Ustav Hydrologie a Hydrauliky S A V , Trnavská 20, Bratislava.
B R E Z N Y , O . , Bratislava, Konzaivzicka 20.
Mm" C E R V E N K Ó V A , J., Ustav Hydrologie a Hydrauliky S A V , Trnavska 20, Bratislava.
D V O R A K , J., Agricultural College, Suchdol v. Frahy, Prague.
K U T I L E K , M . , Soil Science Laboratory, Karlovo N a m . 3, Prague 2 . N E M E C , J., Prague Agricultural College, U . Riegrovych, Sadu 2, Prague.
P Y C H A , M . , l'Institut de Recherche d'Irrigation, Podbabska 219, Prague 6.
S E R M E R , A . , Moyzesova 6, Bratislava.
S U T O R , J., C S A V Ustav Hydrologie a Hydrauliky S A V , Trnavska 20, Bratislava.
S V E H U K , Z . , c/o International Courses in Hydraulic and Sanitary Engineering, O u d e Delft 95, Delft. T h e Netherlands.
D E N M A R K
ANDERSEN, L. J., Geological Survey of Denmark, Radhusvej 36, Charlottenlund.
KRISTENSEN, K . J., Hydroteknisk Laboratorium, Rolighedsvej 26, Copenhagen V . ETHIOPIA
M I K Y A S A B A Y N E H , Haile Selassie I University, Addis Ababa.
FINLAND
P U U S T J A R V I , V . A . , Hiihtomâentie 27 B 13, Helsinki 80.
V I R T A , J., Finnish Hydrological Office, Kasarmikatu 42, Box 10436, Helsinki.
FRANCE
B E R K A L O F F , E . , Bureau de recherches géologiques et minières, 74, rue de la Fédération, Paris-15e. B O N Z O N , M . B . , Office de la recherche scientifique et technique outre-mer, 24, rue Bayard,
Paris-8e.
D A U D E T , F . A . , Station centrale de bioclimatologie, Institut national de la recherche agrono- mique, route de Saint-Cyr, 78 Versailles.
D E G A L L I E R , R . , Comité inter-africain d'études hydrauliques, 26, rue de Vieuville, Paris-18e. D E F O R G E S , J., École nationale supérieure d'horticulture, 78 Versailles.
M A R G A T , J., B . R . G . M . , 74, rue de la Fédération, Paris.
S E R R A , L . , 98, rue Xavier de Maistre, 92 Rueil-Malmaison.
V A C H A U D , G . , Laboratoire de mécanique des fluides, 44, avenue Felix-Viallet, 38 Grenoble.
V I A U D , P . , Laboratoire Biol-Animal, Parc grand'Mont, Tours.
FEDERAL REPUBLIC OF G E R M A N Y
B E N E C K E , P . , Niedersachsisches Landesamt fur Bodenforschung und Bundesanstalt fur Boden- forschung, P . O . B . 54, 3 Hannover-Buchholz.
B O R N H O L D T , A . , Leichtweiss Institut fur Wasserbau und Technische Hochschule Braunschweig, Pockelstrasse 4, 33 Braunschweig.
B R A U E R , J., Forsteinrichtingsamt Koblenz, Jugendherbergstrasse 12, 5552 Morbach (Krs. Bern- kastel).
C O L L I N S , H . J . , Leichtweiss Institut, Technische Hochschule, Braunschweig.
C Z E R A T Z K I , W . , Forschungsanstalt fur Landwirtschaft, Institut fur Bodenbearbeitung, Bundes- allee 50, 3301 Braunschweig.
M r . E G G E L S M A N , Staatl. M o o r Versuchsstation in Bremen, Friedrich Miszler Str. 46-48, Bremen.
D E H A A R , U . , Deutsche Forschungsgemeinschaft, Kennedyallee 40, 5320 Bad Godesberg.
H A R T G E , K . G . , Institut fur Bodenkunde der Techn. Hochschule, Herrenhâuser Strasse 2, 3 Hannover.
H E R R M A N N , R . , Geographisches Institut der Justus Liebig Universitàt Giessen, 6300 Giessen, Landgraf Philipp Platz 2, Neues Schloss.
H O F F M A N N , D . , Forsteinrichtungsamt Koblenz, Jugendherbergstrasse 12, 5552 Morbach (Kr.
Bernkastel).
K A R R E N B E R G , H . , Taubenstr. 71, Krefeld.
K L A U S I N G , O . , Hessisches Landesamt fur Gewàsserkunde und Wasserwirtschaftliche Planung.
Kranzplatz 5/6, 62 Wiesbaden.
K R A M E R , W . , Institut für Bodenkunde, 34 Góttingen, von Sieboldstr. 4.
Frl. K U T S C H K E , I., 463 B o c h u m , Heckerstrasse 25.
M X D E , A . A . , Martin Luther Universitàt, Halle-Wittenberg, Agrarmeteorologisches Institut, Halle (Saale), Gross Steinstrasse 84. ( D . D . R . )
M A N N , G . , N e u e Universitàt Haus 19, Kiel.
M A T T H E S S , G . , Hessisches Landesamt für Bodenforschung, Leberberg 9 - 11, 62 Wiesbaden.
M Ü L L E R , W . , Niedersachsich.es Landesamt für Bodenforschung, Hannover.
N Ô R I N G , F . , Hessisches Landesamt für Bodenforschung, Lessingstr. 9, 62 Wiesbaden.
R E N G E R , M . , Niedersachsisches Landesamt fur Bodenforschung, Hannover.
R I C H T E R , W . , Niedersachsisches Landesamt für Bodenforschung und Bundesanstalt für Boden- forschung, P . O . B . 54, 3 Hannover-Buchholz.
