Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. ASPECTS OF THE WATER BALANCE OF AN OATS CROP GROWN ON A LAYERED SOIL A thesis presented in partial fulfilment of the requirements for the Degree of Doctor of Philosophy in Soil Science at Massey University BRENT EUAN CLOTHIER 1977 ABSTRACT The increasing pressure on our water resources, for irrigation in particular, has resulted in a growing awareness of the importance of water balance studies. In this thesis three aspects of the field \>later balance are investigated� evapotranspiration (ET) from well-watered crops, the upper limit of soil water storage in the field, and drainage. Daily ET values, measured by the Bowen ratio-energy balance method, are presented for an oats crop grown in winter and also for a number of e.urruner crops, all of which were \\1ell-watered. ET measurements were also made over longer periods using a drainage lysimeter. It was found that the Penman, and Priestley and Taylor ET estimation procedures predicted ET with an accuracy of 15-20% and 8% for daily and weekly periods, respectively6 The Priestley and Taylor method is simpler to use but requires an empirical constant ·to relate the 1 equilibriura ET' to ET. This constant was found to be 1.21 for winter, spring and summer over a range of crops in the Hanawatu. Net radiation data on a daylight basis were used to evaluate this constant, as seasonal variations in the constant were introduced when 24-hour data were used .. Also it is easier to empirically estimate daylight than 24-hour net radiation. Long term E'I' estimates using the Priestley and Taylor method with net radiation calculated from incoming solar radiation, were in reasonable agree­ ment with the drainage lysimeter measurements of ET for the oats crop. A theoretical development is presented that describes water retention in soils underlain by a coarse-textured stratum. rrhis development accounts for the physical character of the overlying soil, the depth to the coarse layer, and the coarseness of the underlay. F'ield data are presented for the Manawatu fine sandy loam, a soil with a coarse-textured layer at ·90 cm. For this soil the layering resulted in an additional 55 m of water storage at the cessation of drait-lage, an increase of 31% over a similar hypothetical soil with the coarse stratum absent. iii Drainage from a permeable soil underlain by a coarse­ textured layer is investigated. Simplified theory is used to develop a model relating the drainage flux at the base of the soil to the water stored in the over­ lying soil. Despite significant hysteresis in both the water retentivity curve of the overlying soil and the hydraulic conductivity-pressure potential relation­ ship of the coarse layer, hysteresis had little effect on the storage-flux relation. The model simulated both the field drainage in the Manawatu fine sandy loa1n measured by a lysimeter, and field profile water storage found by neutron probe moisture measurements. The model indicates that only simple field measurements are needed to find the storage-flux relationship. The components of the water balance of an autumn­ so'Ym oats crop grown in the Hanawatu are resolved .. Drainage loss was found to constitute 60% of the rainfall, with the remaining amount being lost as ET. ACKNOWLEDGEMENTS I express my sincere thanks to my supervisors, Drs. Dave Scotter, Jim Kerr and Max Turner for their direction, encouragement and friendship during all the stages of my work. I would also like to thank Prof. Keith Syers and Dr Ken Mitchell for making it all possible. This work was carried out whilst I held a U.G.C. Postgraduate Scholarship and the 1974 B.P. ( N . Z . ) Postgraduate Scholarship, for which I am grateful. To the D .S .I. R. I am grateful for the help that enabled me to do this work. Thanks also to John Talbot, Peter Menalda, Peter Rollinson and Jim Gordon for assistance both in the field and laboratory. To Penny Clothier, thanks for the continual encouragement and warm understanding. For much typing I wish to thank Erin Temperton. TABLE OF CONTENTS Page Abs�ract . .. . . • . . .. . . . . . • • • . • • • • . • • • . • • . • • . . • . ii Ac)<:now 1 edg em en t s • • • • .. • • • • • • • • • • • • • • • • • • .. • • • i v Table of Contents • • • • • • • • • • • • • • • • • • • • • • • • • • v List of Figures • • • • • • • • • • • • • • • • e • • • • • • • • • • • List of Tables • • • • • e • • • • • • • • • • • • • • • • • • • • • • • List of S)"'"riJ:>ols • • • • • • • • • • • • • • • • • • · • • • • • • • • • • CBAPTER 1 viTA'rER BALANCE STUDIES • • • • • • • • • • • • • • • • • • • • • • 1. 1 IJ:\T RODUCTION • • • • • • • • • • • • • • • • • • • • • e • • • • 1. 2 THE FIELD WATER BALANCE EQUATION ...... . 1 . 2 . 1 EVAPOTRANSPIRATION (ET) ...... .. 1 . 2 . 2 MAXIMUM PROFILE WATER STORAGE viii XV xvi 1 2 2 3 ( , ... 7max) • • • • • • • • • • • • 0 • C" • • • • • • • e • 8 1 . 2. 3 PROFILE DRAINAGE ( J) • ., • • • • • • • • 12 1 . 2. LJ. SU�1A.RY &: • • • • • • • • • • • • .., • • • • • • • • • 15 1. 3 MATERIALS A-� METHODS • • • • • • • • • • • • • • • • • 17 CHAPTER 2 !-1EASURED M'D PREDICTED EVAPOTRANSPIRA'I'ION FROM WELL-vll'.TERED CROPS • • • • • • • • • • • • • • o • • • • 2 . 1 INTRODUCTION • • • • • • • • • • • • • • • • • • • • • • • • • 2 . 2 EXPERIMENTAL METHODS AND MATERIALS • • • 2 . 3 RESULTS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 2 . 4 CONCLUSIONS AND SDr�'iMARY • • • • • • • • • • • • • • CHAPTER 3 WATER RETENTION IN SOIL UNDERLAIN BY A COARSE-TEXTURE!D LAYER • • • • • • • • • • • • • • • • • • • 3.1 IJ:\TTRODUCTION • • • • • • • • • • • • • • • • • • • • • • • � • 3. 2 3.3 3.4 3.,5 TfiEORY . .. . . .. .. o • • • • • • • • &; . . . . . . . . .. . . . . EXPERIMENTAL METHODS AND MATERIALS • • • RESULTS • • • • • • • • • • • • • • • • • • • ., e • • • • • • o • • SUi-".J\·IARY AND CONCLUSIONS � o • o • � e • • • • • • • 19 20 22 26 39 40 41 43 53 57 61 CHAPTER 4 DRAINAGE FLUX IN PERHEABLE SOIL UNDERLAIN BY A COARSE-'l'BX'I'URED LAYER ..... .......... . 4.1 INTRODUCTION .. ... .. ................. . 4. 2 THEORY • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 4. 3 !1ATERIALS AND Mr:::'I'HODS • • • • • • • • • • • • • • • 4.4 RESULTS AND DISCUSSION • • • • • • • • • • • • • • 4.5 CONCLUSION • • • • • • • • • • • • • • • • • • • • • • • • • • CI-IAPTER 5 CONCLUSIONS AND SUMMARY • • • • • • • • • • • • • • • • • • 5.1 THE OVERALL WATER BALANCE . ..... . .... . 5.2 SUMMARY OF RESULTS • • • • • • • • • • • • • • • • • • APPENDIX I ERROR ANALYSIS OF THE BOWEN RATIO-ENERGY BALANCE HETHOD OF ET ESTIMATION • • • • • • • • • • Al.l INTRODUCTION • • • • • • • • • • • • • • • • • • • • • • • • Al. 2 TI-IEORY ............................. . . Al.3 RESULTS Al.3.1 1\1.3.2 Al.3.3 • • • • • • • • • • • • • • • • • • • • • 0 • • • • u • • . ERROR CONTRIBUTION DUE TO THE PSYCHROI1ETER CONSTANT • • • • • • TEMPERATURE MEASUREMENT ERROR NET RADIATION MEASURE�SNT �Ftf<()�. • • • • • • • • • • • • • • • • • • • • • • Al. 4 DETER..�INATION OF THE ERROR IN ET ..... APPENDIX II NEUTRON PROBE CALIBRATION • • • • • • • • • • • • • • • • A2.1 INTRODUCTION • • • • • • • • • • • • • • • � • • • • • • • • A2. 2 THEORY • • • • • • • • ., o • • • • e • • • • • • • • • • • • • • • A2 .. 3 EXPERU.1E:t-1TAL . . . . . . . . . . . . . . . . . . . . . . . . Page 63 64 65 66 71 84 87 88 91 94 95 96 97 97 100 lOO 102 103 104 104 106 vi APPENDIX III SCIL PROFILE DESCRIPTION • • • • • • • • • • • • • • • • A3.1 SPATIAL VARIATION • • • • • • • • • • • • • • • • • • A3.2 PROFILE DESCRIPTION • • • • • • • • • • • • • • • • APPEJ\TJ)IX . IV CROP DESCRIPTION • • • • • • • • • • • • • • • • • • • • • • • • A4.1 IN�RODUCTION • • • • • • • • • • • • • • • • • • • • • • • A4. 2 CROP AGRONOMY • • • • • • • • • • • • • • • • • • • • • • BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Page 109 110 110 114 115 115 118 Fig.l.l Fig.l.2 Fig.l.3 Fig.2.1 Fig.2.2 Fig . • 2. 3 LIST OF FIGURES PeP�an and Thornthwaite esti�ates of weekly ET for Palrnerston North over the suwmer of 1974/75 compared to est.imates using Priestley and Taylor's method ( ET ( P & T) ) (After Clothier ll al . 1975 ) . • • • . • • • . • . . . • . • • . • • • . . . • Water content at 30 cm depth in uniform soil, and the same soil underlain by sand at 61 cm and 122 cm depths and by gravel at 12 2 cm,as affected by the time after irrigation . Surface evaporation Page 7 prevented ( After Miller, 1969 ) • • • • • • • 14 Comparison of predicted drainage flux ( Eq. 1.6 ) with that measured for the Yolo loam, Hiller silty clay and Cobb loamy sand {After Davidson et al. 1969 ) . 16 Comparison of measured evapotranspiration ( ET} against computed Penman estima·tes ( ET ) , for oats. The correlation p coefficient (R) and S applu to the yx - .I linear regression equation�c•••••••••• Comparison of measured ET against the 24 hour value of the equilibrium evaporat­ ion rate ( ET ) for oats , S calculated eq yx for the regression line constrained through the origin • • • • • • • • • • • • • • • • • • Comparison of measured ET against the daylight ET , for oats • • • • • • • • • • • • • eq 27 28 30 Fig . 2 . 4 Fig.2 . 5 Fig.2.6 Fig . 2.7 Fig.3.1 Fig.3 . 2 Fig.3 . 3 Regression of incoming solar radiation (K-!< ) against the net radiation (Rn) measured over oats. Both the 24 hour and daylight regressions are shown • • Ratio of daylight ET/E'Feq (i. e. o<} for oats from winter to early summer. Days when free water was· noted on the crop are indicated ( o ) • The mean monthly temperature is sho\m. The limits on 0< of 1 and ( s + � ) / s suggested by Eq . 2 . 3 are also shown (---) • . . • • . . . . . • . • . . . • • . . • . • • . . • . . . . Predicted ET (1.22 ET ) for selected eq periods against the ET measured from a water balance applied to the lysimeter growing oats. The error band is ± 0.05 ix Page 3 2 3 3 (rainfall) over the period • • • • o • • • • • • • 35 Comparison of measured ET over oats ( 0 ) and lucerne , paspalum or pasture (0} against the daylight ETeq • • • • • $ c � · Variation in the water retentivity curve due to changing the value of the pore 38 size distribution index A ., • .. • • • • • • • • • • 44 The pressure potential profile in a layered soil and in a uniform soil at the cessation of drainage • • • • • • • • • • • • • The increase in storage 6W 1 as a function of the pore size distribution index A. , for varying -y}i 1 the cut-off potential in the underlay . Inset. The increase in storage as a function 46 of y,., for A = A • • • • • • • • • • • • • • • 49 1 max Fig.3.4 Fig.3.5 Fig.3.6 Fig.3.7 Fig .. 3.8 The increase in storage Aw, as a function of the pore size distribution index A , for varying z. the soil depth. Inset. The l. . increase in storage as a function of z . for A = A . . . . • • . • . . . • . 1. max The increase in storage �W, in a soil with secondary layering at depth zL. The subscript '11 refers to the soil zL < z � zi and 121 to the soil 0 � z � zL. Inset. The increase in storage as a function of .A 2 for A 1 = Almax. • • • • • • • • • • • • • • • • • • • • • • • • • • • Drying water retentivity curves for the three profile elements of a Manawatu fine sandy loam • • • • • • • • • • • • • • • • • • • • Hydraulic conductivity curves for two of the profile elements of a Manawatu . fine sandy loam. Drainage is considered X Page 50 52 negligible wl1en K < 10-l cm/day e • • · · · 56 Field tensiometer pressure potential data showing the decline in potential for a Manawatu fine sandy loam following a heavy w�nter rainfall of 29 mm. Over the subsequent 35 day period evapo­ transpiration losses of 70.5 mm were offset by 19 small rainfalls totalling 66.2 rmn. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 58 Fig. 3. 9a Predicted profiles of v1ator con·tent in a Manav>Tatu fine sandy loam, with and without the gravelly coarse sand layer xi Page Fig.3.9b Field neutron probe data for Pig.4.1 Fig.4.2 Fig.4.3 Fig.4.4 a .Hanawatu sandy loam compared with the predicted profile of water content • • • • • • • • • • • • • • • • � • • • The -.-vater retentivity curves for the three profile elements of a Manawatu fine sandy loam. Measured hysteresis loops ( + ) and compu·ted scanning curves (·�·) are shown for the gravelly coarse sand and fine sand. The scanning loops for various soil profile depths are shown for the fine sand. Field data for the fine sand ( l!l ) and fine sandy loam ( 0 ) are also presented . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hydraulic conductivity curves for all three profile elements of a Manawatu 60 68 fine sandy loam • • • • • • • • • • • • • • • • • • • • • • 69 Predicted wettest and driest profiles ( ignoring evapotranspiration ) of water content in a Manawatu fine sandy loam. The two wettest and driest water content profiles recorded between May and September 1975 are also shown · • • • • • • • • • • • • • • • 7 3 Measured tensiometer pressure potential in the gravelly coarse sand at 100 cm depth during the winter of 1975, and predicted tensiometer pressure potential in comparison with field measurements at depths of 40 cm and 60 cm in the soil profile.,., • • o • • • • • • 7 5 Fig .4 .5 Fig. 4 . 6 Fig. 4. 7 Fig .4 . 8 Fig.4. 9 Predicted wetting and drying drainage flux - profile water storage .relatio� xii Page ships for a Manawatu fine sandy loam • • • 76 Predicted decline in profile water storage with time in comparison with that measured by the neutron probe at two sites following two heavy winter rainfalls • e e • • • • • • • • • o • • • • • • • • o • • • • • • • 78 Predicted decline in drainage flux with time in comparison to the drainage flux computed from the neutron probe data in Fig.4. 6 , and the mean of that measured by the lysimeter over four drainage events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutron probe profile water content data at two sites, in comparison with that predicted for 1974 and 1975. Also , the drainage flux predicted , in comparison with that measured by the 79 lysimeter in 1974 and 1975.. . . . . .... . 81 Predicted drainage in relation to that measured by the lysimeter , for both 1974 and 1975 • • • • • • • • • • • • • • • • • • • • • • • • 82 Fig .4. 10 The decline in profile water storage for a uniform soil of fine sand , predicted using the model of Black et al . ( 1969 ) , in comparison to the decline predicted for a fine sand underlain by a layer of gravelly coarse sand using Eq. 4 .6 • • • • • • • • • • • • • • • • • • • Fig.Al. l Ratio of the psychrometer to the psychrometric constunt as a function of the aspiration flow rate for four 85 different experimental runs .. . . . . . . . . • .. 99 Fig.Al.2 Comparison of daily net radiation measured by t\"lo different net radiometers. The daily total of one found by integration of 1 minute sampling on a data logger and the other by analogue integrationo••• Fig.A2.1 Soil moisture content ( cm3/cm3 ) in comparison with the count ratio . ­ Also sho\v.n is the calibration curve xiii Page 101 supplied by Troxler • • • • • • • • • • • • • • • • 108 Fig.A3 . 1 The profile of Hanawatu fine sandy loam • • . ft e . . . . . . . . . . . . . . . . . . . . . . . . . . 112 Fig.A3.2 The interface between the fine sand and gravelly coarse sand of Manawatu fine sandy loam. The range.in height of the interface in this photo is 10 cm . 113 Fig.A4 . 1 Seasonal changes in yield components and dry matter % (Dm) of total forage for the 1974 oats crop ( After Kerr and Menalda , 1976 ) • • • • • • • • • • • • • • • • • • 116 Fig.A4.2 Seasonal changes in the height and leaf area index (LAI) of the 1974 oats crop . • . . . • . . . . . . • • . . • . • . . . • . . . . . . . . . • 117 Table 1 . 1 Table 2 . 1 Table 3 . 1 Table 5 . 1 LIST OF TABLES Page Estimates of the available water storage based on \'1 at a pressure max potential of -340 cm, in relation to that observed in the field, for 4 soils underlain by a coarse layer. (Miller, 1969 ) • • • • • • • • • • • • • • • • • • • • • 11 Comparison of monthly values of 1.22 ET and Penman estimates of evapo­eq transpiration ( ET ) for Palmerston p North • . . . • • • . • • . • . . • • • • . . . • • • • . • • . • 36 Physical characteristics of Manawatu fine sandy loam • • • • e • • • • • • • • • • • • • • • 55 Estimates of the components of the water balance of oats grown in the Manawatu during 1974 and 1975 . The figures in brackets are the values of the components in terms of % rainfall. Also shown is the mean rainfall { 1941-1970 ) . All values 1.n nun • • • • • • • • • • • • • • ., • • • • • • • 0 • • • • • • 89 Table A3.1 Profile description of the Manawatu fine sandy loam • • • • • • • • • • • • • • • • • • • 111 a b c C. R. e .Ae ET" eq f(u) f(w} G H J J, l. LIST OF SW.LBOLS empirical constant in Eq. 1.3 exponent in Eq. 1.3 convective term in the combination evaporation equation counts per second in soil/counts per second in neutron probe radiation shield specific heat capacity of air soil depth soil water diffusivity plant dry matter % change in surface water detention vapour pressure difference in vapour pressure betwe.en two levels above crop saturated vapour pressure evapotranspiration Penman's evapotranspiration estimate· equilibrium evapotranspiration rate daylight equilibrium evapotrans­ piration rate nocturnal equilibrium evapotrans­ piration rate wind function in Penman's equation drainage flux-profile storage - relationship soil heat flux sensible heat flux drainage flux drainage flux in coarse underlay UNITS dimensioriless -1 mm day dimensionless �1 -1· J g c cm 2 _, cm day - dimensionless mm mb mb mb -1 mm day or -2 \''lm mm day-l mm day-l -1 rnrn day -1 mm day mm day-l mb-1 -1 mm day mm day-1 Wm-2 -] mm day - \!Jm -2 mm day-l mm day-l or or K I<. � Kf K s K-!