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Influence of subsurface drainage and subirrigation practices on soil drainable porosity Gao, Yuncai 1990

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I N F L U E N C E OF S U B S U R F A C E D R A I N A G E A N D  SUBIRRIGATION  P R A C T I C E S O N SOIL D R A I N A B L E P O R O S I T Y By Yuncai Gao B . Sc., Hebei Agricultural University,  1982  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE  in THE FACULTY OF GRADUATE STUDIES THE DEPARTMENT OF BIO—RESOURCE ENGINEERING  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA A p r i l 1990 © Yuncai Gao, 1990  In  presenting this  degree at the  thesis  in  University of  partial  fulfilment  of  the  British Columbia, I agree that the  freely available for reference and study. I further copying  of  department  this thesis for or  by  his  or  requirements  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department  of  6u.P- RgLSottyCg.. c^nSiyJl^yu  The University of British Columbia Vancouver, Canada  DE-6 (2/88)  Abstract  Subsurface drainage affects water table fluctuation patterns by removing the excess water from the soil. The annual average water table depths of the drained ( A ) and undrained (D) regimes are 0.83 and 0.48 m from the soil surface respectively. Subirrigation continuously provides water to the upper soil by capillary rise. The annual water table depths of the subirrigated regimes (B and C ) are 0.61 and 0.70 m respectively. It is found that there is a significant curvilinear correlationship between the drainage flow rate and the water table height above the drain. Soil drainable porosity of different regimes was investigated by using the soil water balance approach.  The average drainable porosity of regimes A and B are 6.0% and  4.9% from water table rise, and 5.9% and 4.5% from water table drawdown , respectively. Subirrigation adversely affects the soil drainable porosity. Soil drainable porosity is often considered as a constant. However, the results of this study indicate that it varies with the wa/ter table height above the drain. In the case of water table drawdown, this dependence can be successfully expressed by a negative exponential equation. In the case of water table rise, the correlation is not as significant, but there is still a trend that the drainable porosity decreases with the increase of the water table height above the drain. Evapotranspiration ( E T ) is often neglected in soil water balance models for the drainable porosity determination. This may result in some errors. In this study, the potential E T rate was computed by the Penman and Hargreaves methods.  These two methods  give very similar E T values for the studied area. It is assumed that actual E T equals to the potential E T rate when the ground water table is close to the soil surface.  n  Table of Contents  Abstract  ii  Table of Contents  iii  List of Tables  vi  List of Figures  vii  Acknowledgements  ix  1  Introduction  1  2  Literature Review  5  2.1  Subsurface Drainage  5  2.1.1  Subsurface Drainage and Farm Operations  6  2.1.2  Subsurface Drainage Improves Soil Physical Properties  7  2.1.3  Soil Water Management and Crop Production  8  2.2  Drainable Porosity in Subsurface Drainage Design  10  2.3  Evapotranspiration in Soil Water Balance  15  2.3.1  Definitions  15  2.3.2  Factors Affecting Evapotranspiration  16  2.3.3  Determination of Evapotranspiration  20  2.4 3  Subirrigation  25  Experimental Layout  28  iii  4  3.1  Background  28  3.2  Experimental Layout  29  3.3  Data Collections and Analyses  33  Results and Discussion  35  4.1  Weather D a t a  35  4.2  Water Table Fluctuation  35  4.3  Drainage Flow Rate and Water Table Height  44  4.4  Solar Radiation  45  4.4.1  Extraterrestrial Radiation  45  4.4.2  Relationship between Extraterrestrial and Global Solar Radiation  47  4.4.3  Hourly Distribution of the Global Solar Radiation  50  4.4.4  Net Radiation  50  4.5  Computation and Verification of Potential Evapotranspiration  54  4.6  Coefficient between Potential E T and P a n Evaporation  57  4.7  Drainable Porosity  58  4.7.1  Soil Drainable Porosity of Different Regimes  58  4.7.2  Drainable Porosity and Water Table Height above the Drain  4.8  5  Error Sources  . . .  60 63  4.8.1  Precipitation  .  64  4.8.2  Evapotranspiration  64  4.8.3  Surface runoff and deep seepage  65  4.8.4  Water table height  65  4.8.5  Drainage flow rate  66  Conclusions and Suggestions  67  5.1  67  Conclusions iv  5.2  Suggestions  69  Bibliography  70  Appendices  76  A  C o m p u t a t i o n of the parameters required by Penman equation  76  A.l  Slope of the Saturation Vapor Pressure-temperature Curve  76  A.2  Psychrometric Constant  76  A.3  Vapor Pressure  77  A.4  W i n d Speed and W i n d Speed Coefficients  78  B  C  D  A . 5 Net Radiation  79  C o m p u t a t i o n of Solar Radiation  83  B. l  Extraterrestrial Radiation  83  B. 2  Global Solar and Net Radiations  84  C o m p u t i n g of Potential Evapotranspiration  86  Cl  Computing of Potential Evapotranspiration  86  C. 2  Computed Potential Evapotranspiration Values  87  C o m p u t a t i o n and Statistical Analyses of Soil Drainable Porosity  96  D. l  Computation of Soil Drainable Porosity  96  D.2  Statistical Analysis  101  v  List of Tables  4.1  Water table depths during different seasons  42  4.2  Annual and seasonal potential E T in m m  55  4.3  Evaporation coefficients  57  4.4  Soil drainable porosity, %  59  A.5  W i n d speed coefficients  79  C.6  Potential E T computed by using Penman method(1985-1988)  88  C . 7 Potential E T computed by using Hargreaves method( 1985-1988)  92  D . 8 T h e computed soil drainable porosity  97  vi  List of Figures  2.1  Crop yield-water table depth curve for two different soils i n Netherland (after Smedema and Rycroff, 1983)  2.2  9  Soil water content curves plotted above water table to evaluate drainable porosity (after Bouwer and Jackson, 1974)  2.3  12  Energy balance components and related parameters (after van Bavel and Ehrler, 1968)  2.4  18  Schematic representation of the daytime radiation balance (after Gates, 1962)  18  3.5  Annual water balance of L F V (after Chieng, 1987)  29  3.6  Experimental field layout (after Chieng, 1987)  31  4.7  Monthly mean precipitation of Vancouver  36  4.8  Monthly mean wind speed of Vancouver  37  4.9  Monthly mean temperatures of Vancouver  38  4.10 Water table fluctuation for regimes A , B , C , and D (1985) 4.11 Water table fluctuation for regimes A , B , C . and D (1986)  39 .  39  4.12 Water table fluctuation for regimes A , B , C , and D (1987)  40  4.13 Water table fluctuation for regimes A , B , C , and D (1988)  40  4.14 Relationship between water table height above the drain and the drainage flow rate  44  4.15 Annual distribution of extraterrestrial radiation i n Vancouver  vii  46  4.16 Relationship between extraterrestrial and global solar radiation based on the Penman method (1985-1987)  48  4.17 Comparison of the global solar radiation computed by different methods.  49  4.18 A n n u a l distribution of the global solar radiation of Vancouver  51  4.19 Hourly distribution of the global solar radiation of Vancouver during different seasons  52  4.20 Distribution of the net radiation of Vancouver  53  4.21 Water table height and drainable porosity based on water table drawdown.  61  4.22 Water table height and drainable porosity based on water table rise. . . .  62  vm  Acknowledgements  I wish to extend my sincere appreciation to D r . S. T . Chieng for continued support, guidance and valuable criticisms, and to D r . J . Keng for consultation and encouragement. I would also like to thank Dr. T . A . Black and D r . P. Richard for reviewing this study and sitting i n the committee. I wish to thank D r . J . de Vries, D r . M . Novak for their consultation and valuable suggestions. In addition, my sincere thanks go to the graduate students i n the department  and  my friends, especially M r . G . W u , M s . M . Q i and M r . J . Y u , who provided much encouragement and assistance throughout this study. Special thanks go to D . Bartlett for editing this thesis. Last but not least, I would like to extend my deep gratitude to my family. W i t h o u t their love and support, this thesis would never be finished. This study was financially supported by the Natural Sciences and Engineering Research Council of Canada and the British Columbia Agricultural Science Coordinating Committee.  ix  Chapter 1  INTRODUCTION  Subsurface drainage is the removal of water from the crop root zone by lowering the water table. It has been a widely recognized agricultural water management method in both humid and arid regions. W i t h the increasing world population and demand for food and fiber but the decreasing availability of arable land, subsurface drainage will become more and more important for the improvement of agricultural land and sustainable agriculture. The  main purpose of subsurface drainage is to remove the excess water and salts  from the root zone, and to improve the growth conditions for the crops. In humid areas, precipitation is often in excess of evapotranspiration ( E T ) . If the natural drainage of a soil is not adequate, the water table will rise, resulting i n a series of problems such as poor soil workability, impaired aeration, deficient nutrient supply, etc. In semi-arid and  arid regions, soil salinity is a common problem.  To keep the soil salinity from  reaching damaging concentration, more water than crops need is often applied to leach the soluble salts from the root zone (Bernstein, 1974). If the applied excess water can not be removed by natural drainage, artificial drainage system is required to achieve the leaching requirement and salt balance. The most important design parameters of a subsurface drainage system are the drain depth and drain spacing. The drain depth mainly depends on the availability of the excavating equipment, the soil profile, and the discharge outlet. Once the drain depth is determined, the drain spacing will be the only design parameter which needs to be determined based on the hydrological conditions, soil properties and crop requirements.  1  Introduction  2  M a n y theories have been developed for the computation of the drain spacing. B a sically, there are two categories:  steady state and non-steady state.  In steady state  theories, it is assumed that the replenishment rate of the water table is equal to the drainage flow rate (Luthin, 1978). Water table height remains constant during drainage. In non-steady state theories, the water table is considered to vary with time. A t present, steady state theories are commonly used i n the agricultural drainage design due to their simplicity and practicability i n most situations.  However, i n cases where the soil wa-  ter table fluctuations must be considered, more complex and relatively more realistic non-steady state theories should be used. In both steady and non-steady state theories, information of climatological conditions, soil properties and crop requirements are necessary for the calculation of drain spacing (Chieng, 1983). This information includes soil drainable porosity, drainage flow rate (drainage coefficient), E T , precipitation, etc. Drainable porosity is one of the most important soil properties used i n non-steady state theory. B y definition, drainable porosity is the volume of water that can be drained from a unit volume of saturated  soil when the water potential decreases by a specific  amount (Luthin, 1978). It is necessary i n most equations that predict water table drawdown (Taylor, 1960). For example, Tapp and M o o d y (1964) developed their equation for the computation of the drain spacing based on the soil drainable porosity, hydraulic conductivity etc. In some studies drainable porosity is considered as a constant (Childs, 1960; van Schilfgaarde, 1965). However, this is not always the case. Investigations have found that soil draina,ble porosity is a function of the water table depth from the soil surface (Taylor, 1960; Bhattacharya and Broughton, 1979), and also depends on the rate and direction of the water table fluctuation ( W u , 1988). Drainable porosity is traditionally determined by the changes i n soil water content  Introduction  3  as the water table is lowered (Taylor, 1960).  However, this procedure is very time-  consuming. More often, drainable porosity is evaluated i n the laboratory by measuring the volume of water released when the water table is lowered by a certain amount. This method has given reasonable evaluation of the drainable porosity i n laboratory i f the water table falls slowly enough to allow the drainage of the pores to "keep up" (Talsma and Haskew, 1959). However, much more work needs to be done using field data. In the soil water balance models for the determination of soil drainable porosity, E T is a very important component. This is particularly true during the summer period when both evaporation and transpiration rates are high. However, E T is often ignored due to the difficulties i n measurements.  T h e drainable porosity thus estimated is considered to  be quite misleading. To accurately determine the soil drainable porosity, it is necessary to include E T i n the soil water balance. Evapotranspiration can be measured by lysimeters, growth chambers, etc. If E T is not directly measured, it can be computed by using a number of methods such as energy balance and aerodynamic methods, the combination of the two, or the empirical formulae, depending on the availability of the climatological data (Svehlik, 1987). A s each method was originally developed under specific climatological conditions, some modifications are needed before they can be applied to the local conditions. Even i n humid regions, supplemental irrigation is often necessary due to the uneven distribution of the precipitation. Subirrigation is one of the irrigation methods that has the advantages of labor and energy saving. In many cases, subirrigation can be combined with the subsurface drainage system, resulting i n good use of the land. T h e disadvantage of this irrigation method is its potential adverse effects on the physical properties of the soil such as soil drainable porosity. Based on the statements above, the objectives of this study can be summarized as follows.  Introduction  4  1. To investigate the water table fluctuation patterns of a flat agricultural land i n the Lower Fraser Valley ( L F V ) of British Columbia under different water management regimes. 2. To compute the E T rate i n the L F V by using several commonly used methods. 3. To establish the relationship between pan evaporation and potential E T for L F V condition. 4. To establish the relationship between the ground water table height and the soil drainable porosity. 5. To examine the effects of subirrigation on soil drainable porosity.  Chapter 2  LITERATURE REVIEW  Extensive research has been done on subsurface drainage, subirrigation and evapotranspiration ( E T ) all over the world.  This chapter provides an overview of the previous  studies on the effects of subsurface drainage and subirrigation on soil properties, the determination of E T , the computation of soil drainable porosity and some other relevant subjects.  2.1  Subsurface Drainage  In humid areas with poor natural drainage, artificial land drainage is often required for increased or sustained crop production. Subsurface drainage is one of the most commonly used drainage methods to lower the water table, remove the excess soil water and improve the growth conditions for the crop. The main purpose of subsurface drainage in arid or semi-arid areas is for the soil salinity control. Subsurface drainage is the removal of water from the root zone by lowering the ground water table. It is accomplished by a system of open ditches and buried drains into which water seeps by gravity (Donnan and Schwab, 1974; Raadsma, 1974; L u t h i n , 1978). The drains can be arranged i n parallel, random or herringbone patterns, depending on the topographic and soil features of the field (van der Gulik et al, 1986).  5  Literature Review  2.1.1  6  Subsurface Drainage and F a r m Operations  In humid areas, seed bed preparation, planting, fertilizing, harvesting, etc.  are often  delayed due to a high water table i n the soil. Subsurface drainage can lower the water table and allow timeliness i n conduction of these farm operations. Timeliness means that various farm operations can be accomplished at the time they are required without any adverse effects on the soil conditions. Timely conduction of farm operations improves the efficiency of the production system (Reeve and Fausey, 1974). Delays in performing operations, for whatever reason, increase the costs or reduce the production potential of the system, thereby increasing the economic risks. In practice, whether or not the field can be cultivated is largely dependent on the trafficability of the soil. Soil trafficability is the ability of a soil to provide traction and allow overland passages of vehicles without soil structure deterioration (Hillel, 1980a). It largely depends on the bearing capacity and the consistency of the soil, both of which are affected by the soil moisture conditions. Whether there is damage to the productive capacity of the soil by decreased permeability to air and water, altered thermal relations, and resistance to root penetration are major factors i n soil trafficability (Reeve and Fausey, 1974). A soil is workable when its cultivation produces good tilth (de Vries, 1983). M e d i u m and fine textured soils are workable at water contents below the plastic limit.  Plastic  hrnit is the water content at which soil becomes plastic. T h e number of days that the soil can be worked on without soil compaction is called opportunity days. If the natural drainage of a soil is poor, most of the excess water must be removed by E T . During early spring and late fall, the soil drying period may be excessively long because of the low level of incoming solar radiation and low evaporative demand of the atmosphere.  