S C H A F F E R , G . , Techn. University, 33 Braunschweig, Pockelstrasse 4.
S C H E N K , E . , Professorenweg 6, 63 Giessen.
S C H M I D T , K . , Dortmunder Stadtwerke A . G . , Semerteichstrasse 106, 46 Dortmund-Hórde.
S C H W I L L E , F . , Bundesanstalt für Gewàsserkunde, Kaiserin Augusta Anlagen 15, 54 Koblenz.
S U N K E L , R . , Landesanstalt für Immissions- und Bodennutzungsschutz, Eststrasse 160, 43 Essen- Bredeney.
W E I S F L O G , D . , Bundesanstalt für Gewàsserkunde, Kaiserin Augusta Anlagen 15, 54 Koblenz.
W I C H T M A N N , H .
H U N G A R Y
KovÁcs, G . , Tôvis u. 3/b., Budapest II.
S T E L Z C E R , K . , Torontál u. 23-25, Budapest XIV.
U B E L L , K . , Rákóczi Ut 41, Budapest VIII.
I N D I A
B A N E R J E E , S., "The Observatory", Lodi Road, N e w Delhi 3.
RAJ K U M A R , Executive Engineer to the State Govt, of Uhtar Pradesh, L . S . G . Eng. Dept., Lucknow, (UP).
R A T A N K U M A R D A S G U P T A , Civil Engineering Dept., Jadavpur University, Calcutta - 32.
IRAN
B Y B O R D I , M . , C / O Churchill College, University of Cambridge, Cambridge, England.
I R A Q
NAJ A B D U L K A D I R , Dean of Engineering College, University of Baghdad.
I R E L A N D
D O O G E , J.C.I., Professor of Civil Engineering, University College, Cork.
G A L V I N , L . F . , The Agricultural Institute, Kinsealy, Malahide, C o Dublin.
S W A N , M . H . , 22 Upper Merrion St, Dublin.
W A L S H , J.A., Department of Agricultural Engineering, University College, Upper Merrion St., Dublin 2.
I S R A E L
J A C O B S , M . , Mayot 42, Jerusalem.
I T A L Y
C U C C H I N I , C , Secrétaire du Cours international post-universitaire en hydrologie, Université de Padoue, Via Loredan 20, Padoue.
V A A D I A , Y . , C/O Instituut voor Biologisch en Scheikundig Onderzoek van Landbouwgewasstn, Bornsestege 65/67, Wageningen. The Netherlands.
J A P A N
KOBAYASHI, H . , Faculty of Agriculture Gifu University Naka-Monzenchr Kagamigahara City Gifu Ken.
K O T O D A , K . , Tokyo Kyoiku University, 24 Otsuka, Bunkyo-ku, Tokyo.
JORDAN
SAAD SHAMMOOT, P.O. Box 7, Amman.
KOREA
L E E S U N H O , Bureau of Water Resources, Ministry of Construction, Seoul.
K E N Y A
S H A H , P. D . , c/o International Courses in hydraulic and Sanitary Engineering, O u d e Delft 95, Delft. The Netherlands.
M A L A Y S I A
T H ' N G Y O N G H U A T , Hydro-Electric Division, National Electricity Board, Kuala Lumpur.
THE NETHERLANDS
V A N A A R T , R . , Prins Bernhardlaan 50, Bennekom.
V A N D E N B E R G , C , Instituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
B E E R E N , J.T. J., Prof. Ritzema Bosweg 4 , Wageningen.
B O L T , G . H . , Afd. Landbouwscheikunde, Landbouwhogeschool, D e Dreijen 3, Wageningen.
V A N D E N B U R G , J., Algemeer 39, Bennekom.
C A V E L A A R S , J . C , K o n . N e d . Heidemaatschappij, Lovinklaan I, A r n h e m .
D R I J V E R , J., Internationaal Agrarisch Centrum, Generaal Foulkesweg 1, Wageningen.
E R N S T , L . F., Instituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
F E D D E S , R . A . , Dr. Niemeyerstraat 5, Wageningen.
F O K K E N S , B . , N . V . Grontmij., Utrechtseweg 170, D e Bilt.
FRIESEL, M . J., Instituut voor Toepassing van Atoomenergie in de Landbouw, Keyenbergseweg 6, Wageningen.
G R O E N E V E L T , P . , Laboratorium voor Landbouwscheikunde, D e Dreijen 3, Wageningen.
H A A N S , J . C F . M . , Stichting voor Bodemkartering, Bovenweg 7, Bennekom.
J A N S E , A . R . P . , Laboratorium voor Landbouwscheikunde, D e Dreijen 3, Wageningen.
D E J O N G , C . H . , Dienst der Zuiderzeewerken, Sweelinckplein 14, 's-Gravenhage.
K O E N I G S , F . F . R . , Laboratorium voor Landbouwscheikunde, D e Dreijen 3, Wageningen.
K R A I J E N H O F V A N D E L E U R , Landbouwhogeschool, Duivendaal 1, Wageningen.
V A N D E R L A A N , J . C . , Bosbeekseweg 7, Bennekom.
M A K K I N K , G . F . , I.B.S., Bornsesteeg 65, Wageningen.
M E L L A A R T , E . A . R . , Laboratorium Natuur- en Weerkunde, Duivendaal 2, Wageningen.
M E U L E N K A M P , J. J., International Courses in Hydraulic and Sanitary Engineering, O u d e Delft 95, Delft.
V A N D E R M O L E N , W . H . , Oranje Nassaulaan 9, Bilthoven.
V A N D E N É S , T.J., Hoogstraat I, Wageningen.
R Y C K B O R S T , H . , V a n Vollenhovenplein 89, Leiden.