- L LAI Ll' m p Ph r s R n RO RF R S.D .. s - T Tma::x: L2 Tmin Td,TW ATd' ATW hydraulic conductivity hydraulic conductivity of the coarse underlay hydraulic conductivity of the over­ lying soil saturated hydraulic conductivity incoming solar radiation latent heat of vapourization leaf area index characteristic length of soil particles slope of the K-loge(S) curve atmospheric pressure energy used in co2 fixation by photosynthesis crop resistance to water vapour net radiation run off rainfall simple correlation coefficient standard deviation crop hea·t storage change slope of the saturated vapour pressure-temperature curve standard error of the regression estimate mean daily temperature maximum daily temperature minimum daily temperature dry bulb, wet bulb temperature dry bulb, wet bulb temperature difference betvveen two levels above crop xvi UNITS -1 cm day -1 cm day cm day-l -1 cm day -1 mm day or \'lrn-2 Wm -3 dimensionless mm mb -1 mm day or YVm-2 -1 sec cm -1 mm day or Wm -2 . mm mm dimensionless -1 mm day or 'Nm-2 c c c c c t u Vl max w . m1n z z. 1 0( time wind speed saturation vapour pressure deficit profile soil water storage profilG soil v1ater storage at time t uniform soil profile water storage layered soil profile water storage WL - Wu maximum profile soil water storage minimum profile soil water storage soil cl�pth measured from soil surface soil depth to coarse layer interface soil depth to secondary layering aerodynamic surface roughness depth defined by Eq. 3.8 empirical constant, ET/ETeq Bowen ratio psychrometric constant psychrometer constant error operator slope of the log K- loge curve volumetric soil v1ater content volumetric soil ,.,ater content at time t saturated volumetric water content difference between �* and � (Eq.Al.l2) pore size distribution index pore size distribution index when d ( AVJ)/dA. = 0 xvii UNI'rS day -1 m sec or -1 k.rn day mb cm cm cm cm cm cm cm cm cm cm cm cm dimensionless dimensionless mb c-1 mb c-1 cm3 cm-3 3 -3 cm cm 3 -3 cm cm dimensionless dimensionless ' ratio of the molecular weight of water to air soil bulk density time tensiometer pressure potantial air entry pressure potential -1 pressure potential when J = 1 mm day ' -1 pressure potent�al when Ji = 1 mm day xviii UNI'l.'S dirnensionless -3 g ern day ern ern ern ern CHAPTER 1 WATER BALANCE STUDIES 1.1 INTRODUCTION Late last century the soil physicist F.H.· King stated that "It is doubtful if there are agricultural soils to be found anywhere under existing climatic conditions where, in the majority of seasons, deficiency of available moisture must not become a marked limiting factor in yield" (I{ing, 1896). Since existing climatic conditions have not chang�d signif.icantly over the last 80 years, this statement is probably just as applicable to present day dryland farming. However, as 14% of the world's farmland is now irrigated (Rawlins and Raats, 1976 ) , the deficiency of available moisture can be reduced, if not overcome, in such soils. Improvement of both dryland and irrigated agricul­ tural production systems must be based on an understanding of both the size and seasonal changes in the components of the soil water balance. Under irrigation, water balance information can be used to develop schedules by which water can be applied. Efficient use of water is important particularly where supplies are limited, and where application costs are significant. Also fertilizer leaching losses that may result from over-watering can in the case of nitrogen, transform an expensive agricultural input into a potentially dangerous pollutant. �'later balance information can be used in dryland farming management strategies so that maximum use.can be made of the soil water reserves. 1.2 THE FIELD vll\TER BALANCE EQUATION The water balance of a soil growing a crop can be expressed simply in terms of the conservation of water mass, and written per unit surface area for a soil profile of depth d belO\v the root. zone and over the time interval t = 0 to � , as _(1.1 ) 2 In Eq . ( 1. 1} RF is the rainfall or irrigation (mm), ET the evapotranspiration rate (mm/day), J the drainage rate (mm/day), and V?'t and w0 the water storage i n the 3 soil profile to depth d (rnrn) at times 't and 0 respectively , with \'It = fdet d-:r. where et is the volumetric wat er c ontent . 0 at time t , AD is the c hange in surface detention (mm), RO the surface runoff (m ), and z the depth from the s oil surface. In most relatively flat agricultural areas with permeable soils RO a nd LlD may be assumed zero with little error . Eq. (l.l) may be solved to find the soi l water storage (Wt) and infer when crop growth is likely t o be affected by root zone water shortage. 'I'herefore, the quantity of irrigation water that should be applied to replenish this deficit without causing drainage, c an be estimated. Rainfall data f or a particular site are generally available, or may be easily measured. However evapo­ transpiration and drainage data are more difficult to measure or estimate. This thesis examines the measure­ ment and estimation of t he evapotranspiration a nd drainage c omponents of the \vater balance, plus the related problem of the retention of water i n the s oil profile. lo2. 1 EVl�POTRANSPIRP.TION ( ET ) None of the various direct or indirect methods f or measuring ET have complete preference as they differ in both short- and long-term accuracy, and in convenience and cost . The selection of the method of measurement depends on the way in which the results are t o be applied. As ET is an important component i n the water balance there is a need for means of predicting it. In this secti on it is proposed to review the methods presently available for both ET measurement and estimation. For direct measurement of ET a weighing lysimeter may be used to provide ET information, or to check indirect methods of ET measurement or estimation. Ho'tlever the expense involved, and the n·eed to ensure that a representative soil volt�e and crop is used, can limit the applicability of this approach. 4 In principle the eddy-flux technique (Swinbank, 1951} could be used to provide accurate measurements of ET, however until a reliable fast-response humidity sensor is developed, application of this approach will be limited to specific micrometeorological research problems. Even given such a technological developmen·t, it. is unlikely that routine measurement of ET over long periods of time, such as during crop growing seasors, will eventuate. Current micrometeorological methods of measuring or estimating ET are often less direct and involve an assessment of the surface energy budget, as a large amount of latent heat is involved in the change of sta·te that takes place during evaporation of water. In fact unless the crop is under severe water stress, ET is likely to be energy-limited rather than limited by the supply of water. 'l'he energy balance for a crop may be written (Tanner, 1960) Rn = H + L. ET + G + Ph +AS - ( 1.2} where Rn is the net radiation at the crop surface, H the sensible heat flux, L the latent heat of vapourization . T -3 . 1n � , G the so1l heat flux, Ph the energy used in the fixation of co2 in photosynthesis,and�S the heat storage changE in the crop canopy. GenerallyPh anddS are less than about 2% Rn' and so can be ignored. The units of the terms in Eq.l.2 are Wm-2, or alternatively if the equation is divided through by L, in units of equivalent depth of water (m, or rrm1 as is u.sual ) . The Bowen ratio-energy balance method (Tanner, 1960} used in this study involves measuring (R -�G) . n and determination of the Bowen rat:io ( f1 = H/ET) from measurements of the tempera·ture and vapour pressure gradient above the crop. This procedure is discussed in more detail in Appendix I. The use of on-line mini-computers has made this method more tractable for research studies conducted over many da.ys, however it is still unsuitable for routine use. Because of the presect intractability of direct or indirect ET measurement over long time periods,means of empirical ET estimation are often used in water balance studies. The starting point for any such procedure is to consider the ET from a well-watered surface. Since in this case ET is dominantly controlled by ·the available energy at the surface and the state of the i��ediately overlying air, estimates of ET may be based on meteorological information. The character of the evaporating surface limits the accuracy of all ET estimation procedures based solely on meteorological data because of variations in the resistance offered by the crop to the transport of water vapour. However the methods of ET estimation based on the 'Vlork of Pemnan (1948, 1 956) and Priestley and Taylor (1972) have been shown to provide reasonable estimates of well-watered crop ET (Tanner and Pelton, 1960� Tanner and Jury, 197 6). Thornthwaite's (1948) method of ET estimation is not based on sound physical principles and employs empirical constants found in the continental climate of the lJ.S.A. Rickard and Fitzgerald in 1970 stated that 'there have been no published references to the measurement of evapotranspiration in New Zealand, and the majority of workers have relied on the Thornthwaite estimates' • . Since 197 0 there appears to have been only one New Zealand publication presenting measured daily water use by crops (Kerr et al� 1973). Clothier et al . (197 5) showed that for Palmerston North,ET estimates based on Penman's (1956} method and that of Priestley and Taylor (197 2) were in reasonable agreement (Fig. l . l). This is t o be expected because of the dominance of the radiation t erm in both equations. However the estimates based on T hornthwaite's (1948) f ormulation did not correlate well and were l ower t han those based on t he other two methods. Numerous overseas s·tudies have shown Thornthwaite estimates to oft en be seriously in error (van Wijk and de Vries, 1954: C hang , 1968), and in New Zealand Coulter (197 3a)found Thornth'v'laite values to be significantly l ower t han Penman values or pan evaporation estimates, particularly in summer. For mid-Canterbury, Fitzgera.ld and Rickard (1960) found Thornthwaite values t o c ompare well with ET estimated from soil profil e water storage c hanges. They worked on a shallow Lismore stony silt l oam, where some plant water uptake may have occ urred belm.,r t he 30 cm profile depth, l eading to an under­ estimate of t he water balance value of ET . This possibility of water upt.ake is supported by the unusually l ow values for the 1 crop factor11 f in t he 1948 Penman equation, inferred from their wat er balance ET datae The main reason f or its widespread application is probably that Thornthwaite' s method req ... :lires only temperature data . Because of its weak physical basis Thornthwaite's method will not be c onsidered further. In Chapter 2 ET from well-watered full-cover crops is considered. Since this constraint is generall y fulfilled in irrigation studies, suc h information is pertinent . The divergence of ET away from the well­ watered rate f orms the basis of many crop yield-·water use models (Hanks, 197 4). The accuracy of the Penman and Priestley-'l'aylor estimates of ET is examined by c omparison with ET measured using t he Bowen ratio-energy balance method over a range of cl imatic conditions and for a variety of well-watered crops. 6 � CD CD � -E §. ... ... Fig.l. l 40 • PENMAN 30 20 o THORTHWAITE 10 ET 0 0 0 0 0 0 0 0 0 20 30 (P & T) (mm/week) 0 0 0 0 40 Penman and Thornthvvaite estimates of weekly ET for Palmerston North over the summer of 1974/75 compared to estimates using Priestley and Taylor's method 7 (ET (P & T) ) .. (Aft.er Clothier et al. 1975}. 1 . 2 . 2 MAXH1UM PROFILE WATER STOR.l1GE (\'lmax} The decline in W due to evapotranspiration is a continuous process, its replenishment by rainfall or irrigation is intermittent, thus the ability of the soil to store plant available water is important. The upper limit of available water storage capacity in the root zone is conventionally considered as some· maximum profile water storage, Wmax (traditionally termed the 'field capacity'} which may occur after heavy rain or irrigation. The lower limit of this storage capacity, W . , is the profile water storage when the crop is m1n unable to extract further soil water by root uptake (termed the 'permanent wilting point'). -The available water storage is found as the difference between \'l max and Wfl1in· In this section it is proposed to review the concept of field capacity and outline its subsequent misuse. The inapplicability of laboratory estimates of W is also discussed. max Viehmeyer and Hendrickson (1949} defined field capacity as "the amount of water held in the soil after excess water has drained away and the rate of downward movement of water has materially decreased • • • • • • as compared to the rate of extraction of water by plants". They realised however that soil texture, unifortnity, soil depth and other factors affected the value of the field capacity. In 1931 they conducted field flooded­ plot experiments and found the measured field capacity moisture content to be effectively the same as the moisture equivalent, in fine textured uniform soils. 8 The moisture equivalent is the water content after centrifuging a soil sample for 30 minutes at 1000 times the acceleration due to gravity. Viehmeyer and Hendrickson (1931) concluded "that the moisture equivalent can be used to indicate the field capacities of deep, well-drained soils with no decided changes in texture or structure • • • • • • • at least for the fine textured soils". 9 They found that an impermeable plough sole impeded water movement in one of their soils and mentioned the work of Jl.lway and HcDole ( 1917 ), which showed that coarse layering results in an increase in field capacity . They also cited the problems found by Harding (1919 ) using laboratory estimates to infer field capacity in a study involving 10,000 soil samples . Subsequently the use of the moisture equivalent was replaced by use of the water content at -1/3 bar pressure potential, which is usually similar to the former {Richards and Weaver , 1944� Colman , 1947). However because of the desire to obtain easily an estimate of maximum profile water storage , many workers have estimated W solely on the basis of a laboratory max measurement of the water content at an arbitrary pressure potentialo This useage frequently ignores Viehmeyer and Hendrickson's carefully worded definition of field capacity , and their qualifications as to the applicability of laboratory estimates. Because of this flagrant misapplication , Richards (1960) suggested a moratorium on the use of the term 'field capacity' and considered that , 11 although it is the author's prejudice the concept of field capacity has done more harm than good11• Richards {1960) however recognised that retentivity values over a certain range of potentials are usefully correlated with the upper limit of soil water storage in the field {i. e. W ). . max It is the dynamics of the soil-water system that are responsible for determining the retentivity values at which water redistribution has for all practical purposes ceased. The reduction in the drainage flux and hence the reduced decline in N when ET::::::: 0, is a continuous process , generally occurring as a result of the marked reduction in the hydraulic conductivity {K) with decreasing pressure potential {� ). Hence the selection of Wmax is somewhat arbitrary, and is often considered to occur when the drainage flux is less than about 1 mm/day (Miller , 1969). Thus such co�nonly used e�1ilibrium values as the moisture equivalent , the -1/10 , -1/5 or the -1/3 bar 1 0 pressure potential are related to W only to the extent max that they are related to the unsaturated hydraulic conductivity of the soil. The K ( 1/J" ) relationship varies markedly within the soil profile and from soil to soil . Also, the rate at vvhich the drainage flux becomes negligible at any given depth in the soil depends also on the character of the soil above and below it, a fact tha·t cannot be easily taken into account in laboratory measurements. For soils underlain by coarse layers Miller (1969) found that the available water storage found from a conventional field capacity estimate of the -1/ 3 bar water content, can in some cases be 55% lower than the value measured in a field plot several days after irrigation (Table 1 . 1). In view of such possible errors, Richards' (1960) suggestion that the determination of maximum water storage in soil profiles should be based on theory involving both the retentivity and unsaturated conductivity functions along with appropriate initial and boundary conditions, warrants consideration. In Chapter 3· a theory is derived that incorporates the factors involved in determining the water storage in soils with a coarse-textured layer underneath . Such soils are important as most of the irrigation schemes presently u�der consideration in New Zealand are on soils underlain by a coarse layer. Similar soils are common overseas. Soils underlain by a coarse layer display quite a clear cut Hmax value, (Miller, 1 969) because after wetting the pressure pot.ential profile fairly rapidly approaches a quasi-static equilibrium. The value of \·'l can be influenced markedly by the max coarse-textured layer. Table 1 . 1 Estimates of the available water storage based on w at a pressure potential of max -340 cm , in relation to that observed in the field, for 4 soils underlain by a coarse layer· (Miller , 1969 ) . 