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Runoff generation and water erosion in the uplands of the Lower Fraser Valley Brown, Sandra J. 1990

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RUNOFF GENERATION AND WATER EROSION IN THE UPLANDS OF THE LOWER FRASER VALLEY By Sandra J. Brown B. Sc. (Physical Geography) University of British Columbia A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES SOIL SCIENCE We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1990 (c) Sandra J. Brown, 1990 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely 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 or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of SOIL SCIENCE The University of British Columbia Vancouver, Canada Date April 26, 1 990 DE-6 (2/88) ABSTRACT An understanding of runoff generation is a requirement for efficient erosion control and land management practices. This research is designed to investigate the processes by which runoff occurs on a Whatcom soil at an upland site in the Lower Fraser Valley. The objectives of this study are to summarize water erosion measurements, to determine soil hydraulic properties, to predict infiltration for typical rainstorms and to determine the mechanism of runoff generation. Rill, interrill and rainsplash measurements, and previous erosion measurements made at the study site are used to qualitatively assess the magnitude of water erosion. Soil loss is dominated by rill erosion and erosion rates are greatest from November to January. Runoff coefficients are relatively low (<26%), but erosion rates are anticipated to be in excess of 35-45 t ha_1yr_1. Soil hydraulic properties are measured using a low tension absorption technique de scribed by Clothier and White (1981). The sorptivity tube device provides a simple method for obtaining S, A* and K-i- Measured values of i and x* depend on t1!2 as ex pected from the constant-concentration absorption theory. Soil hydraulic variables and constant-concentration absorption theory are used to determine the soil-water diffusivity characteristics. Measured D(8) functions for the field varied widely in a and b, especially for the lower horizons. The Van Genuchten (1980) 9(h) expression provides a good fit to the water retention data. D(8) functions predicted from the soil-water retention curves and the conductivity at satiation are at least 1-2 orders of magnitude greater than the measured functions. Hysteresis effects may account for a 1 order of magnitude increase in D($), but the predictions are poor without matching at D(8a). ii The measured hydraulic properties are used to predict infiltration, runoff and drainage. Constant-flux infiltration theory is used to model soil moisture profiles for various rainfall events. High field moisture contents necessitate the inclusion of gravity effects during infiltration. Rainfall, runoff and soil loss measurements at the Mahal farm indicate that rainfall intensities <10 mm h_1 cause considerable runoff and erosion. For rainfall in tensities known to cause runoff and erosion, runoff is not predicted for most Ap horizon cores. Infiltration may be restricted at some sites by the lower horizon but runoff is not predicted at many sites. To evaluated soil moisture conditions between rainfall events, drainage is estimated from a unit gradient model. A rapid decrease in 8 between rainfall events predicted by the unit gradient model, but 6 measured at the Mahal farm suggests limited drainage between rainfall events. Rainfall, runoff and soil loss measurements sug gest that factors other than those measured are contributing to the runoff observed in the field. Compaction, surface sealing and subsurface seepage may be factors influencing runoff and moisture conditions in the field. The high moisture contents observed in the field suggest the water table is perching on a layer of lower conductivity which in consis tent with Dunne runoff. However, the measured infiltrabilities suggest Hortonian runoff and the resultes of the thesis are not conclusive with respect to the mechanism of runoff generation. in Table of Contents ABSTRACT ii List of Tables viList of Figures ix Acknowledgement xii INTRODUCTION 1 1 SURFACE WATER EROSION AT THE MAHAL FARM 3 1.1 INTRODUCTION 3 1.2 METHODS 4 1.3 EROSION MEASUREMENTS 9 1.4 PREVIOUS EROSION STUDIES 16 1.5 COMPARISON OF RESULTS 8 2 SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 21 2.1 INTRODUCTION 22.2 THEORETICAL BACKGROUND 21 2.2.1 LOW TENSION ABSORPTION2.2.2 CALCULATING D{9) FROM RETENTION CURVE DATA ... 24 2.3 METHODS 25 2.3.1 SAMPLINGiv 2.3.2 ADDITIONAL SITE PROPERTIES 29 2.3.3 SORPTIVITY TUBE 30 2.3.4 WATER RETENTION 5 2.4 RESULTS AND DISCUSSION 36 2.4.1 SITE CHARACTERISTICS2.4.2 MEASURED D(6) 41 2.4.3 D(9) CALCULATED FROM RETENTION CURVE DATA ... 57 2.5 CONCLUSIONS 63 3 RUNOFF GENERATION AT THE MAHAL FARM 64 3.1 INTRODUCTION 63.2 THEORETICAL BACKGROUND 64 3.2.1 CONSTANT-FLUX INFILTRATION 64 -3.2.2 DRAINAGE CALCULATION 6 3.3 RESULTS 67 3.3.1 FIELD MOISTURE CONDITIONS 63.3.2 RUNOFF GENERATION 69 3.3.3 DRAINAGE CALCULATION 74 3.4 DISCUSSION . 1 78 3.5 CONCLUSIONS 83 CONCLUDING REMARKS 84 Bibliography 86 Appendices 91 A LIST OF SYMBOLS 9v B RAW DATA 95 C CONSTANT-CONCENTRATION ABSORPTION PROGRAM 103 D VAN GENUCHTEN WATER RETENTION PROGRAM 109 E CONSTANT-FLUX INFILTRATION PROGRAM 112 F SISSON DRAINAGE PROGRAM 116 vi List of Tables 1.1 Rill meter cross section areas 12 1.2 Calculated rill volumes 3 1.3 Interrill erosion determined by erosion pins 15 1.4 Cumulative rainsplash erosion 11.5 Soil loss on drained versus undrained plots 18 2.1 Hypothetical representative elementary volumes (REV) (Bouma, 1984). . 27 2.2 Low tension absorption variables for field and air-dried values of 9n. . . . 34 2.3 The effect of core drying on tg. . . 32.4 Munsell dry soil colour 39 2.5 Texture based on USDA particle size classes (textured by Dr. S.M. Smith). 39 2.6 Summary statistics for pb and / 40 2.7 Median values of tf, r2 and intercept used in the calculation of S and A*. 41 2.8 Summary statistics of K-2, a and b for grid representative samples. ... 44 2.9 Summary statistics of K-2, a and b for detailed grid samples from unit 9. 44 2.10 Summary statistics of K-2, a and b for the combined data set 46 2.11 The maximum time for gravity effects to be negligible 47 2.12 Values of D„, a and 6 for core UC with forced values of /? 47 2.13 The effects of core drying on constant- concentration absorption 56 2.14 Sensitivity of a and b to input variables for sample 1A 56 2.15 Summary of the output from the water retention data 58 2.16 Sensitivity analysis for K(9) calculated from retention curve data 62 vii 3.1 Moisture conditions at the Mahal farm from September to April 68 3.2 Range in 0_2, 0.85/, pi, and / for the Ap and lower horizons 69 3.3 Rainfall intensity, duration and return periods generating runoff for Septem ber values of 0n 73 3.4 Storm intensities and durations generating soil loss for plot studies. ... 74 3.5 Sensitivity of the unit gradient drainage model to changes in input vari ables for sample 1A 77 B.l Ap horizon site characteristics of infiltration cores 95 B.2 Lower horizon site characteristics of infiltration cores 96 B.3 Ap horizon measured variables for the low tension absorption 97 B.4 Lower horizon measured variables for the low tension absorption 98 B.5 Ap horizon low tension absorption variables 99 B.6 Lower horizon low tension absorption variables 100 B.7 Ap horizon water retention variables 101 B.8 Lower horizon water retention variables 102 viii List of Figures 1.1 Location of the Mahal farm site, Matsqui, British Columbia 4 1.2 Rill erosion at the Mahal farm, April, 1985 5 1.3 The portable photographically recording rill meter 6 1.4 Rill, interrill and rainsplash sampling schemes 7 1.5 Erosion pins 8 1.6 Splash pan apparatus 9 1.7 Irregularity of cross sections down a rill in January, 1986 10 1.8 Rill cross section projections over time at the left rill, site 1 1 1.9 Accelerated rill erosion due to a blocked ditch culvert 14 1.10 Cross section infilling by upslope material at right rill site 2 14 1.11 BCMAF plot study layout 17 1.12 Cumulative soil erosion losses for the Wood (1983) plot study, 1982-1983. 19 1.13 Cumulative soil erosion losses for the Wood (1984) plot study, 1983-1984. 20 2.1 Sampling design for soil hydraulic properties 26 2.2 Absorption core sampling 28 2.3 The unsaturated sorptivity tube device 31 2.4 Spatial distribution of the depth to C horizon 37 2.5 Soil horizon determination from cone penetration resistance 38 2.6 Rill erosion exposing the Ap horizon and the underlying C horizon .... 40 2.7 Example plots of water inflow (i) and wetting-front advance (x*) versus t1!2 for the Ap horizon. 42 ix 2.8 Example plots of water inflow (?) and wetting-front advance (x*) versus t1/2 for the C horizon 43 2.9 Example moisture profiles over time for constant-concentration absorption. 45 2.10 The range of a for grid representative samples and detailed grid samples from unit 9 48 2.11 The range of b for grid representative samples and detailed grid samples from unit 9 9 2.12 The range of K-2 for grid representative samples and detailed grid samples from unit 9 50 2.13 The distribution of a for the Ap horizon 52 2.14 The distribution of 6 for the Ap horizon2.15 The distribution of a for the lower horizons 53 2.16 The distribution of 6 for the lower horizons2.17 The diffusivity characteristics of the Ap horizon 54 2.18 The diffusivity characteristics of the lower horizons 55 2.19 Example plots of the water retention characteristic curves 59 2.20 Measured and predicted D(6) for 50"* percentile values of a and b of the Ap horizon 60 2.21 Measured and predicted D(9) for 50th percentile values of a and b of the lower horizons. 1 3.1 The distribution of K-2 for the Ap horizon 71 3.2 The distribution of K-2 for the lower horizons3.3 Example infiltration moisture content profiles over time for R = 20 mm h-1. 72 3.4 Soil drainage over time for the Ap horizon 75 3.5 Soil drainage over time for the lower horizons 6 x 3.6 Rill formation in trafficked interrows along the secondary slope, 1985-1986. 79 3.7 Rill formation along the main slope in low spots, 1985-1986 80 3.8 Rill spacing corresponding to wheel tracks, 1986-1987 81 3.9 Rill direction affected by tractor wheelings, 1986-1987 81 3.10 Surface sealing at the Mahal site 82 xi Acknowledgement I would like to thank the British Columbia Agricultural Sciences Coordinating Committee for the financial support, Dr. Mike Novak for his comments and suggestions and Dr. Steven Smith for his assistance in the field. xn INTRODUCTION Soil erosion in Canada is recognized as an important agricultural issue. In British Columbia, water erosion is a major soil degradation problem. Water erosion is particu larly severe in the uplands of the Lower Fraser Valley due to many row crops being grown in this region (Sparrow, 1984). In the late 1970's and early 1980's, high market prices for fruits and vegetables induced the cropping of land traditionally in pasture. Land was converted to perennial row crops such as strawberries and raspberries, and annual cole crops such as cauliflower. After the crops are harvested, the soil is often left unprotected through the heavy rains of fall and winter. As a result, there are higher than tolerable soil losses by surface water erosion (Wood, 1983; 1984). The predominance of erodible soils, steep complex topography, and the lack of adequate crop cover (due to poor farm management) are considered the major factors that have led to this soil degradation. An understanding of runoff generation is a requirement for efficient erosion control and land management practices. Runoff occurs when the soil becomes saturated at the surface or when the rainfall rate exceeds the infiltrability of the soil. This thesis mainly investigates the rainfall infiltration process for a Whatcom soil on an upland site in the Lower Fraser Valley. There are three specific objectives to this work: 1. To summarize rill and interrill erosion measurements. 2. To determine the soil hydraulic properties of the surface and lower horizons. 3. To use these properties to predict infiltration rates for typical rain storms and 1 Chapter 1. INTROD UCTION 2 determine the mechanism of runoff generation. Chapter 1 describes water erosion on a typical Whatcom soil in the uplands of the lower Fraser Valley. Introductory rill, interrill and rainsplash measurements are presented along with previous erosion measurements made at the study site. The magnitude of water erosion is qualitatively assessed from these data. Chapter 2 describes the theory and methods used to measure the basic soil properties of the surface and lower horizons. Soil hydraulic diffusivity functions, water retention functions and saturated hydraulic conductivities are presented. Chapter 3 uses the soil hydraulic properties determined in Chapter 2 to model soil moisture profiles for various rainfall events. Rainfall intensities, durations and return periods required to generate runoff are compared to typical storms measured at the study site. Drainage rates are estimated from a unit gradient model to evaluate soil moisture conditions between rainfall events. Chapter 1 SURFACE WATER EROSION AT THE MAHAL FARM 1.1 INTRODUCTION Water erosion for a typical soil in the uplands of the Lower Fraser Valley was qualitatively assessed at the Mahal farm, located in the Matsqui region (Fig. 1.1). The study area was under pasture for 22 years prior to cultivation in 1981. Erosion problems developed during the first year of cultivation, when strawberries were planted up-and-down the slope. Sediment eroded from the site was washed into a tributary of the Fraser River. Sedimentation of salmon spawning habitat below the farm prompted a fisheries concern and the British Columbia Ministry of Agriculture and Food began a series of erosion plot studies on the farm. The soil is the Whatcom series (Luttmerding, 1980) disturbed by clearing and cul tivation. Typically 15-30 cm SiL aeolian material, with a weak fine granular structure, and less than 5% organic matter, overlies variably permeable, weakly stratified SiCL glaciomarine material (Wood, 1983). The soil classification is Luvisolic Humo-Ferric Podzol (Luttmerding, 1981). Rainfall accumulation from October to April is approxi mately 1200 mm (Wood, 1983). The average duration storm is 4.5 h, with a 12 day return period and a 2.0 mm h_1 intensity (AES, 1987). The study site is approximately 3.2 ha in area. In the spring of 1985, the study site was cultivated across the slope and cauliflower was planted with an approximately 1 m spacing between row centres. Tillage was not along the contour and slight gradients 3 Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 4 SCALE 5 10 km FIELD SITE x */ ABB0TSF0RD / Figure 1.1: Location of the Mahal farm site, Matsqui, British Columbia. existed along rows and interrows. Non-harvested cauliflower plants were left in the field to rot over winter. Water erosion occurs over much of the study area in winter (Fig. 1.2). Introductory measurements of rill, interrill and splash erosion are compared to previous erosion measurements made at the study site. The magnitude of water erosion at the Mahal farm is assessed qualitatively using this data. 1.2 METHODS Soil erosion was monitored at the Mahal farm from January to May, 1986. The methods used in the erosion measurements are outlined for rill, interrill and rainsplash erosion. Rill erosion was measured using a portable photographically-recording rill meter (Fig. 1.3) (McCool et al., 1981). On January 11, 1986, 1 m lengths of 1.6 cm diam eter rebar were driven approximately 0.9 m into the soil to mark the locations of rill cross sections. Pairs of rebar were placed 2.3 m apart at 6 randomly spaced locations along the 2 most dominant rills (Fig. 1.4). The rills were identified as left and right and Figure 1.2: Rill erosion at the Mahal farm, April, 1985. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM G Figure 1.3: The portable photographically recording rill meter. cross section sites were labelled 1-6 indicating the location along each rill. The rill meter was placed across the rill, between each rebar pair and levelled by adjusting the legs and tripod. A series of equally spaced pins were lowered to conform with the topography. A photograph was taken from the tripod of the pins against a graph paper background. Projection of the resulting slides allowed the determination of the cross section areas using a planimeter (McCool et al., 1981). The rill meter is capable of measuring depths up to 0.5 m. For cross sections deeper than 0.5 m the depth below the rill meter pins was estimated using a metric tape. Before rill measurements were taken, 2 cross section locations on the right rill were relocated. Site 1 was moved upslope due to lateral expansion of the rill beyond the width of the rill meter, and site 4 was shifted laterally due to undercutting of the rill bank. Rill meter measurements were taken over the winter on January 18, February 13, and April 18, 1986. The approximate distances between cross sections were measured from aerial Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 7 Figure 1.4: Rill, interrill and rainsplash sampling schemes. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 8 photographs taken on April 7, 1986. The volume of the rill between 2 sites was estimated by multiplying the average cross section area of the 2 sites by the distance between the sites. Erosion pins were utilized to measure net interrill erosion. On January 25, 1986, pairs of steel rods, placed approximately 15 cm apart, were pushed into the soil to mark the locations of the interrill erosion sites. Eight interrill erosion sites were randomly scattered over the study area (Fig. 1.4). The rods were placed parallel to the rows and along both rows and interrows. To avoid frost heave, 1 mm diameter, 0.7 m lengths of rod were pushed approximately 0.6 m into the soil. The rods were notched near the top and a flexible wire was strung tightly between the notches (Fig. 1.5). Measurements were taken below 2 marks on the wire on February 1, March 9 and May 4, 1986. The distance to the soil surface was measured to the nearest mm using a metric tape. Figure 1.5: Erosion pins Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 9 Rainsplash erosion was qualitatively assessed with a splash pan apparatus (Fig. 1.6). The apparatus consisted of an aluminum box 40 by 40 by 25 cm in size, with one open side. Four removable trays, 1600 cm2 in area, were stacked 10 cm above each other. The splash pan apparatus was placed facing upslope parallel to the rows with the open side between 2 rows. The splash pan apparatus was tied to the ground with stakes to avoid being blown over by the wind and was left in the field from February 13 to May 7, 1986. The trays were dried and weighed, then cleaned, dried and re-weighed; the difference being the weight of the soil retained. Time constraints prevented the construction of more splash pans, so the results are a very preliminary and exploratory assessment. Figure 1.6: Splash pan apparatus. 1.3 EROSION MEASUREMENTS Projections of rill cross sections determined with the photographically-recording rill meter provide rill size and shape. Projections of cross sections down a rill on a given date Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 10 display the irregularity of rill shape. Fig. 1.7 shows channel splitting due to a more resistant section, in this instance a decaying cauliflower plant. Projections of a cross section versus time display channel enlargement. Fig. 1.8 shows cross section 1 of the left rill in January, February and April of 1986. LEFT RILL 18/01/86 SITE 6 SITE 3 SITE 2 SCALE 0 15 30 cm I I I Figure 1.7: Irregularity of cross sections down a rill in January, 1986. Rill cross section areas and volumes are given in Tables 1.1 and 1.2 respectively. The rill cross section areas and volumes measured in January and February, relative to those measured in April, 1986, indicate that the majority of rill erosion occurs prior to January. The volume of the right rill is substantially greater than the left rill. The total volumes of soil removed in the formation of the measured portions of the left and right rills were approximately 1 m3 and 4 m3 respectively. Rills with cross section areas as large as the right rill were not noted in previous work conducted at the Mahal farm (Crudge, 1987). The accelerated erosion (Fig. 1.9) is assumed due to a blocked culvert above the study area which diverted the flow in a field ditch into the right rill. The blocked culvert was Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 11 LEFT RILL SITE 1 18/01/86 .1. Figure 1.8: Rill cross section projections over time at the left rill, site 1. noticed on January 25, 1986 but it is speculated that the culvert was blocked earlier as the majority of rill erosion occurred prior to January, 1986. Not all cross sections enlarge over time due to infilling by upslope material (e.g. site 2 of the right rill shown in Fig. 1.10). Cross sections 4 and 5 of the left rill contained multiple rills which expanded laterally beyond the width of the rill meter in April, 1986. Minimum cross section areas are therefore presented for these 2 sites on the last measurement date. As numerous rills cover the field (Fig. 1.2), the contributing area for the 2 measured rills is unknown. Assuming a contributing area of 3.2 ha (the total area of the study site), the soil loss from the two partial rills alone is 1.6 t ha_1yr_1. Interrill erosion between February 1 and March 9, 1986 was determined by erosion pins. The change in the surface position and the average change over the 8 sites is given in Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 12 Table 1.1: Rill meter cross section areas. Date Site Left Rill Right Rill Area % of Final Area % of Final [cm2] Area [cm2] Area 18-01-86 6 157 73 604 92 5 241 88 500 63 4 240 91 754 73 3 206 70 735 47 2 287 98 1141 85 1 124 56 971 76 13-02-86 6 209 98 657 100 5 275 100 477 60 4 265 100 809 78 3 249 84 735 47 2 291 99 1126 84 1 173 78 1131 89 18-04-86 6 214 100 655 5 > 258 792 100 4 > 262 1038 100 3 296 100 1561 100 2 293 100 1341 100 1 221 100 1273 100 Table 1.3. Negative values indicate erosion and positive values indicate deposition. The average interrill erosion is less than the measurement error (± 1 mm). The negligible interrill erosion suggests that both rain splash and sheet flow erosion are small. The negligible net interrill soil loss was not surprising as crop rows were nearly on the contour and both deposition and erosion were likely to occur throughout the interrill region. The cumulative downslope rainsplash is given in Table 1.4. The soil collected over 84 days is minimal except in the lower tray. The value for the bottom tray includes an undetermined amount of sheet flow erosion. During rainfall events, the same soil particles are displaced many times by splash, but once they have been collected in the splash trays they cannot move again. The results are, therefore, a cumulative measurement of the Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 13 Table 1.2: Calculated rill volumes. Date Site Left Rill Right Rill Length Volume %of Length Volume %of N [m3] Final Volume [m] [m3] Final Volume 18-01-86 6-5 9.7 0.19 83 18.8 1.04 76 5-4 5.4 0.13 87 5.4 0.34 69 4-3 11.3 0.25 78 6.9 0.51 57 3-2 3.8 0.09 82 5.4 0.51 65 2-1 6.5 0.13 76 4.9 0.52 81 total 36.7 0.79 81 41.4 2.92 70 13-02-86 6-5 9.7 0.23 100 18.8 1.07 79 5-4 5.4 0.15 100 5.4 0.35 71 4-3 11.3 0.29 91 6.9 0.53 59 3-2 3.8 0.10 91 5.4 0.50 64 2-1 6.5 0.15 88 4.9 0.55 86 total 36.7 0.92 95 41.4 3.00 72 18-04-86 6-5 9.7 >0.23 18.8 1.36 100 5-4 5.4 >0.14 5.4 0.49 100 4-3 11.3 >0.32 100 6.9 0.90 100 3-2 3.8 0.11 100 5.4 0.78 100 2-1 6.5 0.17 100 4.9 0.64 100 total 36.7 >0.97 100 41.4 4.17 100 quantities of soil moved downslope and cannot be interpreted as the quantity of soil transported to the bottom of the slope by rainsplash (Bolline, 1978; 1980). For the rain splash apparatus, the contributing area is unknown and soil loss on a t ha-1 basis cannot be calculated. Similar cumulative soil losses due to splash erosion were measured by Bolline (1980) for a loamy soil and low intensity rains. Over 85 days 2.5-12.3 g of soil were collected in 6-15 cm diameter splash funnels. The net annual soil loss was calculated using the method of De Ploey (1969) to account for the percentages of soil projected upslope and downslope. Based on 3 years of data, the net mean annual soil loss was approximately 0.03 t ha_1yr-1. This low value of soil loss and the negligible interrill soil loss suggests that splash erosion at the Mahal farm is also low. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM \ / INTERPOLATED 13/02/86 SCALE 0 15 30 cm I I I Figure 1.10: Cross section infilling by upslope material at right rill site 2. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM Table 1.3: Interrill erosion determined by erosion pins. 15 Site Change in Soil Position mm ± 1] Feb 1-Mar 9 Mar 9-May 5 Feb 1-May 5 1-1 -4 -3 -7 1-2 -8 -10 -18 2-1 1 -3 4 2-2 1 4 3 3-1 3 -3 0 3-2 2 7 9 4-1 2 2 4 4-2 3 -4 -1 5-1 3 -1 2 5-2 0 -4 -4 6-1 2 -2 0 6-2 2 -3 0 7-1 -3 9 6 7-2 0 -4 4 8-1 -1 3 2 8-2 -5 1 -4 Ave -0.4 -0.7 0 SD 4.8 4.8 6.3 Table 1.4: Cumulative rainsplas d erosion. Tray Splashed Soil [g]° 1 (top) 0.5 2 1.0 3 3.0 4 (btm.) 36.0 "Total over 84 days Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 16 1.4 PREVIOUS EROSION STUDIES Previous erosion studies were conducted at the Mahal farm by Crudge (1987) and Wood (1983; 1984). The results of their work are reviewed to augment the introductory mea surements of rill, interrill and rainsplash erosion. Crudge (1987) estimated the net soil loss due to rill erosion from this site for the winter of 1984-1985. In the fall of 1984, the field was ploughed and a cover crop of rye grass was planted. The field was divided into 144 representative units, 32 of which were sampled on a stratified random basis. The rill volume was determined for each sampled unit in April, 1985. The soil loss calculated from the rill volumes was 38 t ha-1yr~1. C. Wood of the BCMAF conducted plot studies at the site from 1982 to 1984. He maintained two 42 m long plots in the south-east corner of the field (Fig. 1.11). The plots were under strawberries planted up-and-down the slope. A Coshocton-type runoff sampler designed to sample 1% of the runoff through a flume was located at the bottom of each plot. Measurement of the sediment content of the sample allowed the determination of the soil loss. The volume of water collected and rain gauge data yield the percentage of the precipitation generating runoff. On one plot, an interceptor type drainage system was installed at a 15.2 m spacing. The drainage system consisted of a 0.75 m trench with a drainage pipe at the bottom, back filled to the surface with gravel. Table 1.5 and Figs. 1.12 and 1.13 give the results of the plot study by Wood (1983; 1984). Runoff coefficients on the undrained plot are relatively low (19-26 %), but cause considerable erosion. Estimated soil loss ranges from 35-45 t ha-1 over one winter. Erosion is initially low in September and October, and most of the soil loss (75-85 %) occurs between mid-November and January. By March, erosion rates have declined even though precipitation rates remain relatively constant. The decline in erosion rates after January are in agreement with the decrease in the rate of growth of rill cross section areas Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 17 Figure 1.11: BCMAF plot study layout. reported in section 1.3. The high initial erosion rates likely coincide with the formation of rills, and the decline in erosion with the establishment of equilibrium in rill volume (Novak, 1985). The interceptor type drainage system is effective in reducing runoff and soil erosion to negligible amounts. Overland and subsurface flow are intercepted and diverted off the field by the drainage system. However, interceptor drains are impractical to maintain on cultivated land (Wood, 1984). Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 18 Table ..5: Soil loss on drained versus undrained plots. Event October '82-April '83 September '83-July '84 Drained Undrained Drained Undrained Rainfall 887 mm 887 mm 1623 mm 1623 mm Measured Runoff events 11 24 6 31 % of Rainfall as Runoff 6% 26% 2% 19% Soil Loss 0.4 t ha"1 28.7 t ha~la 0.1 t ha"1 26.7 t ha"16 "Runoff exceeded the collecting tank capacity. Wood (1983) estimates an additional soil loss of 12tha_1 "Runoff exceeded the collecting tank capacity. Wood (1984) estimates an additional soil loss of 10-20 t ha"1 1.5 COMPARISON OF RESULTS For this Whatcom soil, the net soil loss due to rainsplash and sheetwash is small com pared to rill erosion, even though these mechanisms are a potentially important source of sediment to rills. The soil loss in the development of rills is estimated at 38 t lia_1yr_1 (Crudge, 1987). Runoff coefficients are relatively low (<26 %), but soil loss is extensive. Net soil losses based on plot studies (Wood, 1983; 1984) are expected to range from 35-45 t ha_1yr_1 and erosion over longer slope lengths is anticipated to be even greater. Most of the erosion occurs from November to January and by March erosion rates have declined even though precipitation rates remain relatively constant. In soil conservation practice, acceptable rates of erosion for shallow soils are 2-5 t ha_1yr-1 (Troeh et al., 1980). Erosion rates at the Mahal farm exceed of these limits. For efficient erosion control and land management practices, an understanding of runoff generation is required. Soil hydraulic properties are necessary to estimate infiltration and drainage, both of which influence runoff. The measurement of the soil hydraulic properties at the Mahal farm is described in Chapter 2. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 19 SEP NOV JAN MAR MAY JUL 1982 1983 Figure 1.12: Cumulative soil erosion losses for the Wood (1983) plot study, 1982-1983. Chapter 1. SURFACE WATER EROSION AT THE MAHAL FARM 20 SEP NOV JAN MAR MAY JUL 1983 1984 Figure 1.13: Cumulative soil erosion losses for the Wood (1984) plot study, 1983-1984. Chapter 2 SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 2.1 INTRODUCTION Soil hydraulic properties can be limiting factors to rainfall infiltration, thereby determin ing the amount of runoff generated. The objective of this chapter is to report measure ments of the hydraulic properties of a Whatcom soil in the uplands of the lower Fraser Valley. Additional measurements of cone penetration resistance, soil colour, texture, bulk density and porosity are used to characterize the site. Measurements of the sorptivity, wetting-front advance and satiated conductivity are made using a low tension absorp tion device. Constant-concentration absorption theory is used to calculate the soil-water diffusivity characteristic from these data. The measured soil-water diffusivity functions are compared to values predicted from the desorption soil-water retention curves and the satiated hydraulic conductivity. The measured hydraulic properties will be used to predict infiltration, runoff and drainage in Chapter 3. 2.2 THEORETICAL BACKGROUND 2.2.1 LOW TENSION ABSORPTION A list of the symbols used in the text is given in appendix A. The soil is assumed to be homogeneous with a hydraulic diffusivity (D) given by (Gardner, 1959; Zachmann et al. , 1980) (2-1) D(8) = Dn exp [3(8-0n) (0s - 8n) 21 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 22 where 9 is the volumetric water content, 9a and 9n are two particular values of 9, generally the saturated value and the air-dry value respectively, D„ is D(9n) and f3 is an exponent. From (2.1) the differential function may be written as D = 6exp(a#) where 0 a = 98 — 9n and ^ (2.2) "~«P<£fc) (2-3) According to Brutsaert (1979), dimensional considerations yield D" = W^y (2'4) where 7 is a function of f3 and S is the sorptivity for the 9S and 9n values. Combining (2.1) and (2.4) gives (Clothier and White, 1981) (2.5) l(9s-9n) For small time (t) and when 9n is less than or equal to field capacity, gravity ef fects may be neglected (absorption). The soil-water flow equation governing 9(x,t) for absorption is given by (Childs and George, 1950) MM where x is the horizontal distance. Initially (t = 0) the soil is assumed to be uniformly Wet,i-e- 9(x,0) = 9n (2.7) For a semi-infinite soil , lim 9(x,t) = 9n (2.8) The constant-concentration surface boundary condition is given by 6(0,t) = 9. (2.9) Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 23 i.e. 9 at the surface is suddenly changed from 8n to 9S. For (2.6) subject to (2.7), (2.8) and (2.9) the Boltzman similarity variable (A) and S are given by (Philip, 1957) m = ff2 (2.io) and i , S = W (2.11) where i is the cumulative inflow. According to Philip (1973) and Philip and Knight (1974), if 8 is a monotonic function of x, then the nondimensionalized solution of (2.6) subject to (2.7), (2.8) and (2.9) is given implicitly by 2tV> p. D(9) -Tie FW) ( } and D{6) ' [9\e-eny F(0) where F(Q) is the flux concentration function (Philip, 1973) and dd (2.13) V« — Vr, 'n Substituting (2.5) into (2.13) gives 7 = (2.15) 9 e\ eexp,3(0)<fO  Z Jo F(O) If 9* is the volumetric water content at the wetting-front, then from (2.10) and (2.12) A _ JO F(Q)AU _ JO F(Q)AKJ where A* is A at the wetting-front. Defining (2.16) *=A^j (2'17) and substituting A* from (2.12) and S from (2.13) with 9 = 9* yields rl QD(Q) JQ JO F(Q) Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 24 Evidently the solution is completely specified when F(0) is known. By definition F(Q) = q(x,t)/q(Q,t), where q(x,t) is the water flux density, so that -F(l) = 1 and F(0) = 0. In general, F = F(Q,t) but for the constant-concentration case F = F(Q) (Philip and Knight, 1974). The lower bound to F(Q) occurs for a delta function soil, and is given by (Philip and Knight, 1974) F(Q) = 0 (2.19) The upper bound to F(Q) occurs for the linear case (D constant and = 0) which according to White et al. (1979) can be closely approximated by F(Q) ~ sin 2 (2.20) The flux concentration relations for delta function absorption and linear absorption provide bounds on F(6). F(Q) for absorption in field soils will lie between (2.19) and (2.20). Data from repacked laboratory columns suggest /? = 8 for a range of soil textures (Miller and Bresler, 1977; Reichardt et al., 1972). As the solution is relatively insensi tive to the form of F(Q) (Philip and Knight, 1974), for /3 > 8 the delta function flux concentration relation (2.19) is assumed. For 0 < /? < 8 the change in /3 is estimated by F(Q) = sin .2 8 8 (2.21) Substituting (2.21) and (2.5) into (2.18) gives an implicit solution for j3 when <j> is known from measurements. 2.2.2 CALCULATING D(9) FROM RETENTION CURVE DATA The hydraulic conductivity (K) of an unsaturated soil may be calculated from (Mualem, 1976) K(9) 9-9r 9„ — 9r 1/2 r6 d<L i2  Jo h re, de LJo h (2.22) Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 25 where Ka is the saturated conductivity, 6a is the saturated moisture content and h is the tension. Therefore K(8) can be calculated when h(9), i.e. the retention curve, is known. Van Genuchten (1980) suggested representing retention data by 6H — 6r 6 = 0r + (2.23) [1 + (ah)»]m where a is a constant, n and m are exponents and 6r is the residual water content. For the Mualem (1976) model ra = 1 n (2.24) Eq. (2.23) with (2.24) contains 4 independent parameters (6r, 8S, a and ra) which are determined by fitting to measured soil-water retention data. Solving (2.23) for h and substituting into (2.22) gives K{9) = K. 8-6r 1/2 1 - e-er -i l/ra^ x6a — 0r J 1 I 0a — 0r where 0 < ra < 1. The soil-water diffusivity is defined as dh m \ 2 D(0) = K{B) Differentiating (2.23) with respect to h gives dB de dh mna(6s — 8r) 6-6/ 8g — 8r i+i/fi ' 8-6r 6S — 8r -l/n (2.25) (2.26) (2.27) Substituting (2.27) and (2.25) into (2.26) yields D(6) 1 - (e-er y/™ \0.-9r) m^2 mna(68 — 6r] '(0-0T r17 \6,-6r) m - 1 m (2.28) 2.3 METHODS 2.3.1 SAMPLING Soil cores were sampled using a stratified random sampling scheme with slight modifi cations. The study area was divided into 17 sampling units (Fig. 2.1). The grid design Figure 2.1: Sampling design for soil hydraulic properties. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 27 corresponded to an earlier topographic survey at the Mahal site by Crudge (1987). Each sampling unit was approximately 2025 m2. Unit 1 was included as free water was ob served along the top of the field in the winter of 1985-1986. Unit 8 was included as the slope of the field concentrated water in unit 8 and rilling was observed in the winters of 1984-1985 and 1985-1986. Unit 17 was included as it was the location of an earlier ero sion study by Wood (1983; 1984). Sampling was conducted at 2 levels of intensity. Grid representative samples consist of 1 site randomly located within each unit. Detailed grid samples include 5 additional sampling sites randomly located in unit 9 for comparison of within versus between site variability. The combined data set is made up of the grid representative and detailed grid samples. Absorption cores were sampled to measure D(9) and water retention cores were sam pled to calculate K{6). The volume of the water retention cores ranged from 60-69 cm3. The volume of the absorption cores (851-961 cm3) were based on the representative elementary volume of a loamy textured soil with small peds (Table 2.1). Table 2.1: Hypothetical representative elementary volumes (REV) (Bouma, 1984). Texture Structure REV [cm3] Sandy No peds 102 Loamy Small peds 103 Clayey Medium peds Continuous macropores 104 Clayey Large peds Continuous macropores 105 At each site, soil profiles were sampled at two depths, corresponding to the Ap and a lower more compact horizon. The Ap horizon was sampled 1-2 cm below the surface to remove potential surface crusting effects and any weed or algae growth. The lower hori zons were identified by soil colour and resistance to shovelling. At the time of sampling Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 28 all lower horizon cores were believed to be C horizon samples. The depth to the subsoil at each site was later verified by additional soil pits and cone penetrometer readings. Soil samples were taken in April 1986 prior to ploughing. Cores were collected in, as near as possible, an undisturbed state. Water retention cores were gently hammered into the soil and dug out with a trowel. Absorption cores were collected in thin walled (0.5 mm) perspex tubes. The perspex was bevelled on the bottom to aid in penetration. The soil surrounding each core was removed with a putty knife before the core was pushed downwards to avoid compression (Fig. 2.2). The perspex tubes were pressed downwards until the soil surface was approximately 1 cm above the upper edge. The core was then dug out with a trowel and trimmed with a putty knife. All cores were then labelled and wrapped in sealed plastic bags to prevent drying. The cores were taken to the laboratory and stored in a refrigerator at approximately 5 deg C to suppress biological activity until the laboratory analysis could be done. Figure 2.2: Absorption core sampling. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 29 2.3.2 ADDITIONAL SITE PROPERTIES The depth to the compact subsoil at each site was verified by additional soil pits and cone penetrometer readings (Davidson, 1965). At each sampling site, soil horizons were identified in soil pits and cone penetrometer measurements were taken with a 2.5 cm diameter cone. The large, absorption cores were used in the determination of soil bulk density, poros ity, texture, and colour, as their larger volume provides a more representative sample. After the completion of the low tension absorption measurements, the cores were dried to constant weight at 105 deg C. The bulk density (pb) was calculated from the oven-dry mass divided by the volume of the core (Blake, 1965). The porosity (/) was calculated from / = 1 - ^ (2.29) Ps where ps is the particle density. The particle density was calculated from Ps = f 1 f (2.30) Jm | Jo v 7 2650 ' 1300 where fm is the mass fraction of mineral soil, fD is the mass fraction of organic soil, 2650 kg m-3 is the particle density of the mineral components and 1300 kg m-3 is the assumed particle density of the organic components. The organic matter content for the Ap horizon is approximately 6% (Harrop, 1987; Crudge, 1987, Brown and Morin, 1985) and for the lower horizons is approximately 3% (Brown and Morin, 1985) giving ps = 2495 and 2570 kg m-3 respectively. Dry soil colour was based on the Munsell soil colour charts. The soil samples were divided into USDA particle-size classes by hand texturing. Statistical analyses were carried out using SPSS/PC+ (Norusis, 1986). Histograms were used to display the distribution of the data. The skewness was used to indicate deviations from normality in the distribution. The mean, median and 50th percentile Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 30 were used to describe the central tendency of the data. The standard deviation (SD), minimum, maximum and range were used to measure dispersion. Linear associations were measured by the square of the Pearson correlation coefficient (r2). Regression lines, fitted by the method of least squares, were used to summarize linear relationships. Differences between group means were determined by the Mann Whitney U test. A non-parametric test was used as the data distributions were not normal. 2.3.3 SORPTIVITY TUBE A low tension absorption technique, described by Clothier and White (1981), was used to measure the hydraulic diffusivity characteristics of the undisturbed absorption cores. The sorptivity tube device of Clothier and White (1981) was modified according to Watson and Luxmore (1986). The sorptivity tube device (Fig. 2.3) consists of a perspex tube with an 80 fxm nylon mesh base. The tube is sealed at the upper end by a rubber stopper. Once sealed, water can only move through the mesh if air enters the hypodermic needle located in the side of the tube. The tension at the base of the mesh is controlled by the height of the hypodermic since (2.31) rhpwg where h is the tension at the bottom of the mesh, I is the height of the hypodermic needle above the mesh, cr is the surface tension (7.26E-2 kg s-2 at 25 degC), r/, is the inside radius of the hypodermic (2.80E-4 m), pw is the density of water (997 kg m-3), and g is acceleration due to gravity (9.81 m s-2). Eq.