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Modelling subsurface movement of manurial nitrogen in a shallow unconfined aquifer Cappelaere, Bernard R. 1978

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MODELLING SUBSURFACE MOVEMENT OF MANURIAL NITROGEN IN A SHALLOW UNCONFINED AQUIFER by BERNARD R. CAPPELAERE Dipl. Ing.., Ecole Centrale de Paris, 1975 ' A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Bio-Resource Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA June, 19 78 © Bernard R. Cappelaere, 1978 In presenting t h i s thesis in p a r t i a l fulfilment of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library shall make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for f i n a n c i a l gain shall not be allowed without my written permission. Department of 6 > o &t b 0 U r c e - E n g i n e e r i n j The University of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date i i ABSTRACT I n c r e a s i n g p r e s s u r e s towards e f f i c i e n t d e c i s i o n -making i n a g r i c u l t u r a l waste management and groundwater p o l l u t i o n c o n t r o l , are c r e a t i n g the need f o r improved p o l l u t a n t r o u t i n g methods. To o p t i m i z e the land a p p l i c a -t i o n of o r g a n i c wastes, the e s t i m a t i o n of the l e a c h i n g l o s s of n i t r a t e - n i t r o g e n from the root zone, and the p r e d i c t i o n of r e s u l t i n g long-term increases of n i t r a t e c o n c e n t r a t i o n s i n the r e c e i v i n g groundwater system, are r e q u i r e d . Two mathematical models are developed, to s i m u l a t e , (1 ) , the s e a s o n a l v e r t i c a l movement of n i t r a t e s beneath a d i s p o s a l f i e l d , and ( 2 ) , t h e i r long-term a r e a l r e d i s t r i b u -t i o n i n the r e g i o n a l unconfined a q u i f e r . The s o l u t e t r a n s -p o r t f o r m u l a t i o n accounts f o r simultaneous c o n v e c t i o n and hydrodynamic d i s p e r s i o n i n the u n s a t u r a t e d and s a t u r a t e d zones. The models are a p p l i e d to a shallow g l a c i a l outwash a q u i f e r i n the Lower F r a s e r V a l l e y o f B.C., to i l l u s t r a t e the methodology f o r t h e i r use as a waste management guide. Data was c o l l e c t e d at a swine farm l o c a t e d on the upper reaches of the a q u i f e r system, f o r a pasture s i t e r e c e i v i n g heavy manure a p p l i c a t i o n s . N i t r a t e l o s s from the f i e l d i s estimated over one l e a c h i n g season. Assuming the c o n t i n u a -t i o n of c u r r e n t p r a c t i c e s on the farm, assessment of the long term impact on r e g i o n a l groundwater q u a l i t y i s attempted. To estimate the p r e c i s i o n o b t a i n e d on the above i i i d e t e r m i n a t i o n s , the s e n s i t i v i t y of the model outputs to the c a l i b r a t i o n i n p uts and to the t r a n s p o r t parameters, i s t e s t e d . T h i s s e n s i t i v i t y a n a l y s i s a l s o allows f o r e s t a b l i s h i n g the importance of the t r a n s p o r t parameters i n c o n t r o l l i n g the system behaviour. V a l i d i t y and a p p l i c a b i l i t y of the models are d i s c u s s e d . Current data l i m i t a t i o n s p r e c l u d e d t h e i r com-p l e t e v e r i f i c a t i o n . Some weaknesses are i d e n t i f i e d and m o d i f i c a t i o n s are recommended. Recommendations are a l s o made f o r data a c q u i s i t i o n procedures, to f u r t h e r v a l i d a t e the models and to apply the proposed methodology to other s i m i l a r s i t e s . i v TABLE OF CONTENTS PAGE Ab s t r a c t i i Table of Contents i v L i s t of F i g u r e s v i i L i s t of Tables i x L i s t of Symbols x Acknowledgements x v i INTRODUCTION 1 A g r i c u l t u r a l Wastes 1 Groundwater Q u a l i t y 2 Research Needs 5 S p e c i f i c O b j e c t i v e s 8 1. LITERATURE REVIEW 10 1.1 I n t r o d u c t i o n 10 1.2 Subsurface Transport Processes 14 1.3 Conceptual R e p r e s e n t a t i o n of S o l u t e Movement i n Porous Media 22 1.4 Modeling F i e l d Problems 28 1.5 D e t e r m i n a t i o n of Transport Model Parameters 37 1.6 A p p l i c a b i l i t y of T h e o r e t i c a l Models to F i e l d Problems 42 2. MODEL DEVELOPMENT 46 2.1 Conceptual Repre s e n t a t i o n of Subsurface N i t r a t e Movement 46 2.1.1 B a s i c p o s t u l a t e s 46 2.1.2 Fundamental equations and hypotheses 47 2.2 D e s c r i p t i o n of the P h y s i c a l System 50 2.2.1 The s h o r t term, l o c a l s c a l e : Model 1 51 2.2.2 The long term, r e g i o n a l s c a l e : M o d e l 2 52 2.3 Model 1 52 2.3.1 B a s i c equations 52 2.3.2 I n i t i a l and boundary c o n d i t i o n s 54 2.3.3 System s i m u l a t i o n 56 2.4 Model 2 71 2.4.1 B a s i c equations 71 2.4.2 I n i t i a l and boundary c o n d i t i o n s 73 2.4.3 System s i m u l a t i o n 73 V PAGE 3. FIELD STUDY 79 3.1 S i t e S e l e c t i o n 79 3.2 S i t e D e s c r i p t i o n 82 3.2.1 Climate 82 3.2.2 Geology 82 3.2.3 Land use 83 3.3 Research Background 84 3.4 O b j e c t i v e s 88 3.5 The P l o t 90 3.5.1 D e s c r i p t i o n 90 3.5.2 Land management 92 3.6 Data A c q u i s i t i o n 94 3.6.1 S o i l s 94 3.6.2 Groundwater 95 3.7 Data A n a l y s i s and D i s c u s s i o n 96 3.7.1 S o i l s 96 3.7.2 Groundwater 103 4. MODEL APPLICATION TO STUDY AREA 108 4.1 Model 1: The s h o r t term, l o c a l s c a l e problem 109 4.1.1 System a n a l y s i s 109 4.1.2 Model c a l i b r a t i o n 122 4.1.3 Outputs and s e n s i t i v i t y a n a l y s i s 125 4.2 Model 2: The long term, r e g i o n a l s c a l e problem 130 4.2.1 System a n a l y s i s 130 4.2.2 Outputs and d i s c u s s i o n 132 4.2.3 S e n s i t i v i t y a n a l y s i s 148 5. * GENERAL DISCUSSION 169 5.1 Water Table F l u c t u a t i o n s 169 5.2 The s h o r t term, l o c a l s c a l e problem: De t e r m i n a t i o n of seasonal n i t r o g e n l o s s from the d i s p o s a l f i e l d 170 5.3 The long term, r e g i o n a l s c a l e problem: P r e d i c t i o n of n i t r a t e c o n c e n t r a t i o n d i s t r i -b u t i o n i n the a q u i f e r 173 5.4 Data Requirements 177 5.4.1 Model 1 177 5.4.2 Model 2 179 5.5 F u r t h e r Recommendations 182 v i PAGE CONCLUSIONS REFERENCES APPENDIX A: APPENDIX B: A n a l y t i c a l i n t e g r a t i o n of the s i m p l i f i e d u n s a t u r a t e d flow equation V e r t i c a l v e l o c i t y p r o f i l e i n the s a t u r a t e d zone (Model 1) 184 186 202 208 v i i LIST OF FIGURES FIGURE 1.1 Ranges of n i t r o g e n and phosphorus concen-c e n t r a t i o n s i n v a r i o u s waters. 3.3 Lay-out of the p l o t . 4.8 C y c l i c n i t r a t e - N c o n c e n t r a t i o n p r o f i l e s along the x a x i s . PAGE 11 1.2 Ranges of y e a r l y amounts of n i t r o g e n and phosphorus i n v a r i o u s waters and sediments. 12 2.1 S i m u l a t i o n flow c h a r t f o r Model 1. 57 2.2 S i m u l a t i o n flow c h a r t f o r Model 2. 78 3.1 Map and c r o s s - s e c t i o n of the a q u i f e r system. 80 3.2 V a r i a t i o n s of mean n i t r o g e n c o n c e n t r a t i o n s i n groundwater, f o r the wi n t e r seasons 1973 to 1975. 87 91 3.4 V a r i a t i o n s of mean water t a b l e l e v e l s and n i t r a t e - N c o n c e n t r a t i o n s i n groundwater, 1976 to 1977. 105 4.1 C r o s s - s e c t i o n of the domain of s i m u l a t i o n , f o r Model 1. 110 4.2 H y p o t h e t i c a l s e a s o n a l p a t t e r n s of inputs and outputs of s o i l n i t r a t e . 113 4.3 C a p i l l a r y c o n d u c t i v i t y K and d a i l y d r a inage Q, as a f u n c t i o n of the moisture content 0 of the roo t zone. 4.4 Water t a b l e f l u c t u a t i o n s beneath the p l o t . 4.5 N i t r a t e - N c o n c e n t r a t i o n s (above background) i n piezometers. 124 4.6 V e r t i c a l n i t r a t e - N c o n c e n t r a t i o n p r o f i l e s i n groundwater beneath the p l o t . 129 4.7 T r a n s i e n t n i t r a t e - N c o n c e n t r a t i o n s at 6 l o c a t i o n s on the x a x i s . 134 117 120 135 v i i i FIGURE PAGE 4.9 Steady envelopes of n i t r a t e - N c o n c e n t r a t i o n s along the x a x i s . 136 4.10 C y c l i c Maps of n i t r a t e - N c o n c e n t r a t i o n s due 139 to (a) and (b) to continuous waste a p p l i c a t i o n . 141 4.11 T r a n s i e n t Maps of n i t r a t e - N c o n c e n t r a t i o n s 143 to (a) to (d) f o l l o w i n g d i s c o n t i n u a t i o n of waste 147 a p p l i c a t i o n a f t e r 5 y e a r s . 4.12 Steady n i t r a t e - N envelopes along x a x i s f o r 3 d i f f e r e n t flow v e l o c i t i e s V, . 150 n 4.13 Steady n i t r a t e - N envelopes along x ax i s f o r 3 d i f f e r e n t l o n g i t u d i n a l d i s p e r s i v i t i e s . 151 4.14 Steady n i t r a t e - N envelopes along x a x i s f o r 3 d i f f e r e n t d i s p e r s i v i t y r a t i o s r Q . 152 4.15 E f f e c t s of l o n g i t u d i n a l vs. t r a n s v e r s e d i s p e r s i v i t i e s on steady n i t r a t e - N concen-t r a t i o n s . 156 -»• 4.16 Steady n i t r a t e - N envelopes along x a x i s f o r l a r g e c o n v e c t i v e f l u x vs. l a r g e d i s p e r s i v e f l u x . 161 4.17 C y c l i c Maps of n i t r a t e - N c o n c e n t r a t i o n s , f o r 162 to (a) and (b) s m a l l c o n v e c t i v e and l a r g e d i s p e r s i v e f l u x e s . 164 4.18 C y c l i c Maps of n i t r a t e - N c o n c e n t r a t i o n s , f o r 165 to (a) and (b) l a r g e c o n v e c t i v e and small d i s p e r s i v e f l u x e s . 167 i x LIST OF TABLES TABLE PAGE 3.1 N i t r o g e n a n a l y s i s of swine waste and forage crop at R & H Farms. 85 3.2 M o i s t u r e , o r g a n i c matter, and n i t r o g e n analyses of s o i l p r o f i l e s . 97 3.3 Computed m i n e r a l - n i t r o g e n content (kg/ha) i n the top 30 cm (1 f t ) of p l o t s o i l . 101 4.1 Values of t r a n s p o r t parameters f o r s e n s i t i v i t y a n a l y s i s i n r e g i o n a l a q u i f e r . 149 LIST OF SYMBOLS albedo of the l a n d s u r f a c e . l i n e a r i t y c onstant i n r a d i a t i o n e quation 2.13. l i n e a r i t y constant i n r a d i a t i o n equation 2.13. Brenner's number. n i t r a t e - N c o n c e n t r a t i o n i n s o l u t i o n , M.M ^ . c o e f f i c i e n t of p r o p o r t i o n a l i t y i n e x p r e s s i o n 2.11 of c o r r e c t i v e f a c t o r e f o r e v a p o t r a n s p i r a -t i o n , c h a r a c t e r i s t i c of locati'on. i n i t i a l n i t r a t e - N c o n c e n t r a t i o n i n groundwater, M.M-1. n i t r a t e - N c o n c e n t r a t i o n i n water d r a i n i n g from the root zone, M.M~^. n i t r a t e - N c o n c e n t r a t i o n f i e l d i n s a t u r a t e d zone, r e s u l t i n g from a pu n c t u a l u n i t i n j e c t i o n , M.M-*. n i t r a t e - N c o n c e n t r a t i o n f i e l d i n s a t u r a t e d zone, r e s u l t i n g from a uniform impulse u n i t - i n p u t over the d i s p o s a l area, M.M*1 (impulse r e s p o n s e ) . n i t r a t e - N c o n c e n t r a t i o n i n s a t u r a t e d zone, at node j and time step i . dimensionless index of mixing f o r the r o o t zone. bulk d e n s i t y of the r o o t zone. p a r t i c l e d e n s i t y of the r o o t zone. 2 -1 hydrodynamic d i s p e r s i o n t e n s o r , L .T mechanical d i s p e r s i o n ( c o n v e c t i v e d i f f u s i o n ) t e n s o r , L 2 . T - 1 . 2 -1 molecular d i f f u s i o n t e n s o r , L .T 2 -1 molecular d i f f u s i o n c o e f f i c i e n t i n water,L .T l o n g i t u d i n a l and t r a n s v e r s e hydrodynamic d i s p e r s i o n c o e f f i c i e n t s L2.T-1. x i hydrodynamic dispersion c o e f f i c i e n t in u d i r e c t i o n , L 2 . T ~ i . hydrodynamic dispersion c o e f f i c i e n t in v e r t i c -cal d i r e c t i o n , L 2 . T ~ i . depth to the impermeable layer, L. rate of drop of the water table, in the absence of recharge, L.T - 1. corrective f a c t o r , to account for e f f e c t of atmosphere saturation d e f i c i t on evapotranspira-t i o n . daily evaporation, L. equilibrium d a i l y evaporation, L. daily evapotranspiration, L. complementary error function, exponential function. f r a c t i o n of daylength with bright sunshine. f r a c t i o n of i n i t i a l nitrate-N remaining in the root zone. Green function. thickness of saturated zone, L. thickness of saturated zone at center 0 of the p l o t , L. thickness of root zone,L. da i l y water i n f i l t r a t i o n , L year number in long-term simulation ( s t a r t s at J = 1) . convective and dispersive fluxes of solute, M.L~ 2.T _ 1. c o e f f i c i e n t i n exponential expression 2.19 of K(Q) c a p i l l a r y conductivity of the root zone, L.T ^. x i i K saturated hydraulic conductivity of the aquifer a material, L.T" 1. L d a i l y rate of nitrate-N loss by leaching from the root zone, M.L 2 . L and L longitudinal and transverse dimensions of the X ^ disposal area^f^,L. Log natural logarithm function. log decimal logarithm function. m mass of groundwater per unit surface area of saturated zone, M.L~2. M i n i t i a l mass of nitrate-N per unit surface area ° of root zone, at the start of the leaching period, M.L - 2. M(J) mass of nitrate-N per unit surface area of root _^ zone at the st a r t of the Jth leaching season, M.L~ MC moisture content of the root zone, on a wet weight basis, M.M"1. n porosity of the root zone. n & porosity of the aquifer material. 0 center of the disposal area, ori g i n of the coordinate system. p pore volume of drainage effluent from the root zone (or 'number of pore volumes'), dimensionless. CjO domain of (x,y) coordinates defined by the disposal area ( p l o t ) . P daily p r e c i p i t a t i o n , L. PET daily p o t e n t i a l evapotranspiration, L. -2 PS saturation vapour pressure, M.L q flux of water = the Darcy's flow v e l o c i t y , L.T Q daily drainage out of the root zone, L. x i i i c onstant i n drainage e x p r e s s i o n Q(0) (2.20), L, a n R s RH R c RWT y SWT [ T O ) ] cumulated drainage out o f the root zone s i n c e s t a r t of s i m u l a t i o n , L. d i s p e r s i v i t y r a t i o (= a L / a T ) • p o i n t where the flow l i n e downstream from the d i s p o s a l area i n t e r s e c t s the Salmon R i v e r . d a i l y e x t r a t e r r e s t r i a l s o l a r r a d i a t i o n on a h o r i -z o n t a l s u r f a c e , M.T . net d a i l y r a d i a t i o n at the s o i l s u r f a c e , M.T -2 d a i l y glob.al s o l a r r a d i a t i o n at the s o i l s u r f a c e , M. T -2. mean d a i l y r e l a t i v e humidity. groundwater recharge c o e f f i c i e n t = r i s e of the water t a b l e a s s o c i a t e d with a u n i t depth of drainage water from the root zone, L . L - . groundwater recharge, L. slop e of the s a t u r a t i o n vapour pressure curve at ambient temperature. s o l u t e s o u r c e / s i n k r a t e per u n i t mass of f l u i d , M.M _ 1.T-1. s o l u t e s o u r c e / s i n k r a t e per u n i t volume of porous medium, M.L" 3. T ~ l . 3 -3 s p e c i f i c y i e l d of the a q u i f e r m a t e r i a l , L . L . slope of the water t a b l e , L.L ^ . time, T. t o r t u o s i t y t e n s o r , d i m e n s i o n l e s s . o. a i r temperature K e l v i n . mean min mean d a i l y a i r temperature, minimum d a i l y a i r temperature, x i v V macroscopic i n t e r s t i c i a l flow v e l o c i t y of the f l u i d , L . T - 1 . •± •+ h o r i z o n t a l and v e r t i c a l components of the flow h' v v e l o c i t y V , L.T" 1. W amount of water s t o r e d i n the root zone, L. W v a l u e of water storage W at f i e l d c a p a c i t y WAC c o e f f i c i e n t of water a v a i l a b i l i t y to p l a n t r o o t s . x, y, z l o n g i t u d i n a l , t r a n s v e r s e and v e r t i c a l ax^s of the orthogonal c o o r d i n a t e system, L; x and y are h o r i z o n t a l i n the d i r e c t i o n s p a r a l l e l and o r t h o g o n a l to the groundwater flow r e s p e c t i v e l y , and z i s v e r t i c a l downwards. XMIN, XMAX.)extreme h o r i z o n t a l c o o r d i n a t e s d e f i n i n g the s i m u l a -YMIN, YMAX.)tion area , L. z cumulative depth of water p e n e t r a t i o n i n the root P zone, L. ZWT depth of the water t a b l e , L. [a] d i s p e r s i v i t y tensor of the porous medium, L. a , a l o n g i t u d i n a l and t r a n s v e r s e d i s p e r s i v i t y c o e f f i c i e n t s , L. •+ d i s p e r s i v i t y i n the d i r e c t i o n u, L. v e r t i c a l d i s p e r s i v i t y , L. 0 index of d i s p e r s i o n , (or ' d i s t r i b u t i o n f a c t o r ' ) , L. -»• 3 index of d i s p e r s i o n i n the d i r e c t i o n u, L. u £ v v e r t i c a l index of d i s p e r s i o n , L. y p s y c h r o m e t r i c c o n s t a n t . A "change i n . . . " At and Az time step and depth increment f o r s i m u l a t i o n . A. L a p l a c i a n o p e r a t o r (• v". v e c t o r o p e r a t o r ; L ^. * -1 V^. h o r i z o n t a l component of V. , L XV e m i s s i v i t y of the atmosphere. 3 -3 v o l u m e t r i c moisture content, L .L 3 -3 i n i t i a l moisture content i n the root zone, L . L cr-it i c a l moisture content i n the ro o t zone, below which the crop i s under moisture s t r e s s , L 3 . L ~ 3 . f r a c t i o n of the ro o t zone volume from which n i t r a t e i o n s are excluded L 3 . L ~ 3 . values of 0 at f i e l d c a p a c i t y and at the permanent w i l t i n g p o i n t , L 3 . L ~ 3 . c a p i l l a r y c o n d u c t i v i t y c o n s t a n t s i n the e x p o n e n t i a l e x p r e s s i o n of the :  K(0), L 3 . L ~ 3 . -2 -1 l a t e n t heat of e v a p o r a t i o n M.T .L per u n i t volume of water. mean a i r content of the root zone at pF 2.0 ( t e n s i o n « 100 cm), L 3.L"3. -3 s p e c i f i c g r a v i t y of the groundwater solution,M.L Boltzman's co n s t a n t . s t a n d a r d d e v i a t i o n of the p r o b a b i l i t y ^ d i s t r i b u t i o n f o r t r a c e r l o c a t i o n i n the d i r e c t i o n u. v a r i a b l e of i n t e g r a t i o n over time, v a r i a b l e s of i n t e g r a t i o n over space. x v i ACKNOWLEDGEMENTS The author extends h i s a p p r e c i a t i o n to Dr. T.H. Podmore f o r h i s s u p e r v i s i o n and guidance throughout the p r o j e c t . S i n c e r e g r a t i t u d e i s expressed to Dr. N.R. B u l l e y f o r h i s v a l u a b l e advice and encouragement i n the pre-p a r a t i o n of t h i s t h e s i s , and to Dr. M. and Mrs. M. Micko who performed most of the l a b o r a t o r y work i n v o l v e d . S p e c i a l thanks are due to Mr. J . Reams, Manager, R & H Farms, f o r making h i s farm a v a i l a b l e f o r the p r o j e c t , to Mrs. E. Stewart f o r her d e d i c a t i o n i n ty p i n g the manuscript, and to Mr. I. Jamal f o r h i s a s s i s t a n c e i n drawing the f i g u r e s . The enthusiasm and a c t i v e p a r t i c i p a t i o n of Mr. Doug Alexander i n the winter f i e l d work has made t h i s progress i n the study p o s s i b l e . 1. INTRODUCTION A g r i c u l t u r a l Wastes Agriculture in B r i t i s h Columbia i s facing greater pressures to minimize i t s p o l l u t i o n p o t e n t i a l and maximize i t s waste u t i l i z a t i o n e f f i c i e n c y (Bulley and Holbek, 1977). A shrinking land base and requirements for greater productivity have led to the i n t e n s i f i c a t i o n and concentra-tion of l i v e s t o c k operations, making the need for better management of animal manure very acute. These enterprises generate large amounts of wastes, most of which are re-turned to cropland for their valuable nutrient content. Too often, unfortunately, these organic wastes are applied to a g r i c u l t u r a l land beyond i t s carrying capacity. Nutrient loss e n t a i l s a f e r t i l i t y reduction as well as a p o l l u t i o n hazard. P o t e n t i a l for loss from the plant-root environ-ment is greatly increased when the wastes are applied to the land at rates exceeding the plants nutrient uptake, or at times when the plants are unable to u t i l i z e . t h e nutrients. Improved management of wastes depends on our a b i l i t y to keep a more r e l i a b l e nutrient inventory at the farm scale, under varying environmental and operational conditions. Of a l l nutrients, nitrogen (N) has been i d e n t i f i e d as the main element of concern with respect to manure app l i c a t i o n , both at the p r o v i n c i a l l e v e l (Bomke, 1976; Bulley and Holbek, 1977), and at the national l e v e l 2. (Canada Department of Agriculture, 1974). Ewing and Dick (1970) asserted that "the retention capacity of the entire environment of the s i t e for nitrogen" also appears to be the l i m i t i n g factor for application rates of municipal sludges. This widespread concern for nitrogen stems from the high mobility of i t s inorganic forms i n the s o i l envir-onment. Of prime importance i s the subsurface movement of . • * in the l i q u i d phase. Leaching can represent nitrate-nxtrogen* i f & f a very s i g n i f i c a n t economic l o s s , for the farmer as well as for the society as a whole. From a water resources perspec-tive n i t r a t e content often i s the factor l i m i t i n g the use of groundwater for human and animal consumption. Land disposal of animal wastes i s exempt under the regulations pursuant to the B.C. P o l l u t i o n Control Act (1967). In this Province, no coherent l e g i s l a t i o n yet exists regar-ding the degradation of groundwater resources that can result from poor waste management practices. This present s i t u a t i o n r e f l e c t s the tremendous lack of information r e l a t i n g to the nitrogen contribution of livestock operations to groundwater res e r v o i r s . Groundwater Quality Presenting the importance of groundwater as a resource for t h i s Province i s beyond the scope of this text. * In this text, a l l quantities (mass, concentration, flux, loading rates...) of nitrogen compounds are expressed in terms of the elemental nitrogen content. 3. Yet, i t must be emphasized that groundwater reservoirs usually provide a more r e l i a b l e source of water supply than surface waters. Fluctuations in both quantity and quality are generally considerably smaller. Aquifers are separated from pollutant sources by the s o i l f i l t e r , and often by several layers of sediments. Unfortunately, this very c h a r a c t e r i s t i c too often turns into groundwater's greatest disadvantage. Being out-side man's v i s u a l environment, i t i s more subject to misunderstanding and careless attitudes. Also, p o l l u t i o n detection i s considerably more d i f f i c u l t . This i s aggrava-ted by the absence of safeguards in the form of b i o l o g i c a l indicators common in surface waters, such as f i s h and algae. Due to the long retention times and comparatively slow movement of water in the ground, the e f f e c t s of a p o l l u t i o n load may take years or even decades before com-plete d i s s i p a t i o n . Once a pollutant reaches groundwater, l i t t l e b i o l o g i c a l degradation w i l l take place, the only possible attenuation occurring by dispersion in the aquifer. Unlike surface water, groundwater movement i s hard to pre-d i c t , and does not necessarily match topography. Thus i t i s d i f f i c u l t to forecast the appearance of contaminants in groundwater supplies. The slow response c h a r a c t e r i s t i c of groundwater systems often results in a substantial time lag between this appearance and the input event, e s p e c i a l l y in large aquifers. Hence, the magnitude of developing A. groundwater p o l l u t i o n problems may not be adequately a n t i c i -pated by monitoring groundwater quality (Gelhar and Wilson, 197A). For a complete evaluation, the o v e r a l l p o l l u t i o n loading on the system must be evaluated. Of greatest s i g n i f i c a n c e with respect to the movement of pollutants o r i g i n a t i n g at the s o i l surface, are unconfined aquifers (also c a l l e d gravity, phreatic, or water table aquifers). Economically, these are desirable, because of considerably higher storage c o e f f i c i e n t s . The storage c o e f f i c i e n t of an aquifer expresses i t s water-yielding capacity (Todd, 1959). Unconfined aquifers are usually easier to develop and manage. Unfortunately, they are more susceptible to contamination, as the water table i s gener-a l l y quite close to the surface i n our humid or sub-humid climates. Also, unconfined aquifers rely on the s o i l as a single f i l t e r i n g layer for downward percolating water which produces groundwater recharge*. Their coarse texture, necessary from a water-yield point of view, does not provide them with adequate solute-sorptibn capacity. This i s com-pounded by the fact that unconfined reservoirs often are * In this text, groundwater 'recharge' s p e c i f i c a l l y desig-nates the rate of ri s e of the water table due to addition of water to the saturated system by deep percolation. This d e f i n i t i o n d i f f e r s from the common use of the term by groundwater hydrologists (e.g. Freeze, 1969) as the saturated flow v e l o c i t y away from the water table, which depends only on the water table configuration. The two d e f i n i t i o n s coincide only in the rare cases where the water table i s stable. 5. quite shallow, as a r e s t r i c t i n g layer is usually encoun-tered at small depth. L i t t l e v e r t i c a l dispersion i s then possible, and pollutants t r a v e l l a t e r a l l y to wells and r i v e r s . C l e a r l y , environmental strategies for ground-water protection must be preventive rather than corrective. Therefore, emphasis should be put on the control of the p o l l u t i o n at the source, with the aim of ensuring the long term preservation of the resource. Simple and r e l i a b l e pollutant routing methods are needed for e f f i c i e n t waste management and water p o l l u t i o n control in r u r a l areas where suburbia and l i v e s t o c k operations are in close proximity. Research Needs In this context, estimation of nitrogen loss by deep percolation from manure disposal f i e l d s i s c r u c i a l to the assessment of any given livestock operation, for both optimum waste u t i l i z a t i o n and water protection. Since the same pollutant load can generate widely d i f f e r e n t concen-trations in d i f f e r e n t aquifer systems, evaluation c r i t e r i a should be based on s i t e - s p e c i f i c hydrogeologic characteris-t i c s . S p e c i f i c a l l y , for a l l land disposal s i t e s overlying a shallow unconfined aquifer, the two following goals should be set: a) Determine the periods and amounts of n i t r a t e c o n t r i -buting to the groundwater re s e r v o i r , under given waste disposal practices and varying weather conditions. 6. b) P r e d i c t the long term n i t r a t e c o n c e n t r a t i o n d i s t r i -b u t i o n i n the a q u i f e r r e s u l t i n g from a given waste d i s p o s a l p o l i c y . C o n t r i b u t i o n s from non-point sources to ground-water are extremely hard to estimate and p r e d i c t . Such c o n t r i b u t i o n s have been given importance only r e c e n t l y . M e t h o d s c u r r e n t l y a v a i l a b l e f o r a s s e s s i n g these c o n t r i b u -t i o n s c o n s i s t p r i m a r i l y of three t y p e s : a. P u r e l y e x p e r i m e n t a l . b. E m p i r i c a l or r e g r e s s i o n - t y p e models. c. P h y s i c a l l y - b a s e d mathematical s i m u l a t i o n . A common f e a t u r e of a l l three groups i s the l a c k of t r a n s -f e r a b i l i t y from one s i t u a t i o n to another, thereby genera-t i n g the requirement f o r c o n s i d e r a b l e expensive f i e l d data at each s i t e of concern. P u r e l y e x p e r i m e n t a l procedures c a l l f o r p r o h i b i t i v e l y l a r g e numbers of samples. The need f o r e x t e n s i v e o n - s i t e c a l i b r a t i o n of the p h y s i c a l l y - b a s e d models r a i s e s doubts about the v a l i d i t y of t h e i r t h e o r e t i c a l foundations as a mathematical d e s c r i p t i o n of subsurface mass t r a n s p o r t p r o c e s s e s . Consequently, d e s p i t e the c o n s i d e r a b l e r e s e a r c h e f f o r t on the m o b i l i t y of s o l u b l e compounds from v a r i o u s o r i g i n s , both i n the unsatu r a t e d and i n the s a t u r a t e d zones, l i t t l e of i t has found a p p l i c a t i o n to the management of a g r i c u l t u r a l l a n d . O p e r a t i o n a l m o d e l l i n g has so f a r been conducted u s i n g e s s e n t i a l l y s i m p l i s t i c r e p r e s e n t a t i o n of 7. nitrogen movement, based on gross approximations such as complete mixing or plug flow which are conveniently easy to use but hardly s a t i s f a c t o r y . With the ultimate purpose of optimizing farm nutrient management, a methodology i s needed to estimate and predict the rate And time of nitrogen movement into groundwater. Direct determination by groundwater sampling is complicated by the v e r t i c a l s t r a t i f i c a t i o n of concentra-tions beneath the disposal f i e l d (Behnke and Haskell, 1968; Hughes and Robson, 1973; Spalding et a l . , 1976; John et a l . , 197 8). Data in t e r p r e t a t i o n must there-fore be based on simulation of subsurface n i t r a t e movement. If the method i s to be e f f e c t i v e l y r e p l i c a t e d at each p o l l u t i o n - s e n s i t i v e s i t e , such a model should combine up-to-date mathematical representation of the physical processes and straightforward on-site c a l i b r a t i o n , based on low-cost f i e l d data a c q u i s i t i o n . If one has to conduct extensive f i e l d studies with precision lysimeters and intensive sampling, the benefit of the simulation i s l o s t and the model i s only of academic i n t e r e s t . A second model, which simulates n i t r a t e transport in the regional aquifer system, i s necessary to achieve the second goal of predicting the long-term impact of a given waste management po l i c y on the groundwater q u a l i t y . Again, a constraint put on model development should be that a minimum of f i e l d data c o l l e c t i o n and analysis w i l l be required for c a l i b r a t i o n . 8. Two models are r e q u i r e d because of th_e d i s t i n c t time and space s c a l e s of the two problems. While the models should be based on a common con c e p t u a l r e p r e s e n t a t i o n of s o l u t e movement i n porous media, the a c t u a l s i m u l a t i o n procedures are l i k e l y to d i f f e r a c c o r d i n g to the r e s p e c t i v e time frame and domain c o n f i g u r a t i o n of the system c o n s i d e r e d . S p e c i f i c O b j e c t i v e s In t h i s t h e s i s , two such s i m u l a t i o n models, ad d r e s s i n g the s h o r t - t e r m , l o c a l s c a l e problem and the lo n g -term, r e g i o n a l s c a l e problem, are developed. S p e c i f i c a l l y , f o r a h y p o t h e t i c a l s h a l l o w , uncon-f i n e d a q u i f e r s u b j e c t to contamination from a non-point source, the r e s p e c t i v e o b j e c t i v e s of each model are: a. Model 1: the sho r t - t e r m , l o c a l s c a l e problem To s i m u l a t e the s e a s o n a l n i t r o g e n movement under the d i s p o s a l f i e l d , over the d u r a t i o n of the groundwater recharge p e r i o d (roughly October to A p r i l ) , f o r a h y p o t h e t i c a l amount of n i t r a t e - N i n excess of crop requirements and a v a i l a b l e i n the root zone at the end of the growing season. T h i s model i s to be used f o r i n t e r p r e t a t i o n of groundwater samples, w i t h the purpose of determining n i t r a t e l o s s ( i n terms of r a t e and time of the season) under the c u r r e n t waste management p r a c t i c e . b. Model 2: the long-term, r e g i o n a l s c a l e problem. To simulate the a r e a l r e d i s t r i b u t i o n of n i t r a t e s c o n t r i b u t e d 9. by s u c c e s s i v e p o l l u t i o n f r o n t s o r i g i n a t i n g from the d i s p o s a l f i e l d , i n the r e g i o n a l s a t u r a t e d a q u i f e r system. T h i s model i s to be used to p r e d i c t over any number of years the impact on groundwater q u a l i t y of a given waste a p p l i c a t i o n p o l i c y . L o c a l weather c h a r a c t e r i s t i c s are i n p u t s to both models. The models are developed i n Chapter 2. For both models, an i n t e r m e d i a r y step c o n s i s t s i n the s i m p l i f i e d s i m u l a t i o n of subsurface water storage and movement, to be c a l i b r a t e d on weather data and observed water t a b l e l e v e l s . In Chapter 3, i n f o r m a t i o n i s c o l l e c t e d and analysed f o r a t y p i c a l s i t e i n the Lower F r a s e r V a l l e y of B.C. T h i s s i t e f u l f i l l s a l l of the c o n d i t i o n s f o r which the models were b u i l t , and has been under study at U.B.C. f o r over f i v e y e a r s . Based on t h i s i n f o r m a t i o n , s i m u l a t i o n i s c a r r i e d out i n Chapter 4 to i l l u s t r a t e the a p p l i c a b i l i t y of the models, and the model performance i s t e s t e d . S e n s i t i v i t y of the models to the t r a n s p o r t parameters i s a n a l y s e d to e s t a b l i s h the importance of these parameters i n groundwater q u a l i t y s t u d i e s . P r e d i c t i o n of long-term n i t r a t e concen-t r a t i o n s i s attempted, based on the e s t i m a t e of excess n i t r a t e - N i n the root zone of the d i s p o s a l f i e l d , to e v a l u a t e the impact of c o n t i n u i n g present-day waste d i s p o s a l p r a c t i c e s at the farm. 10. 1. LITERATURE REVIEW 1.1 Int roduct ion E x t e n s i v e g e n e r a l reviews of the scope and magni-tude of groundwater p o l l u t i o n have been c a r r i e d out r e c e n t l y , both i n the United S t a t e s (Todd and McNulty, 1976) and i n Europe (Cole, 1972; Bureau des Recherches Geologiques et M i n i e r e s , 1977). The c o n t r i b u t i o n from a g r i c u l t u r e to the water p o l l u t i o n problem has been the focus of conferences h e l d i n the United S t a t e s ( C o r n e l l U n i v e r s i t y , 1970) and B r i t a i n ( M i n i s t r y of A g r i c u l t u r e , F i s h e r i e s and Food, 1974). I t has a l s o been the t o p i c of a l a r g e number of books (Brady, 1967; E n g l e s t a d , 1970; W i l l r i c h and Smith, 1970) and review p a p e r s ( F e t h , 1966; U.S. F e d e r a l Water Q u a l i t y A d m i n i s t r a t i o n , 1969; Robbins and K r i z , 1969; F r i n k , 1971; K i l m e r , 1974; Stewart et a l . , 1976). Water p o l l u t i o n by n u t r i e n t s from cropl a n d s i n v o l v e s one of the three t r a n s p o r t p r o c e s s e s : l e a c h i n g , r u n o f f and e r o s i o n . In n a t u r e , the r e s u l t s of these processes are not always easy to d i s t i n g u i s h . F i g u r e s 1.1 and 1.2 (from F r e r e , 1976) c o n s t i t u t e an attempt at comparing the u s u a l ranges of n i t r o g e n and phosphorus i n v a r i o u s types of waters and sediments. They show that the l o s s of n i t r o g e n with drainage water i s one of the most s i g n i f i c a n t water p o l l u t i o n phenomenon. N u t r i e n t l o s s e s i n sediments from surface e r o s i o n can a l s o be c o n s i d e r a b l e ( F i g u r e 1.2), but they can u s u a l l y be avoided by proper c r o p l a n d and n u t r i e n t C O N C E N T R A T I O N - p p m O.OJ O.I 1.0 10.0 100.0 • P PRECIPITATION v mill iiuinu CROPLAND RUNOFF P' " T r r r w ^ / / / / / u u m r r mN iiiii/imintt NON-CROPLAND RUNOFF P' => DRAINAGE 111111111 lllZmH F i g u r e 1.1: Ranges of n i t r o g e n and phosphorus c o n c e n t r a t i o n s i n va r i o u s waters, ( a f t e r F r e r e , 1976) . SPATIAL RATE - kg/ha/year 0.01 O J IO 100 I0Q.0 PRECIPITATION P| • unnm mzzxmti tumult n u iiiimiiiuiiinui II ItlllJIiUmU CROPLAND RUNOFF NON-CROPLAND RUNOFF DRAINAGE Mill I ll 11 / /72JN N CROPLAND SEDIMENT \ll ll 11 ll 11 llll 111 III 111 ll 11111 llll lllll\ NON-CROPLAND P SEDIMENT P, Ml 111 ll III ll [11111 tllllHH F i g u r e 1.2: Ranges of y e a r l y amounts of n i t r o g e n and phosphorus i n v a r i o u s waters and sediments, ( a f t e r F r e r e , .1976). 