D r . Ir. R I J T E M A , P . E . , Instituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
S T A K M A N , W . P . , Instituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
V A N S T A V E R E N , J. M . , Internationaal Instituut voor Landaanwinning en Cultuurtechniek, Post- bus 45, Wageningen.
V E R H O E V E N , B . , Rijksdienst voor de Usselmeerpolders, Molenstraat 28, K a m p e n .
VISSER, W . C , Instituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
V O L K E R , A . , Westlaan 61, Pijnacker.
V O Û T E , C , Internationaal Opleidingscentrum voor Luchtkartering, Kanaalweg 3, Delft.
W A R T E N A , L . , K o n . N e d . Heidemaatschappij, Lovinklaan 1, A r n h e m .
W E S S E L I N G , J., lnstituut voor Cultuurtechniek en Waterhuishouding, Postbus 35, Wageningen.
W I N D , G . P . , Edeseweg 143, Bennekom.
N O R W A Y
M Y H R , E., Institute of Agricultural Hydrotechnics, Agricultural College of Norway, Box 19, Vollebekk.
R O G N E R U D , B., The Board of Agriculture, Box 19, Vollebekk.
P A K I S T A N
FAIZ A H M E D , Chief Engineer Hydrology East Pakistan, Wapda, Dacca.
JAFRI, S . A . , 174, VII, D , Latifabad, Hyderabad, West Pakistan, (4871/171).
POLAND
J A W O R S K I , J., Ul. Podlesna 61, Warszawa.
PORTUGAL
G O N C A L V E S D O S S A N T O S Jr., c/o 55 Chesterton R o a d , Cambridge, England.
R O U M A N I A
Mrs. A R C A N , L., Institut de Recherches Hydrotechniques, Spl. Independentei 294, Bucharest 17.
C A N Á R A C H E , A . , Institut de Recherches Hydrotechniques, Spl. Independentei 294, Bucharest 17.
G A S P A R , E . , Applied Radioactivity Laboratory Institute of Atomic Physics, P . O . Box 35, Bucharest.
PIETRARU, V . , Institut de Recherches Hydrotechniques, Spl. Independentei 294, Bucharest 17 SPAIN
R O M A N A L B A , R . , c/o Faculteit Bodemkunde en Géologie, Rijkslandbouwhogeschool, Gent.
Belgium.
SUDAN
K A R K A N I S , B . G . , c/o Geological Survey Dept., P . O . B . 410, Khartoum.
O M E R E L S H E I K H O M E R , Geological Survey Dept., P . O . B . 410, Khartoum.
S W E D E N
V O N BRÔMSSEN, U . , Villa Pomona, Stockholm 50.
D A N F O R S , E . , Nyhagavagen 6, Vallentuna.
POUSETTE, J., Ymergatan 16, Uppsala.
W I K N E R , T . , Sveriges Geologiska Undersôkning, Stockholm 50.
S W I T Z E R L A N D
K Ü H N E L , H . , Institut fur Kulturtechnik, Eidg. Techn. Hochschule, Leonhardstr. 33, CH-8006, Zurich.
SYRIA
CHASSAN KATRANJI, Travaux publics, Hama.
T U N E S I A
H A M E D REBAI, Laboratoire de Physique du Sol, Cruesi, Route de la Soukra, Ariana.
T U R K E Y
D O G A N D I N C E R , Director, Soil and Water Conservation, Station P . O . Box 253, Bakanliklar, Ankara.
S A H I N , Y . , Hasan A m i r Sok, no. 4/7, Kadikov-Istanbul.
T U R K M E N , A . , I . T . Ü . Insaat Fakultesi, Istanbul.
Y A V U Z , H . Y . , International Courses in Hydraulic and Sanitary Engineering, O u d e Delft 95, Delft. The Netherlands.
U . A . R . (Egypt)
H A S S A N , A h m e d A . , Desert Institute, Mataria, Cairo.
K A M A L H E F N Y H U S S E I N H E F N Y , Groundwater Research Office, 13 Giza Street, Cairo.
UNITED K I N G D O M
B A R T O N , M . E . , Department of Civil Engineering, University of Southampton, Southampton.
B E L L , J.P., Hydrological Research Unit, Howbery Park, Wallingford, Berkshire.
C A M P B E L L , L . G . , c/o National College of Agricultural Engineering, Silsoe, Beds.
C O L E , J. A . , The Water Research Association, Ferry L a n e , M e d m e n h a m , Marlow.Buckinghamsh.
F I S H E R , R . , Water Resources Board, Reading Bridge House, Reading, Berkshire.
G R E E N , M . J . , T h e Water Research Association, Ferry Lane, M e d m e n h a m , Marlow, Bucking- hamsh.
I N E S O N , J., Water Resources Board, Reading Bridge House, Reading, Berkshire.
K I T C H I N G , R . , 8 Wilton Place, Basinestoke Hants.
L O V E L O C K , P . E . R . , Institute of Geological Sciences, Exhibition Road, South Kensington, London S . W . 7.
M C C U L L O C H , J. S . G . , Hydrological Research Unit, Howbery Park, Wallingford, Berkshire.
P E N M A N , H . L . , Rothamsted Experimental Station, Harpenden, Herts.
R O S E , D . A . , Rothamsted Experimental Station, Harpenden, Herts.
R U S S A M , K . , Road Research Laboratory, Harmondsworth, Middlesex.
S A L T E R , P. J., National Vegetable Research Station, Wellesbourne, Warwick.
Y O U N G S , E . G . , A . R . C . Unit of Soil Physics, Huntington Road, Cambridge.
U . S . A .
V A N B A V E L , C . H . M . , United States Department of Agriculture, Agricultural Research Service, U . S . Water Conservation Laboratory, 4331 East Broadway, Phoenix, Arizona 85040.