11 Estimated available water based on :- Soil Soil observed field the -340cm water Ratio depth value minus content minus ( cm) the -15,000 cm the -15 , 000 cm water content water content ( cm ) ( cm ) Ephrata 0-60 14 . 6 6 . 4 2 . 28 Timrnerrnan 0-75 15 . 3 6 . 6 2 . 32 Rupert 0-7 5 9 . 2 4 . 5 2 . 04 Scooteney 0-90 26 . 6 21 . 0 1 . 27 1 . 2 . 3 PROFILE DRAINAGE (J ) In most field . water balance studies when 'Y� exceeds W , drainage is often assumed to be ( RF-ET ) and occur max instantaneously so that always W' � W • However field max drainage i s never instantaneous , often occurring over a number of days . As the downward movement of water throu9h the soil has important implications in both water and fertilizer balance studies , it i s often necessary to account for it more realistically than a s outlined above . Profile drainage is difficult to 1 2 measure and presently there i s no direct method for reliable and representative measurement of J. Consequently in water balance studies J is often solved for a s the unknown in Eq . l . l . In this section methods of describing the decline in J with time since wetting are discussed . Also the numerical techniques and simplified analytical methods u sed to predict drainage are discus sed. Much of the early drainage work was carried out in covered plots , and the results analysed qualitatively a s the experiments were designed solely to find the " field capacity 11 • Some workers however have sought to exoress J as a function of time . Richards et al . { 19 56 ) L - - used an expression of the form -b W -· at - ( 1 . 3 ) or J = dW/dt =-abt- ( b+l ) -(1 . 4} with a and b being found by regression . Later Gardner et al . ( 1970 ) showed that an equation of the form of 1 . 3 could be derived analytically by specific solution of the one-dimensional unsaturated flow equation . Miller and. Aarstad (197 4) . rearranged Eq . l . 4 to give J == ab { vv/a ) (b-l )/b - ( 1 . 5 ) and found that the value of W in 100 cm long soil columns , which were initially saturated and subjected to known evaporation rates , could be predicted. Wilcox ( 1959) presented values f or a and b f or a rang� of soils and f ound statistical correlations between the texture of the soil ( as typified by the bulk density and the value of a ) and J at various times . However such an approach is applicable only to deep uniform soils , because .Hiller • s ( 1969) data ( Fig . l . 2) show that layering in t he profile has 1 3 a marked effect on the W ( t ) relationship f or the overlying soil . In addition empirical drainage e stimation using this approach requires that every drainage event begin at W = a . Consequently this procedure has • limited application • A general analytical soluti on describing the redistribution of water withi� the soil fol lowing infiltration does not exist . Therefore it is impossible to analytically predict drainage f rom soil water properties given the boundary and initial c onditions . Usually the problem is further c onfounded by l1ysteresis ( Phil ip , 1957 � Dane and Wierenga , 197 5). Because of the i mportance of the process approximate ways of predicting drainage have been proposed . Numerical techniques of solving the unsaturat.ed fl ow equation have been developed (Hanks and Bowers, 1962) and applied { de �·lit and van Keulen, 1 97 2 ) .. These solutions require accurate retentivity and unsaturated conductivity data, and a large c omputer. S ome success in the estimation of field drainage has been achieved using simplified analytical s olutions . Black et al. ( 1969) assumed that d�/dz=O, which holds approxiina·tely f or a deep unif orm soil, and showed that the one-dimensional flow equation could be simplified so that the flux at depth z �ould be expressed as some function of the \'later stored above that depth .. They found this procedure� to be successful in predicting drainage from the unifo::cm Plainfield sand. Extending this, by assuming an exponential relationship between 40 �--------- -----------------------� 0 > 1-z � 2 0 z 0 u 0::: ...., !;( 1 0 3; - - --- 18% ( 1 / 3 - ba r p e r c e nt a g e) A SA N D, 30 c m . at 6 1 - c m . d e p t h o SAND , 3 0 cm . a t 1 2 2 - c m . d ep t h "' G RAV E l , 30 cm . o t 1 2 2 - c m . d e pth • U N I F O RM SO I L - 0 ..L-�-_�_-c--_ ___j_ _____ L __ � ___ _! __ · J_ -· .. __! __ Fig. l.2 0 1 0 20 3 0 40 s o 60 70 DAY S A FT E R I RR IGAT ION Water content at 30 cm depth in uniform sandy loam s oil , and the same s oil underlain by sand at 61 cm and 122 cm depths and by gr.::tvcl at 122 cm, as affected by the time after irrigation . Surface evaporation prevented . (After Hiller, 1969). 14 K and e I Davidson et al . ( 1969 ) showed that J = K I ( 1 + mK t/d ) s s - ( 1 . 6 ) where Ks is the saturated conductivity , d the soil depth and m the slope of the IZ-loge (S ) function . It can be seen in Fig . l . 3 that Davidson et al . ( 1969 ) found Eq . l . 6 to successfully predict drainage in the relatively uniform Yolo loam and Miller silty clay . The poorer agreement in the Cobb loamy sand was attributed to the non-homogeniety of the soil profile . This physically­ based relationship of drainage to storage is an improvement on the empirically ' calibrated ' relationship ( Eq . l . S ) arrived at from the drainage time recession curve , but neither approach is applicable to layered soils . In Chapter 4 the relationship between J and W is investigated for layered soils . 1 . 2 . 4 SUMMARY . 15 Much remains to be done in the area of water balance research so that the field soil water status as a function of time can be predicted . In this thesis three aspects of the field v;ater balance of a soil with a coarse underlay are investigated ; well-watered crop evapotrcns­ piration , maximum field profile ·water storage and drainage . The accuracy of the Penman and Priestley-Taylor estimates of ET is examined by comparison with ET measured using the Bowen ratio-energy balance method over a range of cl imatic conditions and for a variety of well-watered crops . A theory is derived to determine the maximum field water storage in soils underlain by a coarse-textured l ayer . Al so the relationship between the drainage flux and the profil e water storage is invest.ignted for such layered soils . The main part of the study was conduc'cecl over the winter-spring-early summerperiods of 1974 and 1.9 7 5 so Fig . l. 3 >-0 � .E 2.0 YO LO L OA M FLUX AT 1 80 c m 0 - X :::::> ...J LL 0:: w 1 .0 CALC U L ATED LI NE � - :: ...J 0 en • • • 0o�--�--�I0�--�--�20�--�--�30����4·0 ' -;:. 0.8 " d "0 ' � ..£ 0.6 X :::> � 0.4 a: w � 0.2 ..J 0 M I L L E R S I LTY CLAY FLUX AT 1 52 cm • F I RST D RA INAGE o SECOND ORA l N AGE CALCULATED L l NE � 0o�----�------�170------�----�2�0-----� -;:.2.0 d "0 ' E= � 1 .5 X :::> _j u... 1.0 - 0:: w � 0.5· _j 0 � 0 C O B B L OAMY S A N D FLU X AT 1 5 2 cm • F I RST DRA I NAG E n SE COND DRA I N AGE �CALCULATED L I N E • 0 0 0o�----�5------7.10�----�1�5-- -�2�0-----�25 T I M E ( d a ys ) Comparison of predicted drainage f lux (Eq . l. 6) with that measured for the Yolo loam, Miller silty clay and Cobb loamy sand. (After Davidson et a l. 1969). 16 that maximum water storage and drainage could be effectively studied , and so that it would be possible to determine the accuracy of 0npirical means of e stimating well-watered ET rates over a range of climatic conditions . Oats were selected for this study because they grow well during the cool season in tl).e Nanawatu . The use of an annual crop , rather than a perennial pasture subjected to defoliation made long�term measurement of the physical and biological environment easier . Oats may have value as a cool season complementary forage crop to summer gro\m maize thus giving high annual yields per hectare ( Kerr and Menalda , 1976 } . In testing empirical ET estimation procedures for well-watered full-cover crops it is useful to obtain data over a wide range of climatic conditions and surface roughness to form a wide empirical base . By p.sing an oats crop sovm in autumn it is possible to measure the ET from a well-watered full-cover crop , from the middle 17 of \._.inter through into early summer . Soil water tensiometer pressure potentials at 40 cm depth riever fell below -250 cm so the crop v:as not water-limited . 1 . 3 MATERIALS AND METHODS The soil of the 1 hectare plot on which the study was conducted is a Manawatu fine sandy loam and is situated on the No . l Dairy Unit , Massey University. The soil profile description is given in detail in Appendix III . The profile can be broadly subdivided into 0--50 cm of fine sandy loam, underlain by 40 cm of fine sand , v.rith gravelly coarse sand below 90 cm. In 1974 a crop of oats ( Avena sativa L . cv . Mapua ) was planted on 26 April , and ha.rvested on 21 November yielding 13 , 200 kg/ha of dry ma·tter . In 1975 the oats ( cv . Achilles ) were planted on 7 r1ay and harvested on 15 November yielding 12 , 400 lg/ha ., A description of the crop development and management for the 1974 oats crop , on which ET measurements were Inade , is given in Appendix IV . Specific details on soil , site and crop factors are given in the material s and methods section of each chapter . Detailed error analysis of the Bmven ratio method i s given in �ppendix I . The calibration of the neutron probe is discussed in Appendix II. 18 CHAPTER 2 MEASURED AND PREDICTED EVAPOTR.fu"'JSPIRATION FR0�1 WELL-WATERED CROPS 2 . 1 INTRODUCTION Evapotranspiration data are important in many agricultural studies . The quantity of water lost by 20 a surface is useful in the interpretation of crop yields , in the understanding of watershed hydrology , in the planning of irrigation schemes , a.nd in the development of schedules tha.t attempt to optimize the amount of irrigation water applied . Continual direct measurement of ET is not easy , thus empirical means of estimation are often used . P resently the two main methods of ET estimation are based on the work of Penman ( 1948 ) and Priestley and Taylor ( 1972 ) . Penman ' s formula has been both studied and applied extensively . It may be written ET = [s/( S+ �> J(Rn- G) + [�/] f(u) VPD - ( 2 . 1 } where s is the slooe of the saturation vapour pressure­ temperature function , � the psychrometric constant , R the n net radiation , G the soil heat flux ( usually assumed zero ) , VPD the average daily vapour pressure deficit and f ( u ) an empirically determined v,rind function . The radiation� based first term is the " equilibrium evaporation rate " ( Slatyer and Mcilroy , 1961 ) and the second term , for which several forms of the function f have been proposed , may be termed the convective term since it attempts to account for the turbulent transfer of vapour . Equation 2 . 1 has been found to give reasonable estimates of ET from vegetation in many situations ( Tanner and Pelton , 1960 ) . However Penman ' s ( 1956 ) comment that the method . ' has been used , rather than tested is particularly applicable in New Zealand , so in this chapter measured ET is compared with Penman predictions . In recent years the ET estimation method of Priestley and Taylor ( 19 7 2 ) , where ET is considered to be proportional to the equilibrium evaporation rate ( ET .) , has been - E�q used because of its simplicity and accuracy . It may be written - ( 2 . 2 ) where 0( i s an empirically determined constant , which for well-watered surfaces in non-advective situations is constrained by - ( 2 . 3 ) 21 From data obtained over land and open water surfaces Priestley and Taylor found « to have a mean value of 1 � 26 . Subsequent research over crops has returned values of « from 1 to 1 . 4 ( Tanner and Jury , 1976 ) . Equation 2 . 2 has been empirically modified further to account for non energy-limited ET ( Davies and Allen , 197 3 ) , advective enhancement ( Jury and Tanner , 1975 ) and changes in leaf area ( Tanner and Jury , 1976 ) . Although somewhat conservative , � is not a universal constant and may vary with period of integration , location , season or crop . Davies and Allen ( 197 3 ) stated that " the value of 0( at low temperatures could not be examined due to the dearth of spring and fall data 11 hence the applicability of overseas data to the lower temperature and Rn conditions often experienced in New Zealand is not known . The majority of studies presenting data have been conducted in U . S .A . or Canada . Thus the use of measured ET data to evaluate � and determine its value for a range of seasons and crops would be worthwhile and enable assessment of the useful­ ness of the Priestley and Taylor method in such climates as experienced in New Zealand . Thi s study examines values of « for oat s (Avena sativa L. cv. Mapua ) over a wide range of conditions : from winter days with � as low a s 0 . 47 mm/day (water equivalent ) and average temperatures as low as 5 c ,. through to early summer with Rn as high as 6 . 6 mm/day and average temperatures up to 19 c . Few data have been presented showing the stability of o< on a day-to-day or seasonal basis , which determinE�s the accuracy of short and long term ET predictions by this method . It i s important to remember that the character of the evaporating surface l imits the accuracy of all purely meteorologically-based ET estimation procedures , because o f variations in the resistance offered by the crop to the transport of water vapour . This present study is concerned only with ET estimation from well­ watered crops . Such a procedure is useful because in most irrigated situations , where ET estimates are most commonly used , this constraint is fulfilled . Also, most current crop yield-water use models are based on the divergence of Er away from the well-watered rate ( Hanks , 19 7 4 ) • 2 . 2 EXPERIMENTAL METHODS AND MATERIALS The Bowen ratio apparatus used to measure ET has 2 2 been described by Kerr et al . ( 197 3 ) . The unit was placed . abo.ve the oat crop so that the wet and dry bulb gradients were measured over 60 to 75 cm , with the bottom sensor less than 20 cm above the crop canopy . The unit was shifted slightly in late September to avoid lodged areas that occurred upwind from the sensors . The siting of the instrument enabled the fetch-height ratio to be 70 in the dominant westerly wind direc�ion . The lowest ratio was to the south-east , being 2 2 . The crop possessed a leaf area index ( LAI ) of at ·least four and so was considered full-covered ( Tanner and Jury , 1976 ) , and was 40 cm high when ET measurements began . It reached a final height of 1 2 2 cm , with a final LF.I of 1 2 (Appendix IV) . Net radiation was measured 7 5 cm above the crop with a polythene-shielded net radiometer . Incoming sola r radiation was measured using a thermopile pyranometer . Calibration of both instruments in the field against a Linke-Feussner pyrheliometer was carried out at the conclusion of the study . 2 3 Three soil heat flux plates were placed in the soil at a depth of 5 cm , whilst heat storage in the 0 to 5 cm layer was calculated calorimetrically from the temperature change measured at 1 . 5 cm by 3 diodes . A constant soil -3 -1 heat capacity of 1 . 7 J cm C was assumed as variation in the surface soil water content was small . Total soil heat flux was obtained by s1�mming the flux and the storage change . Half�hourly Bowen ratio-energy balance data were collected on 105 days between 4 July and 11 November 1974 , with 70 days data being sufficiently complete to enable daily ET totals to be computed . Data were gathered part of the time ( 24 days ) with a Hewlett Packard 2012 B data logger , scanning every minute from dawn to dusk and punching directly t� paper tape . Subsequently a PDP 11/10 mini-computer was used to compute the half hour averages which were punched to paper tape . Inconsistent data and data when the Bowen ratio (/3 ) fell I below -0 . 5 , were edited out . Linear interpolation was used to estimate values for missing points between data , provided the gap did riot exceed two half-hour means . Integrated values o f the measured variables and energy balance computations were found for both 24-hour and daylight (when incoming short wave radiation exceeded 1 \\"'rn-2 ) periods. The error in the Bowen ratio-energy balance measurements of ET is considered , on the basis of an error analysis (Appendix I ) to be less than 11%, this being similar to that found by. Fritschen ( 1965 ) , Tanner ( 1960 ) and Blad and Rosenberg ( 1974 ) Q The error in Rn was estimated, by comparison of two radiometers , to be 5%. The 24 hour ET total was considered to be the same as the daylight ET total , that is nocturnal ET was assumed to be zero . Dewfall , measured as negative ET on two nights wH:h positive values of (3 , was found to be 0 . 11 and 0 . 2 3 nun. The latter was one of the heavier dew falls observed . Consequently dewfall was estimated to be less than about 0 . 1 mm/night and so ignored . Nocturnal evaporation was considered negligible also , , as positive vapour pressure gradients observed on several nights were an order of magnitude less than typical daylight values . Monteith ( 1956 , 1963 ) suggested that the nocturnal latent heat flux above a crop is usually small (< 0 . 2-0 . 4 mm/night ) . 24 In the application and testing of the ET estimation procedures , it was necessary to u se standard meteorol­ ogical data . For this purpose mean temperature , saturation vapour pressure deficit ( VPD ) , windspeed and rainfall data from the Grasslands Division , D . S . I . R . , meteorological site about 1 km away were used . The daily mean temperature {T ) was e stimated as ( T + T . ) /2 . Assuming the vapour pressure to be max m1n diurnally constant , the wet ( TW) and dry bulb ( Td ) temperaturcs recorded in the Stevenson screen a t 0900 hours were used to compute the mean daily VPD from - ( 2 . 