13. management practices, outlined by Frere (1976) and the B.C. Department of Agriculture (19 75 ). On the other hand, leaching is a chronic problem, which can hardly be circumven-ted under present-day farming p o l i c i e s . ITitrate and n i t r i t e are the forms of nitrogen most susceptible to leaching by drainage water (see Section 1.2), thereby generating potential health problems when reaching groundwater supplies. The methemoglobinemia hazard, associa-ted with n i t r a t e s and n i t r i t e s in drinking water, was d i s -cussed by Bailey (1966), Lee (1970) and Vinton (1970). Nitrates can also lead to t o x i c i t y hazards for plants and catt l e when they accumulate in s o i l s . According to Marriott Bartlett(1975), forage containing over 0.2% of nitrate-N should make up only part of the c a t t l e r a t i o n , while inges-tion of material containing over 0.4% may result in n i t r a t e p ois oning. Case studies of nitrogen contamination of ground-waters are extremely abundant i n the l i t e r a t u r e . Extensive well water surveys in the Central United States in p a r t i -cular (e.g. I l l i n o i s , Kansas, Minnesota, Missouri, Nebraska, Texas) have revealed large percentages of samples approaching or exceeding recommended l i m i t s for n i t r a t e s and n i t r i t e s (Todd and McNulty, 1976). In most cases, agriculture was i d e n t i f i e d as the main n i t r a t e contributor due to animal wastes and f e r t i l i z e r s as well as to the ecolo g i c a l changes brought on by the plow ( K r e i t l e r and Jones, 1974). Unfor-1 4 . t u n a t e l y , most of these i n v e s t i g a t i o n s were e s s e n t i a l l y d e s c r i p t i v e . In a few i n s t a n c e s (e.g. Mielke et a l . , 1970) s i m p l i s t i c q u a n t i t a t i v e analyses of subsurface n i t r a t e movement have been conducted, based on gross assumptions, such as complete mixing i n the groundwater r e s e r v o i r . To date, the l a r g e body of knowledge of subsurface t r a n s p o r t processes ( S e c t i o n 1.2), and the c o n s i d e r a b l e r e s e a r c h e f f o r t i n theory b u i l d i n g ( S e c t i o n 1.3) have h a r d l y bene-f i t e d the study of n i t r a t e p o l l u t i o n of groundwater from a g r i c u l t u r a l a c t i v i t i e s . 1.2 Subsurface Transport Processes The degree of n i t r o g e n m o b i l i t y i n a porous medium is s t r o n g l y dependent upon the form in which i t i s present.Hence the f a t e of n i t r o g e n o u s wastes a p p l i e d to a g r i c u l t u r a l land w i l l be c o n t r o l l e d to a l a r g e extent by the b i o c h e m i c a l t r a n s f o r m a t i o n s they w i l l undergo i n the s o i l environment. The review of these t r a n s f o r m a t i o n s has been c a r r i e d out by a l a r g e number of workers (Gasser, 1964; Bartholomew and C l a r k , 1965; A l l i s o n , 1966; Stevenson and Wagner, 1970; Broadbent, 1973) and i s beyond the scope of t h i s t h e s i s . D i g i t a l models f o r s i m u l a t i o n of these processes have a l s o been developed ( S h a f f e r et a l . , 1969; Beek and F r i s s e l , 1973; B u l l e y and Cappelaere, 1978). Water being the major t r a n s p o r t agent, the s i n g l e most important p r o p e r t y c o n t r o l l i n g the m o b i l i t y of a given n i t r o g e n compound i s i t s s o l u b i l i t y i n water. At the bottom 1 5 . of tha s o l u b i l i t y s c a l e are c o s t of the s o i l o r g a n i c compounds. L i k e phosphorus t h e i r removal from the s o i l r e q u i r e s sediment t r a n s p o r t , and i s t h e r e f o r e l i m i t e d to i s o l a t e d cases where s i g n i f i c a n t s u r f a c e e r o s i o n i s o c c u r r i n g . Urea and some amino compounds are s o l u b l e i n water; being only m i l d l y adsorbed, by s o i l p a r t i c l e s , they can move r e a d i l y with water. However, these substances are r e a d i l y hydrolyzed to ammonium + NH^ , and g e n e r a l l y have a t r a n s i e n t e x i s t e n c e i n s o i l s (Ilarmsen and Ko lenbrander , 1965). The l i t e r a t u r e p r o v i d e s few examples of high con-c e n t r a t i o n s of s o l u b l e n i t r o g e n compounds i n s u r f a c e r u n o f f . K l a u s n e r , et a l . (1974) r e p o r t that the p r o b a b i l i t y of s o l u b l e - N c o n c e n t r a t i o n s above 10 ppm in s u r f a c e r u n o f f was extremely s m a l l , compared to t i l e e f f l u e n t , f o r v a r i o u s treatments with d a i r y manure. The f i r s t r a i n that f a l l s u s u a l l y c a r r i e s h i g h l y s o l u b l e n i t r o g e n compounds i n t o the s o i l . When water excess over the s o i l i n f i l t r a t i o n c a p a c i t y o c c u r s , g e n e r a t i n g overland flow, very l i t t l e s o l u b l e - N i s a v a i l a b l e at the s u r f a c e f o r r u n o f f . In f a c t , the n i t r a t e content of r u n o f f water o f t e n i s lower than the average n i t r a t e content of r a i n w a t e r ( F i g u r e s 1.1 and 1.2), as the f i r s t r a i n sweeps most of the n i t r a t e s from the a i r and c a r r i e s i t i n t o the ground. Because of i t s c a p a c i t y f o r a d s o r p t i o n onto the n e g a t i v e l y - c h a r g e d s i t e s of c l a y m i n e r a l s and o r g a n i c p a r t i c l e s , the ammonium ion (NH^ +) g e n e r a l l y e x h i b i t s l i t t l e 16. mobility in s o i l s . Of greater s i g n i f i c a n c e i s the v o l a t i l i -zation of gaseous ammonia, NH^. The factors c o n t r o l l i n g t h i s loss from the s o i l were analysed by Avnimelech and Laher (1977) . Mathematical treatment of NH^-NH^ movement i s complex, as i t involves various physico-chemical processes, and w i l l depend on the r e l a t i v e concentrations of NH^+ + ++ ++ 3+ + and other cations (K , Ca , Mg , Al , H ). Simplified mathematical models have been developed by Gardner (1965) , Cho (1971), Dutt, et al.(1972), F r i s s e l and Reiniger (1974), Kirda et a l . (1974). In a we ll.-aeratad s o i l environment, ammonium com-pounds are rapidly converted to n i t r a t e s (NO^ ) by n i t r i -fying bacteria. N i t r i t e ions ( N O 2 ) constitute an i n t e r -mediary state in this transformation, but they have a very transient existence in s o i l s and w i l l not be further consider-ed. Because of their extreme locations at the end of the microbial oxidation chain, at the top of the s o l u b i l i t y scale and at the bottom of the scale of a f f i n i t y for clay p a r t i c l e s , n i t r a t e s are of greatest importance from a groundwater p o l l u t i o n standpoint. Nitrate can be weekly adsorbed by sesquioxides when the s o i l pH i s 6 or below. Experiments on red subsoils in the southeastern U.S. have shown adsorp-tion of NO^" and CI to be s i m i l a r and considerably smaller than adsorption of sulfates SO^ (Thomas, 1970). More generally, n i t r a t e s are repulsed away from the p r e v a i l i n g negatively-charged mineral and organic s o i l p a r t i c l e s . This anion exclusion from the small pores, 17. sometimes c a l l e d 'negative a d s o r p t i o n ' reduces the volume of l i q u i d a v a i l a b l e f o r n i t r a t e t r a n s p o r t ( E l p r i n c e and Day, 1977), and enhances l e a c h i n g from the s o i l . Such d i s c r e p a n c i e s between f l u i d and s o l u t e r a t e s of movement were observed i n l a b o r a t o r y m i s c i b l e d i s p l a c e -ment experiments, using n i t r a t e and c h l o r i d e as t r a c e r s ( B i g g a r and N i e l s e n , 1962). The importance of the phenomenon depends mostly on the s o i l t e x t u r e , i n c r e a s i n g with the p r o p o r t i o n of c l a y p a r t i c l e s . Data obtained by B r e s l e r and L a u f e r (1974) from n u m e r i c a l s i m u l a t i o n and l a b o r a t o r y experiments i n d i c a t e d that anion e x c l u s i o n e f f e c t s were of minor importance f o r the loam s o i l i n v e s t i g a t e d i n I s r a e l . Thomas (1970) quotes the v a l u e s 1.8, 9.6 and 12.6 f o r anion e x c l u s i o n i n s i l t loam, s i l t y c l a y loam and c l a y s o i l s i n C a l i f o r n i a , expressed i n percentage of the moisture which i s f r e e of anions. Subsurface movement of n i t r a t e ions o c c u r s mainly as the r e s u l t of two major independent p r o c e s s e s : c o n v e c t i o n ( a l s o c a l l e d a d v e c t i o n , or c o n v e c t i v e displacement) due to the mass flow of the s o i l s o l u t i o n , and molecular (or i o n i c ) d i f f u s i o n i n the l i q u i d phase. The d r i v i n g f o r c e s are h y d r a u l i c and chemical p o t e n t i a l g r a d i e n t s , r e s p e c t i v e l y . While there are other p o s s i b l e mechanisms, such as movement of i o n s due to e l e c t r i c a l f i e l d s and mass flow due to d e n s i t y g r a d i e n t s ( a r i s i n g from temperature or c o n c e n t r a t i o n d i f f e r e n t i a l s ) , t h e i r r e l a t i v e c o n t r i b u t i o n to n i t r a t e t r a n s p o r t i n the f i e l d i s s m a l l (Bear, 1972). Subsurface 18. mass flow i s g e n e r a l l y assumed to remain laminar (De Wiest, 1969). For a given c o n c e n t r a t i o n g r a d i e n t , the d i f f u s i v e f l u x J , observed i n the s o i l water at r e s t i s s i g n i f i c a n t l y d s m a l l e r than the d i f f u s i v e f l u x J i n water, due to the o t o r t u o u s nature of the d i f f u s i v e flow path i n porous media. Higher f l u i d v i s c o s i t y caused by a d s o r p t i o n near the s u r f a c e s of the c l a y m i n e r a l s r e s u l t s i n a f u r t h e r r e d u c t i o n of the d i f f u s i v e f l u x , which decreases s h a r p l y w i t h the v o l u m e t r i c moisture content 0 of the porous medium (Gardner, 1965). The d i m e n s i o n l e s s r a t i o / J q i s c a l l e d t o r t u o s i t y T(0) (Bear, 1972) and c h a r a c t e r i z e s the boundary e f f e c t s of the s o l i d m a t r i x and the s o i l atmosphere on the moving s o l u t e . In the t h r e e - d i m e n s i o n a l space, i t i s a tens o r . Experience proves t h a t , when the f l u i d i s moving in the porous medium, the mixing process which smoothes out s p a t i a l c o n c e n t r a t i o n d i f f e r e n c e s , u s u a l l y proceeds c o n s i d e r a b l y f a s t e r than would be expected from the d i f f u s i o n mechanism alone (Bear, 1972). T h i s departure i n c r e a s e s w i t h the macroscopic v e l o c i t y of the f l u i d , p o i n t i n g to an a d d i t i o n a l d i f f u s i o n - l i k e mechanism, generated by the mass flow of the s o i l s o l u t i o n . T h i s macroscopic p r o c e s s , o f t e n r e f e r r e d to as 'mechanical d i s p e r s i o n ' or 'c o n v e c t i v e d i f f u s i o n ' , i s a t t r i b u t e d to the v a r i a t i o n s i n the l o c a l m i c r o s c o p i c v e l o c i t y d i s t r i b u t i o n , both i n magnitude and d i r e c t i o n , w i t h i n each pore and between adjacent flow paths, due to the boundary e f f e c t s of the s o l i d and gaseous phases 19. on the moving f l u i d ( F r i e d , 1975). Me c h a n i c a l d i s p e r s i o n i s t h e r e f o r e c o n t r o l l e d by the water flow net and the geometric c o n f i g u r a t i o n of the pore system, which determines the com-p l e x i t y ( t o r t u o s i t y ) of the m i c r o s c o p i c flow paths. Contrary to m o l e c u l a r d i f f u s i o n , i t i s g e n e r a l l y assumed to be indepen-dent of s o l u t e c h a r a c t e r i s t i c s , as long as the s o l u t e does not change the flow p r o p e r t i e s of the f l u i d . Whereas d i f f u s i o n i s caused by the random thermal motion of the s o l u t e molecules, mechanical d i s p e r s i o n i s due to the e r r a t i c flow of the f l u i d through complex pore systems (Kirkham and Powers, 1972). However, because of t h e i r s i m i l a r mixing e f f e c t s on s o l u t e d i s t r i b u t i o n and the d i f f i -c u l t y of s e p a r a t i n g them in p r a c t i c e , the two processes are u s u a l l y combined to y i e l d a macroscopic concept c a l l e d 'hydrodynamic d i s p e r s i o n ' or 'apparent d i f f u s i o n ' or more simply ' d i s p e r s i o n ' , which i s s u f f i c i e n t to d e s c r i b e the macroscopic behaviour of the d i s s o l v e d c o n s t i t u e n t s . For a given s o l u t e , the r e l a t i v e c o n t r i b u t i o n of each mechanism w i l l vary l a r g e l y as a f u n c t i o n of flow c h a r a c t e r i s t i c s . While m o l e c u l a r d i f f u s i o n can g e n e r a l l y be d i s r e g a r d e d i n s a t u r a t e d a q u i f e r systems because of the comparatively l a r g e flow v e l o c i t i e s , there i s disagreement as to i t s s i g n i f i -cance i n s o i l s . The e f f e c t of v e l o c i t y on the r e l a t i v e importance of the two mechanisms i s analysed e x t e n s i v e l y by Bear (1972). Changes of the s o l u t e c o n c e n t r a t i o n due to p h y s i c o -chemical r e a c t i o n s w i t h i n the l i q u i d phase (e.g. r a d i o a c t i v e decay) or to i n t e r a c t i o n s between the l i q u i d and s o l i d phases (e.g. ion exchange, p r e c i p i t a t i o n , uptake by plant roots or microorganisms, b i o l o g i c a l transformations) are not included i n the dispersion process. Thus, th i s process alone does not change the t o t a l mass of substance in the moving f l u i d . Biochemical transformations pertaining to groundwater quality were reviewed by Sepp (1970) and Dunlap and McNabb (1973), while physical aspects were d i s -cussed by Cherry et a l . (1975). Solute transport processes are investigated by means of tracers. Bear (1972) defines an 'ideal tracer' as "one that is inert with respect to i t s l i q u i d and s o l i d surroundings, and that does not affect the l i q u i d ' s properties". Others r e f e r to i t as a 'perfect tracer' ( F r i e d , 1975) or a 'conservative substance' (Orlob, 1974). When b i o l o g i c a l a c t i v i t y i s r e s t r i c t e d , anions such as n i t r a t e and chloride approach the perfect tracer case as t h e i r concentrations in solution decrease. The phenomenon of anion exclusion can introduce substantial departure between solute and solvent movements, as the moisture con-tent decreases in fine-textured s o i l s (Biggar and Nielsen, 1962). The assumption that n i t r a t e behaves as a perfect tracer of water is widely accepted for saturated aquifer systems, but is more hazardous for f i e l d s o i l s . Laboratory i n v e s t i g a t i o n of miscible displacement in s o i l columns was i n i t i a t e d i n the early s i x t i e s , mostly with the well-known work of Biggar and Nielsen 0-962) , .and Nielsen and Biggar (1961 , 1962). 21. I n f o r m a t i o n on the mixing process between the d i s p l a c i n g and d i s p l a c e d f l u i d s under steady h y d r a u l i c c o n d i t i o n s i s p r o v i d e d by the breakthrough curve, o b t a i n e d by p l o t t i n g the e f f l u e n t c o n c e n t r a t i o n a g a i n s t the pore volume of e f f l u e n t c o l l e c t e d at the bottom of the column. The pore volume of e f f l u e n t p ( a l s o c a l l e d 'number of pore volumes', or 'pore volume') i s the r a t i o of the cumulated volume of e f f l u e n t to the t o t a l volume of water contained i n the column. R e s u l t s and c o n c l u s i o n s from m i s c i b l e displacement e x p e r i -ments were summarized by Biggar and N i e l s e n (1967). Methods of a n a l y s i s of experiments on hydrodynamic d i s p e r s i o n were d i s c u s s e d by Rose and P a s s i o u r a (1971). An important c o n c l u s i o n from these experiments i s the major r o l e p l a y e d by the s o l u t e d i s t r i b u t i o n over the range of pore s i z e s i n c o n t r o l l i n g the f l u x of s o l u t e through the s o i l column. C o n s i d e r a b l e data o b t a i n e d e i t h e r i n the l a b o r a t o r y (Dyer, 1965; Biggar and N i e l s e n , 1967; T e r k e l t o u b , 1971) or i n the f i e l d (Reeve, 1967; Warrick et a l . , 1971) show that f o r the same volume of d i s p l a c i n g water, s i g n i f i c a n t l y more s o l u t e displacement i s achieved when the s o i l i s maintained at lower moisture content. The i n c r e a s e d l e a c h i n g e f f i c i e n c y of i n t e r m i t t e n t i n f i l t r a t i o n over continuous ponding i s a t t r i b u t a b l e to the h i g h e r s o l u t e c o n c e n t r a t i o n i n s o l u t i o n , the h i g h e r p r o p o r t i o n of flow o c c u r r i n g through the s m a l l pores, and the lower flow v e l o c i t i e s a l l o w i n g f o r more d i f f u s i o n . 22. 1.3 Conceptual R e p r e s e n t a t i o n of S o l u t e Movement i n  Porous Media The t h e o r i e s developed f o r s o l u t e movement i n porous media were e x t e n s i v e l y reviewed and compared by Bear (1972). Scheidegger (1954, 1961) f i r s t proposed a mathe-m a t i c a l d e s c r i p t i o n of the d i s p e r s i o n p r o c e s s , i n the form of a s t a t i s t i c a l a n a l y s i s of p a r t i c l e p o s i t i o n s i n a homogeneous i s o t r o p i c medium, under s t a t i o n a r y flow con-d i t i o n s . T r e a t i n g displacement as a 'random walk' p r o c e s s , he showed that the p r o b a b i l i t y of a given i o n , i n i t i a l l y at a known r e f e r e n c e p o i n t 0, to be l o c a t e d at time t at any given p o i n t M of the t h r e e - d i m e n s i o n a l space, i s normally d i s t r i b u t e d around the p o i n t C of c o n v e c t i v e t r a n s -f e r . This p o i n t C i s the l o c a t i o n the p a r t i c l e would occupy had i t t r a v e l l e d along a macroscopic flow l i n e , with the macroscopic pore v e l o c i t y V. He f u r t h e r showed that the 2 ->• v a r i a n c e a of the d i s t r i b u t i o n i n a d i r e c t i o n u i s pro-u p o r t i o n a l to the time t : a 2 - 2 D . t (1.1) u u 2 -1 where D , [L . T ] , i s the hydrodynamic d i s p e r s i o n -»• c o e f f i c i e n t i n the d i r e c t i o n u. In the t h r e e - d i m e n s i o n a l space, a d i s p e r s i o n t e n s o r [Dj i s thereby d e f i n e d (Bear, 1961; D e J o s s e l i n de Jong, 1969), which i s a c h a r a c t e r i s -t i c of the porous medium geometry, and of the a s s o c i a t e d flow system. 23. When applied to a large number of p a r t i c l e s at any given point M, the theory allows for quantifying the macro-scopic fluxes of solute, i n the porous medium regarded as a continuous domain with t w i c e - d i f f e r e n t i a b l e v e l o c i t y and concentration f i e l d s (Fried , 1975). The macroscopic 'continuum' representation assumes that there exists a f i n i t e r e f e r e n t i a l elementary volume (R.E.V.) of porous medium centered at M, characterized by a single flow v e l o c i t y vector V and a single solute concentration variable c (Bear, 1972). This representation neglects a l l possible velocity and concentration differences at the macroscopic scale, between and/or within pores. Convective and -2 -1 dispersive fluxes [M. L . T ] are obtained as the vec tors: J y = pc . q and J*d = -[D]. 9 gfad (pc) (1.2) where q i s the volumetric water flux , c a l l e d 'Darcy v e l o c i t y ' [L. T _ 1 ] (q = 0. V, where V i s the macroscopic flow v e l o c i t y , c a l l e d 'pore v e l o c i t y ' ) , c is the concentration, or massic f r a c t i o n , of ions in the solution [M. M -3 p is the s p e c i f i c gravity of the f l u i d [M. L ] 3 -3 0 i s the volumetric moisture content [L . L J. The expression of the dispersive flux can be viewed as an extension of Fick's f i r s t law of d i f f u s i o n . [D] i s obtained as the sum of the molecular and convective d i f f u s i o n tensors, [ n c ] and[D r f]. 24 . [DJ » [D ] + [ D J = D . [ T O ) ] + V m. l a (0)] C.1.3) s d o where D i s the c o e f f i c i e n t of molecular d i f f u s i o n in water, °2 -1 [L . T X J [T(0)_] i s the tortuosity tensor, (dimensionless) [a(0)] i s the d i s p e r s i v i t y (or ' i n t r i n s i c dispersion') tensor, [L] (after Bear, 1972, and F r i e d , 1975). The d i s p e r s i v i t y and tortuosity tensors are inherent c h a r a c t e r i s t i c s of the geometric configuration of the l i q u i d phase* In the absence of s o l i d and gaseous phases (0 = 1), these tensors degenerate into the r e a l value 0 and 1, respectively, and Fick's law i s retrieved. The exponent m of the flow v e l o c i t y V i n equation 1.3 was found to vary* from approximately 2 at very low v e l o c i t i e s , to 1 as the flow v e l o c i t y increases and the mechanical dispersion component becomes preponderant ('dynamic dispersion regime'). In p r a c t i c e , a l i n e a r relationship(m=l) i s used a t . a l l flow regimes fo r most purposes Physical s i g n i f i c a n c e of the d i s p e r s i v i t y concept can be gained by returning to Scheidegger's i n t e r p r e t a t i o n of the dispersion process. Under the dynamic dispersion regime (molecular d i f f u s i o n i s neglected), the variance 2 a_ (equation 1.1) i s obtained as; u a 2 = 2 D . t = 2 a , V , t = 2 a . OC (1.4) u u u u where is the d i s p e r s i v i t y c o e f f i c i e n t i n the d i r e c t i o n u and OC i s the distance between points 0 and C 25. along the macroscopic flow l i n e . Since i s a constant f o r a given system geometry, i t appears that the s o l u t e d i s t r i b u t i o n depends only on the i n i t i a l d i s t r i b u t i o n and on the d i s t a n c e t r a v e l l e d by the f l u i d along the macroscopic flow l i n e s , i r r e s p e c t i v e of the flow v e l o c i t y or of the time necessary to cover the d i s t a n c e . The c o e f f i c i e n t of p r o p o r t i o n a l i t y $ u = 2 of the v a r i a n c e a 2 to the d i s t a n c e t r a v e l l e d OC, i s c a l l e d 'index of d i s -u p e r s i o n ' , or ' d i s t r i b u t i o n f a c t o r ' i n the d i r e c t i o n u , [ L ] . The e q u a t i o n e x p r e s s i n g mass c o n s e r v a t i o n of a p e r f e c t t r a c e r under a c o n v e c t i v e f l u x J y and a d i s p e r s i v e f l u x i s : | ^ (Gpc) + d i v ( J y + J d ) = 0 (1.5) Upon r e p l a c i n g and by the e x p r e s s i o n s (1.2), the g e n e r a l c o n v e c t i o n / d i s p e r s i o n equation i s o b t a i n e d . This e q u a t i o n , a l s o c a l l e d ' a d v e c t i o n / d i s p e r s i o n e q u a t i o n 1 or 'water q u a l i t y t r a n s p o r t e q u a t i o n ' or 'mass t r a n s p o r t e q u a t i o n ' d e s c r i b e s the movement of s o l u t e i n a given flow system. F r i e d (1975) c a l l e d ' d i s p e r s i o n scheme' the set of equations composed of "the d i s p e r s i o n e q u a t i o n , the con-t i n u i t y e q u a t i o n , the Darcy's e q u a t i o n , and the s t a t e equa-t i o n of the m i x t u r e " . Together with the boundary and i n i t i a l c o n d i t i o n s d e f i n i n g the problem, the d i s p e r s i o n scheme i s s u f f i c i e n t to r e p r e s e n t the behaviour of the s o l u t e - s o l v e n t 26. system in the porous medium. The d i s p e r s i o n and d i s p e r s i v i t y t e n s o rs [D] and l a ] at a p o i n t M of the t h r e e - d i m e n s i o n a l space reduce to d i a g o n a l m a t r i c e s i n an orth o g o n a l r e f e r e n c e system (x, y, z) where the x ax i s i s d e f i n e d by the d i r e c t i o n of flow V at t h i s p o i n t M. The c o e f f i c i e n t s D and a i n t h i s d i r e c t i o n are c a l l e d l o n g i t u d i n a l d i s p e r s i o n and d i s p e r s i v i t y c o e f f i c i e n t s , w h i le D , D , a , a are r e f e r r e d to as t r a n s -* y z y z verse (or l a t e r a l ) c o e f f i c i e n t s . These three axes x, y, and z are c a l l e d p r i n c i p a l axes of d i s p e r s i o n (Bear, 1972). In t h i s r e f e r e n c e system, the s i m p l i f i e d a d v e c t i o n / d i s p e r s i o n equation can be w r i t t e n : In an i s o t r o p i c medium, a l l t r a n s v e r s e d i s p e r s i o n ( d i s p e r s i -v i t y ) c o e f f i c i e n t s are e q u a l , and the r a t i o of l o n g i t u d i n a l to t r a n s v e r s e d i s p e r s i o n ( d i s p e r s i v i t y ) c o e f f i c i e n t s g e n e r a l l y l i e s i n the range 5 to 7 (Bear, 1972). Equation 1.6 c o n s t i t u t e s the b a s i s f o r an i n c r e a s i n g number of mass t r a n s p o r t models, d e s p i t e the l i m i t a t i o n s of d i s p e r s i o n theory as a macro-scale approach. While t h i s equation has proven to match s a t i s f a c t o r i l y the r e s u l t s of s t e a d y - s t a t e l a b o r a t o r y t r a c e r experiments w i t h s a t u r a t e d coarse w e l l - s o r t e d m a t e r i a l s (e.g. g l a s s beads, c l e a n sand), there s t i l l i s disagreement as to i t s a p p l i c a b i l i t y to more complex pore geometries and h y d r a u l i c c o n d i t i o n s . From the - V 3c. 3x (1.6) 27. same f i e l d data, W a r r i c k et a l . (1971) and B r e s l e r (1973) held opposing c o n c l u s i o n s concerning the v a l i d i t y of the assumption of complete mixing of the s o l u t e w i t h i n a l l s o i l c a p i l l a r i e s . T h e o r e t i c a l macroscopic c o n c e n t r a t i o n s which appear i n mathematical models, as w e l l as e x p e r i -mentally-measured c o n c e n t r a t i o n s o f t e n are poor r e p r e s e n -t a t i o n s of the a c t u a l d i s t r i b u t i o n of p a r t i c l e s i n complex porous media. I f the average v e l o c i t y i s r e p r e s e n t a t i v e of the flow system, such as i n s a t u r a t e d a q u i f e r s , hydrodynamic d i s p e r s i o n models work f a i r l y w e l l i n p r e d i c t i n g break-through curves (K irkham and Powers, 1972). However, f o r systems with extremely wide ranges i n m i c r o s c o p i c pore v e l o c i t i e s , such as u n s a t u r a t e d s o i l s , the use of an average flow v e l o c i t y may cause s i g n i f i c a n t d e v i a t i o n s between t h e o r e t i c a l and e x p e r i m e n t a l curves ( N i e l s e n and B i g g a r , 1962). C l e a r l y , d i s p e r s i o n theory f a i l s to r e c o g n i z e the importance of m i c r o s c o p i c phenomena on the mass t r a n s p o r t process at the macroscopic s c a l e . F r i e d (1975) made a t h e o r e t i c a l c r i t i q u e of the a d v e c t i o n / d i s p e r s i o n equation and i t s f o u n d a t i o n s . He con-cluded: "The v a r i o u s c o n c e p t u a l approaches to d i s p e r s i o n and the c r i t i c i s m s of the e x i s t i n g models show t h a t the domain of r e s e a r c h i n the f i e l d of d i s p e r s i o n i s p a r t of the pro-blem of change of s c a l e , which i s a very g e n e r a l problem i n p h y s i c s . . . D i s p e r s i o n theory makes sense only f o r l a r g e times, which e x p l a i n s why most of the l a b o r a t o r y work on 28. d i s p e r s i o n has been performed f o r the asymptotic regime, when some s o r t of s t e a d y - s t a t e has been reached". One might t h e r e f o r e q u e s t i o n the fre q u e n t use of the d i s p e r s i o n e q uation to model s h o r t - l i v e d events i n complex systems, such as the r e d i s t r i b u t i o n of n u t r i e n t s f o l l o w i n g r a i n f a l l i n f i l t r a t i o n i n u n s a t u r a t e d f i e l d s i t u a t i o n s (e.g. B r e s l e r , 1973). I t has been f r e q u e n t l y observed i n l a b o r a t o r y experiments with s o i l columns, that the measured d i s p e r s i o n c o e f f i c i e n t i n c r e a s e s w i t h time or with the d i s t a n c e the s o l u t e t r a v e l s w i t h i n the column (Corey et a l . , 1970; Warrick et a l . , 19 7.1). I t i s the author's o p i n i o n t h a t , at the present time, the d i s p e r s i o n c o e f f i c i e n t i s l i t t l e more than an e m p i r i c a l f a c t o r , o b t a i n e d by r e g r e s s i o n of e x p e r i -mental data on a d i f f u s i o n - t y p e e q u a t i o n . While p r o v i d i n g a convenient macroscopic d e s c r i p t i o n of p h y s i c a l p rocesses f o r which more r e f i n e d t o o l s have not yet been developed, the temptation to regard the equation as the u n i v e r s a l mathematical r e p r e s e n t a t i o n of mass t r a n s p o r t i n porous media should be avoided. The nature of the d i s p e r s i o n and d i s p e r s i v i t y c o e f f i c i e n t s i s f u r t h e r i n v e s t i g a t e d i n S e c t i o n 1*5. 1.4 Modeling F i e l d Problems While s o p h i s t i c a t e d t h e o r i e s were developed f o r the r e p r e s e n t a t i o n of su b s u r f a c e s o l u t e m i g r a t i o n , t h e i r a p p l i c a t i o n to f i e l d problems has come about very s l o w l y . A l a r g e number of workers have c o n s i d e r e d only 29. c o n v e c t i o n as the main t r a n s p o r t p r o c e s s . E l a b o r a t e models f o r s o i l s (Gardner and Brooks, 1956) and f o r groundwater a q u i f e r s (Freeze, 1972; Nelson, 1976) were b u i l t on t h a t premise. P r a c t i c a l approaches based on simple water balance procedures were used to e v a l u a t e l e a c h i n g l o s s e s d i r e c t l y from the volume of drainage water (Reeve, 1967; F r i n k , 1969; P r a t t , 1972; H a i t h , 1973; Stewart, 1976). Drainage i s c a l c u l a t e d e i t h e r as the d i f f e r e n c e between p r e c i p i t a t i o n and e v a p o t r a n s p i r a t i o n (which can l e a d to very s e r i o u s e r r o r s , a c c o r d i n g to Gardner and J u r y , 1974), or as the water excess over the s o i l water h o l d i n g c a p a c i t y . A l l the work based on the water h o l d i n g c a p a c i t y concept f a i l s to r e c o g n i z e the importance of s a l t movement at moisture contents below f i e l d c a p a c i t y , when l e a c h i n g e f f i c i e n c y i s a c t u a l l y h i g h e r (see S e c t i o n 1.2). Outputs from such models are very s e n s i t i v e to the c h o i c e of the f i e l d c a p a c i t y v a l u e , which i s i n g e n e r a l q u i t e a r b i t r a r y . Drainage volume alone i s not s u f f i c i e n t to d e s c r i b e the l e a c h i n g process a c c u r a t e l y , as the e f f i c i e n c y of t h i s process i s l a r g e l y dependent on the v e l o c i t y and moisture content d i s t r i b u t i o n i n the p r o f i l e . S u b s t a n t i a l e r r o r s can be made when e s t i m a t i n g the amount of s o l u t e l e a c h i n g past a given s o i l depth by m u l t i p l y i n g the water drainage by the average s o l u t e c o n c e n t r a t i o n i n the s o i l s o l u t i o n (Biggar and N i e l s e n , 1976; Van der P o l , 1977). Noting that the degree of refinement of a chemical t r a n s p o r t model i s l i m i t e d by the degree of hydro-l o g i c d e f i n i t i o n of the system, F r e r e (1976) attempted to improve the l a t t e r by d i v i d i n g the root zone i n t o l a y e r s . 30. Layer or zone modeling based on separate water budgeting for each zone, was also c a r r i e d out by Dutt (1963), Bresler (1967), Terkeltoub (1971), and Jury and Gardner (1974). Chemical equilibrium and uniform concentrations are usually assumed within each layer. To simulate the non-steady chemical, p h y s i c a l and b i o l o g i c a l changes occurring in the unsaturated s o i l matrix and percolating water, Dutt et a l . (1972) used the mixing c e l l concept, which assumes that complete mixing occurs within each c e l l at each time increment. According*to Jury and Gardner (1974), "the rationale behind the zone or black box approach i s simply to i s o l a t e those parts of the system which we do not under-stand in d e t a i l , and treat them on an averaged space and time scale we can model". A black-box model for large scale aquifer p o l l u t i o n studies was described by Fried (1975), using convolution (for p o l l u t i o n forecast) and deconvolution (for prevention) techniques. Gelhar and Wilson (1974) developed a generalized lumped-parameter water quality model, for a phreatic (unconfined) aquifer. This long-term basin-wide model i s characterized by two response-times, one associated with the hydraulics and the other with the solute, which can be estimated from limited data. Mercado (1976) used a s i n g l e - c e l l model for a regional study of n i t r a t e and chloride p o l l u t i o n i n the coastal aquifer of I s r a e l . 