B I G G A R , J . W . , Iowa State University, 310 Westwood, A m e s , Iowa 50012.
H A N S E N , W . W . , c/o International Courses in Hydraulic and Sanitary Engineering, O u d e Delft 95, Delft.1
V A N H Y L C K A M A , T . E . A . , U . S . Geological Survey, P . O . B . 26, Buckeye, Arizona 85326.
K L U T E , A . , University of Illinois, Agronomy Dept. Urbana, Illinois.
L U T H I N , J . N . , Dept. of Water Science and Engineering, University of California, Davis.
R U B I N , J., 345 Middelfield Road, Menlo Park, California 94025.
U . S . S . R .
M r . B O N D O R E N K O , Agrophysical Institute, Grazhdansky pr., 14, Leningrad, K - 2 1 .
M r s . G R A M M A T I C A L , O . , C / O U . S . S . R . Committee for the I . H . D . 12 Pavlik Morozov Street, M o s c o w D-376.
K A T Z , D . M . , C / O U . S . S . R . Committee for the I . H . D . 12 Pavlik Morozov Street, M o s c o w D - 3 7 6 . N E R P I N , S., Agrophysical Institute, Grazhdansky pr. 14, Leningrad, K - 2 1 .
R A S O U M O V A , L . A . , c/o U . S . S . R . Committee for the I . H . D . , 12 Pavlik Morozov Street, M o s c o w D-376.
R O D E , A . A . , Pyzkevsky pezevlov 7, Poderennyi Institut Dovuckaeva, M o s c o w G - 1 7 .
S O U D N I T Z I N E , J. J., c/o U . S . S . R . Committee for the I . H . D . , 12 Pavlik Morozov Street, M o s c o w D-376.
M r . C H U D N O W S K Y , c/o U . S . S . R . Committee for the I . H . D . , 12 Pavlik Morozov Street, M o s c o w D-376.
Y U G O S L A V I A
BORELI, M . , Lole Ribara 10, Beograd.
D I K L I C , S., International Courses in Hydraulic and Sanitary Engineering, O u d e Delft 95, Delft, The Netherlands.
STOJICEVIC, D . , Faculty of Agriculture, University of Belgrade, Nemanjina 6, Z e m u n . Vuëië, N . , Borisa Kidrica 14, Novi Sad.
1 The Netherlands.
INTERNATIONAL ORGANIZATIONS
F . A . O .
A M B R O G G I , R . P . , Land and Water Development Division, Terme di Caracalla, R o m e , Italy.
B O O H E R , L.J., Land and Water Development Division, Terme di Caracalla, R o m e , Italy.
I . A . E . A .
M r . B A R R A D A , International Atomic F A O / I A E A Joint Division of Atomic Energy Agency and F A O , Kàrtnerring 11, Vienna, Austria.
H A L E V Y , E . , International Atomic Energy Agency, Kàrtnerring 11, Vienna, Austria.
UNESCO
D A C O S T A , J. A . , Secretary, Coordinating Council, International Hydrological Decade, Paris, France.
W . M . O .
F O R S M A N , A . , World Meteorological Organization, Hydrometeorological Section. Geneva*
Switzerland.
A 1 H S - I A S H .
TISON L.J. - Professeur à l'Université de Gand, Braamstraat 61, Gentbrugge Belgique.
1 General lectures osés généraux
The three-phase domain in hydrology
C . H . M . van Bavel, U . S . W a t e r Conservation Laboratory Phoenix, Arizona, U . S . A .
A B S T R A C T : A S an introduction to the main theme of the symposium, the importance of the unsaturated zone relative to the hydrologie cycle as a whole is considered. T h e domain of unsaturated water m o v e m e n t is distinguished as a three-phase system in order to stress the point that its essential characteristics derive from a time-variant proportion of gas and liquid in a solid matrix.
This proportion changes as infiltration alternates with drainage and redistribution of water and as—in the superficial layers— recharge is offset by evaporation and transpiration. T h e water content of the matrix—itself an important storage element in the hydrologie chain—determines the mobility of the liquid phase and the direction and magnitude of the resultant driving forces acting per unit mass of water.
Prediction of the behavior of unsaturated systems by either mathematical, numerical, modeling or analog methods is instructive but often too idealized. Practical progress must also lean heavily upon systematic observation of water content and water potential in the zone reaching from the surface to the domain of saturation and of m a x i m u m hydraulic conductivity. M a n y hydrological field studies are completely lacking in this respect.
Yet, a n u m b e r of important hydrologie processes, such as surface evaporation, surface or overland runoff, transpiration by vegetation, interflow and accretion by groundwater reservoirs, are significantly influenced by the physical disposition of the unsaturated zone toward water m o v e m e n t . F r o m a combination of theory and measurement in this area, the behavior of hydro- logical systems with regard to water yields, stream flow characteristics, and transport and emer- gence of pollutants, ought to become better understood and more successfully controlled.
R É S U M É : C o m m e introduction au thème principal de ce symposium, o n attire l'attention sur l'importance de la zone non saturée par rapport au cycle hydrologique considéré dans son ensemble. Le domaine du m o u v e m e n t de l'eau dans la zone non saturée se distingue d u fait qu'il constitue un système à trois phases de sorte que ses caractéristiques essentielles dérivent de la proportion, variant avec le temps, de gaz et de liquide dans une matrice solide.
Cette proportion change du fait que l'infiltration alterne avec le drainage et la redistribution de l'eau et aussi du fait que, dans les couches superficielles, la recharge est contrecarrée par l'évaporation et la transpiration. L a teneur en eau de la matrice — qui constitue d'ailleurs un important élément d'accumulation dans la chaîne hydrologique — détermine la mobilité de la
Exp
phase liquide ainsi que la direction et la grandeur des forces motrices résultantes agissant pat unité de masse de l'eau.