4 ) where es (T ) i s the saturation vapour pressure at temperature r.r . The psychrometer ·constant was taken as the fully ventilated value of 0 . 66 mb c-1 • Although 'I i s often assumed to be 0 . 8 for Stevenson screen measurements , it is of l ittle consequence in Eq. 2 . 4 since usually ( Td-Tw) < 2·. s c . ET measurements for extended periods \vere found from the drainage lysimeter using the water balance equation for the period 0 to � , -(2 .. 5 ) where RF is rainfall , J drainage and w0-w� the change in soil water storage . Data over five periods of a month or longer were obtained in this way . The lysimeter covered an area of 2 m2 and was 1 metre deep . Daily drainage from the lysimeter was measured by monitoring the outflow of water as detailed in Chapter 4 . This to a reasonable approximation simulatE:�s the drainage occurring in the field . If the periods selected for determination of E'.r by Eq . 2 e 5 begin and end at the cessation of a drainage event , vv0 -l�l"t: can be ignored . So for four of the periods it was possiblE• to find ET 25 ·as RF-J . The end of the period September-October 1975 did no� coincide with the cessation of a drainage event , so w0 -li-71: was estimated using neutron probe data from an adjacent area . The absolute error in the measurement of ET by Eq .. 2 .. 5 was estimated as + 0 . 05 ( RF ) . This value includes error due to both measurement and the u se of RF data from a site 1 km away . Comparison of 47 daily RF values measured . above the crop with ·those measured at the meteorological site showed a mean difference of 1 . 8%. In the computation of ET the surface wa s assumed to always be well-watered . The high frequency of rainfall , it i s considered , ensured that the soil surface was sufficient­ ly wet , all the time , before full crop cover was attained . •rhe form of Penman ' s equation used was essentially that which he gave in 1956 ETp = [s!Cs-t-¥)J(Rn-G)+ [�/(s+�)][0·2bb VPDCO·S�0-0052\A)] -< 2 . 6 > whe::re the VPD is in mb, and u is the average wind speed in km/day at a height of 5 . 5 m. This equation i s one of the commonly used Penman formulations , and no significant improvement ba sed on single height meteorol­ ogical data has since been developed. The values of s and � were evaluated at the mean daily temperature , a s i s usual when applying Penman ' s equation . Wind speed was measured 7 5 cm above the crop . The wind speed gradient required in van Bavel's ( 1966 ) formulation of Penrnan ' s convective term was computed using the fact that the wind speed is zero at height z0 , the surface roughness . The surface roughness was estimated on the basis of a regression established between z0 and crop height by periodic wind profile measurements during adiabatic profile conditions . In determining the Priestley and Taylor estimates for the oats ·the 24-hou:c or daylight value of ET was eq computed by sum1ning the appropriate half hour ETeq values . The estimates were not significantly different from those found using s/ ( S + ){ ) computed from the da ily mean temperature and the ( R -G ) for the respective n periods , as the function s/ ( s + }f ) is a slowly varying function of temperature . The soil heat flux was included in the wr term for the oats data . On eq a 24 hour and daylight basis the average fG/Rn } was 4 . 6% and 6 . 8% respectively. Therefore G can be ignored if an equation of the form ET= «[s/(c:.i-¥)] Rn -( 2 . 7 ) is used with ( s/ ( s + 't ) ) calculated at the mean daily temperature . Since Eq. 2 . 7 is applicable only to full-cover crops G is usually small so can be ignored . The summer data ( J . P . Kerr and J . S . Talbot , unpublished data : I 0 :I: V C\J • � � c � E E !: c.o v 0 N I -� (X) CD "" v � m 0 0 11 0 11 0 )( -c: 11 Cl)� a:: 0::: >.. • a � E E .. - � C\1 0 0 Regression of incoming solar radiation ( K �) against the net radiation ( Rn ) measured over oats . Both the 24 hour and daylight regressions are shovm . 3 2 16 0 ,. IJJ 0:: :J � 12 IJJ Q.. � IJJ .... z <( IJJ � 8 Fig ., 2 . 5 · .� · m-------. - - • JULY • • • _ _ _ _ _;; by -( 3 . 1 ) and the diffusivity function ( D ) by = -(3 . 2 ) where L1 and L2 are the characteristic lengths . Thus Miller ( 1969 ) could calculate the functions n2 and �2 for a hypothetical underlay relative to a reference coarse underlay (D1 ,J� , L1 ) by varying the characteristic length ( L2 ) . Use of a finite difference numerical scheme for simulating drainage thus enabled him to calculate the effect of the coarseness of the underlay ( L2 ) on the water storage in the profile , relative to the soil underlain by the reference underlay . rl'his approach , 42 although illustrative , is of l ittle practical use because of the difficulty in measuring the character­ istic lengths . 43 In this chapter , a theory is derived that incorporates the factors involved in determining the water storage and permits analysis of their relative effects . The theory is applied to predict the retention of water in � by a Manawatu fine sandy l�am, which consists of finer textured soil overlying a coarse layer . Similar coarse layers underlie a number of other important agricultural soils in New Zealand , such as the aeolian or alluvial deposits of fine material on coarse Quaternary outwash gravels or volcanic lapilli . 3 . 2 THEORY The water retentivity curve of a soil can be described by modifying the expression developed by Brooks and Corey ( 1966 ) to yield l 9sC'l/le/"rjt) 9(1/r) = -�(3 . 3a ) -( 3 . 3b ) where 9 is the volumetric water content , e the porosity , s '\jl' the pressure potential and 1/le is the air entry pressure potential . To simplify the subsequent analysis � is expressed in units of energy per unit weight e 'rhe parameter A , termed by Brooks and Corey ( 1966 ) the pore size distribution index , describes the shape of the unsaturated portion of the water retentivity curve {Fig . 3 . 1 ) and depends upon the soil texture and structure . In the following analysis only the unsaturated case ( i . e .'f/r�1J!e ) is considered as the sa·t.urated case (Vf>)le > is the sarn.e as the simple unsaturated case of 1Jr� 1/re · when A. = o . Consider first the case of a uniform non-layered soil . Following saturation permeable soils tend to o.-----�----��------�------ -20 -40 I -60 w 0: . :::l CIJ CIJ w a: -80 0.. -100 -120 ____ _... ___ .....�..-___ L-.. __ ....J 0 Fig . 3 . 1 0.1 0.2 0.3 0.4 ·WATER CONT ENT. 8 Variation in the water retentivity curve due to changing the value of the pore size distribution index A � 44 drain to a uniform pressure potential (Gardner , 1960 � Davidson et al . 1969 ) . Let 1/lc be the pressure potential at which K, the hydraulic conductivity becomes very small , and hence drainage effectively ceases . Then in a uniform soil of depth z . when drainage has ceased J. consequently by Eq . 3 . 3, l 8(z) = es ( 1/re 11/lc ) -(3 . 4 ) -{ 3 . 5 ) that is the water content i s uniform with depth . Since the water stored in the profile is given by w = j2'S(z) dz. -{3 . 6 ) 0 then the water stored in a uniform profile {Hu ) i s given by . . A Vlu = es ( 11te/1frc ) z� -{3 . 7 ) However , should the same soil be underlain at depth· zi by a will cease at coarse-textured stratum, then drainage a wet:ter pressure potential , "''" · at z . �J. J. { Fig . 3 . 2 ) . Immediately above this interface , since there is negligible flux it follows that 2rt/J/2Jz = 1 (Miller , 1969 , 197 3 ) . This unity pressure potential gradient is considered to apply only until the pressure potential reaches Vt at some depth , z * . * Above z the effect of the layering is negligible because the K (1/J) relationship is steep . Therefore , * for z < z the pressure potential profile becomes that * of a uniform soil , namely (Jt/dz = 0 . The depth z can be defined by 45 * 0 - ( 3 . 8a ) z = _;_ { 3 . 8b ) 46 0�----��--------------------� E z• t..) N ::r:: t- c... L.U Cl Z · I Fig . 3 . 2 - T-- ' ' LAYERED SO I L ' UN I FORM SO I L lt o dz � -- 1/{ ' d f - 1 '$az - ' ' ' ' ' ' PRESSURE POTENTIAL I 1/1' The pressure potential profile in ' -r- I I J 1/'i - cm a layered soil and in a uniform soil at the cessation of drainage . - 0 I so , in the layered case 1/ti. - Z;. + Z * z�z. * Z< Z Consequently the water content profile . .A 47 -(3 . 9a ) -{3 . 9b ) is given by 9s ['Vre /(1/Jt -Zt.+Z)] * z�z -� 3 . 10a ) 9(z) = A es [1/re j'ljlc] * z5 . 0 ) soils gain little extra water storage in layered situations , whereas the greatest increase occurs for sandy soils (A� l ) . It is possible to determine the maximal value of A. numerically . The resulting A values are sho\� in Figs . 3 . 3 and 3 . 4 , rnax and indicate that , given the fixed parameterS e 1 �ff I s )lie ... J,. and z . � 25 cm , then 0 . 7< A < 1 . 4 for -lOO -' 'l/r. � 'Pc 1 rnax ri ' -30 cm. That is sandy soils in layered situations , tend to have larger values of Aw. CO >< ro E 1 .< .q :S: E < ro E -< - � <3 I I I I I W:J � · I � I E u I � 0 ...... ...... I C\.1 0 5 I CO C\1 3SV3H3NI 39VH01S 49 X u.l Cl z C\l u.J N en u.l a: 0 0.. Fig . 3 . 3 The increase in storage AW, as a function of the pore size distribution index A , for varying1/fi , the cut-off potential in the underlay . Inset . The increase in storage as a function of .... 1, . for ). = A . 1' 1. max 0 0 ll) ,... )( ; E 11 u ..< 0 I lO N � ' I (") I I � E I < E E E � E u u u � u ,... ....... o o o - I Cf) C') C') C') � N d I � I n 11 11 11 I CJS� u� I I Fig . 3 . 4 I 0 0 ,... CO CO � (\J 0 W:J - M V 3SV3M:JNI 39VHO!S The increase in storage 6W, as a function of the pore size distribution index A , for varying zi , the soil depth . Inset . The increase in storage as a function of z. � for A = � • rnax 50 ..< X LU Cl z z C) 1-:=J CD � 1-Cl) a LU N Cl) LU � 0 a.. The effect of varying �b: , the cut-off pressure y� potential in the coarse underlay at which drainage effectively ceases � is also depict.ed in Fig . 3 . 3 where llw c�·lr. } is shmvn for A= A • The sensitivity of V'i · max AVl to slight changes in 1/ri for high values of "'j/i is striking . c:hanging ?.J;i from -30 to .-50 cm halves �w. As the soil profile becomes more . uniform, i o e . Y.,i approaches )Vc ' the effect of layering on the amount of water retained becomes very small ; From Fig . 3 . 4 it can be seen that deep soil profiles ( i . e . large z . ) enable the textural and structural � variations described by A to express their influence more than for shallow profile s . Also , the graph of �W ( z . ) for A = A shows that only small increases in � max 5 1 AW occur for zi > 5 0 cm. In fact , doubling the soil depth from 50 cm to lOO cm increases AW by only 16%.. This de.rnonstrates the known fact that most of the increased storage in layered soils is in the region immediately above the interface . In the case where secondary lgyering occurs at zL ' Fig . 3 . 5 shows that the main contribution to AW, as expected from Fig . 3 . 4 , comes from the zone immediately above the interface at z . • In fact in this case it � matters little what value � assumes . The theorel:ical expressions derived for w0, NL and AW show that the shape of the water retentivity curve of the soil overlying the coarse stratum is a major factor controlling the field capacity of layered soils . Further , the theory clarifies the role that soil depth and coarseness of the underlay play in water retention in such soils . It serves a s a useful basis for the analysis and interpretation of field data , since Eqs . 3 . 7 , 3 . 11 and 3 . 13 can be applied easily to field situations . X e � 11 � 0 ....... E E u u I'- ('1') 0 0 Q ('l') $2 I HN 11 11 Cl!'.:#,;.,- &r � Fig . 3 . 5 CX) � 5 E E E '"' (.,) u o 0 o lD $2 ('1') 1 1 I I 1 1 1 1 .... � �� <0 � 0 A WJ - M\7 3SV3H:JN I 38VHOJ.S The increase in storage AW, in a soil with secondary layering at depth zL. The subscript ' 1 ' refers to the soil � ('I') C\1 � zL < z ' z i and ' 2 ' to the soil 0 � z ' zL. Inset . The increase in storage as =A. a function of A2 for A1 lmax· 5 2 ... � X u.l Cl � � t= ::;:) CO a: 1-en Cl u.l N en u.l a: Cl n. I . 53 3 . 3 EXPERIHENTAL HETI!ODS AND MATERIALS Most of the work to date has involved experimental studies of the effect of varying the depth and coarseness of the underlay in artificially constructed soil profiles . Th� paucity of research on naturally occurring layered soils in �� is in part due to the inapplicability of " flooded-plot" experiments ( Rose � al . , 1965 ) because of significant horizontal flow of water that occurs in such soils during these experiments (Miller , 1963 ) . As discussed in Appendix III the profile of the Manawatu fine sandy loam may be subdivided into three elements . The first 50 cm consists of a fine sandy loam, which is underlain to a depth of 90 cm by a fine sand , and beyond 90 cm by a gravelly coarse sand . The physical characteristics of these profile elements are given in Table 3 . 1 . The soils of the Manawatu series typically are made up of these three elements , although there is variation in -the depth of the layers ( Cowie , 1972 ) . To a first approximation spatial variation in water storage can be accounted for by variations in zi and zL (Appendix III ) . Haines ' method (Vomocil , 1965 ) was used to obtain the water retentivity greater than -150 cm. Eq. 3 . 3 were fitted to data for pressure potentials Equations of the form given in the data in this range , and are shown in Fig . 3 . 6 . 'I'he functions can be seen to fit the data reasonably well , particularly in the portion of the curve required in the subsequent analysis ( i . e . 'ljr ' Vri � -35 cm) . The -1000 cm water contents given in Table 3 . 1 were determined using the pressure plate apparatus . Linear interpolation of log (y) vs log (e ) was used to obtain water contents in the -1000 cm to ...:150 cm range . The laboratory hydraulic conductivity data shown in Fig . 3 . 7 were obtained using th<.� long-colu.lllil method of Childs ( 1945 ) . Conductivity data at low pressure t-3 � tJ' � (!) w • � Depth Texture HI '"Cl ( cm ) ... ;t !j '< (!) {I) ... m () PJ Pi 0-50 Fine sandy ::::5 !-' 0.. loam '< () '""' ...... 1-' OJ 0 li 50-90 Fine sand � PJ () rt (!) > 90 Gravelly li ... coarse sand (I) rt ... 0 tll 0 HI OJ :3: !.lJ ::::5 p; � OJ rt c es a at'l.jt= 1fre -1000 cm ( cm) 0 . 37 0 . 17 5 . 2 0 . 38 0 . 05 28 . 7 0 . 27 0 . 04 8 . 8 ---- A 0 . 06 0 . 94 1 . 16 K s ( cm/day) lJ:.O 251 784 l1l � 0 -20 E (.) -40 _, 102 CO "'C - E u I >- I- 101 - > I- (..) :::J 0 z 0 (..) (..) 10° ' , __, :::J <( a: Cl >- ::c 10-1 Fig . 3 .. 7 : I LABORATORY DATA GRAVELLY COARSE SAND DRA I NAG E C ESSAT ION - 10 1 10° TENS IOMETE R PRESSURE POTENT IAL - cm Hydraulic conductivity curves for two of the profile elements of a Manawatu fine sandy loam. Drainage is considered to become negligible when K < 10-l cm/day . 56 57 potentials were obtained using the theory of Brooks and Corey ( 1966 ) as the basis for extrapolation . From Eq. 3 . 3 Brooks and Corey ( 1966 ) predict that the conductivity function is given by - ( 3 . 15a ) l<('ljr) = - ( 3 . 15b ) where K is the saturated hydraulic conductivity and s "/ is given by ( 2 + 3'A ) • In this present study "( was estimated by a least squares regression , constrained through ( K5 , 1/1' e ) . However the values of "'( found this way did not vary significantly from ( 2 + 3A ) . Tensiometer pressure potential was measured in the long-column and at two sites in the field with mercury­ manometer tensiometers with 10 mm diameter ceramic tips . The pressure potential data were corrected by 8 cm to account for the capillary suppression of the mercury in the manometer tubing ( internal diameter 1 . 2 mm ) . Water content profiles in the field were measured by a Troxler 1265 neutron probe , in 2 access holes . A field calibration curve was established following the technique of Rawls and Asmussen ( 1973 ) (Appendix I I ) . 3 . 4 RESULTS Miller ( 1969 ) considered that drainage becomes negligible when K falls below 0 . 1 to 0 . 01 cm/day . Because of the steepness of the K relationship at these conductivity values , it i s of little consequence which value is selected . On thi s basis it is estimated that the gravelly coarse sand effectively ceased to conduct water once the potential fell to -30 to -40 cm( Fig 3 . 7 Fig . 3 . 8 shows five days after heavy winter rainfall that the 58 20 DAYS AFTER 40 3 5 20 15 10 5 2 1 0 RA IN E u :I: 60 1-Cl- UJ 0 80 d"" = 1 dZ 100 120�- -�----�----�----L---��--� -120 Fig . 3 . 8 -100 - 80 - 60 - 40 - 20 TENS IOMETER PRESSURE POTE NTIAL c m Field tensiometer pressure potential data showing the decline in potential for a Manawatu fine sandy loam following 0 a heavy winter rain of 29 mm. Over the subse��ent 35 day period , evapotranspiration losses of 70 . 5 mm were offset by 19 small rainfalls totalling 66 . 2 �m� 59 pressure potential in the gravelly coarse sand was -26 cm, and it eventually attained a steady state value of -35 cm, which is in good agreement with the predicted cut-off potential . Thus the cut-off potential 1ft'i may be deter.mined in the field by following the decline in the tensiometer pressure potential following heavy rain or irrigation . It can be shO\m that in general WL and .tlW are fairly insensitive to changes in 1/lc • Thus , ?