( 2.31) is only approximate since it excludes pressure differences due to the vertical flow in the tube. The desired tension at the base of the mesh was selected to be —4 cm of water, so that the soil would be nearly saturated but water would not flow down gaps between the soil core and the perspex tube. To obtain a tension of —4 cm of water at the bottom of the mesh, the bottom of Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 31 WATER LEVEL CONTACT SAND WETTING FRONT RUBBER STOPPER PERSPEX TUBE HYPODERMIC SYRINGE NYLON MESH (2.32) Figure 2.3: The unsaturated sorptivity tube device. the hypodermic needle is positioned 1.3 cm above the mesh. For h = —4 cm, the radius of the largest water filled pore (rp) is given by 2a pwgh For h = —4 cm, pores whose radii are greater than 0.37 mm will not influence the absorption of water from the sorptivity tube device. During the low tension absorption measurements no water flow in the gaps between the soil core and the perspex tube was observed. Prior to the low tension absorption analysis, the ends of the absorption soil cores were wrapped in cheese cloth to add stability. The cores were dried under fans, at room temperature, for 10 days. After 10 days, 9 and the change in 9 with time were significantly lowered. For each low tension absorption run, the cheese cloth on the top of the core was Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 32 removed and the initial core weight was measured. The core was placed on a wire stand and the upper edge was sealed with putty. A thin layer of air-dried, fine sand was placed over the top of the core to ensure good contact with the nylon mesh of the sorptivity tube device. The putty seal was used to stop sand from accumulating in and conducting water along the core sides. The sorptivity tube was filled with water, sealed and placed on the soil core. Ob servations of the wetting-front advance and water inflow over time were made using a stop watch and metal rulers attached to the side of the sorptivity tube and the soil core. The wetting front was defined by a sharp contrast in soil colour. For cores displaying unevenness in the wetting-front advance, the distance to the wetting-front (x*) was mea sured at 2-3 positions around the core. The transient measurements continued until the wetting-front was within 2 cm of the bottom of the soil core or for times up to 1.5 hours. The —4 cm tension at the surface was then maintained until steady-state flow was achieved. In this steady-state, the tension at the base of the soil was essentially 0 cm of water and the mean potential for the soil core was h/2 or —2 cm of water. The steady-state outflow was measured using a stop watch and graduated cylinder. The final core weight was then measured. The initial moisture content (6n) and the final moisture content (#-2) were then calculated from the initial and final weights, the oven dry weight and pb of the absorption cores. A* and S were determined from regression analysis of x* and i versus tll2 based on ( 2.10) and ( 2.11), respectively. For cores displaying uneven wetting-front advance, plots of x* versus tll2 were constructed for each lobe of the wetting-front. Values of A* were determined by weighted averages of the slopes of the regression lines. Dn, (3, a and b were calculated as indicated in the theory of section 2.2.1 using a Fortran program (appendix C) and the University of British Columbia main frame computer. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 33 The hydraulic conductivity (K-2) at a mean potential of —2 cm of water is given by where Q is the volumetric outflow, A = 9.15E-3 m2 is the area of the base of the core, and H is the core height. The constant-concentration absorption theory only applies when gravity effects are negligible. The maximum time (tg) for gravity effects to be < 10% of the surface flux is estimated by (Talsma, 1969) t9< 0.0784 (J-)2 (2.34) Trial runs, using 4 Ap horizon cores sampled in late August, 1986, were conducted to determine tg for field and air-dried moisture contents. The low tension absorption results are given in Table 2.2. 5, A*, a and b are not reported for test cores T3 and T4 with field values of 6n as the wetting-front advance was not visible due to their high moisture content. Variations in 0_2 and 9n for a given test core should effect S and A* as they are dependent on #_2 and 0n. However, a and b should be constants for a particular test core. Changes in a and b for a given test core reflect measurement error and the effects of core drying. Variation in h due to changes in the positioning of the hypodermic needle would produce deviations in measured values of a and b. The positioning of the hypodermic needle above the mesh was approximately / = 1.3 ± 0.25 cm yielding h = —4.0 ± 0.25 cm. Core shrinkage due to drying may alter the pore size distribution, but these effects are most pronounced in clay soils (Baver, 1956). Values of tg for test cores TI and T2 are given in Table 2.3. Average values of K„2 from Table 2.2 are used for Ka in the calculation of tg. For field values of 6n, gravity effects become important at times an order of magnitude less than when the samples are air-dried. For cores sampled at wetter field conditions (e.g. April, 1986), tg will be less, necessitating core drying to meet the assumption of negligible gravity effects. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 34 Table 2.2: Low tension absorption variables for field and air-dried values of 9n. Core 9 9-2 9n S [m s"1/2] A [m s-1/*] K-2 [m s-1] a b Ks"1] T1A Field 0.49 0.24 2.69E-4 1.43E-3 8.09E-6 21.6 8.41E-11 T1A Air-dry 0.46 0.06 7.32E-4 2.07E-3 1.26E-5 25.1 1.59E-10 T2A Field 0.50 0.27 3.26E-4 1.96E-3 1.32E-5 21.1 1.37E-10 T2A Air-dry 0.48 0.06 9.44E-4 2.56E-3 1.74E-5 23.0 3.89E-10 T3A Field 0.50 0.29 6.25E-6 T3A Air-dry 0.48 0.09 8.48E-4 2.59E-3 6.85E-6 11.9 1.68E-8 T4A Field 0.47 0.27 7.94E-6 T4A Air-dry 0.46 0.08 6.10E-4 1.99E-3 7.65E-6 10.1 2.27E-8 Table 2.3: The effect of core drying on t. Core 9 t9 [min] T1A Field 0.8 T1A Air dry 6.6 T2A Field 0.6 T2A Air dry 5.0 A thin layer (w 1 mm) of 53-250 fxm sand was placed over each soil core to ensure good contact with the sorptivity tube device. Fine grained sand has an air entry value of 35-70 cm of water tension (Bear, 1972) so the sand should remain saturated at a tension of —4 cm of water. The effect of hydraulic resistance of the sand is estimated from Darcy's Law, i.e. Ah = ^ (2.35) ri.s where q is the flow, Ah is the change in potential due to the sand layer, and Az is the thickness of the sand layer. KB for loose, fine sand is approximately 10_4m s_1 (Hillel, 1980; Freeze and Cherry, 1979; Bear, 1972). Over the first 60 s of absorption, the flow rates were high (1.7E-4 to 8.0E-4 m s_1) and the hydraulic resistance of the sand was Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 35 estimated to cause h to be greater than —4 cm by 0.2-0.8 cm. As the flow rate declined, the change in potential due to the sand layer became negligible and the tension at the soil surface underlying the sand approached to —4 cm. 2.3.4 WATER RETENTION Water retention curves were determined using a pressure plate apparatus (Richards, 1965). The pressures used were 2.5, 5, 10, 33, 50, 100, 200, 400, 800 and 1500 kPa. Up to 9 cores were placed directly on each pressure plate and they were saturated between runs to ensure good hydraulic contact between the plate and the cores. After outflow from the apparatus ceased, the cores were quickly removed from the plate with a spatula and weighed. The measurements were done in order of increasing pressure and the measurement at 2.5 kPa was repeated after the 1500 kPa measurement. Following the completion of the water retention measurements, the cores were dried to constant weight at 105 deg C. The bulk density was calculated from the oven-dry mass divided by the core volume (Blake, 1965). The water contents measured on a mass basis were then calculated on a volume basis. The parameters 9S, 6T, a and ra in the Van Genuchten (1980) expression (2.23), were calculated from the observed soil-water retention data using a least squares curve-fitting technique. Calculations were done using the University of British Columbia mainframe computer and the Fortran curve-fitting subroutine NL2SNO (appendix D). For each core, 8a, a and ra were calculated for various assumed values of 0r in the range from 0 to the measured 9 at 1500 kPa. The 4 parameters giving the lowest sum of squared residuals (J2 C2) determined the best fit curve for each sample. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 36 2.4 RESULTS AND DISCUSSION 2.4.1 SITE CHARACTERISTICS The raw data for the soil pb, /, colour, and texture, and the depth to the subsoil are presented in appendix B, Tables B.l and B.2. The spatial distribution of the depth to the C horizon is shown in Fig. 2.4. The depth to the C horizon ranges from 7-65 cm, with a median depth of 26 cm. The depth to the C horizon is not consistently low near the top of the field and greater toward the base as expected in an erosional landscape. The sampling depth was initially determined by soil colour and the resistance to shovelling. In verifying the depth to the subsoil, 5 of the lower horizon samples were identified as B horizon samples. Cone penetrometer resistance readings greater than 10 kg cm-2 were found to correspond with the C horizon and intermediate values correspond with the B horizon. Fig. 2.5 displays the separation of soil horizons by penetration resistance. Soil colour was used to distinguish between the Ap and C horizons in the field. Ta ble 2.4 lists the number of samples (n) in each horizon with a given Munsell soil colour. In general, the differences between the Ap and C horizons are visually distinct (Fig. 2.6), but the same soil colours are found in the Ap, B and C horizons (Table 2.4). The number of samples in each horizon in a given USDA particle size class are listed in Table 2.5. The texture ranges from coarse silty to fine loamy in the Ap horizon, fine to coarse loamy in the B horizon, and fine silty to sandy in the C horizon. Summary statistics for pb and / are given in Table 2.6. The maximum and minimum values are found in the C horizon, and the SD is smallest in the Ap horizon. Due to the effects of ploughing, the Ap horizon is expected to be more homogeneous than the B or C horizons. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 37 ^ NORTH 0.55 Figure 2.4: Spatial distribution of the depth to C horizon. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 38 > 10 Ld O < CN 00 if) Ld £ < Ld Ld Q_ 8H 6H 4j 0-0, 4 5 A • a • ••• A HORIZON n = 22 IUBBB B HORIZON n = 5 ,AAAA c HORIZON n = 17 "i—i—i—r i—i—i—r i—i—i—r i i i r 0 0.1 0.2 0.3 1—i—i—i—|—i—i—i—r 0.4 0.5 0.6 SAMPLE Z (m) Figure 2.5: Soil horizon determination from cone penetration resistance. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 39 Table 2.4: Munsell dry soil colour. Horizon Colour n A 2.5Y4/4 Olive Brown 2 2.5Y5/4 Light Olive Brown 3 10YR4/3 Brown Dark Brown 3 10YR4/4 Dark Yellowish Brown 4 10YR5/3 Brown 4 10YR5/4 Yellowish Brown 6 B 2.5Y5/4 Light Olive Brown 1 10YR4/3 Brown Dark Brown 1 10YR5/3 Brown 3 C 2.5Y5/4 Light Olive Brown 1 2.5Y6/2 Light Brownish Gray 1 2.5Y6/4 Light Yellowish Brown 5 2.5Y7/2 Light Gray 2 10YR4/3 Brown Dark Brown 1 10YR5/3 Brown 2 10YR5/4 Yellowish Brown 1 10YR6/3 Pale Brown 4 Table 2.5: Texture based on USDA particle size classes (textured by Dr. S.M. Smith). Horizon Texture n AP coarse silty 10 fine loamy 12 B fine loamy 4 coarse loamy 1 C fine silty 3 coarse silty 5 fine loamy 8 sandy 1 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 40 Figure 2.6: Rill erosion exposing the Ap horizon and the underlying C horizon Table 2.6: Summary statistics for pb and /. Property Horizon n Mean Median S.D. Skew. Max. Min. Range pb [kg m-3] AP 22 1056 1051 90 0.410 1238 912 326 B 5 1129 1121 156 -0.601 1304 901 403 C 17 1260 1247 259 0.422 1734 861 873 / [m3m-3] A 22 0.58 0.59 0.036 -0.411 0.64 0.51 0.13 B 5 0.56 0.56 0.061 0.599 0.65 0.49 0.16 C 17 0.51 0.51 0.100 -0.411 0.66 0.33 0.33 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 41 2.4.2 MEASURED D(6) Example plots of the i and x* versus tll2 relationships used to determine S and A* are shown in Fig. 2.7 and 2.8. All plots display strong i1!2 relationships as expected from the constant-concentration absorption theory. Table 2.7 lists median values of the parameters from the regression analysis used to calculate S and A*. and tj are the initial and final times used in the regression, r2 and intercept values are also given, i and x* were typically measured over 20 minutes and the high r2 values (r2 > 0.99) confirm negligible gravity effects for t < tj. All Ap horizon cores displayed even wetting-front advance. One B horizon and 17 C horizon cores displayed unevenness in the wetting-front advance. Values of i and x* display minor initial deviations from the t1!2 relationship (t < £,). Data points displaying deviations from the t1!2 relationship are not included in the regression analysis used to determine S and A*. Typically, points over the first 20-84 seconds are excluded (Table 2.7). Minor, initial decreases in i and x* are anticipated due to resistance and storage effects in the sand layer. Initial decreases in i and x* are indicated by negative intercept values in Table 2.7. Minor increases in x* were noted (positive intercepts) for some cores and presumably were due to the difficulty in measuring x* accurately near t = 0. Table 2.7: Median values of i/, r2 and intercept used in the calculation of S and A*. Horizon n S A* U r2 Intercept U r2 Intercept H [min] [m] M [min] [m] A 22 20 20 0.999 -1.73E-3 45 20 0.995 1.51E-4 B 5 60 20 0.999 -2.10E-3 40 20 0.997 -2.12E-5 C 17 20 18 0.999 -1.53E-3 84 15 0.993 3.81E-3 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 42 0.20 0.15 0.10 H 0.05 -\ i = 5.65E-4 t 1/2 (r 2 = 0.999) = 1.70E-3 t 1/2 / wf (r 2 = 0.998) • A" A A A A A Wf h0.08 0.00 11 i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i | i i i i i i i i i [ 0.00 0 10 20 30 40 50 •0.10 0.06 0.04 X •0.02 t 1/2 ^ 1/2 Figure 2.7: Example plots of water inflow (i) and wetting-front advance (x*) versus t1!2 for the Ap horizon. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 43 0.15 o.io H 0.05 i = 5.66E-4 t 1/2 (r 2 = 0.999) = 1.57E-3 t 1/2 wf (r 2 = 0.994) wf 0.08 •0.06 h0.04 •0.02 0.00 j i i i i i i i i i | i i i i i i i i i i i i i i i i i i i i i i i i i i i i i | 0.00 0 10 20 30 40 1/2 / 1/2 t1/2 (s ,/2 ) X Figure 2.8: Example plots of water inflow (i) and wetting-front advance (a;*) versus t1 for the C horizon. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 44 An example moisture profile over time for constant-concentration absorption is shown in Fig. 2.9. The Ap and lower horizon cores required approximate 1.5-10 h and 2.5-68 h respectively to reach steady state outflow. Summary statistics for K-2 are given in Tables 2.8 to 2.10. Values are given for grid representative samples, detailed grid samples from unit 9 and for the combined data set. Table 2.8: Summary statistics of K-2, a and b for grid representative samples. Variable Horizon n Mean Median SD Skew. Max. Min. K-2 AP 17 4.70E-6 4.25E-6 8.28E-7 1.88 1.50E-5 1.53E-6 (m s"1) B 3 1.36E-6 7.67E-7 1.33E-6 1.61 2.88E-6 4.33E-7 C 14 4.70E-6 2.48E-6 5.84E-6 1.82 2.08E-7 2.50E-7 a Ap 16 23.4 19.4 16.7 2.53 77.3 10.9 B 3 19.7 16.7 5.9 1.70 26.6 15.9 C 13 27.2 28.5 11.4 0.08 46.4 8.5 b Ap 16 3.67E-9 8.51E-10 4.87E-9 1.28 1.51E-8 4.80E-22 (mV1) B 3 1.12E-15 1.08E-15 1.14E-15 0.18 2.29E-15 5.32E-21 C 13 6.63E-9 1.29E-10 5.82E-9 3.55 7.61E-8 1.57E-14 Table 2.9: Summary statistics of K-2, « and b for detailed grid samples from unit 9. Variable Horizon n Mean Median SD Skew. Max. Min. K-2 Ap 5 6.24E-6 5.95E-6 2.11E-6 1.28 9.65E-6 4.25E-6 (m s"1) B 2 3.19E-6 3.19E-6 3.43E-6 5.62E-6 7.67E-7 C 3 6.35E-6 2.48E-6 8.49E-6 1.22 1.61E-5 4.83E-7 a Ap 5 17.4 13.6 9.0 1.89 32.9 11.4 B 2 19.2 19.2 1.1 20.0 18.4 C 3 21.7 12.0 26.2 1.22 51.3 1.7 b AP 5 1.03E-8 6.16E-9 1.15E-8 0.95 2.75E-8 8.47E-13 (mV1) B 2 3.31E-17 3.31E-17 3.83E-17 6.04E-17 5.93E-18 C 3 5.28E-8 1.82E-8 7.62E-8 1.22 1.40E-7 9.21E-15 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 45 Figure 2.9: Example moisture profiles over time for constant-concentration absorption. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 46 Table 2.10: Summary statistics of K-2, a and b for the combined data set. Variable Horizon n Mean Median SD Skew. Max. Min. K-2 AP 22 5.05E-6 4.74E-6 3.19E-6 1.55 1.50E-5 1.53E-6 (m s-1) B 5 2.09E-6 7.67E-7 2.20E-6 1.37 5.62E-6 4.33E-7 C 17 4.99E-6 2.48E-6 6.09E-6 1.54 2.08E-5 2.50E-7 Lower 22 4.33E-6 2.03E-6 5.54E-6 1.82 2.08E-5 2.50E-7 a Ap 22 22.0 16.5 15.3 2.67 77.3 10.9 B 5 19.5 18.4 4.2 1.53 26.6 15.9 C 16 26.1 27.0 3.5 0.12 51.3 1.7 Lower 21 24.56 21.33 2.78 0.46 51.313 1.68 b Ap 22 5.17E-9 1.31E-9 7.16E-9 1.79 2.75E-8 4.80E-22 (mV1) B 5 6.86E-16 6.04E-17 1.01E-15 1.36 2.29E-15 5.32E-21 C 16 1.53E-8 1.31E-10 9.58E-9 2.87 1.40E-7 9.21E-15 Lower 21 1.16E-8 1.73E-11 7.39E-9 3.36 1.40E-7 5.32E-21 Values of tg based on (2.34) are given in Table 2.11. Times are shown for samples with the minimum, 50th percentile and maximum values of tg for the Ap, B and C horizons. The short time behaviour is limited to 2-8 minutes of constant-concentration absorption in the worst cases. Gravity effects are typically negligible in the Ap, B and C horizons at times less than 20, 44 and 62 minutes, respectively, supporting the t1/2 behaviour displayed by i and x* for t < tf. For absorption at h = —4 cm, 9S = 9-4 in section 2.2.1. However, 9-2 was measured. Measured water retention curves for absorption in sand and silt loams (Topp, 1971; Poulovassilis, 1970; Staple, 1965) indicate that 9-2 is very near 9-4 as 9(h) is relatively constant at these low tensions. The data for the low tension absorption variables 9-2, 9„, S, A*, K-2, Dn, f3, a and b are presented in appendix B, Tables B.3 to B.6. Values of 9 at the time of sampling (Apr. 1986) are also given. Values of S and A* are generally conservative, ranging from 10~3-10-4 m s-1/2. Summary statistics for a and b are given in Tables 2.8 to 2.10 respectively. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 47 Table 2.11: The maximum time for gravity effects to be negligible. Variable Sample tg [min] tamin 13A 4.6 *fl50 1A 19.3 £3max 5A 147.6 tgmm 9-6B 7.5 tg50 8B 62.2 tgmax 9-3B 72.4 tgmm 9-2C 1.6 tg50 IC 43.8 tgmax 4C 937.3 Values are given for grid representative samples, detailed grid samples from unit 9 and for the combined data set. For sample 11C /? is > 100. The effects of forcing /? = 100, 75, and 50 are given in Table 2.12. Sample 11C has the largest value of a, and smallest value of b, of the measured diffusivity functions. K-2 = 3.522 — 7 for core 11C is in the lower range of values measured at the Mahal farm (Table 2.10). Core 11C is an extreme case and due to the uncertainty in the diffusivity function, is not included in a and b of Tables 2.8 to 2.10 or in further calculations involving a or 6. Table 2.12: Values of Dn, a and b for core 11C with forced values of \3. p Dn [mV1] b [mV1] a 100 3.16E-49 9.57E-72 370 75 1.71E-38 2.20E-55 278 50 8.19E-28 4.51E-29 185 The range of a, b and K_2 for grid representative samples and detailed grid samples from unit 9 are shown in Figs. 2.10 to 2.12. Figs. 2.10 to 2.12 and the SD values of Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 48 100 75 O 50 25 GRID REPRESENTATIVE DETAILED GRID 0 ABC HORIZON FigTire 2.10: The range of a for grid representative samples and detailed grid samples from unit 9. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 49 10 -6 10 -10. 10 -14. _Q 10 -18J 10 -22. 10' -26. GRID REPRESENTATIVE DETAILED GRID A B C Figure 2.11: The range of b for grid representative samples and detailed grid samples from unit 9. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 50 10 -4 6 4 10-5 Ul CN I 4 2 10-6 6 h 4 10-7 GRID REPRESENTATIVE DETAILED GRID A B HORIZON C Figure 2.12: The range of K-2 for grid representative samples and detailed grid samples from unit 9. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 51 Tables 2.8 and 2.9 indicate that the variability over shorter sampling distances (within unit 9) is of the same order of magnitude as between sampling units. The detailed grid samples from unit 9 are within the range of grid representative samples and are considered part of the same population. The combined data set is therefore used in following analyses. Values of a and K-2 for the B horizon cores are within the range of values for the C horizon (Fig. 2.10 and 2.12). Values of b for the B horizon cores are generally smaller than the C horizon cores. Due to the small number of B horizon samples, there is some uncertainty in the median values of a, b and K-2. For comparison with the overlying Ap horizon cores, the B and C horizon cores are combined and presented as the lower horizons. The distributions of a and b for the Ap and lower horizons are shown in Figs. 2.13 to 2.16. The diffusivity characteristics (2.1) of the Ap and lower horizons are shown in Figs. 2.17 and 2.18. The diffusivity characteristics display high variability, typical of soil hydraulic properties (Warrick and Nielsen, 1980). The variability of the Ap horizon is less than the lower horizons, possibly due to the mixing effects of ploughing. There are strong negative correlations between a and In b. The inverse relationship between a and In b is related to the conservative nature of S and A* as the process of absorption is determined by the integral behaviour of the diffusivity function (Eqs. 2.12 and 2.13). To test the reproducibility of the sorptivity tube method, seven of the Ap horizon cores were re-dried and the low tension absorption repeated. Values of 9-2, 9n, S, A*, a and b are given in Table 2.13. Changes in a and b for a given sample indicate the magnitude of measurement errors, hysteresis and the effects of core redrying. As the texture of the Ap horizon samples are coarse silty to fine loamy (Table 2.5), drying effects are expected to be small. The changes in a and b for a given sample are relatively large, but a and b are sensitive to errors in the input variables. The effect of 5% increases in 9S, 9n, S and Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 52 ID 20 30 40 50 60 70 80 SO 100 Figure 2.13: The distribution of a for the Ap horizon. CO u z LJ CY CY CJ CJ O L_ O # 8 4 2 0 E-24 E-22 E-20 E-18 E-1S E-14 E-12 E-10 E-8 E-B b (m2s_1 ) Figure 2.14: The distribution of b for the Ap horizon. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 53 CO LJ CJ z Ld CY CY ID CJ CJ O LL o # 10 8 4 2 0 o in i D K ^1 K -4-o CM I cr 10 20 30 40 50 60 a 70 80 370 Figure 2.15: The distribution of a for the lower horizons. E-72 E-22 E-20 E-18 E-16 E-14 E-12 E-10 E-8 E-S b i m2s _1 ) Figure 2.16: The distribution of b for the lower horizons. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 54 Figure 2.17: The diffusivity characteristics of the Ap horizon. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 55 e Figure 2.18: The difFusivity characteristics of the lower horizons. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 56 A* on a and b are presented for core 1A in Table 2.14. Errors in the range of 5% would account for the observed differences in a and b between redried cores. Table 2.13: The effects of core drying on constant- concentration absorption. Sample 0n S [m s"1] A [m s"1/2] K-2 [m s"1] a b [m s"1/2] 1-2A 0.47 0.03 5.08E-4 1.31E-3 2.41E-6 22.1 1.96E-10 1-2AR 0.46 0.14 4.24E-4 1.57E-3 2.60E-6 25.1 6.82E- 11 2A 0.46 0.07 3.91E-4 1.32E-3 1.53E-6 14.3 4.10E- 9 2AR 0.45 0.10 3.96E-4 1.30E-3 1.65E-6 17.2 1.58E- 9 3A 0.50 0.06 7.47E-4 2.13E-6 9.41E-6 14.8 6.03E- 9 3AR 0.50 0.10 6.01E-4 2.05E-3 5.46E-6 12.5 1.15E- 8 5A 0.50 0.09 6.94E-4 2.35E-3 2.06E-6 24.7 6.31E- 11 5AR 0.51 0.09 7.38E-4 1.94E-3 2.28E-6 28.4 9.60E- 12 8A 0.49 0.09 6.39E-4 1.82E-3 2.35E-6 23.8 1.06E- 10 8AR 0.50 0.11 5.53E-4 1.60E-3 2.90E-6 26.1 2.20E- 11 12-2A 0.53 0.05 6.48E-4 2.14E-3 2.80E-6 7.3 7.82E- 8 12-2AR 0.52 0.12 5.32E-4 1.87E-3 2.76E-6 11.6 1.06E-8 15A 0.47 0.06 6.96E-4 1.88E-3 6.38E-6 29.0 2.06E- 11 15AR 0.46 0.11 6.50E-4 2.06E-3 4.55E-6 32.8 5.53E- 12 Table 2.14: Sensitivity of a and b to input variables for sample 1A. Input Variable a b [m2s"1] Original 13.6 6.76E-7 5% T 0S 11.0 1.44E-6 5% T 0* 14.0 5.76E-7 5% T S 16.0 2.65E-6 5% T A 11.9 1.43E-6 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 57 2.4.3 D(9) CALCULATED FROM RETENTION CURVE DATA The water retention characteristic curves are summarized using Van Genuchten's (1980) expression (2.23) relating 9 to h. The transformed data for the water retention variables 9S, 9r, ct, n, XX2 and pi are presented in appendix B, Tables B.7 and B.8. Summary statistics for the water retention variables are given in Table 2.15. The histograms of 9S, 9r and n for the Ap and lower horizons display similar distributions, but values of a for the lower horizons are more variable than in the Ap horizon. Example plots of the water retention data and the corresponding curves from (2.23) are shown in Fig. 2.19. The good fit of (2.23) is indicated by the low £(2 in 9 (Table 2.15). The magnitude of measurement error in the water retention measurements is indicated by the differences in the replicate 9 at 2.5 kPa. Average differences in the replicate 9 at 2.5 kPa are 0.04 and 0.01 m3m-3 for the Ap and lower horizons respectively. Example difFusivity characteristics calculated from (2.28) and the corresponding mea sured D(9) functions are shown in Figs. 2.20 and 2.21 for samples with the 50th percentile values of a and b. The discrepancy between the measured and calculated values of D(9) are 1-3 orders of magnitude. The calculated D{9) functions are desorption curves, while the measured D(9) functions are absorption curves. Additionally, in the calculation of D(9), Kg in (2.28) is assumed equal to K-2 measured for absorption. By definition, the diffusivity function is given by D{9) = K{9)hd-^> (2.36) K(0) measured for a range of soil textures show no noticeable hysteresis (Scotter and Clothier, 1983; Topp, 1971; Elrick and Bowman, 1964). Based on measured water re tention curves from Scotter and Clothier (1983), Topp (1971), Poulovassilis (1970) and Elrick and Bowman (1964) is similar for sorption and desorption cycles. Thus hys teresis in D(9) can be estimated from differences in h between sorption and desorption Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 58 Table 2.15: Summary of the output from the water retention data. Variable Horizon n Mean Median SD Skew Max Min 9. AP 22 0.52 0.52 0.039 0.67 0.63 0.47 B 5 0.56 0.52 0.068 0.65 0.65 0.49 C 17 0.51 0.52 0.067 -0.50 0.61 0.38 Lower 22 0.52 0.52 0.069 -0.28 0.65 0.38 9r Ap 22 0.04 0.03 0.040 0.55 0.12 0.00 B 5 0.06 0.00 0.093 1.32 0.21 0.00 C 17 0.02 0.00 0.46 2.60 0.16 0.00 Lower 22 0.03 0.00 0.060 2.13 0.21 '0.00 a AP 22 3.10E-3 3.14E-3 6.44E-3 0.29 4.62E-3 1.96E-3 B 5 2.77E-3 2.80E-3 1.34E-3 -0.14 4.59E-3 8.72E-3 C 17 2.57E-3 2.02E-3 2.54E-3 1.97 1.02E-2 2.59E-4 Lower 22 2.62E-3 2.26E-3 2.29E-3 1.93 1.02E-2 2.59E-4 n AP 22 1.37 1.35 0.086 0.75 1.58 1.25 B 5 1.35 1.31 0.128 2.03 1.58 1.26 C 17 1.32 1.27 0.124 1.50 1.65 1.20 Lower 22 1.33 1.30 0.123 1.42 1.65 1.20 EC2 Ap 22 6.46E-4 4.77E-4 4.27E-4 0.71 1.59E-3 9.57E-5 B 5 1.04E-3 6.11E-4 6.20E-4 0.60 1.73E-3 5.52E-4 C 17 7.85E-4 6.43E-4 5.27E-4 0.94 2.00E-3 2.07E-4 Lower 22 8.43E-4 6.27E-4 5.45E-4 0.80 2.00E-3 2.07E-4 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 59 Figure 2.19: Example plots of the water retention characteristic curves. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM GO Figure 2.20: A„ horizon. Measured and predicted D(9) for 50"* percentile values of a and b of the Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 61 Figure 2.21: Measured and predicted D(9) for 50th percentile values of a and b of the lower horizons. Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 62 cycles. Based on hysteretic water retention data from Scotter and Clothier (1983), Topp (1971), Staple (1965) and Elrick and Bowman (1964), D(6) for desorption may be up to an order of magnitude greater than for sorption. Additional differences between calculated and measured values of D(8) may be due to errors in the input variables. For some samples (e.g. 1A) #_2 is greater than 9S. In order to calculate K{9) over the range from 9n to 9-2, 8s is set equal to 9-2- The sensitivity of (2.25) to changes in the input variables is tested by increasing the input variables by 5% and recalculating K(9). As an example, results for core 1A are presented in Table 2.16. K(9) is calculated for 9 at h = 100 kPa . The effects of increasing the input variables and of setting 9S = 9-2 on K(9) are seen to be small. Attributing an order of magnitude increase in the calculated D(9) to hysteresis effects, the discrepancy between measured and calculated D(9) is still large for some samples. The Mualem (1976) model for predicting K(9) generally gives reliable predictions, but may overestimate K(9) by up to 2 orders of magnitude for some soils (Mualem, 1976). The calculated D(9) functions have similar slopes to measured D(9) functions and if matching were done at D(9S) a good fit would be generated. Table 2.16: Sensitivity analysis for K{9) calculated from retention curve data. Variable K{9) Original 6.57E-9 5% T 0T 6.57E-9 5% T 8s 4.10E-9 5% T rn 8.68E-9 5% T K-2 6.89E-9 8S - 9-2 4.39E-9 Chapter 2. SOIL HYDRAULIC PROPERTIES AT THE MAHAL FARM 63 2.5 CONCLUSIONS The sorptivity tube device provides a simple method for obtaining S, A* and K-2 • Mea sured values of i and x* depend on t1!2 as expected from the constant-concentration absorption theory. However, core drying was necessary for gravity effects to be negli gible. The D(6) functions determined from constant-concentration absorption theory display high variability in a and b, especially in the lower horizons. The Van Genuchten (1980) 6(h) expression provides a good fit to the water retention data. The D(6) functions calculated from the Mualem model and the Van Genuchten (1980) water retention expression are at least 1-2 orders of magnitude greater than the measured functions. Hysteresis effects explain 1-order of magnitude increase in D(6), but without matching at D(6S) the predictions are poor. Chapter 3 RUNOFF GENERATION AT THE MAHAL FARM 3.1 INTRODUCTION Runoff may be generated when the soil becomes saturated at the surface (Dunne runoff) or when the precipitation intensity is larger than the infiltrability of the soil (Hortonian runoff). The objective of this chapter is to determine whether typical rainfall events for the Lower Fraser Valley will generate runoff on a typical Whatcom soil. Constant-flux infiltration theory and the soil hydraulic properties determined in Chapter 2, are used to generate soil moisture profiles over time. Rainfall intensities, durations and return periods required to generate runoff for the sampled cores are compared to precipitation data for the Abbotsford airport and to storms known to cause runoff and soil loss at the Mahal farm. To evaluate soil moisture conditions between rainfall events, drainage for each core is estimated from a unit gradient model. 