A t this time, crop transpiration is also very low.  Subsurface  drainage  removes the excess water from the soil more rapidly than the natural process of E T .  Literature Review  7  Therefore, the soil can be operated on much sooner without the deterioration of the structure.  Chieng et al (1987) found that 64, 86 and 60 more opportunity days were  obtained between 1 March and 31 M a y in 1983, 1984 and 1985, respectively, on drained area compared with the undrained area. In temperate regions like the Lower Fraser Valley ( L F V ) i n B . C , the extension of the growing season is very important for agricultural production.  2.1.2  Subsurface Drainage Improves Soil Physical Properties  Subsurface drainage lowers the soil water table, changes the soil water content, therefore it alters the characteristics of the soil. M u c h research has shown that many of the soil physical properties are greatly affected by subsurface drainage (Hundal et al, 1976). At high water content, soil particles may swell, particularly when the soil has a high clay content. Soil aggregates become unstable. Subsurface drainage lowers the soil water content and increases the stability of the aggregates, thereby improving the soil structure (Hillel, 1980a). Soil structure can be characterized by the soil porosity and the pore size distribution.  Soil porosity is the fraction of pore volume in a soil profile.  High porosity and  large ratio of macro-pores or air-filled pores indicate good soil structure.  H u n d a l et al  (1976) reported that subsurface drainage evidently resulted i n higher proportions of both large and medium-sized pores, indicating better soil structure.  W i t h the improved soil  structure, gas exchange between soil and the atmosphere can be promoted, there will be sufficient supply of oxygen for the crop growth. Soil hydraulic conductivity, which is the measure of the ability of a soil to conduct water, is significantly influenced by the size of the large pores. Therefore it is also affected by subsurface drainage. Hundal et al (1976) observed that subsurface-drained soils had much higher hydraulic conductivity than the undrained ones. W i t h the same amount of  Literature Review  8  rainfall, there was much less water ponding on the drained soil. Subsurface drainage also has influences on the soil temperature  (Wesseling, 1974a).  Water has much higher specific heat capacity and thermal conductivity than air. B y lowering the water content, subsurface drainage can increase the soil temperature.  In  temperate regions like the L F V , this is very critical for the crop growth in the spring when the soil temperature is low. Germination, emergence, and early growth of crops are all related to soil temperatures.  Under favorable soil temperatures, crops can ripen  earlier and higher market prices can be expected.  2.1.3  Soil Water Management and C r o p Production  As subsurface drainage improves the physical conditions and trafficability of the soil, it has a favorable influence on the crop growth. Also, the soil organic matter is decomposed at a greater rate i n the drained soil because the growth and activities of the microbes are promoted. A s a result, more nutrients can be supplied to the crops. M u c h research has been done to determine the effects of subsurface drainage on crop production. A three year field experiment conducted by Chieng et al (1987) suggested that subsurface drainage increased corn, forage grass and strawberry yields by 61, 38 and 725%, respectively. Campbell et al (1977) observed that potato 3'ields responded to subsurface drainage very well. T h e total potato yield increase per unit length of row with subsurface drainage was 32% and 24% respectively for 1974 and 1975. T h e quality of potatoes was also improved as indicated by the 56% and 35% increase i n No. 1 grade potatoes respectively for 1974 and 1975. However, it should be noted that subsurface drainage can only improve the crop production within a certain water table range. adversely affected.  Beyond this range, crop yields will be  Smedema and Rycroff (1983) graphically described the relationship  between the crop yield and water table depth (Figure 2.1). It is believed that the decrease  Literature Review  optimum at higher watertables for th« sandy l o a m , reflecting the lower moisture holding capacity and better aeration c a p a c i t y of this soil 0  £  20  C OJ  1  20  .40  60  80  100  120  140  160  watertoble depth below soil surface ( c m )  Figure 2.1: Crop yield-water table depth curve for two different soils in Netherland (after Smedema and Rycroff, 1983) of crop yield at the greater water table depth is due to the water deficit during the dry period. Therefore, subsurface drainage rate should never be designed larger than necessary to remove the excess water for adequate crop growth and farm operations (Chieng et al, 1978). O n organic soils, subsurface drainage may result i n subsidence of the soil.  With  the improved growth conditions, soil microbes decompose the soil organic matter at a considerable rate. This may be beneficial for the crop nutrient supply, but it damages the soil structure because the organic matter is one of the most important binding substances in the formation of soil aggregates, particularly water-stable aggregates (Hillel, 1980a; Tisdale and Oades, 1982). Stephens (1956) reported that the subsidence rate of organic soil is proportional to the water table depth.  Thus the optimum water table depth  maintained for organic soil should be a compromise between the crop yield and the subsidence rate.  Literature Review  2.2  10  Drainable Porosity in Subsurface Drainage Design  In subsurface drainage design, drain depth and drain spacing are two important design parameters.  Drain depth is determined according to the availability of the excavating  equipment, soil properties and water table levels in the collector ditches (Raadsma, 1974). Once the drain depth is determined, the drain spacing can be calculated considering the climatic conditions, soil characteristics, crop requirements, and economic conditions of the drainage area.  M a n y theories have been developed to calculate the drain spacing  for the subsurface drainage system. In general, these theories can be divided into two categories:  steady state theories and non-steady state theories.  theories, the water table is assumed to be constant.  In the steady state  In real practice, this is true only  under special conditions (Bouwer, 1974). For most drainage problems, the water table fluctuates  w i t h time.  Subsurface drainage design should be carried out based on the  non-steady state theories. In both steady state and non-steady state theories, many equations have been developed for the calculation of the drain spacing. To solve these equations, a number of input parameters are required. Drainable porosity is one of the basic input parameters for predicting the water table fluctuation (Skaggs et al, 1978) and for the computation of the drain spacing. Soil drainable porosity is the volume of water that can be drained from a unit volume of soil when the soil water potential is decreased from the atmospheric pressure to some specific negative value (Nwa and Twocock, 1969; Bouwer and Jackson, 1974; L u t h i n , 1978). Prasher (1982) defined drainable porosity as the volume of water taken up by a unit area of unsaturated soil above the water table for a unit rise in the water table. The importance of the soil drainable porosity in subsurface drainage design results from its effects on the drainage flow rate (drainage coefficient). Drainage flow rate is the  Literature Review  11  amount of water that must be  remoA'ed  in a 24 hour period (Luthin, 1978). High drainable  porosity means that more water can be drained when the water table is lowered by a specific amount. Chieng et al (1978) used soil drainable porosity i n their model to predict the water table fluctuation patterns under subsurface drainage. Recently, the hydraulic conductivity-drainable porosity ratio, K/ f, has been considered as a basic parameter for subsurface drainage design (Bouwer and Jackson, 1974; Bhattacharya and Broughton, 1979). W u (1988) reported that soil drainable porosity and hydraulic conductivity have the same amount of influence on the values of the drain spacing. In many studies, drainable porosity is assumed as a constant (Jackson and Whisler, 1970; Skaggs, 1975). constant.  However, research has shown that drainable porosity is far from  Its values vary with the water table depth, and the rate and direction of  the water table  fluctuation  (Taylor, 1960; van Schilfgaarde, 1974; Bhattacharya and  Broughton, 1979). According to Luthin (1978), drainable porosity / is a function of the capillary pressure h (i.e., the negative pressure head, also called suction head) and can be written as f(h).  A s the water table drops from hj to h , the volume of water v drained 2  out of a column will be  (2.1) T h e function f(h)  is related to the soil moisture characteristics and is generally a  complex function. However, it is sometimes possible to write an approximate expression for the relationship between the drainable porosity and the suction head and still end up with a reasonable prediction of the amount of water that drains out of a soil in which the water table is dropping (Hillel, 1980b). T h e usual technique to determine the soil drainable porosity is through the equilibrium water content profiles above two successive water table levels. It is schematically  12  Literature Review  VOLUMETRIC  WATER  CONTENT  Figure 2.2: Soil water content curves plotted above water table to evaluate drainable porosity (after Bouwer and Jackson, 1974). shown i n Figure 2.2. Curves 1 and 2 are the water contents when the water table is at positions 1 and 2 respectively. Drainable porosity is the water content difference between the two curves.  Soil water content can be measured by gravimetric method, neutron  scattering, gamma ray attenuation or other methods (Cope and Trickett, 1965; Gardner, 1965; Bouwer and Jackson, 1974). The drainable porosity is estimated by the relationship between the soil water content and the (negative) pressure head. This technique may give a reasonable estimation i f the water table drawdown is slow enough to allow the drainage of the pores to "keep up" (Talsma and Haskew, 1959; French and O'Callaghan, 1966). Although drainable porosity can be determined from soil water content profiles, the procedure is very time consuming (Taylor, 1960). Sometimes it is difficult to accurately measure the water content of the soil.  Taylor suggested an evaluation method which  uses measurements of drainage outflow and water table levels. The water table is first set at the surface of the soil column, then successively lowered by small increments. The  Literature Review  13  drainable porosity is given by the volume of water released, divided by the total volume of the soil drained. Skaggs et al (1978) did similar experiments with large soil columns (51 cm i n diameter and 100 c m in length). Tensiometers were installed in the soil columns at vertical increments of 10 cm. The soil water tension was measured each time when the water head was decreased at an increment of 10 cm. The volume of water released was also measured.  These data were used to calculate the soil drainable porosity and the soil  water characteristics curve. Under field conditions, soil water balance is much more complex than that in the laboratory. T h e soil water budget consists of components such as precipitation ( P P T ) , crop consumption, soil storage, etc. Soil water table position at any time depends on the water balance between the inflow, outflow, and the change in soil moisture storage. A water balance model used by Chieng et al (1978) has the following form: Inflow = Outflow ± Change in storage Where, Inflow includes natural P P T and irrigation water; Outflow consists of subsurface drainage, E T , deep seepage and surface runoff. T h e term "Change in storage" used i n the above water balance model is defined as the change of soil moisture content above the water table. In this study, the concerned period is the winter time. T h e soil is almost saturated. Thus the change i n moisture content above the water table is assumed to be insignificant and neglected in the computation of soil drainable porosity. Based on the above model, Chieng (et al, 1978) developed another model to predict the water table fluctuation in the soil, which states:  AZ = ™ therefore  (2.2)  Literature Review  14  r  DAt  ,  ,  where  AZ  =  water table change from the start to the end of the related rainfall or drainage event. Positive AZ is taken when the water table rises. AZ is negative i n the case of water table drawdown;  At  =  time interval between water table rise or fall and the start of rainfall or drainage event.  Chao (1987) reported that A t was approximately 12  hours; D  =  drainage rate (drainage coefficient);  /  =  drainable porosity.  Similarly, drainable porosity, / , can be determined by the total amount of rainfall, E T , the drainage discharge and the water table level changes (Chieng, 1989, personal communication). W i t h i n a specific time, this relationship can be expressed as:  _ (PPT - ET 1  ~  D)At  AZ  [  ]  Where P P T and E T are precipitation and evapotranspiration rate respectively; / , A t , D and AZ all have the same definitions as i n Equation 2.2 and 2.3 It can be seen from Equation 2.4 that when P P T is greater than the sum of E T and D , water table will rise; otherwise water table will drop (i.e. when P P T = 0 ) .  Literature Review  2.3  15  Evapotranspiration in Soil Water Balance  Evapotranspiration ( E T ) is one of the major components i n the soil water balance. E T from the water table plays an important role i n lowering the water table. In most of the existing drainage formulae, this factor is neglected due to the difficulties i n measurement (Skaggs, 1975; Hillel, 1980b). It is desirable to include E T i n the soil water balance for the estimation of the drainable porosity. If E T is not directly measured, it can be computed based on climatological data. The complexity and accuracy of these estimation formulae vary greatly. The following sections provide a brief review of the methods used for the measurement and computation of E T .  2.3.1  Definitions  Evapotranspiration Evapotranspiration, also called consumptive use, is the sum of evaporation and transpiration (Hansen tt al, 1980). Evaporation is the water loss from surfaces of soil, water and plant leaves. Transpiration is the quantity of water entering the plant roots, used for the building of plant tissues and being passed through plant leaves into the atmosphere. E T is expressed as the depth of water lost or used i n a specific time (Svehlik, 1987), usually in millimeters (mm) per day.  Potential Evapotranspiration The definitions of potential E T given by different researchers  vary slightly.  Penman  (1956a) defined potential E T as "the amount of water transpired i n unit time by a short green crop, completely shading the ground, of uniform height and never short of water (Jensen, 1973)." M a n y researchers have extended this definition to all crops rather than  Literature Review  16  limiting it only to short crops. Svehlik (1987) referred to potential E T as "the E T of a disease-free  crop, growing i n a large field (one or more hectares) under optimal soil  conditions including sufficient water and fertility and achieving full production potential of the crop under the given growing environment." Generally speaking, potential E T can be defined as the E T which occurs i f there is no water deficiency i n the soil for the crop growth, i.e., it is the m a x i m u m value of E T . Actual E T of a crop is often lower than the potential value due to deficits i n water and/or energy sources. As there are differences i n aerodynamic characteristics of crops, as well as i n the growth rates and soil water depletion processes, it can be expected that the values of potential E T for different crops are not the same. For convenience and comparison, the potential E T of a preselected crop (reference crop) is usually calculated. Alfalfa and short grass are the two most commonly used reference crops (James, 1988). The potential E T of other crops is then determined by the following equation:  ET  C  =  fc ET c  D  (2.5)  where  ET  C  =  the crop E T ;  ET  D  =  the reference crop E T ;  —  the crop coefficient.  k  c  2.3.2  Factors Affecting Evapotranspiration  Both evaporation and transpiration are influenced by general climatic conditions such as the availability of energy, the evaporation demand of the air, etc. The computation of E T should take these factors into consideration.  Literature Review  17  Heat Energy W h e n water changes from liquid form to gaseous form a certain amount of energy is required. This energy is called latent heat (Shaw, 1983). Its values vary with temperature. A t 20 degree  Celsius,  584.8 calories (2447 joules) of heat are required to evaporate 1 cubic  centimeter of free water (Hansen et al, 1980). In nature, latent heat is from solar (short wave) and terrestrial (long wave) radiation. Of these two, solar radiation is the principal source of the heat energy (Jensen, 1973). Solar radiation affects the E T rate according to the latitude and season (Shaw, 1983). The fraction of solar radiatfon which can provide energy for E T is the net radiation. Net radiation can be considered as the primary climatological factor controlling E T where water is not limiting (Jensen, 1973). Net radiation is the incoming short wave and long wave radiation less the reflected and outgoing thermal radiation.  Figure 2.3 and 2.4  illustrate the soil energy components and energy balance of a day. During the day time, net radiation is positive, meaning that there is available energy for E T . After sunset and before sunrise only thermal or long wave radiation is involved. Long wave outgoing is normally in excess of the long wave incoming radiation during the night, hence, the net radiation is negative (Black, 1990). This means that no E T occurs during this period of the day.  