31. Of i n c r e a s i n g p o p u l a r i t y are s i m u l a t i o n methods based on d i s p e r s i o n theory. These methods a l l attempt to s o l v e the d i s p e r s i o n scheme ( S e c t i o n 1.3), a n a l y t i c a l l y f o r simple porous medium c o n f i g u r a t i o n and boundary c o n d i t i o n s , or n u m e r i c a l l y by f i n i t e - d i f f e r e n c e approximations of the d i f f e r e n t i a l equations f o r more complex s i t u a t i o n s . F i n i t e -element methods d i s c r e t i z e time and space, thus a l l o w i n g f o r complex i n i t i a l and boundary c o n d i t i o n s as w e l l as macroscopic h e t e r o g e n e i t i e s to be accommodated (Remson, et a l . , 1971; F r i e d , 1975). On the other hand, a n a l y t i c a l s o l u t i o n s e x i s t only f o r i d e a l i z e d systems, and p r o p e r t i e s of the porous medium such as macroscopic homogeneity and i s o t r o p y must u s u a l l y be assumed. In many cases, the assumption of s t e a d y - s t a t e h y d r a u l i c behaviour i s a l s o n e c e s s a r y . D e s p i t e these r e s t r i c t i o n s , a n a l y t i c a l methods o f t e n are d e s i r a b l e , c o n s i d e r i n g the l e v e l of u n c e r t a i n t y c h a r a c t e r i z i n g our understanding of a c t u a l p r o c e s s e s , and our knowledge of a c t u a l boundary c o n d i t i o n s . S i m p l i f y i n g assumptions and t r a n s f o r m a t i o n s can o f t e n be performed to convert the a c t u a l problem i n t o a t h e o r e t i c a l image problem f o r which an a n a l y t i c a l s o l u t i o n i s a v a i l a b l e . R e s p e c t i v e advantages and a p p l i c a b i l i t y of a n a l y t i c a l and n u m e r i c a l schemes are f u r t h e r d i s c u s s e d i n S e c t i o n 1.6. Mathematical t o o l s f o r a n a l y t i c a l s o l u t i o n s of the d i s p e r s i o n d i f f e r e n t i a l equation 1.6 were reviewed by Bear (1972) and Kirklxam and Powers (1972). One-dimensional a n a l y t i c a l models of s o l u t e t r a n s p o r t i n i d e a l i z e d systems 32. were f i r s t developed by chemical engineers (see Brenner, 1962). F r i e d (1975) devoted a whole chapter to an overview o f the methods of n u m e r i c a l a n a l y s i s f o r groundwater p o l l u -t i o n problems. Van Genuchten (1976) d i s c u s s e d the accuracy and e f f i c i e n c y of s e v e r a l n u m e r i c a l schemes f o r s o l v i n g the c o n v e c t i v e / d i s p e r s i v e e q u a t i o n . A p a r t i c u l a r d i f f i c u l t y i n h e r e n t to these i t e r a t i v e , d i g i t a l procedures i s the p o s s i b i l i t y of n u m e r i c a l i n s t a b i l i t y , c a l l e d 'numerical d i s p e r s i o n ' or 'numerical d i f f u s i o n ' which causes the n u m e r i c a l s o l u t i o n t o d i v e r g e from the exact s o l u t i o n . T h i s problem a r i s e s from compounding the t r u n c a t i o n e r r o r s a s s o c i a t e d with the approximation of the v a r i o u s terms i n the t r a n s p o r t e q u a t i o n s . T h i s phenomenon was e x p e r i e n c e d by Pinder and Cooper (1970), Goudriaan (1973), Van Genuchten and Wiereixga (1974), and analysed by Lantz (1971). A l g o r i t h m s that minimize or e l i m i n a t e n u m e r i c a l d i s p e r s i o n are a v a i l a b l e (Shamir and Harleman, 1966; Chaudari, 1971; B r e s l e r , 1973; P i n d e r , 1973; F r i e d , 1975). To a v o i d n u m e r i c a l i n s t a b i l i t i e s a r i s i n g when the c o n v e c t i v e term dominates the mass t r a n s p o r t equation 1.5 , the time step s h o u l d be taken s m a l l e r than the time of water t r a v e l between any two nodes (Perez et a l . , 1974). F r i e d (1975) recommended t e s t i n g of any model with a u n i t c o n c e n t r a t i o n s t e p - i n p u t f u n c t i o n to a d j u s t time steps and g r i d s p a c i n g before u s i n g i t f o r g e n e r a l boundary c o n d i t i o n s . By a p p l y i n g one-dimensional a n a l y t i c a l models to s e a s o n a l i n t e r m i t t e n t l e a c h i n g phenomena i n the f i e l d , 33. v a l u e s f o r the v e r t i c a l index of d i s p e r s i o n 3 ( d i s t r i b u t i o n f a c t o r ) have been o b t a i n e d : 5 to 15 cm by Van der ; Molen (1956) f o r Butch s o i l s , 20 cm by Gardner (1965) f o r a c l a y s o i l , 8 to 12 cm by Kolenbrander (1970) f o r medium to coarse t e x t u r e d s o i l s . These val u e s should be c o n t r a s t e d to r e s u l t s from short experiments w i t h f i l l e d - i n columns under continuous l e a c h i n g , which v a r i e d from 0.17 to 6.3 cm, with an average of 2 to 3 cm (Biggar and N i e l s e n , 1967; F r i s s e l and P o e l s t r a , 1967; Kolenbrander, 1970). B values between 2 and 10 cm were ob t a i n e d from a n a l y t i c a l s i m u l a t i o n of a 17-hr i n f i l -t r a t i o n event i n a Panoche c l a y loam column (Warrick, et a l . , 1971). The c a l c u l a t e d d i s t r i b u t i o n d i d not p e n e t r a t e the s o i l p r o f i l e as deeply as the measured d i s t r i b u t i o n , most of the water moving through the l a r g e r w a t e r - f i l l e d pore sequences. ACTM0, an a g r i c u l t u r a l chemical t r a n s p o r t model ( F r e r e et a l . , 1975) l i n k s t ogether a hydrology model, an e r o s i o n model and a chemical model, to p r e d i c t a n a l y t i c a l l y the c o n c e n t r a t i o n s and amounts of p e s t i c i d e s and n u t r i e n t s i n drainage and r u n o f f , on a storm-by-storm b a s i s , f o r a f a r m - s i z e d watershed. The hydrology and e r o s i o n models have been t e s t e d at a number of l o c a t i o n s , but the chemical model i s e s s e n t i a l l y u n t e s t e d ( F r e r e , 1976). A n a l y t i c a l methods were a l s o implemented by Shamir and Harleman (1966, 1967) f o r l a y e r e d media, Bruch and S t r e e t (1967), F r i s s e l and P o e l s t r a (1967), Cho (19 71), 34. K i r d a et a l . , (1974), Lindstrom and Boersma (1973), Walter et a l . , (1974), Selim et a l . , C1976). The l a s t ten years have seen a boom In the develop-i ment of n u m e r i c a l methods f o r s i m u l a t i n g subsurface chemical t r a n s p o r t from d i s p e r s i o n theory. D i g i t a l s o l u t i o n s were f i r s t implemented f o r s a t u r a t e d porous media, under steady-s t a t e flow c o n d i t i o n s (Shamir and Harleman, 1966, 1967; Oster et a l . , 1970; R e d d e l l and Sunada, 1970). In 1969, Water Resources E n g i n e e r s , Inc., developed a n u m e r i c a l model f o r s i m u l a t i o n of groundwater q u a l i t y i n g r a v i t y a q u i f e r s . The model has been a p p l i e d s u c c e s s f u l l y to the Santa Ana R i v e r B a s i n , i n southern C a l i f o r n i a , and i s used i n p l a n n i n g f o r groundwater p o l l u -t i o n c o n t r o l . P i n d e r and Cooper (1970) c a l c u l a t e d the t r a n s i e n t p o s i t i o n of the s a l t w a t e r f r o n t i n groundwater by c o u p l i n g and s o l v i n g n u m e r i c a l l y the mass t r a n s p o r t equation 1.5 and the equation of motion, f o r m i s c i b l e f l u i d s of d i f f e r i n g d e n s i t i e s . The U.S. G e o l o g i c a l Survey developed a two-d i m e n s i o n a l n u m e r i c a l model f o r a r e a l mass t r a n s p o r t s i m u l a -t i o n i n an i s o t h e r m a l groundwater system, i n the absence of chemical r e a c t i o n s (Bredehoeft and P i n d e r , 1973). The model was a p p l i e d to a v a r i e t y of a q u i f e r types, f o r w e l l documented contamination cases (Bredehoeft and P i n d e r , 1973; Hughes and Robson, 1973; P i n d e r , 1973; Robertson and B a r r a c l o u g h , 1973; Konikow and B r e d e h o e f t , 1974; Robson, 1974). These a p p l i c a t i o n s were reviewed by Bredehoeft 35. et a l . , (1976), who compiled the v a r i o u s d i s p e r s i v i t y c o e f f i c i e n t s o b t a i n e d from these f i e l d s t u d i e s . They f e l l i n 2 the range of 10 - 10 m, which i s s e v e r a l orders of magni-tude g r e a t e r than would be expected from l a b o r a t o r y determin-a t i o n . Bredehoeft and P i n d e r (1973) found the computed output to be q u i t e s e n s i t i v e to the d i s p e r s i v i t y v a l u e s . P o r o s i t y of the a q u i f e r was i d e n t i f i e d as a c r i t i c a l f a c t o r i n the waste t r a n s p o r t model (Robertson and B a r r a c l o u g h , 1973). T h i s two-dimensional a r e a l model was used by Hughes and Robson (1973) to a n a l y s e a case of sewage con-t a m i n a t i o n of a shallow r i v e r a l l u v i u m a q u i f e r , at Barstow, C a l i f o r n i a . Due to v e r t i c a l s t r a t i f i c a t i o n of water q u a l i t y w i t h i n the a q u i f e r , d i s c r e p a n c i e s o c c u r r e d between the s i m u l a t e d water q u a l i t y data and the water pumped from a p a r t i c u l a r w e l l . I t was noted t h a t , owing to a q u i f e r h e t e r o g e n e i t i e s , w e l l s may not d e r i v e water u n i f o r m l y throughout the p e r f o r a t e d p r o f i l e . Two-dimensional n u m e r i c a l models f o r t r a n s p o r t s i m u l a t i o n i n a v e r t i c a l c r o s s - s e c t i o n of a q u i f e r were developed by Freeze (1972) (without d i s p e r s i o n ) , Perez et a l . , (1974), Cherry et a l . , (1975), Pickens and Lennox, (1976). A major d e f i c i e n c y of the c r o s s - s e c t i o n a l models i s that they completely d i s r e g a r d the e f f e c t s of h o r i z o n t a l t r a n s v e r s e d i s p e r s i o n , shown by Bredehoeft et a l . , (1976) to be a major component of the s o l u t e t r a n s p o r t process i n the s a t u r a t e d zone. 36. A s e r i e s of d i g i t a l computer models f o r one-dimensional s i m u l a t i o n of n u t r i e n t and chemical behaviour i n s o i l s , was developed i n the Netherlands ( F r i s s e l et a l . , 1970; De Wit and Van Keulen, 1972; Beek and F r i s s e l , 1973; F r i s s e l and R e i n i g e r , 1974). These compartment models are w r i t t e n i n the CSMP s i m u l a t i o n language (IBM, 1972). B r e s l e r (1973) si m u l a t e d v e r t i c a l waste t r a n s -p o r t i n the s o i l , under t r a n s i e n t u n s a t u r a t e d flow con-d i t i o n s d u r i n g non-steady i n f i l t r a t i o n , r e d i s t r i b u t i o n or drainage, and e v a p o r a t i o n . The n u m e r i c a l r e s u l t s compared w e l l with Brenner's a n a l y t i c a l s o l u t i o n (1962) f o r steady i n f i l t r a t i o n of constant c o n c e n t r a t i o n s o l u t i o n s , and with Warrick et a l ' s f i e l d data (1971) f o r t r a n s i e n t i n f i l t r a -t i o n . Numerical models of chemical movement i n s o i l water were reviewed by Boast (1973). F i n i t e - d i f f e r e n c e s o l u t i o n s of the one-dimensional s o l u t e t r a n s p o r t equation have been a p p l i e d to s o i l s t u d i e s by many workers s i n c e then, i n c l u d i n g Van Genuchten and Wierenga (1974), Selim et a l . , (1976, 1977), Wierenga (1977). Most models have focused on one zone of subsurface flow, e i t h e r above or below the water t a b l e . An e x c e p t i o n to t h i s i s Perez e t a l ' s work (1974), who attempted to i n t e r f a c e a v a i l a b l e f o r m u l a t i o n s of water and n u t r i e n t t r a n s -p o r t models f o r the unsaturated and s a t u r a t e d zones. How-ever, the v a r i o u s components were l i n k e d together a c c o r d i n g 37. to a s e q u e n t i a l procedure, r a t h e r than on an i n t e g r a t e d b a s i s . Freeze (1967) emphasized the p h y s i c a l and mathematical con-t i n u i t y e x i s t i n g between u n s a t u r a t e d and s a t u r a t e d f l o w s . I n t e g r a t i o n i n Perez model was not f e a s i b l e because of s i z e l i m i t a t i o n s i n computer storage f a c i l i t i e s . In 1970, Kolenbrander concluded: "The movement of water s o l u b l e s a l t s has been i n t e n s i v e l y s t u d i e d i n the past twenty years i n columns f i l l e d with a d s o r p t i o n media or with s o i l . Hereby v a r i o u s mathematical f o r m u l a t i o n s have been developed, d e s c r i b i n g the process of the downward move-ment of s a l t s i n such columns. The problem i s now whether i t w i l l be p o s s i b l e to use these e x p r e s s i o n s f o r the a s s e s s -ment of the l e a c h i n g of s a l t s i n s o i l p r o f i l e s under f i e l d c o n d i t i o n s and to determine the parameters f o r the d i f f e r e n t s o i l s " . E i g h t years l a t e r , i t i s e d i f y i n g to note that Kolenbrander's statement i s s t i l l p e r t i n e n t to today's s i t u a t i o n , with r e s p e c t to the study of subsurface n i t r a t e movement. 1.5 Determination of Transport Model Parameters T h i s s e c t i o n i s r e s t r i c t e d to models based on t h e a d v e c t i o n / d i s p e r s i o n equation 1.5 and 1.6. Transport p a r a -m e t e r s t h e r e f o r e c o n s i s t of d i s p e r s i o n C o r d i s p e r s i v i t y ) c o e f f i c i e n t s and flow v e l o c i t i e s . 38. Regression formulas c o r r e l a t i n g dispersion and d i s p e r s i v i t y c o e f f i c i e n t s with permeability, texture and flow v e l o c i t y , were derived from experiments with columns and tank models of various granular materials (Harleman et a l . , 1963; Hoopes and Harleman, 1965). Kolenbrander (1970) proposed a relationship between the d i s t r i b u t i o n factor in undisturbed f i e l d s o i l s and the a i r content of the s o i l at pF 2.0 (100 cm tension). I t i s widely agreed that dispersion c o e f f i c i e n t s obtained from labora-tory analysis considerably underestimate the f i e l d values (Kolenbrander, 1970; Fr i e d , 1975; Bredehoeft et a l . , 1976). Experiments with f i l l e d - i n columns are usually performed under steady hydraulic conditions, with higher v e l o c i t i e s than i n natural subsurface flow systems, thereby reducing the degree of mixing occurring within the f l u i d . Laboratory methods cannot simulate accurately the inhomo-geneities and anisotropics of undistributed s o i l s and aquifers (Reddell and Sunada, 1970 ; Gardner and Jury, 1974). It has frequently been observed that the disper-sion and d i s p e r s i v i t y c o e f f i c i e n t s greatly increase with the time and space scales at which they are measured, i n the laboratory (Corey et a l . , 1970; Warrick et a l . , 1971) and in the f i e l d (Bredehoeft et a l . , 1976; Pickens and Lennox, 1976), The d i s p e r s i v i t y , just as the permeability, represents some kind of s t a t i s t i c a l average and characterizes the response of the system measured at some scale. D i s p e r s i v i t y in s o i l p r o f i l e s or geological deposits r e f l e c t s the com-ple x i t y of the ve l o c i t y d i s t r i b u t i o n , and i s therefore 39. dependent upon the large scale heterogeneities within the physical system. The greater the well-spacing in a two-well injection-withdrawal t e s t , the larger the sample of the geology and the more chance that one w i l l encounter the heterogeneity of a larger scale, r e s u l t i n g in increased d i s p e r s i v i t y values (Bredehoeft et a l . , 1976). Consequently, i t i s important that the d i s p e r s i v i t y parameters be obtained from f i e l d water quality data representative of the p a r t i c u l a r system under study. To inte r p r e t this data, some kind of mass transport model i s necessary. E x p l i c i t formulas, based on id e a l i z e d one- or two-dimensional a n a l y t i c a l models, were developed to calcu-l a t e the dispersion parameters from system response to simple step-input perturbations (Fried and Combarnous, 1971; Kirkham and Powers, 1972; Fried, 1975). More r e a l i s t i c methods, based on semi-analytical or numerical transport models, are described by Fried (1975). The parameters are obtained by curve f i t t i n g , to adjust model output to the experimental points. If the transport parameters are sought for the pur-pose of system simulation, there i s no doubt that the most r e l i a b l e method of determination i s by c a l i b r a t i o n of the simulation model i t s e l f on known or tested behaviour of the system. This parameter i d e n t i f i c a t i o n procedure,also c a l l e d 'inverse problem', was defined by Murty and Scott (1977) as "the mathematical process whereby the parameters 40. embedded in a d i f f e r e n t i a l equation governing a system are determined from observations of system input and output". For most models, no a n a l y t i c a l solution to the inverse problem e x i s t s , and parameter i d e n t i f i c a t i o n must therefore be based on an i t e r a t i v e c a l i b r a t i o n procedure. While this can be accomplished by t r i a l - a n d - e r r o r adjustment of the parameter values (Pickens and Lennox, 1976), optimization techniques are now available for t h i s s p e c i f i c purpose (Sagar, 1973; Bruch et a l . , 1974; Yih and Davidson, 1975; Murty and Scott, 1977). Most procedures require the observations of. solute concentrations at known distances from a known source, for some time known i n t e r v a l s . Experimental techniques for e f f i c i e n t system t e s t i n g were described by Fried (1975) and c l a s s i f i e d according to the parameter sought (l o n g i t u d i n a l and transverse d i s p e r s i v i t i e s , pore v e l o c i t i e s ) and to the scale of the problem. They include single-well and multiple-well techniques, as well as the use of environmental tracers for c a l i b r a t i o n of regional models. Direct methods to estimate flow v e l o c i -t i e s from the observation of tracer concentrations were also proposed. "Two of the most important considerations are the s e l e c t i o n of the most r e l i a b l e and e f f i c i e n t methods of determining these parameters under f i e l d conditions, and the development of a more quantitative understanding of the uncertainties associated with the f i e l d determinations". (Pickens and Lennox, 1976). 41. The research e f f o r t into parameter i d e n t i f i c a t i o n for water quality transport models i s r e l a t i v e l y recent, and therefore s t i l l remains largely at the deterministic stage. Development of stochastic analysis for subsurface water qu a l i t y has not yet reached the l e v e l achieved for s o i l water retention and movement studies (Rogowski, 1972; Nielsen et a l . , 1973; Baker and Bouma, 1976 ; Peck et a l . , 1977: Warrick et a l . , 1977 ; Rao et a l . , 1977) or for aquifer hydrology problems (Gelhar, 1974; Freeze, 1975 ). F i r s t steps in this direction were Greenkorn and Kessler's study of dispersion in hetero-geneous non-uniform anisotropic porous media (1969), and the work of Biggar and Nielsen (1976) on the s p a t i a l v a r i a b i l i t y of the leaching c h a r a c t e r i s t i c s in a f i e l d s o i l . The l a t t e r found the v e r t i c a l dispersion c o e f f i c i e n t and the pore water v e l o c i t i e s to be log-normally d i s t r i b u t e d . These results were confirmed by Van der Pol et a l . , (1977) for layered f i e l d s o i l . The number of observations necessary to obtain a given accuracy on the estimate of the mean can be com-puted by using s t a t i s t i c a l methods once the mathematical form of the d i s t r i b u t i o n and a measure of the variance are known. Biggar and Nielsen (1976) calculated that 35 s o i l water samples from suction probes are required to estimate the mean value of the apparent d i f f u s i o n (dispersion) c o e f f i c i e n t within one order of magnitude, and 200 samples 42. are necessary to make an estimate within + 50% of i t s true mean value. For the pore v e l o c i t y estimate, the corres-ponding numbers of samples are 20 and 100 respectively, while 1000 samples would y i e l d an estimate within + 10% of the true mean v e l o c i t y . Van der Pol et a l . , (1977) found that only 24 observations were needed for a precision of + 25%, providing the e f f e c t s of possible s o l u t e - s o i l interactions are taken into account. Both papers concluded that substantial errors can be made in estimating solute leaching flux by multiplying average values of the water drainage flux by average solute concentrations in the s o i l s o l u t i o n . Both average values depend ultimately upon the pore water v e l o c i t y d i s t r i b u t i o n and i t s attendant horizontal and v e r t i c a l s p a t i a l v a r i a b i l i t y within the s o i l p r o f i l e . Only in case of a thorough analysis of the frequency d i s t r i b u t i o n of such measurements would quantita-t i v e results be assured. ~> 1.6 A p p l i c a b i l i t y of Theoretical Models to F i e l d Problems. In order to render a precise mathematical descrip-t i o n of nitrogen movement over space and time, i t i s necessary to possess considerable information about subsur-face p h y s i c a l , chemical and b i o l o g i c a l processes. Seldom i s t h i s information a v a i l a b l e . In the f i r s t place, i t i s not possible to measure model input parameters in the laboratory (Section 1.5). Physical properties of f i e l d s o i l s c o n t r o l l i n g the retention and migration of solutes are extremely variable (Nielsen et a l . , 1973; Biggar and Nielsen, 1976), even 43. within a very small area (Van der Pol et a l . , 1977), Pickens and Lennox (1976) stressed the uncertainty i n the values of the input parameters generally encountered in f i e l d studies of groundwater contamination. In l i g h t of these l i m i t a t i o n s , Wierenga (1977) argued that i t i s often j u s t i f i e d and much more convenient to use a steady-state model instead of a transient model for analysing f i e l d data. Because of t h e i r f i n e r resolu-t i o n , numerical solutions of the transient solute transport equation 1.5 require considerably more computer time (10 to 100 times more) and input information (such as the r e l a t i o n s h i p between water content, pressure head, and hydraulic conductivity; or the actual boundary conditions). Such a degree of d e f i n i t i o n of the system i s rarely a v a i l a b l e or j u s t i f i e d . F i n i t e - d i f f e r e n c e solutions are best suited to saturated flow problems (Bredehoeft et a l . , 1976) or for the simulation of short-term i n f i l t r a t i o n , r e d i s t r i b u t i o n or evaporation events i n the unsaturated zone (Bresler, 1973). For long term, intermittent phenomena, the complexity of such mathematical models may be p r o h i b i t i v e (Boast, 1973). Often, the precision obtained from a numerical s o l u t i o n i s simply not needed (Tanner and Jury, 1974). Approximate, s i m p l i f i e d a n a l y t i c a l models have been found to compare well both with more sophisticated numerical , solutions and with experimental data, for saturated (Hoopes and Harieman, 1967) as well as for unsaturated media 44. (Wierenga, 1977), for single events (Warrick et a l . , 19J1) as well as for seasonal phenomena (Kolenbrander, 1970). Frere (1976) stated that i d e a l i z e d d i s t r i b u t i o n s obtained for simple, continuous chromatographic process are adequate for n i t r a t e s . Preliminary data col l e c t e d by Wierenga (1977) indicated that for long-term pred i c t i o n of solute d i s t r i -bution p r o f i l e s undergoing plant uptake and chemical i n t e r a c t i o n s , models based on steady water flow may also be adequate. No mathematical theory for n i t r a t e uptake yet ex i s t s , so one can "do l i t t l e more in dealing with this important process than to assume an empirical uptake func-t i o n , time-scaled according to the rate of growth of the plants (Gardner and Jury, 1974). To achieve s a t i s f a c t o r y simulation,water quality models require substantial on-site c a l i b r a t i o n , showing l i t t l e t r a n s f e r a b i l i t y from one s i t u a t i o n to another (Section 1.5). S e n s i t i v i t y to c a l i b r a t i o n is greatest for f i n i t e - d i f f e r e n c e models as numerical i n s t a b i l i t i e s frequently occur (Section 1.4). The large dependancy of the dispersion c o e f f i c i e n t s on the time and space scales at which they are measured (Section 1.5) shows evidence of our present i n a b i l i t y to b u i l d a representative picture of the microscopic processes governing the mass transport phenomena (Section 1.2). A c r i t i q u e of the dispersion theory as a mathematical description of these phenomena can be found i n 45. Sec tion 1.3. Jury and Gardner (1974) concluded that the status of the leaching theory must be considered to be most unsatis-factory: "The problem of scale i s one of the central pro-blems in s o i l physics at this time and this i s only one more case of our i n a b i l i t y to describe s o i l hydrological problems on a f i e l d or watershed scale". Although the state of the art in hydrologic modeling is at a r e l a t i v e l y advanced stage, much remains to be accomplished in the modeling of a g r i c u l -t u r a l water q u a l i t y . Increasing pressures toward e f f i c i e n t decision-making in waste management and water p o l l u t i o n control are creating the need for improved pollutant routing models that make use of the l a t e s t research advances while keeping in touch with the constraints in data c o l l e c t i o n . Such models can help understand cause and e f f e c t relationships between sources of pollutants and t h e i r ensuing concentrations at various times and locations in a basin. 46. 2. MODEL DEVELOPMENT This chapter i s devoted to the development of two mathematical models for simulation of subsurface n i t r a t e movement at two d i s t i n c t time and space scales, in a speci-f i e d physical system (described in Section 2.2). The two 'scale problems', as presented in the Introduction, are defined as follows: a) Model 1: The short term, l o c a l scale problem. To simulate the seasonal nitrogen movement under the disposal f i e l d , over the duration of the groundwater recharge period, for a given amount of excess nitrate-N available in the root zone at the end of the growing season. b) Model 2: The long term, regional scale problem. To simulate the areal r e d i s t r i b u t i o n of n i t r a t e s contributed from successive p o l l u t i o n fronts o r i g i n a t i n g at the disposal s i t e , in the regional saturated aquifer system. The t h e o r e t i c a l base common to both models i s presented in Section 2.1. 2.1 Conceptual Representation of Subsurface Nitrate Movement 2.1.1 Basic postulates It i s postulated that there exists a f i n i t e r e f e r e n t i a l elementary volume of porous medium for which a unique solute concentration can be defined. This i s equivalent to the hypothesis of complete mixing within a l l 47. s o i l pores, d i s c u s s e d i n the L i t e r a t u r e Review (Chapter 1 ) . F u r t h e r i t i s assumed that subsurface mass t r a n s p o r t i s adequately d e s c r i b e d by the s e t of two d i f f e r e n t i a l equations commonly r e f e r r e d to as the c o n t i n u i t y equation ( s t a t i n g mass c o n s e r v a t i o n of f l u i d ) and the a d v e c t i o n / d i s p e r s i o n equation ( f o r mass c o n s e r v a t i o n of s o l u t e ) . The s o l u t e molecules w i l l be c o n s i d e r e d as con-s e r v a t i v e substances and t h e i r c o n c e n t r a t i o n s too low to a f f e c t the p h y s i c a l p r o p e r t i e s of the f l u i d ( p e r f e c t t r a c e r c a s e ) . Under those assumptions, the s o l u t e t r a n s p o r t i n a given flow system is a l i n e a r p r o c e s s . A l i n e a r t r a n s -formation on the s o l u t e i n p u t s r e s u l t s i n the same t r a n s -formation of the c o n c e n t r a t i o n d i s t r i b u t i o n f i e l d . Hence, the r e l a t i o n s h i p s between s o l u t e i n p u t s , f l u x e s and concen-t r a t i o n s are iso m o r p h i c . 2 . 1 . 2 Fundamental equations and hypotheses. The g e n e r a l 3-dimensional a d v e c t i o n / d i s p e r s i o n equation e x p r e s s i n g mass c o n s e r v a t i o n of a d i s s o l v e d t r a c e r i s : | ^ ( 0 p c ) + V". (pc . q - 0 [D ] . V (pc ) ) - S v = 0 ( 2 . 1 ) where c = s o l u t e c o n c e n t r a t i o n i n the fluid [ M . M ^] 3 -3 0 = v o l u m e t r i c moisture content [L .L ] ^ = the v e c t o r operator [L ^] q = f l u i d f l u x (the Darcy flow v e l o c i t y ) [L.T 1 ] —o p = s p e c i f i c g r a v i t y of the s o l u t i o n [M.L ] 48 2 -1 where [D] = e f f e c t i v e dispersion tensor [L . T ] com-bining the ef f e c t s of molecular d i f f u s i o n and mechanical dispersion (Bear, 1972) S = solute source/sink rate per unit volume of v -3 -1 porous medium [M. L . T ]; > 0 for a source. Combining equation 2.1 with the continuity equation: |^ (p0) + V. (pq) = 0 (2.2) the general expression governing the transient movement of solutes i s obtained: g f f + 0 ' V c I p V ' (0 [D]. V.(pc)) - = 0 (2.3) For unsaturated conditions or for saturated flow under natural gradients in an unconfined aquifer, water can be assumed to act as an incompressible f l u i d (Freeze, 1967). The f l u i d density and s p e c i f i c gravity are therefore con-sidered uniform, and equation 2.3 s i m p l i f i e s to: -*• ->• I 7 - V. ([D] . Vc) + ([D] V0 - V). Vc + S (2.4) 0--> •> where V = q: i n t e r s t i c i a l pore v e l o c i t y [L. T ] 0 c _ v: source/sink rate per unit mass of f l u i d • P9" -1 -1 [M. M . T ]. This formulation was obtained by Warrick et a l . (1971) for the one-dimensional case, i n the absence of source/sink term. Applying equation 2.4 to homogeneous zones of porous medium within which the dispersion tensor [D] and the moisture content 9 can be considered uniform (but not necessarily constant with time), r e s u l t s in further simplica-tion : | f = [D]. -Ac - V. Vc + S ( 2 * 5 * 2 -2 where A = V i s the Laplacian operator, L This i s the most commonly used expression to describe transport of solute i n porous media. Simulation of subsurface n i t r a t e movement i s achieved by solving equation 2.5 over a prescribed domain of integration. To each of the two scale problems previously defined is associated a d i s t i n c t domain, therefore a d i s t i n c t model. The two models w i l l be described in p a r a l l e l by: - s u b d i v i d i n g each domain into homogeneous zones within which f l u i d density, moisture content, porosity, hydraulic con-d u c t i v i t y , and dispersion tensor are assumed uniform. - assigning i n i t i a l and boundary conditions to the above; - solving equation 2.5 within each zone. A necessary f i r s t step in solving the transport problem (equation 2.5) i s to solve for the water retention and movement subproblem, to obtain the moisture content and flow v e l o c i t y at each point of the porous medium. This w i l l be achieved by using simplifying approximations for the flow process, governed by the equation of continuity (2.2) and Darcy's law. 50. It was emphasized in the Literature Review (Section 1.5)that the - dispersion c o e f f i c i e n t s characterize the response of the system observed at some scale and vary considerably depending upon the scale at which they are measured. Therefore, not only w i l l the boundaries of the domain of integration be d i f f e r e n t for each scale problem, but so w i l l be the equation parameters. 2.2 Description of the Physical System The 3-dimensional space i s referred to the orthogonal system of coordinate axes (x y z ) , where z i s v e r t i c a l downwards.. The center of the waste disposal f i e l d , at the ground surface, i s the origin of the coordinate system. The domain of n i t r a t e movement simulation i s the region comprised between the s o i l surface and a surface assumed impermeable to water and solute fluxes at depth z = DIMP. DIMP i s always small in comparison to the h o r i -zontal extent of the domain (more than one order of magni-tude) . The domain can be divided into two hydrological zones, the unsaturated zone and the saturated zone, separated by the water table at depth z = ZWT. Groundwater movement i s predominantly v e r t i c a l i n the unsaturated zone, and horizontal in the saturated zone in the d i r e c t i o n of the x axis. Geologically, the domain i s also composed of two layers, the s o i l layer (or root zone) and the aquifer formation. The l a t t e r consists of coarse-textured, uncon-solidated sediment of uniform porosity n a and conductivity 51. K . The aquifer i s of s i g n i f i c a n t economic importance, SL because of a high K value. a Assuming that the water table remains at a l l times below the root zone, the system can then be s p l i t into three homogeneous sub-systems. 1. The root zone. 2. A subsoil t r a n s i t i o n a l zone, consisting of unsaturated aquifer material. 3. The saturated zone. The depth H of the root zone i s assumed to be constant and uniform. The two models d i f f e r by: - the h o r i z o n t a l configuration of the domain; - the v e r t i c a l configuration of the l a s t two zones. .2.2.1 The short term, l o c a l scale: Model 1. Due to the high hydraulic conductivity of the aquifer material, the slope of the water table i s small. While this slope cannot be neglected from the point of view of hydraulic p o t e n t i a l d i s t r i b u t i o n , the water table can be considered horizontal for the d e f i n i t i o n of zone boundaries. The thickness h 0 f the saturated zone i s uniform but varies with time according to water table f l u c t u a t i o n s . Application rates are uniform. The waste disposal area and the domain of simulation are i n f i n i t e In a l l horizontal d i r e c t i o n s . In p r a c t i c e , the horizontal boundary ef f e c t s can be neglected when the horizontal dimensions of the plot are large in comparison to the depth of the domain and to 52. the distance t r a v e l l e d by groundwater during the simulation period. 2.2.2 The long term, regional scale: Model 2 The thickness of the saturated zone i s constant but not uniform. The water table i s stationary, with a uniform slope SWT in x d i r e c t i o n . A steady-state saturated flow system is commonly used i n regional groundwater models, both for water quantity (Freeze, 1969) and water quality studies (Freeze, 1972; Gelhar, 1974; Pickens and Lennox, 1976). The depth DIMP to the impermeable surface i s variable. The uniform water table slope in a homogeneous aquifer material, results in a uniform horizontal saturated flow v e l o c i t y . The disposal area, and therefore the unsaturated zones (1 and 2), are f i n i t e and rectangular, with one rectangle axis in the dire c t i o n of saturated groundwater flow. The saturated zone has i n f i n i t e h o r i z o n t a l dimensions. Again, this amounts tq neglecting horizontal boundary effects which i s acceptable i f one remains at a s u f f i c i e n t distance from the actual aquifer boundaries. 2.3 Model 1 2.3.1 Basic equations Model 1 considers only the leaching period. Leaching occurs predominantly during the dormant season, when crop growth and b a c t e r i a l a c t i v i t y are minimal. It is therefore assumed that no uptake or accumulation of 53. n i t r a t e s occur d u r i n g the s i m u l a t i o n p e r i o d , and the s i n k / source term S i s withdrawn from the t r a n s p o r t equation 2.5. Th i s p o i n t i s f u r t h e r d i s c u s s e d i n S e c t i o n 4.1.1. Hence, Model 1 focuses on the r o u t i n g of the q u a n t i t y MQ (kg/ha) of excess n i t r a t e - N , a v a i l a b l e i n the root zone when s u r p l u s of p r e c i p i t a t i o n over e v a p o t r a n s p i r a t i o n f i r s t o c c u r s at the end of the growing season. Equation 2.5 i s to be a p p l i e d i n d i v i d u a l l y to every homogeneous zone of the porous medium, with a p p r o p r i a t e i n t e r f a c i n g . Selim et a l . (1977) showed th a t , f o r uns a t u r a t e d m u l t i l a y e r e d p r o f i l e s , the use of average water content f o r each s o i l l a y e r r e s u l t s i n e f f l u e n t c o n c e n t r a t i o n d i s t r i b u t i o n s i d e n t i c a l to those o b t a i n e d where a c t u a l water content d i s t r i -b u t i o n s are used. Equation 2.5 based on a unique time-dependent moisture content 0 w i t h i n each zone can t h e r e f o r e be a p p l i e d to zones 1 and 2. Assuming uniform a q u i f e r p o r o s i t y , the moisture content 0 can a l s o be c o n s i d e r e d uniform in the s a t u r a t e d zone. During the l e a c h i n g p e r i o d , c o n c e n t r a t i o n g r a d i e n t s v"c are predominantly v e r t i c a l , which allows f o r s i m p l i f i c a t i o n of equation 2.5 to i t s one-dimensional form: 3c _ n 3jc. 3c (2.6) T t " v a 2 v 3z a z where z i s the v e r t i c a l c o o r d i n a t e D and V are the d i s p e r s i o n c o e f f i c i e n t and v v pore v e l o c i t y i n the v e r t i c a l d i r e c t i o n , r e s p e c t i v e l y . 