/t' c can be set equal to one of the commonly accepted approximations for � at field capacity in a uniform soil , namely -100 to -350 cm. Having estimated 1/fi and lVc and established the parameters in the Brooks and Corey expression for the water retentivity curve of the soil , it is possible to establish G( z ) and hence WL a�d AW for a layered soil . With the ex·tension to account for secondary layer­ ing above the coarse stratum, Eq . 3 . 10 may be used to describe field capacity in the Manawatu fine sandy loam . The calculated water content profile is shown in Fig . 3 . 9a together with the profile calculated for a soil with the gravelly coarse sand layer absent , but otherwise identical . The increased water storage due to layering is 5 . 5 cm which is a 31% increase over the storage of 175 cm without the coarse stratum. Thi s is water enough for 10-30 days of transpiration . In Fig . 3 . 9b the calculated water content profile is compared with four individual field moisture profiles determined using the neutron probe 10-15 days after he�vy winter rain . Considering the smoothing that is inherent in the use of. a neutron probe ( Cannell and Asbell , 1974 ) , this agreement is very satisfactory. The formation of iron accumulations and mottling immediately above the discontinuity at 90 cm provides evidence that the soil is near saturated there for significant periods of time (Veneman et �. , 1976 ) ( Table A3 . 1 ) . It is interesting to note that secondary layering in a Nanawatu fine sandy loam results , fortuitously , ..d LLI :::) o t!l !1:: t2 � � :5 (..) z o - ..... cci 11 0 Fig . 3 . 9a Fig . 3 . 9b C\1 d .. "' "1"': CD 0 ...... z LLI ; � 1-W.l �� w O w o> z > "' z z < � � "' "" 0 ;;:: �9 •"' 0 "' '-' (..) 0 LLI a: en E a: u LLI :I: - � LLI ....J ....J _, _. "1"': - LLi c 0 u.. :;;:.. z • - -� � <( Q.. (.!) (/) 0 @ � 0 0 0 <0 CX) 0 � Wl Hld 30 Predicted profiles of water content in a Manawatu fine sandy loam , with and without the gravelly coarse sand layer . Field neutron probe data for a Manawatu fine sandy loam compared with the · predicted profile of water content . 60 r I . I in near-maximal additional water storage . In this soil , the important region immediately above the coarse layer is occupied by a fine sand with A = 0 . 94 , which is very close to Amax ( Fig . 3 .o 3 ) . For this reason 4 .4 cm (so %) of the extra storage occurs in the 40 cm of fine sand above the coarse gravelly sand, as expected from Fig . 3 . 5 . Were the secondary layering inverted so that the fine sandy loam ( A = 0 . 06 << Amax> was immediately above the coarse layer , a value for �W of 2 . 0 cm for the whole profile is predicted . This illustrates the importance of A in the determination of �vl. Miller ( 1969 ) presented data on the magnitude of the error in the estimation of WL if the water content at a pressure potential of -340 cm is used, as shown in Table 1 . 1 . Had the -340 cm water content been used to compute WL for the Manawatu fine sandy loam , the estimate would be 9 . 5 cm less than actual field capacity . In this chapter , .it is shown that WL may be found using Eq. 3 •. 11 without reference to hydraulic conductivity data . 3 . 5 S�MARY AND CONCLUSIONS Coarse-layered soils are free draining in the saturated state yet impede water transmission in the unsaturated state , making them particularly valuable for agriculture . A theoretical framework has been e stablished enabling the analysis of the " f ield capacity" water retention in coarse-layered soils . 61 It has been shown that the shape of the water retentivity curve of the soil overlying the coarse stratum is a Ina jor factor controlling the water stored in the soil profile . Further , the theory clarifies the roles which soil depth and coarseness of the underlay play in increasing water retention in layered soils . Field data from a layered soil are presented and application of theory to the field situation is illustrated . 62 The theory can be applied without reference to hydraulic conductivity data . CHAPTER 4 DRAINAGE FLUX IN PERMEABLE SOIL Ul�ERLAIN BY A COARSE-TEXTURED LAYER 4 . 1 · INTRODUCTION Although the drainage flux as a term in the water balance equation is often assmned negligible , or found as the residual when the other terms are evaluated , it can be a significant part of the water balance in permeable soils . Further , a knmyledge of this flux is of relevance in leaching studies in assessing the losses of ions from the root zone or their accumulation in groundwater (Jury et al . 1976 ) . 64 Presently , much remains to be achieved in the development of readily applicable ways of measuring or calculating the drainage flux. Attempts to measure drainage in the field directly with flux meters ( Cary , 197 3 ) have met with qualified succ_ess , but the ir practical value has yet to be demonstrated . If the hydraulic conductivity-pressure potential relation is known and the gradient in pressure potential measured , the drainage flux may be calculated ( La Rue et al . 1968 � van Bavel et al . 1968 ) . However spatial variability in soil water properties means that extensive replication is usually necessary ( Nielsen � al . 1973 ) . Also the requirement of frequent pressure potential readings makes this method unsuitable for most long term water balance or leaching studies . Alternatively , finite-difference or finite-element solutions of the flow equation have been used to predict changes in soil water content during infiltration or drainage in both laboratory soil columns ( Hanks and Bowers , 1962 ) and in the field ( Wang and Lakshrninarayana , 1968 ) . Subsequertt.ly these solutions have been developed so as to include effects due to layering in the profile , hysteresis , root uptake and salt movement . However such solutions need detailed and accurate soil physical data as well as a large computer . They are often difficult and costly to obtain especially if flux data for an extended period are to be corr�uted . The reasonable success in the estimation of field drainage that has been achieved by using simplified analytical solutions was discussed in Chapter 1 . 6 5 In a permeable , uniform soil profile Black et al . { l969 ) , . - - by assurning . zero pressure potential gradient during drainage , showed the flux of water at the base of the profile to be a function of the storage of water in the soil above . However Davidson � al . { 1969 ) using this approach found for the less uniform Cobb loamy sand the agreement was poorer as shown in Fig . l . 3 . They suggested that reliable e stimates of drainage in such heterogeneous soils require detailed conductivity and retent-:ivity data so u.s to enable numerical simulation . Black et al . ( 1969 ) are more optimistic stating that although 11 the drainage situation will be quite different in layered soils • • • • • • the general approach may apply • • • • • • "That is , it may be possible to describe drainage �s a simple function of profile storage 11 • In this chapter drainage from a Manawatu fine sandy loam is investigated. The soil has a moderate saturated conductivity throughout and is underlain by a coarse­ textured layer ( Table 3 . 1 ) . Field data , and theory coupled with basic physical data. for such a profile , are used to test a simple model that relates the drainage flux to the water storage in the soil above the coarse­ textured layer . 4. 2 THEORY The vertical flux of water through a soil may be described by -{ 4 . 1 ) where J is the water flux, K the hydraulic conductivity , 1/r the pressure potential and z the soil depth . For a soil underlain by a deep homogeneous coarse layer it is reasonable to assume that 2J1{/2J z = 0 and so , J =-KCVr) below the interface ( Eagleman and Jamison , 1962 ) . During drainage , the flux in the overlying soil must be less than or equal to K . , where the subscript ' i ' refers to � the coarse underlay below the interface . Further , i f wate:r is moving downward the pressure potential gradient will be less than unity. Thus in the overlying soil it follows that - (4 . 2 ) 66 where the subscript ' f 1 refers to the finer textured soil above . For soil underlain by an unsaturated coarse layer it is expected that Ki/IJ and also a water content profile in the soil above the. interface at depth zi using an equation similar to Eq . 3 . 9 , namely - ( 4 . 3 ) and the appropriate wetting or drying water retentivity curve . By integrating the water stored above the coarse­ textured layer at each pressure potential , two relation­ ships between the flux (Ji ) and the profile water storage o·n can be found , . one for wetting and one for drying . So it follows that in soils of moderate saturated hydraulic conductivity underlain by a coarse-textured stratum a relationship between Ji and W exists . If the effects of hysteresis are small , a unique relation between J . and W can be expected . � 4. 3 MATERIALS AND HETHODS The soil used for this study was a Mana\.,atu fine sandy loam as described in Chapt:er 3 and in more detail in Appendix III . Hysteretic wat(�r retentivity data for 67 the two lower profile elements , and draining retentivity data for the fine sandy loam, were measured ·using Haines ' apparatus ( Vomocil , 196.5 ) , and are presented in Fig . 4 . 1 . These data are different to the drying curve data presented in F;ig . 3 . 6 _as the main wetting and drying envelopes are included . Undisturbed core samples were used for the top two layers , but repacked loose 1naterial had to be used for the gravelly coarse sand . Scanning curves within the main hysteresis loops were calculated using the procedure described by Mualem ( 1974 ). . Field water retentivity data for the fine sand and fine sandy loam were obtained using simultaneous tensiometer and water content measurements . These are shown also and are in reasonable agreement with the laboratory data . · Field data could not be obtained for the gravelly coarse sand underlay because of the difficulty of inserting neutron probe access tubes to· sufficient depth in the underlay . Hydraulic conductivity data are . shown in Fig . 4 . 2 . The fine sand and gravelly coarse sand data are the same as in Fig . 3 . 7 . The saturated conductivity of the fine sandy loam was found by maintaining a shallow free water surface over two undisturbed cores 140 cm3 in volume and monitoring the steady-state efflux . Conductivity data at low pressure potentials on the main drying curve from saturation for the fine sandy loam were obtained using the theory of Brooks and Corey ( 1966 ) as ·the basis for extrapolation ( Eq . 3 . 15 ) from the measured values of K s and�e ( Table 3 . 1 ) . Water content profiles in the field were measured at 10 cm depth increments by the neutron probe at two sites . Comparison with gravimetric sampling showed that the water content measured by . the neutron probe at 10 cm depth provided a reasonable estimate of the mean water content of the 0 to 15 ern zone ( Appendix II ) . Drainage was found by monitoring the outflow of water from the lysimeter described in Chapter 2 . For selected periods the drainage was also calculated from the water balance equation using neutron probe , rainfall -20 E -40 (.J I � Cl) Cl) LU g: -80 -100 GRAVEllY COARSE SAND F INE SAND -·- SCANNING CURVES FINE SANDY LOAM • • • • • • • • • 68 • - 120..._ ___ .,..._ __ ---�... ___ ....__ _ .....J 0 ·1 0·2 0 ·3 0 ·4 VvATER CONTENT .8 The water retentivity curves for the three profile elements of a Manawatu fine sandy loam. Measured hysteresis loops ( � ) and computed scanning curves (·+· ) are shown for the gravelly coarse sand and fine sand . �be scanning loops for various soil profile depths are shov-1.1 fo:c t.he fine sand . Field data for the fine sand (ef) and fine sandy 'e loam (a ) are also presented . >- t- > t-u :::> Cl 2 0 u u ::J ::> -:I: Fig . 4 . 2 101 10° 1CJ1 ·: l LABORATORY­ • DATA GR AVELLY CO ARSE s AND 10° TENS IOMETE R PRESSURE POTENT IAL - cm 69 Hydraulic conductivity curves for all three profile elements of a Manawatu fine sandy loam. and evaporation data . The layering found in the field was replicated in the 1 m soil profile in the lysimeter when it was filled five years prior to _this study . 70 Nine ceramic plates , each 46 cm2 in area and of air entry value approximately -20 cm of water were situated in the gravelly coarse sand about 8 cm below the fine sand interface , and the daily drainage was considered to be the amount of water removed by these plates following the application of a suction of -40 cm of water for 2 hours. A potential of about -20 cm at the base of the lysimeter is within the range of the pressure potentials measured in the gravelly coarse sand outside the lysimeter , as sho\ffi in Figs . 3 . 8 and 4 . 4 . Tensiometer pressure potential data within the lysimeter were found to be in fairly close agreement ( 5 to 10 cm) with those measured in the field nearby . Consequently lysimeter drainage measurements are thought to be reasonably representative of drainage in the adjacent field . 1�e lysimeter would tend to underestimate drainage at lower pressure potentials , but as the flux at this stage is small it is of little consequence . The drainage model described later is applied over two 6 month periods to the Manawatu fine sandy loam. To enable computation of the profile water storage , evapotranspiration and rainfall data are also required . Evapotranspiration ( ET ) was estimated following the method of Priestley and Taylor ( 197 2 ) . The value of � used in this chapter was based on the data presented in Fig . 2 . 2 . It was assumed that the surface was always well-watered , an assumption discussed in Chapter 5 . To obtain ET in 1974 R was measured above the crop , eq n however in 1975 it was estimated from the regression of R11 on solar radiation found from the 1974 data ( Fig . 2 . 4 ) and using solar radiation data from the meteorological site . RF was also measured at the meteorological site . 71 4.4 RESULTS AND DISCUSSION In the Manawatu fine sandy loam the gravelly coarse sand underlay is homogeneous and deep , therefore it is reasonable to assume that "d1/J/2n. = 0, and so J = K (ljr) below the interface at 90 cm. The expected maximum daily rainfall is of the order of 20 mm� Figs . 4 . 1 and 4 . 2 show that a flux of 20 mm/day would cause the gravelly coarse sand to wet up to a pressur� potential of -15 cm , approximating the maximum m'ean daily potential e>..'Pected there . The steepness of the K (y) relationship in the gravelly coarse sand means this potential is fairly insensitive to the value of the maximum flux chosen . For all pressure potentials in the underlay drier than -15 cm it can be seen from Fig . 4 . 2 that for the fine sand Ki/Kf < 10 -2 and hence by Eq . 4 . 2 , 2J1jr/ 2Jz � 1 . An exception i s in the wettest case for the fine sandy loam when Ki/Kf is not small , and 2Jy/2Jz probably tends to be smaller in this zone � However as the expected pressure potential , at this stage , at the base of the fine sandy loam is -55 cm, Ki/Kf rapidly becomes negligible as the gravelly coarse sand and fine sand drain . On a daily time scale the wettest pressure potential profile to be expected in this soil thus corresponds to an interface pressure potential of -15 cm with 2J1(/2JZ = 1 in the soil above . The conductivity of the gravelly coarse sand falls steeply with decreasing pressure potential , and if it is assumed that the flux of water is negligible when I< . � {1/r) is less than about 10-l cm/day (Miller , 1969 ) , Fig . 4 . 2 shows drainage becomes negligible when a pressure potential of -30 to -40 cm i s attained at the interface as already noted in Chapter 3 . Again , from Eq . 4 . 2 , it can be expected that 2J'l/r/2Jz = 1 in the soil above . In F'ig . 3 . 8 is shown thr� tensiometer pressure potential measured in the field following a winter rainfall event. The data shm'l this distinct w .. �ttest and driest envelope . 7 2 The pressure potentials at lOO cm depth , in the gravelly coarse sand , are within the expected values and d�/dz in the soil above approaches one . An exception occurs on the day of the rain in the fine sandy loam, but this is expected since Ki/Kf is not yet sufficiently small . This is of little consequence as the steep retentivity curve in the fine sandy loam means that only relatively small amounts of water are lost from it during drainage , the major contribution being from the fine sand layer . In computing the water content profile from pressure potential data it is necessary to account for the effect of hysteresis in the fine sand. As water initially enters the fine sand it is wet up along the wetting curve indicated in Fig . 4 . 1 , until the potential reaches approximately 'J/r(z) = -15 - ( in the underlay are known , it is possible to determine Ji (W ) . The wetting and drying storage-flux relationships resolved in this way are sho'vn in Fig � 4 . 5 . As there is little difference between the t.wo curves a unique relationship for J (W ) can be assumed with little error . This is a result of the relatively small variation in 1/J' in the fine sand ( Fig . 4 .4 ) giving a narrow envelope between the wetting and drying curves , despite the wide envelope between the main wetting and drying curves ( Fig . 4 .1 ) . Further the scanning loop between -15 and -35 cm in the gravelly coarse sand is narrow, so that hysteresis in its hydraulic conductivity- pressure potential relationship is quite small . In the application of this relationship the drying curve was used . If only drainage contributes to the change in w then dW/dt = Ji = f (W ) - (4 . 6 ) where t is time and f (W) is the solid line in Fig . 4 . 