3.2 THEORETICAL BACKGROUND 3.2.1 CONSTANT-FLUX INFILTRATION The soil water flow equation governing z(9, t) for a homogeneous soil is given by (Philip, 1969) (3-1) 64 Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 65 where z is the vertical distance. Initially (t = 0) the soil is assumed to be uniformly wet, i.e. 0{z,0) = 0n (3.2) For a semi-infinite soil • lim 2(0, <) = oo (3-3) The constant-flux surface boundary condition is given by d8~{Vo,t) where 9Q — 0(0, t) and R is the constant flux. According to White (1979) the solution of (3.1) subject to (3.2), (3.3) and (3.4) can be written implicitly as z = m Je F(0, t) [R - K(0n)] - K(0) + K(0n) and the time dependence of the surface moisture content is given by [R-K(0n)]t-Jdn mt)[R_K{0n)]_m + K{0n)M (3-6) The solution is not sensitive to F, sp that we can assume F(0,t) ~ F(Q), where B = (0- 0n)/(Oo(t) - 0n) (3.7) The dependence of F on t is then implicitly via #o(^) in ©• According to White (1979), for large j3 at t —> oo F(0) » 0 (3.8) The upper bound to F(Q) occurs with a linear soil (constant D) which according to White et al. (1979) can be closely approximated by F(Q) ~ Q2-4'* (3.9) Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 66 For 0 = 0, F(Q) is given by (3.9). For 0 > 8, F(Q) is assumed equal to (3.8). For 0 < 0 < 8 the change in F(Q) with 0 is estimated by F(0) = 02-4/* + (3.10) Calculations of moisture profiles over time were done using a Fortran program (ap pendix E) and the University of British Columbia mainframe computer. 3.2.2 DRAINAGE CALCULATION Assuming a unit gradient in the hydraulic head throughout the soil, the equation gov erning the one-dimensional flow of water is given by (Sisson et al., 1980) at ~ de dz Considering only the drainage phase, (3.11) may be solved subject to the conditions 9(z,0) = 9s (3.12) and 9(0,t) = 9m (3.13) i.e. 6 at z = 0 instantaneously declines to 0m, where 0m is the minimum obtainable 0 and the soil is infinitely deep. The initial-value problem given by (3.11), (3.12) and (3.13) is a Cauchy-Riemann or characteristic-value problem (Sisson et al., 1980; Aris and Amundson, 1973; Lax, 1972). According to Sisson et al. (1980) the solution of (3.11) subject to (3.12) and (3.13) is 9 = 9* t< ^ (3.14) t d9 dTle«) 1e(e™> 9 = 9m ^^fVl (3-16) Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 67 where z is the depth of the draining front and ^>0 (3.17) K(9) from 2.25 appears to satisfy 3.17. Substitution of the expression for dK/dd from (2.25) into (3.15) yields z K, . . (2e1/2[i-(i-01/m)m][(i-01/mr-1][e1/m-1] + i[i-(i-01/m)m]2} td "s — "m I 2 J (3.18) where tj is the time required to drain a soil from 9S to 6 at a given z and 0 = ^f- (3.19) A Fortran program (appendix F) and the University of British Columbia mainframe computer were used to calculate td. 3.3 RESULTS 3.3.1 FIELD MOISTURE CONDITIONS In Chapter 1, it was shown that erosion rates at the Mahal farm are initially low in September and October, are high between November and January, and decline from January to March. Runoff coefficients increase when the moisture content of the soil prior to the rainfall event increases. The volumetric water content of the soil as determined at the study site on April 18, 1986, February 9, 14 and 25, March 31, and September 12, 1987 (Table 3.1). The April 18 values were determined for the infiltration cores collected in the Ap B and C horizons. The moisture content for each core was calculated from the initial core weight, oven dry weight and bulk density. Moisture contents were measured gravimetrically at the 22 sampling sites from February to March, 1987 using moisture tins. In February, 9 at depths greater than 15 cm were not measured. Walking on the Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 68 Table 3.1: Moisture conditions at the Mahal farm from September to April. Median 9 [m3m-3 AP Lower Apr. 18/86 0.42 0.40 Feb. 09/87 0.54° Feb. 14/8.7 0.53a Feb. 25/87 0.52" Mar. 31/87 0.49 0.39 Sep. 12/87 0.36 0.40 / 0.59 0.53 9-2 0.49 0.45 9-2 — OinSep 0.13 0.05 "possible sampling error field was difficult due to the wet conditions and holes dug into the soil would fill with water making gravimetric sampling difficult. Free water was often sampled with the soil producing error in 9 and unrealistic values as noted in Table 3.1. In March soil pits were dug at each site and gravimetric moisture contents were measured in the Ap, B and C horizons. In September, 9 was determined gravimetrically at 11 locations scattered over the field, which do not correspond to the sampling sites. In calculating runoff, a range of initial 9 (9n) from dry to wet conditions are of interest. 0n = 9-2 is used to represent initially wet conditions. The lowest values of 0 measured were in September and these are used to represent initially low values of 9n. The median values of 9 measured in September for the Ap and lower horizons may be greater than 9-2 for some of the soil cores. Therefore, for each core 9n is estimated by subtracting the average difference between 9-2 and the September values of 9. The average differences for the Ap and lower horizons are 0.13 and 0.05 m3m-3 respectively (Table 3.1). Theoretically, when 9o(t) reaches 9S ponding will occur, and assuming negligible sur face storage, runoff will be generated. In the constant-flux infiltration model, 9S is as sumed equal to #_2. The February values of 9 are greater than 9-2 (Table 3.1). Some Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 69 of the difference may be accounted for by sampling error due to the wet field conditions. 9-2 is generally less than the calculated porosity (Tables B.l to B.4). Poulovassilis (1970) found that for his wetting curves, 9a w 0.85/ due to air entrapment. Table 3.2 lists pb, / and 0.85/ for the minimum, 50th percentile and maximum values of 9-2. The results show that for the Mahal soil, 9-2 ~ 0.85/. Additionally, wetting scanning curves for sand and silt loams indicate that 9-2 is very near 9 at 0 cm of water tension (Topp, 1971; Poulovassilis, 1970; Staple, 1965). Setting 9a = 9-2 in the constant-flux infiltration model is considered to be a good approximation, but runoff generation may be overestimated. Table 3.2: Range in 9-2, 0.85/, pb and / for the Ap and lower horizons. Variable Sample 9-2 0.85/ Pb [kg m-3] / 0_2min 4A 0.37 0.43 1238 0.51 0_25O 14A 0.50 0.50 1041 0.59 0_2max 17A 0.54 0.54 912 0.64 #_2min 16C 0.31 0.28 1734 0.33 0_25O 4C 0.44 0.41 1356 0.48 #_2max 10C 0.54 0.57 861 0.67 3.3.2 RUNOFF GENERATION To estimate runoff generation at the Mahal site, infiltration into the Ap and lower horizons are considered separately. The hydraulic properties for each core are used to calculate hypothetical moisture content profiles over time for constant-flux infiltration. For the Ap horizon cores, no influence of the underlying soil is considered. For the lower horizon cores, the overlying soil is removed. Differences between infiltration into the hypothetical profiles are used to qualitatively assess the effects of layering on infiltration. To determine if gravity effects were important for the moisture conditions measured Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 70 between September and April, the constant-flux infiltration solution was calculated with and without gravity terms. Excluding the gravity terms in the constant-flux infiltration model reduced the infiltration rate and the advance of the wetting-front. For 8 measured in the field, even in September, gravity effects cannot be neglected and the dK/d8 term in (3.1) must be retained. For runoff to be generated, R > Ka is required. Ks is assumed equal to K-2- As the actual Kg may be greater than K-2 due to macropores, the values of R that will generate runoff will be minimum values. The distributions of K-2 for the Ap and lower horizons are shown in Figs. 3.1 and 3.2. For a given R, the minimum storm duration (ta) which will generate runoff is given by the time when 8o(t) = 0_2. A return period (T) for each storm is then calculated from (3.20) where I is the rainfall intensity [mm h-1], T is the return period [yr] and t8 is the storm duration [h]. The parameters 10.8, 0.28 and 0.48 were estimated directly from the 19 77-1986 intensity-duration curves from the Abbotsford Airport. Example moisture content profiles over time are shown in Fig. 3.3. For the September values of 8n, the values of R, ta, T and x* for some rainfall events which generate runoff are shown in Table 3.3. Samples with the minimum, 50th percentile and maximum values of K-2 for the Ap and lower horizons are listed. Typically, high intensity, short duration storms with long return periods are required to generate runoff. February values of 8 (Table 3.1) suggest that 8 remains near saturation over much of the winter. For saturated conditions runoff will be generated when R > K-2 and the constant-flux infiltration model is not required to predict runoff. Whether runoff is generated at the Mahal farm for saturated conditions is dependent on the intensity of rainstorms in the region. Continuously recording rain gauge data at the Mahal site are Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM t-i r-i K_2 (mm h~1) I LJ CD I Ul ID K-2 (m s-1) 10 I Figure 3.1: The distribution of K_2 for the Ap horizon. Figure 3.2: The distribution of K-2 for the lower horizons. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM Figure 3.3: Example infiltration moisture content profiles over time for R = 20 mm Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 73 Table 3.3: Rainfall intensity, duration and return periods generating runoff for September values of 8n. Variable Sample K-2 R T X* [mm h_1] [mm h_1] [min] [days] M 7<"_2min 2A 5.5 6.6 1717 20255 1.03 13.8 118 1262 0.22 K-250 1A 16.7 20.1 114 54745 0.45 K-2 max 13A 54.0 64.8 82 3.96E5 0.47 iiT_ 2 min 4C 0.9 1.08 9967 620 2.02 2.25 513 24 0.42 4.5 34 6 0.11 9.0 7 4 0.05 K-250 12C 5.7 68.3 12 17245 0.14 142.2 <1 620 0.03 284.4 <1 155 0.01 if-2 max 17C 74.9 89.9 3200 7.09E8 47.19 available for September, 1983 to March 1984 (Wood, 1984) and are assumed to represent typical winter rainfall data at the study site. For the majority of storms I was < 5.5 mm •h-1, the minimum K-2 for the Ap horizon, and only 4 storms were recorded with I > 5.5 mm h-1. The maximum I recorded during a storm was 10 mm h_1 for a 0.5 h duration. Some storm intensities and durations generating soil loss on the plot studies (Wood, 1984) from October 1983 to March 1984 are given in Table 3.4. In September and October, runoff and erosion are low, but some soil loss was measured for storms with maximum intensities less than 2.7 mm h-1. For September values of 0n, a 3.1 mm h_1, 7.5 h duration storm will not generate runoff for any soil core; and a 4.5 mm h-1, 2 h storm will generate runoff for only 6 lower horizon cores. Runoff and erosion between November 1983 and March 1984 (Table 3.4) was measured for individual storms with maximum J as low as 2.3 mm h_1. For saturated conditions and I < 2.3 mm h_1, none of the Ap core and only 7 lower horizon cores can potentially Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 74 Table 3.4: Storm intensities and durations generating soil loss for plot studies. Date # Storms Max. / Storm Soil Loss [t ha"1] J [mm h-1] t W Ave. J [mm h_1] t Oct. 17, 1983 1 2.7 1.5 1.5 9 0.001 Oct. 21 1 4.5 2 3.1 7.5 0.002 Nov. 14-16 1 5.0 1 1.8 43 1.091 Nov. 24-25 2 3.0 2 1.4 9 8.0 3 2.9 12 0.604 Nov. 26 1 2.3 6 1.5 18 0.260 Jan. 04,1984 1 7.0 1 2.0 6 2.318 Feb. 14-20 3 3.5 1 1.2 10 1.2 6 1.2 6 2.7 6 1.3 34 0.999 Mar. 25 1 3.2 3 2.2 6 0.269 Mar. 28 1 10.0 0.5 1.6 10 0.217 generate runoff. For the storm with the maximum recorded J (10 mm h l) only 6 Ap horizon cores and 13 lower horizon cores can potentially generate runoff (Figs. 3.1 and 3.2). 3.3.3 DRAINAGE CALCULATION To estimate moisture contents between rainfall events at the Mahal site, drainage of the Ap and lower horizons are considered separately, as in section 3.3.2 for infiltration. Differences between the times required to drain the hypothetical profiles are used to qualitatively assess the effects of layering on drainage. The moisture content during drainage versus time for the Ap and lower horizon sam ples corresponding to the minimum, 50th percentile and maximum values of K_2 are shown in Figs. 3.4 and 3.5. The residual moisture content at the surface is assumed equal to the air-dry moisture content. For comparative purposes, drainage at z = 0.2 m Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 75 Figure 3.4: Soil drainage over time for the Ap horizon. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 76 Figure 3.5: Soil drainage over time for the lower horizons. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 77 is shown. The time required to drain cores 1A and 12C (typical Ap and lower horizon cores) from #_2 to September values of 8 are 5 and 0.5 days respectively. The sensitivity of (3.18) to changes in the input variables is tested by increasing the input variables 5% and recalculating td. As an example, results for core 1A are presented in Table 3.5. In the original calculation, drainage at z = 0.2 m is shown with a residual moisture content equal to air-dried and a final moisture content of 8a — 0.13. 8m is actually greater than the assumed air-dry value. The unit gradient drainage model is fairly sensitive to 5% increases in the input variables but drainage is still quite rapid. Table 3.5: Sensitivity of the unit gradient drainage model to changes in input variables for sample 1A. Variable U [days] Original 5.0 5% T m 3.1 5% T K-2 4.8 5% T z 5.2 5% T 0 2.9 5% T 8S 8.6 4% T 8m 4.4 The average time between rainfall events limits the time available for soil drainage. From the continuously recording rain gauge data at the Mahal farm (Wood, 1984) the average time between rainfall events from September until March is approximately 2 days. Values of 8 predicted after two days of drainage are typically 0.40 and 0.38 for the Ap and lower horizons respectively. These moisture contents are near April values of 8 (Table 3.1) and contradict values of 8 « #_2 measured in February. In February the field was very muddy and walking was difficult while on April 19, the field was ploughed. The drainage calculation assumes unit gradient drainage at infinite depth. A water table or Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 78 a layer of restricted drainage at depth will slow drainage and 9 would be increased. 