54. Equation 2.6 regards the v e r t i c a l d i r e c t i o n as a p r i n c i p a l a x i s of d i s p e r s i o n ( f o r d e f i n i t i o n see Bear, 1972). However, equation 2.6 does not imply mass c o n s e r v a t i o n of s o l u t e i n a v e r t i c a l column, s i n c e f l u i d i s not conserved i n the v e r t i c a l d i r e c t i o n . The v a l i d i t y of equation 2.6 i n the s a t u r a t e d zone decays as the e f f e c t of h o r i z o n t a l d i s p e r s i o n and the a t t e n u a t i o n of v e r t i c a l s t r a t i f i c a t i o n p r o g r e s s i v e l y i n -crease the r e l a t i v e importance of the h o r i z o n t a l concen-t r a t i o n g r a d i e n t ^ c , and thus of the h o r i z o n t a l c o n v e c t i v e ->• term V, . V, c i n e quation 2.5. As a r e s u l t , the a p p l i c a t i o n n h of equation 2.6 i s l i m i t e d to the p e r i o d of l e a c h i n g . The assumption that the h o r i z o n t a l component of the n i t r a t e c o n c e n t r a t i o n g r a d i e n t i s n e g l i g i b l e i n com-p a r i s o n to i t s v e r t i c a l component should be s u b j e c t e d to a - p o s t e r i o r i t e s t i n g on the model output. 2.3.2 I n i t i a l and boundary c o n d i t i o n s The f o l l o w i n g i n i t i a l and boundary c o n d i t i o n s were a p p l i e d to e q u a t i o n 2.6: I n i t i a l c o n d i t i o n s : Time t = 0 i s chosen a r b i t r a r i l y a few days b e f o r e the s t a r t of the l e a c h i n g p e r i o d . 55. rH c ( z , t ) . ( 0 . - 0 ,1. dz = M f o r t-0; 0 < z < H (2.7 v ' l e x c l o — — c ( z , t ) = c i ( Z) f o r t=0; H < z < DIMP (2.7 where 0, 3 -3 = i n i t i a l s o i l moisture content [L .L ] 0 , = volume f r a c t i o n from which n i t r a t e ions are e x c l 3 - 3 excluded [L .L ] H = i n i t i a l mass of n i t r a t e - N i n the root zone, o -2 per u n i t land area [M. L ] c ^ = i n i t i a l n i t r a t e - N concentration of ground-water [M. M - 1] H = depth of the root zone [L] DIMP = depth of the impermeable l a y e r [ L ] . Boundary Conditions J. l 0 ( z , t ) . V y ( z , t ) = I (t) - E ( t ) V v ( z , t ) . c ( z , t ) - D v 5 % ^ Z > t ) = 0 0 ( z , t ) . V v ( z , t ) = 0 = -D 9c(z ,t) 3z (2.8.la) f o r z=0 (2.8.lb) (2.8.2a) >for z=DIMP (2.8.2b) where I ( t ) E( t ) q r q o J i ^ o = i n f i l t r a t i o n rate = evaporation r a t e = water f l u x e s i n and out of the system = n i t r a t e f l u x e s i n and out of the system. 5 6 . Equation 2.8.1a expresses that the f l u x of water q^ across the ground surface i s equal to the difference between i n f i l t r a t i o n and evaporation rates. Equation 2.8.1b neglects the n i t r a t e content of r a i n -water. Equations 2.8.2a and 2.8.2b express the impermeable layer condition, for water and n i t r a t e fluxes, respectively. 2.3.3 System simulation A n a l y t i c a l , semi-analytical and numerical methods are used to solve the d i f f e r e n t i a l transport equations within each zone and interface the solutions between zones. The simulation procedure i s schematized by the flow chart presented on Figure 2.1. I n i t i a l n i t r a t e and moisture contents of the root z o n e . i n i t i a l position of the water table, and weather data are the inputs. The model produces daily values for remaining n i t r a t e in the root zone, position of the water table, and v e r t i c a l n i t r a t e concentration pro-f i l e in the saturated zone. A l l components of the system depicted in Figure 2.1 are recycled within each time step, with a time increment of one day. The three sub-systems corresponding to the d i f f e r e n t zones of porous medium are examined i n d i v i d u a l l y . 1. The root zone Daily moisture inputs ( i n f i l t r a t i o n I) and outputs (evapotranspiration ET and drainage Q) are estimated 57 WEATHER EXTRATERRESTRIAL DAYLENGTH RADIATION DURATION CLOUD . TEMPERATURE PRECIPITATION EVAPOTRANSPIR ATION INFILTRATION 5 2 O N o o ii-o to o LU z o Isl II co to . 2 < Z o a < to F i g u r e 2 . 1 : S i m u l a t i o n f l o w c h a r t f o r M o d e l 1 . 58. independently, based on the i n i t i a l moisture V i n the root zone at the s t a r t of the day. They are subsequently i n c o r p o r a t e d i n the s o i l water budget equation at the end of the day: AW = I - ET - Q (2.9) Because of the t h i n c a p i l l a r y f r i n g e i n the coarse t e x t u r e d t r a n s i t i o n zone, i t i s assumed that the p o s i t i o n of the water t a b l e does not i n f l u e n c e s o i l moisture content. a) INFILTRATION, I I t i s assumed that no r u n - o f f occurs from the p l o t , and p r e c i p i t a t i o n i n f i l t r a t e s d u r i n g the same time step (I = P) . In the r a r e case when the p r e c i p i t a t i o n r a t e exceeds the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y of the t o p s o i l , water excess i s allowed to pond and i n f i l t r a t e at the next time s t e p . b) EVAPOTRANSPIRATION, ET D a i l y p o t e n t i a l e v a p o t r a n s p i r a t i o n PET i s estimated by a c l i m a t o l o g i c a l method i n i t i a l l y proposed by P r i e s t l e y and T a y l o r (1972), and f u r t h e r t e s t e d and m o d i f i e d by Jury and Tanner (1975). This method, based on an energy balance approach, expresses atmospheric water demand i n the form: PET = (1 + e) . ( s S + j . R n/X (2.10) where R^ i s the net r a d i a t i o n , y i s t n e p s y c h r o m e t r i c constant, s i s the slope of the s a t u r a t i o n vapor p r e s s u r e curve at ambient temperature, e i s a c o r r e c t i v e f a c t o r which would be zero i f the atmospheric s u r f a c e l a y e r was s a t u r a t e d (PET=E o -. 59. E e ^ : e q u i l i b r i u m e v a p o r a t i o n r a t e ) , X i s the l a t e n t heat of e v a p o r a t i o n . The net s o i l heat f l u x i s n e g l e c t e d . Tanner and Jury (1974) suggested a l i n e a r r e l a t -i o n s h i p between e and the atmospheric s a t u r a t i o n d e f i c i t . Average s a t u r a t i o n d e f i c i t on a given day i s estimated by the d i f f e r e n c e between s a t u r a t i o n vapour p r e s s u r e s at the mean and minimum temperatures f o r the day, T and mean T . . This approximation assumes 100% r e l a t i v e humidity m in at T=T m^ n and unchanging vapour pressure during the day. I t was found s a t i s f a c t o r y i n widely v a r y i n g c l i m a t i c s i t u a t i o n s . F o l l o w i n g t h i s concept, the c o r r e c t i v e f a c t o r i s expressed as e = C . (1-RH) , RH = PS(T , ) / PS(T ) (2.11) min mean where PS(T) i s the s a t u r a t i o n vapour pressure at temperature T, and C i s a di m e n s i o n l e s s constant, c h a r a c t e r i s t i c of the l o c a t i o n . S a t u r a t i o n vapour pressure i s computed using Brooker's mathematical model of the p s y c h r o m e t r i c c h a r t (1967). Net r a d i a t i o n i s c a l c u l a t e d by the e x p r e s s i o n R = (1-a) . R + (£ A - 0.96). 0 . T 4.(0.2 + 0.8f) n s •» B k (2.12) where R g i s the g l o b a l s o l a r r a d i a t i o n , T^ i s the d a i l y mean s h e l t e r (screen) temperature i n degree K e l v i n , a i s the albedo of the land s u r f a c e , 60. £ i s the emissivity of the atmosphere, 0.96 i s the ^ emissivity of the vegetation, 0* is the Boltzman's constant, B f is the f r a c t i o n of time during the day when clouds do not obstruct the sunshine. (after Linacre, 1968; Tanner and Jury, 1974). Linacre (1968) showed that the solar radiation term R varies l i n e a r l y with the e x t r a t e r r e s t r i a l radiation s J R a (radiation outside the atmosphere) and with the sunshine duration factor f, in the form: R = R . (A + B. f) (2. 13) s a Formulas are available to calculate the daily extraterres-t r i a l solar radiation R on a horizontal surface and the a daylength at a given location (Duffie and Beckman, 1974). The emissivity e i s expressed as: A e A = 1 - 0. 261 exp(-7.77 . I O - 4 . (T k~273) 2) (2.14) by Idso and Jackson (1969). f can be computed from meterorological data as the r a t i o of daily number of direct sunshine hours to the computed daylength for the l o c a t i o n . The actual evapotranspiration estimate ET i s derived from the p o t e n t i a l evapotranspiration PET by apply-ing a factor WAC, to account for the e f f e c t of s o i l water d e f i c i t s . WAC i s assumed to decrease l i n e a r l y with s o i l moisture content 0, from a value of 1 above a c r i t i c a l moisture content 0 , to zero at the permanent (2.15) 61. w i l t i n g p o i n t © Wp• (For review see B a i e r , 1972). ( WAC = 0 f o r 0 ^ 0 I T_ ^ Wr ( W A C = ce - e w p ) / ( 0 c - e w p ) f o r 0 w p < 0 < 0 c ( WAC = 1 f o r 0 > 0 c Tanner and R i t c h i e (1975) found that the r e l a t i o n s h i p ( 0 c - 0 w p ) - 0.3 ( 0 p c - 9 w p ) (2.16) where 0 p ( , i s the s o i l moisture content constant at f i e l d c a p a c i t y , holds f o r a l a r g e v a r i e t y of v e g e t a t i o n . c.) DRAINAGE, Q Methods have been developed f o r s o l v i n g the flow equation i n the u n s a t u r a t e d zone u s i n g s i m p l i f y i n g assump-t i o n s (Black et a l . , 1969 and 1970 ; Gardner et a l . , 1970; C l o t h i e r et a l . , 1977; M i l l e r and A a r s t a d , 1972). Using those approximations, the drainage f l u x at the base of the root zone can be estimated as a unique f u n c t i o n of the amount of water s t o r e d i n that zone. W. Black et a l . (1969) developed the theory f o r a deep uniform permeable s o i l . C l o t h i e r et a l . (1977) s t a t e d that the approach appears to work even b e t t e r i n a permeable s o i l u n d e r l a i n by a c o a r s e - t e x t u r e d l a y e r . A l l methods e x p r e s s i n g d a i l y drainage rates as an e x p l i c i t f u n c t i o n of water s t o r a g e can be i n t e r c h a n g e a b l y i n c o r p o r a t e d i n t o our model. In the development of the model, i t was assumed that drainage out of the root zone occurs under the p r e -62. dominant g r a v i t a t i o n a l g r a d i e n t , due to the coarse t e x t u r e of the s u b s o i l . In e f f e c t , n i t r i c p o t e n t i a l g r a d i e n t s are n e g l e c t e d d u r i n g drainage events, and the c a p i l l a r y conduc-t i v i t y K of the root zone i s con s i d e r e d as the r a t e l i m i t -i n g f a c t o r f o r drainage f l u x e s : dQ = K ( 0 ) . d t . Black et a l . (1969) reviewed s t u d i e s showing that the d i f f u s i v i t y term D&0 i n the e x p r e s s i o n DD_0 + K o f the downward water f l u x 3z dz o f t e n i s r e l a t i v e l y s m a l l d u r i n g a l a r g e f r a c t i o n of the drainage p r o c e s s . Black et a l . (1970) and Gardner and Jury (1974) expressed d a i l y drainage out of the root zone d i r e c t l y as the space-average c a p i l l a r y c o n d u c t i v i t y of the s o i l i n which r o o t i n g o c c u r r e d . In medium or f i n e r t e x t u r e d s o i l , t h i s procedure generates n u m e r i c a l i n s t a b i l i t y at high moisture content, due to the l e n g t h of the time s t e p . Numerical i n s t a b i l i t y can be e l i m i n a t e d by i n t e g r a t i n g a n a l y t i c a l l y over one time s t e p , the system of d i f f e r e n t i a l equations ( dQ - K ( 0 ) . dt ) ( ) (2.17) ( dW = K.dO =-dQ ) e x p r e s s i n g f l u i d c o n s e r v a t i o n , where: 0 i s the space-average v o l u m e t r i c moisture c o n t e n t , K is the c a p i l l a r y c o n d u c t i v i t y , H i s the t h i c k n e s s of the root zone, W i s the s o i l water storage ( i n the root zone). The drainage moisture l o s s Q over a one-day.period i s t h e r e -fore expressed as an i m p l i c i t f u n c t i o n of the i n i t i a l moisture content 0 b y the e q u a t i o n : 63. QCe ) 9 1 i H de - l (2.18) 1 K(9) H e The unsaturated flow c h a r a c t e r i s t i c curve K(0) can g e n e r a l l y be f i t t e d to an e x p o n e n t i a l f u n c t i o n , at l e a s t w i t h i n the range of moisture contents encountered i n the f i e l d (e.g. see N i e l s e n et a l . , 1973; Gardner and J u r y , 1974; Warrick et a l . , 1977); K ( 9 ) = exp ( k Q . (0 - 0 Q ) ) (cm/day) (2.19) wh ere 0 o i s the m o i s t u r e content at which K = 1 cm/day k i s d e f i n e d as k = 2.3/A.0 , where A9 i s the o o c c change i n v o l u m e t r i c moisture content a s s o c i a t e d with one l o g a r i t h m i c c o n d u c t i v i t y c y c l e . With t h i s e x p o n e n t i a l f o r m u l a t i o n of the c o n d u c t i v i t y K ( 0 ) , i n t e g r a t i o n of equation 2.18 y i e l d s the d a i l y drainage Q, i n cm of water, as Q(0.) = Q g. Log (1 + K(0 i/Q e) ) (2.20) where Q i s a constant = H/k (cm) e o The procedure f o r i n t e g r a t i o n of equations 2.17 and 2.18 i s f u l l y developed i n Appendix A. An e x p r e s s i o n s i m i l a r to 2.20 was obtained by N i e l s e n et a l . (1973) and used as a t o o l f o r f i e l d d e t e r -m i n a t i o n of s o i l h y d r a u l i c c h a r a c t e r i s t i c s . For a given time step t, the drainage term Q(t) can now be obtained 64. by equation 2.20 based on the moisture content 0^ of the root zone at the s t a r t of the time s t e p . Jury and Gardner (1974) noted that a s t r o n g n e g a t i v e feedback e f f e c t i s one of the very r e a l advantages i n the method of e s t i m a t i n g drainage rate as a d i r e c t f u n c t i o n of water s t o r a g e . I f drainage i s o v e r e s t i m a t e d d u r i n g one time s t e p , then too low a value of storage w i l l be p r e d i c t e d , with a lower than a c t u a l drainage p r e d i c t i o n f o r the next step and v i c e - v e r s a . T h i s confers s t a b i l i t y to the n u m e r i c a l procedure. C l o t h i e r et a l . (1977) observed that s i g n i f i c a n t h y s t e r e s i s i n the water r e t e n t i v i t y and c o n d u c t i v i t y c h a r a c t e r i s t i c s of the s o i l i n v e s t i g a t e d , had l i t t l e e f f e c t on the storage - f l u x r e l a t i o n . d) LEACHING, L. F o l l o w i n g Kolenbrander's a n a l y t i c a l s o l u t i o n (1970) to equation 2.6 f o r the l e a c h i n g of surface a p p l i e d anions out of a root zone of t h i c k n e s s H, the f r a c t i o n F of n i t r a t e s remaining i n the root zone a f t e r Q^ , cen timeters of water have d r a i n e d i s expressed as: F = f (u) + exp {— ) . f (v) (2.21) H wi th x exp (-: J _ o o f (x) = 1 - (211) 1 / 2 (-1/2 C 2 ) d£ P-1 P+l u = > v = £  65. where p i s the pore volume of e f f l u e n t ( d i m e n s i o n l e s s f u n c t i o n of Q,j, > , see S e c t i o n 1,2), i s a d i m e n s i o n l e s s index of mixing f o r the p r o f i l e , d e f i n e d as 3/H, where 3 = 2 , D /V and was c a l l e d ' d i s t r i b u t i o n f a c t o r ' by \ v v Kolenbrander (1970). ( I t can be noted that the d i s t r i b u -t i o n f a c t o r 3 i s i t s e l f twice the d i s p e r s i v i t y c o e f f i c i e n t a v ) . H is the t h i c k n e s s of the root zone. Kolenbrander (1970) conducted f i e l d t e s t s w i t h s o i l s ranging from sand to heavy c l a y and peat, and pro-posed the f o l l o w i n g r e l a t i o n s h i p : 3 = 4 - 5 \ ( H - 1 0 ) + 9 (2.22) $r where ft i s the mean a i r content i n the p r o f i l e below the upper 10 cm at pF 2.0 (ft i s expressed as a v o l u m e t r i c p e r c e n t a g e ) . Kolenbrander gave the pore volume of e f f l u e n t p as the r a t i o of the t o t a l amount of water Q^ , moved downward through the p r o f i l e , s i n c e l e a c h i n g s t a r t e d , to the amount of water W__ h e l d i n the p r o f i l e at f i e l d c a p a c i t y . T h i s d e f i n i t i o n i s somewhat r e s t r i c t i v e , as i t assumes t h a t the moisture content remains at f i e l d c a p a c i t y throughout the drainage p e r i o d . T h i s assumption i s c o n s i d e r e d u n s u i t a b l e i n our model because of the wide s o i l moisture v a r i a t i o n s i n response to p r e c i p i t a t i o n p a t t e r n s . The f i e l d c a p a c i t y concept i s b e l i e v e d to be p a r t i c u l a r l y inadequate f o r the purpose of l e a c h i n g s i m u l a t i o n as l e a c h i n g e f f i c i e n c y 66. ( r a t i o of solute movement to moisture movement) i n c r e a s e s s i g n i f i c a n t l y w i t h d e c r e a s i n g moisture content. Warrick et a l . (1971) showed that the s o l u t e d i s t r i b u t i o n advanced with K(0)/O while the downward water f l u x was K(0). Th i s simply s t a t e s that the s o l u t e c o n c e n t r a t i o n i n the s o i l s o l u t i o n i s i n v e r s e l y p r o p o r t i o n a l to the mois t ure-.con ten t. I t f o l l o w s that the v a r i a b l e z d e f i n e d by P d Z p " 0 ~ ~0~~ d t (2.23) p r o v i d e s a more a c c u r a t e measure of l e a c h i n g than the cumulated amount of drainage water Q^ , i t s e l f ; d z o can be viewed as the depth of water p e n e t r a t i o n d u r i n g the time dt i n the s o i l at moisture content 0. The g e n e r a l i z e d pore volume p i s then d e f i n e d as the normalized depth of water p e n e t r a t i o n with r e s p e c t to the depth of the root zone, i . e . P = Zp/U, dp = d z P / H " d ^ / W - dQ/ (H. Q) (2.24) The g e n e r a l e x p r e s s i o n f o r p i d e n t i f i e s to Kolenbrander's d e f i n i t i o n i f the moisture content e f f e c t i v e l y remains con-s t a n t d u r i n g the l e a c h i n g process. In summary, an amount Q(t) (cm) of drainage water d u r i n g a given time step t w i l l l e a c h a q u a n t i t y L ( t ) (kg/ha) of n i t r a t e s and w i l l have an average c o n c e n t r a t i o n c ^ ( t ) (ppm)" computed by the eq u a t i o n s : L ( t ) - M q. [F(p) - F(p+Ap)] with Ap = Q(t)/CH.0) and c L ( t ) = 10 . L ( t ) / Q ( t ) ' (2.25) M i s the i n i t i a l amount of n i t r a t e s i n the t o p s o i l at the o s t a r t of the s i m u l a t i o n p e r i o d . The s u b s o i l t r a n s i t i o n zone Non-uniform s u b s o i l water movement a s s o c i a t e d with i n s t a b i l i t y of the we t t i n g f r o n t at the f i n e - c o a r s e i n t e r -face commonly occ u r s when a coarse and porous m a t e r i a l u n d e r l a y s the root zone ( H i l l and Pa r l a n g e , 1972 ; Nagpal and De V r i e s , 1976). Under those c o n d i t i o n s , the form a t i o n of v e r t i c a l w e t t i n g f i n g e r s with s a t u r a t e d cores r e s u l t s i n r a p i d downward p e r c o l a t i o n w i t h i n p r e f e r e n t i a l channels. These f i n g e r s c o n s t i t u t e a smal l f r a c t i o n of the t o t a l h o r i z o n t a l c r o s s - s e c t i o n a l area of the porous medium. The high h y d r a u l i c c o n d u c t i v i t i e s along these p r e f e r e n t i a l flow paths l e a d to t r a v e l times s m a l l e r than onetime increment between the bottom of the root zone and the water t a b l e . Consequently, the un s a t u r a t e d s u b s o i l i s co n s i d e r e d as a t r a n s i t i o n zone i n which s o l u t e movement o c c u r s by con-v e c t i o n o n l y , no d i s p e r s i o n or mixing t a k i n g p l a c e . I t i s a l s o assumed that no water or n u t r i e n t e x t r a c t i o n by p l a n t s , b i o l o g i c a l t r a n s f o r m a t i o n or a d s o r p t i o n to s o i l c o l l o i d s occur below the root zone. The water q u a n t i t y and q u a l i t y out o f the root zone are t h e r e f o r e t r a n s f e r r e d unchanged to the water t a b l e , and fed at the next time step as an input to the s a t u r a t e d zone submodel. The s a t u r a t e d zone As was the case f o r the root zone subsystem, the o b j e c t i v e here again i s to o b t a i n an e x p l i c i t d i r e c t 68. r e l a t i o n s h i p between water f l u x and water storage , to be plugged i n t o the d i f f e r e n t i a l s o l u t e t r a n s p o r t equation 2.6. a) WATER TABLE POSITION D a i l y drainage p r e d i c t i o n s are compared to observed water t a b l e l e v e l s over a t e s t season. During p e r i o d s of no -2 recharge (e.g. when the drainage value i s lower than 10 cm/day), the v e r t i c a l component \*v(ZWT) of the s a t u r a t e d flow v e l o c i t y at the water t a b l e i s estimated as the observed r a t e of d e c l i n e of the water t a b l e , and i s expressed as a f u n c t i o n DWT(ZWT) of the water t a b l e depth ZWT. DWT(ZWT) i s d e f i n e d f o r 0 < ZWT < DIMP, and decreases with i n c r e a s i n g ZWT. For ZWT = DIMP, DWT(ZWT) = 0. (2.26) For recharge p e r i o d s , the r i s e RWT of the water t a b l e a t t r i -buted to deep p e r c o l a t i o n i s taken as p r o p o r t i o n a l to the drainage from the root zone, with a l i n e a r i t y c o e f f i c i e n t R £, c a l l e d recharge c o e f f i c i e n t . The change of water t a b l e depth can then be p r e d i c t e d as: AZWT(t) = V (ZWT) - RWT = DWT(ZWT) - R . Q ( t - l ) (2.27) v c The c o e f f i c i e n t of p r o p o r t i o n a l i t y R £ i s obtained by c a l i b r a t i o n of 2.27 on recorded water t a b l e f l u c t u a -t i o n s over the t e s t i n g p e r i o d . 69. b) VELOCITY PROFILE The pore v e l o c i t y p r o f i l e V(z) i n the s a t u r a t e d zone, i s determined by the e q u a t i o n of c o n t i n u i t y , 2.2, Darcy's law and the f o l l o w i n g set of boundary c o n d i t i o n s : K . • water t a b l e ( V(z) . x = V (z) = — SWT(zK ( . a ^ f o r z=ZWT (2.28.1) ( V(z) . z = V y ( z ) - DWT(z) j impermeable + ( . z = V (z) = 0 f o r z = DIMP (2.28.2) s u r f a c e v where n and K are the p o r o s i t y and the s a t u r a t e d conduc-t i v i t y of the outwash m a t e r i a l . I t i s shown i n Appendix B that the v e l o c i t y f i e l d V i s independent of the time v a r i a b l e , and i s t h e r e f o r e c o n t r o l l e d e n t i r e l y by the p o s i t i o n of the water t a b l e , ZWT. I t can be noted from equations 2.26 and 2.28 that the f u n c t i o n DWT(z) s a t i s f i e s both boundary c o n d i t i o n s f o r the v e r t i c a l v e l o c i t y component V^(z) i r r e s p e c t i v e of the water t a b l e p o s i t i o n . In p a r t i c u l a r V^(ZWT) = DWT(ZWT) fo r a l l ZWT. Since s a t u r a t e d flow i n the unconfined a q u i f e r behaves l i k e a steady system, V^(z) depends on the depth z only, and V^(z) can t h e r e f o r e be obt a i n e d as the e x p l i c i t f u n c t i o n DWT(z) d e r i v e d from water t a b l e o b s e r v a t i o n s (see pr e v i o u s s e c t i o n ) . T h i s r e a s o n i n g is j u s t i f i e d i n more d e t a i l s i n Appendix B. 70. c) NITRATE CONCENTRATION DISTRIBUTION Using the simulated depth of vater t a b l e ZT'T f o r the boundary of the s a t u r a t e d domain, the water q u a l i t y equation 2.6 i s then s o l v e d by the f i n i t e - d i f f e r e n c e method, f o r the f o l l o w i n g i n i t i a l and boundary c o n d i t i o n s : I n i t i a l p r o f i l e c ( z , t ) = c 1 ( z ) f o r t = 0 (2.29.1) At water t a b l e c ( z , t ) = c L ( t - 1 ) = 1 0 . L ( t - l ) / Q ( t - l ) and V v(z)=DWT(z) (2.29.2) f o r z=ZWT 3 c At impermeable s u r f a c e -sr— (z,t)=0 ) ) f o r z=DIMP (2.29.3) V v(z)=0 ) At time step i and node j , the f i n i t e - d i f f e r e n c e e x p r e s s i o n of equation 2.6 i s : At ,. (Az V (j) Th- - c 5 - i > ( 2 - 3 0 > where At and Az are the time and depth increments r e s p e c t i v e l y , Node j = l corresponds to the impermeable boundary (z=DIMP), and the depth z t h e r e f o r e decreases with i n c r e a s i n g j . To avoid n u m e r i c a l i n s t a b i l i t y , the product (V ) . A t should not exceed the depth increment Az. v max (V ) i s the maximum v e r t i c a l v e l o c i t y p o s s i b l e d u r i n g v max the s i m u l a t i o n p e r i o d . S i n c e , f o r convenience, we want to work with a time step At = 1 day, t h i s l i m i t s the degree 71. of s p a t i a l r e s o l u t i o n that can be obtained. In p r a c t i c e , d i s t a n c e between nodes of the order of one centimeter or or one i n c h can g e n e r a l l y be achieved because of the s m a l l v e r t i c a l v e l o c i t i e s , and t h i s i s s u f f i c i e n t f o r our pur-poses. P r e l i m i n a r y t e s t i n g with a u n i t - c o n c e n t r a t i o n s t e p - i n p u t f u n c t i o n i s recommended to a d j u s t time steps and g r i d s p a c i n g before u s i n g the model f o r g e n e r a l boun-dary c o n d i t i o n s ( F r i e d , 1975). The v e r t i c a l component V of the s a t u r a t e d pore v e l o c i t y i s estimated as a f u n c t i o n of depth by the e x p r e s s i o n DWT(z) (see l a s t s e c t i o n ) . The system of l i n e a r equations 2.30 with the boundary c o n d i t i o n s 2.29 i s s o l v e d by Gaussian e l i m i n a t i o n , u s i n g the t r i d i a g o n a l a l g o r i t h m method (Remson ' et a l . , 1971) . 2.4 Model 2 The one-dimensional f o r m u l a t i o n f o r the u n s a t u r a -ted component (root zone and t r a n s i t i o n zone subsystem) i s common to both models, and was d e s c r i b e d i n S e c t i o n 2.3. Hence, only the s a t u r a t e d zone subsystem i s c o n s i d e r e d h e r e a f t e r . Model 2 simulates the two-dimensional t r a n s i e n t a r e a l m i g r a t i o n and d i s p e r s i o n of a c o n s e r v a t i v e substance i n a s t e a d y - s t a t e s a t u r a t e d groundwater flow system. 2.4.1 B a s i c equations The system can be r e p r e s e n t e d by a two-dimensional 72. model, due to the l a r g e time and space s c a l e s c o n s i d e r e d : the depth of the a q u i f e r i s two or more orders of magnitude s m a l l e r than i t s h o r i z o n t a l e x t e n t ; - the l e n g t h of time necessary to, achieve n e a r l y complete mixing i n the v e r t i c a l d i r e c t i o n i s s m a l l compared to the o v e r a l l time frame of t h i s problem (over a de cade). In e f f e c t , v e r t i c a l f l u x e s can be n e g l e c t e d , and concen-t r a t i o n g r a d i e n t s are con s i d e r e d mostly h o r i z o n t a l , with the p o l y g o n a l p l o t as a uniform source of contaminants. Complete mixing i s assumed to occur i n s t a n t a n e o u s l y along any v e r t i c a l l i n e , to which i s a s s o c i a t e d a s i n g l e concen-t r a t i o n v a r i a b l e c ( x , y ) . The two-dimensional form of equation 2.5 i s : 3x 9y in the p r i n c i p a l system of r e f e r e n c e (x, y ) , where x ' i s the d i r e c t i o n of groundwater movement and y i s the h o r i z o n t a l a x i s p e r p e n d i c u l a r to x. and D^ , are the l o n g i t u d i n a l and t r a n s v e r s e d i s p e r s i o n c o e f f i c i e n t s , p r o p o r t i o n a l to the v e l o c i t y (dynamic d i s p e r s i o n regime). The c o e f f i c i e n t s of p r o p o r t i o n a l i t y are the l o n g i t u d i n a l and tr a n v e r s e d i s p e r s i v i t i e s r e s p e c t i v e l y (see S e c t i o n 1.3): D L = Q L ' V h ' D T = Q T ' V C2'32) Equation 2.31 i s s o l v e d i n an i n f i n i t e p l a n e , f o r a homogeneous, monolayered, s a t u r a t e d a q u i f e r of t h i c k n e s s 73. h(x,y) . 2.4.2 I n i t i a l and boundary c o n d i t i o n s I n i t i a l c o n d i t i o n s a p p l i e d to equation 2.31 are: c ( x , y , t ) = c. (x,y) f o r t=0 (2.33) Boundary c o n d i t i o n s a r e : c ( x , y , t ) = 0 f o r x=°° or y- 0 0 (2.34) The source term S i n equation 2.31 i s expressed as where f i s the h o r i z o n t a l area d e f i n e d by the waste d i s p o s a l f i e l d , L ( t ) i s the rate of i n j e c t i o n of n i t r a t e - N i n t o the s a t u r a t e d system at time t [M.L .T ] m(x,y) i s the mass of groundwater per u n i t s u r f a c e area of a q u i f e r , at p o i n t (x,y) [M . L - ^ ] . L ( t ) i s obtained as an i n t e r m e d i a r y output from the unsaturated submodel ( S e c t i o n 2.3.3), f o r a s p e c i f i e d -2 amount M(J) of n i t r o g e n [M.L ] a p p l i e d i n excess of p l a n t requirements at year j and a v a i l a b l e f o r l e a c h i n g i n the form of n i t r a t e s at the end of the growing season. The term m (x,y) i s equal to the product (h(x,y) . rt • P) , cl where n i s the a q u i f e r p o r o s i t y and p i s the s p e c i f i c a g r a v i t y of the groundwater. 2.4.3 System s i m u l a t i o n Here again the system i s s i m u l a t e d u s i n g a com-S (x,y ,t) .= L ( t ) /m(x,y) S(x,y,t ) = 0 f o r ( x . y ) ^ ) f o r <x,y)£9> (2.35) 74. b i n a t i o n of a n a l y t i c a l and n u m e r i c a l methods, to s o l v e the water q u a l i t y t r a n s p o r t equation 2.31. For the i n s t a n t a n e o u s i n j e c t i o n of a u n i t mass of p o l l u t a n t at the o r i g i n 0 at time t=0, the s o l u t i o n to the system of equations 2.31 to 2.34 i s d e f i n e d by the two-d i m e n s i o n a l Green f u n c t i o n G ( x , y , t ) , r e p r e s e n t i n g the s o l u t e mass d i s t r i b u t i o n per u n i t s u r f a c e area of a q u i f e r ( F r i e d , 1975). 2 2 r , N 1 r (x-X) y , G(x,y,t) = Yn e x P [ _ 477~x To~X] (2.36) 4 n x ( a L a T ) 1 / z * a L A . * a T * where X = . t i s the d i s t a n c e t r a v e l l e d by water s i n c e i n j e c t i o n of the substance. The r e s u l t i n g s o l u t e c o n c e n t r a t i o n i n groundwater i s : c Q ( x , y , t ) = G(x,y,t)/m(x,y). (2.37) I f a u n i t mass per u n i t area i s i n j e c t e d at time t=0 u n i f o r m l y over the area^P, the response i s o b t a i n e d by i n t e g r a t i n g the Green f u n c t i o n , 2.36, over the domain Ch J c o n s i d e r e d as a set of p o i n t s o u r c e s : C l ( x , y , t ) = m ( x , y ) _ 1 . //G (x-S , y-£,t) d£ d£ (2.38) JJU,E)C<P The f u n c t i o n c ^ ( x , y , t ) i s c a l l e d impulse response of the system, s i n c e i t d e s c r i b e s the c o n c e n t r a t i o n f i e l d r e s u l t i n g from an impulse l o a d i n g f u n c t i o n L d e f i n e d as: L (t) = 1 f o r t = 0 ) ) (2.39) L ( t ) = 0 f o r t 4 0 ) 75. For a r e c t a n g u l a r source of dimensions L and L centered x y at p o i n t 0, equation 2.38 can be w r i t t e n . J+Lx f+Ly -1 I 2 c 1(x,y,t)=m(x,y) G(x -C ,y -C,t )dc :dC (2.40) 2 This e x p r e s s i o n can be i n t e g r a t e d a n a l y t i c a l l y by separa-t i n g the v a r i a b l e £ and £ , ... m(x ,y) ^ (x,y,t)= 7 rTo« 1 4 n x ( a L a T ) 1 / z 'VLx 2 AJ Lx **+Ly 2 2 (2.41) where x = V, . t . n The v a r i a b l e t r a n s f o r m a t i o n s x - X - Lx/2 u = /2 o, X u+ = X + Lx/2 / 2 ^ X v = y - Ly/2 (2.42) 76. y i e l d c . ( x , y , t ) = 2 ^ L > » A T T V / -1 4HX(ct L a T ) 1/2* exp (- p dC.I e x p ( - | i ) d C ( 2 > 4 3 ) w h i c h c a n be e x p r e s s e d i n t e r m s o f t h e c o m p l e m e n t a r y e r r o r f u n c t i o n E r f c : c, ( x , y , t ) = m(x,y) -1 . [ E r f c ( u _ ) - E r f c ( u ) ] . [ E r f c ( v _ ) - E r f c ( v ) ] (2.44) F o r t h e g e n e r a l p r o b l e m o f a c o n t i n u o u s ( b u t v a r i a b l e ) i n j e c t i o n r a t e L ( t ) p e r u n i t a r e a o f t h e r e c t a n g u -l a r s o u r c e ^ p e r u n i t t i m e , t h e r e s u l t i n g c o n c e n t r a t i o n d i s t r i b u t i o n c ( x , y , t ) i s o b t a i n e d by i n t e g r a t i o n o v e r t i m e o f t h e i m p u l s e r e s p o n s e f u n c t i o n c ^ w e i g h t e d by t h e l o a d i n g f u n c t i o n L ( t ) t c ( r c x , y , t ) = L ( T ) . c 1 ( x , y , t - T ) d x = t — r ) d x = | L ( t - T ) . c 1 ( x , y , T ) d T (2.45) C o m b i n i n g w i t h e q u a t i o n 2.44: t c ( x , y , t ) m ( x , y ) -1 L ( t - x ) . [ E r f c ( u _ ) - E r f c ( u + ) J . . [ E r f c ( v ) - E r f c ( v , ) ] . d x o — + (2.46) w h e r e u , u v , and v a r e d e f i n e d by e q u a t i o n s 2.42 i n w h i c h — + , — + X = V u . T. n 77 . T h i s e x p r e s s i o n cannot g e n e r a l l y be i n t e g r a t e d a n a l y t i c a l l y , and must t h e r e f o r e be approximated by summation of f i n i t e elements on the d i g i t a l computer. A time step At = 1 week (7 days) was chosen f o r the n u m e r i c a l procedure. In f i n i t e element form, equation 2.45 i s w r i t t e n : i = t / A t c ( x , y , t ) = ^ A t * L ( t " T i ) ' c 1 ( x , y , T i ) (2.47) i = l w ith T = ( i - 1/2) At, i C N c^(x,y,T^) i s d e f i n e d by equation 2.44. Let us r e c a l l that L ( t ) i s o b t a i n e d a-s an output from the u n s a t u r a t e d submodel, f o r a s p e c i f i e d amount M(J) of n i t r o g e n a v a i l a b l e f o r l e a c h i n g i n the form of n i t r a t e at the end of the J t h growing season. The s i m u l a t i o n flow chart f o r Model 2 i s shown i n F i g u r e 2.2. In chapter 4 (Model A p p l i c a t i o n to the study a r e a ) , i t w i l l be shown how Model 1 can be used to d e r i v e an estimate of M(J) from groundwater samples c o l l e c t e d during the J t h l e a c h i n g season ( s h o r t term, l o c a l s c a l e problem). This estimate can then be fed as an i n p u t to Model 2, to simulate long-term n i t r a t e r e d i s t r i b u t i o n i n the a q u i f e r . DECLARE PARAMETERS AND TIME STEP AT 1 SELECT X/ Y, T 1 I N I T I A L I S E . J (YEAR NUMBER) AND I (STEP NUMBER) I T T = d-1/2). AT No Yes SOIL NITRATE-N M(j) LEACHING L ( T ± ) c = c + A T - L ( T 1 ) . C 1 ( X , Y , T - T 1 ) I 1 = 1 + 1 No CONCENTRATION c ( X , Y , T ) = C Yes NITRATE-N CONCENTRATION DISTRIBUTION 78, J = J + 1 UNSATURATED COMPONENT • Weather data IMPULSE RESPONSE C i U / Y / T ) F i g u r e 2.2: S i m u l a t i o n flow chart f o r Model 2. 79. 3. FIELD STUDY 3 .1 S i t e S e l e c t i o n A shallow unconfined a q u i f e r on the Langley Upland i n the Lower F r a s e r V a l l e y of B.C. ( F i g u r e 3.1) was s e l e c t e d as p r e s e n t i n g a p o t e n t i a l l y acute n i t r o g e n p o l l u t i o n problem. The groundwater resource i s of major economic importance s i n c e i t serves as the s o l e source of water f o r a r u r a l community of r e s i d e n c e s and c o n f i n e d l i v e s t o c k o p e r a t i o n s i n c l o s e p r o x i m i t y . An extreme of 60 ppm NO^-N was recorded i n January 1974 i n a domestic w e l l n e i g h b o u r i n g a p o u l t r y e n t e r p r i s e , ( H a l s t e a d , 1976). The development of a l t e r n a t i v e water s u p p l i e s , i n c l u d i n g deeper c o n f i n e d a q u i f e r s (over 100 m d r i l l i n g r e q u i r e d ) as w e l l as the Langley m u n i c i p a l d i s t r i b u -t i o n system, would i n v o l v e c o n s i d e r a b l e c a p i t a l investments. The unconfined a q u i f e r system p r e s e n t s a number of fe a t u r e s that make i t t y p i c a l of p o l l u t i o n - s e n s i t i v e b a s i n s : a compacted r e s t r i c t i n g l a y e r i s encountered at s m a l l depth; the flow i s predominantly l a t e r a l i n the s a t u r a t e d zone ; - the coarse porous m a t e r i a l i s i d e a l from a water y i e l d p o i n t of view, but has l i t t l e f i l t e r i n g c a p a c i t y ; the t o p s o i l has a low water h o l d i n g c a p a c i t y ; the water t a b l e shows wide s e a s o n a l f l u c t u a t i o n s and f a s t response to i n d i v i d u a l hydrometeorplo-g i c a l events; suburban growth without concurrent development 80. L E G E N D *"» SPRING • MONITORED DOMESTIC WELL f777i PLOT ( The arrow shows the d irec t ion of groundwater movement ) 7 7 " IMPERMEABLE STONY CLAY LAYER -2- HATER TABLE F i g u r e 3.1: Map and c r o s s - s e c t i o n of the a q u i f e r system. 