La prévision du comportement des systèmes non saturés par des méthodes mathématiques numériques, par modèles ou analogies est instructive, mais souvent trop idéalisée. Les progrès pratiques doivent aussi profondément s'appuyer sur une observation systématique de la teneur en eau et du potentiel en eau dans la zone s'étendant de la surface au domaine de saturation et de conductivité hydraulique m a x i m u m . Il y a un m a n q u e sérieux d'études hydrologiques, en campagne, à cet égard.
O n peut encore ajouter que nombre de processus hydrologiques, c o m m e 1'evaporation de surface, l'écoulement de surface, la transpiration par la végétation, l'action des réservoirs d'eau souterraine, sont considérablement influencés par la dispositions physique de la zone non saturée à l'égard du mouvement de l'eau. Le comportement des systèmes hydrologiques en rapport avec la production d'eau, les caractéristiques de l'écoulement des rivières et le transport et l'émergence des polluants seraient mieux compris et seraient contrôlés avec plus de succès par une combinaison de la théorie et des mesures dans le domaine de la zone non saturée.
I. INTRODUCTION
The purpose of this paper, and that of the current symposium, is to give a special e x a m - ining effort to a segment in the hydrologie cycle that appears, by comparison, to have been ignored or neglected. F r o m a general discussion and from the presentation of specialized reports, w e m a y assist in overcoming this deficiency.
Conventionally, hydrology is separated into four parts: oceanography, surface waters, groundwater and hydrometeorology. In any of these long-standing and well defined branches of earth science and their subdivisions, w e consider water in a two-phase system.
That is, the status and the mobility of water can, in all these systems, be described by considering the water substance itself and s o m e matrix, either air or rock, soil or similar materials.
Specifically, dealing with terrestrial hydrology, w e can describe the occurrence and behavior of water in terms of its confinement either by open channels—exemplified by rivers and lakes—or by the reticule of interconnecting pores and fissures that m a k e u p the aquifers below the visible surface. In emphasizing this division, w e tend to forget that events at the surface and underground waters are connected, not just as a matter of geologic contiguity, but in a real sense in that there is continuous m o v e m e n t of water from one domain into the other. This connecting link constitutes the unsaturated or vadose zone which forms a transition between the relatively stable state of the groundwater and the rapidly and continually varying conditions in the surface layers.
The existence of a physical connection between surface and groundwater w a s first noted in studies of the origin of rivers w h e n crude measurements of streamflow, precipi- tation and evaporation in the Seine watershed in France showed that the three were in approximate balance and that there w a s n o need to invoke primordial sources of water to explain the presence of springs and seeps. The early w o r k of Dalton in England around 1800 w a s done not to elucidate evaporation as such, but to s h o w that there also, the rivers carried off the residual of the evaporation process and that water continually must seep from the surface to the aquifers and, hence, to their intersections with the land surface.
Qualitatively, this fact is reflected in all standard texts on hydrology w h e n it is recognized that in areas where rainfall exceeds évapotranspiration over sufficiently long periods, there exists a quantity of water that is in a state of d o w n w a r d migration to the groundwater. It is the quantitative description and understanding of this process of accretion that concerns us here because so little has been said or done about it in the past.
Yet, it is of obvious importance because the deep seepage controls the m a n n e r in which changes in net infiltration (infiltration - accumulating évapotranspiration) will be reflected in
changes in water table height and the resulting effects o n the yields of natural effluent or arti- ficial withdrawal from the aquifer. Further, in problems of water pollution with relatively stable c o m p o u n d s such as radioactive waste or excessive crop fertilizer, the travel time or residence time in the zone above the aquifer is a factor of practical significance. In the recharge and purification of organically polluted water, w e are interested in the extent of the unsaturated zone because it contains the required oxygen.
It is of interest to note here that a committee of the Hydrology Section of A G U in 1964 listed as the first of 63 research areas needing emphasis in hydrology, the topic " F l o w in Unsaturated Porous M e d i a " , (Linsley, 1964). This situation clearly reflects an unsatis- factory state of affairs.
Part of the confusion stems from the arbitrary classification of soil water in categories, each having specific properties. Concepts such as field capacity, capillary water, gravita- tional water and others are still being perpetuated in the literature, whereas, w e k n o w them to be faulty and at best, coarse approximations.
II. THE THREE-PHASE D O M A I N
T h e peculiarities of the vadose zone between surface and equifer can be brought out best by comparison. In surface waters the forces acting u p o n the water are gravity and the frictional and inertial forces that derive from its turbulent flow in the confining channel.
In the saturated aquifer w e also have gravity and frictional forces, n o w derived from laminar flow through the matrix, inertial forces being negligible. It is important to remember that in the latter case the fluid pressure—referred to ambient—need not be positive, as long as the matrix is saturated or, at least, as long as there exists n o continuous gas phase. Thus, the phreatic surface does not delineate the boundary of the saturated aquifer and the significance of this fact for saturated flow systems has been considered by numerous authors (e.g., Bouwer, 1964 and Childs, 1959).
In contrast to the previous two systems, the vadose zone is a three-phase system in which both air and water are flowing simultaneously and where, in addition to gravita- tational and frictional forces, w e have a third category of force acting upon the water, forces of significant magnitude originating in the confining surfaces.
In the vadose zone w e find also that the third body force m a y vary, depending upon the water concentration or the degree of saturation itself, and, at times, m a y balance the gravitational force. M o r e important, perhaps, is the fact that the conductivity for water decreases sharply with progressing desaturation. In this fact, the idea of "capillary water"
and other related categories have their historical origin.