Temperature Both air and soil surface temperatures are important for E T . Temperatures also depend on the energy source, i.e. solar radiation (Shaw, 1983). T h e higher the air temperature, the more water vapor it can hold therefore the higher the E T value. Similarly, if the temperature of the soil is high, the soil water is more readily to be evaporated. more water is evapotranspired during the summer than during the winter.  Thus  Literature  i»  Review  — i — r — i — r — r -  18  -,—|—|—I—I—l—I—1—I—1—r  i  !—1 !  '•  1  1.4 /  IJ  _ to  1  JU9I»TI0»  //""\\  z  5 • a • o •J  ' " f  / /  ^  ]  5ol0r radiation at>ove atmosphere  MtT B A 0 U T I O I T % ^ \  0  •2 -.4 7  ) • |—(—1—1—1—1—1—r-i—f  1 !  Mi  1. I I I  t  u  a. *  N  e  *Ve--V~L*Ttl(T  /  i.o  T .» Z  MC»T  A ^  /  SCNSIILt Ht*T  i  _  Absorption Thermal rorjiotion  •  J«t loss  / \ \  3 .»  4N £  -4  S  1  ^ 1  t  1 • .  /  \  =  4  S  *  w  ^  >  (' 1  ,-Am  Si  8  Surface of the earth J  00  l—;—  MST  ,  •  °*  *  *  •  J  » '  *  l  1  1  '  • '  "  1  1  • —:— 1  i  **  Figure 2.3: Energy balance components and  Figure 2.4: Schematic representa-  related parameters (after van Bavel and  tion of the daytime radiation bal-  Ehrler, 1968)  ance (after Gates, 1962)  V a p o r Pressure Vapor pressure is a measurement of the capacity of the atmosphere to hold water vapor (Shaw, 1983). It is the amount of water vapor in the air, expressed in millibars (mbar). The  value of vapor pressure is directly related to temperature.  It has been observed  that there is a unique relationship between the air temperature and the saturated vapor pressure, which is the vapor pressure when the air contains a maximum amount of water vapor. E T is affected by the saturation deficit of the air, which is the difference between  i  Literature Review  the saturation vapor pressure at air temperature  19  and the actual vapor pressure.  The  saturation deficit represents the further amount of water vapor that the air can hold before becoming saturated. The larger the saturation deficit, the higher the E T demands.  W i n d Speed As water evapotranspires from the soil and crop, the water vapor accumulates i n the air above the ground. W i n d moves away the moist air above the soil surface and replaces it with drier air. Thus, wind speed is another important factor influencing the E T rate.  Water Availability A t a given amount of available energy, the actual E T rate is strongly influenced by the availability of soil water (Denmead and Shaw, 1962). This is particularly true during the dry season when there is a water deficit. If the water table is close to the soil surface, evaporation rate from the soil is almost equal to that of a free water surface (Hansen et al, 1980). As the water table drops, evaporation decreases until it becomes negligible when water can not reach the surface by capillary rise. Zhang (1983) reported that for fine textured soil, the critical ground water table depth is about 1.5-1.7 m f r o m the soil surface. A t deep water table levels, crop roots also have difficulties extracting water. Thus, transpiration is restricted.  Stewart  and Miels (1967) experimented with sod crops grown on sandy soils during the periods of very low rainfall. It was found that when the water table was 90 cm (36 inch) below the soil surface, the E T value was only 88% of that when the water table was 60 cm (24 inch) from the soil surface.  Literature Review  Crop  20  Conditions  Crop growth stages, species, even densities all influence E T rate.  For example, young  crops use only a. small amount of water. Water consumption increases with crop growth and reaches a peak during some part of the growth period. B y harvest time water use decreases again (Erie et al, 1965). Generally speaking, crops having long growth period and/or deep rooting systems will consume more water than crops with short growth seasons and shallow root systems.  2.3.3  Determination of  Evapotranspiration  Various methods have been used for the determination of E T . Principal methods include: direct measurements,  mass transfer, energy balance, combination methods, empirical  formulae, or using evaporation measurements as indices (Al-Sha'Lan and Salih, 1987). Direct measurements are considered to be the most reliable (Svehlik, 1987; A l - S h a ' L a n and Salih, 1987). They can be used not only for the design of drainage and irrigation systems, but also for the calibration of other methods for calculating E T . Because of. the time and expense involved i n measuring E T i n the field, and the inherent spatial variability in such measurements, usually, E T is determined by using weather data and one or a number of the recognized formulae (Elliott et al, 1989).  T h e selection of a  proper estimating method depends on many factors including the geographic location, the availability of the weather data, the comparative performance of the various equations, etc. The following will be a description of these methods.  Direct measurements Direct measurements  are based on the conservation of mass principle (James, 1988).  Usually, a portion of the crop is isolated from the surroundings and the E T value is  Literature Review  21  determined by measurements. T h e measurements can be performed by using many techniques including tanks or lysimeters, growth chambers, soil moisture balance, and heat and mass transfer.  In the weighing lysimeter method, for example, crops are grown in  buried soil-filled tanks. The soil in the tanks is hydrologically isolated from the surrounding soil. The amount of water consumed by the crop is determined by weighing the tanks. In the soil moisture balance method, the soil water content is measured periodically by techniques such as gravimetric analysis, neutron scattering, gamma ray attenuation, etc. (Hansen et al, 1980).  Aerodynamic  method  This method is based on the principle that moisture is moved away from evaporating and transpirating surfaces due to the turbulent mixing of the air and the vapor pressure gradient (Svehlik, 1987). To estimate the potential E T rate, wind velocity and air humidity must be measured accurately at least at two elevations near the evaporating surface. The general form of this method can be written as (Shaw, 1983):  E T = f(u)(e - e ) s  td  "  (2.6)  Where  ET  =  evapotranspiration rate;  f(u)  =  a function of wind speed;  s — £ad  e  =  saturation deficit.  Energy balance method This method takes into consideration of the energy affecting E T (Shaw, 1983). W h e n a vapor pressure gradient exists and water is available, E T is controlled by the availability  Literature Review  22  of the energy for vaporizing water (James, 1988). The energy, available for E T can be computed by the following equation.  A E T = Rn-G-A-C-PS  (2.7)  where  A  =  latent heat of vaporization (refer to A . 2 in A p p e n d i x A )  —  net radiation;  G  =  heat flux to the soil;  A  =  heat flux to the air;  C  =  heat storage in crop;  PS  =  photosynthesis.  R  n  The term R  n  is the amount of solar radiation that reaches the earth's surface minus  the reflected and radiated energy. Terms AD, G, C and PS are often neglected because they are very small compared with Rn. Then Equation 2.7 can be written as:  ET = Rn - A  (2.8)  T h e combination method In a classical study of natural evaporation, Penman (1948) combined the energy balance and mass transfer methods and developed a formula for calculating open water evaporation. This is the so-called combination method. It is based on fundamental physical principles, w i t h some empirical concepts incorporated, to enable standard meteorological observations to be used (Shaw, 1983). This latter facility has resulted i n Penman formula being enthusiastically acclaimed and applied world wide. Over the years, the original formula has been modified and extended to estimate not only the evaporation  Literature Review  23  from a water surface but also the actual E T of various crops (Tanner and Pelton, 1960; Saxton et al, 1974).  The modified Penman equation can be written as (Hansen et al,  1980): ET  P  = - A - ( R n + G)-r—^—-Ih.Z^ IS  -j-  +  w u )(e - e ) 2  2  s  (2.9)  ed  IS + "f  -y  where  ET  =  P  reference  crop potential E T , well-watered short grass or alfalfa i n  cal/cm /day ("Cal"  stands for calories); it can be converted  2  to  m m / d a y by dividing A (see A . 2 in A p p e n d i x A ) ; A  =  slope of saturation  vapor pressure-temperature  curve (de/dT) i n  mbar/°C; 7  — psychrometric constant; =  R  n  G  =  net radiation in c a l / c m / d a y ; 2  soil heat flux in c a l / c m / d a y ; since G is only a small fraction of R^, 2  it is often ignored (Tanner and Pelton, 1960); u  =  wind movement i n k m / d a y at 2 meters above ground;  e„  =  saturation vapor pressure, mean of values obtained at daily maximum  2  and daily m i n i m u m temperatures in mbar; =  e,d  mean actual vapor pressure i n mbar or saturation vapor pressure at dew point temperature;  W\,w  2  —  wind term coefficients.  To solve Equation 2.9, numerous additional equations and calculations are required. Details about the formulae and calculations involved are discussed in Appendices A and B.  Literature Review  24  The empirical formulae The Penman formula has repeatedly given good results for the estimate of daily potential ET (Eagleman, 1967). Frequently, however, the necessary data for this method are not available. Therefore, equations which are based on a smaller number of parameters are more appropriate. Many simpler methods of estimating ET based on one or more of the basic parameters controlling ET have been developed (James, 1988). Air temperature and solar radiation are the most commonly used parameters. In general, these methods are more convenient to use although they may not be as accurate as the Penman equation for the estimation of ET over short time periods. One of the most widely applied empirical formulae is the Hargreaves equation (Hansen et al, 1980). The Hargreaves equation was obtained on the basis of the data from grass lysimeters (Hansen et al, 1980). This empirical formula allows the estimate of the potential ET with only temperature and solar radiation data. Some unpublished comparisons have shown that it performs as well as more complicated equations at many sites. This feature is very important in practice. The Hargreaves equation can be expressed as: E T = 0.0135(T + 17.78)# P  (2.10)  5  where ET  =  P  potential ET for well-watered grass in cal/cm /day; it can be converted 2  to mm/day by dividing A (see A.2 in Appendix A); T  =  R„ =  average daily temperature in °C; solar radiation in cal/cm /day. R„ can be obtained the same way as in 2  the Penman method.  Literature Review  25  Pan evaporation method Evaporation pans provide a measurement of integrated effects of meteorological factors on evaporation under conditions of adequate water supply. The amount of water evaporating from a pan is determined by measuring the changes in the water level i n the pan correcting for the precipitation (James, 1988). The frequency of the pan evaporation  measurement  varies from hourly, to daily, to weekly. Daily pan evaporation is the most commonly used.  There are many types of evaporation pans.  the U . S. Weather Bureau is widely used.  The Class A pan recommended by  This type of pan is a cylindrical container  fabricated of galvanized iron or monel metal with a depth of 25.8 cm (10 inches) and a diameter of 124 cm (48 inches) (Jensen, 1973). M a n y studies have suggested relating the pan evaporation data to potential E T of a reference crop by a single factor, the pan coefficient, K . p  As the E T of a crop depends on  the type of the crop, stage of growth, etc., this coefficient also varies from crop to crop and also changes during the growing season. T h e E T values determined by the methods described above are very important in the calculation of the soil drainable porosity. It also provides the basic information for the scheduling of irrigation one of which is subirrigation.  2.4  Subirrigation  Subirrigation is the apphcation of irrigation water beneath the surface of the soil (Skaggs et al, 1972). T h e objective of this type of irrigation is to raise and maintain the water table at a depth sufficient to supply the water requirements of growing crops. In many cases subirrigation can be combined with the subsurface drainage systems (Skaggs, 1981). During the rainy season, the system performs the function of subsurface drainage to prevent crop damage due to excessive soil water, while i n the dry season, it provides  Literature Review  26  water for the crops by capillary rise. To practically use subirrigation, either an impervious layer or a permanent  water  table should exist at a rather shallow depth from the soil surface to prevent excessive losses due to deep seepage (Bournival et al, 1987). T h e hydraulic conductivity of the soil, which determines drain spacing, should be high enough to enable the system to function both for drainage and subirrigation. Another important parameter is the topography. The field should be relatively flat to get a uniform water table distribution. Otherwise the water table might be at an optimum depth from the surface on one side of the field while the plants are suffering from too much or too little water on the other side of the field (Skaggs et al, 1972). Massey et al (1983) recommended that the slopes of the fields  j be less than 0.5%.  The spacing and optimum water table level again depend on the  soil properties, the crop to be grown and climatological factors, w hich are a function of r  location. The advantages of combining subirrigation and subsurface drainage include (Skaggs et al, 1972): 1. One system providing both drainage and irrigation. 2. Low labor and energy costs for operation and maintenance. 3. N o delays in cultural practices because of irrigation. 4. Little or no natural leaching from the root zone. Because subirrigation operates under gravity, less energy is required to deliver a unit volume of water than other irrigation systems such as sprinkler or trickle irrigation. Strickland et al (1981) reported that subirrigation of corn during 1980 required only 70% as much energy as a center pivot system near Orangeburg, South Carolina, U S A .  27  Literature Review  With the increasing energy costs for irrigation, energy-saving is becoming more and more important. Under subirrigation, the water table fluctuation patterns are different from the patterns under subsurface drainage only. This has certain effects on the soil properties. Chieng (1987) observed that the water table in the subirrigated plots rose closer to the soil surface than in the plots without subirrigation in the same rainfall event.  It was  also found that both saturated and satiated hydraulic conductivities of the subirrigated soils are lower than those of the unirrigated soils. Subirrigation also adversely affects the structure and drainable porosity of the soil. Chao (1987) reported that the closer the water table is kept to the soil surface, the smaller the soil drainable porosity. The decrease in drainable porosity was possibly due to the transportation and deposit of fine soil particles brought about by subirrigation. However, the results are obtained in the laboratory with soil columns. More research needs to be done under field conditions.  Chapter 3  EXPERIMENTAL L A Y O U T  3.1  Background  The experiment was carried out in the Lower Fraser Valley ( L F V ) of the province of British Columbia ( B . C . ) .  The L F V is located in the south-west corner of the province  and is a very important agricultural area.  Although the L F V makes up less than one  tenth of the total area of the improved land in B . C . , it generates more than one half of the dollar values of the farm sales (de Vries, 1983). W i t h i n the valley, lowland makes up 90% of the total area of the improved farmland. The L F V is a humid area with the total annual precipitation of about 1100 m m (Hare and Thomas, 1974). The annual evapotranspiration is about 550 m m . There is a annual water surplus of 550 mm. Most of the precipitation occurs during the winter time. Summer rainfall is quite small.  Figure 3.5 shows the 30 year annual water balance in  this area ( E T is the potential values). From the figure, it is obvious that there is a great water surplus from October to A p r i l , and there is a water deficit from M a y to September. The topography of this area is low and flat. The natural drainage condition of the land is poor. Thus artificial land drainage has been the traditional water management  approach  for profitable crop production. During the summer time, supplemental irrigation is often required for optimum crop yields, particularly for high value crops. Of all the irrigation methods, subirrigation is the most recently adopted one and is receiving more and more attention due to its low energy and labor costs. In addition,  28  Experimental  29  Layout  200180160 Legend o ' PRECIPITATION, PPT  140 -  E  a  EVAPOTRANSPIRATION, ET  120 r LU  "O C D  10080-  J—  Q. Q_  WATER  / WATER SURPLUS  DEFICIT  60WATER S U R P L U S  X '  40 -  2  0  7  —  - '  •G Or  ^  tf*  ^  ^  &  c0'  QS  Q  ^  ^  MONTHS  Figure 3.5: Annual water balance of LFV (after Chieng, 1987) the land resource is becoming more and more limited and expensive in this agricultural area. Thus many researchers and farmers have been trying to use the existing subsurface drainage system for irrigation. Chieng et al (1987) conducted field experiments by using an existing subsurface drainage system for subirrigation during the summer months. It was found that successful subirrigation could be practiced through the subsurface drainage system in this area although no significant increase in crop yields was observed for the three year (1982-1985) field trial.  