81. of water and sewer systems encroaches i n t o i n t e n s i v e a g r i c u l t u r a l a c t i v i t i e s g e n e r a t i n g l a r g e amounts of organic wastes. One such a c t i v i t y i s the i n d u s t r i a l r a i s i n g of commercial hogs i n a c o n f i n e d environment, w i t h a l l feed i n p u t s being imported from o u t s i d e sources. T h i s t r a n s -l a t e s i n t o a gross i n b a l a n c e whereby 70 to 80% of the n i t r o g e n contained i n the feed ( P h i l l i p s , 1967 ; Yeck et a l . 1975) i s r e j e c t e d with the animal wastes and allowed to accumulate i n the immediate environment of the p r o d u c t i o n u n i t , without being- r e c y c l e d back to the animals. Neglec-t i n g m a r g i n a l forms of n i t r o g e n export from the farm, maintenance of a c c e p t a b l e n i t r o g e n l e v e l s i n the s u r r o u n -ding a i r , s o i l s , and waters w i l l t h e r e f o r e depend on the magnitude of gaseous, s o l i d and s o l u t e f l u x e s w i t h i n and out of the b a s i n . A f i e l d study was conducted to s p e c i f i c a l l y i n v e s t i g a t e movement i n the subsurface l i q u i d phase. A swine p r o d u c t i o n u n i t (R & H Swine Fa r m s ) * , l o c a t e d on the upper reaches of the a q u i f e r system (Eigure 3.1) was s e l e c -ted f o r t h i s purpose. P r i o r to t h i s r e s e a r c h , a t h r e e - y e a r groundwater m o n i t o r i n g program on the farm r e v e a l e d f l u c t u a t i o n s of n i t r a t e - N c o n c e n t r a t i o n i n w e l l water up to l e v e l s above the recommended 10 ppm l i m i t . F i n d i n g s were r e p o r t e d by S t a l e y et a l . (1976). Together with o t h e r water q u a l i t y s t u d i e s i n the watershed, they are summarized i n * 5075 - 256th S t . , A l d e r g r o v e , B.C. 82 . S e c t i o n 3.3 e n t i t l e d "Reseach Background", f o l l o w i n g a g e n e r a l s i t e d e s c r i p t i o n ( S e c t i o n 3.2). The s i t e - s p e c i f i c o b j e c t i v e s of the study are then r e s t a t e d i n S e c t i o n 3.4. S e c t i o n 3.5 d e s c r i b e s the p l o t which w i l l s e r v e as the b a s i s f o r model a p p l i c a t i o n to the study area. The m a t e r i a l s and methods f o r data a c q u i s i t i o n are o u t l i n e d i n S e c t i o n 3.5 F i n a l l y , these data are analysed and d i s c u s s e d i n S e c t i o n 3.7, p r i o r to i n c o r p o r a t i o n i n t o the models (Chapter 4). 3.2 S i t e D e s c r i p t i o n 3.2.1 Climate This Upland area of the c e n t r a l Lower F r a s e r V a l l e y i s c h a r a c t e r i z e d by. m i l d wet w i n t e r s and g e n e r a l l y c o o l dry summers. Y e a r l y p r e c i p i t a t i o n ranges from 1.0 to 2.0 meters, c o n s i s t i n g mostly of r a i n f a l l with l a r g e i n t e n s i t y i n the f a l l and e a r l y w i n t e r p e r i o d . The widest temperature range i s from -6^C (January) to 32°C ( J u l y ) . (Data from B a i e r et a l . , 1969, f o r the Abbotsford l o c a t i o n ) . The estimated mean f o r y e a r l y p o t e n t i a l e v a p o t r a n s p i r a t i o n i s 58 cm, with a p o s s i b l e v a r i a t i o n of + 20%. 3.2.2 Geology The a q u i f e r i s composed of w e l l - s o r t e d A b b o t s f o r d g l a c i a l outwash m a t e r i a l (sand, g r a v e l and stones) d e p o s i t e d at the end of the l a s t g l a c i a t i o n by meltwater f l o w i n g west-ward, i n a d e l t a - f o r m i n g p r o c e s s . The t h i c k n e s s of the d e p o s i t v a r i e s from approximately 3-4m (10-15 f t ) along the upper boundary to more than 35m (120 f t ) at what was the. land/ocean i n t e r f a c e at the time of d e p o s i t i o n (see F i g u r e 3.1). The s i z e of p a r t i c l e s decreases from stones and g r a v e l s near the e a s t e r n boundary to f i n e beach sands along the western 'edge 1. The u n d e r l y i n g stratum i s an u n c o n s o l i d a t e d , compacted, p o o r l y s o r t e d g l a c i o - m a r i n e d e p o s i t , r e f e r r e d to as Whatcom Stony c l a y . I t was con-s i d e r e d as an impervious l a y e r f o r the purpose of t h i s study, and c o n s t i t u t e s the predominant s u r f a c e m a t e r i a l i n the surrounding area of the b a s i n . Recharge of groundwater storage i s achieved by r a i n f a l l i n f i l t r a t i o n over the e s s e n t i a l l y l e v e l outwash ar e a . C o n t r i b u t i o n of r u n o f f from the upstream area i s harder to q u a n t i f y but i s probably s i g n i f i c a n t . N a t u r a l d i s c h a r g e occurs by means of s p r i n g s along the western edge of the a q u i f e r where the water t a b l e meets the steep land s u r f a c e . Groundwater a l s o feeds the Salmon R i v e r , which carved a deep bed i n t o the formation down to the stony c l a y l a y e r . The gen e r a l d i r e c t i o n of groundwater movement roughly f o l l o w s the n o r t h w e s t e r l y course of the r i v e r and i s i n d i c a t e d i n Figure 3.1. Average water t a b l e s l o p e s of 0.011 m/m (60 f t / m i l e ) were r e p o r t e d by H a l s t e a d (1957) . 3.2.3 Land Use Development of the area has brought r e l a t i v e l y l i t t l e change to the h y d r o l o g i c balance of the r e s e r v o i r , as water tapped from w e l l s i s subsequently r e t u r n e d to the system i n the form of waste water. Human wastes are d i s -84. posed of by s e p t i c tanks; animal wastes are mostly spread on g r a s s l a n d . The most s i g n i f i c a n t impact on the water budget probably c o n s i s t s of an i n c r e a s e i n the evapotrans-p i r a t i o n term. Of g r e a t e r concern i s the e f f e c t of man's a c t i v i t y on the chemical n u t r i e n t c y c l e s i n the system. S o i l s on top of the a q u i f e r are g e n e r a l l y shallow and w e l l d r a i n e d , having medium to coarse t e x t u r e . A l a r g e f r a c t i o n of the l a n d remains s p a r s e l y wooded. Crop pro-d u c t i o n i s l i m i t e d to b e r r i e s and no l o n g e r c o n s t i t u t e s a major a c t i v i t y i n the area. 3 ..3 Research Background N i t r o g e n analyses of swine waste and forage from the farm are summarized i n Table 3.1. Water was c o l l e c t e d through two c o n s e c u t i v e w i n t e r s from s i x l o c a t i o n s beneath a 2.5 ha (6.5 acre) pasture area r e c e i v i n g heavy manure a p p l i c a t i o n s i n the immediate neighbourhood of the swine p r o d u c t i o n f a c i l i t i e s . Samples were a l s o taken from the three surrounding w e l l s ( F i g u r e 3.1). Data f o r e i g h t water q u a l i t y parameters (pH, COD, T o t a l K j e l d a h l - , Ammonium-and N i t r a t e - N i t r o g e n , C h l o r i d e , T o t a l - a n d Ortho-Phosphate) were analysed and r e p o r t e d by S t a l e y et a l . (1976).They r e v e a l e d h i g h n i t r o g e n content of groundwater, but f a i l e d to c l e a r l y evidence the c o n t r i b u t i o n of the waste s p r e a d i n g o p e r a t i o n . T h i s was due both to the s h o r t l e n g t h o f time (5 months) when sampling was p o s s i b l e , and to the masking e f f e c t of a b u r i a l p i t immediately upstream from the TABLE 3.1 NITROGEN ANALYSES OF SWINE WASTE AND FORAGE CROP AT R & H FARMS. 1974 1975 1976 TKN W — 0.11 0.28 (SD) — 0.02 0.05 Waste* (M) — 0.086 0.12 N H 3 - N ( S D ) — 0 .015 0.02 TKN 2.1 2.4 2.5 Forage ** P r o t e i n 13.3 15.0 15.6 * A l l values expressed as % wet weight (M) Mean (SD) Standard D e v i a t i o n ** A l l samples taken i n e a r l y June, values expressed as % dry matter. 86. sampling p o i n t s . While n i t r o g e n was mostly i n the form of n i t r a t e s i n the domestic w e l l s , i t was s u r p r i s i n g l y found i n g r e a t e r q u a n t i t i e s i n the ammonium and o r g a n i c forms i n the 'pasture' samples. These compounds were a t t r i b u t e d to the b u r i a l p i t . Phosphates remained very low, but h i g h COD l e v e l s confirmed the c o n c l u s i o n that the major source of p o l l u t a n t s at t h i s s i t e was l o c a t e d beneath the biochemi-c a l l y a c t i v e t o p s o i l l a y e r . The c o n s i s t e n t p a t t e r n of sharp N c o n c e n t r a t i o n decay ( F i g u r e 3.2) observed i n the pasture samples from December to A p r i l suggested the p o s s i b l e occurrence of s i g n i f i c a n t n i t r o g e n l o s s from the t o p s o i l , as shock loads i n the f a l l p r i o r to the i n i t i a t i o n of sampling. The sharp r i s e of the water t a b l e i n the f a l l p e r i o d evidences con-s i d e r a b l e downward water p e r c o l a t i o n capable of l e a c h i n g a l a r g e f r a c t i o n of the d i s s o l v e d n i t r o g e n from the root zone. Under the c l i m a t i c c o n d i t i o n s of the Lower F r a s e r V a l l e y , B.C., c h a r a c t e r i z e d by heavy f a l l r a i n s , the f a l l appears as the most c r i t i c a l p e r i o d from a l e a c h i n g stand-p o i n t , as l a r g e amounts of mobile n i t r a t e s have been pro-duced by m i c r o b i a l a c t i v i t y over the summer, whereas p l a n t uptake, both of water and n u t r i e n t s , has v i r t u a l l y ceased (Bomke, 1976). From the p l o t of e q u i c o n c e n t r a t i o n l i n e s over t h i s p asture area, i t was concluded ( S t a l e y et a l . 1976) that groundwater flows i n a n o r t h w e s t e r l y d i r e c t i o n i n the e a s t e r n s e c t i o n of the a q u i f e r . 301 201 z 10 © 0 © •*• o 8 7 9 0 % C O N F I D E N C E I N T E R V A L S Jm NOV D E C J A N F E B MAR APR MONTH , 15. 12 Each point i s the mean from 6 piezometers + Season 1 ( 1 9 7 3 - 1 9 7 4 ) O Season 2 ( 1 9 7 4 - 1 9 7 5 ) n i e i © +• © I 9 0 % C O N F I D E N C E INTERVALS + © NOV D E C J A N F E B MONTH MAR APR J 4- © ure 3 . 2 : V a r i a t i o n s of mean n i t r o g e n c o n c e n t r a t i o n s i n g r o u n d w a t e r , f o r the w i n t e r s e a s o n s 1 9 7 3 to 1 9 7 5 ( a f t e r S t a l e y e t a l . , 19 7 6 ) . 88. N i t r a t e - N c o n c e n t r a t i o n s i n the domestic w e l l s f l u c t u a t e d between 2.0 and 10.5 ppm without any apparent s e a s o n a l p a t t e r n or b u i l d - u p over the 3-year r e c o r d . In a comprehensive i n v e s t i g a t i o n of the s u r f a c e water q u a l i t y of the Salmon River watershed, Beale (1976) concluded that the sampling s t a t i o n l o c a t e d at p o i n t R on the r i v e r ( F i g u r e 3.1) y i e l d e d the h i g h e s t TKN and n i t r a t e - N values (19.0 and 8.3 ppm, r e s p e c t i v e l y ) together with the l a r g e s t v a r i a t i o n s (lows: 0.22 and 0.4 ppm). N i t r a t e - N was found s i g n i f i c a n t l y c o r r e l a t e d with g l a c i a l outwash m a t e r i a l s , both at high and low streamflows. Over the whole watershed, TKN and NO^-N were c o n s i s t e n t l y h i g h e r at low streamflows than at h i g h (> 750 c f s ) streamflows, i n d i c a t i n g that groundwater d i s c h a r g e might be a g r e a t e r c o n t r i b u t o r than storm r u n o f f . Beale (1976) a l s o conducted a n a l y s i s of chemical i n p u t from atmospheric p r e c i p i t a t i o n i n the b a s i n . TKN and NO^-N c o n c e n t r a t i o n s i n r a i n f a l l samples remained below 1.7 ppm and 1.9 ppm, r e s p e c t i v e l y . I t was concluded that more d e t a i l e d i n f o r m a t i o n on groundwater c h a r a c t e r i s t i c s i s needed to i d e n t i f y s p e c i f i c p o i n t and non-point sources of water p o l l u t a n t s . 3.4 Obj e c t i v e s With t h i s background, i t was decided that emphasis of t h i s p r o j e c t should be put on i n v e s t i g a t i o n of water q u a l i t y d u r i n g the r e c h a r g e p e r i o d , when l e a c h i n g i s l i k e l y 89. to occur. T h i s 'wet season' s t a r t s i n the f a l l , when p r e -c i p i t a t i o n f i r s t exceeds d e c l i n i n g e v a p o t r a n s p i r a t i o n and s o i l s t o r a g e . This p e r i o d roughly corresponds to the r i s e of the water t a b l e , from i t s s e a s o n a l low to i t s w i n t e r h i g h l e v e l . The o b j e c t i v e here was to q u a n t i f y the y e a r l y n i t r o g e n c o n t r i b u t i o n to groundwater from the waste s p r e a d i n g p r a c t i c e . Because of the expected v e r t i c a l s t r a t i f i c a t i o n generated by the p o l l u t i o n f r o n t s i n the p o r t i o n of a q u i f e r d i r e c t l y beneath the d i s p o s a l s i t e (e.g. see John et a l . , 1977; S p a l d i n g et a l . , 1976) i t was a n t i c i p a t e d that t h i s e s timate could not be o b t a i n e d d i r e c t l y by simple computation from experimental data. Such an e s t i m a t i o n , however, would be p o s s i b l e u s i n g Model 1 to s i m u l a t e the v e r t i c a l s u b s urface n i t r a t e movement d u r i n g the recharge p e r i o d . The second o b j e c t i v e was to attempt an impact assessment of these s u c c e s s i v e y e a r l y p o l l u t i o n f r o n t s on the water q u a l i t y i n the whole a q u i f e r . A p a r t i c u l a r d i f f i c u l t y here l i e s i n the slow movement of groundwater r e l a t i v e to the a q u i f e r dimensions, which makes i t i m p o s s i b l e to observe both the l e a c h i n g of a substance and i t s subsequent r e c o v e r y i n a w e l l , w i t h i n the time framework of t h i s study. S t a l e y et a l . (1976) emphasized the l a c k of d i r e c t c o r r e l a t i o n between water samples from the pasture and from the w e l l s , over the two years of r e c o r d . S e v e r a l years or decades f o r n i t r a t e r e s i d e n c e 90. time i n a q u i f e r s have been r e p o r t e d i n the l i t e r a t u r e (e.g. P r a t t , 1972). Long term water q u a l i t y p r e d i c t i o n s p r o v i d e d by Model 2 should t h e r e f o r e be regarded as s p e c u l a t i v e i n d i c a t i o n s , s i n c e t e s t i n g i s beyond the scope of t h i s p r o j e c t . 3.5 The P l o t 3.5.1 Des c r i p t i o n A r e c e n t l y c l e a r e d 4.5 ha (11 acre) pasture s i t e at R & H Swine Farms ( F i g u r e 3.3) was s e l e c t e d to i n v e s t i -gate the impact of animal waste management p r a c t i c e s on groundwater q u a l i t y . Topography of the s i t e i s l e v e l to g e n t l y u n d u l a t i n g , with hummocky m i c r o r e l i e f caused by u p r o o t i n g t r e e s i n u n c l e a r e d areas. S c a t t e r e d a l d e r s , cedars and Douglas f i r s are p r e s e n t on the p l o t . The s o i l i s a s i l t loam of the Abbotsford s e r i e s , composed of shallow a e o l i a n d e p o s i t s and/or slopewash eroded from surrounding g l a c i o - m a r i n e d e p o s i t s . G r a v e l and stones from the u n d e r l y i n g outwash were brought to the s u r -face by uprooted t r e e s and land c l e a r i n g (Luttmerding and Sprout, 1966). Numerous hard c o n c r e t i o n s are found i n the upper p a r t of the column. The s o i l depth i s 30 to 45 cm (1.0 to 1.5 f t ) with few grass roots below the r e l a t i v e l y sharp f i n e / c o a r s e i n t e r f a c e . The s o i l has a h i g h i n f i l t r a t i o n c a p a c i t y but a low water h o l d i n g c a p a c i t y , and d r a i n a g e i s w e l l to r a p i d a c c o r d i n g to the BCMA c l a s s i f i c a t i o n (Luttmerding and Sprout, 1966). The water t a b l e f l u c t u a t e s widely through-9 1 F i g u r e 3.3: Lay-out of the p l o t ( s c a l e : 1/2000). 92. out the y e a r from at or near the s u r f a c e d u r i n g the w i n t e r to below 2.5 m d u r i n g the summer. Approximately 0.2 ha (0.5 acre) of the pasture area i s submerged f o r h a l f o f the year. 3.5.2 Land Management L i q u i d swine waste i s a p p l i e d to t h i s f i e l d twice a week du r i n g the w i n t e r (January to A p r i l , i n c l u s i v e ) by means of a l a r g e spray i r r i g a t i o n 'gun'. The manure i s a n a e r o b i c a l l y s t o r e d and c o n t a i n s approximately 0.2% n i t r o g e n i n the storage p i t (Table 3.1). 3 Roughly 50 m (13,000 g a l l o n s ) of s l u r r y are spread at each s e t t i n g , over a .35 ha c i r c u l a r area. This amounts to a t o t a l n i t r o g e n l o a d i n g of over 800 kg/ha durin g the dormant season. Over h a l f of t h i s amount may be " i n the form of ammonia. Although t h i s might r e s u l t i n s i g n i f i c a n t v o l a t i l i z a t i o n l o s s e s , a f i e l d study by S t a l e y (1973) showed that l o s s e s are hard to q u a n t i f y and suggested that they probably are of l e s s e r importance i n the w i n t e r . Minor amounts are a p p l i e d i n the summer. No commercial f e r t i l i z e r has so f a r been been a p p l i e d on the p l o t . The p l a n t cover c o n s i s t s of a g r a s s / c l o v e r mixture. Non-uniformity of manure a p p l i c a t i o n caused l o c a l 'burning' of the forage cover. The p a s t u r e i s i n t e r -m i t t e n t l y grazed by young beef c a t t l e and sheep, no crop being m e c h a n i c a l l y harvested from the f i e l d . 93. N i t r o g e n c o n v e r s i o n e f f i c i e n c i e s range from 15 to 20% f o r c a l v e s and c a t t l e and from only 5 to 15% f o r sheep and lambs ( P h i l l i p s , 1967; Yeck, 1975). This means that 80 to 95% of the forage n i t r o g e n i n g e s t e d by the animals i s immediately r e t u r n e d to the s o i l as manure. The lowest c o n v e r s i o n e f f i c i e n c y values are g e n e r a l l y achieved by f r e e -f o r a g i n g and stock animals. E s t i m a t i n g the average e f f i c i -ency at 15% and the y e a r l y n i t r o g e n uptake by the forage crop at 200 kg N/ha (8 tonnes/ha of dry matter* at 2.5% average N c o n t e n t ) , the a c t u a l net removal of n i t r o g e n from the p l o t i n the form of meat i s only 30 kg/ha/year. This r e p r e s e n t s a very small f r a c t i o n (< 4%) of the y e a r l y n i t r o g e n i n p u t to the p l o t as swine waste, and can f o r a l l i n t e n t s and purposes be n e g l e c t e d i n the s o i l n i t r o g e n balance f o r the p l o t . Consequently, the h i g h manure l o a d i n g r a t e may r e s u l t i n a l a r g e n i t r o g e n b u i l d - u p i n the s o i l and/or a very s i g n i f i c a n t n i t r o g e n l o s s to groundwater. A s o i l and groundwater sampling program was set up to i n v e s t i g a t e these two processes and p r o v i d e a data base f o r a p p l i c a t i o n of the two modela to the s i t e . * B.C. M i n i s t r y of A g r i c u l t u r e , Farm Economics Branch, (May, 1977) "Grass-legume, greenchop, s i l a g e and hay pro-d u c t i o n i n the Western F r a s e r V a l l e y " (Producers' consen-sus c o s t s and r e t u r n s ) CDS 211. 94. 3.6 Data A c q u i s i t i o n D a i l y p r e c i p i t a t i o n , minimum and maximum tempera-tures were ob t a i n e d from the Aldergrove m e t e o r o l o g i c a l s t a t i o n (Environment Canada). D a i l y sunshine records were a v a i l a b l e at the Abbotsford I n t e r n a t i o n a l A i r p o r t . 3.6.1 S o i l s S o i l samples were c o l l e c t e d with a hand-driven s o i l auger at s i x l o c a t i o n s on the p l o t on March 11 and November 27, 1976, and at one l o c a t i o n i n an un c l e a r e d area on March 11. Samples were taken with a 15 cm depth i n t e r v a l on the p l o t , down to 30 or 45 cm depending on the depth of the coarse g r a v e l l a y e r . Sampling was t r i p l i c a t e d , the samples were then f r o z e n , composited and subsampled f o r a n a l y s i s . They were analysed f o r moisture content, o r g a n i c matter content, T o t a l K j e l d a h l N i t r o g e n (TKN), ammonium-N and n i t r a t e - N . Ammonium-N and n i t r a t e - N were e x t r a c t e d a c c o r d i n g to standard methods (Black, 1965) and were analysed on a Technicon Autoanalyser II (Technicon I n d u s t r i a l S3 rstems, 1971). TKN was determined u s i n g a b l o c k d i g e s t e r and the Technicon Autoanalyser I I , a c c o r d i n g to the method of Schuman et a l . (1973). To convert n i t r o g e n c o n c e n t r a t i o n s i n t o a c t u a l amounts i n s o i l s l i c e s and moisture contents from a weight b a s i s to a volume b a s i s , s o i l samples were a l s o analysed f o r p a r t i c l e d e n s i t y by the pycnometer method (3lack,1965). 95. The d e n s i t y r a t i o d i s d e f i n e d as the r a t i o of the s o i l P p a r t i c l e d e n s i t y to the d e n s i t y of d i s t i l l e d water at 23°C. 3.6.2 Groundwater In February 1976, 3.75 m (12.5 f t ) long piezome-t e r s were i n s t a l l e d with a backhoe at f i v e l o c a t i o n s on the p l o t ( F i g u r e 3.3), down to an average depth of 3.0 m (10 f t ) . They were i n i t i a l l y pumped out f o r f l u s h i n g a c t i o n , and subsequently p r o v i d e d year-round groundwater samples. An amount of water e q u i v a l e n t to the volumn present i n the piezometer was removed p r i o r to each sampling. Samples were taken with a hand pump, at 23 dates from May 1976 to A p r i l 1977. Sampling i n t e r v a l s were scheduled to range from 1 week d u r i n g the s e n s i t i v e October to January p e r i o d , to 3 weeks d u r i n g the s p r i n g and summer. Background con-c e n t r a t i o n s were obtained from the three domestic w e l l s s u r r o unding the s i t e ( F i g u r e 3.1). A l l samples were analysed f o r pH and chemical oxygen demand (COD) a c c o r d i n g to standard methods (APHA, 1971), and f o r c h l o r i d e , n i t r a t e - N , ammonium-N and TKN on the Technicon Autoanaly-ser I I . A permanent r e c o r d of the water t a b l e f l u c t u a t i o n s was p r o v i d e d by a stage r e c o r d e r i n s t a l l e d i n a A.2 m (14 f t ) deep w e l l ( r e f e r r e d to as 'gauge w e l l ' on F i g u r e 3.3). An e x t e n s i v e water t a b l e survey c o n s i s t i n g of depth measure-ments at a l l w e l l s and piezometers was i n i t i a t e d at the s t a r t of the water t a b l e r i s e , and was performed at a l l sampling 96. dates from November to February. H y d r a u l i c head d i s t r i b u t i o n s were ob t a i n e d a f t e r land s u r v e y i n g the farm p r o p e r t y . A pump t e s t was performed i n A p r i l 1976 at the gauge w e l l , to determine the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y of the outwash m a t e r i a l . Water was pumped out at a constant r a t e u n t i l the drawdown i n the w e l l reached e q u i l i b r i u m , at 1.43m (4.75 f t ) below the i n i t i a l l e v e l . Pumping was then stopped and the water t a b l e recovery i n the w e l l was monitored as a f u n c t i o n of time. 3.7 Data A n a l y s i s and D i s c u s s i o n 3.7.1 S o i l s The p a r t i c l e d e n s i t y a n a l y s i s y i e l d e d a mean value f o r the d e n s i t y r a t i o d of 2.62 and a standard d e v i a t i o n of P 0.07. The r a t i o d^ decreased q u a s i - l i n e a r l y with i n c r e a s i n g o r g a n i c matter. The p o r o s i t y of the s i l t loam was estima-ted at n = 0.56 from the data p u b l i s h e d by Nagpal and De V r i e s (1976), and the bulk d e n s i t y d^ was then c a l c u l a t e d as: d b = d p . (1-n) - 1.15 (3.1) Th i s estimate was l a t e r confirmed by comparing the moisture contents 0 and MC on November 27, 1976, r e s p e c t i v e l y o b t a i n e d on a v o l u m e t r i c b a s i s by s i m u l a t i o n ( S e c t i o n 4.1) and on a weight b a s i s by experimental d e t e r m i n a t i o n . For the three sets of samples ( u n d i s t u r b e d p r o f i l e -springy p l o t - s p r i n g , p l o t - f a l l ) , l a b o r a t o r y r e s u l t s are summarized i n Table 3.2 by the means and standard d e v i a t i o n s , TABLE 3.2 ~ MOISTURE, ORGANIC MATTER AND NITROGEN ANALYSES OF SOIL PROFILES. H o r i z o n t Mois t u r e * * 7 Organ!c 7 Matter* TKN* ppm NH.-N* 4 ppm N0 3~N* ppm (M) (SD) fo (M) (SD) (M) (SD) (M) (SD) (M) (SD) ^  Undisturbed L-H (0-8) 56. 39. 0 5660. 88. 6 31.8 P r o f i l e Ah( 8^20) 42. 15.5 1580. 31. 2 2.8 Ae(20-30) 38. 8.1 473. 36.9 14. 5 Bf(30-35) 33. 7.5 528. 142. 48. 2 Spring C (35-45) 20. 1.9 284. 10.2 3.8 P l o t 0-15 34. 3.3 12.0 1.0 1193. 636. 76.6 64. 36. 6 27 . 15-30 33. 3.8 9.1 1.3 512. 139. 38. 9 46. 5.6 4.8 3 0-4 5 30. 5.0 6.0 1.8 405. 63. 9.7 1.6 7.2 8.2 Spring A l l samples 32. 7 3.9 9.7 2.6 775. 530. 48.1 54. 18.3 23. P l o t 0-15 30. 2.8 10.7 2 . 5 1655. 890. 13.4 5.2 17.3 3.3 15-30 26. 5.8 9.1 2.4 526. 152. 17. 3 6.9 13.0 4.7 30-45 28. 5 . 0 9.8 3.6 606. 390. 19. 2 10.3 24.4 26. F a l l A l l samples 27. 7 4.4 9.9 2.4 970. 760. 15. 1 7.7 17.5 11. * dry weight b a s i s ** wet weight b a s i s (M) Mean (SD) Standard d e v i a t i o n , t depths i n cm. 98. on a weight b a s i s , f o r the f i v e f o l l o w i n g parameters: mois-ture content (MC), o r g a n i c matter content COM), TKN, ammonium-N and n i t r a t e - N . I t can be seen that a l l of the. above c h a r a c t e r i s t i c s show c o n s i d e r a b l y l e s s v a r i a t i o n with depth i n the p l o t samples than i n the u n d i s t u r b e d p r o f i l e . In p a r t i c u l a r , the downward decrease of o r g a n i c -matter content i s e v i d e n t l y s m a l l e r i n the p l o t than i n the un d i s t u r b e d p r o f i l e , presumably as a r e s u l t of land c l e a r i n g and l e v e l i n g . The impact of t u r n i n g the land to a g r i c u l t u r e can a l s o c l e a r l y be seen on the moisture content and TKN v a r i a b l e s , which show very h i g h c o r r e l a t i o n with the organic matter content. While moisture content d i f f e r e n c e s between sampling dates can be detected i n the p l o t , the v a r i a t i o n s with depth are not s i g n i f i c a n t ; t h e r e f o r e , i t i s not unreasonable to assume uniform moisture content i n the root zone, during wet p e r i o d s . Since no s i g n i f i c a n t d i f f e r e n c e s i n o r g a n i c matter or TKN can be observed between s p r i n g and f a l l , the data do not allow q u a n t i f i c a t i o n of net m i n e r a l i z a t i o n over the growing season. On the other hand, i t i n d i c a t e s a l o s s of ammonium in the upper l a y e r s of the p l o t between the sampling dates. Since ammonia v o l a t i l i z a t i o n i s probably s m a l l i n t h i s medium a c i d s o i l CpH 5.5 to 6.0), t h i s d e c l i n e shows that m i n e r a l i z a t i o n of o r g a n i c n i t r o g e n proceeds at a slower o v e r a l l r a t e than crop uptake and n i t r i f i c a t i o n combined. 99. At the same time, no o v e r a l l gain of n i t r a t e s can be detec-ted i n the p r o f i l e , and some downward n i t r a t e movement seems apparent. This leads to the p o s s i b l e c o n c l u s i o n that the f a l l l e a c h i n g f r o n t might have occurred p r i o r to November 27 sampling; t h i s i n t e r p r e t a t i o n w i l l l a t e r be t e s t e d a g a i n s t output from l e a c h i n g s i m u l a t i o n . The shape of the s p r i n g n i t r a t e p r o f i l e i n the p l o t , with a c o n c e n t r a t i o n s i g n i f i -c a n t l y h i g h e r i n the top l a y e r , i n d i c a t e s that some n i t r i -f i c a t i o n has a l r e a d y taken p l a c e i n t h i s s u r f a c e h o r i z o n i n the e a r l y s p r i n g . Luttmerdingand Sprout (1966) noted that the s o i l s of the Abbotsford s e r i e s warm up e a r l y i n the s p r i n g . The low c o n c e n t r a t i o n s i n the lower l a y e r s r e f l e c t the n i t r a t e l o s s that occurred d u r i n g the p r e c e d i n g l e a c h i n g p e r i o d , and show that most of the n i t r a t e s can be removed from the s o i l by l e a c h i n g during the wet season. An i n t e r e s t i n g p a r t i c u l a r i t y of the m i n e r a l n i t r o g e n p r o f i l e at the u n d i s t u r b e d l o c a t i o n i s the c o n c e n t r a t i o n 'bulges', observed both f o r ammonium and n i t r a t e i n the B h o r i z o n . This suggests that l e a c h i n g is r e t a r d e d i n the undisturbed p r o f i l e compared to the p l o t p r o f i l e , as a r e s u l t of the l a r g e r water r e t e n t i o n c a p a c i t y of the former. Somewhat s u r p r i s i n g i s the depth to peak ammonium concen-t r a t i o n i n the u n d i s t u r b e d p r o f i l e , s i n c e the ammonium ion u s u a l l y e x h i b i t s l i t t l e m o b i l i t y i n the s o i l e n v i r o n -ment. However, i t should be kept i n mind that t h i s s o i l p r o f i l e , developed under humid c o n d i t i o n s , has been h i g h l y 100. weathered, as evidenced by the e l u v i a t e d Ae h o r i z o n . The Bf h o r i z o n t h e r e f o r e c o n t a i n s most of the c l a y p a r t i c l e s , and has the h i g h e s t c a t i o n exchange c a p a c i t y i n the u n d i s -turbed p r o f i l e . Beside an i n c r e a s e d l e a c h i n g r a t e i n the p l o t com-pared to the un d i s t u r b e d p r o f i l e , i t i s a l s o probable that m i n e r a l i z a t i o n proceeds at a f a s t e r r a t e as a r e s u l t of i n c r e a s e d a e r a t i o n and temperature a s s o c i a t e d with improved drainage and change i n v e g e t a t i o n . T h i s s o i l has only r e c e n t l y been turned to a g r i c u l t u r e , and a l o s s of o r g a n i c matter i s t h e r e f o r e to be expected; i t seems apparent from a comparison of o r g a n i c matter data. Stout and Burau (1967) estimated a n i t r o g e n l o s s from the org a n i c matter p o o l of 80 kg /ha/year over a 100 year p e r i o d f o r some t i l l e d g r a s s l a n d s o i l s . Because of i n c r e a s e d m i n e r a l i z a t i o n , n i t r i f i c a t i o n and l e a c h i n g , and decreased d e n i t r i f i c a t i o n due to b e t t e r a e r a t i o n , the re c e n t d i s t u r b a n c e of the n a t i v e s o i l might s i g n i f i c a n t l y i n c r e a s e the n i t r a t e l o s s to groundwater. In Texas, K r e i t l e r and Jones (1974) i d e n t i f i e d n a t u r a l s o i l n i t r o g e n as the cause of n i t r a t e contamination of groundwater under d r y l a n d farming. Table 3.3 shows the amounts of ammonium-N and n i t r a t e - N present i n the f i r s t two s o i l l a y e r s of the p l o t . The 166 kg/ha decrease of t o t a l mineral-N i n the top 30 cm (1 f t ) of s o i l observed between s p r i n g and f a l l i s TABLE 3.3 COMPUTED MINERAL -NITROGEN CONTENT (kg/ha) IN THE TOP 30 cm (1 f t ) OF PI,OT SOIL. NH N0 3 -N T o t a l 0 - 15 cm S : 131 S : 63 S : 194 F: 23 F: 30 F: 53 15 - 30 cm S : 67 S : 10 S : 77 F: 30 F: 22 F: 52 T o t a l S : 198 S : 73 S : 271 F: 53 F: 52 F: 105 S: =• s p r i n g F: - f a l l 102. a t t r i b u t a b l e both to crop uptake and to e a r l y f a l l l e a c h i n g . The t o t a l amount of n i t r o g e n removed i s a c t u a l l y g r e a t e r because of the mineral-N a d d i t i o n from m i n e r a l i z a t i o n of o r g a n i c matter, which cannot be estimated with the data a v a i l a b l e . However, some of i t i s returned with the e x c r e t a of the g r a z i n g animals ( S e c t i o n 3.5.2). This d i s c u s s i o n has served to i l l u s t r a t e the tremendous d i f f i c u l t i e s a s s o c i a t e d with s e a s o n a l s o i l p r o f i l e a n a l y s i s as a procedure to estimate s o i l n i t r o g e n movement i n f i e l d c o n d i t i o n s . Such i n h e r e n t d i f f i c u l t i e s are due to the complexity of the s o i l n i t r o g e n balance and to the l a r g e s p a t i a l v a r i a b i l i t y of f i e l d c h a r a c t e r i s t i c s ( B i g g a r and N i e l s e n , 1976). These o b s t a c l e s were a l s o encountered and i d e n t i f i e d by Holbek (1978). Bigg a r and N i e l s e n (1976) and Van der P o l et a l . (1977) emphasized that s u b s t a n t i a l e r r o r s can be made i n e s t i m a t i n g l e a c h i n g by m u l t i p l y i n g average drainage val u e s and average val u e s of the s o i l s o l u t i o n c o n c e n t r a t i o n s . B u l l e y and Cappelaere (1978) noted that s o i l n i t r o g e n balance procedures cumulate a l l the e r r o r s a s s o c i a t e d with the numerous components of the n i t r o g e n c y c l e . In S e c t i o n 4.1, n i t r o g e n l e a c h i n g from the waste d i s p o s a l i s estimated u s i n g Model 1 to i n t e r p r e t the ground-water q u a l i t y data c o l l e c t e d i n - s i t u . T h i s procedure appears more promising as a standard f i e l d method to estimate the l e a c h i n g component of the s o i l n i t r o g e n budget. 103. 