Immobility has been falsely ascribed to water retained at fractional saturation. A classical demonstration of water flux at negative pressures in an unsaturated column w a s given by Richards (1950). T h e initial uniform moisture content in this column was around 0.25 volume fraction, or 0.53 of total pore space, with an attendant fluid pressure of about — 60 c m water. After 4 ^ months the top of the column exhibited a fluid pressure of about - 106 c m water and the bottom of about —14 c m water, implying a large transfer of water by liquid flow.
Another demonstration—under field conditions—of the mobility of water in the unsaturated zone w a s reported by Nielsen, et al. (1964). They showed that three days after infiltration of 12 c m of water into an initially wet clay loam soil, the fluid pressures from the surface to a depth of 150 c m ranged from - 60 to — 150 c m water, and the water contents were m u c h below saturation. Yet, water continued to flow out of the 0-150 c m layer for m a n y days, with the last measured drainage rate being about 2.5 m m per day on the 15th day. T h e corresponding fluid pressures had changed by that time to about
— 220 c m water.
Since the forces exerted by the matrix are dependent upon the physical-chemical
nature of the boundary and temperature as well, w e should allow for the role of soil water chemistry and soil temperature in modifying matrix force gradients and resultant fluxes, rather than consider the water content and the physical nature of the matrix as the only variables. For the purpose of further discussion w e will ignore these two effects and therefore speak about isothermal systems in which the soil water is a very w e a k solution.
A further consideration is the fact that in the interconnecting air space—the second fluid—the ambient pressure m a y not be atmospheric. This effect is n o w being studied but will not be considered further here.
In s u m m a r y , in the vadose zone water is subject to the body forces of gravity a n d those originating in the matrix. Differences in elevation give differences in gravitational potential. Differences in water content in a uniform matrix, or in the nature of the matrix at identical water content, or both together, or differences in previous conditions at identical water content in a uniform matrix, (related to hysteresis, to be discussed later) give rise to differences in matrix potential.
Since the body forces and resulting potentials are additive, w e have the well-known relation:
(p = z + \¡i
in which (j) is the water potential, z the elevation referred to an arbitrary d a t u m , often the soil surface, and \ft the matrix potential, referred to ambient (gauge) pressure. All can conveniently be expressed in c m water, though joule per kg is a m o r e fundamental unit.
(At 25 °C and 1000 m b , one joule per kg equals 10.26 c m water. T h e use of decimeters in hydrologie engineering might be considered in order to obtain approximate equivalence of numbers with fundamental studies in soil water physics.)
Since both components are referred to arbitrary datums, the absolute magnitude of (f>
is arbitrary—generally it will be a negative quantity. W h e n water is moving and inertial effects can be ignored, the equality of body forces and firction forces is embodied in the Darcy equation:
v = -k\/(j)
v being a macroscopic velocity and k the conductivity—a property of matrix and water content. In this important aspect the m o v e m e n t of water in the transition zone is entirely different from that in the saturated aquifer in which k is a constant with time.
III. T W O F U N D A M E N T A L RELATIONSHIPS
T h e character of the unsaturated matrix is for the present purpose defined by two independent relations. The first is the conductivity characteristic, which gives the relation of k to w, the volumetric moisture content. T h e hydraulic conductivity is very sensitive to moisture content and it appears not to be subject to hysteresis, that is, to exhibit at a given moisture content, a single value, rather than a range of values, depending upon previous conditions. The experimental measurement of k is difficult and tedious. A s an alternative, procedures have been suggested to calculate it from poresize distribution data.
These efforts have met with s o m e success. A s u m m a r y of experimental conductivity characteristics found in the laboratory w a s given by Bouwer (1964). O n e of the very few field measurements of k(w) w a s reported by Nielsen et al. (1964), for a Panoche clay loam.
T h e second fundamental relation is that between \ji and 6, the water characteristic.
It has been the subject of a voluminous literature and a number of methods of measure- ment exist. T h e important thing is that \¡i decreases rapidly with moisture content, except for a transition range that gives the characteristic its typical S-shape. In this area the hysteresis p h e n o m e n o n is observed and rather than a single valued relation, the \\i — w
relation can be described as a family of scanning curves that lie between two enveloping curves of continued wetting from dryness to saturation and from saturation back to a dry state. A good example is given in a study by Poulovassilis (1962). It should be observed that m a n y field determinations of the \jj(w) relation d o not s h o w the typical S-shape found in the laboratory with disturbed a n d selected materials, presumably because large holes, channels and cracks cause c o m e desaturation, even at slightly negative pressures.
T h e complexity of applying the fundamental flow equation (Darcy)
i; = - kV<¡>
becomes readily apparent, w h e n the general flow equation is derived
— = V[/cV0A + z)]
dt
in which both k and \¡J are functions of w, x, y and z ; moreover, k m a y be anisotropic and {¡/ depends u p o n previous history. Analytical and analog solutions of very m u c h simplified versions are out of the question. In contrast, digital computers allow a calculation of the distribution of w in space and time, given an initial set of conditions, as shown for example by Whisler and Klute, (1965). There are alternative ways of writing the general flow equation, but for digital computer solutions the above one is as convenient as any and it contains the two matrix characteristics k and ijj explicitly.
A great deal of effort is currently going on in solving the above equation numerically for a n u m b e r of situations, usually under somewhat simplified conditions. W e m a y well ask what the significance is of such w o r k for hydrological problems. A t the present it does not seem practical to completely define a physical situation and then—starting from a k n o w n initial condition—predict the consequences with passage of time of each k n o w n event such as a rainstorm, or a period of évapotranspiration. Rather, the computer solutions give us a feeling for the relative significance of parameters (this would even be more true for analog computer solutions if they could be devised) and they predict the behavior of closely controlled model experiments that can be realized in the laboratory.