3.2  Experimental Layout  The experimental site was located at Boundary Bay, Delta in the LFV. The total area was 3.4 ha. The field had a low-lying and flat topography with an elevation of only 1.2 m  Experimental Layout  30  above the mean sea level. The soil was classified as Ladner series, a humic gleysol. It was developed on moderately fine to fine textured deposits of both marine and fresh water origin, overlying sandy deposits at a depth of over 100 cm (Luttmerding, 1981). Surface and subsurface soil textures varied from silty clay loam to silty loam.  The drainage  condition of the land was moderately poor to poor (Driehuyzen, 1983). There were four water management regimes i n this study. The size of each treatment plot was 4200 m , 100 m long and 42 m wide. Polyethylene drains (100 m m in diameter) 2  were installed at an average depth of 1.1 m , a spacing of 14 m . and a length of 100 m. Thus, each plot had three drain fines. These drains were installed in a parallel pattern and in the east-west direction. Detailed layout of the experimental plots can be found i n Chieng (1987). A nonlined open ditch was used as the collector of the drains. T h e ditch was divided into three segments. These segments were interconnected with plastic pipes at the bottom of the ditch. T h e water table i n each segment could be controlled separately with overflow standpipes for subirrigation. A pump was installed to empty the collector ditch into the main ditch from where the drainage water was carried away from the experimental field. The water table control system and the arrangement of the water management plots are schematically illustrated i n Figure 3.6 a and b. The four water management regimes were: 1. Regime A : subsurface drainage all the time; water table was controlled at or below the drains; 2. Regime B : subsurface drainage during the high precipitation periods; subirrigation by maintaining the water table at 60 cm below the soil surface during the periods of water deficit;  Experimental Layout  31  PLOT D  100  mm P L A S T I C  DRAIN  TUBE  •  GRASS FORAGF.\\.  CJJ  STRAWBERRIES  ACCESS  POTATOES  ROAD  o  GROUND WATER SAMPLING LOCATION AND RECORDER DRAIN WATER SAMPLING LOCATION  Figure 3.6: Experimental field layout (after Chieng, 1987)  Experimental Layout  32  3. Regime C : subsurface drainage during the high precipitation periods and subirrigation by maintaining the water table at 30 cm below the soil surface; 4. Regime D : check plot; no subsurface drainage and subirrigation at any time of the year.  In the two subirrigated regimes, the set up of the water table depths at 30 and 60 cm below the soil surface is based on both the drainage experience of the workers i n this area and the information reported i n the literatures. For most of the soils in the L F V , it was found that the water table should be maintained at about 50 cm below the soil surface for suitable trafncability (Chieng, 1989, personal communication). In the B . C . Agricultural Drainage Manual (van der Gulik et al, 1986), the required water table depth was at 50 cm or more from the soil surface within 48 hours after a storm rainfall event ceased so that crop and soil structure damages were minimized. Based on the guidelines mentioned above, the water tables in this study were maintained at 30 and 60 cm below the soil surface respectively i n the two subirrigation regimes to cover the lower and upper ranges of minimum water table depths to avoid reduced crop yields and trafficabihty. Four different crops were planted on each plot. These crops included: grass forage, corn, potatoes and strawberries. T h e crops were randomly arranged in the plots with the corns planted on the west side to eliminate its shading effects on the other crops (Chao, 1987). The subdrains and ditches were installed i n the winter of 1981. drainage system was then put into use.  T h e subsurface  The pump was installed i n early 1983 and  started operation for subirrigation i n the summer of 1983. The water table height midway between the drains was recorded with automatic water table recorders since 1981. There  Experimental Layout  33  is one recorder in each plot. The data collected from 1985 to 1988 are used in this study.  3.3  Data Collections and Analyses  The physical and hydrological characteristics of the soil, including satiated hydraulic conductivity, bulk density, particle size distribution, moisture retention curve, etc. were analyzed by Chao (1987). Detailed information can be obtained from Chao (1987) and Chieng (1987). T h e water table fluctuation and climatological data used in this study were collected from different sources due to the lack of observations at any one single weather station. The soil water table heights in each plot and the daily rainfall were recorded by the automatic water table and rainfall recorders respectively. T h e charts from the recorders were traced into the computer by the Talos C Y B E R G R A P H digitizer at the Computing Center of the University of British Columbia ( U B C ) . T h e digitizer could be used in either of the two modes: connected to the mainframe M T S v i a U B C - n e t , or connected to a microcomputer. T h e data produced from the digitizer then can be used for studying the water table fluctuation patterns and some other analyses by using programs such as L O T U S 123 (Release 2), T E L L - A - G R A F (in the mainframe), etc. Monthly precipitation, maximum, minimum, mean and dew point temperatures, and wind speed were measured at the Vancouver International Airport ( V I A ) by Environment Canada; global solar radiation was measured at the U B C weather station. V I A and U B C weather stations are about 10 k m and 20 k m away from the experimental site respectively. T h e latitude of V I A , U B C weather station are 4 9 ° 1 1 ' and 49°15' respectively. Thus it is assumed that the climatological data collected at the above mentioned weather stations can be used in this study. The potential evapotranspiration values of the studied area were computed by using  Experimental Layout  34  Penman and Hargreaves methods described in Chapter 2 and Appendix A and B . Soil drainable porosity of regimes A and B were calculated using Equation 2.4 i n Chapter 2. Since actual E T is assumed to be equal to the potential E T , this study is interested i n the rainy period when the water table is close to the soil surface.  Thus  the errors resulted from the water deficit can be eliminated. In the computation, typical rainfall events, which caused significant water table rise, were selected from the rainfall and water table fluctuation charts. Appendix D .  Detailed computation procedures are described i n  Chapter 4  RESULTS A N D DISCUSSION  4.1  Weather D a t a  M o n t h l y mean precipitation, w i n d speed, and monthly mean maximum, minimum, mean and dew point temperatures from 1985 to 1988 are graphically shown in Figure 4.7, 4.8 and 4.9 respectively. M a x i m u m monthly precipitation (260 mm) occurred i n November of 1988. W h i l e in J u l y of 1985 and August of 1986, there was no rainfall for the whole month. In general, most of the precipitation occurred during the period from November to M a y .  M o n t h l y average wind speed at 2 meters above the ground varied from 80  k m / d a y to 246 km/day. During the four year period, M a x i m u m daily air temperature seldom exceeded 25°C; the lowest m i n i m u m daily air temperature was about —5°C. The seasonal variation of the dew point temperatures was very similar to that of the mean m i n i m u m air temperatures.  This indicates that when dew point temperatures are not  available, m i n i m u m temperatures can be used instead. The result is i n agreement with that reported by Merva and Fernandez (1985). The information about the solar radiation is described in the section 4.4 of this chapter.  4.2  Water Table Fluctuation  Continuous water table positions midway between two drains i n each water management regime were recorded by the automatic water table recorders. Figure 4.10, 4.11, 4.12 and 4.13 show the water table fluctuation curves from 1985 to 1988.  35  S3 ft  Precipitation (mm)  Precipitation (mm)  cn  cn O l  o o  cn  I  i  o  ro o o _L_  M  cn  o  <3 CO  JAN-  co cn  *M*-j« \ssBSsassass  APR  HAYJUNJUL AUG SEP-. SBSSSS OCT-  NovOtC  Precipitation (mm)  Precipitation (mm) Oi O  _» O O  _* Cn O  '  I  I  JAN -ftiwwwwmrag • ESS fire-  K) O . O  I  M cn O  Cn O I  I  o o  JAN  fee  cn  KJ O O  K) cn O  I  _L_  I  o  LO CO  cn  .  n m m u m n H m m m i M  APR  MAY •fcuuuuuiuwu JUNJUL AUG  sa>  OCT  HAY  ? •'UN 2. JUL * AUG SEP OCT  NOV  ore CO  Results and  37  Discussion  1986  1985  ^ >o  1 9 9 CL U>  "D  C  350 -i  350  300-  300 O  250-  250-  200-  200-  150 -  © o  150-  T> C  100-  Q_ M  100-  50  50V *t V P P ¥ 9 V \ _ — ' ^ w w ^ ^ ,ui < a. x o a o w  ^  A tt; ^2 u, ^  O  Month  300-  >» o  250-  0 ©  150-  "O  1 x» e • O.  CL  0>  c  f T ¥ T f w © o. * - > p 3 ^ O ^ 10 O ^ Q  350-i  o  200-  3  1988  350-j  >£  *  Month  1987  1  Or 0. X  300250200150  CO  •D C  100-  10050-  50i  a«  & >. t  J  Month  o a *• > o Month  Figure 4.8: Monthly mean wind speed of Vancouver.  .V  if  Monthly mean temperature ( C)  Monthly mean temperature ( C)  Results and Discussion  39  1.2  0.8  c o  0.4-i  OT O  0  a  o 9 O  -0.4  -  -0.8-  Legend  -1.2-  Regime A Regime B  •1.6  —I  0  30  Regime C Regime_ D_  1  1  1  1  1  60  90  120  150  180  1  1  1  1  1  1  210 240 270 3 0 0 3 3 0 3 6 0  Time (day) Figure 4.10: Water table fluctuation for regimes A, B. C, and D (1985). 1.2  c o  *S  o o.  _©  -Q O 9  -0.4-  Legend  "o -0.8  Regime A Regime B  -  -1.2  — I 0  30  1  1  60  90  Regime C Regime D  1  1  1  120  150  180  1 1 1 1— I 1 210 240 270 3 0 0 3 3 0 3 6 0  Time (day) Figure  4.11: Water  tablefluctuationfor regimes  A, B, C, and D (1986).  40  Results and Discussion  1.2 0.8  c o W o CL  0.4 0  9  -O O  5  -0.4 -0.8  Legend  -1.2  Regime A Regime B  -1.6 0  — I 30  1  1  60  90  Regime C Regirne_ D 1 1 1 1 1 1 1 I 120 150 180 210 240 270 3 0 0 3 3 0  I 360  Time (day) Figure 4.12: Water table fluctuation for regimes A , B , C, and D (1987). 1.2 - i  1  c o m O  tx.  _2 .a o  -0.4-  Legend Regime A Regime B  -0.8-  -1.2 0  —1 30  1 60  1 90  Regime C Regime D_ 1 1 1 1 1 1 1 1 120 150 180 210 240 270 3 0 0 3 3 0  Time (day) Figure 4.13: Water table fluctuation for regimes A, B, C , and D (1988).  "I  360  Results and Discussion  41  T h e water tables in the undrained regime (D) remained at or close to the soil surface for most of the time from October to A p r i l . The flat fluctuation curves during this period indicate that there were no rapid changes in the water table positions. This is because, without subsurface drainage, the excess water could only be removed from the upper soil layer by the processes of evapotranspiration ( E T ) and deep seepage. During this period of the year, however, both evaporation and transpiration rates were very low due to the limited energy source from the sun. Thus only a small amount of water could be naturally removed from the soil. The low E T rate, combined with high precipitation, made the water tables maintained close to the soil surface. High water table i n the soil could further decrease the infiltration rate to its minimum value (i.e. constant infiltration rate when the soil is saturated), de Vries (1983) observed that the infiltration rate of an undrained fine textured soil, under saturated condition, in the L F V was only 1.8 mm/day. Thus, during heavy rainfall events, surface ponding occurred very frequently in fields without subsurface drainage. Since the L F V is a very flat, surface runoff seldom occurs. The water table fluctuation patterns i n the subsurface drained regimes ( A , B , C ) were quite different from those i n the undrained regime. There were many "sharp peaks" i n the water table fluctuation curves. These peaks correspond to the heavy rainfall events and the subsurface drainage. During this period of the year, soils are almost saturated; when rainfall occurred, water recharged to the ground water and brought up the water table.  Subsurface drainage system removed the excess water and rapidly lowered the  water table. W i t h subsurface drainage, the water tables were maintained at about 50 cm or more below the soil surface for most of the time during the wet seasons (see Figure 4.10, 4.11, 4.12, 4.13). The average water table depths of different regimes are summarized i n Table 4.1. Among the drained regimes, regime A had the lowest water table levels; regime B was in the middle and regime C had the highest levels (refer to Table 4.1). The phenomenon  Results and Discussion  42  Table. 4.1: Water table depths during different seasons. Season  Year A  Regimes B C  D  Winter  1985 1986 1987 1988 Average  0.700 0.631 1.095 0.594 0.755  0.549 0.518 0.787 0.384 0.560  0.530 0.423 0.733 0.554 0.560  0.339 0.165 0.695 0.227 0.357  Summer  1985 1986 1987 1988 Average  1.684 1.096 1.446 1.038 1.316  1.261 0.810 0.965 0.732 0.942  1.033 0.773 0.768 0.692 0.816  0.992 0.538 1.255 0.641 0.857  Annual  1985 1986 1987 1988 Average  1.081 0.803 1.225 0.732 0.960  0.731 0.636 0.866 0.507 0.685  0.697 0.558 0.753 0.596 0.651  0.501 0.779 0.885 0.380 0.522  were consistent through the experimental period (from 1985 to 1988). These observations suggest that subirrigation has an influence on the soil water table fluctuations. In regime A , the subsurface drainage system was operated during the wet seasons, but there was no subirrigation during the dr} seasons. The water table dropped to a greater r  depth i n the soil profile by the end of the summer due to the continuous water loss by E T and deep seepage. The lowest water table position during the four year experimental period reached to approximately 1.5 m below the drains (2.6 m from the soil surface). In the subirrigated regimes (B and C ) , the water tables were also lowered by deep seepage and the increasing E T rate starting from the spring. However, the water tables in ditches were controlled at 30 and 60 cm from the soil surface, respectively, during the summer. Water could continuously move to the upper soil layer by capillary rise. For this  Results and Discussion  43  fine-textured soil, the capillary fringe, which is the region of a soil above the water table with uniform moisture content and the same hydraulic conductivity with the saturated soil (Luthin, 1978), was approximately 20 cm (Chao, 1987). E T requirements could be met by the water supplied from the capillary activities. Thus the water tables remained higher than those i n regime A which was not subirrigated. The water table fluctuation patterns were quite similar during the four year experimental period. T h e highest water table positions all occurred from November to February and the lowest from late June to September. In 1985, the annual precipitation (768 mm) was lower than normal (1055 m m ) , thus there were fewer "sharp peaks" compared with the other three years. It should be noted that i n late summer i n 1987, the water table positions of the four regimes were very similar.  This is because subirrigation had to be stopped during the  period for some management reasons. The characteristics of the water table fluctuation patterns presented above indicate that, i n the L F V , the removal of the excess water was very critical i n early spring to assure timely farm operations such as seedbed preparation, planting, fertilizing, etc. without any damages to the soil structures.  For the same soil, Chieng et al (1987) found that  with subsurface drainage, an average of 60 more opportunity days could be gained i n the spring. In temperate regions like the L F V , the total growing season is quite short compared to areas such as California. Good quality and high market prices are expected if the crop can grow and mature earlier. In addition, more varieties may be grown due to the extended growing season.  Results and Discussion  1  44  -i  E  D = -0.416+5.975(WTH)-2.584(WTH) r = 0.994  c  2  2  0-0  0.5  1  1.5  2  2.5  3  Drainage flow rate ( mm/day) Figure 4.14: Relationship between water table height above the drain and the drainage flow rate. 4.3  Drainage Flow Rate and Water Table Height  Drainage flow rates were computed from the total volume of discharge water divided by the drainage area.  As the drainage water was collected from the middle of each  water treatment regime, the total drainage area for each regime was 1498 m . The water 2  discharge volumes were measured during different periods of a year from 1985 to 1987. D a t a collection was limited to the regimes of regimes A and B . Measurements were done by using a stop watch and a graduated cylinder. Figure 4.14 indicates that a significant negative exponential correlationship exists between the drainage flow rate and the water table height (r =0.994). 2  This is i n agreement with the results obtained by Wesseling  (1974b). He reported that drain outflow was related to hydraulic head by a quadratic function and is inversely proportional to the square of the drain spacing. T h e above relationship illustrates that, the higher the water table, the higher the  Results and Discussion  45  drainage flow rate. During the winter period, when the water table was close to the soil surface, subsurface drainage was the major process i n the removal of the excess water from the soil. During the summer time, however, the water table dropped to a greater depth, drainage rate was quite low, the water removal from the soil was mainly dependent on the E T rate and/or deep seepage. If the water table drops below the drains, no water will be released from the drains. The curvilinear relationship between the drainage flow rate and the water table height mentioned above was used in the soil water balance for computing the drainable porosity.  4.4  Solar Radiation  4.4.1  Extraterrestrial  Radiation  The annual distribution of the extraterrestrial radiation (R )  computed by the James  a  method (James, 1988) is shown in Figure 4.15. R of water evapotranspired.  a  is expressed as an equivalent depth  In the computation, the latitude of U B C weather station  (49° 15') was used because the global solar radiation was measured at this station.  