5 . -20 -40 E u . _. c::x: ._ 2 LU t;-60 a_ LU a: ::::> Cl) Cl) LU I a: a.. -80 I a: LU tu-60 2 0 Cl) 2 LU ._ -80 -100 Fig . 4 . 4 7 5 MEASURED • PREDICTED • • • 60cm • • '-MEASURED • • • • • • • • • - · • ' PREDICTED • • -. . • .. • '· ' 40 crn • � MEASURED JUNE JULY AUGUST SEPTEMBER OCTOBER 1975 Measured tensiometer pressure potential in the gravelly coarse sand at 100 cm depth during the winter of 1975 and predicted tensiometer pressure potential in comparison with field measurements at depths of 40 cm and 60 cm in the soil profile . 1 - > ea '"C -- E E 8 .. X ::::> .....J U- u.J c..!:) � 4 - <( a: Cl Fig . 4 . 5 D ' ' \ \ \ \-ooli!\;rc-c...- WETTING \ DRYING 260 PROF ILE STORAGE mm . , 76 220 Predicted wetting and drying drainage flux - profile water storage relationships for a ManavTatu fine sandy loam. 77 It is possible to solve Eq . 4 . 6 numerically using a finite difference approximation of dvl/dt , \17 mm) . Changes in storage due to water losses by evapotranspiration were accounted for in the field data . The variability in the field measured storage data is to be expected since W is a function of the depth to the coarse layer, and for a Manawatu fine sandy loam a 5 cm variation in this results in a 10 mm change in W ( see Fig .A3 . 2 ) . However the changes in storage with time are similar at each site . �1e predicted flux-time relationship is compared in Fig . 4 . 7 with that calculated from the field neutron probe data and also the mean curve established for four winter drainage events from the lysimeter . As expected the agreement with the lysimeter is better over the first 6 days when the pressure potential is still quite high . Also within the accuracy possible for fluxes calculated from neutron probe data , the recession curve found this way is compatible with that predicted . The predicted amount of water lost between days 1 and 9 is 20 . 3 mm which is comparable to the 24 . 6 (± 3 .. 7 ) nun drained from the lysimeter and the 25 . 8 mm measured by the neutron probe . \Vhile the J (W) relationship derived assumes only the drainage flux to be responsible for decreasing the soil water storage , evapotranspiration also removes water from the soil profile . If the soil is bare the water extracted by evapotranspiration will come from near the surface and so deep drainage will be little affected , as demonstrated by Davidson � al . ( 1969 ) . This water loss must subsequently be replaced by rainfall E E LU 280 270 � 260 a: � en LU __, � 250 a: a... 240 Fig . 4 . 6 • \ \ \ ' 4 - e - I NDIVIDUAL HOLE AND MEAN NEUTRON PROBE " DATA 8 TIME , days 12 PREDiCTED . CURVE I 16 78 Predicted decline in profile water storage with time in comparison with that measured by the neutron probe at two sites following two heavy winter rainfalls . � :g_ E E w (.!) 265 . Drainage below 0 . 2 mm/day is ignored . The predicted drainage for May to November 1974 and a similar period in 1975 can be seen in Figs . 4 . 8 and 4 . 9 to be in reasonable agreement with that measured from the lysimeter , _ in terms of both the timing and amount of drainage . Within the bounds of variability in the data , the changes in profile water storage measured by the neutron probe also can be seen to verify the applicability of the model ( Fig . 4 . 8 ) . The model can be expected to work in any soil with a coarse-textured stratum at some depth , and a saturated hydraulic conductivity of at least say 50 nw/day throughout the profile above . In such situations the unsaturated hydraulic conductivity of the coarse-textured stratum controls the rate of drainage at all times , except possibly during and immediately after very heavy rain . During drainage and in the quasi-equilibrium condition o e 0 o• 0 0 0 0 0 0 • 0 • ... 8 R: 0 � ... .... u �- � Ei ::l e( � � 0 ---oe I • I 0 � ... .... � 5� � -�a 0 • a: � a: I ... t � .... "' . g 10 . C( a: 0 S; "' ,... � .... � � � 0 � � f I ! • i I »'I--+ a: 0 ... � .... !.! ... liE 0 � ... f • 0 � 0 • 00 • 0 0 ._....� • I I 0 • • 0 0 • • • •• � � � � � 52 0 UAU • �!NMOLS 311.:10Hd I.VfJ/ww ' 3�NIY�Q Fig . 4 . 8 Neutron probe profile water content data at two sites , in comparison with that predicted for 1974 and 1975 . Drainage flux predicted in comparison wit.h that measured by the lysimeter in 1974 and 1975 . 81 � .g 30 ...... E E w (!) � Z 2Q � a: 0 0 w � 0 0 10 w a:: • a.. Fig . 4 . 9 . • • • • 1 : 1 LINE • • • • • 0 • • • 10 20 30 MEASURED DRAINAGE, mm /day Predicted drainage in relation to that measured by the lysimeter , for both 1974 and 1975 . 82 I 1 - 83 follo•..,ing , the hydraulic conductivity of the soil above the coarse stratum remains relatively high . Thus , unless the profile has been dried out by evapotranspiration , the time lag between a rainfall input and the correspond­ ing . adjustment of the drainage rate will be small , usually less than a day . This contrasts with the situation in a uniform profile , where a much longer response time is usual . In the uniform Plainfield sand, Black et al . ( 1969 ) found it took about 2 days for an increase in storage to a ffect the drainage rate at 1 . 5 m depth . This simple model can also be used as an analytical tool , when applied to a soil that satisfies all the necessary conditions outlined . In the Manawatu fine sandy loam, with both fine sandy loam and fine sand layers . above the gravelly coarse sand , the model predicts that it takes 6 . 7 days for the drainage flux to drop to 1 mm/ day , following wetting of the profile . Over thi s period the soil loses 20 . 3 mm of water . Hypothetically however , if the gravelly coarse sand was still at 9 0 cm depth l:;>ut overlain by only fine sand , it is predicted that to attain a drainage rate of 1 mn1/day would take 15 days and 50 mm of water would have been removed during drainage . Although drainage persists for longer from fine sand it is this type of soil that undergoes the greatest increase in water storage due to the layering , by virtue of the shape of its retentivity curve as shown in Figs . 3 . 3 and 3 . 4 and discussed in Chapter 3 . Alternatively if the gravelly coarse sand were at a depth of 20 cm under fi.ne sand it would only take 4 . 3 days for the drainage rate to drop to 1 mm/day , with a drainage loss of only 13 mm. The existence of a coarse-textured stratum in a permeable profile does not necessarily mean a rapid cessation of drainage , but rather the time course of the drainage recession depends on the nature of both the overlying soil and the underlay , and the depth to the interface . 84 The model of Black et al . ( 1969 ) was applied to a 90 cm deep soil of uniform fine sand . The initial condition chosen was the soil wet to 1fr = -15 at 90 cm with cf/cz = o . The decline in profile water storage is shmm in Fig . 4 . 10 in comparison to that predicted by Eq .4 . 6 for 90 cm of fine sand wet up to 'JY= -15 at 90 cm with ct/c2 = 1 , but underlain by gravelly coarse sand . It can be seen layering results in more water being stored in the profile when quasi-equilibrium is reached ( c . f . Figs . 3 . 3 and 3 . 4 ) and causes the drainage recession curve to be much flatter , with the flux becoming < 1 mm/day more quickly . 4 . 5 CONCLUSION The theory proposed by Black � al . ( 1969 ) , that the drainage flux can be treated simply as a function of soil water storage , would appear to work even better in permeable soils with a coarse-textured stratum at depth than in the uniform permeable soils for which it was first proposed . In such layered soils the hydraulic conductivity of the coarse-textured underlay usually controls the drainage flux at all times ensuring et I cz �1 , whilst the soil above maintains a high hydraulic conductivity . Thus , firstly , the total potential gradient in the overlying soil will approach zero during drainage , in contrast to the unit gradient of a uniform profile and secondly , the response in the drainage flux to an input of water at the soil surface will usually be more rapid than in a uniform soil . While the drainage flux is controlled by the conductivity of the coarse stratum, the drainage- storage relation is determined by the depth and the water retentivity of the soil above the stratum, as wel l as the pressure potential-conductivity relation o f the underlay. ! I - en _ CD - � 22 CD 0:: � >- V � -a m . � til 10'" w z - � 10 per month ) would ensure that the soil surface was sufficiently wet all the time , and that this assumption was valid. The water balance data are based on an initial storage ( vl0 ) measured by the neutron probe . The average rainfall data show that both the 1974 and 1975 seasons were wetter than normal . �ne monthly rainfall totals between years have a mean difference of 61 mm . For ET between the years there was a mean monthly difference of only 5 mm. Year to year variation in ET is much less than for rainfall ( Tanner , 1967 ) . Because of this consistency , year to year variation is often ignored in the monthly ET values used in approximate water balance studies ( Coulter , l97 3b ) . The strong dependence of J on RF causes monthly totals of drainage to vary markedly between years . Over the May-October periods. outlined , approximately 60% of the rainfall was lost as drainage , and about 40% as ET . Drainage during the summer period i s unlikely. As the mean annual rainfall is 1000 mm, the annual drainage loss will be about 30-35% of the rainfall input . ET will account for the remaining 65-70%. I . 89 Table 5 . 1 Estimates of the components of the water balance of oats grown in the Manawatu during 1974 and 1975 . The figures in brackets are the values of the components in terms of % rainfall . Also shown is the mean rainfall ( 1941-1970 ) . All values in mm. 1974 Measured Predicted Predicted Predicted Mean RF ET J * May 119 36 71 June 47 21 24 July 2 37 27 218 August 72 47 32 September 118 62 45 October 126 92 39 TOTAL 7 20 285 { 40%) 428 { 59%) * Period 5 May - 31 May only 1975 t.· May 101 22 94 June 7 7 29 49 July 1 30 33 85 August 143 47 101 September 51 64 19 October 83 91 1 TOTAL 585 285 ( 49%) 348 { 60%) * Period 1 2 May - 31 May only w0 - \'l� RE' 13 86 2 99 -7 91 -7 84 12 69 -6 89 7 ( 1%) 518 -15 0 12 -5 -32 -9 -49 ( 9% ) As has been shown , the daily drainage flux from a soil is intimately related to the physical properties of the entire soil profile . But once the soil profile is fully rewetted ( \-'1 = W ) , overall during winter max J 90 .if the profile saturated hydraulic conductivity is high , since W tends to W , J � RF-ET . That the layer-ed max Manawatu fine sandy loam possesses a sufficiently high value of K is evidenced in July 1974 when a massive s 218 mm ( 9 2% RF} was lost as drainage . Whether a soil i s underlain by a coarse-layer below the root zone or not makes no difference to the value of W . , the minimum profile wa·ter content that occurs m�n during a dry summer . However the value of Wm ax for a coarse-layered soil is greater by �W than that of a uniform soil . Consequently when the soil is rewet in autumn or early winter the storage in a uniform soil will reach W and begin draining before a slinilar soil max underlain by a coarse layer . This results in the drainage component of a layered soil being AW less than that of the uniform soil . During a dry spring-summer period under dryland conditions , since in a layered soil Wmax -wmin is Aw greater than for a uniform soil , ET will be approximately AH greater in the water balance of the layered soil . Under irrigation the increase in v� caused by the max coarse-textured layer means· that irrigation need be applied less frequently . In the Manawatu fine sandy loam .AW was found to be 55 mm, which is water enough for an additional 10-30 days plant use during the growing season . Because of the size of W the soil may be · max irrigated to a value of less than \'l without fear of max . a shortage of soil water and so allowing for the chance of recharge by rainfall , thus minimising the risk of drainage loss . 91 Applied water balance studies require good estimates of both \'v • and W as well as es.timates of ET for m�n max a well-watered crop . The results presented in Chapter 2 confirm that simple , yet accurate methods of calculating ET for well-watered crops , based on physical principles , and re�1iring only meteorological data , are available . Conversely , in Chapter 3 , it was shown that simple estimates of W based on standard laboratory measurements max may be quite inaccurate , particularly in non-uniform soil profiles . A theory that predicts W in layered soils max was presented and successfully applied to the Manawatu silt loam. Often in water balance studies when \'1 � W it is max assumed that J = RF-ET on a daily basis . However it is sometimes necessary to account for drainage more realistically . In Chapter 4 it was shown that a simple relationship could be developed , and used to predict the drainage in the coarse-layered Manawatu fine sandy loam. This was not significantly. affected by hysteresis . The highly variable components of soil water movement and storage are important in applied water balance studies . This work provides relatively simple models for estimating W and drainage fluxes in permeable soils underlain max by a coarse-textured stratum. 5 . 2 SUMMARY OF RESULTS 1 . ET estimates from meteorological data using either Penman ' s equation or Priestley and Taylor • s procedure were found to be 15-20% accurate on a daily basis in comparison to Bowen ratio-energy balance ET measurements , and about 10% accurate over weekly periods . 2 . If only the daylight period was considered , the empirical coefficient in Pr�estley and Taylor • s procedure was found to be constant («= 1 . 21 ) over a range of crops and climatic conditions . Under I I I . I 92 low net radiation conditions , significant nocturnal long-wave radiation loss not associated with a vapour flux was considered to be the reason for the lesser success of Priestley arid Taylor ' s method over the 24 hour period . Fair agreement · was found between the daylight Priestley and Taylor est�ates and ET measured using the water balance of a drainage lysimeter over periods greater than a month . 3 . A theoretical framework was established to enable analysis of the maximum profile water retention in soil underlain by a coarse layer . As well as the depth of the overlying soil and the coarseness of the underlay , the shape of the water retention curve of the overlying soil plays a major part in controlling the quantity of water stored in the soil profile . Water storage in sandy soils is more affected by the occurrence of a coarse-textured underlay , than finer- or coarser-textured soils . 4 . In the Manawatu fine sandy loam, coarse layering at 90 cm depth was found to increase the profile water storage 55 mm above that of a hypothetically similar soil without the coarse layer . Good agreement was obtained between the quasi­ equilibrium profile of water content predicted by the theory and profiles of water content measured in the field by neutron probing after drainage s . had ceased . It was shown that for certain layered soils it is possible to develop simple theory relating the drainage flux to the water stored in the overlying soil . This theory also enables the pressure potential profile in the soil to be predicted during drainage . Significant hysteresi s , in both the \'later retentivity curve of the overlying soil and to a lesser extent in the hydraulic conductivity- pressure potential curve of the coarse was shown to be of little consequence . relationship bet\veen the drainage flux profile storage could be assumed . layer , A unique and 6 . The drainage theory was shown to be applicable to the Manawatu fine sandy loam. Drainage predicted by the model was in agreement with that measured by the lysimeter , an? the predicted soil water storage was found to be similar to that measured by neutron probing . The theory was also used to show that soils underlain by a coarse layer have a much flatter drainage recession curve compared to that of a similar uniform soil . This results in the greater water storage capacity of layered soils . 9 3 APPENDIX I ERROR ANALYSIS OF THE BOWEN RATIO-ENERGY BALANCE METHOD OF ET ESTIMATION 95 Al . l INTRODUCTION In the Bowen ratio-energy balance method evapo­ transpiration ( ET ) i s calculated from the energy balance equation ET = (�-G ) I ( 1 + f3 ) -(Al . l ) where the Bowen ratio j1 = H/ET , where Rn is the net radiation , G the soil heat flux, and H the sensible heat flux. Rn ' G , H and ET are in units of equivalent depth of water (mm ) , having divided through by .the latent heat of vapourization of water . Using the aerodynamic equations for heat and mass transfer , and assuming similarity of the diffusivities of H and ET it can be shown that (J = ��Tit.e -(Al . 2 ) where (( is the psychrometric constant , and AT and Ae are the temperature and humidity differences be·tween two levels above the evaporating surface . It is possible to measure �T by use of temperature sensors and �e by wet bulb psychrometers . Following Fuchs and 'l'anner ( 1970 ) Eq. Al . 2 can be rewritten to give - (Al . 3 ) where s is the slope of the saturated vapour pressure- • temperature curve , � the psychrometer constant ( as distinct from the thermodynamically defined psychrometric constant ) , and ATW the difference in the wet bulb temperature between the two levels . Eq.Al . 3 relates to a psychrometer assembly where the value of ..6·rw is measured at the same dry bulb temperature ( Slatyer and Bierhuizin , 1964 ) . A similar isothermal block arrangement was used in this study and has been previously described by Kerr � al . ( 1973 ) . Errors in the measurement of �T and ATW cc;n be seen to affect (3 via Eq. Al . 