3.7.2 Groundwater An i n - s i t u estimate f o r the s a t u r a t e d h y d r a u l i c c o n d u c t i v i t y K of the outwash d e p o s i t was obtained from a the pump t e s t at the 'gauge' w e l l . The r e c o v e r y of the water l e v e l i n the w e l l a f t e r a 1.43 m drawdown, was analysed by the method of Bouwer and Rice (1976) , which y i e l d e d the value K = 75 m/day. a Water t a b l e contour maps showed a very constant and uniform slope SWT = 0.2% i n the d i r e c t i o n shown i n F i g u r e 3.1. This value i s q u i t e s m a l l compared to the average of 1.1% given by H a l s t e a d (1957) f o r the a q u i f e r . Taking t h i s measured value SWT as the h o r i z o n t a l h y d r a u l i c g r a d i e n t and a p c r o s i t y n = 0.25 f o r the outwash m a t e r i a l (Todd, 1959), the h o r i z o n t a l pore v e l o c i t y was e s t i m a t e d : V _ Ka . SWT , n k = 60 cm/day (3.2) a T h e r e f o r e , the average d i s t a n c e t r a v e l l e d d u r i n g the 6-month recharge p e r i o d i s approximately 100 m, c o n s i d e r -ably l e s s than the 400 m extent of the p l o t i n the d i r e c -t i o n of flow. I n s i g n i f i c a n t amounts of TKN and ammonium-N (^ 1 ppm) were found i n the groundwater samples, i n sharp c o n t r a s t with r e s u l t s o b t a i n e d by S t a l e y et a l . (1976). Mean and standard d e v i a t i o n s f o r COD l e v e l s were 11,7 and 18.7 ppm, r e s p e c t i v e l y , values c o n s i d e r a b l y s m a l l e r than 104. those r e p o r t e d by S t a l e y et a l . (100 and 217 ppm f o r 1973-1974; 55.1 and 63.8 ppm f o r 1974-1975). These TKN, ammonium-N and COD r e s u l t s f o r the p l o t could not be d i f f e r e n t i a t e d from the l e v e l s i n the w e l l s , and i n d i c a t e that the new p l o t i s l o c a t e d o u t s i d e the zone of i n f l u e n c e of the b u r i a l p i t . When compared to the TKN and ammonium-N l e v e l s i n the s o i l samples (Table 3.2), both i n the s p r i n g and i n the f a l l , the c o n c l u s i o n can be drawn that s u b s u r f a c e movement of n i t r o g e n i n the o r g a n i c and ammonium forms i s not a s i g n i f i c a n t phenomenon at t h i s s i t e . F i g u r e 3.4 ehows the f l u c t u a t i o n s of mean water t a b l e l e v e l s and n i t r a t e - N c o n c e n t r a t i o n s over the sampling p e r i o d , and gives evidence of the c o r r e l a t i o n between these two v a r i a b l e s . A two-way a n a l y s i s of v a r i a n c e was performed on the water t a b l e l e v e l and n i t r a t e - N c o n c e n t r a t i o n data f o r the p l o t , to detect the e f f e c t s of the l o c a t i o n and time f a c t o r s on the two v a r i a b l e s . Both f a c t o r s were found h i g h l y s i g n i f i c a n t (prob-value < 1%) f o r both v a r i a b l e s . The Duncan m u l t i p l e range t e s t was performed to i d e n t i f y which p a r t i c u l a r sampling dates d i d or d i d not d i f f e r s i g n i f i c a n t l y f o r the two v a r i a b l e s . At the 1% s i g n i f i c a n c e l e v e l , the t e s t was able to d i f f e r e n t i a t e a l l mean water t a b l e p o s i t i o n s except the groups (November 6, November 13)and (December 22, January 1). At the 5% l e v e l , the p e r i o d s (June 20 to November 18) and (December 4 to January 22) were i d e n t i f i e d as two homogeneous s i g n i f i c a n t l y 50 B p. c o •H U 4J c y c o y !Z I OJ 4J rt I-I 4J •H a 40 30 -J 20 H 10 -I mean of 9 water table depths • mean concentration in 6 piezometers O mean concentration in 3 wells O • o • • • G O I I May June July 1976 1 1 1 1 1 1 Aug. Sept. Oct. Nov. Dec. Jan. Feb, Time I- 1 March Apr i l 1977 h- 2 s! rt (T> H rt to V rt cr I- 3 o Figure 3.4: Variations of mean water table levels and nitrate-N concentrations in groundwater, 1976 to 1977, 106. d i f f e r e n t subsets of means* f o r n i t r a t e c o n c e n t r a t i o n s . In. S e c t i o n 4.1, i t w i l l be shown how model 1 can be used to e x p l a i n t h i s s t r o n g time f a c t o r by s i m u l a t i n g the system's response to seasonal weather p a t t e r n s . The same t e s t performed f o r the l o c a t i o n f a c t o r , d e t e c t e d the e f f e c t of the d i r e c t i o n of groundwater move-ment on the water t a b l e l e v e l v a r i a b l e . Since water t a b l e s l o p e s remain very c o n s t a n t , t h i s e f f e c t i s q u a s i - l i n e a r . On the other hand, the s t r o n g l o c a t i o n e f f e c t on n i t r a t e c o n c e n t r a t i o n s in the p l o t could not be e x p l a i n e d by known d i f f e r e n c e s i n h y d r a u l i c c h a r a c t e r i s t i c s between piezometer s i t e s . I t can be a t t r i b u t e d to the l a r g e a r e a l v a r i a b i l i t y of s o i l l e a c h i n g c h a r a c t e r i s t i c s . The s p a t i a l n o i s e (unexplained v a r i a t i o n s ) on s o l u t e c o n c e n t r a t i o n measure-ments i n groundwater i s g e n e r a l l y normally d i s t r i b u t e d (Biggar and N i e l s e n , 1976; Van der P o l , 1977). This l e d to the use of space-averaged v a r i a b l e s f o r the purpose of c a l i b r a t i n g the one-dimensional model 1 ( S e c t i o n 4.1). The averaging procedure does not d i m i n i s h the c r e d i b i l i t y of the modeling procedure, s i n c e confidence on the means i s g r e a t e r than the c o n f i d e n c e on i n d i v i d u a l piezometer v a l u e s . Although not understood, the l o c a t i o n e f f e c t on * Any two means are s i g n i f i c a n t l y d i f f e r e n t i f and only i f they belong to d i f f e r e n t subsets. 107. n i t r a t e c o n c e n t r a t i o n s i s c o n s i s t a n t and e x p l a i n s a l a r g e p a r t of the n i t r a t e v a r i a t i o n s . I t must t h e r e f o r e be taken i n t o account when e v a l u a t i n g the u n c e r t a i n t y on the means, to reduce the v a r i a b i l i t y of c a l i b r a t i o n i n p u t s . Computation of 90% confidence i n t e r v a l s on i n d i v i d u a l means y i e l d e d an u n c e r t a i n t y of 1.5 ppm on n i t r a t e con-c e n t r a t i o n s p r i o r to November 20, 5.6 ppm f o r the whole sampling p e r i o d , and 3.8 cm (1.5 inch) f o r water t a b l e p o s i t i o n s over the p e r i o d of survey. 108 . A. MODEL APPLICATION TO STUDY AREA In t h i s c hapter, the s i t e i n v e s t i g a t e d i n chapter 3 w i l l serve to i l l u s t r a t e how Models 1 and 2 (developed i n chapter 2) can be used to meet the goals d e f i n e d i n the I n t r o d u c t i o n and r e s t a t e d i n S e c t i o n 3 .A . S p e c i f i c a l l y , the methodology to be implemented i s o u t l i n e d h e r e a f t e r : 1. C o l l e c t year-round groundwater q u a l i t y data on the farm prop e r t y ( S e c t i o n 3 . 6 . 2 ) . 2. Define system geometry, choose values f o r geometry parameters, and v e r i f y b a s i c model assumptions (S e c t i o n s A . 1 . 1 and A . 2 . 1 ) . 3. C a l i b r a t e Model 1 on groundwater q u a l i t y data, to o b t a i n v e r t i c a l d i s p e r s i o n parameters i n unsaturated and s a t u r a t e d zones ( S e c t i o n A . 1 . 2 ) . A. Determine n i t r a t e l o a d i n g of a q u i f e r r e s u l t i n g from present waste d i s p o s a l p r a c t i c e s on the p l o t , by s c a l i n g output from Model 1 to observed concen-t r a t i o n s ( S e c t i o n A . 1 . 3 ) . 5. Test s e n s i t i v i t y of Model 1 to d i s p e r s i o n parameters and c a l i b r a t i o n i n p u t s ( S e c t i o n A . 1 . 3 ) . 6. Simulate a r e a l mass t r a n s p o r t i n s a t u r a t e d zone (Model 2) to p r e d i c t long term n i t r a t e c o n c e n t r a t i o n s i n r e g i o n a l a q u i f e r r e s u l t i n g from continued d i s -p o s a l p r a c t i c e s ( S e c t i o n A . 2 . 2 ) . 7. Test system response to management a l t e r n a t i v e s ( S e c t i o n A . 2 . 2 ) . 109. 8. Test s e n s i t i v i t y of Model 2 to t r a n s p o r t parameters ( S e c t i o n A.2.3) . 4.1 MODEL 1: The s h o r t term, l o c a l s c a l e problem. A.1.1 System a n a l y s i s We are concerned with the v e r t i c a l movement of n i t r a t e s d u r i n g the s e a s o n a l groundwater recharge p e r i o d , i n the p o r t i o n of porous medium immediately beneath the d i s p o -s a l s i t e , and above the c l a y l a y e r , c o n s i d e r e d as an impermeable s u r f a c e . This domain, shown s c h e m a t i c a l l y i n F i g u r e A . l , was assumed to be .uniformly 5.0 m (16.4 f t ) deep, and i n f i n i t e i n a l l h o r i z o n t a l d i r e c t i o n s . The h o r i z o n t a l boundary e f f e c t s can be n e g l e c t e d due to the l a r g e h o r i z o n -t a l dimensions of the p l o t i n comparison to the depth of the domain, and to the d i s t a n c e t r a v e l l e d by groundwater d u r i n g the s i x months . recharge p e r i o d ( S e c t i o n 3.7.2). The three zonal subsystems w i l l now be examined s e p a r a t e l y . 1) The root zone The root zone i s assumed to be a homogeneous, 0.3 m (1.0 f t ) deep s i l t loam. S p a t i a l v a r i a t i o n s of moisture d i s t r i b u t i o n d u r i n g the s i m u l a t i o n p e r i o d are expected to remain s m a l l w i t h i n the root zone f o r the f o l l o w i n g reasons: 1 E v a p o t r a n s p i r a t i o n i s minimal during the l e a c h i n g season. The p e r e n n i a l v e g e t a t i o n possesses a shallow and 1 H= 0.3 m DPZM=z3m SL D I M P = 5 m ROOT ZONE SUBSOIL SL SATURATED ZONE Rainfall ET i 1 Storage Drainaqe „ I R echarge - r - 0 ZWT + N-1 N-2. > 3 Z / / / / / / / / / / / / • / / / / / / / IMPERMEABLE STRATUM. z a x i s F i g u r e 4 . 1 : C r o s s - s e c t i o n o f the domain o f s i m u l a t i o n , M o d e l 1. 111. w e l l developed root system, so that the assumption of uniform uptake throughout the s u r f a c e s l a b i s not unreasonable. The s m a l l t h i c k n e s s of the root zone does not allow f o r l a r g e moisture content v a r i a t i o n s . When water i s moving downward, the v e r t i c a l p r e s s u r e p o t e n t i a l g r a d i e n t w i l l remain l e s s than u n i t y ( C l o t h i e r et a l . 1977). Because of the low s p e c i f i c moisture c a p a c i t y * (0.075 m - 1 approximately, a f t e r Nagpal and De V r i e s , 1976), a maximum t e n s i o n d i f f e r e n c e of .3 m over the p r o f i l e w i l l be a s s o c i -ated with a d i f f e r e n c e i n moisture content of 0.0225. I f n e g l e c t e d , the r e l a t i v e e r r o r i s 5% at the most. In f a c t , f o r t h i s p r o f i l e , Nagpal and De V r i e s data shows t h a t , i n the absence of e v a p o t r a n s p i r a t i o n , the h y d r a u l i c p o t e n t i a l g r a d i e n t remains g r e a t e r or equal to 0.5 ( p r e s s u r e p o t e n t i a l g r a d i e n t 0.5) s e v e r a l days a f t e r a r a i n f a l l event, when pressure p o t e n t i a l s f a l l below -100 cm. The s o i l d r a i n s most of i t s pore space at h i g h p r e s s u r e p o t e n t i a l s (low t e n s i o n s ) as i s u s u a l (Baver et a l . , 1972). During most of the drainage p e r i o d , the h y d r a u l i c g r a d i e n t i s equal to 1, showing a very uniform * Change i n v o l u m e t r i c moisture content per u n i t change i n p r e s s u r e p o t e n t i a l . 112. moisture content. This i s c o n s i s t e n t with Gardner and J u r y ' s statement (1974) that g r a v i t y drainage i s a s s o c i a t e d with very n e a r l y a uniform moisture content over a sub-s t a n t i a l p a r t of a homogeneous p r o f i l e . Due to the coarse nature of the u n d e r l y i n g m a t e r i a l , water i s r e t a i n e d i n the root zone u n t i l i t s c a p i l l a r y c o n d u c t i v i t y allows drainage to occur under the p r e -dominant g r a v i t a t i o n a l g r a d i e n t . Only i n the case where the water t a b l e comes c l o s e to the drainage zone w i l l the h y d r a u l i c g r a d i e n t become l e s s than u n i t y . Small moisture g r a d i e n t s w i t h i n the root zone t r i g g e r c o mparatively l a r g e t e n s i o n g r a d i e n t s , thereby g e n e r a t i n g strong feedback which prevents these moisture g r a d i e n t s from d e v e l o p i n g . T h i s water r e d i s t r i b u t i o n process w i l l be q u i t e e f f e c t i v e due to the low s p e c i f i c moisture c a p a c i t y of the root zone compared to the s u b s o i l zone. This argumentation b r i n g s s u f f i c i e n t evidence that equation 2.6 a c c u r a t e l y d e s c r i b e s the l e a c h i n g process i n t h i s s o i l p r o f i l e . It a l s o v a l i d a t e s the assumptions f o r the drainage component of Model 1 ( S e c t i o n 2.3.3). Model 1 d i d not i n c l u d e any s i n k / s o u r c e term in equation 2.6. F i g u r e 4.2 schematizes the extent to which uptake and accumulation of n i t r a t e s on one hand, and n i t r a t e GROWING SEASON DORMANT SEASON w high temperature low temperature 3 low moisture content , high moisture content 3 o high aeration status low aeration status CO 3 P. C A p r i l May June July Aug. Sept. Oct. Nov. Dec. Jan. Feb. March F i g u r e 4.2: H y p o t h e t i c a l Seasonal P a t t e r n s of Inputs and Outputs of S o i l N i t r a t e . 114. l e a c h i n g on the other hand are mutually e x c l u s i v e . Leaching c o i n c i d e s with moisture s u r p l u s and d e c l i n i n g temperatures, c o n d i t i o n s which hin d e r the o x i d a t i o n of o r g a n i c matter and of ammonium n i t r o g e n , as w e l l as p l a n t growth. More-over, i t i s g e n e r a l l y r e c o g n i z e d that the r a t e of n i t r o g e n uptake by the p l a n t r e l a t i v e to i t s growth drops s h a r p l y i n the l a t e stages of the growing season. Poor a e r a t i o n might favour the process of d e n i t r i f i c a t i o n by anaerobic b a c t e r i a , but t h i s phenomenon, hard to q u a n t i f y and p o o r l y understood, w i l l proceed slowly and i s o f t e n d i s r e -garded a l t o g e t h e r . The s o i l c o n sidered i n t h i s study remains s u f f i c i e n t l y u n s a t u r a t e d that the e r r o r i n v o l v e d might be s m a l l . However, t h i s stands as one of the b i g g e s t unknowns with s i m u l a t i o n of the present k i n d . While the s t r o n g a d s o r p t i o n of ammonium ions to s o i l p a r t i c l e s r e s t r i c t t h e i r movement out of the root zone, i t can be s a f e l y assumed that no n i t r a t e a d s o r p t i o n o c c u r s . In most temperate r e g i o n s , the opp o s i t e phenomenon of anion e x c l u s i o n from s m a l l pores predominates ( S e c t i o n 1.2) and i s r e f l e c t e d by the parameter @exc1_ (equation 2.7.1). The value 0 . = 0.02 was used f o r t h i s s o i l . 115. EVAPOTRANSPIRATION Values f o r the c o e f f i c i e n t s A, B and C i n the e x p r e s s i o n s : R. - R .(A+B.f) (2.13)and e - C.(l-RH) (2.11) S 3. must be p r o v i d e d to the model. The f i g u r e s A=0.23 and B=0.53 were obtained e x p e r i m e n t a l l y by Black (1977) f o r the Lower F r a s e r V a l l e y of B.C. P r i e s t l e y and T a y l o r (1972) c a l c u l a t e d the r a t i o a of the maximum 24-hour r a t e of e v a p o t r a n s p i r a t i o n (PET) to the e q u i l i b r i u m e v a p o r a t i o n r a t e (E ) at s e v e r a l e q experimental s i t e s , f o r well-watered crops under non-advec-t i v e c o n d i t i o n s . The found an average a v a l u e of 1.26 (+ 5%), which corresponds to an e value of C.26, and i s c o n s i s t e n t with B l a c k ' s data (1977). The v a l u e C=0.8 was t h e r e f o r e adopted, so that e i d e n t i f i e s with P r i e s t l e y and T a y l o r ' s e x p r e s s i o n f o r the average r e l a t i v e humidity l e v e l s i n the Lower F r a s e r V a l l e y . F i n a l l y , a value a=0.26 was taken f o r the albedo of grass ( L i n a c r e , 1968). DRAINAGE The g r a v i t a t i o n a l g r a d i e n t i s c o n s i d e r e d as the only d r i v i n g f o r c e f o r moisture drainage. Because of the high t r a n s m i s s i v i t y of water i n p r e f e r e n t i a l channels w i t h i n the coarse zone, the s m a l l e r c a p i l l a r y c o n d u c t i v i t y K i n the root zone i s the f l u x l i m i t i n g f a c t o r . The 116. u n s a t u r a t e d flow c h a r a c t e r i s t i c f o r the root zone was obtained from Nagpal and De V r i e s (1976). The curve was f i t t e d to the e x p o n e n t i a l f u n c t i o n : K(9) = exp'k . CQ" 0 )] (2.19) o o with k = 45 and 0 = 0.48 (see F i g u r e 4.3)'. o o  b I t can be seen from the d a i l y drainage e x p r e s s i o n 2.20 that at low moisture content 9 v a l u e s , K(9) w i l l be s m a l l , a l l o w i n g f o r the approximation: Log [1+K(0)/Cv] = K ( 0 ) / Q e (4.1) I t f o l l o w s t h a t : Q(0) = K ( 0 ) . (4.2) F i g u r e 4.3 shows t h a t as 0 i n c r e a s e s , Q(9) d i v e r g e s markedly from K ( 0 ) . Divergence between c a p i l l a r y conduc-t i v i t y and observed d a i l y drainage values at h i g h moisture content was a l s o r e p o r t e d by Black et a l . (1970). . U n a v a i l a b i l i t y of c o n d u c t i v i t y data at low moisture content p r e c l u d e d a more r e f i n e d a n a l y s i s . Drainage r a t e s might p o s s i b l y be overestimated as the moisture content con-tent decreases, but t h i s i s of l i t t l e p r a c t i c a l s i g n i f i c a n c e s i n c e most of the drainage occurs at h i g h e r moisture content v a l u e s . LEACHING The c o e f f i c i e n t C 0 i n equation 2.-21 c h a r a c t e r i z i n g p the degree of n i t r a t e mixing o c c u r r i n g in the p r o f i l e during 117. Figure 4.3: C a p i l l a r y conductivity K and d a i l y drainage Q, as a function of the moisture content 9 of the root zone. 118. the l e a c h i n g p r o c e s s , w i l l be obtained by c a l i b r a t i o n of the model on f i e l d data ( S e c t i o n 4.1.2). The mixing index C„ i s r e l a t e d to Brenner's number B r (1962) by the e q u a t i o n : Cg . B r = 2 (4.3) When Cg tends to zero, l e a c h i n g occurs as p i s t o n flow (no m i x i n g ) . When C e ^ , _ .. ^ . „ „ t . r . ° B tends to 1, equation 2.21 i d e n t i f i e s c l o s e l y to the s o l u t i o n given by Mulqueen and Kirkham (1972) f o r the assumption of complete mixing at a l l times w i t h i n the r o o t zone: F = exp(-p). (4.4) In p r a c t i c e , Cg values u s u a l l y l i e somewhere between 0 and 1. 2. The t r a n s i t i o n zone .The non-uniform s u b s o i l water movement a s s o c i a t e d with i n s t a b i l i t y of the w e t t i n g f r o n t at the f i n e / c o a r s e i n t e r f a c e was r e p o r t e d and analysed by Nagpal and De V r i e s (1976) . The very h i g h h y d r a u l i c c o n d u c t i v i t y (10 to 20 ra/day) along the p r e f e r e n t i a l s a t u r a t e d channels j u s t i f i e s the s i m p l i f i c a t i o n of the mass t r a n s p o r t phenomenon to a pure t r a n s f e r process. 3. The s a t u r a t e d zone POSITION OF THE WATER TABLE D a i l y drainage p r e d i c t i o n s were compared to the 119. observed water t a b l e l e v e l s over the 4-month p e r i o d mid-June to mid-October, 1976. I t was assumed that no recharge o c c u r s when the p r e d i c t e d drainage from the root zone i s lower than -3 -3 4.10 cm/day (1.5 10 i n c h / d a y ) . The observed r a t e of drop DWT (cm/day) of the water t a b l e during those p e r i o d s was f i t t e d to an e x p o n e n t i a l f u n c t i o n of the depth ZWT(cm) of the water t a b l e : DWT = Z . (DIMP/ZWT - 1) . 10~ 2 (4.5) o was obtained with Z = 63.5 cm and DIMP = 500 cm. o The c o e f f i c i e n t of p r o p o r t i o n a l i t y f o r groundwater recharge, , was found by c a l i b r a t i n g the water t a b l e p r e d i c t i o n submodel on the observed p o s i t i o n s of the water t a b l e , over the 4-month summer t e s t i n g p e r i o d . A value R = 13. (=0.077 _ 1) was found. How w e l l the l i n e a r i t y c approximation d e s c r i b e s groundwater recharge i s evidenced by the c l o s e agreement between simulated and observed water t a b l e depths ZWT, throughout the s i m u l a t i o n p e r i o d ( F i g u r e 4.4). T h i s good agreement a l s o v a l i d a t e s the s o i l m o isture e s t i m a t i o n procedure. E s t i m a t i n g the a q u i f e r p o r o s i t y n at 0.25 and i t s s p e c i f i c y i e l d (= e f f e c t i v e p o r o s i t y ) at 0.20, i t was concluded that s i g n i f i c a n t r u n o f f from the s u r r o u n d i n g areas of low i n f i l t r a t i o n c a p a c i t y feeds the a q u i f e r , s i n c e apparent water t a b l e r i s e due to a i r entrapment ( F r e e z e , 1969) and c a p i l l a r y r i s e i n the u n s a t u r a t e d zone cannot account f o r Water t a b l e d e p t h (m) OJ K3 !-• . ' OZT 1 2 1 . the l a r g e d i f f e r e n c e between R ^ and S . & c y This upstream c o n t r i b u t i o n was very r a p i d and pro-p o r t i o n a l to the water s u r p l u s f o r the p l o t . S i m u l a t i o n of the water t a b l e p o s i t i o n ZWT was p o s s i b l e at the s i t e because of t h i s f a s t and c o n s i s t e n t h y d r o l o g i c response. NITRATE CONCENTRATION DISTRIBUTION Using the sim u l a t e d depth ZWT of the water t a b l e f o r boundary of the s a t u r a t e d domain, the n i t r a t e t r a n s -p o r t equation 2.6 was then s o l v e d by the f i n i t e - d i f f e r e n c e method, with a 2.5 cm (1.0 inch ) depth increment and a one-day time s t e p . 122 . 4.1.2 Model C a l i b r a t i o n 1) Water Quantity Submodel: The p e r i o d Mid-March to Mid-October, 1976, p r i o r to water q u a l i t y t r a n s p o r t s i m u l a t i o n , was used s o l e l y f o r the purpose of c a l i b r a t i n g the water movement submodel. S o i l water content on June 15 was obtained from a pre -l i m i n a r y run over the p e r i o d March-June, 1976, s t a r t i n g with the measured moisture content on March 11 ( S e c t i o n 3.7.1). The s p r i n g p e r i o d was s u f f i c i e n t to b u f f e r the e f f e c t s of uncer-t a i n t y on the i n i t i a l s o i l water estimate s i n c e v a r i a t i o n of the i n p u t value was not r e f l e c t e d i n the output from the water q u a n t i t y submodel a f t e r a 4-month run. H y d r a u l i c parameters f o r the s a t u r a t e d subsystem obtained by c a l i b r a t i o n over the summer p e r i o d , were d i s c u s s e d i n S e c t i o n 4.1.1. No f u r t h e r adjustment of the water q u a n t i t y submodel was made on data past Mid-October, 1976. Simulated and observed water t a b l e f l u c t u a t i o n s over the p e r i o d June 1976 - A p r i l 1977 are p l o t t e d i n F i g u r e 4.4. Because the s p r i n g and summer p e r i o d was used s o l e l y f o r c a l i b r a t i o n of the water q u a n t i t y submodel, no q u a l i t y s i m u l a t i o n was attempted p r i o r to Mid-October, 1976. 123. 2) Water Q u a l i t y Submodel: The n i t r a t e - N c o n c e n t r a t i o n s i n the w e l l s were averaged f o r each sampling date, and were considered as background l e v e l s i n t h i s r e g i o n of the a q u i f e r . The n i t r a t e c o n c e n t r a t i o n s a t t r i b u -ted to l e a c h i n g were o b t a i n e d from the d i f f e r e n c e between the mean piezometer and mean w e l l values f o r each sampling date, and are p l o t t e d i n F i g u r e 4.5. Using a u n i t i n i t i a l amount of n i t r a t e a v a i l a b l e f o r l e a c h i n g i n the root zone, the water q u a l i t y submodel was then c a l i b r a t e d on these p o i n t s to match the time of i n i t i a l r i s e and the time of peak c o n c e n t r a t i o n . The c a l i b r a t i o n y i e l d e d values f o r the mixing parameters i n the unsaturated and s a t u r a t e d zones: 2 C D = 0.2 to 0.3; D = 260 to 320 cm /day. P v The low value of the index of mixing Cg i n the root zone i n d i c a t e s that u n s a t u r a t e d s o l u t e t r a n s p o r t at t h i s s i t e occurs p r i m a r i l y by c o n v e c t i o n , r a t h e r than by d i f f u s i o n or d i s p e r s i o n . I n d i c e s of d i s p e r s i o n can be d e r i v e d f o r both zones : 3 ^ = C 0 . H = 6 to 9 cm ) unsat 3 s D I (4.6) 3 _ = 2 . a = 2 . r - ^ = 10 cn sat v V, ) h F i g u r e 4.5: N i t r a t e - N c o n c e n t r a t i o n s (above b a c k g r o u n d ) i n p i e z o m e t e r s • o b s e r v e d s i m u l a t e d (mean of s i x measurements) to 125. The f o l l o w i n g comments apply to these v a l u e s : a) Using Kolenbrander's procedure (1970) to evaluate P ^ from the mean a i r content of the root zone unsat at pF 2.0, a value of approximately 10 cm i s o b t a i n e d , which i s i n c l o s e agreement with the v a l u e y i e l d e d by our model. b) The c o e f f i c i e n t a c t u a l l y r e p r e s e n t s a t r a n s v e r s e d i s -p e r s i v i t y s i n c e the main component of the s a t u r a t e d v e l o c i t y i s h o r i z o n t a l . Transverse d i s p e r s i v i t i e s n o r m a l l y are s u b s t a n t i a l l y s m a l l e r than l o n g i -t u d i n a l d i s p e r s i v i t i e s . T h i s p o i n t s out to the f a c t that f o r a longer s i m u l a t i o n p e r i o d , h o r i z o n t a l s o l u t e d i s p e r s i o n should be c o n s i d e r e d . 4.1.3 Outputs and S e n s i t i v i t y A n a l y s i s Once the model i s c a l i b r a t e d , the t o t a l amount M ' o of excess n i t r a t e - N i n the root zone at the end of the growing season can be estimated, by s c a l i n g the simulated response to a u n i t input ( S e c t i o n 4.1.2) to the observed n i t r a t e c o n c e n t r a t i o n s i n the a q u i f e r ( F i g u r e 4.5), over the l e a c h i n g p e r i o d (Mid-October, 1976 to Mid-February, 1977). This i s j u s t i f i e d by the assumption of l i n e a r i t y of the n i t r a t e t r a n s p o r t process i n the range of f i e l d c o n c e n t r a t i o n s ( S e c t i o n 2.1.1). S p e c i f i c a l l y , M i s computed as the r a t i o of the observed s e a s o n a l peak concen-t r a t i o n , estimated to be 25 ppm (+ 15%), to the p r e d i c t e d 126 peak c o n c e n t r a t i o n generated by a u n i t amount of n l t r a t e - N a v a i l a b l e f o r l e a c h i n g from the root zone. The a c t u a l amount of excess n i t r a t e - N was estimated to be Mo=200 kg/h which was almost completely leached by February, 1976. This l a r g e n i t r o g e n l o s s f i g u r e i s a r e s u l t of the i n e f f e c t i v e n e s s of the p r e s e n t management system ( i n t e r m i t t e n t grazing) i n removing the heavy n i t r o g e n loads (roughly 800 kg TKN/ha) a p p l i e d every year to the f i e l d . The r e l a t i v e u n c e r t a i n t y i n neasurement of the peak c o n c e n t r a t i o n (15%) i s c f the same order as the uncer t a i n t i e s a r i s i n g from the d e t e r m i n a t i o n of C, and D . The 3 v p r e d i c t e d peak c o n c e n t r a t i o n v a r i e d by 12% when i n c r e a s e d from C. 2 to 0.3, and by 16% when D increased J v 2 from 260 to 320 cm /day. I t should be noted that the s e n s i t i v i t y of the n i t r a t e - N excess e s t i m a t e , M , to the c a l i b r a t i o n of the model i s s u b s t a n t i a l l y reduced by the s t r o n g n e g a t i v e feedback e f f e c t between the c a l i b r a t i o n parameters, and , whose estimates are not independent For example, i f a h i g h e r value i s assumed, the c a l i b r a -t i o n procedure w i l l y i e l d a lower v a l u e , c o u n t e r a c t i n g the e f f e c t of the f i r s t parameter v a r i a t i o n on the d e t e r -mination of the peak c o n c e n t r a t i o n . S i m i l a r n e g a t i v e feed back a l s o attenuates the e f f e c t of u n c e r t a i n t i e s . - i n v o l v e d i n e s t i m a t i n g the depth of the piezometers and of the impermeable l a y e r . V a r i a t i o n s i n p r e d i c t e d puak concen-t r a t i o n of 17% and 5% occurred due to 10% v a r i a t i o n s i n 127. the above r e s p e c t i v e depths. The combined e f f e c t of a l l these u n c e r t a i n t i e s on the n i t r a t e - I I l o s s (M ) estimate d i d o not exceed 25%. This i s b e l i e v e d to be b e t t e r than the e s t i m a t i o n s produced by analyses of s o i l p r o f i l e s or s o i l n i t r o g e n balance procedures. Bi g g a r and N i e l s e n (1976) and Van der P o l , et a l . (1977) emphasized that s u b s t a n t i a l e r r o r s can be made i n e s t i m a t i n g l e a c h i n g by m u l t i p l y i n g average drainage values and average v a l u e s of the s o i l s o l u t i o n c o n c e n t r a t i o n s . B u l l e y and Cappelaere (1978) noted that s o i l n i t r o g e n balance' procedures cumulate a l l the e r r o r s a s s o c i a t e d w i t h the numerous components of the n i t r o g e n c y c l e . When the p e r i o d of s i m u l a t i o n was extended i n t o the s p r i n g , the simulated c o n c e n t r a t i o n s showed some divergence with measured valu e s f o r March and A p r i l , as shown i n F i g u r e 4.5 (broken l i n e ) . The a c t u a l r a t e of c o n c e n t r a t i o n d e c l i n e was g r e a t e r than p r e d i c t e d , due p r i m a r i l y to two f a c t o r s : 1) The water input to the system from s l u r r y s p r a y i n g , s t a r t i n g in l a t e January, was not taken i n t o account as an input to the water q u a n t i t y sub-model, due to the uneven s p a t i a l d i s t r i b u t i o n of each a p p l i c a t i o n . Over the four-month manuring p e r i o d , an average of 2.5 cm (1 inch) of water was a p p l i e d to the area, i n d u c i n g an estimated 30 cm (1 f t ) of unaccounted groundwater recharge, 128. which i s e s s e n t i a l l y n i t r a t e - f r e e . 2) The assumption of a n e g l i g i b l e e f f e c t of h o r i z o n t a l d i s p e r s i o n i n the a q u i f e r p r o g r e s s i v e l y degrades in t h i s n i t r a t e r e d i s t r i b u t i o n p e r i o d , a f t e r the peak c o n c e n t r a t i o n has o c c u r r e d , as the margin between v e r t i c a l and h o r i z o n t a l c o n c e n t r a t i o n g r a d i e n t s i s reduced. A t h r e e - d i m e n s i o n a l model becomes necessary to simulate the n i t r a t e concen-t r a t i o n decay i n the s a t u r a t e d zone. F i g u r e 4.6 shows the n i t r a t e c o n c e n t r a t i o n p r o f i l e s i n the s a t u r a t e d zone, produced by the model f o r three times during the l e a c h i n g p e r i o d . The p r o f i l e s i n d i c a t e the p r e -d i c t e d c o n c e n t r a t i o n at the piezometer i n t a k e and i l l u s t r a t e the s e n s i t i v i t y o f the model output to the sampling depth, due to s i g n i f i c a n t v e r t i c a l s t r a t i f i c a t i o n of groundwater q u a l i t y . In t u r n , t h i s s t r a t i f i c a t i o n makes a model such as Model 1 necessary f o r the i n t e r p r e t a t i o n of groundwater samples. The s i m u l a t e d p r o f i l e s show that n i t r a t e concen-t r a t i o n s are c o n s i d e r a b l y more v a r i a b l e with time and depth i n the uppermost s t r a t a of the groundwater body, as i t i s o f t e n r e p o r t e d i n the l i t e r a t u r e (e.g. Behnke and H a s k e l l , 1968). Model 1 s u c c e s s f u l l y p r e d i c t e d the time of n i t r o g e n c o n c e n t r a t i o n r i s e i n the piezometer samples f o r the f a l l of 1977, the f i r s t season f o l l o w i n g i t s c a l i b r a t i o n . F u r t h e r 129.. Nitrate-N concentration (ppm) F i g u r e 4.6: V e r t i c a l n i t r a t e - N c o n c e n t r a t i o n p r o f i l e s i n groundwater beneath the p l o t . 130. t e s t i n g has not yet been c a r r i e d out. 4.2 Model 2; The long term, r e g i o n a l s c a l e problem. 4.2.1 System a n a l y s i s The s a t u r a t e d domain i s con s i d e r e d homogeneous, with a p o r o s i t y n = 0.25, and a h y d r a u l i c c o n d u c t i v i t y 3. K = 7 5 m/day. The water t a b l e i s assumed to be steady, with a uniform slope SWT = 0.2%, i n the d i r e c t i o n i n d i c a t e d i n F i g u r e 3.1. This r e s u l t s t h e r e f o r e i n a uniform flow, with a h o r i z o n t a l pore v e l o c i t y V, = 0.6 m/day. n For l a c k of b e t t e r i n f o r m a t i o n , the impermeable c l a y l a y e r i s assumed to have a uniform slope, of 1% i n the d i r e c t i o n of groundwater movement. The e l e v a t i o n d i f f e r e n c e h(x,y) between the water t a b l e and the impermeable s u r f a c e i s hp = 4.0 m at the o r i g i n 0 (center of the p l o t ) . T h i s s i m u l a t e d l i t h o l o g y i s c o n s i s t e n t with a v a i l a b l e p r o f i l e data f o r the area. Dimensions of the d i s p o s a l s i t e are L = 313 m x (1040 f t ) and L y = 140 m (470 f t ) i n the x and y d i r e c t i o n s -»• r e s p e c t i v e l y . The s i m u l a t i o n area i s l i m i t e d i n the x d i r e c t i o n by XMIN = -500 m (-1670 f t ) ( e a s t e r n edge of the a q u i f e r ) and by XMAX = 2000 m (6670 f t ) . Past t h i s l a t t e r l i m i t , the flow system d i s c h a r g e s i n t o the Salmon R i v e r , n i t r a t e t r a n s p o r t o c c u r r i n g mostly by co n v e c t i o n . The s i m u l a t i o n area i s d e f i n e d by YMIN = -1000 m (3330 f t ) and YMAX = + 1000 m in the y d i r e c t i o n . 131. S i m u l a t i o n s t a r t s June 1, 1976 and the time step i s At = 1 week. C o n c e n t r a t i o n d i s t r i b u t i o n s are computed every 4 weeks, i . e . 