R  a  values computed from James equations have the unit of mm/day. It is clear that there is a considerable seasonal variation i n the total daily solar radiation incident upon a horizontal surface i n Vancouver. R  a  intensity has the lowest  values in winter. F r o m spring, the intensity starts to increase gradually and reaches to the peak values i n July. From the fall, the intensity of R  a  starts to decrease again. This  means that there is a greater energy source for E T i n the summer than i n the winter. Low energy source i n the winter, combined with the high precipitation, results i n the excess water i n the soil. R  a  intensities computed by James method were compared with the results reported  46  Results and Discussion  1200  20  1000 15  > o-  800  X>  D X)  600  o o or  io £ E D  400 -5 200  Gales 1 T-0  60  120  180  240  300  360  Time (day)  Figure 4.15: Annual distribution of extraterrestrial radiation in Vancouver. by Gates (1962). R intensities given by Gates were obtained by tracing the extratera  restrial radiation distribution curve into the computer using the digitizer described in Chapter 3. Gates obtained the R values based on the solar constant. Solar constant is a  the amount of energy received in unit time on unit area of a surface placed outside the earth's atmosphere and perpendicular to the sun's rays at the mean distance of the earth, 1.5x 10 km, from the sun (Gates, 1962; Monteith, 1973; Shaw, 1983). It varies from 8  1.94 to 2.0 cal/cm /min. In Gates' calculation, a solar constant of 1.94 was assumed 2  (curve Gates 1). Curve Gates 2 is obtained by the author just simply multiplying the R intensities in curve Gates 1 by a constant  a  to obtain the R values when a solar cona  stant of 2.0 cal/cm /min is used. Figure 4.15 shows that there is a very good agreement 2  between the R values given by James and Gates methods. It seems that solar constant a  2.0 cal/cm /minfitsJames method better. 2  Results and Discussion  4.4.2  47  Relationship between Extraterrestrial and Global Solar Radiation  Because the global solar radiation (R ) data of the whole year of 1988 and some days a  in 1985-1987 are not available from the U B C weather station or Environment Canada (Vancouver branch), two different methods were used to establish the relationship between R  a  and the global solar radiation. First, the Penman method was modified for  the local conditions of Vancouver. T h e ratios between the actual R measured at U B C e  weather station and the R computed by James method was plotted against the ratios a  between the actual and possible sunshine hours (N /N ).  Figure 4.16 shows that there  is a significant linear correlation between R jR  p  a  B  indicates that the higher the R and N /N a  a  p  a  p  and N /N a  (r =0.816, n =223). This 2  values, the higher the global solar radiation  intensities. O n clear days, larger proportion of the R reaches the earth surface. a  There  is more energy available for E T . W h i l e during cloud}' days, large amount of the solar radiation is absorbed or scattered by the clouds. Only a small portion of the R can a  reach to the earth surface. Black (1990) reported similar relationship between R and R, for the U B C Research a  Forest at Haney, B . C . which has similar latitude with the U B C weather station. T h e intercept (a) and slope (b) of his regression curve are 0.23 and 0.53 respectively. Selirio et al (1971) observed that during the summer at Guelph, Ontario, a and b were equal to 0.23 and 0.57 respectively. The global solar radiation was also computed by using the Hargreaves and Samani method (Hargreaves and Samani, 1982).  In this method, R  a  was the same as i n the  Penman method, which was computed by James equations; the maximum and m i n i m u m temperatures were measured at the V I A by Environment Canada. Samani and Pessaeakli (1986) reported the calibration coefficient (KT) values of different areas i n the United States. These values were based on the average monthly radiation and temperature data  48  Results and Discussion  Na/Np Figure 4.16: Relationship between extraterrestrial and global solar radiation based on the Penman method (1985-1987). for a period of 25 years. Since Vancouver has similar latitude and climatological conditions with Seattle, Washington State, the calibration coefficient of this area (7^=0.160) was used in the present study. T h e global solar radiation values estimated from the above two methods were compared with the actual global solar radiation measured at the U B C weather station (Figure 4.17). These values were expressed as the equivalent depth of water evapotranspired. The data in the graph were randomly picked up from 1985-1987 because the measured global solar radiation data of 1988 were not available. The regression coefficients ( r ) 2  between the actual global solar radiation and the global solar radiation by the Penman and Samani and Pessaeakli methods are 0.932 and 0.747 respectively (n =59). Although the measured R, is significantly related to the calculated R, in both of the methods, obviously, the Penman method gives much better results than the Hargreaves method.  49  Results and Discussion  oH 0  1  1  2  4  1  1  1  1  1  6  8  10  12  14  i 8 10 6 Actual Rs ( m m / d a y )  12  14  Actual Rs ( m m / d a y )  14  -i Rsa = 1.32Rsc-0.91  12-  o  1  r = 2  0.747  n = 57 108-  oc X»  j>  6  jo 3  O  o o  42i 2  i 4  Figure 4.17: Comparison of the global solar radiation computed by different methods.  Results and Discussion  50  T h e Penman method was used to compute the global solar radiation for the determination of potential E T . The average global solar radiation from 1985 to 1988 computed by the Penman method, expressed as equivalent depth of water evapotranspired, is shown in Figure 4.18.  4.4.3  H o u r l y Distribution of the Global Solar Radiation  W h e n rainfall occurs, E T from the soil and plant is about equal to zero even during daytime because the air is almost saturated.  In many cases, it is necessary to know the  hourly E T values for accurate estimation of soil drainable porosity. Unfortunately, the hourly solar radiation was not measured i n this study. Since the driving force of E T is mainly from the global solar radiation, it is reasonable to divide the daily total E T based on the distribution of the global solar radiation. Solar radiation directly comes from the sun, it is distributed i n the daytime. Thus E T mainly occurs i n the day time. M i l b u r n (1987) also assumed that E T was equal to zero during the night. Figure 4.19 shows the hourly distribution of the global solar radiation during different seasons of a year. It is based on four years' data. During the winter, the daytime period is short and the solar radiation concentrates i n the several hours around noon time. In the summer, the daytime period is much longer, the global solar radiation is more evenly distributed within a day. This difference causes the variation i n the distribution of E T rate. Thus it is taken into consideration i n this study.  4.4.4  Net Radiation  Net radiation (Rn) computed by Brunt method (James, 1988; refer to A p p e n d i x A and B ) is shown i n Figure 4.20. T h e data are on 24 hour basis. These values are expressed as the equivalent depth of water that can be evapotranspired. For the studied area, the  Results and  Discussion  51  1985  1986  14 -i  14  12 -  12 -  10 o  10 D  8 -  E  E  6 -  <x.  8 6 -  in  4 2  4 2 -  ~  0 -  1  1  1  1  1  0 -  1  60  60 120 180 240 300 360 Time (day) 1987 14  120 180 240 300 360 Time (day)  1988  -i  12 10 E  o  8 -  E JE  6 w cc  w  4 2 0 -  — I  1  1  1  1  60 120 180 240 300 360 Time (day)  1  60  1  1  1  1  I  120 180 240 300 360 Time (day)  Figure 4.18: Annual distribution of the global solar radiation of Vancouver.  Results and Discussion  52  Time (hour) Figure 4.19: Hourly distribution of the global solar radiation of Vancouver during different seasons. maximum amount of water that could be removed by net radiation was approximately 7 m m per day during the summer. It may be immediately noticed that negative radiation values occurred from November to January. A t the first sight, this seems impossible, but for areas with such a high latitude, it is reasonable. Net radiation is the balance between the energy gains and losses including incident short wave, absorbed long wave, reflected and transmitted short wave, and emitted long wave radiations. O f these terms, short wave radiation is a dominant factor. In general, net radiation is positive during the day time and negative during the night. In the summer, there is a greater amount of global solar radiation, daily net radiation is positive. Soils obtain energy from the atmosphere. Large amount of water can be removed from the soil by evapotranspiration process. During the winter, the global solar radiation reaching the earth surface is very small. Sometimes the total energy balance is negative. E T rate is very low sometimes even negative E T , i.e., dew deposition occurs as shown in Table C.6  53  Results and Discussion  1985  1986 10-,  10-i  8H o  o  I c  c  oc  OC  0  60  0  120 18 0 240 3 0 0 3 60  60  120 18 0 240 3 0 0 360  Time (day)  Time (day)  1987  1988  o  O  f  1  c  c or  OC  "i 60  1 1 I r 120 180 240 3 0 0 360 Time (day)  0  60  120 180 240 3 0 0 360 Time (day)  Figure 4.20: Distribution of the net radiation of Vancouver.  Results and Discussion  54  in Appendix C . Gates (1962) reported that the net radiation at Turukhansk, Siberia, was negative during the season from mid-September to A p r i l . Giles et al (1985) also obtained negative net radiations through the winter time for an area on Vancouver Island (latitude 48°50'). To avoid the frequent negative values, day time net radiation values were used in their experiment, instead of 24-hour values.  C o m p u t a t i o n and Verification of Potential Evapotranspiration  4.5  One of the major objectives of this study is to determine the E T values for the computation of soil drainable porosity by using the soil water balance approach. Since four different crops: grass, potatoes, strawberries ancUcorn were planted i n each regime during the experimental period, it is difficult to estimate the potential E T of each individual crop.  Therefore, the potential E T of grass was calculated and used to represent that  of the other three crops. In the calculation, the heat flux into the ground was ignored because it was very small compared to the net radiation. Penman (1948) and some other researchers (Allen, 1986; James 1988) also neglected the soil heat flux term. T h e annual total and seasonal potential E T values computed by using the Penman and Hargreaves methods (1985 to 1988) are shown i n Table 4.2. In the table " P " stands for the Penman method; " H " stands for the Hargreaves method.  Daily potential E T  values are computed and presented i n Tables C.6 and C.7, in Appendix C . Comparing the above results, it is found that the Penman method gives slightly higher potential E T values than the Hargreaves method. However the difference is not significant  (t  < £0.05)-  Similar results were reported by Hansen et al (1980). Thus it may be concluded  that both the Penman and Hargreaves methods can be used for the computation of potential E T for Vancouver area or even the entire L F V . This is very useful i n practice.  Results and Discussion  55  Table 4.2: A n n u a l and seasonal potential E T i n m m .  Year 1985 1986 1987 1988 Average  Annual P H 781.0 739.1 832.8 799.1 789.0  698.1 715.2 803.0 746.1 753  Growing P 533.2 482.0 527.3 505.3 512.0  season H 449.3 452.0 500.3 474.2 469.0  Off-season P H 247.8 248.8 257.1 263.2 305.5 303.3 293.8 272.0 276.1 271.8  In many cases, the estimation of potential E T by the Penman method is limited due to the lack of the climatological data. These data may be estimated, but it will bring about additional errors to the computed potential E T values. T h e Hargreaves equation only requires the global solar radiation and daily average temperature data. These data are available at most of the weather stations or they can be computed accuratety.  In  the present study, the traditional Penman method was used because most of the data required were available. The potential E T was also computed by using Priestley-Taylor method (Black, 1990). The average annual potential E T value (1985-1988) calculated using this method is about 150 m m lower than that by using the Penman and Hargreaves methods. Further studies are in process. For the potential E T computed with the Penman equation, some negative values occurred (refer to Table C.6., in Appendix C ) . This is resulted from the negative net radiation. A s mentioned before, the Penman equation is the combination of aerodynamic and energy balance methods. W h e n the potential E T , as the function of wind and water vapor deficits, can not offset the negative values caused by the negative net radiation, potential E T is negative. If there is enough water vapor i n the air, condensation may have occurred.  Results and Discussion  56  B o t h the Penman and Hargreaves methods only provide potential E T values, which depend primarily on the energy supplied to the ground surface by solar radiation. T h e actual E T , however, is generally a function of potential E T but is also affected by soil water availabilit3 , plant canopy coverage of the surface, etc. A c t u a l E T from an actively r  growing crop i n the field constitutes a fraction, often i n the range between 60% and 90%, of the potential E T as determined by the Penman equation or by evaporation pans. Hillel (1980b) reported that the actual steady E T rate was determined either by the external evaporativity or by the water-transmitting properties of the soil, depending on which of the two was lower. If the external evaporativity was not limiting, evaporation rate remained at maximum values within a certain range of ground water table below the soil surface. Gardner (1958) found that a sandy loam soil could still evaporate 8 m m of water per day if the suction head at the soil surface was above 600 cm of water. Ripple et al (1972) observed that the ratio between the actual and potential evaporation rates remained at unity if the water table was 60 cm below the soil surface and the potential evaporation rate was no greater than 6.0-7.0 m m per day. In this study, all the water table rise and drawdown events were selected from the wet seasons. In all the cases, the water table depths were less than 60 cm from the soil surface. During these seasons, daily potential E T during the same period was less than 4 m m . In addition, the soil texture was moderately fine to fine. The capillary rise was 20 cm (Chao, 1987). Soil water availability was not be a limiting factor for E T . Thus it could be assumed that the actual E T was equal to the potential E T during the studied periods. It should be noted that although the daily E T during the winter period is quite small, it accounts for about 20-30% of the water table drawdown (i.e. E T = 0.8mm/day and D — 2.3mm/day when the water table was at about 60 cm below the soil surface in February).  Results and Discussion  57  Table 4.3: Evaporation coefficients Potential E T (mm/day) 3.8 4.0 5.7 5.0 5.9 4.5 5.4 6.1 3.2 3.3 3.1 2.9 3.6 3.0 3.1  4.6  Ep (mm/day) 4.0 4.4 6.1 7.0 6.6 6.0 6.5 6.1 4.3 5.2 4.8 3.8 4.8 2.8 3.0  Coefficient 0.95 0.91 0.93 0.71 0.89 0.75 0.83 1.00 0.74 0.63 ' 0.65 0.76 0.75 1.07 1.03  Potential E T (mm/day) 2.8 5.6 3.9 4.3 4.9 5.9 5.4 4.7 5.5 4.0 4.2 3.5 3.9 4.0  E (mm/day) 3.0 5.4 5.5 5.0 6.3 6.1 6.9 5.7 5.7 4.6 4.0 3.4 4.2 4.8 p  Coefficient 0.93 1.04 0.71 0.86 0.78 0.97 0.78 0.82 0.96 0.87 1.05 1.03 0.93 0.83  Coefficient between Potential E T and P a n Evaporation  Evaporation coefficients are ratios between E T (actual or potential) and the evaporation rate ( E p ) . In this study, potential E T was used. E p was measured in the studied field by using the U . S . Class A pan. T h e potential E T was computed by using the Penman method. The computed evaporation coefficients are presented i n Table 4.3. T h e mean of the evaporation coefficients was 0.87 and the standard deviation was 0.12. This is consistent with the values obtained by Lake and Broughton (1969). Since potential E T was used i n the above computation, crop factors did not affect the evaporation coefficients.  Thus the variance might have been resulted from the effects of some other  factors such as the wind speed and direction, the temperature of the air and soil, the color of the pan, etc.  Results and Discussion  58  The results show that there is a close relationship between the pan evaporation and the (potential) E T rates. As the pan was inexpensive and easy to operate, evaporation from the pan is considered to be a suitable index for qualifying the amount of water removed from the soil.  4.7  Drainable Porosity  4.7.1  Soil Drainable Porosity of Different Regimes  In the undrained regime (D), the water table was almost always at or close to the soil surface during the rainy season. Surface ponding occurred very often. Thus, only the drainable porosity of the subsurface drained regimes was calculated. Since the two subirrigated regimes (B and C ) had very similar water table fluctuation patterns, the computation of the drainable porosity was limited to regimes A and B . Deep seepage for the studied soil varies from 0.005 to 0.02 m/day.  These values  were obtained from the water table drawdown curves (below the drains' level) during the summer months. It is believed that E T has no effect on the water table drawdown when the water table drops below the drains' level (1.1m) as the capillary fringe of this soil is only 20 cm (Chao, 1987). Deep seepage is the dominant factor of the water table drawdown. In the winter, however, the lowering of the ground water table is mainly due to the removal of water by the drainage system as the E T values are quite low and the water table is above the drains. Since this study was concentrated on the rainy season, deep seepage is ignored in the calculation of soil drainable porosity. Only typical rainfall events were selected.  