In the last case, w e are really testing the specific flow (Darcy) equation as well as the physical realism and accuracy with which the functions k(w) and \p(iv) can be ascertained.
IV. T H E UNSATURATED FLOW EQUATION
A n y interpretation of field data or any numerical or physical modeling effort requires that the flow (Darcy) equation applies. In contrast with the saturated case, the verification under unsaturated conditions is not easily m a d e .
M a n y reports in the literature deal with a comparison of a predicted behavior from the general flow equation and actually measured moisture content, usually in vertical or horizontal columns of especially prepared material. These proofs, though not without value, are not sufficiently direct and sensitive because in the calculation of predicted moisture content a number of other uncertainties are involved: the consideration of hysteresis, the measurement of the water characteristic and the correct application of the conductivity characteristic. Thus, there are a n u m b e r of possibilities to get the right answer for the wrong reason.
Traditionally, direct verification of the flow equation has involved a steady-state or equilibrium experiment. T h e classic example is the experiment devised by Childs (1945), in which a column of a porous material through which water flowed at a fractional rate of the saturated conductivity, was tilted to different angles to produce a varying gradient.
For a given constant water content below the saturation value, the flux was found to be proportional to the gradient. Similar experiments have been carried out by others, not always with due consideration for the experimental difficulties involved in insuring steady-state conditions.
M o r e recently, Watson (1966) has given an elegant derivation of the hydraulic conduc- tivity relationship from a transient experiment which has strongly supported the conten- tion that Darcy's L a w is applicable to unsaturated flow. By simultaneous and repeated measurement of water content and water pressure in a column in which water w a s redistributing itself after an initial saturation, a number of pairs of values of flux and gradient were obtained. W h e n the quotient of these paired values was plotted against moisture content, a single relation was easily identifiable. For a given moisture content, a range of gradients resulted in essentially identical k(w) values, thus directly supporting the flow equation.
Occasionally, reports are published implying non-Darcy behavior in unsaturated flow, several having recently been summarized by Swartzendruber (1966). A totally convincing experiment demonstrating significant deviations from the Darcy equation has not been performed in this writer's opinion.
V. APPLICATIONS TO REAL SYSTEMS
So far, this discussion has dealt with the broadest possible generalities. All these are k n o w n in m u c h greater detail to m a n y participants in this symposium. Also, I have not referred to a large number of particular theoretical or experimental results because w e are dealing with a n o w generally accepted model for the movement of water in the vadose zone.
Nevertheless, applications to real systems have seldom been m a d e . I presume that this is true for two reasons. First, the complexity of a real situation, such as possible aniso- tropy of k, its variation in space and time and the absence of order-of-magnitude estimates for both k(w) and ip(w) m a k e the use of the generalized flow equation by computer or analog unattractive.
Second, for applying the specific flow (Darcy) equation, it is necessary to measure \j/
and 9 considerable depths and record their variation with time. Only recently has there been a real improvement in the required instrumentation to allow such observations.
It is suggested that the manner in which aquifers are recharged be m u c h more extensively studied by the use of tensiometer banks and by using the neutron scattering method for measuring volumetric moisture content. Several papers in the symposium deal with these experimental methods.
Tensiometers at present are still predominantly of the mercury manometer type, being devised as early as 1930 (see e.g. Krause, 1931, or Richards and Gardner, 1936). M o r e recently, pressure transducers are being used to m a k e multiple measurements (Klute and Peters, 1962) and, eventually, w e m a y be able to bury simple transducers in place and have only the wiring emerge at the surface. With either mercury manometers or trans- ducers, a resolution of 1 c m water can easily be obtained. Continuous recording and telemetering will only be feasible through the use of a transducer.
T h e neutron method is newer and, although widely used, it is still not perfected (Van Bavel, 1963). With the use of Americium alpha sources that have n o g a m m a emission, m u c h greater neutron fluxes can safely be used in the field and the accuracy of the method can be enhanced. A t our laboratory w e have recently been able to resolve changes in moisture content as small as 0.002 volume fraction. Similar precision has been reported from studies m a d e at Rothamsted, also using specially adapted equipment.
F r o m a simultaneous record of w and \\i throughout the unsaturated zone, w e can—by graphical or computer methods—ascertain the values of the function \¡/(w) and k(w) over
their natural range of variation and, thus, m o r e accurately predict by numerical methods the fluxes to the aquifer for future events or hydrogeologically similar situations.
This leads us to an application in the study of infiltration and subsequent recharge.
It is sometimes implied that infiltration during rainfall and the accretion flux are a saturated flow p h e n o m e n o n regulated by capacity factors. Certainly, the old idea of classifying water in a "capillary" and "gravitational" category gives rise to the notion that in infiltration any unfilled "capillary" capacity is replenished and any "gravitation"
water moves at saturated conductivity to the aquifer. Physically and analytically these ideas d o not stand u p . Experimentally, they are consistently refuted.
Analyses and model experiments by Y o u n g s (1957) and Philip (1957) s h o w that constant infiltration at rates below the saturated conductivity will eventually result in a semi-equilibrium at all points in the profile where water contents and pressures are invariant with time. Perturbations in the surface application are transmitted to greater depths with a damping of the amplitude with depth, as Gardner (1964) has suggested, in proportion to the so-called diffusivity D ( = kd\¡/¡dz). In natural systems the alternation of rainfall, drought and withdrawal by évapotranspiration can be viewed as perturbation of a secular infiltration that must equal the secular recharge rate at a depth where all perturbations are d a m p e d out.