13 times a year over any number of y e a r s . The a l g o r i t h m b u i l t f o r summation of equation 2.47 optimizes the e f f i c i e n c y of computer o p e r a t i o n s . For the purpose of t e s t i n g the r e g i o n a l water q u a l i t y t r a n s p o r t model, s t e a d y - s t a t e c l i m a t e and waste d i s -p o s a l data were fed to the two-dimensional model. S p e c i f i -c a l l y , weather inputs c o n s i s t e d of long term average weekly p r e c i p i t a t i o n and temperature extrema d e r i v e d from data p u b l i s h e d by B a i e r et a l . (1969) f o r the Abbotsford l o c a t i o n . A l s o , average number of b r i g h t sunshine hours f o r each week of the year were computed from d a i l y recorded data at the A b b o t s f o r d A i r p o r t . No supplemental i r r i g a t i o n was i n c l u d e d , although t h i s c o u l d be e a s i l y i n c o r p o r a t e d i n the model. As a consequence of steady c l i m a t e and waste d i s -p o s a l c h a r a c t e r i s t i c s , a constant amount "A of n i t r a t e excess over p l a n t requirements was a v a i l a b l e f o r l e a c h i n g at the end of each growing season. M was given the v a l u e 200 kg/ha obtained i n S e c t i o n 4.1.3 f o r the 1976-1977 p e r i o d , a f t e r s o l v i n g the s h o r t term, l o c a l s c a l e problem with Model 1. S i m u l a t i o n with Model 2 w i l l t h e r e f o r e enable p r e d i c t i o n of the long term e f f e c t s of present-day o p e r a t i o n . Under steady boundary c o n d i t i o n s , the system r e -sponse converges towards a steady s t a t e a f t e r a t r a n s i e n t 132. phase whose l e n g t h depends on the v a l u e s a t t r i b u t e d to model parameters. These are the l o n g i t u d i n a l and t r a n s -verse d i s p e r s i v i t y c o e f f i c i e n t s and cc^, assumed to be uniform over the s i m u l a t e d area, as w e l l as the h o r i z o n t a l flow v e l o c i t y a l r e a d y mentioned. The l i t e r a t u r e was scanned f o r values of the d i s p e r s i v i t y c o e f f i c i e n t s f o r s i m i l a r groundwater systems. The set of values ctT = 60 m and o. = 12 i was obtained from Li X. Bredehoeft et a l . , (1976) as r e p r e s e n t a t i v e of f i e l d -measured d i s p e r s i v i t i e s f o r P l e i s t o c e n e g l a c i a l outwash (sand and g r a v e l ) . T h i s d i s p e r s i v i t y r a t i o r Q = — commonly approaches the v a l u e r Q = 5 f o r i s o t r o p i c media. (De J o s s e l i n de Jong, 1958; Bear, 1972). With those parameter values and a v e l o c i t y = 0.6. m/day, a s i m u l a t i o n p e r i o d of approximately 15 years was n e c e s s a r y to achieve s t e a d y - s t a t e i n the p o r t i o n of a q u i f e r east of the Salmon R i v e r . A time l i m i t of 15 years was t h e r e f o r e adopted f o r most runs. 4.2.2 Model Outputs and D i s c u s s i o n Output was f i r s t generated at 18 d i s t i n c t l o c a -t i o n s on the flow l i n e p a s s i n g through the c e n t e r 0 of the 133. p l o t (x a x i s ) , at a b s c i s s a -500, -400, -300, -200, -150, -100, 0, 100, 150, 200, 300, 400, 600, 800, 1000, 1200, 1500, 2000 (meters). The l e n g t h of time necessary to reach s t e a d y - s t a t e v a r i e d from l e s s than 5 years upstream of p o i n t 0 to over 15 years at p o i n t (x=2000, y=0). The t r a n s i e n t phases f o r s i x d i f f e r e n t l o c a t i o n s on the x a x i s are shown i n F i g u r e 4.7. The curves c l e a r l y evidence the s t r o n g b u i l d - u p e f f e c t f o r p o i n t s o u t s i d e the p l o t (| x. | > 150), whereas c o n c e n t r a t i o n s i n s i d e the p l o t (|x | £ 150) are l a r g e l y determined by the l e a c h i n g of n i t r a t e s o c c u r r i n g that p a r t i c u l a r year. T h i s adds c r e d i b i l i t y to Model 1, which a t t r i b u t e s a l l the concen-t r a t i o n v a r i a t i o n during one season, at p o i n t 0, to the l e a c h i n g process d u r i n g that season. A c c o r d i n g to F i g u r e 4.7, the e r r o r a s s o c i a t e d with t h i s assumption i s q u i t e s m a l l , past the f i r s t year of o p e r a t i o n . As could be expected, the steady c y c l e p e r i o d i s equal to one y e a r , at a l l l o c a t i o n s . F i g u r e 4.8 p r e s e n t s n i t r a t e - N c o n c e n t r a t i o n pro--r f i l e s along the x a x i s f o r s i x d i f f e r e n t times of the year, once the steady s t a t e has been reached. In F i g u r e 4.9, only the steady envelopes, i . e . the extremum c u r v e s , have been r e p r e s e n t e d . The extent of the p l o t i n the x d i r e c -t i o n i s a l s o i n d i c a t e d . This d i s c o n t i n u i t y of a q u i f e r l o a d i n g along the x a x i s i s c l e a r l y r e f l e c t e d i n the shapes the c o n c e n t r a t i o n envelopes. The maximum curve shows a * vex 137. « t s t r o n g p i s t o n e f f e c t , w i t h a t r a n s i t i o n zone c o n s i d e r a b l y s m a l l e r on the upstream side than on the downstream s i d e . The average maximum c o n c e n t r a t i o n on the s e c t i o n of x a x i s w i t h i n the p l o t i s approximately 23.5 ppm. I f 25 meters are omitted on each s i d e of the segment ( i . e . a 16% l e n g t h r e d u c t i o n ) , t h i s average maximum becomes 24 ppm and the v a r i a t i o n i s l e s s than 12.5% of the mean. Again, t h i s remark adds substance to the assumption of one-dimension-a l i t y made i n the study of the l o c a l system (Model 1) , where c a l i b r a t i o n was performed on the b a s i s of the average of the recorded maximum c o n c e n t r a t i o n s . I f the sampling p o i n t s (piezometers) are p l a c e d more than 25 meters away from the e x t r e m i t i e s of the d i s p o s a l s i t e , boundary e f f e c t s can be n e g l e c t e d , without i n t r o d u c i n g s i g n i f i c a n t e r r o r , compared to the r e c u r r e n t measurement u n c e r t a i n t y . The ' p i s t o n ' shape of the maximum c o n c e n t r a t i o n curve, w i t h a very n e a r l y uniform l e v e l w i t h i n the p l o t , p o i n t s out the f a c t that the maximum c o n c e n t r a t i o n c l o s e l y f o l l o w s the p a t t e r n of a q u i f e r l o a d i n g , and i s a f f e c t e d to a l e s s e r degree by the h o r i z o n t a l r e d i s t r i b u t i o n phenomenon w i t h i n the s a t u r a t e d zone. On the other hand, the l i n e a r i n c r e a s e of c o n c e n t r a t i o n minima across the p l o t means t h a t base l e v e l c o n c e n t r a t i o n b u i l d s up p r o g r e s s i v e l y along the flow l i n e s i n the zone where l o a d i n g o c c u r s . The peak i s reached c l o s e t o the downstream boundary, and the base l e v e l then decreases away 138. from t h i s boundary under the e f f e c t s of d i s p e r s i o n and d i l u t i o n . This q u a s i - l i n e a r i n c r e a s e could be taken i n t o account i n f u t u r e development of the l o c a l system s i m u l a t i o n (Model 1). Maps of n i t r a t e - N c o n c e n t r a t i o n s were then obtained by g e n e r a t i n g e q u i c o n c e n t r a t i o n l i n e s (with a c o n c e n t r a t i o n increment of 2 ppm) i n October and November of the 15th y e a r , r e s p e c t i v e l y b e f o r e and a f t e r the s t a r t of the f a l l l e a c h i n g p e r i o d ( F i g u r e s 4.10(a) and 4.10(b)). The r e c t a n g u l a r extent of the d i s p o s a l f i e l d can be c l e a r l y seen on the l a t t e r due to the ' p i s t o n ' i n p u t of n i t r a t e s over the p l o t . Once the l e a c h i n g i s over, the n i t r a t e 'mound' d i s p e r s e s as i t moves westward with groundwater flow, and r e t u r n s to i t s l a t e summer c o n f i g u r a t i o n r e p r e s e n -ted by F i g u r e 4.10(b). These two maps correspond to the two extreme d i s t r i b u t i o n s ; at any time past the 15th y e a r , the a c t u a l contour map w i l l be somewhere between the two above r e p r e s e n t a t i o n s . Figures 4.7 to 4.10 enable d i s c u s s i o n of l o n g -term water q u a l i t y i n w e l l s tapping the a q u i f e r . A l a r g e number of w e l l s are l o c a t e d c l o s e to the x a x i s , between the a b s c i s s a x = 500 and x = 1500 m. Figures 4.7 to 4.10 a l s o allow f o r e s t i m a t i o n of n i t r a t e c o n c e n t r a t i o n i n groundwater discharge to the Salmon R i v e r , assuming that no f u r t h e r d i s p e r s i o n occurs past the x = 2000 m l i m i t . The three w e l l s l o c a t e d on the farm p r o p e r t y have the f o l l o w i n g c o o r d i n a t e s : 139 . F i g u r e 4.10: C y c l i c maps of n i t r a t e - N c o n c e n t r a t i o n i n c r e a s e s i n groundwater due to continuous waste a p p l i c a t i o n . (a) : October of Year 15 (b) : November of Year 15 Parameter values : V, = 0.6 m/day a T = 60 m a_ = 12 m. n L T 142 . Well 1 (350,70); Well 2 (-325,350); Well 3 (-400,0). I t can be seen on F i g u r e 4.10 that the c o n c e n t r a t i o n i n c r e a s e s i n Wells 2 and 3 are n e g l i g i b l e ; t r i a l s with v a r i o u s d i s p e r s i o n c o e f f i c i e n t s ( S e c t i o n 4.2.3) w i l l show t h a t these c o n c e n t r a t i o n s remain below 1 ppm, a f t e r 15 years of continued d i s p o s a l p r a c t i c e s . T h i s i s due to l i m i t e d c o u n t e r c u r r e n t s o l u t e t r a n s p o r t . On the other hand the long-term c o n c e n t r a t i o n i n W e l l 1 i n c r e a s e s by a p p r o x i -mately 7.0 ppm over background, s t e a d y - s t a t e being reached a f t e r about 6 y e a r s . To i l l u s t r a t e how the contaminated a q u i f e r i s r e s t o r e d to i t s i n i t i a l s t a t e by n a t u r a l groundwater r e -charge and t r a n s p o r t p r o c e s s e s , the n i t r a t e i nput to groundwater was d i s c o n t i n u e d a f t e r f i v e years of steady waste d i s p o s a l . The t o t a l n i t r o g e n l o a d i n g of the a q u i f e r i s 4.4 m e t r i c tonnes over the f i v e year p e r i o d . F i g u r e s 4.11(a) to 4.11(d) present the r e s u l t i n g n i t r a t e - N d i s t r i b u t i o n s i n the a q u i f e r , i n November of year 5, 6, 7, and 10, r e s p e c t i v e l y . At the end of year 10, i . e . 5 years a f t e r the c o n t r i b u t i o n was i n t e r r u p t e d , the maximum r e s i d u a l c o n c e n t r a t i o n was l e s s than 2.0 ppm: the groundwater q u a l i t y was n e a r l y completely renovated. F i g u r e 4.11 serves to i l l u s t r a t e how Model 2 can be used to t e s t v a r i o u s management a l t e r n a t i v e s f o r the p l o t . Of course, the n i t r a t e l o s s from the p l o t w i l l never be completely n i l , even when no waste i s a p p l i e d . P r i o r 143. F i g u r e 4.11 T r a n s i e n t maps of n i t r a t e - N c o n c e n t r a t i o n i n c r e a s e s i n groundwater, f o l l o w i n g d i s -c o n t i n u a t i o n of waste a p p l i c a t i o n a f t e r f i v e years . (a) : November of Year 5 (b) : November of Year 6 (c) : November of Year 7 (d) : November of Year 10 Parameter v a l u e s V h = 0.6 m/day cxL = 60 m a T = 12 m. \ / \ 148. to t e s t i n g , the n i t r a t e excess over p l a n t requirements must t h e r e f o r e be e s t i m a t e d f o r a given management p o l i c y . Mathematical t o o l s are a v a i l a b l e f o r that purpose (e.g. B u l l e y and Cappelaere, 1978). 4.2.3 S e n s i t i v i t y A n a l y s i s A s e n s i t i v i t y a n a l y s i s was performed on the a q u i f e r flow and d i s p e r s i o n c h a r a c t e r i s t i c s , to e s t a b l i s h t h e i r importance i n mass t r a n s p o r t problems. More s p e c i f i c a l l y , the parameters t e s t e d were the flow v e l o c i t y V^, the l o n g i t u d i n a l d i s p e r s i t y , the t r a n s v e r s e d i s p e r s i t y , and the d i s p e r s i v i t y r a t i o r a = aL/a^,. The l a t t e r was used by Pickens and Lennox (1976) i n the s e n s i t i v i t y a n a l y s i s of a f i n i t e - e l e m e n t model f o r waste movement i n a c r o s s -s e c t i o n a l s u b s urface flow system. T h i s r a t i o i s a convenient di m e n s i o n l e s s parameter which e x h i b i t s l e s s v a r i a b i l i t y than the d i s p e r s i v i t y c o e f f i c i e n t s and themselves, s i n c e these are very h i g h l y l i n e a r l y c o r r e l a t e d . Values of u s u a l l y range between 1 and 10, w i t h a common average of 5 f o r i s o t r o p i c porous media. For each of the three t r a n s p o r t parameters V, , a T , h L and r Q , a set of three l e v e l s was adopted (low, median, h i g h ) , with the e s t i m a t e used i n S e c t i o n 4.2.2 as the median v a l u e . The 3x3x3 v a l u e s , i n d i c a t e d i n Table 4.1, y i e l d 27 p o s s i b l e combinations, each of them c o r r e s p o n d i n g to a d i f f e r e n t p o l l u t a n t behaviour i n the s a t u r a t e d groundwater system. 149. TABLE 4.1 VALUES OF TRANSPORT PARAMETERS FOR SENSITIVITY ANALYSIS IN REGIONAL AQUIFER P arameter Symb o l Unit Low Median High Flow V e l o c i t y V h m/day 0.3 0. 6 1 L o n g i t u d i n a l D i s p e r s i v i t y a L m 10 60 100 D i s p e r s i v i t y R a t i o r a 1 5 10 To i s o l a t e the e f f e c t s of each parameter, output was f i r s t generated by v a r y i n g only one parameter at a time, the other two remaining at t h e i r median l e v e l . F i g u r e s 4.12 to 4.14 present the steady c o n c e n t r a t i o n envelopes along the x ax i s between x=0 and x=2000 (m), f o r v a r y i n g flow v e l o c i t y , l o n g i t u d i n a l d i s p e r s i v i t y , and d i s p e r s i v i t y r a t i o , r e s p e c t i v e l y . In a l l three f i g u r e s , the median curves, drawn i n p l a i n l i n e s , correspond to the case V = 0.6 m/day, a T= 60 m, r.= 5, d i s c u s s e d i n S e c t i o n 4.2.2, which serves as a r e f e r e n c e . Flow V e l o c i t y I t can be seen t h a t , with a s m a l l e r change o f magnitude than the d i s p e r s i v i t y parameters, the v e l o c i t y v a r i a t i o n s have a s i g n i f i c a n t l y g r e a t e r e f f e c t on the con-c e n t r a t i o n envelopes, p r i n c i p a l l y i n the zone c l o s e to the d i s p o s a l area (z < 500 m). This c o n c l u s i o n i s p a r t i c u l a r l y important i n view of the u n c e r t a i n t y a s s o c i a t e d with flow 153. v e l o c i t y estimation in groundwater studies, where an error of one order of magnitude i s generally regarded as a f a i r l y good achievement. Cle a r l y , the convective term plays a dominant role in mass transport problems, and the error on the pollutant concentration estimate w i l l be clo s e l y related to that on the v e l o c i t y estimate. Unfor-tunately, while a v e l o c i t y v a r i a t i o n of one order of magnitude w i l l not have s i g n i f i c a n t e f f e c t on the hydro-l o g i c behaviour of a regional groundwater system, the same v a r i a t i o n in n i t r a t e concentration would be of considerable importance to water quality measurement and water supply a c c e p t a b i l i t y . This point can be seen as a strong objection to groundwater quality modeling, as i t r e l i e s on better v e l o c i t y determinations than can presently be achieved with conventional hydraulic or geophysical methods. However, when associated with extensive long-term groundwater quality monitoring, simulation could in turn provide a much more accurate estimate of flow v e l o c i t i e s than conventional methods. In that perspective, a r e l i a b l e water quality transport model i s necessary. As could be expected, lower v e l o c i t i e s generate higher concentrations at a l l points of the aquifer, i n d i c a -ting a slower rate of n i t r a t e f l u s h i n g . Absolute variations progressively decrease with distance from the source. Beyond the point where the envelope curves j o i n to form a single hyperbola-shaped l i n e (z > 500 m), the concentration 154. i s c l o s e l y p r o p o r t i o n a l to the i n v e r s e of the v e l o c i t y , f o r a given s e t of d i s p e r s i v i t y c o e f f i c i e n t s . The c o e f f i c i e n t of p r o p o r t i o n a l i t y decreases with d i s t a n c e , as d e s c r i b e d by the lower curve i n F i g u r e 4.12 (V^ = lm). For a L = 60 m and r Q = 5, the s t e a d y - s t a t e c o n c e n t r a t i o n was f i t t e d to the h y p e r b o l i c e x p r e s s i o n : c i n ppm c(x) = Y~ . ( | | y j - 0.35) x i n m (x>500m) (4.7) h i n m/day This e x p r e s s i o n shows that one order of magnitude decrease of the v e l o c i t y estimate V. r e s u l t s i n one order of h magnitude i n c r e a s e of the p r e d i c t e d c o n c e n t r a t i o n s . C l e a r l y , the major e f f e c t of the conv e c t i o n term is to c o n t r o l the number of s u c c e s s i v e f r o n t s that overlap i n the' a q u i f e r , which determines the magnitude of the con-c e n t r a t i o n b u i l d - u p . I t can be noted that f o r any v e l o c i t y V, i n c l u d e d between the c r i t i c a l v a l u e s h n p o l l u t a n t s f r o n t s w i l l superimpose s u c c e s s i v e l y , L x being the l e n g t h of the f i e l d (Lx = 313 m) and T the l e a c h i n g c y c l e p e r i o d (T = 365 days). I t can be seen that the c r i t i c a l v e l o c i t i e s = 0.86 m/day and - 0.46 m/day separate the values = 1, 0.6, and 0.3 (m/day) chosen i n t h i s study. T h e r e f o r e , these 3 valu e s correspond to the s t a c k i n g of 1, 2, and 3 f r o n t s , r e s p e c t i v e l y . 155. D i s p e r s i v i t y The flow v e l o c i t y w i l l now be kept constant V. - 0.6 m/day. F i g u r e 4.13 shows that i n c r e a s i n g the d i s -h p e r s i v i t i e s (while m a i n t a i n i n g the d i s p e r s i v i t y r a t i o constant) r e s u l t s i n a n o n - l i n e a r decrease i n c o n c e n t r a t i o n s . Indeed, as c o n c e n t r a t i o n s decrease, so do the c o n c e n t r a t i o n g r a d i e n t s , and t h e r e f o r e d i s p e r s i v e f l u x e s i n c r e a s e more slo w l y than the d i s p e r s i v i t i e s themselves. In the zone past the 500 m mark, a one order of magnitude i n c r e a s e of the d i s p e r s i v i t y c o e f f i c -i e n t s r e s u l t s i n a c o n c e n t r a t i o n decrease of approximately 60%. When the l o n g i t u d i n a l d i s p e r s i v i t y i s kept constant ( F i g u r e 4.14), a one order of magnitude decrease of the d i s -p e r s i v i t y r a t i o ( c o r r e s p o n d i n g to a one order of magnitude i n c r e a s e of the t r a n s v e r s e d i s p e r s i v i t y ) a l s o r e s u l t s i n a 60% decrease i n c o n c e n t r a t i o n . T h i s o b s e r v a t i o n prompted a comparison of the r e l a t i v e e f f e c t s of the l o n g i t u d i n a l and t r a n s v e r s e d i s p e r s i v i t i e s , a and a , on the steady n i t r a t e Li X c o n c e n t r a t i o n s . In that purpose, the and v a l u e s used f o r the v a r i o u s runs were p l o t t e d on a l o g - l o g graph ( F i g u r e 4.15). Near each p o i n t corresponding to a s i m u l a t i o n run, the value obtained f o r the steady c o n c e n t r a t i o n at x = 1000m is i n d i c a t e d . I t can be seen on t h i s p l o t t h at e q u i c o n c e n t r a -t i o n l i n e s are very n e a r l y p a r a l l e l to the a L a x i s . T h i s means that most of the v a r i a t i o n s i n c o n c e n t r a t i o n i s due to a change i n t r a n s v e r s e d i s p e r s i v i t y . I n c r e a s i n g the l o n g i t u d i n a l d i s p e r s i o n by one order of magnitude r e s u l t s i n a decrease of the 1000m-concentration of only about 3%,which i s s m a l l e r than the r e c u r r e n t experimental e r r o r on water q u a l i t y data. 100 -H •H ' > • H CO !-l CU CX CO •rH T3 crj c •H T3 3 4-1 •H 00 c o 10 - J ,12 .26 .40 6.73 I 6 .85 i • 1 6.97 4.42 4.48 4.55 1 1 I I 3.52 3.57 3.62 2.55 2.58 2.61 10 Transverse d i s p e r s i v i t y , (m) 1,49 1.51 1.15 1.17 1.53 1.19 100 Figure 4.15: Effects of longitudinal vs. transverse dispersiyities on steady nitrate-N concentrations. Each point shows the concentration at (x=1000m ; y=0) produced by one simulation run,: for V = 0.6m/day. Broken lines are equiconcentration lines obtained by regression on these points, h 157. T h i s o b s e r v a t i o n , at f i r s t s u r p r i s i n g , must be emphasized i n i t s c o n t e x t . Compared to the t r a n s v e r s e d i s -p e r s i v i t y , the l o n g i t u d i n a l d i s p e r s i v i t y c o e f f i c i e n t has l i t t l e e f f e c t on the long-term c o n c e n t r a t i o n generated by steady c l i m a t i c and management c o n d i t i o n s , at a p o i n t on the x axis s u f f i c i e n t l y remote from the source area. T h i s would not be t r u e f o r a s i n g l e p o l l u t i o n event, i n the t r a n s i e n t phase of contamination p a t t e r n development, or at a p o i n t l o c a t e d c l o s e to or i n the source area. a l s o s t r o n g l y a f f e c t s the time necessary to reach s t e a d y - s t a t e . But once s t e a d y - s t a t e i s reached, the l o n g i t u d i n a l extent of the contamination plume i s c o n s i d e r a b l y l a r g e r than i t s width (see F i g u r e s A.10 and 4.11). Thus, l o n g i t u d i n a l c o n c e n t r a t i o n g r a d i e n t s are s i g n i f i c a n t l y s m a l l e r than l a t e r a l g r a d i e n t s , and the c r o s s - s e c t i o n a l area where d i s -p e r s i v e f l u x e s occur i s much l a r g e r i n the t r a n s v e r s e d i r e c t i o n than i n the l o n g i t u d i n a l d i r e c t i o n . T h e r e f o r e , the s t e a d y - s t a t e contamination p a t t e r n w i l l be l a r g e l y determined by the d i s p e r s i v e mass t r a n s p o r t i n the y 1 d i r e c t i o n , p r o p o r t i o n a l to the d i s p e r s i v i t y c o e f f i c i e n t , the c o n c e n t r a t i o n g r a d i e n t and the c r o s s - s e c t i o n a l area i n t h a t d i r e c t i o n . T h i s t r a n s v e r s a l d i s p e r s i v e f l u x w i l l be c o n s i d e r a b l y more s e n s i t i v e to i t s a s s o c i a t e d d i s p e r s i -v i t y c o e f f i c i e n t than i t s l o n g i t u d i n a l c o u n t e r p a r t . T h i s p o i n t should be s t r o n g l y emphasized i n view of the l a r g e amount of s i m u l a t i o n work, based on the premises that the h o r i z o n t a l t r a n s v e r s e d i s p e r s i o n process could be 158. n e g l e c t e d compared to the l o n g i t u d i n a l d i s p e r s i o n (e.g. Perez et a l . , 1974; Cherry et a l . , 1975; Pickens and Lennox, 1976). These models assume t h a t a l l contaminant movement occurs i n the v e r t i c a l plane of l o n g i t u d i n a l c r o s s - s e c t i o n , which i s true only i f the l a t e r a l extent of the contaminant source i s s e v e r a l orders of magnitude l a r g e r than the t r a n s v e r s e d i s p e r s i v i t y c o e f f i c i e n t , and i f the plane of the s e c t i o n i s s u f f i c i e n t l y remote from the l a t e r a l b o u n daries. In t h i s study, t h i s d i s t a n c e i s no g r e a t e r than 70 meters; i n the range of t r a n s v e r s e d i s p e r s i v i t y values to be expected f o r t h i s a q u i f e r , the assumption of no l a t e r a l mass f l u x e s i s t r u e f o r the v e r t i c a l symmetry plane only. With the data p l o t t e d on F i g u r e 4.15, i t was p o s s i b l e to express the s t e a d y - s t a t e c o n c e n t r a t i o n at the 1000 m l o c a t i o n c(x=1000 m) as an a n a l y t i c a l f u n c t i o n of t r a n s v e r s e d i s p e r s i v i t y a T , f o r a v e l o c i t y = 0.6 m/day,. n e g l e c t i n g the e f f e c t of l o n g i t u d i n a l d i s p e r s i v i t y , with an e r r o r no g r e a t e r than 3%. T h i s r e g r e s s i o n e x p r e s s i o n was then r e l a t e d to the c o n c e n t r a t i o n C Q = 3.3 ppm o b t a i n e d f o r a_ = 60 m, a = 12 m, and V = 0.6 m/day, to y i e l d the T L n equation c(x=1000m) = C Q . f ( l o g a T) (4.9) c(x) and C i n ppm, a_, i n meters. 159. where ( f ( u ) = • 3 ; ° 1 . 7 - 0.80 i f u > 0.85 (C (4.9) ( f ( u ) = 2.6 - 1.5.u i f u < 0.85 To t e s t whether a g e n e r a l i z e d a n a l y t i c a l e x p r e s s i o n of steady c o n c e n t r a t i o n s c o u l d be o b t a i n e d , the e x p r e s s i o n f ( l o g a ) 2 5 0 Q c ( x , V h , a L , a T ) — ± . ( f f f f - 0.35) (4.10) which combines equations 4.7 and 4.9, was compared to the p o o l of a v a i l a b l e s i m u l a t i o n output and was found to match the data very s a t i s f a c t o r i l y . The r e l a t i v e e r r o r remained at or below 10%, which i s the best that can be expected s i n c e only two s i g n i f i c a n t d i g i t s were sought f o r the r e g r e s s i o n c o e f f i c i e n t s i n the a n a l y t i c a l e x p r e s s i o n s . This remarkable agreement proves t h a t , f o r the -»• l o n g term n i t r a t e d i s t r i b u t i o n along the x a x i s , there e x i s t s very l i t t l e i n t e r a c t i o n between the flow v e l o c i t y , the d i s p e r s i o n p r o c e s s e s , and the d i s t a n c e from the source. A s i g n i f i c a n t advantage of e q u a t i o n 4.10 i s to p r o v i d e an a n a l y t i c a l e x p r e s s i o n of the steady c o n c e n t r a t i o n s e n s i -t i v i t y to the t r a n s p o r t parameters and the d i s t a n c e x. Although e x p r e s s i o n 4.10, l i k e a l l r e g r e s s i o n models, i s v a l i d only i n the range of parameters v a l u e s f o r which i t was e s t a b l i s h e d ( i . e . 500 <_ x _< 2000 (m) , 0.3 i V h < 1 (m/day), 10 < a L <_ 100 (m) , 1 < a T < 100 (m)) , i t can p r o v i d e a f i r s t e s t i m a t i o n of c o n c e n t r a t i o n s r e -s u l t i n g from more extreme parameter v a l u e s , without r e s o r t i n g to a f u l l s i m u l a t i o n run. 160. Convection, versus D i s p e r s i o n Within the range of parameters values used f o r t h i s v s e n s i t i v i t y a n a l y s i s , a l a s t t e s t was performed to compare the e f f e c t s of the c o n v e c t i v e and d i s p e r s i v e terms on the r e s u l t i n g c o n c e n t r a t i o n d i s t r i b u t i o n s . The outputs from a run w i t h comparatively l i t t l e c o n v e c t i v e t r a n s p o r t (V^=0.3 m/day; a^=100m; a^ ,= 100m) and a run with c o m p a r a t i v e l y l i t t l e d i s p e r s i v e t r a n s p o r t (V h=lm/day; a L=lm; a T=lm) are p l o t t e d on Figure 4.16. With the f i r s t s et of parameters, t h r e e s u c c e s s i v e f r o n t s superimpose on each other (V^ > > V ^ ) , which r e s u l t s i n high c o n c e n t r a t i o n v a l u e s w i t h i n the p l o t a r ea. However, as the d i s t a n c e from the p l o t i n c r e a s e s , the e f f e c t s of the l a r g e d i s p e r s i v i t i e s become predominant, to such an extent that beyond x=600m, c o n c e n t r a t i o n s drop below the values obtained when p o l l u t i o n f r o n t s do not o v e r l a p (V, > V . ) , with the second s e t of n l parameters. This drop shows that the hydrodynamic d i s p e r s i o n phenomenon occurs p r e c i s e l y because of the water movement, and i s a d i r e c t f u n c t i o n of the d i s t a n c e t r a v e l l e d by the f l u i d . F i g u r e s 4.17 and 4.18 show the n i t r a t e d i s t r i b u -t i o n maps before and a f t e r the s t a r t of l e a c h i n g in the 15th y e a r , f o r the f i r s t and second set of parameters r e s p e c t i v e l y . They r e p r e s e n t the extreme p o s s i b l e cases. In F i g u r e 4.18, where the d i s p e r s i o n process and the o v e r l a p p i n g of p o l l u t i o n f r o n t s are s l i g h t , these f r o n t s can c l e a r l y be seen moving 162 . F i g u r e 4.17: C y c l i c maps of n i t r a t e - N c o n c e n t r a t i o n i n c r e a s e s i n groundwater, f o r smal l c o n v e c t i v e and l a r g e d i s p e r s i v e f l u x e s . (a) : October of Year 15 (b) : November of Year 15 Parameter v a l u e s : = 0.3 m/day = 100 m a T = 100 m. 165. F i g u r e 4.18: C y c l i c maps of n i t r a t e - N c o n c e n t r a t i o n i n c r e a s e s i n groundwater, f o r l a r g e c o n v e c t i v e and sm a l l d i s p e r s i v e f l u x e s . October of Year 15 November of Year 15 Parameter v a l u e s : V, = 1 m/day otT = 1 m a T = 1 m . (a) : (b) : 168. westward, a l t e r e d mostly by d i l u t i o n i n the i n c r e a s i n g l y deep a q u i f e r . In F i g u r e 4.17 on the other hand, the n i t r a t e plume extends widely i n the t r a n s v e r s e d i r e c t i o n , but r e q u i r e s c o n s i d e r a b l e time to reach the r i v e r . Since these maps are obtained f o r the same d i s p e r s i v i t y r a t i o , the wide d i f f e r e n c e s i n the shapes of the plumes show the importance of the v e l o c i t y e f f e c t . However, the ab s o l u t e maximum c o n c e n t r a t i o n s at a given date d i f f e r by no more than 25% between these two extreme cases, and t h e i r r e s p e c t i v e p o s i t i o n s are no more than 150 meters a p a r t . T h e r e f o r e , i t appears that i f water p o l l u t i o n c r i t e r i a are to be e s t a b l i -shed i n terms of the long-term maximum a l l o w a b l e concen-t r a t i o n i n an a q u i f e r , Model 2 can be used as a management t o o l with a s e n s i t i v i t y no g r e a t e r than the exp e r i m e n t a l u n c e r t a i n t y . 169. 5. GENERAL DISCUSSION 5.1 Water t a b l e f l u c t u a t i o n s P r e d i c t i o n of the p o s i t i o n of the moving boundary f o r the s a t u r a t e d zone i s c r u c i a l to good n i t r a t e movement s i m u l a t i o n by Model 1. E x c e l l e n t agreement between p r e d i c -ted and observed water t a b l e f l u c t u a t i o n s t e s t i f i e s to the r e l i a b i l i t y of the water balance procedure f o r the r o o t zone and of the v e r t i c a l v e l o c i t y p r o f i l e f o r the s a t u r a t e d zone. The s o i l m o isture balance i n p a r t i c u l a r must be a c c u r a t e , s i n c e a l a r g e p a r t of n i t r a t e l e a c h i n g o c c u r s by c o n v e c t i o n with drainage water (the s m a l l v a l u e of the index of mixing C^ shows that c o n v e c t i o n i s predominant at the s i t e i n v e s t i g a t e d ) . Not only does the s o i l moisture content c o n t r o l the a b s o l u t e amount of drainage l e a v i n g the root zone, but i t a l s o l a r g e l y determines the c o n c e n t r a t i o n of s o l u t e i n the drainage water. At many p o l l u t i o n - s e n s i t i v e s i t e s such as the one s t u d i e d , s o i l s w i t h r e l a t i v e l y low w a t e r - h o l d i n g c a p a c i t y o v e r l a y a coarse s u b s o i l c o n s t i t u t i n g the w a t e r - b e a r i n g stratum. L i t t l e b u f f e r i n g between h y d r o l o g i c event and r e s e r v o i r response r e s u l t s i n sharp and wide water t a b l e f l u c t u a t i o n s . Such s i t u a t i o n s can be s a t i s f a c t o r i l y modelled using s i m p l i f i e d s o l u t i o n s of the flow e q u a t i o n . Black et a l . (1969) noted that i t i s a c h a r a c t e r i s t i c of 170. the unsaturated flow equation that f l u x e s i n and out of a s o i l system may be es t i m a t e d with s u r p r i s i n g p r e c i s i o n , u s i n g very gross approximations. S e v e r a l i n v e s t i g a t o r s ( N i e l s e n et a l . , 1973; Warrick et a l . , 1977) observed that the s i m p l i f i e d drainage e x p r e s s i o n 2.20, based on the u n i t y h y d r a u l i c head g r a d i e n t approximation i n the roo t zone, adequately d e s c r i b e s experimental r e s u l t s . Freeze (1967) showed that the gover-n i n g equation f o r s a t u r a t e d , unsteady flow e s s e n t i a l l y s i m p l i f i e s to i t s s t e a d y - s t a t e e x p r e s s i o n , i n unconfined a q u i f e r s . These concepts, on which the water movement com-ponent of both models i s based, appear v a l i d at the s i t e i n v e s t i g a t e d . Wierenga (1977) concluded that f o r p r e d i c -t i n g the q u a l i t y of drainage water, the use of a steady-s t a t e water movement model i s j u s t i f i e d . I t i s more d e s i r a b l e i n s t u d i e s of i r r i g a t i o n r e t u r n flow and ground-water p o l l u t i o n which may r e q u i r e s i m u l a t i o n over a p e r i o d of s e v e r a l y e ars. The a p p r o p r i a t e n e s s of such s i m p l i f i c a -t i o n s was d i s c u s s e d i n S e c t i o n s 1.4 and 1.6. 5.2 The short term, l o c a l s c a l e problem: D e t e r m i n a t i o n  of seasonal n i t r o g e n l o s s from the d i s p o s a l f i e l d . Based on Model 1, S e c t i o n A.1.3 r e v e a l e d the importance of the s t r a t i f i c a t i o n phenomenon i n the s a t u r a -ted zone of a shallow a q u i f e r , immediately below a waste d i s p o s a l s i t e , d u r i n g the l e a c h i n g p e r i o d . E x p e r i m e n t a l i n v e s t i g a t i o n of v e r t i c a l groundwater q u a l i t y p r o f i l e s by 171. Behnke and H a s k e l l (196S) , Hughes and Robson (1973), S p a l d i n g et a l . , (1976) and John et a l . , (1977) showed s i m i l a r r e s u l t s . Three important consequences f o r the determina-t i o n of non-point c o n t r i b u t i o n to groundwater a r e : 1) I n t e r p r e t a t i o n of groundwater samples must be based on a comprehensive s i m u l a t i o n of v e r t i c a l sub-s u r f a c e p o l l u t a n t movement i n the shor t term p e r i o d d u r i n g the wet season. 2) Sampling d e v i c e s must be made d e p t h - s p e c i f i c , because of the s e n s i t i v i t y of the method to the depth of sampling. 3) This l a r g e s e n s i t i v i t y poses the q u e s t i o n of space-averaging of data c o l l e c t e d at d i f f e r e n t depths on the p l o t , otherwise d e s i r a b l e to add s t a t i s t i c a l s i g n i f i c a n c e to the procedure ( S e c t i o n 3.7.2). Since the depth v a r i a t i o n s between piezometers remained w i t h i n 30 cm (1 f t ) t h i s l a s t p o i n t was not a s i g n i f i c a n t problem at the s i t e i n v e s t i g a t e d . P o i n t 2 w i l l be f u r t h e r developed i n the s e c t i o n devoted to data requirements. P o i n t 1 w i l l now be d i s c u s s e d . Model 1, developed and t e s t e d i n t h i s p r o j e c t , appears to c o n s t i t u t e a good t o o l f o r e s t i m a t i o n of n u t r i e n t l o s s from the ro o t zone. One-dimensional s i m u l a t i o n of water movement produced water t a b l e f l u c t u a t i o n s i n 172. remarkable agreement with recorded l e v e l s . P r e d i c t e d time of n i t r a t e appearance i n piezometers was c o n s i s t e n t with o b s e r v a t i o n . Simple model c a l i b r a t i o n i s p o s s i b l e from weekly to biweekly sample c o l l e c t i o n , at a given depth i n the s a t u r a t e d zone. Sampling frequency can be a d j u s t e d , a c c o r d i n g to recorded water t a b l e l e v e l s or water t a b l e p r e d i c t i o n s , to optimize the sampling program. Once the d i s p e r s i o n parameters are obtained from model c a l i b r a t i o n , an estimate of the n i t r a t e c o n t r i b u t i o n from the f i e l d to groundwater can be d e r i v e d by comparing measured peak c o n c e n t r a t i o n and p r e d i c t e d peak response to a t h e o r e t i c a l u n i t i n p u t . Model 1 s u c c e s s f u l l y p r e d i c t e d the time of n i t r o g e n r i s e i n the piezometers i n the f a l l 1977, f o r the f i r s t season f o l l o w i n g i t s c a l i b r a t i o n . S i m u l a t i o n output i s s t a b l e , due to important n e g a t i v e feedback e f f e c t s between v a r i a b l e s and c a l i b r a t i o n para-meters, both f o r the water q u a n t i t y and q u a l i t y components of the model. C o n s i d e r i n g the u n c e r t a i n t y i n v o l v e d with other estimates of the l e a c h i n g term in the s o i l n i t r o g e n budget, t h i s procedure n i g h t c o n s t i t u t e a d e s i r a b l e a l t e r n a t i v e . I t should however be the o b j e c t of f u r t h e r t e s t i n g to e s t a b l i s h i t s s t a t i s t i c a l v a l i d i t y . Because h o r i z o n t a l c o n c e n t r a t i o n g r a d i e n t s s t a r t to develop and v e r t i c a l g r a d i e n t s decay a f t e r most n i t r a t e s have been le a c h e d , the v a l i d i t y of the one-dimensional / 173. approximation d e t e r i o r a t e s i n the medium term Cup to a year) r e d i s t r i b u t i o n p r o c e s s . Three-dimensional f i n i t e - e l e m e n t s i m u l a t i o n would thus be r e q u i r e d i n the p o r t i o n of porous medium d i r e c t l y beneath the p o l l u t a n t source (medium term, l o c a l s c a l e problem). Because of the n o n - u n i f o r m i t y of manure a p p l i c a t i o n , and of the l a r g e s p a t i a l v a r i a b i l i t y of l e a c h i n g c h a r a c t e r i s t i c s of f i e l d s o i l s ( B i g g a r and N i e l s e n , 1976), such modeling r e q u i r e s a c o n s i d e r a b l y l a r g e r data base than commonly a v a i l a b l e , thereby d e f e a t i n g the i n i t i a l purposes d e f i n e d i n the I n t r o d u c t i o n . The n i t r a t e r e d i s t r i b u t i o n process i s of p r a c t i c a l i n t e r e s t only when i t s e f f e c t s on water q u a l i t y i n w e l l s tapping the a q u i f e r are c o n s i d e r e d . At t h i s l a r g e s c a l e , the system can be regarded as two-dimensional, because of the i n s i g n i f i c a n c e of depths compared to h o r i z o n t a l dintensions . 