The maximum, minimum and mean drainable porosity, and the  standard deviation (Std) of regimes A and B are presented in Table 4.4. For both regimes A and B , the drainable porosity computed from the water table rise is lower than that from the water table drawdown. However, t-test (see A p p e n d i x D )  59  Results and Discussion  Table 4.4: Soil drainable porosity, %  Regime Water Table Max Min Mean No. of D a t a Std  Rise 12.3 3.4 5.9 56 1.7  A Drawdown 12.2 2.0 6.0  51 2.2  B Rise 8.4 2.3 4.5 46 1.6  Drawdown 15.3 2.2 4.9 84 2.2  shows that there is no significant difference between the mean drainable porosity of the two (tpgjpgjj <  £0.05)-  The slight difference may be caused by the entrapment of air i n  the process of water table rise. In the cases of both water table rise and drawdown, f-test (see Appendix D ) shows that there is a significant difference between the drainable porosity of regimes A and B  (t >  £0.05)-  These phenomena indicate that subirrigation decreases the drainable porosity  of the soil. Subirrigation adversely affects the soil drainable porosity due to several reasons. One is the transportation  and decomposition of the soil fine particles (Chao, 1987).  The  irrigation water contains considerable amount of clay and silt (Ravina, 1982). The fine particles may also come from the deterioration of the soil. Under subirrigation, the water table was maintained at high position, some soil aggregates might be degraded. The fine particles are transported by the upward flow of water during subirrigation. Some of them may deposit i n the large pores between the aggregates and results i n a massive soil. The type of pores is closely related to the soil structure.  In the massive soil, the  soil structure is deteriorated, and smaller aggregates are prevalent. The volume of small storage pores increases, while the volume of large pores decreases.  A s the soil drain-  able porosity is closely related to the proportion of large pores, decreased large pores  Results and Discussion  60  results in reduced soil drainable porosity. Large pores are most useful for water transmission purpose. Thus associated with the reduced drainable porosity, a lower hydraulic conductivity is also expected. The soil drainable porosity computed in this study has the same variation trend as reported by Chao (1987) for the same soil, but the magnitudes are smaller. Chao obtained the drainable porosity in laboratory with undisturbed soil columns. The average drainable porosity at a tension of 120 cm of water for regimes A , B , C and D was 9%, 7%, 5% and 9% respectively. The average values obtained i n this study for regimes A and B are 5.9% and 4.7% respectively.  4.7.2  Drainable Porosity and Water Table Height above the D r a i n  The soil drainable porosity of regimes A and B computed using Equation 2.4, and the water table rise and drawdown data is plotted against the water table height above the drain (see Figure 4.21, 4.22). For both regimes A and B , there is a trend that the soil drainable porosity decreases with the water table height above the drain, i.e., increases with the depth from the soil surface to the water table. In the case of water table drawdown, the correlation between the water table height and the drainable porosity can be expressed by negative exponential equations.  For  regimes A and B , the equations can be written as the follows. Regime A : / = 26.59e -2.902F ( r = 0.493, n = 49)  (4.11)  / = 15.32e -l.685.ff/_2 (r = 0.403, n = 82)  (4.12)  2  Regime B : 2  Where  Results and Discussion  61  Regime A  ?vt  '1  c  0  2  4  6  8  10  12  14  16  Drainable porosity (%)  Figure 4.21: Water table height and drainable porosity based on water table drawdown.  Results and Discussion  62  Regime A 1 -i to  c 5 i_  T3  0.8-  9  > O o T  x:  0.6-  OS 9  -Q O  0.4-  O  3:  0.2  i 2  6  8  Drainable p o r o s i t y  10  T"  -1  12  14  12  14  (%)  Regime B  1 -i CO  c  s  0.8-  T3 9  > O Xt 5O  0.6  9 9  Xt O  0.4-  o 0.2  i 2  r i i 6 4 8 Drainable porosity  ~T~ 10  (%)  Figure 4.22: Water table height and drainable porosity based on water table rise.  Results and Discussion  /  =  H  — water table height above the drain in m.  63  soil drainable porosity in %;  In the case of water table rise, no significant correlation between soil drainable porosity and the water table height is found. This may have been resulted from the storage of rainfall water and air entrapment i n the upper soil layer.  As the water table was at  different positions previous to each rainfall, different amount of water was stored in the soil above the water table. For the same amount of rainfall, various water table rises are expected.  Thus, it can be concluded that to estimate soil drainable porosity by using  the water table drawdown condition may be more reliable than that from the case of the water table rise. Taylor (1960) reported that soil drainable porosity was not a constant, but varied with the water table depth. Bhattacharya and Broughton (1979) also obtained a strong dependence of drainable porosity on the water table depth. They found that drainable porosity was curvilinearly related to the water table depth and the type of relations were different for the sand and clay soils.  4.8  E r r o r Sources  Almost all the data used in the computations of the soil drainable porosity were measured by experiment. T h e equations used were empirical. T h e possible errors are resulted from all these measurement procedures and depend upon the suitability of the formulae to the local conditions.  Results and Discussion  4.8.1  64  Precipitation  Trie rainfall is recorded by the automatic recorder set up i n the field and traced into the computer with a digitizer. There may be some errors i n the recording and digitizing.  4.8.2  Evapotranspiration  As evapotranspiration ( E T ) is one of the important components i n the soil water balance, all the error sources in the computation of the potential E T will contribute to the errors in the estimation of the drainable porosity.  Net Radiation As indicated by Penman (1956b), solar radiation term is a considerably important factor in the computation of the potential E T . Errors i n the estimation of the net radiation include the computation of extraterrestrial radiation, measurement of global solar radiation, possible sunshine ratio, reflection coefficient (albedo), vapor pressure, etc. For example, Merva and Fernandez (1985) reported that when the global solar radiation varied for 20%, it caused about 30% of the potential E T change, the percent of sunshine caused about a 11.5% change i n the potential E T when it was varied by 20%. The change of albedo negatively affected the potential E T with a m a x i m u m variation of about 8%. In this study, the energy storage by the soil was assumed to be zero. In actual practice, more or less, certain amount of the heat energy would have been transferred into the soil.  W i n d Speed W i n d term is not a very important component in the computation of potential E T . Merva and Fernandez (1985) reported that a variation of plus or minus 20% of the wind speed  Results and Discussion  65  caused less than 2.5% variation i n the potential E T . In this study, it is found that, when the wind speed varied from 80 k m / d a y to 110 k m / d a y (i.e. 38% change), the potential E T changed about 9%.  Temperature In many cases, as in this study, the daily mean temperature was obtained by simply averaging the daily maximum and minimum temperature.  This might arise some errors  because the time factor was not taken into consideration. It should also be emphasized that, the potential E T was assumed equal to the actual E T during the study period (from late fall to early spring).  Although this is true for  most of the cases, there still may be some slight difference between the two, particularly when the ground water table is at a greater depth.  4.8.3  Surface runoff and deep seepage  Although the rainfall i n the L F V occurs i n low intensity and long duration, and the land is quite flat, sometimes the rainfall intensity may exceed the infiltrability of the soil, particularly during heavy storms. W i t h o u t considering the runoff factor, the drainable porosity computed may be lower than the actual value. As i n many other subsurface drainage researches, deep seepage was ignored. This also results i n lower drainable porosity values.  4.8.4  Water table height  T h e water table height of each regime was only measured at midway between the drains. There may be some spatial variance i n the water table positions.  Results and Discussion  4.8.5  66  Drainage flow rate  The drainage flow rate in this study was measured randomly from 1985 to 1987 at different times of a year. T h e n a correlationship was established between the water table height above the drain and the drainage flow rate. The drainage discharge at any time of the four year period was calculated based on this relation. There may be some errors i n the computation of the drainage discharge.  Chapter 5  CONCLUSIONS A N D SUGGESTIONS  5.1  Conclusions  The experiments were carried out to study the effects of subsurface drainage and subirrigation on the soil drainable porosity and to establish the relationship between the drainable porosity and the water table height above the drain. Soil drainable porosity was determined by using the soil water balance approach. The effect of evapotranspiration ( E T ) was taken into consideration. Several methods for E T estimation were evaluated and the Penman method  Avas  used i n this study. From the experiments, the following  conclusions are made. 1. Total precipitation during the off-season always exceeds evapotranspiration ( E T ) in the Lower Fraser Valley of British Columbia. Subsurface drainage is found to be an effective method to remove the excess water from the crop root zone. During the growing season, there are periods of water deficits.  Supplemental irrigation  is required for profitable crop production. Subirrigation can be used i n this area but the result indicates that adverse effects on soil hydraulic properties may be expected. 2. Subsurface drainage removed the excess water in the soil and altered the water table fluctuation patterns. The study shows that, during the rainy season, water tables i n the drained regimes remained at or below 50 cm from the soil surface. This is very critical i n temperate areas like the Lower Fraser Valley i n which the total 67  Conclusions and Suggestions  68  growing season is short. W i t h the lowered water table, the soil can be worked on earlier in the spring and the growing period is extended. Increased crop production can be expected. 3. The drainable porosities of regimes A and B were determined by using water balance analysis. For both of the regimes, the average drainable porosity from the water table rise is slightly higher than from water table drawdown, but the difference is not significant. T h e drainable porosity of regime A (5.9%) is significantly higher than that of regime B (4.7%), indicating that subirrigation has an adverse effect on the soil drainable porosity. 4. Soil drainable porosity is not a constant but varies with the water table depth. In the case of water table drawdown, this dependence can be expressed by the negative exponential equation. In the case of water table rise, the correlationship is not significant but still there is a trend that drainable porosity decreases with the increases of water table height. 5. In the computation of soil drainable porosity, the effect of evapotranspiration ( E T ) was taken into consideration.  During certain period in the winter, E T accounts  for up to 30% of the water table drawdown. The potential E T rate was estimated by two methods: Penman and Hargreaves. Although the complexity of these two equations varies considerably, they give very similar E T values. W h e n the climatic data required by Penman equation are not all available, Hargreaves method can be used. 6. A close relationship between pan evaporation and the potential E T was found i n this study. T h e average evaporation coefficient was 0.87.  Conclusions and Suggestions  5.2  69  Suggestions  Based on this study, the following recommendations are suggested.  1. A systematic experiment should be carried out to directly measure the evapotranspiration rate. Thus the accuracy and reliability of the Penman and Hargreaves methods can be determined. 2. Surface runoff of the drainage area needs to be measured so that the drainable porosity of the undrained regime can also be estimated. 3. Continued measurements  of drainage flow rate will supplement the estimation of  the drainable porosity. 4. Replications of each regime will help the statistical analysis of the results.  Bibliography  [1] Allen, R . G . 1986. 112(4):348-368.  A Penman for all seasons. J . Irri. and Drainage D i v . A S C E  [2] A l - S h a ' L a n , S . A . and A . M . A . Salih, 1987. Estimates of potential evapotranspiration in extremely arid areas. J . Irri. and Drainage E n g . 113(IR3):565-574. [3] Bernstein, L . , 1974. Crop growth and salinity. In: J a n van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:39-54. Amer. Soc. Agronomy. Madison, W i s . [4] Bhattacharya, A . K . and R . S . Broughton, 1979. Variable drainable porosity i n drainage design. J . Irri. and Drainage E n g . 105(IRl):71-85. [5] Black, T . A . , 1990. Class notes for the course: Bio-Meteorology (SOIL 414). Department of Soil Science, University of British Columbia, Vancouver, B . C . , Canada. [6] Bournival, P., S. Prasher, B . V o n Hoyningen Huene, R . S . Broughton, 1987. Measurements of head losses in a subirrigation system. Trans. A S A E . 30(1):181—186. [7] Bouwer, H . , 1974. Developing drainage design criteria. In: J a n van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:67-80. Amer. Soc. Agronomy. Madison, W i s . [8] Bouwer, H . and R . D . Jackson, 1974. Determining soil properties. In: Jan van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:611-666. Amer. Soc. Agronomy. Madison, W i s . [9] B u r m a n , R . D . , P . R . Nixon, J . L . Wright, and W . O . P r u i t t , 1980. Water requirements. In: Jensen (Ed.) design and operation of farm irrigation systems. A S A E Monograph No. 3. 189-225. St. Joseph, Michigan. [10] Campbell, K . L . , J.S. Rogers and D . R . Hensel. 1977. Watertable control for potatoes in Florida. Trans. A S A E . 21(4):701-705. [11] Chao, E . , 1987. Water Table Depth Simulation for F l a t Agricultural L a n d under Subsurface Drainage and Subirrigation Practices. A thesis submitted to the University of British Columbia, Vancouver, British Columbia, i n partial fulfillment of the requirements for the degree of the Master of Applied Science.  70  Bibliography  71  [12] Chieng, S.T., 1983. Basics of drainage design. In: Proc. of British C o l u m b i a (B.C.) Drainage Workshop, B . C . Ministry of Agriculture and Food. [13] Chieng, S.T., 1987. Subirrigation and soil hydraulic properties. C a n . Soc. Agri. E n g . Paper No. 87-308. [14] Chieng, S.T., 1989. Personal communications. 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Availability of soil water to plants as affected by soil moisture content and meteorological conditions. Agron. J . 54:385-390. [21] Donnan, W . W . and G . O . Schwab, 1974. Current drainage methods i n the U S A . In: J a n van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:93-114. Amer. Soc. Agronomy Madison, W i s . [22] Driehuyzen, M . G . , 1983. Boundary Bay water control project. In: Proc. of British Columbia ( B . C . ) Drainage Workshop, B . C . Ministry of Agriculture and Food. [23] Eagleman, J . R . , 1967. P a n evaporation, potential and actual evapotranspiration. J . Applied Meteorology. 6:482-488. [24] Elliott, R . L . , E . L . Johns and P . A . Weghorst, 1989. Estimating evapotranspiration with a knowledge-based system. A S A E Paper No. 897575. [25] Erie, L . J . , O . F . French, and K . Harris, 1965. in Arizona. Tech. B u l l . 169:5-7.  Consumptive use of water by crops  [26] French, B . E . and J . R . O'Callaghan, 1966. 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H y -  [48] Penman, H . L . 1948. Natural evaporation from open water, bare soil, and grass. Proc. Roy. Soc. London A193:120-145. [49] Penman, H . L . 1956a. Estimating evaporation. Trans. Amer. Geophys. Union. 37:4350. [50] Penman, H . L . 1956b. Evaporation: 1:9-29. Discussion: 87-97, 151-153.  A n introductory survey. Neth. J . A g r i . Sci.  [51] Prasher, S.O., 1982. Examination of the design procedures for drainage/subirrigation systems in the Lower Fraser Valley, British Columbia. Thesis submitted to the University of British Columbia, Vancouver, Canada, i n partial fulfillment of the requirements of the degree of Doctor of Philosophy. [52] Raadsma, S., 1974. Current drainage practice in flat areas of humid regions in E u rope. In: J a n van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:115-140. Amer. Soc. of Agronomy. Madison, W i s . [53] Ravina, I., 1982. Soil salinity and water quality. In: C R C Handbook of Irrigation Technology. V o l . I. [54] Reeve, R . C . and N . R . Fausey, 1974. Drainage and timeliness of farming operations. In: Jan van Schilfgaarde (Ed.) Drainage for Agriculture. Agronomy Monography 17:55-66. Amer. Soc. of Agronomy. Madison, W i s . [55] Ripple, C D . , J . Rubin, and T . E . A . van Hylkama, 1972. Estimating steady-state evaporation rates from bare soils under conditions of high water table. U . S . Geol. Survey, Water Supp. Pap.2019-A.  Bibliography  74  Samani. Z . A . and M . Pessaraldi, 1986. Estimating potential crop evapotranspiration with m i n i m u m data in Arizona. Technical notes. Trans. A S A E . 29(2):522-524. Saxton, K . E . , H . P . Johnson, and R . H . Shaw, 1974. Watershed evapotranspiration estimated by the combination method. Trans. A S A E . 