3.4 DISCUSSION Rainfall, runoff and soil loss measurements (Wood, 1984) indicate that runoff is low in September and October but considerable runoff and soil loss are generated from November to January. Most runoff appears to occur after the soil moisture content increases in the fall. Storms with relatively low intensities generate considerable erosion. For rainfall events known to cause runoff and erosion, runoff is not predicted for most Ap horizon cores. Infiltration may be restricted at some sites by the lower horizon, especially with high antecedent moisture contents, but runoff is not predicted at many sites. Between rainfall events, the unit gradient drainage model predicts typical values of 9 of 0.40 and 0.38 in the Ap and lower horizons respectively (3.4 and 3.5). Moisture contents measured at the Mahal farm suggest limited drainage between rainfall events. If 9 predicted by the unit gradient drainage model is correct the constant-flux infiltration results indicate that runoff would be negligible. The rainfall, runoff and soil loss mea surements suggest that factors other than those measured are contributing to the runoff observed in the field. Wheel compaction, surface sealing, topography, subsurface seepage and restricted soil-air movement may contribute to runoff in the field. Wheel compaction may reduce infiltration on trafficked interrows by 30%-50% com pared with rows and non-trafficked interrows (Cassel, 1983; Lindstrom and Voorhees, 1980). An increase in surface runoff is attributed to the reduced infiltration capacity of the compacted soil and the channelling effect of the wheeling (Bender, 1987; Martin, 1979). The effects of tractor wheelings on rill erosion are evident from the first year of cultivation. In 1981-1982, when strawberries were planted up and down the slope, rills occurred mainly in the trafficked interrows. In the 1985 growing season the Mahal site Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 79 was cultivated across the slope and cauliflower was left in the field to rot over the winter. Tillage was not precisely along the contour and gradients along interrows transported water to low spots. Rills formed in between rows along the secondary slope (Fig. 3.6), and along the main slope where water collected in low spots (Fig. 3.7). In the fall of 1986, the cauliflower crop was turned under parallel to the main slope. Rill spacing corresponds to the wheel tracks (Fig. 3.8) and rill direction follows the tractor wheelings (Fig. 3.9). Figure 3.6: Rill formation in trafficked interrows along the secondary slope, 1985-1986. In the fall of 1986 a cover crop of winter rye grass was planted at the Mahal farm. Cover crops are effective in reducing erosion (Meyer, 1985; Hussein and Laflen, 1982), but the vegetation should cover at least 70% of the ground surface to give adequate protection (Elwell and Stocking, 1976). An adequate cover crop was not achieved at the Mahal site (Fig. 1.2) and surface sealing was visually evident (Fig. 3.10). High intensity rainfalls (50-70 mm h-1) are generally associated with the formation of soil crusts with Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 80 Figure 3.7: Rill formation along the main slope in low spots, 1985-1986. reduced hydraulic conductivities (Morin et al., 1981; Hoogmoed and Stroosnijder, 1984; Morin and Benyamini, 1977; Hillel and Gardner, 1969). However, Mclntyre (1958) noted crusting and reduced permeability of up to 1 order of magnitude in loam soils subjected to rainfalls of 2.6 mm h-1 in intensity. In the Abbotsford region, rainfall with intensi ties greater than 40 mm h_1 and durations longer than 30 minutes have return periods greater than 25 years (AES, 1987). However, storms with intensities of 2-10 mm h_1 occur frequently and may wash fines into interrows to form a surface seal with reduced infiltrability. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 81 Figure 3.9: Rill direction affected by tractor wheelings, 1986-1987. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 82 Figure 3.10: Surface sealing at the Mahal site. Runoff and subsurface seepage from the farm upslope of the study area may transport additional water to the site and contribute to the wet field conditions observed over winter. The ditch between the 2 farms is poorly maintained and free water was observed in sampling unit 1 (Fig. 2.1) over much of the winter. The low tension absorption procedure allows for the escape of soil-air. Restricted soil-air movement in the field may reduce infiltration by up to 55% (Suhr et al. 1984; Dixon and Linden, 1977). Field conditions usually prevent the free escape of soil-air. A restricting zone may be a layer or horizon of lower permeability or may be due to an increase in moisture content with depth (Youngs and Peck, 1964). Field values of 9 for the lower horizons appear to be less than the Ap horizon except in the fall (Table 3.1). Median values of A'_2 for the lower horizon cores are similar to the Ap horizon cores. Restricted soil-air movement is not expected to effect infiltration at the Mahal farm. Chapter 3. RUNOFF GENERATION AT THE MAHAL FARM 83 3.5 CONCLUSIONS High field moisture contents necessitate the inclusion of gravity effects during infiltration modelling. For September moisture contents the rainfall intensities necessary to generate runoff are infrequent and low in volume. For saturated moisture conditions runoff gener ation is dependent on values of R > K-2- The majority of storms measured at the Mahal farm have maximum I < 5.5 mm h-1. For rainfall intensities known to cause runoff and erosion, runoff is not predicted for most Ap horizon cores. Infiltration may be restricted at some sites by the lower horizon, especially at high antecedent moisture contents, but runoff is not predicted at many sites. The average time between rainfall events from September to March was approximately 2 days. A rapid decrease in 8 between rainfall events is predicted by the unit gradient model, but 8 measured at the Mahal farm sug gests limited drainage between rainfall events. If the values of 8 predicted by the unit gradient model are correct, negligible runoff is predicted for / measured at the site. Rainfall, runoff and soil loss measurements suggest that factors other those measured are contributing to runoff observed in the field. The results of Wood (1983, 1984) indi cate that relatively low runoff coefficients (<26%) cause extensive erosion. Compaction, surface sealing and subsurface seepage may be factors influencing runoff and moisture conditions in the field. The high moisture contents observed in the field suggest the wa ter table is perching on a layer with lower conductivity, which is consistent with Dunne runoff. However, the measured infiltrabilities suggest Hortonian runoff and the results of the thesis are not conclusive with respect the mechanism of runoff generation. CONCLUDING REMARKS This research was designed to investigate the processes by which runoff is generated on a Whatcom soil on an upland site in the Lower Fraser Valley. The objectives were to summarize water erosion measurements, to measure soil hydraulic properties and to determine the mechanism of runoff generation. Water erosion occurs over most of the field in winter. Soil loss is dominated by rill erosion and erosion rates are greatest from November to January. Runoff coefficients are relatively low (<26%), but erosion rates are considerable, ~ 35 t ha_1yr-1. For efficient erosion control and land management practices, an understanding of runoff generation is required. Soil hydraulic properties relative to the rainfall intensity determine the proportion of water which will runoff. Measurements of soil-water diffu-sivities were made using a low tension absorption technique (Clothier and White, 1981). The sorptivity tube device provides a simple method for obtaining S, A* and Ji"_2. Mea sured values of i and x* depend on txl2 as expected from the constant-concentration absorption theory. Constant-concentration infiltration theory is used to determine the soil-water diffusivity. Measured D(0) functions for the field display high variability in a and b especially for the lower horizons. The Van Genuchten 0(h) expression provides a good fit to the water retention data. D(8) functions calculated from the soil-water retention curves and If_2 following Van Genuchten (1980) are at least 1-2 orders of mag nitude greater than the measured functions. Hysteresis effects may explain 1 order of magnitude increase in D(0), but the predictions are poor without matching at D(0S). 84 Chapter 4. CONCLUDING REMARKS 85 The measured hydraulic properties are used to predict infiltration, runoff and drainage. Constant-flux infiltration theory is used to model soil moisture profiles over time for vari ous rainfall events. High field moisture contents necessitate the inclusion of gravity effects during infiltration. The rainfall, runoff and soil loss measurements at the Mahal farm indicate that rainfall intensities < 10 mm h_1 cause considerable runoff and erosion. For rainfall intensities known to cause runoff and erosion, runoff is not predicted for most Ap horizon cores. Infiltration may be restricted at some sites by the lower horizon, espe cially at high antecedent moisture contents, but runoff is not predicted at many sites. A rapid decrease in 8 between rainfall events is predicted by the unit gradient model but 8 measured at the Mahal farm suggests limited drainage between rainfall events. Rainfall, runoff and soil loss measurements suggest that factors other than those measured are contributing to the runoff observed in the field. Compaction, surface sealing and subsurface seepage may be factors influencing runoff and moisture conditions in the field. 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[58] Warrick, A.W. and D.R. Nielsen. 1980. Spatial Variability of Soil Physical Properties in the field. In D. Hillel (ed.) Applications of Soil Physics. Academic Press, Toronto. 319-355. [59] Watson, K.W. and R.J. Luxmoore. 1986. Estimating Macroporosity in a Forest Watershed by Use of a Tension Infiltrorneter. Soil Sci. Soc. Am. J. 50:5 78-582. [60] White, I. 1979. Measured and Approximate Flux-Concentration Relations for Ab sorption of Water by Soil. Soil Sci. Soc. Am. J. 43: 1074-1080. [61] White, I., D.E. Smiles and K.M. Perroux. 1979. Absorption of Water by Soil: The Constant-Flux Boundary Condition. Soil Sci. Soc. Am. J. 43: 659-664. [62] Wood, C. 1983. Soil Erosion Control with Interceptor Drains: Project Specifications and Preliminary Data, B.C. Ministry of Agriculture and Food D.A.T.E. Project #106. 2pp. [63] Wood, C. 1984. Annual Report. D.A.T.E. Project #106: Water Runoff and Soil Erosion Control Demonstration. Summary of Runoff and Erosion September, 1983 - July, 1984. B.C. Ministry of Agriculture and Food. 4pp. [64] Youngs, E.G. and A.J. Peck. 1964. Moisture Profile Development and Air Compres sion during Water Uptake by Bounded Porous Bodies: 1. Theoretical Introduction. Soil Sci. 98: 290- 294. [65] Zachmann, D.W., H.R. Gardner and P.C. DuChateau. 1980. A Mathematical Treat ment of the Initial Stages of Drying of a Soil Column. Soil Sci. Soc. Am. J. 44: 235-237. Appendix 91 Appendix A. LIST OF SYMBOLS 92 LIST OF SYMBOLS a = parameter in Van Genuchten water retention function /3 = exponent in exponential D(8) function 7 = parameter in exponential D(9) function 9 = volumetric moisture content [m3 m-3] 9m -• minimum obtainable 9 at z = 0 9n = initial volumetric moisture content 9r = residual volumetric moisture content 9S — saturated volumetric moisture content 9^1 = 0 at -2 cm of water tension 0o = 9(0, t) 9* = 9 at the wetting-front 0 = nondimensionalized volumetric moisture content O* = 0 at the wetting-front A = Boltzman similarity variable A* = A at the wetting-front p = density Pb = bulk density [kg m-3] pa = particle density [kg m-3] pw = density of water [kg m-3] a = surface tension [kg s_1] (j) = parameter in exponential D(9) function J2(2 = sum of squared residuals a = parameter in exponential D(9) function Appendix A. LIST OF SYMBOLS 93 A area of absorption soil core ave. average b D Dn f = porosity fm = mass fraction of mineral soil f0 = mass fraction of organic soil F = flux concentration function g = acceleration due to gravity h = tension H = height of absorption soil core [m] i = cumulative water inflow [m] I = rainfall intensity K — hydraulic conductivity [m s_1] Ka = saturated hydraulic conductivity K-2 = K at an average tension of -2 cm of water tension / = height of hypodermic above mesh m = exponent in Van Genuchten water retention function min = minimum max = maximum n = sample number n = exponent in Van Genuchten water retention function Appendix A. LIST OF SYMBOLS 94 q = f 111x [m s-1] Q • volumetric water outflow [m3] R = constant-flux; constant rainfall rate r2 - - Pearson's correlation coefficient rh - inside radius of hypodermic rP pore radius REV representative elementary volume S sorptivity SD standard deviation skew. - skewness t = time ts = storm duration td = drainage time if = final time t9 = maximum time for gravity effects to be negligible U initial time T = return period X = horizontal distance X* depth to the wetting-front [m] z = height below datum (ground surface) 50 50th percentile value Appendix B RAW DATA Table B.l: Ap horizon site characteristics of infiltration cores. Sample Pb / Colour Texture z [kg m-3] M 1A 1171 0.53 10YR5/4 coarse silty 0.07 2A 1186 0.53 10YR5/3 coarse silty 0.20 3A 1066 0.58 10YR5/3 fine loamy 0.15 4A 1238 0.51 2.5Y5/4 coarse silty 0.17 5A 1085 0.57 10YR5/4 fine loamy 0.40 6A 1130 0.55 10YR5/4 fine loamy 0.15 7A 1061 0.58 10YR5/3 coarse silty 0.60 8A 1092 0.57 2.5Y4/4 fine loamy 0.50 9-1A 965 0.62 10YR4/4 coarse silty 0.13 9-2A 948 0.62 10YR4/4 fine loamy 0.20 9-3A 998 0.60 10YR4/3 fine loamy 0.55 9-4A 986 0.61 10YR4/3 coarse silty 0.17 9-5A 1006 0.60 10YR5/3 coarse silty 0.20 9-6A 1024 0.59 10YR4/3 fine loamy 0.65 10A 1088 0.57 10YR4/4 fine loamy 0.35 11A 1096 0.56 2.5Y5/4 fine loamy 0.22 12A 1205 0.52 2.5Y5/4 fine loamy 0.30 13A 935 0.63 10YR4/4 coarse silty 0.40 14A 1041 0.59 2.5Y4/4 fine loamy 0.55 15A 1015 0.60 10YR5/4 fine loamy 0.15 16A 989 0.61 10YR5/4 coarse silty 0.32 17A 912 0.64 10YR5/4 coarse silty 0.55 95 Appendix B. RAW DATA 96 Table B.2: Lower horizon site characteristics of infiltration cores. Sample Pb [kg m-3] / Colour Texture 1C 1535 0.40 2.5Y7/2 fine silty 2C 1432 0.44 2.5Y7/2 fine silty 3C 1345 0.48 2.5Y6/4 coarse silty 4C 1356 0.47 10YR5/3 fine loamy 5C 1171 0.54 2.5Y6/4 fine loamy 6C 1096 0.57 10YR6/3 coarse silty 7B 1304 0.49 10YR5/4 fine loamy 8B 1121 0.56 10YR4/3 fine loamy 9-1C 1006 0.61 2.5Y5/4 fine loamy 9-2C 1254 0.51 10YR6/3 fine loamy 9-3B 1239 0.52 10YR5/3 fine loamy 9-4C 1085 0.58 10YR4/3 fine loamy 9-5C 1136 0.56 10YR5/3 fine loamy 9-6B 901 0.65 10YR5/4 fine loamy