5.3 The long-term, r e g i o n a l - s c a l e problem: P r e d i c t i o n of n i t r a t e c o n c e n t r a t i o n d i s t r i b u t i o n i n the a q u i f e r . S e c t i o n A.2.2 showed t h a t i t i s p o s s i b l e to p r e d i c t the n i t r a t e c o n c e n t r a t i o n d i s t r i b u t i o n r e s u l t i n g from s u c c e s s i v e p o l l u t i o n f r o n t s emanating from the d i s p o s a l s i t e , u s i n g Model 2. T h i s s e m i - a n a l y t i c a l model s i m u l a t e s the two-dimensional t r a n s i e n t a r e a l movement and d i s p e r s i o n of a c o n s e r v a t i v e substance, i n a s t e a d y - s t a t e s a t u r a t e d groundwater flow system. Advantages of Model 2 over the a r e a l , f i n i t e - d i f f e r e n c e model f o r s i m u l a t i o n of r e g i o n a l 17A. groundwater q u a l i t y developed by the U.S. G e o l o g i c a l Survey CBredehoeft et a l . , 1976) i n c l u d e s i m p l i c i t y , s t a b i l i t y and c o n s i d e r a b l e s a v i n g s i n computer time and volume of core memory. R e q u i r i n g s u b s t a n t i a l l y l e s s input i n f o r m a t i o n f o r system d e f i n i t i o n , Model 2 can be r e a d i l y a p p l i e d to f i e l d s i t u a t i o n s f o r f i r s t a n a l y s i s and p r e d i c t i o n s of p o l l u t i o n problems. S i m i l a r advantages e x i s t over Perez et a l ' s c r o s s - s e c t i o n model (1974), which d i s r e g a r d s h o r i z o n t a l t r a n s v e r s e d i s p e r s i o n , an assumption shown to be i n a p p r o p r i a t e i n most p r a c t i c a l cases ( S e c t i o n 4.2.3). S i m u l a t i o n at the s i t e i n v e s t i g a t e d was performed u s i n g long-term c l i m a t i c averages, a value M f o r excess n i t r a t e s i n the r o o t zone of the d i s p o s a l f i e l d determined by c a l i b r a t i o n of Model 1, and estimates of s a t u r a t e d v e l o c i t y and d i s p e r s i t y parameters. I t was shown that from 5 to 15 years are necessary before n i t r a t e concen-t r a t i o n s stop r i s i n g i n the 2 km long p o r t i o n of a q u i f e r downstream from the d i s p o s a l s i t e and upstream from the p o i n t of d i s c h a r g e i n t o the r i v e r , R . The long-term c o n c e n t r a t i o n i n c r e a s e s are s i g n i -f i c a n t as f a r as the p o i n t R , where i t i s of the order of 1 ppm. One might be tempted to d i s r e g a r d t h i s c o n t r i b u t i o n s i n c e i t i s of the same magnitude as the c o n c e n t r a t i o n i n r a i n f a l l over the watershed (Beale, 1976). However, t h i s i value r e p r e s e n t s the i n c r e a s e caused by a 5 ha p l o t o n l y , and when cumulated with other sources the increment i s s i g n i f i c a n t with r e s p e c t to the 10 ppm recommended l i m i t . 175. C o n c e n t r a t i o n i n c r e a s e s i n domestic w e l l s tapping the a q u i f e r are even l a r g e r . E x c l u d i n g w e l l s on the farm p r o p e r t y , l o n g -term increases range approximately from 2 to 8 ppm. T h i s range r e f l e c t s the v a r i a t i o n i n w e l l d i s t a n c e s from the p l o t , but a l s o the u n c e r t a i n t y a s s o c i a t e d with the t r a n s p o r t para-meters used i n the model. The flow v e l o c i t y i n p a r t i c u l a r was shown to have a c o n s i d e r a b l e e f f e c t on r e s u l t i n g concen-t r a t i o n s i n the a q u i f e r . A more r e l i a b l e e s t i m a t e , r e p r e s e n -t i n g a l a r g e r s e c t i o n o f the a q u i f e r than attempted i n t h i s r e s e a r c h , should t h e r e f o r e be o b t a i n e d . E x p e r i m e n t a l data f o r d e t e r m i n a t i o n of the d i s p e r s i v i t y c o e f f i c i e n t s should be c o l l e c t e d i n the f i e l d . In p a r t i c u l a r , t r a n s v e r s e d i s p e r -s i v i t y , o f t e n n e g l e c t e d i n the l i t e r a t u r e , was proved to have s i g n i f i c a n t impact on long-term c o n c e n t r a t i o n s . Pickens and Lennox (1976) s t r e s s e d the u n c e r t a i n t y i n the values of the input parameters g e n e r a l l y encountered in f i e l d s t u d i e s of groundwater conta m i n a t i o n : "Two of the most important c o n s i d e r a t i o n s are the s e l e c t i o n of the most r e l i a b l e and e f f i c i e n t methods of determining these parameters under f i e l d c o n d i t i o n s and the - development of a more q u a n t i t a t i v e understanding of the u n c e r t a i n t i e s a s s o c i a t e d with the f i e l d d e t e r m i n a t i o n s " . Methods to o b t a i n these f i e l d parameters are d i s -cussed i n S e c t i o n 5.4. I t was o r i g i n a l l y b e l i e v e d that the u n c e r t a i n t y a s s o c i a t e d with a l l phases of modeling and c a l i -b r a t i o n c o u l d be e s t i m a t e d and r a t e d i n the form of proba-b i l i t y d i s t r i b u t i o n s , w i t h i n the framework of t h i s p r o j e c t . 176. S p e c i f i c a l l y , the 'noise' on the p o r o s i t y , water content and s o l u t e c o n c e n t r a t i o n v a r i a b l e s can be represen-ted by normal d i s t r i b u t i o n s , whereas the v a r i a b i l i t y of the t r a n s p o r t parameters ( c o n d u c t i v i t y , t r a n s m i s s i v i t y , d i s p e r s i v i t i e s ) and f l u x e s i s best approximated by l o g -normal d i s t r i b u t i o n s ( N i e l s e n et a l . , 1973; Biggar and N i e l s e n , 1976; Van der P o l et a l . , 1977). In view of the complexity of the t r a n s p o r t problem, i t i s u n l i k e l y that the s t a t i s t i c a l d i s t r i b u t i o n s d e s c r i b i n g the p r e d i c t e d outputs (e.g. l e a c h i n g l o s s e s , n i t r a t e c o n c e n t r a t i o n s i n ground-water) could be obtained d i r e c t l y by e v a l u a t i n g a n a l y t i c a l l y the p r o b a b i l i t y i n t e g r a l s . S u c c e s s i v e s t a c k i n g and m a t r l c i a l c o m p o s i t i o n of d i s c r e t i z e d p r o b a b i l i t y d i s t r i b u -t i o n s have been used with success f o r decision-making in the f i e l d of water resources f o r l i n e a r - c h a i n systems (Hershman, 1974; W a l t e r s , 1975; Brox, 1976). Monte-Carlo s i m u l a t i o n techniques ( K l e i j n e n , 1974) have been found best s u i t e d f o r subsurface water movement (Freeze, 1975; Rao et a l . , 1977; Warrick et a l . , 1977) and f o r groundwater q u a l i t y s i m u l a t i o n i n a r e g i o n a l a q u i f e r system (Mercado, 1976). U n f o r t u n a t e l y , because of l i m i t a t i o n s i n r e s e a r c h time and data c o l l e c t i o n , the p r o j e c t has not been c a r r i e d that f a r . However, the author f i r m l y b e l i e v e s that s t o c h a s t i c modeling could and should f o l l o w the d e t e r m i n i -s t i c stage achieved so f a r . Since the i n t e r r e l a t i o n s h i p s 177. between most v a r i a b l e s i n Model 2 are expressed i n e x p l i c i t forms, such an approach should not r a i s e s e r i o u s d i f f i c u l t t i e s . 5 . 4 Data Requirements General methods a v a i l a b l e f q r f i e l d d e t e r m i n a t i o n of t r a n s p o r t model parameters were reviewed i n S e c t i o n 1.5. We w i l l now focus on f u r t h e r c o n s i d e r a t i o n s r e l a t i v e to data a c q u i s i t i o n f o r c a l i b r a t i o n of the models developed i n t h i s t h e s i s . 5.4.1 Model 1 C a l i b r a t i o n of Model 1 i s based on a permanent re c o r d of water t a b l e f l u c t u a t i o n s and on d i s c r e t e (weekly to biweekly) groundwater sample c o l l e c t i o n , at a known depth i n the s a t u r a t e d zone. Sampling frequency can be a d j u s t e d a c c o r d i n g to water t a b l e o b s e r v a t i o n s or p r e d i c t i o n s , to o p t i m i z e the sampling program. S e v e r a l advantages are r e c o g n i z e d f o r the ground-water sampling procedure, as an i n - s i t u data a c q u i s i t i o n me thod : I t p r o v i d e s a d i r e c t measurement of the v a r i a b l e we are u l t i m a t e l y concerned with, namely the s p a t i a l and temporal d i s t r i b u t i o n of n i t r a t e c o n c e n t r a t i o n s i n the a q u i f e r . - I t i s a low-cost, n o n - d i s t u r b i n g f i e l d method. Large numbers of samples can be obtained with minimal time e x p e n d i t u r e . 178. I t performs an a r e a l and temporal i n t e g r a t i o n which a l l e v i a t e s the problems a s s o c i a t e d with the v a r i -a b i l i t y of f i e l d - m e a s u r e d s o i l - w a t e r p r o p e r t i e s , analysed by N i e l s e n et a l . (1973) and Biggar and N i e l s e n C1976). This l a s t p o i n t i s of great s i g n i f i c a n c e with r e s p e c t to the n o n - u n i f o r m i t y of waste a p p l i c a t i o n i n the f i e l d . A l s o , because of the l a r g e g r a v i t a t i o n a l i n f l u e n c e on flow, s u r f a c e and i n t e r f a c e i r r e g u l a r i t i e s can produce flow v a r i a t i o n s that w i l l not be q u i c k l y smoothed out by l a t e r a l mixing and d i s p e r s i o n . To minimize the number of measurements necessary f o r macroscopic d e s c r i p t i o n of the system, the f i e l d sampling device must t h e r e f o r e perform a n o n - d i s t u r b i n g space and time i n t e g r a t i o n on the measured v a r i a b l e s . Such averaging i s produced by the groundwater sampling procedure. In view of the d i f f i c u l t i e s a s s o c i a t e d with s o i l p r o f i l e a n a l y s i s as a method to estimate n i t r o g e n movement i n f i e l d c o n d i t i o n s ( d i s c u s s e d i n S e c t i o n 3.7.1), groundwater sampling t h e r e f o r e appears as a more promising i n - s i t u data a c q u i s i t i o n method f o r e s t i m a t i o n of n i t r a t e l e a c h i n g from waste d i s p o s a l s i t e s . Jury and Gardner (1974) s t a t e d that the problem of scale i s one of the c e n t r a l problems i n s o i l p h y s i c s at t h i s time, simply because we do not know how to s c a l e up from p o i n t measurements and c a l c u l a t i o n s to achieve an average over the e n t i r e area of i n t e r e s t . 179. Because of the c o n c e n t r a t i o n v a r i a t i o n s with depth i n the s a t u r a t e d zone (see S e c t i o n 4.1.3), i t i s important that sampling be performed at s p e c i f i c , d i s c r e t e depth i n t e r v a l s . F u r t h e r t e s t i n g of the model should be based on data c h a r a c t e r i z i n g the whole groundwater p r o f i l e . In t h a t r e s p e c t , shallow w e l l s 'or piezometers, such as used i n t h i s p r o j e c t , c o n s t i t u t e r a t h e r crude sampling t o o l s and p r o v i d e i n f o r m a t i o n that can be hard to i n t e r p r e t . More s o p h i s t i c a -ted, accurate and f l e x i b l e instruments have been devised r e c e n t l y , f o r the s p e c i f i c purpose of m o n i t o r i n g groundwater q u a l i t y below t a b l e i n shallow a q u i f e r s or l i t t o r a l sediments (Hansen and H a r r i s , 1974; S p a l d i n g et a l . , .1976 ; John et a l . , 1977). These are d r i v e n i n t o the ground f o r a 'once-o n l y ' c o l l e c t i o n or f o r permanent m o n i t o r i n g , and can provide l a r g e numbers of d i s c r e t e , d e p t h - s p e c i f i c groundwater samples.-Reported advantages i n c l u d e low-cost, s i m p l i c i t y , p o r t a b i l i t y , the d e t a i l with which temporal and s p a t i a l v a r i a t i o n s i n chemical composition can be monitored, and the ease with which submerged s i t e s can be sampled. To escape boundary e f f e c t s , the sampling p o i n t s should be l o c a t e d more than 25 meters away from the d i s p o s a l area boundaries. This c o n s t r a i n t should not i n t r o d u c e e x c e s s i v e i n t e r f e r e n c e w i t h normal machinery o p e r a t i o n on the s i t e . 5.4.2 Model 2 I t was shown ( S e c t i o n 4.2.3) that the p r e c i s i o n 180. on the s a t u r a t e d flow v e l o c i t y estimate needed f o r the model can seldom be e x p e r i m e n t a l l y o b t a i n e d , u s i n g the c o n v e n t i o n a l h y d r a u l i c methods. These i n d i r e c t p r o c edures, based on Darcy *« law, r e q u i r e the e s t i m a t i o n of heads d i s t r i b u t i o n , h y d r a u l i c c o n d u c t i v i t y and p o r o s i t y , and t h e r e f o r e compound u n c e r t a i n t i e s and e r r o r s . C o n v e r s e l y , t h i s suggests the p o s s i b i l i t y of using f i e l d s t u d i e s of groundwater q u a l i t y to a c t u a l l y measure the v e l o c i t y . t e r m vdLth b e t t e r p r e c i s i o n . D i r e c t v e l o c i t y e s t i m a t e s , based on s i n g l e - w e l l and m u l t i p l e - w e l l t r a c e r t e c h n i q u e s , were reviewed by F r i e d (1975). For t h i s purpose, a r e l i a b l e water q u a l i t y t r a n s p o r t model i s needed. I n - s i t u c a l i b r a -t i o n can then y i e l d the t r a n s p o r t parameters, namely flow v e l o c i t y , l o n g i t u d i n a l and t r a n s v e r s e d i s p e r s i v i t i e s , by s o l v i n g t h e ' i n v e r s e problem' ( S e c t i o n 1.5). The piezometer data obtained at the d i s p o s a l s i t e alone are i n s u f f i c i e n t to c a l i b r a t e Model 2, i . e . o b t a i n v a l u e s f o r the t r a n s p o r t parameters, s i n c e ( 1 ) These are s h o r t term data; long term i n f o r m a t i o n i s needed to ensure adequate p r e c i s i o n f o r the c a l i b r a t i o n procedure, (2) These are l o c a l - s c a l e data; to o b t a i n adequate p r e c i s i o n , i n f o r m a -t i o n from p o i n t s at s u f f i c i e n t d i s t a n c e from the d i s p o s a l s i t e i s needed, to sample a r e p r e s e n t a t i v e s e c t i o n of the s i m u l a t e d system. (3) Model 1 showed i n S e c t i o n 4.1.3 that c o n c e n t r a t i o n s i n p i e z o m e t e r s , beneath the d i s p o s a l f i e l d , are very s e n s i t i v e to depth of c o l l e c t i o n , and, t h e r e f o r e , 181. bear l i t t l e r e l a t i o n s h i p with the average v e r t i c a l concen-t r a t i o n s produced by Model 2. C a l i b r a t i n g Model 2 on w e l l s o u t s i d e the s p r e a d i n g area r e q u i r e s that s e p a r a t i o n of observed c o n c e n t r a t i o n s between the c o n t r i b u t i o n from the spreading p r a c t i c e and t h a t from other sources can be performed. For t h i s to be p o s s i b l e a f a r more e x t e n s i v e f i e l d study i s n e c e s s a r y . Rather than c a l i b r a t i n g the model f o r n i t r a t e s , a l e s s u b i q u i t o u s substance could be used, which p r e f e r a b l y has the same i n t e r a c t i o n with water and the s o l i d matrix as n i t r a t e s . The e x p e r i m e n t a l d e t e r m i n a t i o n of groundwater p o l l u t i o n parameters was analysed i n a comprehensive review by F r i e d (1975). Methods f o r the f i e l d d e t e r m i n a t i o n of the d i s p e r s i o n c o e f f i c i e n t s were s e l e c t e d a c c o r d i n g to the s c a l e of the problem. D i r e c t f i e l d methods f o r the d e t e r m i n a t i o n of ' p o l l u t i o n v e l o c i t i e s ' are a l s o i n v e s t i g a t e d . Because the d i s p e r s i v i t y c o e f f i c i e n t s depend on the s i z e of the sample of geology on which the experiment i s conducted, i t i s n e c e s s a r y to conduct a t e s t at a s c a l e approaching the s c a l e of the problem. U n f o r t u n a t e l y , p r a c t i c a l c o n s i d e r a t i o n s g e n e r a l l y r e s t r i c t the s p a c i n g between the w e l l s i n a 2-well t r a c e r t e s t to having the w e l l s no more than f i f t y to s i x t y meters apart (Bredehoeft et a l . , 1976). These workers c o n t r a s t e d t e s t s to determine the t r a n s m i s s i v i t y and storage c o e f f i c i e n t s of an a q u i f e r , 182. and t e s t s t o d e t e r m i n e i t s p o r o s i t y and d i s p e r s i v i t y c h a r a c t e r i s t i c s . The p r e s s u r e r e s p o n s e t o pumping an a q u i f e r o c c u r s q u i c k l y and e x t e n d s t o g r e a t d i s t a n c e s i n a r e l a t i v e l y s h o r t t i m e . F o r t h i s r e a s o n , t e s t s to d e t e r m i n e the h y d r a u l i c p r o p e r t i e s o f an a q u i f e r sample a l a r g e segment o f t h e s y s t e m u s u a l l y i n a s h o r t t i m e . T h i s c o n t r a s t s t o the a c t u a l movement o f some t r a c e r t h r o u g h the s y s t e m , n e c e s s a r y t o d e t e r m i n e the d i s p e r s i v i t y . A c t u a l t r a n s p o r t o f w a t e r m o l e c u l e s o c c u r s s l o w l y t h u s p l a c i n g p r a c t i c a l r e s t r i c t i o n s on t e s t s w h i c h r e q u i r e s u c h t r a n s p o r t i n t h e s y s t e m . One w o u l d t h e r e f o r e s e r i o u s l y q u e s t i o n w h e t h e r i t i s f e a s i b l e to c o n d u c t a f i e l d e x p e r i m e n t on a s u f f i c i e n t l y l a r g e s c a l e t o measure the d i s p e r s i v i t y c o e f f i c i e n t s t h a t w o u l d a p p l y t o p r o b l e m s o f r e g i o n a l f l o w . F i n a l l y , i t must be s t r e s s e d t h a t b e f o r e s t a r t i n g s u c h a d a t a c o l l e c t i o n p r o g r a m , the w o r t h o f a d d i t i o n a l d a t a must be f u r t h e r e v a l u a t e d , by c o m p a r i n g i t s c o s t to t h e p o t e n t i a l i n c r e a s e i n c o n f i d e n c e on t h e model p r e d i c t i o n . 5.5 F u r t h e r Recommendations In t h i s p r o j e c t , b i o c h e m i c a l t r a n s f o r m a t i o n s o f n i t r o g e n were i g n o r e d . However, th e y c o n t r o l t o a l a r g e d e g r e e the amount o f n i t r a t e s a v a i l a b l e f o r l e a c h i n g at t h e end o f the g r o w i n g s e a s o n . T h i s c a l l s f o r a c o m p r e h e n s i v e model o f the n i t r o g e n c y c l e i n t h e s u b s u r f a c e e n v i r o n m e n t . Such a model i s p r e s e n t l y u n d e r d e v e l o p m e n t ( E u l l e y and 183. Cappelaere, 1978). S i m u l a t i o n of the s o i l n i t r o g e n balance could be e a s i l y i n t e r f a c e d with the models developed i n t h i s t h e s i s . The upgraded model should then be used to t e s t the a l t e r n a t i v e of sp r e a d i n g the same amount of waste on a l a r g e r s u r f a c e area. Crop uptake and s o i l r e t e n t i o n might be g r e a t e r i n ab s o l u t e v a l u e s , and d i s p e r s i o n might be enhanced because of a g r e a t e r c r o s s - s e c t i o n a l area a v a i l a b l e f o r d i s -p e r s i v e f l u x . I n c o r p o r a t i n g r e s t p e r i o d s i n the land management by a l t e r n a t i n g s i t e s should also be c o n s i d e r e d , keeping the l o a d i n g r a t e c o n s t a n t . T h i s might i n c r e a s e the c a r r y i n g c a p a c i t y of the s o i l and avoid e x c e s s i v e b u i l d - u p of con-taminants i n the a q u i f e r . Should the s i z e of the hog o p e r a t i o n i n c r e a s e i n the f u t u r e , h i g h e r l o a d i n g rates on the same s i t e should be avoided, and t e s t s should be performed -with the model by i n c r e a s i n g the s u r f a c e area of l o a d i n g , keeping the l o a d i n g r a t e at i t s p r e s e n t l e v e l . 184. CONCLUSIONS 1. With a simple approximation of the flow e q u a t i o n , i t was p o s s i b l e to p r e d i c t the water t a b l e f l u c t u a t i o n s based on d a i l y weather data f o r the s i t e . T h i s approximation i s best s u i t e d f o r a s o i l w i t h low w a t e r - h o l d i n g c a p a c i t y . 2. Model 1 can p r e d i c t v e r t i c a l n i t r a t e c o n c e n t r a t i o n pro-f i l e s i n groundwater under the d i s p o s a l a r e a , r e s u l t i n g from a given amount of excess n i t r o g e n a v a i l a b l e f o r l e a c h i n g i n the form of n i t r a t e s at the end of the growing season. Model output i l l u s t r a t e d the s t r o n g s t r a t i f i c a t i o n phenomenon du r i n g the l e a c h i n g p e r i o d , and s t r e s s e d the importance of depth and time of sampling f o r sample i n t e r p r e t a t i o n . 3. A f t e r c a l i b r a t i o n of Model 1 at a s p e c i f i c s i t e , i t i s p o s s i b l e to o b t a i n an estimate f o r the s e a s o n a l l o s s of n i t r a t e s to groundwater, based on a l i m i t e d number of groundwater samples c o l l e c t e d at j u d i c i o u s times d u r i n g the l e a c h i n g p e r i o d at s p e c i f i c depths i n the s a t u r a t e d zone. C o n s i d e r i n g the u n c e r t a i n -t i e s i n v o l v e d with other estimates of the l e a c h i n g term in the s o i l n i t r o g e n budget, t h i s method might c o n s t i t u t e a d e s i r a b l e a l t e r n a t i v e , s u b j e c t to f u r t h e r t e s t i n g . 185. Model 2 allows f o r p r e d i c t i o n of long-term changes i n n i t r a t e c o n c e n t r a t i o n s i n the r e g i o n a l a q u i f e r system, due to a given waste management p o l i c y at a d i s p o s a l s i t e , e n a b l i n g t e s t i n g of a l t e r n a t i v e s . The long term s e n s i t i v i t y a n a l y s i s showed t h a t u s i n g l o n g i t u d i n a l d i s p e r s i v e f l u x i n i s o l a t i o n i s i n s u f f i c i e n t f o r mass t r a n s p o r t s i m u l a t i o n , s i n c e the long-term output from Model 2 i s more s e n s i t i v e to the t r a n s v e r s e d i s p e r s i v i t y . The p r e d i c t e d long-term groundwater q u a l i t y i n the a q u i f e r i s very s e n s i t i v e to the s a t u r a t e d flow v e l o c i t y e s t i m a t e . 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For a homogeneous s o i l l a y e r of t h i c k n e s s A z , I and E are the depths of water r e s p e c t i v e l y i n f i l t r a t e d and evaporated ( o r t r a n s p i r e d ) at constant r a t e s I q and E , over a time step of d u r a t i o n A t (I = I / A t ) . For the o o sake of s i m p l i c i t y , the time t=0 i s taken at the s t a r t of t h i s time s t e p . The v o l u m e t r i c moisture content 0 i s always assumed uniform i n the s o i l l a y e r , with an i n i t i a l v a l ue 0^. The o b j e c t i v e i s to c a l c u l a t e the depth Q of water d r a i n i n g out of the s o i l l a y e r over the time step A t , and the f i n a l moisture content 0^ at t = A t . While the moisture content 0 p a r t l y c o n t r o l s the r a t e s of i n f i l t r a t i o n and e v a p o t r a n s p i r a t i o n I and E Q , these can be f a i r l y a c c u r a t e l y estimated on the b a s i s of the known i n i t i a l moisture content 0^ alone, p r o v i d e d A t i s not too l a r g e (e.g. A t = 1 day). However, f o r any time step A t longer than a few minutes, using a s i m i l a r procedure f o r the drainage Q l e a d s to c o n s i d e r a b l e i n s t a b i l i t y , because of the l a r g e s e n s i t i v i t y of drainage to moisture content. The method developed i n t h i s appendix t h e r e f o r e i n t e g r a t e s a n a l y t i c a l l y the s i m p l i f i e d form of the flow equation (see S e c t i o n 2.3.3) over the time step A t . As for m u l a t e d here, the problem is more g e n e r a l than the s o i l moisture component of Model 1 ( S e c t i o n 2.3.3). The l a t t e r c o n s i d e r s I =E =0 o o over the time s t e p , and i n c o r p o r a t e s I and E i n t o the s o i l 2 0 3 . water budget (equation 2 . 9 ) at the end of the time s t e p , by a simple b a l a n c i n g procedure. A l s o , i n t h i s appendix, the s o i l l a y e r can, be one zone of a l a r g e r p r o f i l e . For a time t between 0 and A t , i ( t ) , e ( t ) and q ( t ) are d e f i n e d as the cumulated depths of water i n and out of the s o i l l a y e r s i n c e t = 0 . I t f o l l o w s that I = i ( A t ) , E - e ( A t ) , and Q = q(At) (A. 1 ) For any f u n c t i o n f ( t ) of time, the f o l l o w i n g n o t a t i o n s are used: 2 f - f (t) ; f - 4 f ; f - -M- ( A . 2 ) d t d t 2 Since the moisture content 0 i s assumed uniform ( h y d r a u l i c g r a d i e n t equals u n i t y ) , the f l u x q out of the s o i l l a y e r i s equal to the c a p i l l a r y c o n d u c t i v i t y K(0) of the s o i l m a t e r i a l ( f o r d i s c u s s i o n , see S e c t i o n s 2 . 3 . 3 and 4 . 1 . 1 ) . During a s m a l l time increment dt (dt << A t ) , water r e t e n t i o n and movement i s t h e r e f o r e completely des-c r i b e d by the set of e q u a t i o n s : Az . d9 = d i - de - dq ( A . 3 ) i ' = I Q (A.4 ) e' = E o ( A . 5 ) q' - K(0) ( A .6 ) The c a p i l l a r y c o n d u c t i v i t y K i s expressed as an e x p o n e n t i a l f u n c t i o n of the moisture content 0 (equation 2 . 1 9 ) : 204. K(0) = exp [k . ( 0 - 0 )] (A.7) o o where 0 i s the moisture content at which K = 1 cm/day o k i s d e f i n e d as k = 2.3/A3 , where A3 i s the o o c c change i n moisture content a s s o c i a t e d with one l o g a r i t h m i c c o n d u c t i v i t y c y c l e . D i f f e r e n t i a t i n g A.6 w i t h respect to time and combining with A.7 , we o b t a i n q" = k Q K ( 0 ) . | | (A.S) The v a r i a b l e 0 can be e l i m i n a t e d by a p p l y i n g equations A.3 and A.6: q" - ^ f - (i» - e' - q') (A.9) which, when combined with A.4 and A.5, y i e l d s Q eq" - R q q' - q ' 2 (A.10) where Q = Az/k and R = I - E are two c o n s t a n t s , e o o o o This i s a n o n - l i n e a r , 2nd order d i f f e r e n t i a l equation i n t , which we w i l l c a l l s i m p l i f i e d flow e q u a t i o n . The i n i t i a l c o n d i t i o n s a r e : q( t ) - 0 and q ' ( t ) - K(0 ), f o r t = 0 (A.11) Equation A.10 can be s o l v e d f o r q' by s e p a r a t i n g the v a r i a b l e s q' and t : 205. Equation A.12 can be i n t e g r a t e d a n a l y t i c a l l y between time 0 and t , to y i e l d : t = ^ Log [b . ,1* R ] (A.13) o o where b i s an i n t e g r a t i o n constant to be determined l a t e r . The f l u x q 1 can be i s o l a t e d and expressed as an e x p l i c i t f u n c t i o n o f t : R q t „ -° _ (A.14) n 1 - b e x p ( - c t ) R R .k where c = rr— - —x i s a constant. The v a r i a b l e q can Q Az e t h e r e f o r e be expressed as the i n t e g r a l over time of the r i g h t member of equation A.14. Appl y i n g the v a r i a b l e t r a n s f o r m a t i o n : x = exp(-ct) dt - - (A.15) c. x y i e l d s : dx J (A.16) •b ) which can again be i n t e g r a t e d a n a l y t i c a l l y : q — Q e • Log I _ X b x (A.17) where a i s another constant of i n t e g r a t i o n . A f t e r i s o l a t i n g x and s u b s t i t u t i n g back to t , the drainage e x p r e s s i o n i s o b t a i n e d : q ( t ) = Q e . Log [ a ( b _ 1 . e x p ( c t ) - l ) ] (A.18) 206. The constants of i n t e g r a t i o n remain to be d e t e r -mined, by a p p l y i n g the i n i t i a l c o n d i t i o n s A.11 to the expressions A.18 and A.14 f o r drainage and f l u x . The system of equations i n a and b i s o b t a i n e d : (A.19) a . ( b - 1 - 1) = 1 ) ) and R .(1-b) = K ( 0 . ) ) i } The s o l u t i o n to t h i s system i s : b = 1 - R /K(G.) and a » ( b - 1 - l ) - 1 (A.20) o 1 S u b s t i t u t i n g A.20 i n t o A . 1 8 , s e t t i n g t = At and r e p l a c i n g c by i t s value R Q/Q e y i e l d s the e x p r e s s i o n of the cumulated drainage Q over the time s t e p : K(0.) R Q = Q e.Log [1 + 1 . (exp (-f- At)-1) ] (A.21) o e with Q = and R - ( I - E ) / A t . ^e k o o The f i n a l moisture content 0^ at the end of the time step i s o b t ained by water budgeting: 0 f = 0 + Az . [I - E - Q] (A.22) In the p a r t i c u l a r case where I = E = 0, such as i n the s o i l moisture component of Models 1 and 2, Q i s o b t a i n e d as the l i m i t of e x p r e s s i o n A.21 when R q tends to z e r o . S i n c e : R R Lim (exp (^ °- . At) - 1)/ (pp-At) - 1 (A.23) R ->o ^e ^e o 207. the s i m p l i f i e d form of equation A.21 i s : K(0.) Q = Q . Log [1 + . At] (A.24) e w e which i s e q u i v a l e n t to equation 2.20 f o r At = 1 day. In t h i s case (I = E = 0) , equation A.22 becomes: -1 K ( 0 i > 0, = 6 - k . Log [1 + - r - i . A t ] (A.25) ° ^e ( N i e l s e n et a l . , 1973). 208. APPENDIX B: VERTICAL VELOCITY PROFILE IN THE SATURATED ZONE (Model 1). -> The d e t e r m i n a t i o n of the v e l o c i t y f i e l d V i n the s a t u r a t e d domain r e a l l y i s a two-dimensional problem, i n the v e r t i c a l c r o s s - s e c t i o n d e f i n e d by the axes x and z: V w i l l be dependent on both c o o r d i n a t e s , x and z. However, i n the context of Model 1 ( S e c t i o n 2.3), we only need to know the v e l o c i t y p r o f i l e V ( z ) , along the v e r t i c a l l i n e p a s s i n g through the cente r 0 of the p l o t (x = 0 ) . Assuming a s m a l l , uniform slope of the water t a b l e , v e l o c i t y v a r i a t i o n s along the x d i r e c t i o n are n e g l e c t e d over the extent of the p l o t . More s p e c i f i c a l l y , the o b j e c t i v e i s to determine the v e r t i c a l component V^(z) of the v e l o c i t y along the z a x i s , to be plugged i n t o equation 2.6, d e s c r i b i n g the v e r t i c a l n i t r a t e movement i n the s a t u r a t e d zone. I t must be p o i n t e d out t h a t , because V^(z) i s l i k e l y to remain s m a l l , a g r e a t e r f r a c t i o n of v e r t i c a l n i t r a t e t r a n s p o r t i s achieved by the d i s p e r s i v e f l u x beneath the d i s p o s a l f i e l d . The pore v e l o c i t y p r o f i l e V(z) i n the s a t u r a t e d zone i s d e f i n e d by the equation of c o n t i n u i t y 2.2 and the set of boundary c o n d i t i o n s 2.28. Upon r e p l a c i n g the Darcy v e l o c i t y q by n V, where n i s the a q u i f e r p o r o s i t y , t h i s system of equations can be w r i t t e n : ?-rr (p0) + $ . (p n a V) = 0 ( B . l ) V(z).x = V (z) = SWT ( z ) \ a j f o r z=ZWT (B.2) V ( z ) . z = V v ( z ) = DWT (z) ) 209. V ( z ) . z - V v ( z ) = 0 f o r z = DIMP (B.3) At s a t u r a t i o n , 0 = n . Assuming uniform p o r o s i t y , equation B.1 s i m p l i f i e s t o : . | f + $ . (p V) = 0 : (B.4) According to Freeze (1967), i t i s reasonable to assume t h a t groundwater f l o w i n g under n a t u r a l g r a d i e n t s i n an unconfined a q u i f e r , w i l l act as an i n c o m p r e s s i b l e f l u i d . I t f o l l o w s that ^— = 0 and = 0; B.A t h e r e f o r e becomes at Vs . V = 0 (B.5) which i s i d e n t i c a l to the s t e a d y - s t a t e form of the c o n t i n u i t y equation. In o t h e r words, the v e l o c i t y p r o f i l e , d e f i n e d by the boundary v a l u e problem B.2 + B.3 + B.5 wit h a moving upper boundary, i s independent of the time v a r i a b l e , and i s t o t a l l y determined by the p o s i t i o n of the upper boundary, ZWT, and i t s s l o p e SWT. I t w i l l now be proven that the v e c t o r f i e l d V (z) d e f i n e d by: o K V . x = (V ) = ~ SWT (z) ) o o n n . 3 (B.6) V . * = <Vv " DWT (z) o i s a s o l u t i o n of the system of equations B.2 + B.3 + B.5. The v e l o c i t y f i e l d V q(Z) s a t i s f i e s the boundary c o n d i t i o n s B.2 and B.3: 2 1 0 . by i t s very d e f i n i t i o n V q (ZWT) i s equal to the v e l o c i t y v e c t o r at the water t a b l e : V(ZWT) = V (ZWT) ( B . 7 ) o - V (DIMP) s a t i s f i e s equation B . 3 , s i n c e DWT (DIMP) = 0 o (see S e c t i o n 2 . 3 . 3 ) . I t remains yet to be demonstrated that V (z) s a t i s f i e s the o d i f f e r e n t i a l equation B . 5 , over the s a t u r a t e d domain, which i s e q u i v a l e n t to V"(z) = V Q ( z ) Y z,(ZWT < z < DIMP) ( B . 8 ) T h i s w i l l be performed by an i t e r a t i v e procedure based on s u c c e s s i v e i n f e r e n c e s , u s i n g a finite-element r e p r e s e n t a t i o n of the domain. F i r s t , a degree of r e s o l u t i o n must be chosen, i . e . a depth increment dz, as s m a l l as d e s i r e d , i s adopted. Nodes 1 and n r e p r e s e n t the impermeable s u r f a c e and the water t a b l e , r e s p e c t i v e l y . The depth of node j i s d e f i n e d by Z j = DIMP - (j - 1) . dz ( B . 9 ) The o b j e c t i v e then i s to prove that f o r a given n value ( 1 < N < 1+ M M ? ) : — a z V ( j ) = V Q ( j ) -V j , ( 1 < j < n) ( B . 1 0 ) The i n t e g e r n w i l l be c a l l e d 'rank' of p r o p o s i t i o n B . 1 0 . The p r o p o s i t i o n B . 1 0 w i l l be demonstrated i n three s t a g e s . 211. a) Stage 1: rank n = 1. This i s the t r i v i a l case where the water t a b l e touches the impermeable s u r f a c e (no water i n the a q u i f e r ) . While t h i s case i s improbable i n p r a c t i c e , i t can s t i l l be t r e a t e d t h e o r e t i c a l l y : We know that V (n) = V (n) (equation B.7). b) Since n - 1, i t f o l l o w s t h a t V<1) = V Q ( 1 ) , and B.10 i s t r u e f o r t h i s t r i v i a l case. Stage 2: The p r o p o s i t i o n B.10 i s assumed true at an a r b i t r a r y rank » a . I t w i l l now be i n f e r e d that B.10 i s tr u e at rank n = n + 1 . Since B.10 i s a true at rank n , a * • v„ (J) Y j , (1 < 3 < n ( B . l l ) We a l s o know that V" . V ( j ) = 0 j , (1 < j < n) and ( V(j) . z = V Q ( j ) . z [ V(j) = v o ( j ) f o r j = 1 f o r j n (B.12) Let us d e f i n e the v e c t o r f i e l d DV = V - V " o Hence, f o r a l l j,( 1 < j < n ), ~~ """"" £1 v".DV(j) = VY ( V ( j ) - V ( j ) ) = ^ . V ( j ) - ^ . V ( j ) = 0 a l s o , ( f o r j - 1, D V ( j ) . z=V(j).z - V ( j ) . 2 5 f o r j = n, DV(j) = V ( j ) . V ( j ) (B.13) 212. T h e r e f o r e , the v e c t o r y i e l d DV s a t i s f i e s the system of e q u a t i o n s : $ • X ( j ) - 0 V j , ( l < j < n ) X ( j ) .- (5 f o r j = n ) (B.14) X ( j ) . z = 0 f o r j " - 1 T h i s i s a boundary value problem w r i t t e n i n f i n i t e - e l e m e n t form, f o r which an obvious s o l u t i o n i s X ( j ) = 0* f J , ( l < j < n ) Since such a boundary value problem only has one s o l u t i o n , i t f o l l o w s that DV(j) = 3 f j , (1 < j < n ) T h e r e f o r e , V ( j ) = V Q ( j ) VJ ( 1 1 * 1 n ) w h i c h expresses p r o p o s i t i o n B.10 at the rank n = n f l + 1. Stage 3:" I t has been demonstrated t h a t : - p r o p o s i t i o n B.10 i s true at rank 1. - T n , i f B.10 i s t r u e at rank n , then i t i s t r u e •' a a at rank n = n + 1 . a I t can t h e r e f o r e be i n f e r r e d that p r o p o s i t i o n B.10 i s t r u e at a l l ranks n (1 _< n < 1 + D ^ P ) , i . e . f o r a l l water t a b l e p o s i t i o n s ZWT •= DIMP - ( n - 1 ) . dz. Since the depth increment dz can be chosen a r b i -t r a r i l y s m a l l , i t f o l l o w s that equation B.8 can be shown to be true at a l l p o i n t s of the s a t u r a t e d domain. 213. In c o n c l u s i o n , the v e c t o r f i e l d V q ( Z ) , d e f i n e d by equation B.6, r e p r e s e n t s the v e r t i c a l v e l o c i t y p r o f i l e i n the s a t u r a t e d zone. In p a r t i c u l a r , the v e r t i c a l component of the v e l o c i t y i s obt a i n e d as: V (z) - V ( z ) . z = DWT(z) V* zC]0,DIMP] . 

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