17(4):668-672. Seliro, I.S., D . M . Brown and K . M . K i n g , 1971. Estimating of net and solar radiation. Can. J . Plant Sci. 51:35-39. Shaw, E . , 1983. Hydrology i n Practice. V a n Nostrand Reinhold ( U K ) C o . L t d . 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Soc. of Agronomy. Madison, W i s . Wesseling, J . , 1974b. Subsurface flow into drains. In: Drainage Practice and A p p l i cations. Chapter 8, p p l - 5 8 . International Inst, for L a n d Reclaimation and Improvement. Wageningen, The Netherlands, Publication 16. W u, G . , 1988. Sensitivity and Uncertainty Analysis of Subsurface Drainage Design. A thesis submitted to the University of British Columbia, Vancouver, British Columbia, i n partial fulfillment of the requirements for the degree of Master of A p plied Science. T  Zhang, W . , 1983. Non-steady State G r o u n d Water Flow Calculation and Ground Water Resource Evaluation (in Chinese. Science Press. Beijing, C h i n a .  Appendix A  COMPUTATION OF T H E PARAMETERS REQUIRED BY P E N M A N AND HARGREAVES  EQUATIONS  To solve the Penman and Hargreaves equations for the estimates of potential E T , numerous input parameters are required. The following sections discuss the computation of these parameters. These calculations are after Hansen et al (1980) unless specified.  A.l  Slope of the Saturation  V a p o r Pressure-temperature Curve  A = 33.86[0.05904(0.00738r + 0.8072) - 0.0000342] 7  (A.13)  where  A  =  slope of the saturation vapor pressure-temperature curve for T> — 23°C in m b a r / ° C ;  T A.2  =  mean air temperature i n ° C .  Psychrometric Constant  The psychrometric constant depends on the atmospheric pressure and temperature.  Its  thermal dynamic value can be obtained from:  7 = - ^ T ' 0.622A  76  v  (A.14) '  Computation  of the Parameters  Required  by Penman  and Hargreaves  Equations  77  where  7 C  p  =  psychrometric constant;  =  specific heat of the air at constant pressure.  C varies with the atp  mospheric pressure ranging between 0.239 and 0.241 c a l / g / ° K (Jensen, 1973). 0.240 c a l / g / ° K is used i n this study; P  =  A  =  0.662 A.3  =  atmospheric pressure i n mbar; P  =  1013 - 0.1055 E L  EL  =  elevation i n meters.  latent heat of vaporization of water i n cal/g; A  =  595.9 - 0.55T  T  — average air temperature i n °C.  ratio between the molecular weight of water and dry air (Jensen, 1973).  V a p o r Pressure  Saturation vapor pressure, e „ : e, = ^ ( e + e ) a  (A. 15)  fc  Where  e e  t  a  e{,  =  average saturated vapor pressure i n mbar;  =  saturated vapor pressure at mean maximum temperature i n mbar;  =  saturated vapor pressure at mean minimum temperature i n mbar.  =  33.8639[(0.00738r + 0.8072) 8  a  0.000019(1.87; + 48) + 0.001316]  (A.16)  Computation of the Parameters Required by Penman and Hargreaves Equations  e  b  =  33.8639[(0.00738T + 0.8072)  -  8  fc  0.000019(1.8T + 48) + 0.001316] fc  (A.17)  where T and T\> are the mean maximum and m i n i m u m temperatures respectively in °C. a  M e a n actual vapor  pressure:  e  Bd  =  33.8639[(0.00738T + 0.8072) d  8  -  0.000019(1.8T + 48) + 0.001316]  (A.18)  d  Where T  d  is the dew point temperature i n ° C . W h e n T  d  is not available, it can be  calculated by the following equation (James, 1988):  m T  d  4 2 9 . 4 - 237.31ne -  e  TO  I n c . - 19.08  m  = e,{RH/100)  ( A  -  1 9 )  (A.20)  where e  m  =  vapor pressure of the air in mbar;  e„  =  saturation vapor pressure at the average temperature in mbar, it can be computed by using Equation A . 1 9 - A . 2 1 .  RH A.4  — relative humidity i n %. W i n d Speed a n d W i n d Speed Coefficients  In the Penman equation, wind speed is the one at 2 meters above the ground. If the measurement is made at a height different than 2 meters, then the wind speed can be  78  Computation of the Parameters Required by Penman and Hargreaves Equations  79  Table A . 5 : W i n d speed coefficients. W 0.0106  Location Mitchell, Nebraska  Reference crop alfalfa  0.0115 0.0062  Kimberly, Idaho Penman  alfalfa short grass  2  1.10 0.75 1.00  converted by using the following formula: U2=u (^) hz 0  (A.21)  2  z  where u  — wind speed at any height hz i n k m / d a y ;  z  h  — height of anemometer above ground in meters.  z  W i n d speed coefficients Wi and u> should be determined by experiment. 2  Some em-  pirical values are listed i n Table A . 5 (Hansen et al, 1980):  A.5  Net Radiation  Net radiation is the amount of solar radiation that reaches to the earth surface minus the reflected and reradiated energy. It can be directly measured by using hemispherical net radiometer or it can be estimated from the net short wave and net long wave radiation (Jensen, 1973): Rr, = (1 - a)R - R s  where  R  n  =  net radiation i n ca,l/cm /day; 2  b  (A.22)  Computation of the Parameters Required by Penman and Hargreaves Equations  a  =  80  the short wave reflectance or albedo. For free water surface, a = 0.05 (Shaw, 1983); for a green growing crop, a = 0.23 (Burman et cd, 1980);  R  e  Rb  =  global solar radiation i n c a l / c m / d a y ;  =  the net back or outgoing thermal radiation (as described i n Equa-  2  tion A.25 i n Appendix A ) i n c a l / c m / d a y . 2  If the solar radiation data are not available, net and/or solar radiation can be estimated from the extraterrestrial radiation (R )a  T h e extraterrestrial radiation is the  daily total undepleted solar energy incident on a horizontal surface outside the earth's atmosphere (Jensen, 1973; Gates, 1962). Gates stated that the extraterrestrial radiation is dependent only upon the latitude of the station and the time of the year. James (1988) proposed that R be estimated by the following equations. a  R  a  =  1.26714(^)[fc.-^sin(*)sin(*) + cos ( $ ) cos (6) sin (h )] e  h r  d0  ve  =  12.126 - 1.85191(10)  =  0.98387 - 1.11403(10)- (J)-f 5 . 2 7 7 4 ( 1 0 ) - ( J ) -  -3  A B S ( $ ) + 7.61048(10)" ($) 5  4  6  2.68285(10) (J) + 3.61634(10)- (J) _8  h  s  — =  n  _ 1  on  — ( 0 . 0 0 6 9 1 8 - 0.399912 cos 9 + 0.070257 sin 6 7T  0.006758 cos 26 + 0.000907 sin 26 0.002697 cos 30 - 0.001480 sin 36) 6  where  =  4  cos ( — tan $ tan 6) 1  8  3  2  0.9863(J - 1)  2  Computation of the Parameters Required by Penman and Hargreaves Equations  R  =  extraterrestrial radiation i n m m / d a y ;  hjo  =  daytime hours at zero declination i n hours;  r  =  radius vector of the earth;  h,  =  sunrise to sunset hour angle i n degrees;  $  =  location latitude i n degrees ( $ is positive for north latitudes and  a  ve  negative for south latitudes); 8  =  declination of the sun in degrees;  J  =  days from J a n . 1 (e.g., J — 1 for J a n . 1, J — 2 for J a n . 2,..., J = 365 for Dec. 31);  0  =  day of year expressed i n degree's (i.e., 6 = 0° is Jan. 1, 8 = 9 0 ° is A p r . 2, 6 = 180° is J u l y 2, ...).  There is a unique relationship between extraterrestrial and solar radiations, and the ratio between actual and possible sunshine hours. Penman (1948) found that this relationship can be written as: = (0.18+ 0 . 5 5 ^  (A.23)  where  R„ N lN a  R  a  = v  Solar radiation, in c a l / c m / d a y ; 2  — ratio between actual and possible sunshine hours; =  extraterrestrial radiation i n c a l / c m / d a y . 2  For a specific area, the slope and intersection of the above regression hne needs to be adjusted for better estimate results of solar radiation. Another method to estimate solar radiation from extraterrestrial radiation is given  81  Computation of the Parameters Required by Penman and Hargreaves Equations  by Hargreaves and Samani (1982). The equation can be written as:  R = K xR xTD  (A.24)  05  e  T  a  where  R  =  global solar radiation in c a l / c m / d a y ;  =  extraterrestrial radiation in c a l / c m / d a y ;  TD  —  difference between maximum and m i n i m u m temperature i n ° C ;  KT  —  calibration coefficient.  s  R  a  2  2  For a coastal area with latitude of about 49°,  i^r%0.160 (Samani and Pessarakli, 1986). To estimate the net radiation from the global solar or extraterrestrial radiation, Brunt (James, 1988) suggested the following equation. It was also used by Penman. R  n  =  0.80i2 — Rb  =  0.80#, - 2 . 0 1 ( 1 0 ) ( T + 273.16)  s  - 9  4  (0.56 - 0 . 0 9 2 y i ^ ) ( 0 . 1 0 + 0 . 9 0 ^ )  (A.25)  A p  where  R  n  =  net radiation i n c a l / c m / d a y ;  R  B  =  solar radiation;  T ed t  = =  2  average air temperature i n ° C ; saturation vapor pressure at dew point temperature i n mbar.  It can  be calculated by Equation A.18. W h e n Td is not available, it can be estimated by Equation A . 19.  82  Appendix B  COMPUTATION  B.l  OF SOLAR  RADIATION  Extraterrestrial Radiation  The calculation of extraterrestrial radiation of Vancouver was carried out with the method described i n Chapter 2 and A p p e n d i x A . . T h e following tables illustrate the cell addresses in L O T U S  123 (Release 2) spreadsheets, their corresponding parameters, and the cal-  culation formulae by an example. Cell addresses: A  =  day of the year, J ;  B  =  daytime hours at zero declination, h^Q, in hours;  C  =  radius vector of the earth, r y e !  D  =  day of the year, 6, expressed i n degrees (6 = 0° for J a n . 1,0 = 90° for A p r . 2, 6 = 180° for J u l y 2, ...);  E  =  day of the year, 6, i n radians;  F  =  declination of the sun, 6, i n degrees;  G  =  declination of the sun, S, in radians;  H  =  sunrise to sunset hour angles, h„, i n radians;  I  =  extraterrestrial radiation, R , i n mm/day. a  Calculations:  83  Computation of Solar Radiation  A  4  =  1  B  4  =  1 2 . 1 2 6 - 1 . 8 5 1 9 1 * 1 ( T ( - 3 ) * @ A B S (49.25)47.61048*1(T(-5)*(49.25) 2 A  (49.25 is the latitude of the U B C weather station) C  =  4  0.98387-1.11403*10"(-4)*A +5.2774*10 (-6)*A ^2-2.68285*10' A  4  4  (-8)*A '3+3.61634*l(r(-ll)*A '4 4  4  D  4  =  0.9863*(A -1)  E  4  =  @PI*D /180  F  4  =  (180/@PI)*(0.006918 - 0 . 3 9 9 9 1 2 * @ C O S ( E ) - r - 0 . 0 7 0 2 5 7 * @ S I N ( E ) -  4  4  4  4  0.006758*@COS(2*E )+0.000907*@SIN(2*E )4  4  0.002697*@COS(3*E )-0.001480*@SIN(3*E )) 4  4  G  4  =  +F *@PI/180  H  4  =  @ACOS(-(@TAN(49.25*@PI/180))*@TAN(G ))  I  4  4  4  = (1.26714*B /C "2)*(H *@SIN(49.25*@PI/180)*@SIN(G )+ 4  4  4  4  @COS(49.25*@PI/180)*@COS(G ) * @ S I N ( H ) ) 4  B.2  4  G l o b a l Solar and Net Radiations  Cell addresses: A  =  day of the year;  B  =  extraterrestrial radiation, R , i n m m / d a y ;  C  =  actual and possible sunshine hour ratio,  D  =  global solar radiation, j^,, i n m m / d a y ;  E  =  mean temperature i n ° C ;  a  N /N ; a  p  Computation of Solar Radiation  85  F  =  saturation vapor pressure at dew point temperature i n mbar;  G  =  net radiation, R , in m m / d a y ;  H  =  net radiation, R , in c a l / c m / d a y .  D  =  G  = 0.77*D -2.0in0 -9*(E +273.16)"4*(0.56-  n  2  n  B *(0.23+0.52*C ) 4  4  A  4  4  0.092*(F )"0.5*(0.10+0.90*C 4  H  =  4  )  G *(595.9-0.55*E )/10 4  4  Note: The subscripts used in the above expressions indicate the row numbers of the L O T U S ' s spreadsheet.  Appendix C  COMPUTING OF THE POTENTIAL EVAPOTRANSPIRATION  The following tables show the computation processes and results of the daily potential ET by Penman and Hargreaves methods. The computation is accomplished by using LOTUS 123 (Release 2). C.l  Computing of Potential Evapotranspiration  Cell addresses: A  =  day of the year;  B  =  saturation vapor pressure at dew point temperature, -E j, in mbar;  C  =  saturation vapor pressure, E„, in mbar;  D  =  daily mean temperature in °C;  E  =  global solar radiation, R in mm/day;  F  =  net radiation, Rn, in cal/cm /day;  G  =  wind speed at 10 meters above the ground in km/day;  H  =  wind speed at 2 meters above the ground in km/day;  I  =  slope of saturation vapor pressure—temperature curve, A , (de/dT) in  sc  ei  2  mbar/°C; J  psychrometric constant;  K  potential evapotranspiration by Penman method in cal/cm /day; 2  86  Computing  of the Potential  Evapotranspiration  87  L  =  potential evapotranspiration by Penman method i n mm/day;  M  =  potential evapotranspiration by Hargreaves method i n mm/day;  Calculating processes: H  =  G *(2/10) 0.2  I  =  (33.8639*(0.05904*(0.00738*D +0.8072)*7-0.0000342))  J  =  0.24*(1013-0.1055*3)/(0.622*(595.9 - 0 . 5 5 * D )  A  6  6  6  3 (m) is the elevation of the U B C weather station. K  =  (I /(I +J ))*F +(J /(I +J ))*15.36 *(1+0.0062*H )*(C -B )  L  =  K *10/(595.9-0.55*D )  M  =  0.6l35*(D +17.78)*E  C.2  6  6  6  6  6  6  6  6  6  6  6  6  6  6  Computed Potential Evapotranspiration Values  Daily, monthly and annual potential evapotranspiration ( E T ) values computed by using Penman and Hargreaves methods are given in Table C.6 and C.7.  Computing of the Potential Evapotranspiration  88  Table C.6: Potential E T computed by using Penman method(1985-1988). 1985 (Penman) Date Jan 1 0.2 2 -0.3 3 0.1 4 0.2 5 -0.3 6 0.1 7 0.1 -0.4 8 9 0.0 10 0.1 11 0.2 12 0.0 13 0.3 14 0.4 15 0.2 16 0.0 17 0.2 0.2 18 19 0.2 20 -0.1 21 0.2 22 0.1 23 0.3 24 0.2 25 -0.2 0.2 26 27 0.3 28 0.3 29 -0.1 30 0.5 31 0.0 Sum 3.2 Total  Feb 0.4 0.7 0.3 0.5 0.3 0.5 0.5 0.4 0.5 0.6 1.0 1.0 0.8 0.9 0.8 0.9 0.6 0.8 0.7 0.8 0.4 0.6 0.6 0.9 1.1 0.8 0.9 1.0  19.3  Mar 1.4 1.4 0.9 0.8 1.2 1.2 1.0 1.0 1.2 1.2 1.3 1.3 1.5 1.3 1.3 1.8 1.5 1.3 1.3 1.4 1.5 1.8 1.6 1.2 1.0 1.6 1.5 1.7 1.4 1.2 1.2 41.0  Apr 1.5 1.4 1.3 1.5 2.1 2.3 2.7 2.6 2.7 1.8 1.4 2.3 1.5 2.0 2.3 2.3 2.2 2.8 2.8 2.5 2.8 2.0 2.9 2.6 2.1 1.5 2.7 2.4 2.5 2.7 66.2  May .2.5 3.1 2.8 3.3 2.4 2.7 3.7 2.9 3.5 2.4 3.7 3.6 2.2 3.3 3.9 4.6 5.5 3.4 3.0 2.9 3.5 3.7 2.9 3.4 3.7 4.1 3.6 2.8 1.9 2.5 4.3 101.8  Month Jun Jul 4.8 4.6 3.8 6.1 2.7 6.5 4.1 6.0 3.8 5.1 2.5 5.5 2.9 5.9 4.4 6.5 4.9 6.7 4.8 6.1 3.7 6.2 3.2 5.4 2.9 5.4 4.0 4.7 5.1 5.5 4.3 5.5 5.6 5.5 6.3 6.3 5.2 6.3 6.4 5.7 5.5 5.8 4.7 5.8 4.1 4.9 4.4 4.7 5.2 5.2 5.2 5.6 4.7 5.6 5.3 5.7 3.5 5.7 5.2 3.4 2.9 132.5 171.5 781.0  Aug 2.1 2.7 5.1 4.8 5.0 3.5 3.5 4.6 3.2 4.3 4.1 4.3 5.2 4.9 5.4 5.8 5.2 4.8 2.7 3.8 3.9 3.9 4.5 4.5 4.3 4.0 4.2 3.7 3.4 2.5 3.5 127.4  Sept 3.3 3.6 2.9 1.4 1.8 1.7 2.5 2.6 2.6 3.2 2.0 2.3 2.5 1.7 1.7 1.1 1.8 1.5 1.9 1.4 1.8 1.8 1.7 2.0 2.1 2.4 2.5 2.2 1.9 1.4 63.3  Oct 1.6 2.2 1.6 1.3 1.7 2.8 2.1 1.2 1.1 1.0 1.4 0.9 0.2 0.9 1.7 1.2 0.9 1.3 1.3 1.0 1.3 1.2 0.8 1.3 0.8 0.5 1.3 1.0 0.6 0.7 -0.2 36.7  Nov 0.6 0.6 1.0 1.1 0.3 0.4 0.6 0.7 1.6 0.6 0.2 0.1 0.2 0.1 0.9 1.1 0.6 0.1 0.9 0.5 1.2 0.0 0.0 .0.7 0.6 0.5 0.0 0.5 0.0 0.1 15.8  Dec -0.3 -0.2 0.1 0.1 0.3 0.2 0.4 -0.2 0.1 0.1 -0.2 -0.2 -0.2 0.1 -0.2 0.2 0.2 0.2 0.3 0.0 -0.1 0.2 0.1 0.2 0.0 0.3 0.3 -0.3 0.3 0.3 0.2 2.3  Computing of the Potential Evapotranspiration  89  1986 (Penman) Date Jan 1 0.2 2 0.4 3 0.3 4 -0.1 5 0.5 6 0.7 7 1.2 8 0.9 9 0.5 10 0.9 11 0.2 12 0.3 13 0.8 14 0.5 15 0.3 16 0.7 17 0.6 0.4 18 19 0.1 0.1 20 21 0.7 22 0.7 23 0.7 24 0.3 25 0.1 26 0.5 27 0.6 28 0.1 29 0.5 30 0.4 31 0.6 Sum 14.7 Total  Feb 0.6 0.6 0.7 0.4 0.3 0.0 0.0 0.4 0.3 0.5 0.9 0.6 1.1 0.7 6.8 1.0 0.8 0.5 0.5 0.9 0.8 0.6 0.6 0.8 1.2 1.2 1.8 1.1  19.7  Max 1.3 0.9 0.9 0.8 0.8 0.8 1.6 1.4 1.4 1.7 1.2 1.4 1.6 1.5 1.2 1.6 1.4 0.9 1.3 2.0 1.6 1.6 1.2 1.7 1.1 1.1 1.1 1.1 1.4 2.3 1.8 41.7  Apr 1.9 2.1 1.8 1.7 1.9 2.2 2.7 1.9 2.4 2.5 1.3 2.0 1.9 1.8 1.6 1.5 2.2 1.5 1.3 1.4 1.6 2.8 3.2 1.8 1.9 1.5 2.7 2.2 2.1 2.6 60.0  May 2.7 2.1 3.2 3.1 2.9 3.5 3.1 3.3 3.5 3.0 2.4 2.0 3.4 3.7 3.7 2.0 1.9 1.8 2.7 3.6 4.0 4.5 3.0 2.9 3.1 2.6 3.9 5.4 5.2 5.3 5.5 103.0  Month Jul Jun 2.4 5.0 4.7 5.0 3.5 4.9 4.8 3.6 3.7 4.4 3.4 5.2 5.3 3.3 3.9 4.5 3.2 4.7 3.0 5.5 2.5 5.3 3.5 5.3 4.1 6.3 3.6 3.9 3.1 2.1 3.5 1.9 2.3 2.6 4.4 3.0 3.0 5.0 3.7 5.1 3.9 5.1 3.1 3.8 4.1 4.6 4.6 4.3 5.2 3.6 3.8 3.5 3.7 5.6 4.2 3.8 2.5 4.3 4.7 4.2 4.2 125.0 120.0 739.1  Aug 5.3 5.1 5.2 4.4 4.8 5.1 5.8 5.5 5.8 3.6 2.8 3.6 4.4 4.6 4.6 4.3 4.1 4.7 3.9 4.7 4.9 4.5 3.7 4.5 4.4 4.7 4.2 3.1 2.0 2.5 3.2 134.0  Sept Oct 3.4 1.3 3.4 0.9 1.2 3.6 0.9 3.8 1.2 4.0 4.2 1.2 1.2 3.6 2.4 1.0 2.2 1.1 2.9 1.2 2.5 1.3 1.1 2.5 2.2 1.0 2.4 1.0 1.9 1.0 2.2 0.8 2.1 0.9 1.7 1.0 2.1 0.7 2.2 1.0 0.9 2.0 1.7 0.7 0.7 1.8 1.8 ' 1.3 1.9 1.1 0.7 1.8 1.1 0.9 1.1 0.8 1.4 0.8 0.9 1.5 0.4 71.4 30.2  Nov  0.5 0.5 0.5 0.6 0.5 0.6 0.3 0.9 0.5 0.9 -0.1 0.5 0.5 0.0 0.6 0.6 0.5 0.7 0.6 0.6 0.5 0.4 0.7 0.0 1.0 0.2 0.4 -0.1 0.4 0.6 14.4  Dec -0.4 -0.2 0.0 0.5 0.1 0.0 0.2 -0.3 -0.3 -0.4 0.3 0.3 0.4 0.3 0.3 -0.3 -0.4 0.4 0.5 0.4 0.3 0.6 0.2 0.1 0.5 0.4 0.3 0.5 0.4 -0.2 0.5 5.0  Computing  of the Potential  Evapotranspiration  90  1987 (Penman) Date Jan 1 0.4 2 0.5 0.5 3 4 0.3 5 -0.3 6 -0.1 7 0.0 8 0.0 9 0.9 10 0.9 11 0.7 12 0.4 0.3 13 14 0.2 0.5 15 16 0.5 17 0.3 0.2 18 0.4 19 20 0.5 21 0.2 22 0.4 0.4 23 24 0.5 0.5 25 0.4 26 27 0.7 28 0.7 29 0.6 30 0.8 31 0.5 Sum 12.8 Total  Feb 0.1  0.3 0.7 0.7 0.9 0.9 0.4 0.8 0.7 0.9 0.8 1.1 0.7 0.6 1.1 1.1 0.7 0.7 0.7 0.9 0.7 0.9 1.3 1.4 1.1 1.3 1.1 1.0  23.6  Mar ' Apr 1.0 2.8 3.4 0.7 0.7 1.5 1.1 1.7 2.1 0.9 2.1 1.3 1.0 1.8 1.1 2.6 1.4 1.5 0.8 2.3 2.1 1.1 2.2 1.1 1.4 2.3 1.2 2.4 1.9 1.3 2.7 1.4 1.4 2.6 3.0 1.3 3.2 1.5 2.6 1.7 2.2 1.7 2.1 3.0 3.6 1.7 3.2 1.7 3.3 1.5 2.2 3.5 1..7 5.1 2.1 2.6 2.3 3.6 2.0 1.6 2.2 44.6 j 78.5  Month May Jul Jun 3.0 5.9 4.6 2.9 3.7 4.7 2.1 5.0 3.8 2.2 3.8 5.1 4.0 4.2 2.1 4.3 4.0 4.3 4.4 5.2 3.4 4.9 2.6 2.7 4.5 4.2 2.6 5.2 5.3 3.0 5.2 2.8 3.6 2.9 6.2 3.0 3.1 5.8 3.8 3.6 5.9 5.0 4.0 5.4 4.6 4.2 . 