O n e of the main problems in hydrology of the unsaturated zone would seem to be a study of the mechanism of damping and its relation to the matrix characteristics. It would, for example, show which aquifers would reflect the incidence of rainstorms, changes in surface vegetation, or application of irrigation waters a n d h o w long it would be before such changes became apparent. Again, it would seem obvious that realism cannot be maintained without extensive measurement in the field of water contents and fluid pressure, in addition to model and numerical studies.
A s an example, a great deal of w o r k has been done o n the hydraulics of seepage losses from irrigation canals. This is generally treated as a saturated flow p h e n o m e n o n even w h e n the seepage is to a deep aquifer, (for example, see Bouwer, 1965). This approach is not criticized here. Nevertheless, for all the theoretical studies m a d e of this problem, this author is not aware of field studies involving measurement of the soil water pressure and water content profile between the bottom of a leaking canal and the water table, not even in a model experiment. With newly developing techniques this approach should preferably parallel theoretical work.
VI. CONCLUSION
In the transition or vadose zone between the surface, where free water occurs ephemerally, and the underground aquifers, water exists in a three-phase d o m a i n , composed of the solid matrix and a gas-liquid mixture of varying proportions. T h e varying degree of saturation as well as the previous history of increase or decrease of water content gives rise to a matrix potential whose gradient co-determines the direction and intensity of water flux. In addition, the conductivity of the matrix varies with water content.
Accordingly, the mathematical description of this part of the hydrologie cycle is complex, though not intractable, particularly if digital computing is employed. T h e physical parameters involved in the flow equation are difficult to obtain in the laboratory.
For this reason, as well as for the purpose of assessing field situations and verifying theoretical concepts, wider use in unsaturated hydrology o f extensive measurement of both fluid pressure and water content is suggested by means of tensiometers and by the neutron scattering technique.
In s u m m a r y , this paper calls attention to two aspects of vadose zone hydrology. First, that in the unsaturated zone water remains mobile and subject to flow equations that are, in principle, well understood. Second, that the application of such knowledge in the field must await a m u c h wider measurement of water content and of driving gradients.
REFERENCES
B O U W E R , H . 1964. Unsaturated flow in groundwater hydraulics. / . Hydr. Die. Proc, A S C E 90:121-144.
— 1965. Theoretical aspects of seepage from open channels. / . Hydr. Div. Proc, A S C E 91:37-59.
C H I L D S , E . C . 1945. T h e water table, equipotentials and streamlines in drained land: 3. Soil Science 59:405-415.
— 1959. A treatment of the capillary fringe in the theory of drainage. / . Soil Sci., 10:83-100.
— 1964. The ultimate moisture profile during infiltration in a uniform soil. Soil Science 97:173-178.
G A R D N E R , W . 1964. Water movement below the root zone. Trans. Eighth Int. Cong. Soil-Set.
(In Press).
K L U T E , A and D . B . P E T E R S . 1962. A recording tensiometer with a short response time. Proc. Soil Sci. Soc. Am., 26:87-88.
K R A U S E , M . 1931. Russische Forschungen auf d e m Gebiete der Bodenstruktur. Landiv. Jahrb., 73:603.
L I N S L E Y , R . K . 1964. Meeting of the A G U Committee on Status and Needs in Hydrology.
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N I E L S E N , D . R . , et al. 1964. Water movement through Panoche clay loam soil. Hilgardia 35:491-506.
PHILIP, J . R . 1957. T h e theory of infiltration: 2. Soil Science 83:435-448.
POULOVASSILIS, A . 1962. Hysteresis of pore water, an application of the concept of independent domains. Soil Science 93:405-412.
R I C H A R D S , L A . and W . G A R D N E R . 1936. Tensiometers for measuring the capillary tension of soil water. / . Amer. Soc. Agron., 28:352-358.
— 1950. Experimental demonstration of the hydraulic criterion for zero flow of water in unsaturated soil. Trans. Fourth Int. Cong. Soil Sci., 1:60-68.
S W A R T Z E N D R U B E R , D . 1968. T h e applicability of Darcy's law. Proc. Soil Sci. Soc. Am., 32: 11-18
V A N B A V E L , C . H . M . 1963. Neutron scattering measurement of soil moisture: development and current status. Proc. Int. Symp. Hum. and Moisture: 171-184.
W A T S O N , K . K . 1966. A n instantaneous profile method for determining the hydraulic conductivity of unsaturated porous materials. Water Resources Research. 2: 109-116
W H I S L E R , F . D . and A . K L U T E . 1965. The numerical analysis of infiltration, considering hysteresis.
into a vertical soil column at equilibrium under gravity. Proc. Soil Sci. Soc. Am., 29:489-494, Y O U N G S , E . G . 1957. Moisture profiles during vertical infiltration. Soil Science 84:283-290.
Discussion
H . L . PENMAN:
Will D r . van Bavel c o m m e n t further o n the concept of field capacity, which I find quite useful in practice.
C. H . M . VAN BAVEL:
First, it is not always recognized that the concept of "field capacity" is not applicable to a soil material but only to a profile and thus reflects m a n y conditions that control drainage after wetting. A laboratory determination or approximation of "field capacity" is thus clearly impossible.
Second, the time required for reading a 9 0 or 95 percent approximation of a long-time water content at a given depth varies from a day or so to m a n y days. Since natural or artificial wetting and drying cycles are generally also of the order of magnitude of one to three weeks, accurate water m a n a g e m e n t practice will not find a simple "field capacity"
concept workable, the m o r e so, since equilibrium depends upon the a m o u n t of water that has infiltrated the surface.
Nevertheless, a substantial part of the total redistribution takes place within a few hours after infiltration ceases and in each case, a m i n i m u m water content is being