3 . Similarly error in � can result in error in the value of f3 . Errors in the measurement of (3 and Rn-G affects the value of ET computed by Eq .Al . l . I I I I . I 96 In this Appendix the magnitude of these errors is examined and their effect on ET determined. Al . 2 THEORY r�chs and Tanner ( 1970 ) analysed the effect of errors in the measurement of �T ATW' R -G , and s on the ' n accuracy of determination of ET , on the basis of maximum error calculations . Hence , using the symbol · � · to denote the error in a quantity , they wrote the relative error in ET from Eq .Al . l as . GET/ET = (&R, + bG)/IRn-GI + �/11 j131 - ( Al . 4 ) Determination of the probable error however is more realistic , whereby the error in a quantity is given as the square root of the sum of squares of the maximum error in each variable ( Topping , 1966 ) . Hence , as Sinclair ( 19 7 2 ) has suggested the relative error in ET can be found as - ( Al . S ) ' � On this basis considering the error in AT, ATw and '! the relative error �f/C1 +f) can be found from Eq.Al . 3 as The quantity �AT represents the error in measurement of the temperature gradient which can be given as - ( Al . 7 ) where &Td is the maximum error involved in the measured temperature Td . Similarly for wet bulb psychrorneters -(Al . 8 ) Equations Al . S and Al . 6 provide a basis for analysing the errors in ET due to the contribution of measurement errors from the various sources . This measurement error analysis procedure does not account for the inadequacy of the steady-state and one-dimensional assumptions inherent 9 7 in the determination of ET by Eq . Al . l . As shown by Rose � al . { 19 7 2 ) this assumption can introduce errors up to 18% in daily ET under very non-steady state conditions . Under steady-state conditions the accuracy was less than 5%. Similarly errors due to the failure of the assumption of similarity between the diffusivities of heat and mass are ignored . These Campbell { 197 3 ) concluded could lead to errors of up to 10%. Al . 3 RESULTS Al . 3 . 1 ERROR CONTRIBUTION DUE TO THE PSYCHROMETER CONSTANT In a perfect psychrometer the change in latent heat content per unit volume when the vapour pressure rises from e to saturation at TW [es { Tw)] is equal to the amount of heat lost as the air cools from Td to TW . Hence it can be shown that - {Al . 9 ) or -( Al . lO ) where P i s the pressure , c the specific heat capacity p of the air , L the . latent heat of vapourization and � the ratio of the molecular weight of water to air . A good empirical expression for � is given by the Ferrel ' s equation { List , 1958 ) , namely -4 ¥ = ( &·bl x lO )[1 +0·0Dl15Tw] P - {Al . ll ) where TW i s in units of C and P in mbar . However in practice psychrometers may not fulfil the adiabatic or other constraints necessary to arrive at Eq .Al . lO . It was necessary then to test the accuracy of the psychrometer assembly used in this study . From consideration of the energy balance of a wick psychrometer it is possible to show that - ( Al . l2 ) 98 .... where }{ = �(i 1-.A) and A can be shown to be related to the thermal conductivity of the wick and the diffusion resistance to heat and vapour leaving the wick . Hence Jl is a function of air velocity ( u ) over the wick for ljl: a given psychrometer . Consequently � is also a function of u , unless the psychrometer is fully ventilated and adiabatic conditions apply. The psychrometer unit used in the field in this study was set up in the laboratory in a way similar to that .. used in the field , so the · form of 'a' ( u ) could be determined . A flow meter was placed in the a spiration line to measure the air flow , as direct measurement of the air velocity over the wet bulb was not possible. The measurement accuracy of the flow meter was 0 . 1 1/min . Rearrangement of Eq.Al . l2 gives - (Al • .l3 ) The value of e was that of the ambient vapour pressure in the laboratory , measured with an Assman psychrometer and found to be effectively constant during the experimental run < < ± 1 rob) . The temperatures Td and TW were measured on a chart recorder so as to ensure that sufficient equilibration time was allowed for, following changing of the flow rate . The results are shown in Fig .Al . l and it can be seen that the aspiration plateau does not begin until a flow rate of about 5 1/min is achieved . A flow of this rate is estimated to produce · an air speed of 2 . 5 m/sec in the chamber just before the wick , which is close to the recommended ventilation rate for psychrometers ( Bindon , 1965 ) . The use of different wick and water level configurations in the wet bulb results in a different value of .A.. for each run causing some of the scatter in the data , especially at low flow rates . As in the field the unit was operated in the range 1-2 1/min it can be seen that x· = 1 . 75 <± 0 . 3 ) � , and �¥lit= 0 . 2 as " = 0 . 66 , in mb/C . 99 I() • • V • . � -� � � � f'() -..;:: w � 0:: z 0 C\l t:{ 0:: a.. (/) <( C\1 Fig .Al . l Ratio of the psychrometer to the psychrometric constant as a function of aspiration flow rate , for four different experimental runs . MASSEY UNIVER�IT.l l.I.B.RALrt. lOO Al . 3 . 2 TEMPERATURE MEASUREMENT ERROR To determine � it is necessary that both the wet­ bulb and the dry-bulb temperature gradients can be measured . Paired diodes with matching calibration curve slopes were used to estimate both AT and 6Tw· In order to el£minate the errors due to inaccurately determined offsets in the diodes used for the gradient measurement , 0 the sensors were rotated through 180 every 15 minutes so that error cancellation would occur when the 30 minute average was formed . Thus errors in llT and �TW will be similar and arise through recorder resolution , the slopes of calibration curves of the paired diodes not being identical , and short term sampling and scanning rate problems . Since it is not possible to determine accurately the magnitude of such errors it was considered that �Td and �Tw were of the order 0 . 05 c . This is of similar magnitude reported by Fuchs and Tanner ( 1970 ) using . similar diode sensors ( iTd = 0 . 01 c , � TW = 0 . 1 C ) and Sinclair { 1972 ) ( 0 . 02 and 0 . 04 C respectively ) . Al . 3 . 3 NET RADIATION MEASUREMENT ERROR The form of Eq .Al . l means that measurement error in the determination of Rn ; can be seen , by Eq. Al . 5 to have an effect on the accuracy of resolution of ET by the Bowen ratio-energy balance method . Comparing two net radiometers Fuchs and Tanner ( 1970 ) estimated the accuracy in measurement of Rn to be 3%. For estimation of �Rn in this study , a comparison \'o occurs , even though ·their effect on slowing down the neutrons is relatively small . Thirdly an increase in ;ob increases the concentration of absorbing elements . The effect of (\ on the count rate of an oven-dry soil will depend on the combined effect of these three processes . Greacen and Schrale {�976 ) suggest that Holmes ' ( 1966 ) data is suspect because of his overestimation of the bound water content of his soil and variability in his f'o data . Greacen and Schrale * ( 1976 ) found that the plot of count ratio against total water content was l inear with a residual variability due ·* Count ratio ( C . R . ) = thermal neutron cps/cps in radiation shield to scattering and absorption effects with changing ito . This residual scatter they could reduce by using an empirical relationship based on � • Variability and measurement error in field data however makes this correction not worthwhile , in most circumstances . A field technique was chosen for calibrating the present instrument , as the calibration established will implicitly account for the effects outlined above . However this approach requires sufficient replication to provide the desired resolution , in order to overcome measurement errors . A2 . 3 EXPERIMENTAL 106 At each calibration site an access hole was installed using a 4 . 4 cm auger , removing 5-10 ern long samples for bulk density and oven-dry gravimetric water content measurements . The hole was reamed out to the correct size with a length of old access tube , and an access tube installed . The neutron probe was then used to establish the count ratio at 5 cm depth intervals down the profile . Surface calibration data for the 0-15 cm depth were obtained by measuring the count ratio at 10 cm depth at two sites and finding the 0-15 cm depth volumetric water content (6 ) of two cores , removed within 50-100 cm of the tubes , for a range of water contents ( van Bavel and Stirk , 1967 ) . The bulk density of the soil , a Manawatu fine sandy loam was found to be 1 . 39 ( + 0 . 10 ) grn/cm3 from 103 samples obtained over the 0-110 cm profile . Applying the empirical model of Greacen and Schrale ( 1976 ) suggests this 7% variation in bulk density will result in only a 3 . 5% change in the count ratio due to scattering and absorption effects . Since the soil on which this study was conducted is of medium texture and low in organic matter ignoring the constitutional. hydrogen content by using oven-dry water contents is considered of little consequence . The value of r b found for each core was used to change the gravimetric water content into volumetric units (e) . Much of the measurement error in establishing e will be due to measurement error in the determination of the length of the core . Since the measurement error in the length is considered to be 107 less than 10% it follows that the error in e from this is also less than 10%. The comparison of G and C .R . i s presented in Fig .A2 . 1 and an error of 10% in the measurement of e can be seen to account for much of the variation . A linear regression through the data yielded the equation a = R = syx = n = 0 . 386 C .R. - **** 0 . 90 0 . 034 103 3 3 cm /cm 0 . 025 -( A2 . 1 ) where R i s the correlation coefficient , Syx the standard error of the estimate and n the number of observations . This line is significantly higher ( 0 . 0 25 cm3/cm3 ) than �he factory calibration curve . The values of R and Syx are of the same order of magnitude as found in other field calibrations ( Rose , 1966 � Rawitz , 1969 � Rawls and Asmussen , 197 3 � Paultineau and Apostol , 1974 ) . The surface calibration data are similar to the depth data and hence Eq. A2 . 1 was also used to determine the water content in the 0-15 cm zone using the 10 cm C .R . data . The upward translation of the field calibration curve in relation to the Troxler supplied curve is at variance with the downward translation found by Rawitz ( 1969 ) and the rotation of Rawls and Asmussen ( 1973 ) , both using similar Troxler probes . This emphasises the need to establish independent calibration curves , and this can be achieved using field procedures . • • i I I l w u :::1: � 6: a: &.U :::1 c en - < c:x: !;;i � c c c _, _, &.U 1.1.1 u: '"'- • 0 � 0 Fig .A2 . l 0 .,:.. z 0 >-� CX:a: Oco u.J • 1-- > U-'a: u.J __, a: • •' -c:x: :::1 u.. u u • ' ' C\1 ' 6 ' \ 0 C'? � "':" 0 0 0 0 e. ' 1NllN03 3Hn1SIOVII l i OS Soil moisture content ( cm3/cm3 ) in comparison with the count ratio . Also shown is the calibration curve supplied by Tro:xler . 108 52 � � :::1 8 APPENDIX III SOIL PROFILE DESCRIPTION . · 110 A3 . 1 SPATIAL VARIATION ( J . D . Cowie , 197 1 , pers . comm. ) The one hectare plot on which the study was carried out was found to contain 5 different phases of Manawatu fine sandy loam, as resolved by auger bores made on a 30 . 5 m grid . For most of the area the overall soil profile was found to be similar , i . e . a brown to yellowish brown fine sandy loam overlying an olive to olive grey medium to fine sand on gravelly coarse sand. Although in fine detail the pattern is very variable , due to the presence of complex alluvial banding , and varying depths to the gravelly coarse sand . Many of the bands are of only small lateral extent . Allowing for thi s variation the soils were grouped , on the basis of the depth to the gravelly coarse sand , and depth of the respective layers . Thus to a first approximation the major variation is due to depth variations rather than textural or structural changes . A3 . 2 PROFILE DESCRIPTION ( J . D . Cowie , R .H . Wilde , 1974 , pers . comm. ) The soil pit to enable the description was dug near the lysimeter , and is shown in Fig .A3 . 1 . Profile description follows Taylor and Pohlen ( 1970 ) ( Table A3 . 1 ) . In order to model water retention and flow of water in this soil it was necessary to simplify this description . For such purposes the profile was subdivided as follows : 0-50 cm fine sandy loam, underlain by 40 cm of fine sand with gravelly coarse sand beyond 90 cm. The physical characteristics of these profile elements are given in Table 3 . 1 . As can be seen in Fig .A3 . 2 the gravelly coarse sand interface varies in terms of its depth a.nd the texture of the underlay im"llediately under the interface . Table A3 . 1 Horizon A { B ) D 111 Profile description of the Manawatu fine sandy . loam Depth 0-23 cm 23-51 cm 51-74 cm 74-87 cm 87-102 cm 102 cm ( + ) Description dark greyish brown ( 2 . 5 YR 4/2 ) fine sandy loam to silt loam : friable , moderately developed medium and fine nutty structure : very few faint grey and reddish brown mottles in lower part of horizon , many roots , distinct wavy boundary . dark greyish brown ( 2 . 5 Y 4 . 2 ) fine sandy loam: friable : weakly developed nutty structure : few roots : distinct wavy boundary. olive grey ( 5 Y 4/2 ) fine sand: very friable : weakly developed blocky structure : 'no roots : distinct wavy boundary . olive ( 5 YR 4/3 ) fine loamy sand : very friable : weakly developed medium blocky structure : many distinct fine reddish brown mottles: thin sand layers throughout and thin iron staining at base : sharp wavy boundary . olive ( 5 YR 4/3 ) medium sand: loose ; single grained : very wavy distinct boundary. gravelly coarse sand ( 5 Y 3/2 ) . 112 ' Fig .A3 . 1 The profile of Manawatu fine sandy loam Fig .A3 . 2 113 The interface between the fine sand and gravelly coarse sand of Manawatu fine sandy loam . The range in height of the interface in this photo is 10 cm. APPENDIX IV CROP DESCRIPTION 115 A4 . 1 INTRODUCTION In this Appendix are given details of t.he development and management of the oats crop over which the Bowen-ratio energy balance ET measurements were made in 1974 . A4. 2 CROP AGRONOMY The experimental area was �loughed out of a ryegrass­ clover pasture in early autumn 1974 and given a final cultivation to prepare a good seedbed . On the day prior to planting , urea and Rustica Blue {N : P :K 1 2 : 5 : 14 ) were both applied at a rate of 250 kg/ha and the paddock was then harrowed . The oats { cv . Mapua 70 ) were sown on the 26 April at 112 kg/ha with 15 cm row spacing . On August 6 an additional 250 kg/ha of urea ( 46% nitrogen ) was applied by air . The development of dry matter production .of the crop over the growing season is shown in Fig . A4 . 1 and the height and LAI in Fig .A4 . 2 . These data were obtained by sampling at 4 sites within the crop every 14 days . The sample area was 1 m long and 4 rows wide . By mid-June the Grop had achieved a stable plant population of 8 x 106 tillers/ha . Evapotranspiration was measured over the period 4 July-11 November 1974. Throughout this period LAI > 6 and as the leaves covered the inter-row space the crop was at full-cover . Seedhead emergence began in early November with an associated increase in the dry matter %. The crop suffered slight barley yellow dwarf virus and lodged in parts during September and contracted Dreschlera (Helminthsporium) and crown rust in October . 1be areas i.n which these were severe was limited and it is considered that they had no significant affect on transpiration . 116 - 16 A M J A tO Palmerston Bra nche d Boot Anthe .c. Pr imord ia 5% - Nort h 0'1 l l l X Oats - Mapua � 12 Sown 26 ·4·74 - >< ...._.. '- <11 ... 8 Stem -0 · - E � ...._.. � '-<11 '- 20 .... 0 4 -0 10 E � '-·· o 0 0 50 250 Time Fig .A4 . 1 Seasonal changes in yield components and dry matter % ( Drn} of total forage , of the 1974 oats crop (After Kerr and Menalda , 1976 } . 120 · 9 . ... 5 80 iij . ::t: Q. 0 5 40 0 0 Fig . A4 . 2 A M J J PALMERSTON NORTH OATS - MAPUA SOWN 26 ·4 ·� .... .... .... ,, , , ,, ,, ,, .... .. 50 lOO TIM£ A .... .... .. .. • days s HEIGHT ... �--� ...... ... . LAI 150 117 0 N 12 8 Ci ..J 4 0 200 250 Seasonal changes in the height and leaf area index ( LAI ) of the 1974 oats crop . BIBLIOGRAPHY Alway , F .J . and G . R . McDole , 1917 . Relation of water retaining capacity of a soil to its hygroscopic coefficient . J . Agr .Res . 9 : 27-7 1 . Bindon , H .H . 1965 . A critical review of tables and charts used in psychrometry. in ' Humidity and Moisture • A . Wexler (Ed . ) , Rienhold Pub . Corp . New York . p 687 . Black , T .A . , W .R . Gardner . and G .W. The prediction of evaporation , storage for a bare soil . Soil 33 : 655-660 . Thurtell , 1969 . . S'oi \ dra1nage and�water Sci . Soc .Am . Proc . Blad , B .L . and N .J . Rosenberg , 19 74. Lysimetric calibration of the Bowen ratio energy balance method for evapotranspiration estimation in the Central Great Plains . J .Appl .Met . 13 : 227-236 . 1 19 Brooks , R .H . and A .T . Corey , 1966 . Properties of porous media affecting fluid flow . ASCE , J . Irrig . Drain . Div. , 4855 , 9 2 : 61-88 . Brown , IC .W . and R .L . Duble , 1975 . Physical character­ istics of soil mixtures used for golf green construction . Agron . J . 67 : 647-652 . Brunt , D . 