4.6 3.3 3.6 5.5 4.9 4.3 4.8 5.3 4.0 5.7 4.0 4.5 4.6 2.5 4.3 5.7 2.8 4.2 5.0 5.1 3.8 4.6 4.3 4.4 4.6 5.4 4.3 6.0 3.1 3.5 6.3 3.5 4.3 2.8 5.9 3.3 6.2 5.0 2.9 6.7 5.6 2.4 7.1 4.9 4.0 4.2 j 116.2 138.7 139.7 832.8  Aug 5.0 5.1 5.1 5.2 4.1 4.9 5.1  5.1 5.1 2.8 4.9 3.7 1.7 3.9 3.2 3.8 4.0 4.4 3.3 4.4 4.1 4.2 4.7 5.2 5.1 3.6 4.4 3.7 3.6 4.6 4.7 132.7  Sept  Oct  Nov  4.8 3.7 2.8 3.2 3.6 3.6 3.5 3.2 2.9 3.4  2.3 2.1 2.2 2.0 1.7 1.7 1.6 1.5 1.7 1.6 1.5 1.3 1.1 1.2 1.1 0.9 1.0 0.9 0.8 1.0 0.9 0.6 0.8 0.9 0.7 0.5 0.8 1.0 0.7 0.7 0.7 37.5  0.5 0.7 0.7 0.6 0.4 0.6 0.9 1.1 0.7 1.2 0.6 0.6 0.8 0.4 0.5 0.1 0.6 0.7 0.7 0.5 0.8 0.6 0.6 0.9 0.4 0.3 0.0 -0.1 0.2 1.1  2.1  1.8 2.3 2.0 2.5 2.4 2.7 2.7 2.8 3.6 2.8 2.7 2.6 1.9 1.5 2.0 2.0 2.0 2.1 2.4 81.6  17.7  Dec 0.5 0.6 0.5 0.2 0.5 0.6 0.6 1.1 0.5 0.6 -0.1 -0.1 0.4 0.5 0.2 -0.1 0.3 -0.1 0.2 0.3 0.3 0.3 -0.2 0.4 0.0 0.1 0.5 0.4 0.3 0.0 -0.1 9.2  Computing of the Potential Evapotranspiration  91  1988 (Penman) Date Jan 1 -0.2 2 -0.2 3 0.3 0.7 4 0.9 5 6 0.7 7 0.3 8 0.5 0.5 9 10 0.5 11 0.1 12 0.7 0.5 13 14 0.9 15 0.9 0.4 16 17 0.5 0.2 18 0.6 19 20 0.1 21 0.6 22 0.3 0.4 23 24 0.6 25 0.3 0.5 26 27. • 0.8 28 0.5 29 0.5 30 0.7 31 0.4 Sum 14.5 Total  Feb Mar 0.7 1.0 0.7 1.2 0.6 1.5 1.2 0.7 0.6 1.2 0.5 1.6 0.6 1.3 0.5 1.0 1.6 0.8 0.6 1.7 1.4 0.7 1.5 1.0 1.0 1.3 0.8 1.7 0.6 2.0 2.1 0.8 0.9 1.8 0.9 2.0 0.8 2.3 0.8 1.7 0.9 1.9 0.7 1.3 0.9 1.7 1.2 1.6 1.4 1.3 0.8 1.7 0.8 ' 2.4 1.0 1.4 1.7 1.8 1.6 22.3 49.5  Apr 1.4 1.5 2.3 2.5 1.3 2.3 2.4 2.3 2.5 2.7 2.4 3.1 2.0 2.5 2.6 1.7 1.6 2.8 3.2 3.7 3.4 2.7 2.6 2.4 2.0 3.4 3.1 2.3 2.3 2.6 73.6  May 2.2 1.7 3.0 3.3 3.3 2.8 3.9 4.1 2.7 3.0 3.6 4.4 2.3 3.9 3.0 2.4 2.8 1.9 3.4 4.3 4.8 2.4 2.5 4.1 4.2 2.6 2.2 3.9 4.2 4.1 3.6 100.6  Month Jul Jun 2.5 2.6 2.1 5.1 4.5 4.5 3.8 3.9 2.7 4.3 3.0 4.0 2.9 5.0 4.7 5.5 5.7 3.9 3.1 4.3 2.4 4.6 5.2 2.1 5.3 4.6 5.8 4.7 6.0 4.8 4.8 5.3 2.5 5.3 5.2 5.7 4.5 6.6 6.4 5.5 3.3 5.1 4.8 3.9 3.8 5.5 5.1 5.7 5.6 6.7 4.1 5.6 4.8 5.5 4.1 4.3 5.2 4.6 3.4 5.2 4.8 127.3, 149.2 799.1  Aug 5.4 5.3 5.7 5.6 3.0 3.1 4.6 3.0 3.8 4.1 4.7 4.6 4.5 3.9 1.7 2.8 3.5 4.1 3.9 3.7 4.0 4.3 4.5 4.9 4.2 4.1 4.2 4.8 4.5 3.8 3.9 128.2  Sept 4.1 4.7 4.9 3.8 3.7 2.5 3.8 2.8 2.7 3.0 3.1 3.3 3.3 3.6 1.8 2.6 2.2 1.4 1.5 2.3 2.2 2.0 1.2 1.3 2.0 1.1 2.3 1.7 2.8 1.7 79.4  Oct 1.9 2.3 1.2 1.1 1.1 1.0 1.3 0.9 1.1 1.6 0.9 1.3 0.9 0.8 0.9 1.0 1.0 0.7 0.8 0.9 1.0 1.0 0.8 0.7 0.7 0.6 0.6 0.9 1.0 0.8 0.7 31.5  Nov 0.8 0.6 0.9 0.6 0.8 0.5 0.7 0.7 0.7 0.5 0.6 0.5 0.4 0.6 0.7 0.5 0.3 0.3 0.5 0.4 0.6 0.5 0.6 0.4 0.5 0.2 0.4 0.8 0.4 0.2 16.2  Dec 0.9 0.4 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.0 0.2 0.4 0.1 -0.2 -0.3 -0.3 -0.2 0.2 0.2 0.3 0.1 0.4 0.2 0.4 -0.4 0.4 0.3 0.2 0.3 0.2 0.7 6.8  Computing of the Potential Evapotranspiration  Table C.7: Potential ET computed by using Hargreaves method(1985-1988). 1985 (Hargreaves) Date Jan 0.1 0.4 0.2 0.2 0.6 0.2 0.3 0.6 0.2 9 0.2 10 11 0.2 12 0.5 0.2 13 14 0.3 0.3 15 16 0.5 17 0.3 18 0.3 19 0.3 20 0.6 21 0.3 22 0.4 0.3 23 24 0.3 25 0.8 0.2 26 27 0.4 0.3 28 29 0.7 0.2 30 0.7 31 Sum 11.1 Total 1 2 3 4 5 6 7 8  Feb 0.6 0.6 0.8 0.2 0.4 0.3 0.6 0.7 0.3 0.3 0.5 0.5 0.4 0.5 1.2 0.8 0.8 0.9 0.4 0.4 0.5 0.6 0.6 1.6 1.1 1.4 1.1 1.1  19.6  Mar 1.4 1.3 0.7 0.6 0.8 1.4 1.6 1.6 1.5 1.7 1.3 1.6 1.7 1.2 1.7 2.0 1.8 0.8 0.7 0.8 1.2 1.7 1.6 0.9 0.8 0.7 1.0 2.1 0.8 0.9 0.9 39.0  Apr 1.0 0.9 0.9 1.3 2.3 2.7 2.2 3.0 3.1 1.5 1.1 1.8 1.1 2.1 2.2 1.4 1.1 2.5 2.7 2.4 2.4 1.1 3.1 2.4 1.3 1.1 2.2 1.7 2.5 2.0 57.4  May 1.8 2.2 2.7 3.3 1.6 2.4 3.7 2.7 3.7 1.8 3.5 3.0 1.4 3.3 4.2 4.8 5.3 3.1 2.8 2.4 3.1 3.5 2.3 2.9 3.6 4.0 3.2 2.3 1.5 2.2 4.7 92.9  Month Jul Jun 4.9 4.6 5.4 3.1 2.0 6.1 3.7 5.7 3.0 4.7 1.7 5.1 1.9 5.7 4.1 6.3 4.9 6.3 4.4 5.8 2.2 6.1 2.1 5.6 2.2 5.7 2.6 4.5 5.3 5.7 5.1 5.7 5.6 5.9 6.2 6.0 4.9 6.2 5.6 6.2 5.5 5.9 4.4 5.7 3.9 3.5 4.1 4.5 5.2 5.5 5.3 5.8 4.1 5.6 4.9 5.8 2.4 5.3 5.0 2.8 2.1 119.5 116.3 748.0  Aug 1.6 1.9  4.8 4.4 4.8 3.0 2.9 3.6 1.6 4.8 4.4 4.3 4.9 4.9  5.2 5.5 5.1 4.6 1.8 3.4 4.0 4.4 4.7 4.5 4.6 4.2 4.0 3.9 3.6 1.8 3.1 120.6  Sept 3.5 4.1 2.8 1.2 1.3 1.4 2.5 2.7 2.4 3.2 1.6 1.5 2.1 1.5 1.5 1.0 1.7 1.3 2.4 1.0 2.2 2.4 1.9 2.7 2.7 2.3 2.7 2.6 2.3 1.9 64.3  Oct 1.7 1.0 2.3 1.4 1.1 2.1 2.2 1.7 0.7 0.7 1.8 1.4 0.7 0.7 0.7 1.7 0.7 0.6 1.1 0.6 0.6 1.0 1.2 0.6 1.5 0.5 0.5 1.3 0.8 1.3 0.4 34.6  Nov  0.5 0.5 0.5 0.6 0.4 0.4 0.7 0.8 0.5 1.0 0.7 0.9 0.9 0.3 0.3 0.4 0.8 0.6 0.2 0.6 0.2 0.4 0.4 0.2 0.2 0.1 0.2 0.1 0.3 0.4 14.2  Dec 0.3 0.2 0.3 0.3 0.3 0.5 0.2 0.7 0.2 0.3 0.6 0.5 0.3 0.2 0.4 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.2 0.3 0.2 8.6  Computing of the Potential Evapotranspiration  1986 (Hargreaves) Date Jan 1 0.4 0.2 2 0.2 3 4 0.5 0.2 5 6 0.3 7 0.3 8 0.3 9 0.3 10 0.3 11 0.7 12 0.5 13 0.3 14 0.3 15 0.3 16 0.3 17 0.4 18 0.3 19 0.7 0.7 20 21 0.3 22 0.3 23 0.4 24 0.5 25 0.8 26 0.5 0.4 27 28 0.7 29 0.3 0.4 30 31 0.6 Sum 12.5 Total  Feb 0.7 0.4 0.4 0.4 0.7 1.1 1.0 0.6 1.0 0.5 0.4 1.2 1.0 0.8 0.4 0.4 0.4 0.8 0.7 0.4 0.4 0.4 0.5 0.6 1.4 1.3 1.0 1.4  20.1  Mar 1.1 1.6 0.6 0.8 0.6 0.7 0.9 1.5 1.6 1.0 0.9 1.1 0.8 1.7 1.2 2.2 1.1 0.8 1.6 1.7 1.5 1.8 0.8 1.5 0.9 0.9 0.9 0.9 0.9 2.7 1.6 38.0  Apr 1.2 2.0 1.1 1.6 2.2 2.5 3.0 1.2 2.5 2.6 0.9 2.0 1.1 1.1 1.2 1.1 1.6 1.1 1.1 1.2 1.2 2.8 3.0 1.0 1.7 1.1 1.8 1.7 1.7 2.6 50.9  May 1.4 1.6 3.3 3.2 2.3 3.7 2.5 3.4 3.4 2.7 1.8 1.4 3.2 3.9 3.9 1.3 1.5 1.5 2.2 3.5 4.2 4.3 1.7 1.7 2.4 2.2 3.8 5.5 5.4 5.6 5.7 94.0  Month Jun Jul 5.3 1.8 5.2 4.6 3.0 4.5 3.1 5.1 3.2 3.8 2.2 5.5 5.2 1.9 4.3 3.3 2.5 4.8 5.4 2.5 5.4 1.8 3.1 5.0 4.2 5.8 3.6 2.3 2.0 1.6 2.7 1.6 1.9 1.8 2.4 4.9 2.4 5.5 3.4 5.5 3.1 5.5 3.7 2.0 4.1 4.6 4.3 4.6 3.4 5.4 3.2 3.3 5.6 3.3 2.9 3.9 2.0 4.3 3.9 5.1 4.2 110.6 115.5 715.2  Aug 5.5 5.2 5.5 4.6 5.1 5.4 5.9 5.7 5.8 3.4 2.1 3.4 4.3 4.5 4.8 4.7 4.4 4.9 4.0 4.9 5.0 4.5 2.8 4.5 4.7 4.8 , 3.9 1.7 1.4 1.8 2.6 131.9  Sept 3.1 3.5 4.1 4.3 4.3 4.1 3.8 2.1 1.6 2.8 2.3 2.7 1.6 2.7 1.8 2.2 2.2 1.5 2.2 2.7 2.4 1.6 1.5 1.9 2.6 2.7 0.9 0.9 1.7 2.0 73.7  Oct 1.9 0.8 0.8 0.8 1.7 1.2 1.4 1.5 1.3 2.1 2.1 1.9 1.5 1.8 1.6 1.8 0.6 0.7 1.5 1.1 1.5 1.2 1.3 1.0 0.9 0.6 1.0 1.3 0.5 0.6 1.3 39.4  Nov Dec 0.8 1.0 0.7 0.5 0.5 0.6 0.2 0.5 0.4 1.1 0.4 0.5 1.2 0.2 0.5 0.6 1.0 • 0.7 0.3 0.6 0.2 1.1 0.4 0.2 0.4 0.2 0.3 1.0 0.4 0.3 0.4 0.6 0.4 0.6 0.5 0.2 0.4 0.3 0.5 0.2 0.5 0.3 0.3 0.3 0.4 0.3 0.9 0.4 0.3 0.3 0.6 0.3 0.6 0.3 0.8 0.3 0.2 0.3 0.3 0.6 0.2 16.9 11.7  Computing  of the Potential  Evapotranspiration  1987 (Hargreaves) Date Jan 1 0.5 2 0.3 0.3 3 0.2 4 5 0.6 6 0.5 7 0.5 0.5 8 0.2 9 0.3 10 11 0.3 12 0.3 0.6 13 14 0.7 0.2 15 0.3 16 0.2 17 0.4 18 0.3 19 20 0.3 21 0.5 22 0.6 0.3 23 24 0.4 0.3 25 0.3 26 .0.3 27 0.4 28 29 0.4 0.7 30 31 0.5 Sum 12.2 Total  Feb Mar 0.9 0.8 0.7 0.5 0.4 0.7 0.4 0.7 0.4 0.7 1.0 1.2 0.8 1.9 0.4 ' 1.3 0.4 0.8 0.5 0.7 0.7 1.0 0.5 0.8 0.6 1.1 1.1 0.8 1.4 0.5 0.5 1.0 0.4 1.0 0.5 1.5 0.5 2.0 0.5 1.0 2.1 1.0 0.9 2.1 1.6 0.9 1.8 1.7 1.0 1.4 0.5 2.4 1.5 1.9 0.6 2.3 2.6 1.9 1.8 20.9 41.5  Apr 3.0 3.0 1.0 1.3 1.4 1.2 1.3 2.5 1.0 2.0 1.9 1.7 1.2 2.1 1.1 2.1 2.9 3.1 3.1 2.9 1.6 3.3 2.7 3.2 3.5 3.4 4.6 1.6 4.0 1.4 69.0  May 2.4 2.3 1.4 3.4 4.3 4.5 4.6 5.0 4.7 5.0 1.6 2.6 2.6 3.1 4.0 4.4 3.3 3.9 3.8 4.7 3.7 4.0 3.8 4.8 4.3 3.1 1.6 2.7 1.8 1.8 3.4 106.7  Month Jul Jun 6.1 4.3 5.0 3.0 5.0 3.0 4.6 1.7 4.1 1.7 3.4 4.3 2.7 5.5 2.2 1.8 4.2 1.9 5.4 2.2 2.6 4.8 6.2 1.9 3.2 6.0 5.1 6.0 4.6 5.2 4.2 2.6 5.1 5.1 5.4 3.6 5.7 3.2 4.2 1.8 1.9 5.7 4.7 5.3 4.2 4.5 5.6 3.8 6.1 2.7 6.3 2.9 4.2 6.1 6.4 5.0 6.6 5.5 4.5 6.8 3.6 131.7 129.3 803.4  Aug 5.3 5.4 5.4 5.3 3.6 5.3 5.5 5.5 5.3 2.1 5.1 3.3 1.5 3.7 2.7 3.6 4.5 4.7 3.2 4.6 4.5 4.6 4.9 5.1 4.9 2.4 4.6 3.2 3.3 4.7 4.8 132.6  Sept 4.3 3.8 3.0 3.8 4.0 4.0 3.8 3.2 3.2 3.7 2.0 1.2 1.8 1.5 2.2 2.7 2.8 2.4 1.9 3.4 3.1 3.1 3.1 1.6 1.0 2.3 2.4 2.6 2.6 2.7 83.3  Oct 2.8 1.8 2.0 2.0 2.4 2.4 1.3 2.1 2.3 2.1 2.1 2.0 1.8 1.3 1.3 1.5 1.3 1.8 1.8 1.8 1.8 1.6 1.5 0.6 0.8 1.5 0.7 0.5 0.6 0.6 0.8 48.7  Nov 1.1 0.5 0.5 1.2 1.0 0.4 0.5 0.5 0.6 0.5 0.5 0.5 0.5 1.0 0.3 1.0 0.5 0.3 0.4 0.4 0.4 0.5 0.3 0.4 0.5 0.5 0.7 0.7 0.5 0.3 17.0  Dec 0.3 0.3 0.3 0.5 0.3 0.3 0.5 0.3 0.3 0.3 0.6 0.7 0.2 0.2 0.3 0.5 0.2 0.5 0.2 0.2 0.2 0.3 0.5 0.2 0.5 0.4 0.2 0.2 0.2 0.5 0.6 10.7  Computing of the Potential Evapotranspiration  95  1988 (Hargreaves) Date Jan 1 0.5 2 0.5 3 0.4 4 0.2 5 0.2 0.2 6 0.4 7 8 0.2 9 0.2 10 0.2 11 0.4 12 0.2 13 0.3 14 0.3 15 0.3 16 0.5 17 0.4 18 0.6 19 0.3 20 0.9 21 0.3 22 0.5 23 0.3 24 0.3 25 0.6 0.4 26 27 0.3 28 0.9 0.4 29 30 0.6 31 0.7 Sum 12.3 Total  Feb 0.3 0.3 0.3 0.4 0.6 0.4 0.4 0.4 0.7 0.4 0.5 0.5 0.7 0.4 1.2 0.6 1.1 0.5 0.5 1.2 1.2 1.4 0.9 1.5 0.6 0.6 1.5 1.5  20.3  Mar 0.6 0.6 1.4 1.0 0.6 1.2 0.6 0.6 1.9 1.6 1.2 1.8 0.7 1.9 2.0 2.1 1.3 1.8 0.9 0.8 1.6 0.8 0.8 0.8 0.8 1.1 2.4 0.8 1.6 1.4 0.9 37.8  Apr 0.9 0.9 1.6 2.1 0.9 1.7 2.5 2.1 2.8 2.4 2.3 3.5 1.2 2.5 2.2 1.2 1.1 2.5 3.5 4.0 3.8 2.1 2.1 1.8 1.1 3.7 1.5 1.4 1.9 2.5 63.8  May 1.6 1.3 2.9 3.6 3.3 2.4 4.3 4.5 1.6 2.0 3.7 3.8 1.7 3.7 1.9 1.9 2.0 1.4 3.2 4.6 4.7 1.6 1.7 4.1 3.7 1.6 1.6 3.7 4.3 3.9 2.8 89.2  Month Jun Jul 2.0 1.8 1.5 4.9 4.1 4.5 3.3 3.1 4.5 2.0 2.5 3.9 2.2 5.3 4.8 5.6 3.7 5.7 2.3 4.0 1.7 4.9 5.4 1.7 5.7 4.9 5.7 4.6 5.7 4.5 4.4 5.6 1.7 5.6 4.8 5.9 4.2 6.5 6.4 5.6 5.2 2.0 4.7 3.5 5.8 3.5 5.4 5.7 5.2 6.1 3.3 5.3 5.4 4.1 4.1 3.1 3.9 5.3 2.1 5.5 4.7 116.5 144.6 746.1  Aug 5.4 5.3 5.7 5.4 2.2 2.2 4.6 1.7 3.3 4.0 5.0 4.8 4.0 3.6 1.4 2.5 3.0 3.7 3.5 3.4 4.6 4.6 4.9 4.6 4.2 4.5 4.5 4.7 4.2 4.1 4.3 123.9  Sept 4.4 4.8 4.6 4.0 3.9 2.1 4.0 2.6 2.3 3.4 3.5 3.6 3.5 3.4 1.1 2.8 2.5 0.9 1.4 2.9 2.2 1.8 1.1 0.9 2.1 0.9 2.4 0.9 2.8 1.8 78.7  Oct 2.6 2.4 1.1 0.9 1.2 1.0 1.9 0.8 1.5 2.2 0.7 0.8 0.8 0.7 0.7 1.0 1.0 0.6 0.6 1.0 1.0 0.6 0.6 1.0 0.5 1.6 1.4 1.1 0.5 0.5 0.6 32.9  Nov 0.7 0.5 0.5 0.5 0.5 1.3 0.8 0.4 0.5 0.4 0.4 0.8 1.2 0.5 0.4 0.4 0.5 0.3 0.3 0.4 0.5 0.5 0.6 0.3 0.4 0.4 03 0.3 0.3 0.5 :  15.2  Dec 0.3 0.3 0.3 0.6 0.3 0.3 0.3 0.3 0.3 0.4 0.3 0.3 0.7 0.7 0.6 0.6 0.6 0.2 0.2 0.2 0.4 0.2 0.3 0.2 0.6 0.2 0.2 0.2 0.2 0.4 0.2 11.0  Appendix  D  C O M P U T A T I O N A N D S T A T I S T I C A L A N A L Y S E S O F SOIL DRAINABLE  POROSITY  Soil drainable porosity is computed using Equation 2.4 i n Chapter 2.  T h e following  sections describe the cell addresses i n L O T U S 123 (Release 2) spreadsheets, their corresponding parameters by an example and the drainable porosity of regimes A and B (1985-1988). T h e calculated average drainable porosity of regimes A and B from water table rise and drawdown is compared by using t-test.  D.l  Computation  of Soil Drainable Porosity  Cell addresses: A  =  precipitation ( P P T ) i n mm;  B  =  evapotranspiration ( E T ) in mm;  C  =  drainage discharge (D) in mm;  D  =  change in water table height (AZ) i n m;  E  =  time period during which the water table rise or drawdown events occurs ( A t ) i n day;  F  =  soil drainable porosity ( / ) i n %.  Calculation: F  4  =  ( ( A - B - C ) / ( D * 1000))*100 4  4  4  4  Where "4" i n the subscripts indicates the row number of the spreadsheet.  96  Computation and Statistical Analyses of Soil Drainable Porosity  97  Table D.8: T h e computed soil drainable porosity  Regime A , water table rise Year 1985  1986  1987  PPT 12.5 14.0 13.0 17.5 31.0 30.5 11.0 8.5 13.5 8.5 15.5 9.0 5.5 9.5 23.0 5.0 11.5 9.5 11.0 27.5 20.0 9.0 12.5 34.5 17.0 25.0 8.0 17.0  ET 1.6 0.0 0.5 1.8 0.2 0.8 1.0 0.0 0.7 0.1 0.4 0.0 0.0 0.3 0.0 0.2 1.4 1.2 1.7 1.1 1.9 1.0 0.7 0.0 0.0 0.0 0.0 0.9  D  AZ  At  1.0 0.4 0.2 0.5 1.5 2.8 1.5 0.7 0.7 1.2 1.6 0.6 0.4 1.1 2.2 1.1 1.8 1.8 1.1 2.7 2.0 0.6 1.6 0.8 0.3 1.1 1.3 1.1  0.121 0.326 0.209 0.124 0.326 0.418 0.154 0.203 0.253 0.113 0.254 0.244 0.064 0.186 0.436 0.056 0.183 0.096 0.220 0.503 0.217 0.136 0.204 0.415 0.327 0.353 0.120 0.335  0.56 0.15 0.06 0.58 0.70 1.07 0.70 0.30 0.82 0.60 0.74 0.24 0.13 0.49 0.72 0.57 0.97 1.15 0.52 0.89 1.25 0.34 0.74 0.41 0.13 0.38 0.64 0.45  /  8.2 4.2 5.9 12.3 9.0 6.4 5.9 3.8 4.8 6.4 5.3 3.4 8.0 4.4 4.8 6.6 4.5 6.8 3.7 4.7 7.4 5.4 5.0 8.1 5.1 6.8 5.6 4.5  Year  1988  PPT 37.0 16.0 15.5 14.5 13.0 17.5 13.5 31.8 6.0 11.7 13.5 7.5 12.2 18.7 12.0 18.5 16.5 20.6 49.0 47.5 45.5 21.5 8.5 22.0 9.0 21.5 19.5 14.5  ET 0.7 0.0 1.0 0.0 0.1 0.3 0.3 0.0 0.5 0.3 0.6 0.2 0.0 0.0 1.7 0.0 1.7 1.4 0.5 1.4 0.0 0.0 0.0 0.4 0.0 0.0 0.0 0.0  D  AZ  At  1.1 2.0 1.1 0.7 1.0 1.6 1.4 0.8 0.9 1.2 1.5 0.7 1.1 0.8 1.2 0.9 1.3 1.8 2.3 8.2 1.6 0.6 1.1 3.1 1.2 0.4 0.8 0.8  0.505 0.364 0.191 0.198 0.110 0.234 0.216 0.453 0.111 0.199 0.297 0.170 0.208 0.276 0.143 0.376 0.313 0.399 0.623 0.589 0.528 0.533 0.109 0.330 0.125 0.452 0.399 0.271  0.38 0.12 0.10 0.39 0.46 0.89 0.75 0.23 0.50 0.60 0.90 0.32 0.51 0.39 0.78 0.52 0.50 0.70 0.68 4.57 0.48 0.22 0.54 1.30 0.50 0.12 0.20 0.32  /  7.0 3.9 6.8 7.0 10.8 6.7 5.5 6.8 4.1 5.1 3.8 3.9 5.3 6.5 6.4 4.7 4.3 4.4 7.4 6.4 8.3 3.9 6.8 5.6 6.2 4.7 4.7 5.1  Computation and Statistical  Analyses  of Soil Drainable  Porosity  Regime A, water table drawdown (PPT=0) Year 1985  1986  1987  ET 3.2 2.2 2.9 11.5 3.8 0.2 5.0 1.7 2.7 2.4 1.3 6.8 5.5 1.7 6.0 5.8 3.4 7.9 16.3 0.8 0.6 2.9 2.2 5.7 1.7 1.6  D 10.6 4.5 5.0 10.3 3.9 10.4 6.9 6.3 16.0 9.9 7.8 15.9 6.6 4.9 8.5 5.6 2.9 7.3 9.7 5.1 2.8 12.9 11.8 17.0 4.9 4.3  AZ 0.452 0.110 0.126 0.297 0.120 0.196 0.279 0.131 0.443 0.133 0.116 0.580 0.159 0.329 0.303 0.127 0.098 0.181 0.299 0.133 0.046 0.215 0.206 0.329 0.110 0.077  At 3.62 2.02 1.97 4.51 1.52 5.55 3.14 3.27 4.18 5.87 4.32 6.98 3.58 1.38 3.66 3.23 1.54 3.67 5.05 2.64 1.38 5.34 4.52 7.20 2.23 2.26  /  3.1 6.1 6.3 7.3 6.4 5.4 4.3 6.1 4.2 9.2 7.8 3.9 7.6 2.0 4.8 9.0 6.4 8.4 8.7 4.4 7.4 7.3 6.8 6.9 6.0 7.7  Year  1988  ET 5.4 1.6 1.4 0.7 0.7 2.9 2.6 0.7 1.9 0.6 1.7 2.0 0.5 2.9 4.3 9.9 2.9 1.6 4.2 3.9 5.5 14.6 0.9 2.9 1.5  D 15.6 3.6 10.6 11.1 6.9 8.2 13.0 2.5 8.1 2.4 6.3 5.0 1.3 6.5 5.1 11.0 2.8 2.0 5.4 6.0 5.6 19.4 3.7 11.5 5.2  AZ 0.471 0.160 0.398 0.124 0.152 0.146 0.508 0.038 0.167 0.068 0.201 0.067 0.027 0.077 0.228 0.299 0.068 0.051 0.226 0.324 0.351 0.677 0.102 0:375 0.110  At 4.06 1.77 4.56 5.18 3.78 5.83 5.30 1.63 4.33 1.13 2.27 2.86 0.73 3.79 2.31 5.42 1.75 1.18 2.31 2.48 2.05 5.94 2.34 4.86 2.62  /  4.5 3.3 3.0 9.5 5.0 7.6 3.1 8.4 6.0 4.4 4.0 10.4 6.7 12.2 4.1 6.7 8.4 7.1 4.2 3.1 3.2 5.0 4.5 3.8 6.1  Computation and Statistical Analyses of Soil Drainable Porosity  99  Regime B, water table rise Year 1985  1986  PPT 14.0 28.0 14.5 10.5 31.0 30.5 6.5 11.0 8.5 13:5 8.5 15.5 9.0 9.5 23.0 5.0 11.5 9.5 20.0 9.0 12.5 34.5 17.0  ET 1.2 4.4 1.5 0.3 1.8 0.4 0.0  0.2 0.1 0.7 0.0 0.0 0.3 0.2 0.0 0.0 1.0 1.2 1.0 0.0 1.4 0.0 0.0  D 1.9 3.4 0.5 0.3 3.7 3.4 0.9 1.2 1.1 2.5 1.2 0.8 0.9 1.3 2.5 1.0 1.9 1.7 1.4 0.4 2.1 1.1 0.7  AZ 0.462 0.462 0.198 0.169 0.359 0.418 0.227 0.249 0.213 0.284 0.154 0.341 0.252 0.272 0.331 0.115 0.260 0.121 0.340 0.206 0.324 0.519 0.367  At 0.56 1.33 0.56 0.20 1.26 1.07 0.33 0.45 0.39 0.90 0.51  0.34 0.31 0.51 0.84 0.41 0.85 0.93 0.73 0.17 0.72 0.44 0.24  /  2.4 4.4 6.3 5.9 7.1 6.4 2.5 3.9 3.4 3.6 4.7 4.3 3.1 2.9 6.2 3.5 3.3 5.5 5.2 4.2 2.8 6.4 4.4  Year 1987  1988  PPT 8.0 17.0 37.0 7.5 29.0 15.5 14.5 13.0 17.5 13.5 6.0 11.7 13.6 7.5 12.2 18.7 18.5 16.5 20.6 62.5 47.5 8.5 14.5  ET 0.0 0.4 0.3 0.2 0.4 0.9 0.0 0.3 0.2 0.3 0.5 0.2 0.6 0.3 0.6 0.0 0.0 1.0 1.5 1.7 0.8 0.0 0.0  D 1.6 2.3 1.7  0.4 0.6 1.4 0.6 1.5 1.7 2.8 1.6 1.2 1.6 0.7 2.0 1.9 0.6 1.2 3.1 2.4 1.5 1.0 1.1  AZ 0.224 0.425 0.567 0.195 0.397 0.156 0.197 0.167 0.346 0.362 0.148 0.339 0.239 0.125 0.362 0.465 0.475 0.427 0.486 1.151 0.502 0.240 0.401  At  0.62 0.73 0.52 0.13 0.51 2.04 0.23  0.53 0.62 0.95  0.63 0.44 0.77 0.23 0.61 0.66 0.16  0.34 0.88 2.32 0.81 0.28 0.31  /  2.9 3.4 6.2 3.5 7.1 8.5 7.1 6.7 4.6 2.9 2.6 3.0 4.8 5.2 2.7 3.6 3.8 3.3 3.3 5.1 9.0 3.1 3.3  Computation and Statistical Analyses of Soil Drainable Porosity Regime B, water table drawdown (PPT=0) Year 1985  1986  1987  ET 6.2 1.2 5.9 1.4 11.7 1.0 0.8 0.4 2.9 1.7 1.4 1.7 1.5 1.4 1.4 4.8 1.3 7.9 5.8 5.8 6.2 3.9 6.9 3.7 4.7 2.6 16.0 0.8 0.0 0.0 2.5 0.3 0.2 0.5 0.7 4.5 0.7 2.5 0.7 0.7 2.1 0.9  D  AZ  10.6 4.2 2.9 2.1 12.8 3.7 4.2 12.9 8.3 6.6 4.0 9.9 9.5 6.9 7.2 16.9 12.6 21.0 7.7 8.8 8.1 6.1 9.3 4.1 5.5 1.8 11.7 7.9 2.9 2.0 14.7 3.4 2.0 3.3 3.6 16.4 2.1 7.9 2.0 2.8 7.1 3.6  0.295 0.183 0.251 0.076 0.490 0.103 0.082 0.307 0.322 0.172 0.141 0.398 0.329 0.208 0.242 0.231 0.201 0.570 0.232 0.358 0.237 0.150 0.285 0.224 0.207 0.114 0.419 0.260 0.120 0.068 0.382 0.149 0.075 0.146 0.123 0.380 0.048 0.236 0.049 0.052 0.136 0.139  At 3.70 1.10 1.85 0.68 4.85 1.47 1.95 5.22 3.34 3.08 1.33 3.31 3.85 2.16 2.74 8.91 6.16 7.29 3.72 3.56 3.37 2.69 3.53 1.41 2.08 0.58 4.61 3.13 0.73 0.55 5.22 0.94 0.49 0.91 0.19 5.71 0.79 2.79 0.76 1.12 2.72 0.80  / 5.7 3.0 3.5 4.6 5.0 4.6 6.1 4.3 3.5 4.8 3.8 2.9 3.3 4.0 3.6 9.4 6.9 5.1 5.8 4.1 6.0 6.7 5.7 3.5 4.9 3.9 6.6 3.3 2.4 2.9 4.5 2.5 2.9 2.6 3.5 5.5 5.8 4.4 5.5 6.7 6.8 3.2  Year  1988  ET D 1.6 1.3 4.3 12.0 2.6 3.5 4.1 5.4 13.2 12.5 0.6 2.9 0.6 1.6 1.5 4.9 1.0 13.6 0.7 •10.6 0.8 11.4 2.2 0.1 14.9 3.9 0.5 1.8 3.3 23.5 2.6 12.9 4.3 11.6 2.2 0.6 2.4 8.3 7.1 1.7 0.7 2.4 1.7 2.9 8.3 14.8 2.9 4.7 1.6 2.5 1.4 2.0 4.2 8.9 5.3 11.4 5.4 8.6 7.2 10.7 0.6 3.0 2.7 0.0 0.7 3.7 2.0 11.9 0.6 5.2 1.0 8.5 0.7 7.4 1.4 13.2 1.3 10.3 0.1 3.6 0.2 5.1 16.3 0.1  AZ  At  0.058 0.481 0.108 0.131 0.198 0.064 0.067 0.207 0.473 0.172 0.235 0.104 0.180 0.053 0.576 0.315 0.104 0.079 0.299 0.327 0.075 0.039 0.450 0.112 0.080 0.114 0.390 0.453 0.442 0.440 0.083 0.047 0.115 0.390 0.088 0.186 0.162 0.282 0.250 0.079 0.097 0.414  0.51 4.21 1.40 2.59 7.22 1.42 0.62 1.80 3.92 4.69 4.48 0.66 7.92 0.67 7.10 4.91 6.18 0.79 2.70 2.14 0.94 1.47 5.14 2.03 1.01 0.50 2.62 3.38 2.44 3.06 1.05 0.67 0.94 3.31 1.98 2.18 1.99 3.80 3.00 0.87 1.24 4.63  /  5.0 3.4 5.6 7.3 13.0 5.5 3.3 3.1 3.1 6.6 5.2 2.2 10.4 4.3 4.7 4.9 15.3 3.5 3.6 2.7 4.1 11.8 5.1 6.8 5.1 3.0 3.4 3.7 3.2 4.1 4.3 5.7 3.8 3.6 6.6 5.1 5.0 5.2 4.6 4.7 5.5 4.0  Computation and Statistical Analyses of Soil Drainable Porosity  D.2  101  Statistical Analysis  The null hypothesis is set as H  0  = 0. If the null hypothesis is not rejected by the test,  then there is no significant difference between the drainable porosities computed.  H : fi = 0 0  t =  f-d  (D.26)  9- -  where  /  =  the average of the di]  d  —  the difference between the average drainable porosities;  —  ^  Sxi-s  2  n e  standard deviation of d i .  For regime A , water table rise (1) and drawdown(2):  SI  S\  3.09  4.86  9  2  9- -  °l+2  " X l —X2  7.95  0.55  t  n  0.18  105  W h e n re=105, io.o5=l-98. t < t ,05, thus there was no significant difference between 0  the drainable porosities computed from water table rise and drawdown for regime A . For regime B , water table rise (1) and drawdown (2):  si  9  2.68  4.92  2  2  9- -  °l+2  •-'xi —X2  7.60  0.50  9  t  n  0.8  130  W h e n 71=130, to.os=l-98. t < to.os, thus there was no significant difference between the drainable porosities computed from water table rise and drawdown for regime B . For water table rise of regimes A and B :  3.09  si  9  2  9- -  '-'1+2  '-'Xi —X2  2.68  5.77  0.47  t  n  3.19  100  Computation and Statistical Analyses of Soil Drainable Porosity  102  W h e n n=100, £o.05=l-98. t > io.oi, therefore, there was significant difference between the drainable porosity of regimes A and B . For water table drawdown of regimes A and B :  si 4.86 W h e n n=133, £o.o5=l-98.  4.92  9  2  9.78  t > io.os-  c  ^Xl  —X2  0.56  t  n  1.99  133  Therefore, there was a significant difference  between the drainable porosity of regimes A and B computed from water table drawdown.  

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