IOC 861 0.66 10YR5/4 fine loamy 11C 1489 0.42 2.5Y6/2 fine silty 12C 1247 0.51 2.5Y6/4 coarse silty 13C 1716 0.33 2.5Y6/4 coarse silty 14B 1083 0.58 2.5Y5/4 coarse loamy 15C 988 0.62 2.5Y6/4 coarse silty 16C 1734 0.33 10YR6/3 sandy 17C 965 0.62 10YR6/3 fine loamy Appendix B. RAW DATA Table B.3: Ap horizon measured variables for the low tension absorption. Sample Apr.'86 9-2 on S A* K-2 9 [m s-1/2] [m s"1/2] [m s-1] 1A 0.39 0.49 0.06 5.65E-04 1.70E-03 4.65E-06 2A 0.40 0.46 0.07 3.90E-04 1.32E-03 1.53E-06 3A 0.39 0.50 0.06 7.47E-04 2.13E-03 9.41E-06 4A 0.31 0.37 0.07 3.38E-04 1.21E-03 1.85E-06 5A 0.43 0.50 0.09 6.94E-04 1.91E-03 2.06E-06 6A 0.44 0.48 0.08 7.35E-04 2.13E-03 4.25E-06 7A 0.39 0.47 0.10 4.03E-04 1.26E-03 5.43E-06 8A 0.47 0.49 0.09 6.39E-04 1.83E-03 2.35E-06 9-1A 0.42 0.51 0.07 8.53E-04 2.00E-03 5.40E-06 9-2A 0.47 0.51 0.09 6.47E-04 1.67E-03 4.25E-06 9-3A 0.39 0.51 0.07 6.55E-04 2.02E-03 9.65E-06 9-4A 0.46 0.51 0.08 7.96E-04 2.55E-03 6.55E-06 9-5A 0.42 0.49 0.07 6.08E-04 1.76E-03 5.95E-06 9-6A 0.41 0.50 0.09 5.67E-04 1.81E-03 4.83E-06 10A 0.40 0.47 0.11 3.83E-04 1.61E-03 2.35E-06 11A 0.37 0.46 0.08 5.59E-04 1.77E-03 6.12E-06 12A 0.39 0.44 0.07 4.84E-04 1.77E-03 2.05E-06 13A 0.42 0.53 0.09 8.94E-04 2.38E-03 1.50E-05 14A 0.45 0.50 0.09 6.36E-04 2.09E-03 4.22E-06 15A 0.40 0.47 0.06 6.96E-04 1.88E-03 6.37E-06 16A 0.44 0.54 0.12 4.96E-04 1.47E-03 1.75E-06 17A 0.43 0.54 0.11 4.78E-04 1.49E-03 5.13E-06 Appendix B. RAW DATA Table B.4: Lower horizon measured variables for the low tension absorption. Sample Apr.'86 9-2 9n S A* K-2 9 [m s"1/2] [m s-1/2] [m s"1] 1C 0.38 0.42 0.09 2.53E-04 8.26E-04 1.38E-06 2C 0.34 0.46 0.13 1.55E-04 5.98E-04 3.00E-07 3C 0.36 0.46 0.12 3.10E-04 1.12E-03 4.83E-07 4C 0.39 0.44 0.13 2.12E-04 8.51E-04 2.50E-07 5C 0.39 0.48 0.12 7.58E-04 2.42E-03 4.32E-06 6C 0.39 0.49 0.10 8.23E-04 2.27E-03 9.72E-06 7B 0.41 0.44 0.12 3.50E-04 1.46E-03 7.67E-07 8B 0.43 0.44 0.17 1.89E-04 1.02E-03 4.33E-07 9-1C 0.41 0.44 0.07 8.92E-04 2.58E-03 5.77E-06 9-2C 0.40 0.42 0.02 5.73E-04 1.51E-03 1.61E-05 9-3B 0.39 0.39 0.03 3.61E-04 1.22E-03 7.67E-07 9-4C 0.44 0.46 0.05 5.37E-04 1.80E-03 2.48E-06 9-5C 0.42 0.42 0.06 1.95E-04 1.48E-03 4.83E-07 9-6B 0.46 0.48 0.05 8.53E-04 2.36E-03 5.62E-06 IOC 0.41 0.54 0.11 8.10E-04 2.93E-03 1.09E-05 11C 0.40 0.41 0.14 1.11E-04 3.14E-04 3.50E-07 12C 0.42 0.46 0.12 4.49E-04 1.50E-03 1.58E-06 13C 0.33 0.37 0.08 1.37E-04 7.86E-04 3.33E-07 14B 0.50 0.50 0.15 6.70E-04 2.20E-03 2.88E-06 15C 0.47 0.53 0.13 5.66E-04 1.57E-03 3.38E-06 16C 0.28 0.31 0.04 6.47E-04 2.79E-03 6.30E-06 17C 0.48 0.52 0.12 1.02E-03 2.81E-03 2.08E-05 Appendix B. RAW DATA 99 Table B.5: Ap horizon low tension absorption variables. Sample Dn P a b [mV1] [mV1] 1A 1.53E-08 5.85 13.6 6.77E-09 2A 1.12E-08 5.59 14.3 4.10E-09 3A 1.46E-08 6.50 14.8 6.03E-09 4A 2.91E-12 15.00 50.0 8.80E-14 5A 5.82E-10 10.12 24.7 6.31E-11 6A 2.31E-09 8.76 21.9 4.01E-10 7A 7.39E-10 8.87 24.0 6.71E-11 8A 9.01E-10 9.51 23.8 1.06E-10 9-1A 1.08E-19 34.02 77.3 4.80E-22 9-2A 1.64E-11 13.82 32.9 8.47E-13 9-3A 3.66E-08 5.12 11.6 1.62E-08 9-4A 6.83E-08 4.90 11.4 2.75E-08 9-5A 5.50E-09 7.25 17.3 1.64E-09 9-6A 2.11E-08 5.60 13.7 6.16E-09 10A 5.02E-08 3.93 10.9 1.51E-08 11A 4.20E-09 7.59 20.0 8.51E-10 12A 2.78E-08 5.14 13.9 1.05E-08 13A 3.54E-09 8.51 19.3 6.20E-10 14A 3.78E-08 5.18 12.6 1.21E-08 15A 1.18E-10 11.89 29.0 2.06E-11 16A 6.40E-09 6.61 15.7 9.69E-10 17A 1.76E-08 5.29 12.3 4.55E-09 Appendix B. RAW DATA 100 Table B.6: Lower horizon low tension absorption variables. Sample Dn P a b [mV1] [mV1] IC 1.02E-12 15.30 46.4 1.57E-14 2C 1.47E-09 6.18 18.7 1.29E-10 3C 2.92E-09 6.92 20.3 2.54E-10 4C 2.14E-09 6.61 21.3 1.34E-10 5C 2.04E-09 9.21 25.6 9.48E-11 6C 1.06E-11 14.97 38.4 2.27E-13 7B 1.65E-08 5.33 16.7 1.08E-15 8B 1.61E-08 4.30 15.9 2.29E-15 9-1C 4.71E-12 16.11 43.5 2.24E-13 11 9-2C 2.57E-14 20.53 51.3 9.21E-15 9-3B 2.76E-09 7.20 20.0 5.93E-18 9-4C 3.31E-08 4.94 12.0 1.82E-08 9-5C 1.55E-07 0.61 16.8 1.40E-07 9-6B 5.70E-09 7.92 18.4 6.04E-17 10C 1.95E-07 3.67 85.3 7.61E-08 11C 3.16E-49 100.00 370.0 9.57E-72 12C 5.28E-10 9.68 28.5 1.73E-11 13C 1.80E-08 3.19 11.0 7.47E-09 14B 1.57E-09 9.30 26.6 5.32E-21 15C 9.95E-11 11.68 29.2 2.24E-12 16C 4.37E-09 8.65 32.0 1.21E-09 17C 2.66E-08 11.88 29.7 7.53E-10 Appendix B. RAW DATA 101 Table B.7: Ap horizon water retention variables. Sample 0s Or a n EC2 Pb [kg m3] 1A 0.47 0.00 3.45E-03 1.303 7.39E-04 1092 2A 0.47 0.00 2.45E-03 1.313 5.94E-04 1157 3A 0.51 0.03 2.69E-03 1.352 7.00E-04 1092 4A 0.47 0.00 1.96E-03 1.299 1.84E-04 1279 5A 0.51 0.10 2.15E-03 1.585 3.25E-04 976 6A 0.52 0.09 3.31E-03 1.482 9.84E-04 1100 7A 0.48 0.03 2.88E-03 1.364 3.32E-04 1048 8A 0.51 0.02 4.12E-03 1.315 2.61E-04 1007 9-1A 0.52 0.08 3.79E-03 1.413 4.39E-04 840 9-2A 0.55 0.00 2.27E-03 1.268 1.22E-03 971 9-3A 0.54 0.00 2.94E-03 1.303 4.18E-04 991 9-4A 0.56 0.04 3.51E-03 1.399 3.64E-04 919 9-5A 0.54 0.00 3.38E-03 1.288 2.10E-04 1013 9-6A 0.54 0.00 4.62E-03 1.251 4.76E-04 977 10A 0.56 0.10 2.97E-03 1.505 9.57E-05 1112 11A 0.49 0.08 3.39E-03 1.411 9.99E-04 1095 12A 0.48 0.03 3.29E-03 1.352 1.04E-03 1174 13A 0.55 0.12 3.45E-03 1.451 1.29E-03 858 14A 0.56 0.03 2.99E-03 1.342 2.46E-04 1011 15A 0.51 0.08 3.43E-03 1.432 4.79E-04 942 16A 0.63 0.01 2.78E-03 1.330 1.59E-03 1020 17A 0.54 0.06 2.43E-03 1.473 1.22E-03 837 Appendix B. RAW DATA 102 Table B.8: Lower horizon water retention variables. Sample e8 0r a n EC2 Pb [kg m3] 1C 0.61 0.00 2.02E-03 1.207 1.48E-03 1277 2C 0.46 0.00 5.09E-04 1.273 7.92E-04 1543 3C 0.59 0.04 4.43E-03 1.224 3.82E-04 1003 4C 0.48 0.00 9.82E-04 1.228 6.43E-04 1443 5C 0.53 0.00 1.02E-02 1.201 3.16E-04 1139 6C 0.51 0.00 2.71E-03 1.248 1.51E-03 1377 7B 0.52 0.00 2.44E-03 1.255 5.52E-04 1236 8B 0.49 0.00 8.72E-04 1.303 6.01E-04 1280 9-1C 0.56 0.11 6.51E-03 1.356 4.69E-04 1107 9-2C 0.58 0.00 2.35E-03 1.255 2.07E-04 1125 9-3B 0.61 0.10 2.80E-03 1.319 6.11E-04 946 9-4C 0.57 0.00 1.60E-03 1.242 2.00E-03 995 9-5C 0.52 0.00 2.17E-03 1.221 2.13E-04 1279 9-6B 0.65 0.21 4.59E-03 1.578 1.71E-03 873 10C 0.52 0.16 2.68E-03 1.646 3.80E-04 1076 11C 0.41 0.00 2.59E-04 1.295 4.03E-04 1510 12C 0.42 0.00 4.18E-04 1.450 9.52E-04 1570 13C 0.38 0.00 1.18E-03 1.398 4.31E-04 1654 14B 0.52 0.00 3.15E-03 1.307 1.73E-03 1124 15C 0.57 0.00 1.68E-03 1.342 9.44E-04 1218 16C 0.53 0.00 3.61E-03 1.297 8.88E-04 1273 17C 0.46 0.00 4.48E-04 1.524 1.33E-03 1303 Appendix C CONSTANT-CONCENTRATION ABSORPTION PROGRAM C DIMENSION AND DECLARE THE VARIABLES IMPLICIT REAL*8 (A-H,0-Z) DIMENSION T(20),W(20),CW(20),XWF(20),TG(20),X(20,20) EXTERNAL FN1,FN2,FN4 LOGICAL LZ COMMON BETA,ALPHA C INPUT PARAMETERS C (A) GENERAL XWFMIN=1.0D-3 XWFMAX=0.30D0 THETAS=0.44D0 THETAN=0.07D0 THD SN=THETAS-THETAN M0DE=1 C (B) MODE 1 - THE SORPTIVITY AND LAMBDA OF THE WETTING C FRONT ARE KNOWN IF(M0DE.EQ.2) GO TO 1 S=6.49386D-4 TLAMWF=2.14424D-3 WRITE(1,96) S,TLAMWF 103 Appendix C. CONSTANT-CONCENTRATION ABSORPTION PROGRAM 96 FORMAT(' S, TLAMWF: '2G15.4) GO TO 2 C (C) MODE 2 - THE DIFFUSIVITY FUNCTION IS KNOWN 1 DNM=9.2545D-7 BETAM=7.091D0 THNM=0.07 THSM=0.44 THDSNM=THSM=THNM B=BETAM/THDSNM A=DNM/DEXP(B*THNM) DN=A*DEXP(B*THETAN) BETA=B*THDSN GO TO 3 C CALCULATE ALPHA, BETA AND GAMMA AND THEN THE C DIFFUSIVITY FOR MODE 1 2 ALPHA=S/(TLAMWF*THDSN) BETA=0.DO BETAMX=100.D0 WRITE(1,97) ALPHA,BETA,BETAMX 97 FORMAT(' ALPHA, BETA, BETAMX: '.3G15.4) ERR=l.D-4 CALL ZER02(BETA,BETAMX,FN4,ERR,LZ) IF(.NOT.LZ) WRITE(1,4) 4 FORMAT(' ZERO2 CANNOT FIND BETA') IF(.NOT.LZ) STOP Appendix C. CONSTANT-CONCENTRATION ABSORPTION PROGRAM GAMMA=1. DO/ (2. DO*DCADRE (FN2,1. D-12,1. DO, 0. DO., 1. D-4,ERR) ) DN=GAMM*S**2/THDSN**2 GO TO 5 C CALCULATE THE SORPTIVITY, LAMBDA AT THE WETTING-FRONT, C ALPHA AND GAMMA FOR MODE 2 3 GAMMA=1.DO/(2.DO*DCADRE(FN2,1.D-12,1.DO,0.DO,1.D-4,ERR)) S=DSQRT(DN*THDSN**2/GAMMA) ALPHA=1.DO/(S.D0*GAMMA) ALPHA=ALPHA/DCADRE(FN1,1.D-2,1.DO,0.DO,1.D-4,ERR) TLAMWF=S/(ALPHA*THDSN) C CALCULATE THE SURFACE FLUX, CUMULATIVE INFLOW, C POSITION OF THE WETTING-FRONT, AND THE WATER C CONTENT PROFILES AT SELECTED TIMES 5 TMIN=(XWFMIN/TLAMWF)**2 TMAX=(XWFMAX/TLAMWF)**2 DT=(TMAX/TMIN).DO/19.DO) DO 6 NT=1,20 T(NT)=TMIN*DT**(NT-1) SQT=DSQRT(T(NT)) W(NT)=S/(2.D0*SQT) WC(NT)=S*SQT XWF(NT)=TLAMWF*SQT DO 6 NX=1,20 THBG=1.DO-(NX-1)/20.DO TH(NX)=THETAN+THBG *THD SN Appendix C. CONSTANT-CONCENTRATION ABSORPTION PROGRAM 106 DUM=2.DO*SN*THDSN*SQT/S 6 X(NT,NX)=DUM*DCADRE(FN1,THBG,1.DO,0.DO,1.D-4,ERR) C WRITE OUT RESULTS WRITE(1 20) 20 FORMAT( 12-2A ') WRITE(1 ,21) THNM,THSM,DNM,BET AM 21 FORMAT( THNMEAS, THSMEAS, DNMEAS, BETAMEAS: WRITE(1 ,22) A,B 22 FORMAT( A B: ',2G13.5) WRITE(1 ,7) THETAN,THETAS,DN,BETA 7 FORMAT( THETAN, THETAS, DN, BETA: ',4G13.5) WRITE(1 ,8) S,TLAMWF,ALPHA,GAMMA 8 FORMAT( ' S, TLAMWF, ALPHA, GAMMA: '.4G13.5) DO 9 N0= =1,20 WRITE(1 ,10) T(NT),W(NT),CW(NT),XWF(NT) 10 FORMAT( ' T, W, CW, XWF: ',4G13.5) WRITE(1 ,11) (X(NT,NX),NX=1,20) 11 FORMAT( ' X:',10G11.3/4X,10G11.3) 9 WRITE(1 ,12) (TH(NX),NX=1,20) 12 FORMAT( ' TH:',10G11.3/4X,10G11.3) STOP END C FUNCTION SUBROUTINES FUNCTION FN1(X) IMPLICIT REAL*8 (A-H.O-Z) Appendix C. CONSTANT-CONCENTRATION ABSORPTION PROGRAM COMMON BETA,ALPHA FN1=DEXP(BETA*X)/FLXCNC(X) RETURN END FUNCTION FN2 IMPLICIT REAL*8 (A-H,0-Z) COMMON BETA,ALPHA FN2=X*DEXP(BETA*X)/FLXCNC(X) RETURN END FUNCTION FN4(X) IMPLICIT REAL*8 (A-H.O-Z) COMMON BETA,ALPHA EXTERNAL FN1,FN2 BETA=X FN4=DCADRE(FN2,1.D-12,1.DO,0.DO,1.D-4,ERR) FN4=FN4/DCADRE(FN1,1.D-2,1.DO,0.DO,1.D-4,ERR) FN4=ALPHA-FN4 RETURN END FUNCTION FLXCNC(X) IMPLICIT REAL*8 (A-H,0-Z) COMMON BETA,ALPHA PI=3.1415926535897932D0 DUMl=DSIN(PI/2.DO*X**(PI/4.DO)) endix C. CONSTANT-CONCENTRATION ABSORPTION PROGRAM DUM2=X FLXCNC=DUM1*(8.DO-BETA)/8.D0+DUM2*BETA/8.DO IF(BETA.GT.8.DO) FLXCNC=DUM2 RETURN END Appendix D VAN GENUCHTEN WATER RETENTION PROGRAM C 3 PARAMETER (THETAS, ALPHA, N) EQUATION WITH NO CONSTRAINTS IMPLICIT REAL*8(A-H,0-Z) DIMENSION P(3),V(252),IV(63) EXTERNAL CALCR COMMON X(10),Y(10),RESID WRITE(6,40) 40 FORMAT (» CORE 7C) C SET INITIAL VALUES; READ IN AND LIST DATA RESID=O.DO N=10 M=3 P(1)=0.003D0 P(2)=1.2D0 P(3)=0.55D0 WRITE(6,60) P(l),P(2),P(3) 60 FORMAT ('P(l)=',G10.4,'P(2)=>,G10.4,'P(3)=',G10.4) DELTAR=0.002D0 WRITE (6,80) N,M 80 FORMAT (' N=',I3,' M=>,13) READ(5,120) (X(I),Y(I),I=,N) 109 Appendix D. VAN GENUCHTEN WATER RETENTION PROGRAM 120 FORMAT(2D15.9) WRITE(6,125) 125 FORMAT('TENSION THETA') WRITE(6,130) (X(I),Y(I),I=1,N) 130 FORMAT (2(D15.9,3X)) C LEAST SQUARED CURVE FITTING 5 IV(1)=0.D0 CALL NL2SN0 (N,M,P,CALCR,IV,V,IPARM,RPARM,FPARM) C WRITE OUT THE RESULTS WRITE(6,15) RESID 150 FORMAT(' THETAR =',G10.4) WRITE(6,140) IV(1) 140 FORMAT(' RETURN C0DE=',I2) WRITE(6,160) (P(0),I=1,M),V(10) 160 FORMAT(' SOLUTION:', 1P3G16.8/ 1 ' SUM OF SQUARES/2=', 1PG16.8) C LOOP TO COVER POSSIBLE RANGE IN RESIDUAL THETA RESID=RESID+DELTAR IF(RESID.GT.O.2OODO)G0 TO 190 GO TO 5 190 STOP END C SUBROUTINE SUBROUTINE CALCR(N,M,P,NF,R,IPARM,RPARM,FRARM) IMPLICIT REAL*8(A-H,0-Z) Appendix D. VAN GENUCHTEN WATER RETENTION PROGRAM DIMENSION P(M),R(N) COMMON X(10),Y(10).RESID C LIMITS ON VARIABLES IF(P(2).LE.l.DO) GO TO 180 IF(P(1).LT.O.CO) GO TO 180 C RESIDUALS IN R DO 100 1=1,N DUM=P(1)*X(I) DEN=1.D0-1.D0/P(2) TM=1.D0-1.D0/P(2) TNUM=P(3)-RESID R(I)=(RESID+TNUM/DEN**TM)-Y(I) 100 CONTINUE RETURN 180 NF=O.DO RETURN END Appendix E CONSTANT-FLUX INFILTRATION PROGRAM C DIMENSION AND DECLARE VARIABLES IMPLICIT REAL*8(A-H,0-Z) DIMENSION T(20),W(20),C2(20),XWF(20),TH(20,20),X(20,20) EXTERNAL FN1,FN2,FN3 COMMON DN,BETA,THDSN,THETAN,THO,TKS,XM,R,THDSR,WRTHR C INPUT PARAMTERS TKS=1.3833D-6 XM-1.DO-1.DO/1.2074D0 WRTHR=O.DO WRTHS=0.42D0 THDSR=WRTHS-WRTHR THETAS=0.42DO THETAN=0.37D0 THD S N=THETA S-THETAN THSM=0.42D0 THNM=0.09D0 THDSNM-THSM-THNM DNM=1.02079D-12 BETAM=15.302D0 A=BETAM/THDSNM 112 Appendix E. CONSTANT-FLUX INFILTRATION PROGRAM B=DNM/DEXP(B*THNM) DN=B*DEXP(A*THETAN) BETA=A*THDSN R=l.2D0*TKS C CALCULATE THE SURFACE FLUX, CUMULATIVE INFLOW, C POSITION OF THE WETTING-FRONT, AND THE WATER C CONTENT PROFILES AT SELECTED TIMES DUM1=THETAN+1.D-12 DUM2=THETAN+0.01D0*THDSN DO 6 NT=1,20 THO=THETAN+NT*THDSN/20.DO T(NT)=DCADRE(FN2,DUM1,THO,0.DO,1.D-4,ERR)/(R-FN3(THETAN)) W(NT)=R XW(NT)=R*T(NT) XWF(NT)=DCADRE(FN1,DUM2,THO,0.DO,1.D-4,ERR) DO 6 NX=1,20 TH(NT,NX)=THO-(NX-1)*(THO-THETAN)/20.DO 6 X(NT,NX)=DCADRE(FN1,TH(NT,NX),THO,0.DO,1.D-4,ERR) C WRITE OUT RESULTS WRITE(1,3) 20 FORMAT(' IC) WRITE(1,21) THNM,THSM,DNM,BETAM 21 FORMAT(' THNMEAS, THSMEAS, DNMEAS, BETAMEAS: \4G13.5) WRITE(1,22) A,B 22 FORMAT(' A B: > ,2G13.5) Appendix E. CONSTANT-FLUX INFILTRATION PROGRAM 114 WRITE(1,7) THETAN,THETAS,DN,BETA 7 FORMAT(' THETAN, THETAS, DN, BETA: \4G13.5) WRITE(1,23) TKS,XM,WRTHR,WRTHS 23 FORMATC TKS, XM, WRTHR, WRTHS: \4G13.5) DO 9 NT=1,20 WRITE(1,10) T(NT),W(NT),CS(NT),XWF(NT) 10 FORMAT( »T, W, CW, XWF: '.4G13.5) WRITE(1,11) (X,(NT,NX),NX=1,20) 11 FORMAT(' X: ',10G11.3/4X,10G11.3) 9 WRITE(1,12) (TH(NT,NX),NX=1,20) 12 FORMAT(' TH: », 10G11.3/3X.10G11.3) STOP END C FUNCTION SUBROUTINES FUNCTION FN1(X) IMPLICIT REAL*8 (A-H,0-Z) COMMON DN,BETA,THDSN,THETAN,THO,TKS,XM,R,THDSR,WRTHR DUM=FN3(THETAN) FN1=DN*DEXP(BETA*(X-THETAN)/THDSN)/(FLXCNC(X)*(R-DUM)- FN3(X)+DUM) RETURN END FUNCTION FN2(X) IMPLICIT REAL*8 (A-H,0-Z) COMMON DN,BETA,THDSN,THETAN,THO,TKS,XM,R,THDSR,WRTHR DUM=FN3(THETAN) Appendix E. CONSTANT-FLUX INFILTRATION PROGRAM 115 DUHA=BETA*(X-THETAN)/THDSN FN2=(X-THETAN)*DN*DEXP(DUMA)/(FLXCNC(X)*(R-DUM)-FN3(X)+DUM) RETURN END FUNCTION FN3(X) IMPLICIT REAL*8 (A-H,0-Z) COMMON DN,BETA,THDSN,THETAN,THO,TKS,XM,R,THDSR,WRTHR DUM=((X-WRTHR)/THDSR)**0.5DO FN3=TKS*(DUM)*(1-(1-((X-WRTHR)/THDSR)**(1/XM))**XM)**2) RETURN END FUNCTION FLXCNC(X) IMPLICIT REAL*8 (A-H.O-Z) COMMON DN,BETA,THDSN,THETAN,THO,TKS,XM,R,THDSR,WRTHR PT=3.1415926535897932D0 DUM=(X-THETAN)/(THO-THETAN) DUM1=DUM**(2.DO-4.DO/PI) DUM2=DUM FLXCNC=DUM1*(8.DO-BETA)/8.D0+DUM2*BETA/8.DO IF(BETA.GT.8.DO) FLXCNC=DUM2 RETURN END Appendix F SISSON DRAINAGE PROGRAM C DIMENSION AND DECLARE THE VARIABLE IMPLICIT REAL*8 (A-H.O-Z) DIMENSION T(20),TH(20) C INPUT PARAMETERS XM=0.3113D0 TKS-1.5004E-6 THETAM=0.19D0 THETAS=0.53DO XMAX=0.30D0 THETAN=0.40D0 C CALCULATE WATER CONTENT PROFILES AT SELECTED TIMES DO 6 NTH=1,19 THBD=1.D0-NTH/20.D0 THD S N=THETA S-THETAM TH(NTH)=THETAN+THBD*(THETAS-THETAN) DUMB=(TH(NTH)-THETAM)/THDSN DUMC=DUMB**(1.DO/XM) DUMD=l.DO-DUMC DUME=(1.DO/XM)-1.DO DUMF=XM-l.DO 116 Appendix F. SISSON DRAINAGE PROGRAM 117 DUHG=TKS/THDSN DUMH=1.DO-(DUMD**XM) DUMI=DUMD**DUMF DUM J=DUMB * * DUME DUMK=DUMH**2.D0 DUML=DUMH*DUMI*DUMJ DUMM=1.D0/(1.DO*DUMB**0.5) 6 T(NTH)=XMA/(DUMG*((2.DO*DUMB**0.5D0*DUML)+(DUMM*DUMK))) C WRITE OUT THE RESULTS WRITE(1,20) 20 FORMAT(' SISSON DRAINAGE MODEL ') WRITE(1,21) THETAM 21 FORMATC CORE 13A THETAM=' ,G13.5) WRITE(1,23) XMAX 23 FORMAT(' XMAX [m]=',G13.5) DO 9 NTH=1,19 WRITE(1,24) TH(NTH) 24 FORMAT(' TH:',G15.5) 9 WRITE(1,25) T(NTH) 25 FORMAT( ' T:\G11.5) STOP END 

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