1932 . Notes on radiation in the atmosphere . Quart .J .Roy .Met . Soc . 5 8 : 389-420 . Burn , K .N . 1965 . Calibration of a neutron soil moisture meter . Research paper 266 , National Research Council , Canada . Campbell , A . P . 197 3 . The effect of stability on evaporation rates measured by the energy balance method . Agric .Heteorol . , 11 : 285-30 2 . Cannell , G .H . and c .w . Asbell , 1974. The effects of soil-profile variations and related factors on neutron-moderation measurements . Soil Sci . 117 : 124-127 .; Cary , J .W . , 1973 � Soil water flow meters with thermocouple outputs . Soil Sci . Soc .Am. Proc . 37 : 176-181 . Chang , Jen-Hu , 1968 . "Climate and Agriculture , an Ecological Survey 11 • Aldine , Chicago . pp . 304 . Childs , E . C . 1945 . The water table , equipotentials and streamlines in drained land . III . Soil Sci . 59 : 405-4 1-; . 120 Clothier , B . E . , J . P . Kerr and D .R. Scatter , 1975 . \'leather and the growth of maize : Evapotranspiration . paper presented at the Symposium on Meteorology and Food Production . 14-15 October 1975 . Wellington . Colman , E .A . 1947 . A laboratory procedure for determining the field capacity of soils . Soil Sci . 63 : 277-283 . Coulter , J .D . 1973a . Prediction of evapotranspiration from climatological data . Proc . Soil and Plant Water Symp . Palmerston North . N � Z . 10-12 April 197 3 D . S . I . R . Inf . Ser . 96 . Coulter , J . D . 197 3b . A water balance assessment of 4h� New Zealand rainfall . J .Hydrol . ( N . Z . ) 1 2 : 83-91 . Cowie , J . D . 197 2 . Soil map and extended legend of Kairanga County , North Island , New Zealand . N . Z . Soil Bureau Publication 538 . Dane , J .H . , P .J . Wierenga , 197 5 . Effect of hysteresis on the prediction of infiltration , redistribution and drainage of water in a layered soil . J .Hydrol . 25 : 229-242 . Davidson , J .M. , L .R . Stone , D .R . Nielsen and M . E . La Rue , 1969 . Field measurement and the use of soil water properties . Water Res . Research . 5 : 1312-1321 . 1 21 Davies , J .A . and C .D . Allen , 1973 . Equilibrium, potential and actual evaporation from cropped surfaces in southern Ontario . J .Appl .Met . 12 : 649-657 . Denmead , O . T . and I . e . Mcilroy , 1970 . Measurements of non-potential evaporation from wheat . Agric . Meteorol . , 7 : 285-302 . de Lisle , J . F . 1966 . Mean daily insolation in New Zealand . N . Z . J . Sci . 9 : 992-1005 . de Wit , C .T . and H . van Keulen , 1972 . Simulation of Transport Processes in Soils . Centre Agric . Publ . Doe . , Pudec , Wageningen , lOO pp. Eagleman , J . R . and v . c . Jamison , 1962 . Soil layering and compaction effects on unsaturated moisture movement . Soil Sci . Soc .Amer . Proc . 26 : 5 19-5 2 2 . Fitzgerald , P . D . and D . S . Rickard, 1960 . A cowparison or � Penman 1 s and Thornth\.,rai te 1 s method of determining soil moisture deficits . N . Z .J .Agric . Res . 3 : 106-112 . Fritschen , L . J . 1965 . Accuracy of evapotranspiration determined by the Boweh ratio method . Bull . i:ntern . Assoc . Sci . Hydrol . 10 : 38-48 . Fuchs , M . and C . B . Tanner , 1970 . Error analysis of Bowen ratios measured by differential psychrometry . Agric .Meteorol . 7 : 329-334. Funk , J . P . 1959 . Improved polythene-shielded net radiometer . J . Sci . Instr . 36 : 267-270 . Gardner , W.R. 1960 . Soil water relations in arid and semi-arid conditions . tnmsco 15 : 37-61 . Gardner , W .R . , D . Hillel and Y . Benyamini , 1970 . 1 2 2 Post irrigation movement of soil water : I . Redistribution . \'later Resources Res . 6 ( 3 ) 851-61 . Greacen , E . L . and G . Schrale , 197 6 . The effect of bulk density on neutron meter calibration . Aust . J . Soil Res . 14 : 159-69 . Hanks , R .J . 1974 . Model for predicting plant yield as influenced by water use . Agron . J . 66 : 660-665 . Hanks , R .J . and S .A . Bowers , 1962 . Numerical solution of the moisture flow equation for infiltration into layered soils . Soil Sci . Soc .Amer . Proc . 26 : 530-534 . Harding , S .T . 1919 . Relation of the moisture equivalent of soils to the moisture properties under field conditions of irrigation . Soil Sci. 8 : 303-312 . Holmes , J .W. 1966 . Influence of bulk density of the soil on neutron moisture meter calibration . Soil Sci . 102 : 355-360 . I .A . E .A . 11Neutron Moisture Gauges " Technical Rep . Series 112 , I .A . E .A . Vienna , 1970 . 123 Jury, W .A . and C . B . Tanner , 1975 . Advection modification of the Priestley and Taylor evapotranspiration formula . Agron . J . 67 : 840-842 . Jury , W.A . , \'l . R . Gardner , P .G . Saffigna and C . B . Tanner , 1976 . Model for predicting simultaneous movement of nitrate and water through a loamy sand . Soil Sci . 122 : 36-43 . Kerr , J . P . , H . G . McPherson and J . S . Talbot , 197 3 . Comparative evapotranspiration rates of lucerne , paspalurn and maize . Proceedings First Australasian Conference on Heat and Mass Transfer . Monash Univ . , Melbourne . Section 3 , pp ._ 1-8 . Kerr , J . P . and M . F . Beardsell , 1975 . Effect of dew on leaf water potentials and crop resistances in a paspalum pasture . Agron .J . 67 : 596-599 . Kerr , J . P . and B . E . Clothier , 1975 . Modelling evapo­ transpiration of a maize crop . Proc .Agron . Soc . of N. Z . 5 : 49�53 . Kerr , J . P . and P .H . Menalda , 197 6 . Cool season forage cereal trials in Manawatu and \'lairarapa . Proc . Agron . Soc . of N . Z . 6 : 27-30 . King , F .H . 189 6 . Irrigation in humid climates . USDA , Farmers Bull . 46 26 pp . La Rue , M. E . , D . R . Nielsen and R .M. Hagan , 1968 . Soil water flux below a ryegrass root zone . Agron .J . 60 ; 625-629 . List , R .J . 1958 . " Smithsonian Meteorological Tables " Washing·ton , D . C . p . 365 . McNaughton , K . G . 1976 . Evaporation and advection I I : evaporation downwind of a boundary separating regions having different surface resistances and available energies . Quart . J . Roy .Met . Soc . 102 : 193-20 2 . Miller , E . E . and R .D . Miller , 1956 . Physical theory for capillary flow phenomena . J .Appl . Phys . 27 : 324-332 . r¥\ D•Sft....-e. Miller , D . E . 196 3 . Lateral� flow as a source of error in moisture retention studies . Soil Sci . Soc . Amer . Proc . 27 : 716-717 . 1969 . Flow and retention of water in layered soils . A .R . S . USDA Conservation Research Rep . 13 pp . 28 . 124 1973 . Water retention and flow in layered soil profiles . I n R .R . Bruce et al . ( ed . ) Field Soil Water Regime . S . S . S .A . special publication No . 5 . S . S . S .A . , Madison , Wise . and w.c . Bunger , 1963 . Moisture retention by soil with coarse layers in the profile . Soil Sci . Soc .Amer. Proc . 27 : 586-589 . ------- and J . s . Aarstad, 1;974 . Calculation of the drainage component of soil water depletion . Soil Sci . 118 : 11-15 . Monteith , J . L . 1956 . Evaporation a t night . Neth . J . Agric . Sci . 4 : 34- 3� . Monteith , J . L . 1963 . Dew: facts and fallacies . In the Water Relations of Plants . ed . Rutter , A . J . and Whitehead , F .H . Blackwell Scientific Publications , Oxford. Monteith , J . L . 1965 . Evaporation and environment Symposium of the Society for Experimental Biology 19 : 205-234 . Moore , R. E . , 1939 . Water conduction from shallow water tables . Hilgardia 12 : 383-426 . Mualem, Y . , 1974 . A conceptual model of hysteresis . \'Jater Resources Res . 10 ( 3 ) : 514-520 . 125 Nielsen , D . R . , J .W . Biggar and K . T . Erh , 1973 . Spatial variability of field-measured soil-water properties . Hilgardia 42 ( 7 ) : 215-219 . �lgaard , P . L . and V . Haahr , 1968 . On the sensitivity of subsurface neutron moisture gauges to variations in bulk density . Soil Sci . 105 : 62-64. Pasquill , F . , 1949 . Eddy diffusion of water vapour and heat near the ground . Proc . Roy . Soc . { Lond. ) ; Ser .A . 198 : 116-140 . Paultinea�� I . L . and I . Apostol , 1974 . Possibilities of using the neutron method for water application efficiency studies in sprinkler and furrow irrigation . in Isotope and Radiation Techniques in Soil Physics and Irrigation Studies 1973 . IAEA Vienna , 1974,� �7�-S� . Penman , H .L . 1948 � Natural evaporation from open water , bare soil and grass . Proc . Roy. Soc . Lond . A 193 : 120-146 . Penman , H . L . 1956 . Evaporation : an introductory survey . Neth . J . Agric . Sci . 4 : 9-29 . Philip , J . R . , 1957 . The physical principles of soil water movement during the irrigation cycle . Third Intern . Comm. on Irrig . and Drain . : 8 . 125-8 . 154 . Poulovassilis , A . , v.o . Krentos , Y . Stylianou and Ch . Metochis , 1974 . Soil water properties of a layered soil determined in situ . in Isotope and Radiation techniques in soil physics and irrigation studies 197 3 . I .A . E .A . Vienna .� ROS-��� Priestley , C .H . B . and R . J . Taylor , 197 2 . On the assessment of surface heat flux and evaporation using large scale parameters . Mon .Weather Rev . 100 : 81-92 . Rawitz , E . , 1969 . Installation and field calibration of Neutron-Scatter equipment for hydrologic research in heterogeneous and stony soils . Water Resources Res . S : 519-523 . 126 Rawlins , S . L . and P .A . C . Raats , 1976 . Prospects for high-frequency irrigation . · Science 188 : 604-610 . Rawls , w. · • and L . E . Asmussen , 197..3 . Neutron probe field calibration for Soils in the Georgia coastal plain . Soil Sci . 116 : 262-265 . Richards , L . A . 1960 . Advances in soil physics . Trans . Intern . Congr . Soil Sci . Madi son , 7 th 1 : 67-69 . Richards , L .A . and L .R . Weaver , 194 • Fifteen -atmosphere percentage as related to the permanent wilting percentage . Soil Sci . 5 6 : 3 31-339 . Richards , L .A . , W .R . Gardner and G . Ogata , 1956 . Physical processes determining water loss from soil . Soil Sci . Soc .Amer . Proc . 20 : 310-314 . Rickard , D . S . and P .D . Fitzgerald , 1970 . Evapotranspiration in New Zealand . Proc . N. Z . Water Conf . 1970 1 : 3 . 1-3 . 13 . Robins , J . S . 1959 . Moisture movement and profile characteristics in relation to field capacity . Intern . Comm. Irrig . and Drain . 8 : 509-521 . Rose , c .w. 1966 . Agricultural Physics . Pergamon Press , Oxford . pp . 226 . Rose , C .W . , W . R . Stern and J . E . Drummond , 1965 . Determination of hydraulic conductivity as a function of depth and water content , for soil in situ . Aust . J . Soil Res . 3 : 1-9 . 127 Rose , c .w. , J . E . Begg , G . F . Byrne , J . H . Goncz and B .W .R . Torssell , 197 2 . Energy exchanges between pasture and the atmosphere under steady and non­ steady state conditions . Agric .Meteorol . 9 : 385-403 . • Sinclair , T . R . 197 2 . Error analysis of latent , sensible and photochemical heat flux densities calculated from energy balance measurements above forests . in Murphy , C . E . , Hesketh , J .D . and Strain , B .R . Modelling the growth of trees . Oak Ridge National Lab . Slatyer , R . O . and I .e . Mcilroy , 196 1 . Practical microclimatology CSIRO Australia and UNESCO . Slatyer , R . O . and J .F . Bierhuizin , 1964 . Differential psychrometer for continuous measurement of transpiration. Plant Physiol . 39 : 1051-1056 . Stewart , R . B . and \'l .R . Rouse , 1976 . A simple method for determining the evaporation from shallow lakes and ponds . Water Resources . Res . 12 : 6 23-628 . Swinbank , w .c . 1951 . The measurement of vertical transfer of heat and water vapour by eddies in the lower atmosphere . J .Met . 8 : 1 35-145 . Tanner , C . B . 1960 . Energy balance approach to evapotranspiration from crops o Soil Sci . Soc . Amer . Proc . 24 : 1-9 . Tanner , C . B . , 1967 . Measurement of evapotranspiration , in Irrigation of Agricultural Lands pp 534-555 . ASA Monograph II . Tanner , C . B . and W .L . Pelton , 1960 . Potential evapotranspiration estimates by the approximate energy balance method of Penman . J .Geophys . Res . 65 : 3 391-3413 . 128 Tanner , C . B . and W.A. Jury , 197 6 . Estimating evaporation and transpiration from a crop during incomplete cover. Agron .J . 68 : 239-243 . Taylor , N .H . and I .J . Pohlen , 1970 . Soil Survey Method Soil Bureau Bulletin 25 , D . S . I .R . , N . Z . pp . 242 . Thornthwaite , c .w. 1948 . An approach toward a rational classification of climate . Geog . Rev. 38 : 55-94. Topping , J . 1966 . ' Errors of Observation and Their Treatment ' Institute of Physics and the Physical Soc . Monographs for Students , Chapman and Hall Ltd. London , 119 pp . Unger , P .W . 1971 . Soil profile gravel layers : I . Effect on water storage , distribution and evaporation . Soil Sci . Soc .Amer . Proc . 35 : 631-634. van Bavel , C .H .M. and G . B . Stirk , 1967 . Soil Water Measurement with an Am241-Be Neutron Source and an application to evaporimetry . Journal of Hydrology 5 : 40-46 . van Bavel , C .H.M . 1966 . Potential evaporation : the combination concept and its experimental verification . Water Resources Res . 2 : 455-467 . van Bavel , C .H .M . , G . B . Stirk and K .J . Brust , 1968 . Hydraulic properties of a clay loam soil and the field measurement of water uptake by roots : I . Interpretation of water content and pressure profiles . Soil Sci . Soc . Am. Proc . 32 : 310-317 . van Wi jk , W .R . and D .A . de Vries , 1954 . Evapotranspiration . Neth .J .Agric . Res. 2 : 105-119 . Veneman , P . L .M. , M . J . Vepraskas and J . Bourna . 197 6 . The physical significance o f soil mottling in a Wisconsin toposequence . Geoderma , 15 : 103-118 . Vomocil , J .A . 1965 . Porosity . In C .A . Black ( ed . ) Methods of Soil Analysis , Part I , Agronomy 9 : 299-314 . 129 Ve i•hmeyer , F .J . and A .H . Hendrickson , 1931 . The moisture +�c . equivalent as a measure ofA field capacity of soils . Soil Sci . 3 2 : 181-193 . Ve \hmeyer , F . J . and A.H . Hendrickson , 1949 . Methods of measuring field capacity and permanent wilting percentage of soils . Soil Sci . 68 : 75-94 . wang , P . C . and v. Lakshminarayana , 1968 . Mathematical simulation of water movement through unsaturated nonhomogeneous soils . Soil Sci . Soc .Am.Proc . 32 : 329-334. Wilcox , _ J . C . 1959 . Rate of soil drainage following an irrigation . I . Nature of soil drainage curves . Can . J . Soil Sci . 39 : 107-ll9 e ADDENDUM Samples of about 140 cm3 volume removed from the soil pit were used to determine the water retentivity curves of the upper two layers . For the fine sandy loam · three undisturbed cores were selected between 20 and 40 cm depth to determine the draining retentivity curve ( Fig . 3 . 6 ) . Four undisturbed cores of fine sand were taken from between 60 and 80 cm depth; two of which were used to determine the draining retentivity curve ( Fig . 3 . 6 ) and the other two for the hysteretic loop between the -15 am and -80 cm potential ( Fig . 4 . 1 ) . Large volumes o f both fine sand, removed between 60 and 80 cm, and gravelly coarse sand taken below lOO cm were brought back to the laboratory . Five samples of 3 . gravelly coarse sand of about 140 cm volume were repacked and the draining retentivity found on four of them ( Fig . 3 . 6 ) . The other was used to determine the hysteretic loop between 0 and -35 cm potential ( Fig . 4 . 1 ) . The remainder of the gravelly coarse sand , and also the fine sand was used for the long column determination of conductivity . Two runs , with new repacked material , were made with the gravelly coarse sand . ADDENDUM ET ETeq ETeq T day�ight 24 hour Date 1974 mm/day nun/day nun/day 0 c July 4 1 . 12 0 . 59 0 . 44 6 . 2 5 1 . 33 1 . 10 0 . 37 5 . 4 6 0 . 28 0 . 3 2 0 . 23 5 . 7 7 1 . 09 0 . 65 0 . 31 6 . 4 8 1 . 15 0 . 94 0 . 63 7 . 8 12 1 . 12 0 . 83 . 0 . 2 5 . 4 13 1 . 63 1 . 0 3 0 . 5 3 8 . 0 14 1 . 12 0 . 85 0 . 59 8 . 7 15 1 . 85 · 0 . 89 0 . 42 10 . 7 August 1 1 . 76 1 . 29 1 . 13 7 . 9 4 1 . 39 0 . 77 0 . 65 9 . 2 8 1 . 55 1 . 18 0 . 33 6 . 5 9 1 . 31 1 . 03 0 . 51 10 . 1 10 1 . 55 1 . 10 0 . 92 10 . 4 .11 1 . 73 1 . 45 1 . 05 9 . 8 12 1 . 30 0 . 88 0 . 62 10 . 4 13 1 . 98 1 . 62 1 . 04 12'. 0 14 0 . 59 0 . 27 0 . 13 10 . 9 15 1 . 85 1 . 71 1 . 43 12 . 0 16 1 . 07 0 . 87 0 . 55 11 . 0 24 1 . 21 0 . 79 0 . 67 9 . 0 25 2 . 45 1 . 95 1 . 68 9 . 7 27 2 . 07 1 . 26 1 . 11 7 . 5 28 3 . 2 2 2 . 20 1 . 88 8 . 8 29 1 . 04 0 . 79 0 . 57 7 . 8 30 2 . 34 1 . 83 1 . 49 8 . 5 31 2 . 40 1 . 09 0 .91 9 . 5 September 4 0 . 57 0 . 57 0 . 33 11 . 5 5 2 . 61 1 . 87 1 . 48 14 . 9 6 2 . 30 1 . 87 1 . 76 12 . 9 ' f 7 2 . 78 2 . 24 2 . 10 13 . 1 8 2 . 61 1 . 71 1 . 45 13 . 9 9 1 . 44 1 . 12 0 . 95 12 . 1 10 1 . 58 1 . 08 0 . 96 13 . 6 14 2 . 66 2 . 12 1 . 58 . 13 . 7 15 2 . 98 2 . 28 1 . 90 11 . 7 17 3 . 43 2 . 15 . 1 . 95 12 . 3 19 1 . 84 1 . 5 3 1 . 49 10 . 4 21 2 . 99 2 . 07 1 . 97 i.3 . a 2 2 2 . 80 2 . 15 2 . 15 12 . 5 2 3 2 . 47 2 . 00 1 . 75 13 . 8 24 1 . 95 1 . 46 1 . 41 11 . 2 2 6 1 . 11 0 . 84 0 . 78 14 . 3 29 3 . 53 2 . 86 2 . 59� 8 . 9 30 3 . 86 3 . 20 2 . 98 10 . 2 October 6 3 . 49 3 . 67 3 . 58 13 . 6 8 1 . 48 0 . 84 0 . 77 16 . 1 10 3 . 12 2 . 63 2 . 5 5 12 . 8 11 4 . 29 2 . 94 2 . 80 12 . 9 12 3 . 94 2 . 34 2 . 26 13 . 8 14 2 . 33 1 . 88 1 . 65 12 . 8 15 4 . 00 3 . 00 2 . 91 13 . 8 16 4 . 07 2 . 63 2 . 44 13 . 6 18 1 . 60 0 . 83 0 . 74 12 . 9 20 4 . 26 4 . 22 3 . 84 16 . 3 21 ' 4 . 53 4 . 09 3 . 93 15 . 5 2 2 3 . 5 2 2 . 60 2 . 35 13 . 6 23 4 . 10 3 . 41 3 . 13 12 . 1 25 2 . 37 1 . 50 1 . 35 10 . 2 •' , 26 2 . 48 1 . 7 3 1 . 58 12 . 6 27 3 . 27 2 . 58 2 . 45 13 . 2 29 3 . 9 2 3 . 0.6 3 . 00 12 . 6 30 3 . 93 3 . 9 3 3 . 78 10 . 6 31 3 . 21 3 . 0 3 2 . 70 10 . 3 November 1 3 . 39 3 . 19 2 . 90 12 . 2 6 5 . 37 4 . 89 4 . 62 18 . 6 7 5 . 38 4 . 34 4 . 23 17 . 7 8 4 . 13 3 . 85 3 . 71 17 . 4 9 4 . 24 3 . 97 3 . 7 3 16 . 8 10 3 . 30 2 . 48 2 . 32 16 . 3 Table Data on which Figs . 2 . 2 and 2 . 3 are based